diff --git a/CHANGELOG.md b/CHANGELOG.md
index 69dcd58..0b713e3 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,64 @@
 
 All notable repository and research-artifact changes are recorded here.
 
+## Unreleased
+
+## 0.3.0 - 2026-08-02
+
+### Added
+
+- An orthogonal 184-case V100 length/batch suite and generated manifest for
+  FFT, NTT, FWHT, and XOR-zeta.
+- Scaling summaries that identify timing quality, throughput saturation, and
+  mapping crossovers without using sub-0.020-ms rows as stable claims.
+- Targeted NCU collection for the FFT saturation gaps and FWHT processing-unit
+  crossover.
+- A V100-calibrated mapping selector with held-out-shape evaluation and
+  explicit separation of mapping family from processing unit.
+- A matching-protocol 120-sample Dao FHT and GPU-NTT baseline refresh.
+- Targeted NCU attribution over 22 FFT/FWHT implementation-shape pairs and 37
+  kernels, plus one command that regenerates all derived V100 analyses.
+- An FP64 prefix address-path experiment that separately reproduces scalar,
+  table, recurrence, XOR-swizzled, and cuFFT timing under one protocol.
+- FP64 online cuFFTDx segment specializations at logN 7/8/9, a 648-point
+  neighboring-length mapping scan, and an interleaved 35-shape batch matrix.
+
+### Changed
+
+- Reworked the root, design, documentation-index, and experiment narratives
+  around the two logical dimensions and their four spatial/temporal unfolding
+  factors, with an explicit mapping from graph work to GPU services.
+- Replaced the high-level concept figure with a hardware-mapping diagram that
+  connects `Ud/Td/Us/Ts`, residence and transport, replaceable processing units,
+  online reordering, and counter-calibrated selection.
+- Updated paper-facing experiment summaries to include the expanded FP64
+  length/batch robustness matrix and fixed-mapping NCU attribution.
+- Regenerated checked-in V100 summaries with the current `shared_layout` and
+  `fp64_thread_instructions` schemas; existing measurement values are unchanged.
+- The comprehensive runner now supports exact case selection, validates batch
+  consistency within comparison groups, and caches identical correctness
+  preflights.
+- The next release is scoped around counter-calibrated mapping selection and
+  refreshed same-protocol external baselines.
+- Cross-GPU validation is deferred until the repository moves to a host with a
+  second GPU generation; it is not a `v0.3.0` release gate.
+- FP64 online staging now hoists invariant global addresses and advances
+  same-period shared permutations by compile-time strides.
+- FP64 online composition now covers total `logN=14..18`; each length selects
+  its split and two physical mappings independently.
+
+### Current Evidence Boundary
+
+- The new scaling evidence remains V100-only.
+- FP32 FFT matches or exceeds cuFFT at selected saturated shapes, but cuFFT has
+  a higher large-batch ceiling at `logN=18` and remains ahead at `logN=20`.
+- The profiled FP64 `logN=16`, batch-64 mapping reaches cuFFT parity at 1.002x.
+  Its updated counter capture attributes this to 26.8% fewer prefix warp
+  instructions and 8.3% lower prefix replay than the prior XOR kernel.
+- In the expanded FP64 matrix, 20/25 stable shapes have higher median
+  throughput than cuFFT and all 13 stable `logN=17/18` shapes are faster.
+- Cross-GPU portability and selector accuracy have not yet been measured.
+
 ## 0.2.0 - 2026-07-24
 
 ### Added
diff --git a/CITATION.cff b/CITATION.cff
index 940c848..6ade7ea 100644
--- a/CITATION.cff
+++ b/CITATION.cff
@@ -6,8 +6,8 @@ authors:
   - name: "TruNcat3"
 repository-code: "https://github.com/TruNcat3/cuButterfly"
 url: "https://github.com/TruNcat3/cuButterfly"
-version: 0.2.0
-date-released: 2026-07-24
+version: 0.3.0
+date-released: 2026-08-02
 keywords:
   - butterfly computation
   - GPU
diff --git a/CMakeLists.txt b/CMakeLists.txt
index f8397de..ac43f9a 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -4,7 +4,7 @@ if(NOT DEFINED CMAKE_CUDA_ARCHITECTURES)
     set(CMAKE_CUDA_ARCHITECTURES 70 CACHE STRING "CUDA architectures to compile for")
 endif()
 
-project(cuButterfly VERSION 0.2.0 LANGUAGES CXX CUDA)
+project(cuButterfly VERSION 0.3.0 LANGUAGES CXX CUDA)
 
 set(CMAKE_CXX_STANDARD 17)
 set(CMAKE_CXX_STANDARD_REQUIRED ON)
@@ -34,16 +34,30 @@ set(CUBUTTERFLY_ARCHITECTURE_SPACE_SPEC "${CMAKE_CURRENT_SOURCE_DIR}/config/butt
     "Canonical operator-independent butterfly architecture-space specification")
 set(CUBUTTERFLY_FFT_CODEGEN_SPEC "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_fft_codegen.json" CACHE FILEPATH
     "Selected FFT template points compiled into this build")
+set(CUBUTTERFLY_FFT_PIPELINE_SPEC "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_fft_pipeline.json" CACHE FILEPATH
+    "FFT processing-unit and mapping search specification")
+set(CUBUTTERFLY_FFT_PIPELINE_CANDIDATES "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_fft_pipeline_candidates.json" CACHE FILEPATH
+    "Generated FFT pipeline candidate manifest")
+set(CUBUTTERFLY_FFT_DISPATCH_SPEC "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_fft_dispatch.json" CACHE FILEPATH
+    "Measured FFT mapping dispatch table")
 set(CUNTT_GENERATED_DIR "${CMAKE_CURRENT_BINARY_DIR}/generated")
 set_property(DIRECTORY APPEND PROPERTY CMAKE_CONFIGURE_DEPENDS
     "${CUNTT_DESIGN_SPEC}"
     "${CUBUTTERFLY_FFT_SPACE_SPEC}"
     "${CUBUTTERFLY_ARCHITECTURE_SPACE_SPEC}"
     "${CUBUTTERFLY_FFT_CODEGEN_SPEC}"
+    "${CUBUTTERFLY_FFT_PIPELINE_SPEC}"
+    "${CUBUTTERFLY_FFT_PIPELINE_CANDIDATES}"
+    "${CUBUTTERFLY_FFT_DISPATCH_SPEC}"
     "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_comprehensive_suite.json"
+    "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_scaling_space.json"
+    "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_scaling_suite.json"
     "${CMAKE_CURRENT_SOURCE_DIR}/scripts/fft_design_space.py"
     "${CMAKE_CURRENT_SOURCE_DIR}/scripts/butterfly_design_space.py"
     "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_fft_codegen.py"
+    "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_fft_pipeline.py"
+    "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_fft_dispatch.py"
+    "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_scaling_suite.py"
     "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_design_points.py")
 file(MAKE_DIRECTORY "${CUNTT_GENERATED_DIR}")
 execute_process(
@@ -85,6 +99,35 @@ execute_process(
 if(NOT CUBUTTERFLY_FFT_CODEGEN_RESULT EQUAL 0)
     message(FATAL_ERROR "cuButterfly FFT code generation failed: ${CUBUTTERFLY_FFT_CODEGEN_ERROR}")
 endif()
+execute_process(
+    COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_scaling_suite.py"
+            --spec "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_scaling_space.json"
+            --check "${CMAKE_CURRENT_SOURCE_DIR}/config/v100_scaling_suite.json"
+    RESULT_VARIABLE CUBUTTERFLY_SCALING_SUITE_RESULT
+    ERROR_VARIABLE CUBUTTERFLY_SCALING_SUITE_ERROR)
+if(NOT CUBUTTERFLY_SCALING_SUITE_RESULT EQUAL 0)
+    message(FATAL_ERROR "cuButterfly scaling-suite validation failed: ${CUBUTTERFLY_SCALING_SUITE_ERROR}")
+endif()
+execute_process(
+    COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_fft_pipeline.py"
+            --pipeline "${CUBUTTERFLY_FFT_PIPELINE_SPEC}"
+            --architecture "${CUBUTTERFLY_FFT_SPACE_SPEC}"
+            --codegen "${CUBUTTERFLY_FFT_CODEGEN_SPEC}"
+            --check "${CUBUTTERFLY_FFT_PIPELINE_CANDIDATES}"
+    RESULT_VARIABLE CUBUTTERFLY_FFT_PIPELINE_RESULT
+    ERROR_VARIABLE CUBUTTERFLY_FFT_PIPELINE_ERROR)
+if(NOT CUBUTTERFLY_FFT_PIPELINE_RESULT EQUAL 0)
+    message(FATAL_ERROR "cuButterfly FFT pipeline validation failed: ${CUBUTTERFLY_FFT_PIPELINE_ERROR}")
+endif()
+execute_process(
+    COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_fft_dispatch.py"
+            --dispatch "${CUBUTTERFLY_FFT_DISPATCH_SPEC}"
+            --header "${CUNTT_GENERATED_DIR}/generated_fft_dispatch.cuh"
+    RESULT_VARIABLE CUBUTTERFLY_FFT_DISPATCH_RESULT
+    ERROR_VARIABLE CUBUTTERFLY_FFT_DISPATCH_ERROR)
+if(NOT CUBUTTERFLY_FFT_DISPATCH_RESULT EQUAL 0)
+    message(FATAL_ERROR "cuButterfly FFT dispatch generation failed: ${CUBUTTERFLY_FFT_DISPATCH_ERROR}")
+endif()
 include("${CUNTT_GENERATED_DIR}/design_points.cmake")
 
 add_library(cuntt STATIC
@@ -100,7 +143,7 @@ if(CUBUTTERFLY_ENABLE_CUFFTDX)
             "cuFFTDx headers were not found under ${CUBUTTERFLY_MATHDX_ROOT}. "
             "Run scripts/install_cufftdx.sh or set CUBUTTERFLY_MATHDX_ROOT.")
     endif()
-    target_sources(cuntt PRIVATE src/cufftdx_fft.cu)
+    target_sources(cuntt PRIVATE src/cufftdx_fft.cu src/cufftdx_fft_fp64.cu)
     target_include_directories(cuntt SYSTEM PRIVATE "${CUBUTTERFLY_MATHDX_ROOT}/include")
     target_compile_definitions(cuntt PRIVATE CUBUTTERFLY_HAS_CUFFTDX=1)
 else()
@@ -191,4 +234,157 @@ if(BUILD_TESTING)
              COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_butterfly_design_space.py")
     add_test(NAME comprehensive_suite
              COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_comprehensive_suite.py")
+    add_test(NAME scaling_suite
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_scaling_suite.py")
+    add_test(NAME mapping_selector
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_mapping_selector.py")
+    add_test(NAME external_baseline_suite
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_external_baseline_suite.py")
+    add_test(NAME scaling_ncu_analysis
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_scaling_ncu_analysis.py")
+    add_test(NAME fft_vectorized_ncu_analysis
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fft_vectorized_ncu.py")
+    add_test(NAME fp64_fft_ncu_analysis
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fp64_fft_ncu.py")
+    add_test(NAME fp64_fft_robustness_analysis
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fp64_fft_robustness.py")
+    add_test(NAME fft_pipeline_generator
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fft_pipeline_generator.py")
+    add_test(NAME fft_pipeline_runner
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fft_pipeline_runner.py")
+    add_test(NAME fft_pipeline_model
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fft_pipeline_model.py")
+    add_test(NAME fft_dispatch_generator
+             COMMAND "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/tests/test_fft_dispatch_generator.py")
+    if(CUBUTTERFLY_ENABLE_CUFFTDX)
+        add_test(NAME fft_fp64_cufftdx_block_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend temporal-tile
+                         --fft-core cufftdx-block --tile-threads 32 --normalization none
+                         --logN 8 --batch 8 --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fp64_cufftdx_online_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 8
+                         --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                         --normalization none --logN 16 --batch 2 --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fp64_cufftdx_online_inverse_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 8
+                         --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                         --inverse --normalization inverse --logN 16 --batch 2
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fp64_cufftdx_recurrence_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 8
+                         --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                         --cross-twiddle recurrence --normalization none --logN 16 --batch 2
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fp64_cufftdx_recurrence_inverse_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 8
+                         --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                         --cross-twiddle recurrence --inverse --normalization inverse
+                         --logN 16 --batch 2 --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fp64_cufftdx_xor_swizzle_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 8
+                         --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                         --cross-twiddle recurrence --shared-layout xor-swizzle
+                         --normalization none --logN 16 --batch 2 --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fp64_cufftdx_xor_swizzle_inverse_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 8
+                         --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                         --cross-twiddle recurrence --shared-layout xor-swizzle --inverse
+                         --normalization inverse --logN 16 --batch 2 --warmup 1 --repeat 1 --verify)
+        foreach(fp64_shape IN ITEMS "14;7" "15;8" "17;8" "18;9")
+            list(GET fp64_shape 0 fp64_log_n)
+            list(GET fp64_shape 1 fp64_local_stages)
+            add_test(NAME fft_fp64_cufftdx_xor_logN${fp64_log_n}_correctness
+                     COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                             --fft-core cufftdx-block --local-stages ${fp64_local_stages}
+                             --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                             --cross-twiddle recurrence --shared-layout xor-swizzle
+                             --normalization none --logN ${fp64_log_n} --batch 2
+                             --warmup 1 --repeat 1 --verify)
+        endforeach()
+        foreach(fp64_shape IN ITEMS "14;7" "18;9")
+            list(GET fp64_shape 0 fp64_log_n)
+            list(GET fp64_shape 1 fp64_local_stages)
+            add_test(NAME fft_fp64_cufftdx_xor_logN${fp64_log_n}_inverse_correctness
+                     COMMAND cubutterfly_bench --operator fft --precision fp64 --backend online-reorder
+                             --fft-core cufftdx-block --local-stages ${fp64_local_stages}
+                             --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+                             --cross-twiddle recurrence --shared-layout xor-swizzle --inverse
+                             --normalization inverse --logN ${fp64_log_n} --batch 2
+                             --warmup 1 --repeat 1 --verify)
+        endforeach()
+        add_test(NAME fft_auto_dispatch_correctness
+                 COMMAND cubutterfly_bench --auto-select --operator fft --precision fp32
+                         --placement in-place --normalization none --logN 18 --batch 2
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_mixed_direct_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 9,11 --prefix-threads 256 --prefix-ept 8
+                         --suffix-threads 256 --suffix-ept 8 --cross-twiddle recurrence
+                         --placement in-place --normalization none --logN 20 --batch 1
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_tiled_transpose_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --local-stages 9 --prefix-threads 256 --prefix-ept 8
+                         --suffix-threads 256 --suffix-ept 8 --cross-twiddle recurrence
+                         --direct-boundary tiled-transpose --placement in-place --normalization none
+                         --logN 20 --batch 1 --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_prefix_tiled_transpose_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 11,9 --prefix-threads 256 --prefix-ept 8
+                         --suffix-threads 128 --suffix-ept 16 --cross-twiddle recurrence
+                         --direct-boundary prefix-tiled-transpose --placement in-place --normalization none
+                         --logN 20 --batch 1 --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_multisegment_d3_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 6,6,8
+                         --segment-threads 256,256,256 --segment-ept 8,8,8
+                         --boundary-twiddle recurrence,recurrence
+                         --placement in-place --normalization none --logN 20 --batch 1
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_multisegment_d4_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 5,5,5,5
+                         --segment-threads 256,256,256,256 --segment-ept 8,8,8,8
+                         --boundary-twiddle recurrence,table,recurrence
+                         --placement in-place --normalization none --logN 20 --batch 1
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fused_boundary_d3_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 7,3,10
+                         --segment-threads 128,128,256 --segment-ept 8,8,16
+                         --boundary-twiddle table,recurrence
+                         --boundary-residency fused,global-scratch
+                         --group-threads 512,512 --group-ept 8,8
+                         --placement in-place --normalization none --logN 20 --batch 1
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_fused_boundary_d4_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 5,5,5,5
+                         --segment-threads 128,128,128,128 --segment-ept 8,8,8,8
+                         --boundary-twiddle table,recurrence,table
+                         --boundary-residency fused,global-scratch,fused
+                         --group-threads 512,512 --group-ept 8,8
+                         --placement in-place --normalization none --logN 20 --batch 1
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_multisegment_inverse_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 6,6,6
+                         --segment-threads 256,256,256 --segment-ept 8,8,8
+                         --boundary-twiddle table,recurrence --inverse
+                         --placement out-of-place --normalization inverse --logN 18 --batch 1
+                         --warmup 1 --repeat 1 --verify)
+        add_test(NAME fft_multisegment_strided_correctness
+                 COMMAND cubutterfly_bench --operator fft --precision fp32 --backend online-reorder
+                         --fft-core cufftdx-block --stage-partition 4,4,4
+                         --segment-threads 128,128,128 --segment-ept 4,4,4
+                         --boundary-twiddle recurrence,table --element-stride 2 --batch-stride 8192
+                         --placement out-of-place --normalization none --logN 12 --batch 2
+                         --warmup 1 --repeat 1 --verify)
+    endif()
 endif()
diff --git a/README.md b/README.md
index 3f1472b..ce7904d 100644
--- a/README.md
+++ b/README.md
@@ -6,54 +6,89 @@
 [![Release](https://img.shields.io/github/v/release/TruNcat3/cuButterfly)](https://github.com/TruNcat3/cuButterfly/releases/latest)
 [![License](https://img.shields.io/badge/license-BSD--3--Clause-blue.svg)](LICENSE)
 
-cuButterfly is a CUDA research prototype that generalizes the
-space-time parallel paradigm from NTT to regular layered transforms. It keeps
-the architecture-level mapping independent of the local arithmetic core, so
-FFT, NTT, FWHT, and XOR-zeta can share one mapping vocabulary while selecting
-different GPU realizations.
+cuButterfly is a CUDA research prototype for mapping regular layered transforms
+onto a GPU. Its central observation is that FFT, NTT, FWHT, and XOR-zeta differ
+in arithmetic but expose the same two-dimensional scheduling problem: many
+independent data groups must pass through an ordered sequence of butterfly
+stages. The project describes how both dimensions are unfolded in space and
+time, then selects the concrete CUDA realization from the target hardware.
 
 The repository contains working kernels, CPU references, a generated
 processing-unit boundary, same-machine library comparisons, Nsight profiling
 scripts, and the raw CSV data used in the reports. It is a research artifact,
 not a drop-in replacement for cuFFT or a production cryptography library.
 
-## Core Idea
+## Why This Design
 
-A regular butterfly graph exposes two logical dimensions: stage and independent
-data unit. cuButterfly unfolds both dimensions in space and time:
+A fast butterfly kernel needs more than a fast butterfly instruction. It must
+decide which independent values execute together, how long dependent stages
+remain on chip, how values move between lanes or warps, and which layout the
+next stage group consumes. If those decisions are embedded in one arithmetic
+core, every new operator, precision, length, or GPU requires another isolated
+kernel design.
 
-```text
-M = (Us, Ts, Ud, Td, Ub, Tb, Hs, Rs, Rd, Rb, L, F, Q)
+cuButterfly instead keeps two layers separate. The **mapping layer** organizes
+the dependency graph and owns parallel placement, temporal reuse, residence,
+synchronization, and layout. The **processing-unit layer** implements a local
+stage group using an appropriate radix, modular core, register hierarchy,
+cuFFTDx block, or WMMA candidate. A stronger local unit can therefore be added
+to the search space without changing the architecture model.
+
+## Mapping Model
 
-Us, Ts  stage-space and stage-time unfolding
-Ud, Td  data-space and data-time unfolding
-Ub, Tb  batch-space and batch-time unfolding
-Hs      physical service for spatial stage edges
-Rs/Rd/Rb residence across stage, data, and batch folds
-L       input, intermediate, and output layout policy
-F, Q    kernel family and hardware realization parameters
+Let `D` be independent data work and `S` be ordered stage work. The fundamental
+factorization is:
+
+```text
+D = Ud * Td       data-space replication x data-time reuse
+S = Us * Ts       stage-space service     x stage-time reuse
 ```
 
+`Ud` and `Us` spend hardware to expose work concurrently. `Td` and `Ts` reuse
+that hardware across logical positions. Batch supplies more independent work
+to `D`; implementation fields `Ub` and `Tb` can refine its scheduling but do
+not create a third dependency dimension. None of these factors is a fixed tile
+constant: register capacity, shared memory, warp and barrier behavior, SM count,
+cache, and memory service determine the useful values on each GPU.
+
 ![cuButterfly concept: a regular butterfly graph is factorized in space and time, combined with a GPU profile and replaceable processing units, and calibrated by measured counters.](figures/cubutterfly_concept.svg)
 
 The editable Graphviz source is
 [`figures/cubutterfly_concept.dot`](figures/cubutterfly_concept.dot).
 
-The processing unit may change without changing the paradigm. Conversely, a
-good codelet does not determine its block shape, residency, permutation policy,
-or cross-kernel schedule. These are searched against the current GPU.
+The diagram is a mapping chain, not a fixed kernel template. Data-space
+unfolding primarily determines grid, CTA, and warp placement. Data-time and
+stage-time unfolding create reuse, whose live state is placed in registers or
+shared memory according to visibility and capacity. Stage-space unfolding
+requires an explicit transport such as shuffle, shared memory, or a barrier.
+The chosen processing unit consumes that schedule. When the next stage group
+needs another ownership or layout, its output store performs an online reorder
+or a global handoff.
+
+Temporal reuse does not mean that all values always remain in registers, and a
+single CUDA source kernel does not provide ordinary CTAs with a grid-wide
+barrier. Thread-private state uses registers, CTA-visible state uses shared
+memory, and a global boundary is retained only where dependency scope or
+capacity requires it. Similarly, online reordering is fused with a required
+handoff but is not assumed free; address work, coalescing, and shared-bank
+behavior are part of measurement and selection.
+
+The [Design Overview](docs/design_overview.md) derives the four factors and
+their execution semantics. [Hardware Mapping
+Methodology](docs/hardware_mapping_methodology.md) gives the resource equations
+and counter-driven selection procedure, while [Complete Butterfly Design
+Space](docs/butterfly_design_space.md) specifies the full mapping descriptor:
 
-Read [Complete Butterfly Design Space](docs/butterfly_design_space.md) for the
-canonical model, [Design Overview](docs/design_overview.md) for the concise view, and
-[Hardware Mapping Methodology](docs/hardware_mapping_methodology.md) for the
-resource equations and counter-driven selection procedure.
+```text
+M = (Us, Ts, Ud, Td, Ub, Tb, Hs, Rs, Rd, Rb, L, F, Q)
+```
 
 ## Implemented Scope
 
 | Operator | Numeric forms | Processing-unit candidates | Mapping families |
 |:--|:--|:--|:--|
 | NTT | 32/64-bit words, compatible primes below `2^63` | radix-2/4/8, Shoup, Barrett, fused coset twiddles | baseline, local tile, Hybrid2D, compact stage, stage pipeline |
-| FFT | FP32, FP64, FP16 input with FP32 accumulation | radix-2/4/8, four-multiply, Gauss-3, thread/CTA/WMMA DFT8 | temporal tile, hierarchical, online reorder, warp hybrid, stage pipeline |
+| FFT | FP32, FP64, FP16 input with FP32 accumulation | radix-2/4/8, four-multiply, Gauss-3, thread/CTA/WMMA DFT8, FP32/FP64 cuFFTDx | temporal tile, hierarchical, online reorder, warp hybrid, stage pipeline |
 | FWHT | FP32, FP64 | radix-2/4/8, shared and warp-register exchange | temporal tile, hierarchical, online reorder, warp hybrid, stage pipeline |
 | XOR-zeta | uint32 | radix-2/4/8 | temporal tile, hierarchical, online reorder, warp hybrid, stage pipeline |
 
@@ -71,7 +106,17 @@ precision, direction, layout, and warmup protocol. Ratios above `1.0x` mean
 cuButterfly has higher throughput. They must not be generalized to other GPUs.
 For the latest controlled cross-workload protocol and its complete evidence
 boundary, use the [V100 Comprehensive Results](docs/comprehensive_v100_results.md);
-the focused rows below retain their original experiment protocols.
+the [V100 Research Status](docs/research_status.md) separates closed claims,
+negative results, remaining work, and the cross-GPU TODO;
+the focused rows below retain their original experiment protocols. The newer
+[orthogonal length/batch scan](docs/v100_scaling_results.md) shows that parity
+is shape-dependent: the best processing unit and the relative library result
+can change as batch exposes additional hardware concurrency.
+The measured [FFT pipeline generator](docs/fft_pipeline_generator.md) turns
+that observation into a processing-unit, mapping, and runtime-dispatch flow.
+Its FFT lowering now treats logical decomposition count and physical execution
+group count as independent parameters: adjacent logical segments can be fused
+without forcing an intermediate global-memory pass.
 
 ### Same-Machine Library Comparisons
 
@@ -80,21 +125,45 @@ the focused rows below retain their original experiment protocols.
 | FP32 DFT8, `2^22` total points | 0.093420 ms | cuFFT 0.086323 ms | 0.924x | generated CTA DFT8 |
 | FP32 FFT, `logN=12`, `2^22` total points | 0.088934 ms | cuFFT 0.089989 ms | 1.012x | contiguous cuFFTDx direct unit |
 | FP32 FFT, `logN=14`, `2^22` total points | 0.131543 ms | cuFFT 0.135383 ms | 1.029x | contiguous cuFFTDx direct unit |
-| FP32 FFT, `logN=18`, `2^22` total points | 0.212019 ms | cuFFT 0.226877 ms | 1.070x | `9+9`, independently tuned 256/256-thread dimensions |
-| FP32 FFT, `logN=20`, `2^22` total points | 0.235971 ms | cuFFT 0.209521 ms | 0.888x | cuFFTDx two-pass composition |
+| FP32 FFT, `logN=18`, `2^22` total points | 0.195942 ms | cuFFT 0.211098 ms | 1.077x | vectorized `9+9`, 256/256-thread dimensions |
+| FP32 FFT, `logN=20`, `2^22` total points | 0.214733 ms | cuFFT 0.210330 ms | 0.979x | vectorized `10+10`, batch-selected dimensions |
+| FP64 FFT, `logN=16`, batch 64 | 0.339364 ms | cuFFT 0.343040 ms | 1.011x | remapped FP64 cuFFTDx `8+8`, recurrence, XOR prefix |
+| FP64 FFT, `logN=18`, batch 16 | 0.354877 ms | cuFFT 0.421970 ms | 1.189x | FP64 cuFFTDx `9+9`, independently mapped dimensions |
 | FP32 FWHT, `logN=8` | 0.043131 ms | Dao FHT 0.043172 ms | 1.001x | integrated register unit |
 | FP32 FWHT, `logN=15` | 0.069243 ms | Dao FHT 0.063949 ms | 0.924x | register-pressure boundary |
 | 60-bit NTT, `logN=16`, natural order | 0.274104 ms | GPU-NTT 0.291133 ms | 1.062x | fused Hybrid2D |
 | 60-bit NTT, `logN=20`, native bit-reversed | 0.341320 ms | GPU-NTT 0.396186 ms | 1.161x | compact-stage mapping |
 
-The generated local core and tiled two-pass composition raise long FFT
-throughput from 32.7%-47.4% to 41.9%-88.8% of cuFFT. Whole-transform cuFFTDx
+The generated local core, fused physical grouping, and vectorized two-pass
+composition bring the selected long FFT shapes to 95.4%-108.5% of cuFFT.
+Whole-transform cuFFTDx
 units at `logN=11..14` isolate the local-unit ceiling: the contiguous paths at
 `logN=11,12,14` reach 1.006x, 1.012x, and 1.029x cuFFT throughput, while
 `logN=13` reaches 0.965x. Independently tuning the two long-transform dimensions
 also raises `logN=18` from 0.881x in the fixed-512 mapping experiment to 1.070x.
 Processing-unit granularity and each dimension's CTA shape are therefore explicit
 hardware-mapping axes rather than fixed properties of the paradigm.
+The pre-address-optimization FP64 counter capture shows recurrence reduces prefix replay
+time by 17.5% and raises its DRAM utilization from 60.2% to 72.9% by trading
+8.4% more FP64 instructions for 6.9% fewer warp instructions. The suffix is
+unchanged. XOR-swizzling the same-capacity prefix layout then cuts its shared
+conflicts by 53.5% and replay time by 5.3%, raising DRAM utilization to 77.0%.
+The path was within 1.8% of cuFFT replay, but still executed 2.19x its warp
+instructions and incurred about 100x its shared conflicts. Hoisting invariant
+global addresses and advancing swizzled shared pointers by compile-time strides
+then lowers CUDA-event time from 0.353526 ms to 0.342098 ms, matching cuFFT at
+1.002x throughput. Updated counters confirm a 26.8% reduction in prefix warp
+instructions and an 8.3% reduction in prefix replay versus the pre-optimization
+XOR kernel. Total replay is 2.5% below cuFFT even though the path still executes
+1.83x its warp instructions, 3.62x its integer instructions, and about 114x its
+shared conflicts. See
+[FP64 NCU Attribution](results/ncu_fp64_fft/analysis.md).
+
+The FP64 online unit now covers two-segment `logN=14..18` compositions rather
+than only `8+8`. A 648-point V100 scan independently selects decomposition and
+both CTA/EPT dimensions. Across the 25 length/batch shapes above the 0.020-ms
+timing floor, cuButterfly has higher median throughput in 20 and non-overlapping
+faster trial ranges in 19. See [FP64 robustness](results/fp64_robustness_batch_analysis.md).
 
 ### Online Reorder at `logN=20`
 
@@ -110,6 +179,13 @@ assumed free: the destination transaction pattern and suffix residency are
 measured separately. See [Experimental Results](docs/experiments.md) and the
 [raw results directory](results/).
 
+Targeted [V100 counter attribution](docs/v100_ncu_attribution.md) shows why
+occupancy alone is insufficient: the long online FFT paths expose as many or
+more active warps than cuFFT, but execute 1.60x-2.00x the warp instructions and
+about 9.4x-9.5x the shared-memory bank conflicts at the measured large-batch
+points. The mapping method therefore separates grid coverage, residency, and
+useful work per resident warp.
+
 ## Quick Start
 
 Requirements: Linux, CMake 3.20+, a C++17 compiler, and the CUDA Toolkit.
@@ -158,6 +234,14 @@ artifact; the clean-clone validation uses CUDA 11.8 with GCC 11.
 
 ## Repository Guide
 
+For a first reading, follow the argument rather than the directory tree:
+[Design Overview](docs/design_overview.md) explains why the graph is split into
+two dimensions and four unfolding factors; [Experimental
+Results](docs/experiments.md) connects each architectural claim to a controlled
+measurement; [Getting Started](docs/getting_started.md) then reproduces a
+verified design point. Readers evaluating the paper claim should continue with
+the hardware model, complete design-space contract, and research-status report.
+
 | Path | Purpose |
 |:--|:--|
 | `include/cuntt/` | public NTT and common butterfly plan APIs |
@@ -169,21 +253,26 @@ artifact; the clean-clone validation uses CUDA 11.8 with GCC 11.
 | `results/` | measured V100 CSV data and counter analyses |
 | `docs/` | architecture, implementation, experiments, and research positioning |
 
-Start with the [Documentation Index](docs/README.md). Candidate processing
-units and future implementation paths are catalogued in
+The [Documentation Index](docs/README.md) provides separate architecture,
+implementation, and reproduction paths. Candidate processing units and future
+implementation paths are catalogued in
 [Candidate Implementations](docs/implementation_candidates.md).
 Development priorities are tracked in [`ROADMAP.md`](ROADMAP.md), and evidence
 requirements for contributions are in [`CONTRIBUTING.md`](CONTRIBUTING.md).
-Versioned changes are recorded in [`CHANGELOG.md`](CHANGELOG.md).
+Versioned changes are recorded in [`CHANGELOG.md`](CHANGELOG.md). The v0.3.0
+research milestone, acceptance criteria, and deferred cross-GPU work are in
+[v0.3.0 Mapping-Selection Milestone](docs/next_phase_v0.3.md).
 
 ## Evidence Boundary
 
 - V100 is the only fully measured GPU generation in this revision. A100, H100,
   and RTX 4090 entries are placeholders, not performance claims.
-- FP32 FFT is at cuFFT parity for the measured `logN=8,14,18` shapes, but the
-  measured `logN=20` path and FP64 `logN=16` path remain behind. Tensor Core
-  DFT8 helps the local unit but does not remove layout, synchronization, and
-  composition costs.
+- FP32 FFT reaches cuFFT parity or advantage at selected direct and long
+  shapes; saturated `logN=20` batch 8/16 remains at `0.962x/0.954x`. The
+  focused FP64 cuFFTDx matrix raises `logN=16`, batch 64 from 0.642x in the
+  scalar comprehensive run to 1.011x and is faster by median on 20/25 stable
+  `logN=14..18` shapes. Tensor Core DFT8 helps the local unit but does not
+  remove layout, synchronization, and composition costs.
 - FWHT closely tracks Dao FHT after importing its validated local register
   hierarchy. This demonstrates processing-unit reuse, not independent invention
   of that core.
@@ -204,7 +293,7 @@ software release as:
   author  = {TruNcat3},
   title   = {cuButterfly: Hardware-Mapped Space-Time Parallelism for Butterfly Computations on GPUs},
   year    = {2026},
-  version = {0.2.0},
+  version = {0.3.0},
   url     = {https://github.com/TruNcat3/cuButterfly}
 }
 ```
diff --git a/ROADMAP.md b/ROADMAP.md
index ea1769e..fe0ea1b 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -3,24 +3,55 @@
 This roadmap separates implementation goals from evidence required for the
 research claim. Ordering may change after profiling or access to new hardware.
 
-## Near Term
-
-- Run an orthogonal `(logN, batch)` sweep instead of coupling all comparisons
-  through constant total points; identify launch-limited, saturation, and
-  throughput regions for every operator.
-- Refresh Dao-AILab FHT and GPU-NTT under the comprehensive-suite clock,
-  correctness, modulus, output-order, and trial protocol.
-- Profile the remaining FP32 `logN=20` and FP64 `logN=16` FFT gaps against
-  cuFFT, separating local-core, permutation, coefficient, and launch costs.
-- Convert the measured architecture space into a calibrated selector and
-  evaluate top-k prediction accuracy before exhaustive timing.
+## v0.3.0 Target: Counter-Calibrated Mapping Selection
+
+Status: the three V100 work packages, vectorized FFT physical unit, FFT
+leave-one-batch-out selector evaluation, and matching-protocol long-FFT refresh
+are complete. The post-vector fixed-mapping NCU capture attributes the gain to
+19.6% fewer warp instructions with unchanged DRAM write volume. Cross-GPU
+validation is deferred until the repository moves to a host with another GPU
+generation.
+
+The next release turns the measured design space into a reproducible mapping
+method rather than adding another isolated kernel. Its primary question is:
+
+> Given an operator contract, transform length, batch, and GPU service profile,
+> which mapping family and processing unit should be selected, and why?
+
+The release is complete when all of the following are true:
+
+1. NCU counters explain the FFT `logN=14` concurrency threshold, the
+   `logN=18/20` throughput ceilings, and the FWHT `logN=15` mapping crossover.
+2. A selector consumes workload and hardware descriptors, returns a ranked
+   top-k candidate set, and reports the resource or service constraints behind
+   the ranking.
+3. Leave-one-shape-out validation records top-1/top-k accuracy and performance
+   regret against the exhaustive V100 measurements.
+4. Dao-AILab FHT and GPU-NTT are refreshed under the same correctness, clock,
+   trial, and semantic protocol as the internal candidates.
+5. One release command regenerates the scaling manifest, summaries, selector
+   evaluation, and the paper-facing tables without modifying raw measurements.
+
+See [Next Phase: v0.3.0](docs/next_phase_v0.3.md) for the execution order,
+artifacts, and decision gates.
+
+## Near Term Backlog
+
+- Extend the measured orthogonal `(logN, batch)` sweep across additional
+  precision, direction, stride, and normalization contracts, then train the
+  selector on the observed saturation and mapping-crossover boundaries.
+- Reduce the remaining saturated FP32 `logN=20` exchange cost and the five
+  FP64 `logN=14..16` crossover deficits, preserving fixed-mapping NCU evidence.
 - Add a device-pointer and CUDA-stream execution API without weakening the
   current typed semantic contract.
 - Reduce template warning volume and record compiled resource envelopes as
   generated metadata.
 - Add focused sanitizer jobs on an available self-hosted GPU runner.
 
-## Cross-GPU Validation
+## Future: Cross-GPU Validation
+
+This work starts only after the repository is migrated to a machine with a
+second GPU generation. It is not a `v0.3.0` release gate.
 
 - Capture A100/H100/RTX 4090 hardware service profiles using the checked-in
   schema.
diff --git a/apps/cubutterfly_bench.cpp b/apps/cubutterfly_bench.cpp
index 7b6463a..181471e 100644
--- a/apps/cubutterfly_bench.cpp
+++ b/apps/cubutterfly_bench.cpp
@@ -3,6 +3,7 @@
 #include <cstdint>
 #include <iomanip>
 #include <iostream>
+#include <limits>
 #include <random>
 #include <stdexcept>
 #include <string>
@@ -19,17 +20,93 @@ std::string take_arg(int& index, int argc, char** argv) {
     return argv[++index];
 }
 
+std::vector<std::uint32_t> parse_stage_partition(const std::string& text) {
+    std::vector<std::uint32_t> partition;
+    std::size_t begin = 0;
+    while (begin <= text.size()) {
+        const std::size_t end = text.find(',', begin);
+        const std::string token = text.substr(begin, end == std::string::npos ? end : end - begin);
+        if (token.empty())
+            throw std::invalid_argument("stage partition contains an empty segment");
+        std::size_t consumed = 0;
+        const auto stages = std::stoul(token, &consumed);
+        if (consumed != token.size() || stages == 0 ||
+            stages > std::numeric_limits<std::uint32_t>::max())
+            throw std::invalid_argument("stage partition values must be positive integers");
+        partition.push_back(static_cast<std::uint32_t>(stages));
+        if (end == std::string::npos)
+            break;
+        begin = end + 1;
+    }
+    return partition;
+}
+
+std::vector<std::string> parse_csv_tokens(const std::string& text) {
+    std::vector<std::string> tokens;
+    std::size_t begin = 0;
+    while (begin <= text.size()) {
+        const std::size_t end = text.find(',', begin);
+        const std::string token = text.substr(begin, end == std::string::npos ? end : end - begin);
+        if (token.empty())
+            throw std::invalid_argument("comma-separated list contains an empty value");
+        tokens.push_back(token);
+        if (end == std::string::npos)
+            break;
+        begin = end + 1;
+    }
+    return tokens;
+}
+
+std::vector<std::uint32_t> parse_positive_list(const std::string& text, const char* name) {
+    std::vector<std::uint32_t> values;
+    for (const auto& token : parse_csv_tokens(text)) {
+        std::size_t consumed = 0;
+        const auto value = std::stoul(token, &consumed);
+        if (consumed != token.size() || value == 0 || value > std::numeric_limits<std::uint32_t>::max())
+            throw std::invalid_argument(std::string(name) + " values must be positive integers");
+        values.push_back(static_cast<std::uint32_t>(value));
+    }
+    return values;
+}
+
+std::string format_stage_partition(const std::vector<std::uint32_t>& partition) {
+    std::string text;
+    for (const auto stages : partition) {
+        if (!text.empty())
+            text += 'x';
+        text += std::to_string(stages);
+    }
+    return text;
+}
+
+template <typename Mapping, typename Getter>
+std::string format_mapping_list(const std::vector<Mapping>& mappings, Getter getter) {
+    std::string text;
+    for (const auto& mapping : mappings) {
+        if (!text.empty())
+            text += 'x';
+        text += getter(mapping);
+    }
+    return text;
+}
+
 void print_usage() {
     std::cout
         << "cubutterfly_bench [--operator fwht|fft|xor-zeta] [--backend temporal-tile|hierarchical|online-reorder|warp-hybrid|stage-pipeline|cufft]\n"
         << "                    [--logN 8] [--batch 16384] [--inverse]\n"
+        << "                    [--stage-partition 9,9]\n"
+        << "                    [--segment-threads 256,256,256] [--segment-ept 8,8,8]\n"
+        << "                    [--boundary-twiddle table,recurrence] [--boundary-layout direct-strided,direct-strided]\n"
+        << "                    [--boundary-residency fused,global-scratch]\n"
+        << "                    [--group-threads 512,512] [--group-ept 8,8]\n"
         << "                    [--normalization none|inverse]\n"
+        << "                    [--auto-select]\n"
         << "                    [--placement in-place|out-of-place]\n"
         << "                    [--batch-stride N]\n"
         << "                    [--element-stride N]\n"
         << "                    [--stage-space 1|2|4|8]\n"
         << "                    [--stage-handoff atomic|named-barrier]\n"
-        << "                    [--tile-threads 32|64|128|256; resident also 512|1024] [--local-stages 5..10] [--reorder-columns power-of-two]\n"
+        << "                    [--tile-threads 32|64|128|256; resident also 512|1024] [--local-stages 5..10; cuFFTDx online 5..12] [--reorder-columns power-of-two]\n"
         << "                    [--prefix-threads 128|256|512|1024] [--suffix-threads 128|256|512|1024]\n"
         << "                    [--prefix-ept N] [--suffix-ept N]\n"
         << "                    [--warp-stages 0..5]\n"
@@ -37,7 +114,9 @@ void print_usage() {
         << "                    [--compute-unit auto|radix2|radix4|radix8]\n"
         << "                    [--complex-multiply four-mul|gauss3]\n"
         << "                    [--cross-twiddle table|recurrence]\n"
+        << "                    [--direct-boundary direct-strided|tiled-transpose|prefix-tiled-transpose]\n"
         << "                    [--local-exchange shared|warp-register]\n"
+        << "                    [--shared-layout linear|xor-swizzle]\n"
         << "                    [--fft-core scalar|thread-dft8|cta-dft8|wmma-dft8|cufftdx-block|cufftdx-direct|cufftdx-resident|turbofft-generated]\n"
         << "                    [--precision fp32|fp64|fp16-fp32|uint32]\n"
         << "                    [--warmup 20] [--repeat 100] [--verify] [--csv]\n"
@@ -101,6 +180,57 @@ int main(int argc, char** argv) {
                 config.log_n = std::stoul(take_arg(index, argc, argv));
             } else if (arg == "--batch") {
                 config.batch = std::stoull(take_arg(index, argc, argv));
+            } else if (arg == "--stage-partition") {
+                config.stage_partition = parse_stage_partition(take_arg(index, argc, argv));
+            } else if (arg == "--segment-threads") {
+                const auto values = parse_positive_list(take_arg(index, argc, argv), "segment threads");
+                if (!config.segment_mappings.empty() && config.segment_mappings.size() != values.size())
+                    throw std::invalid_argument("segment threads and EPT lists must have equal length");
+                config.segment_mappings.resize(values.size());
+                for (std::size_t segment = 0; segment < values.size(); ++segment)
+                    config.segment_mappings[segment].threads = values[segment];
+            } else if (arg == "--segment-ept") {
+                const auto values = parse_positive_list(take_arg(index, argc, argv), "segment EPT");
+                if (!config.segment_mappings.empty() && config.segment_mappings.size() != values.size())
+                    throw std::invalid_argument("segment threads and EPT lists must have equal length");
+                config.segment_mappings.resize(values.size());
+                for (std::size_t segment = 0; segment < values.size(); ++segment)
+                    config.segment_mappings[segment].ept = values[segment];
+            } else if (arg == "--boundary-twiddle") {
+                const auto values = parse_csv_tokens(take_arg(index, argc, argv));
+                if (!config.boundaries.empty() && config.boundaries.size() != values.size())
+                    throw std::invalid_argument("boundary twiddle and layout lists must have equal length");
+                config.boundaries.resize(values.size());
+                for (std::size_t boundary = 0; boundary < values.size(); ++boundary)
+                    config.boundaries[boundary].cross_twiddle = cuntt::parse_cross_twiddle_mode(values[boundary]);
+            } else if (arg == "--boundary-layout") {
+                const auto values = parse_csv_tokens(take_arg(index, argc, argv));
+                if (!config.boundaries.empty() && config.boundaries.size() != values.size())
+                    throw std::invalid_argument("boundary twiddle and layout lists must have equal length");
+                config.boundaries.resize(values.size());
+                for (std::size_t boundary = 0; boundary < values.size(); ++boundary)
+                    config.boundaries[boundary].layout = cuntt::parse_direct_boundary(values[boundary]);
+            } else if (arg == "--boundary-residency") {
+                const auto values = parse_csv_tokens(take_arg(index, argc, argv));
+                if (!config.boundaries.empty() && config.boundaries.size() != values.size())
+                    throw std::invalid_argument("boundary parameter lists must have equal length");
+                config.boundaries.resize(values.size());
+                for (std::size_t boundary = 0; boundary < values.size(); ++boundary)
+                    config.boundaries[boundary].residency = cuntt::parse_fft_boundary_residency(values[boundary]);
+            } else if (arg == "--group-threads") {
+                const auto values = parse_positive_list(take_arg(index, argc, argv), "group threads");
+                if (!config.execution_group_mappings.empty() && config.execution_group_mappings.size() != values.size())
+                    throw std::invalid_argument("group threads and EPT lists must have equal length");
+                config.execution_group_mappings.resize(values.size());
+                for (std::size_t group = 0; group < values.size(); ++group)
+                    config.execution_group_mappings[group].threads = values[group];
+            } else if (arg == "--group-ept") {
+                const auto values = parse_positive_list(take_arg(index, argc, argv), "group EPT");
+                if (!config.execution_group_mappings.empty() && config.execution_group_mappings.size() != values.size())
+                    throw std::invalid_argument("group threads and EPT lists must have equal length");
+                config.execution_group_mappings.resize(values.size());
+                for (std::size_t group = 0; group < values.size(); ++group)
+                    config.execution_group_mappings[group].ept = values[group];
             } else if (arg == "--batch-stride") {
                 config.batch_stride = std::stoull(take_arg(index, argc, argv));
             } else if (arg == "--element-stride") {
@@ -133,8 +263,12 @@ int main(int argc, char** argv) {
                 config.complex_multiply = cuntt::parse_complex_multiply(take_arg(index, argc, argv));
             } else if (arg == "--cross-twiddle") {
                 config.cross_twiddle = cuntt::parse_cross_twiddle_mode(take_arg(index, argc, argv));
+            } else if (arg == "--direct-boundary") {
+                config.direct_boundary = cuntt::parse_direct_boundary(take_arg(index, argc, argv));
             } else if (arg == "--local-exchange") {
                 config.local_exchange = cuntt::parse_local_exchange(take_arg(index, argc, argv));
+            } else if (arg == "--shared-layout") {
+                config.shared_layout = cuntt::parse_shared_layout(take_arg(index, argc, argv));
             } else if (arg == "--fft-core") {
                 config.fft_core = cuntt::parse_fft_core(take_arg(index, argc, argv));
             } else if (arg == "--precision") {
@@ -143,6 +277,8 @@ int main(int argc, char** argv) {
                 config.placement = cuntt::parse_butterfly_placement(take_arg(index, argc, argv));
             } else if (arg == "--inverse") {
                 config.inverse = true;
+            } else if (arg == "--auto-select") {
+                config.auto_select = true;
             } else if (arg == "--normalization") {
                 const std::string mode = take_arg(index, argc, argv);
                 if (mode == "none")
@@ -279,17 +415,30 @@ int main(int argc, char** argv) {
         const auto device = cuntt::current_device_info();
         std::cout << std::fixed << std::setprecision(6);
         if (csv) {
-            std::cout << "device,compute_capability,operator,precision,direction,normalization,placement,backend,compute_unit,complex_multiply,cross_twiddle,local_"
-                         "exchange,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_"
+            std::cout << "device,compute_capability,operator,precision,direction,normalization,placement,auto_select,backend,compute_unit,complex_multiply,cross_twiddle,direct_boundary,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,group_threads,group_ept,local_"
+                         "exchange,shared_layout,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_"
                          "stride,warmup,repeat,h2d_ms,kernel_ms,d2h_ms,"
                          "transforms_s,Gbutterfly_s,points_s,max_error,correct\n";
             std::cout << '"' << device.name << "\"," << device.compute_major << '.' << device.compute_minor << ','
                       << cuntt::butterfly_operator_name(config.op) << ',' << cuntt::butterfly_precision_name(config.precision) << ','
                       << (config.inverse ? "inverse" : "forward") << ',' << (config.normalize_inverse ? "inverse" : "none") << ','
-                      << cuntt::butterfly_placement_name(config.placement) << ',' << cuntt::butterfly_backend_name(config.backend) << ','
+                      << cuntt::butterfly_placement_name(config.placement) << ',' << static_cast<int>(config.auto_select) << ','
+                      << cuntt::butterfly_backend_name(config.backend) << ','
                       << cuntt::compute_unit_name(config.compute_unit) << ',' << cuntt::complex_multiply_name(config.complex_multiply) << ','
                       << cuntt::cross_twiddle_mode_name(config.cross_twiddle) << ','
-                      << cuntt::local_exchange_name(config.local_exchange) << ',' << cuntt::fft_core_name(config.fft_core) << ',' << config.stage_space << ','
+                      << cuntt::direct_boundary_name(config.direct_boundary) << ','
+                      << config.stage_partition.size() << ',' << format_stage_partition(config.stage_partition) << ','
+                      << format_mapping_list(config.segment_mappings, [](const auto& mapping) { return std::to_string(mapping.threads); }) << ','
+                      << format_mapping_list(config.segment_mappings, [](const auto& mapping) { return std::to_string(mapping.ept); }) << ','
+                      << format_mapping_list(config.boundaries, [](const auto& boundary) { return std::string(cuntt::cross_twiddle_mode_name(boundary.cross_twiddle)); }) << ','
+                      << format_mapping_list(config.boundaries, [](const auto& boundary) { return std::string(cuntt::direct_boundary_name(boundary.layout)); }) << ','
+                      << format_mapping_list(config.boundaries, [](const auto& boundary) { return std::string(cuntt::fft_boundary_residency_name(boundary.residency)); }) << ','
+                      << config.execution_group_mappings.size() << ','
+                      << format_mapping_list(config.execution_group_mappings, [](const auto& mapping) { return std::to_string(mapping.threads); }) << ','
+                      << format_mapping_list(config.execution_group_mappings, [](const auto& mapping) { return std::to_string(mapping.ept); }) << ','
+                      << cuntt::local_exchange_name(config.local_exchange) << ','
+                      << cuntt::shared_layout_name(config.shared_layout) << ','
+                      << cuntt::fft_core_name(config.fft_core) << ',' << config.stage_space << ','
                       << cuntt::stage_handoff_name(config.stage_handoff) << ',' << config.tile_threads << ','
                       << config.prefix_threads << ',' << config.suffix_threads << ',' << config.prefix_ept << ',' << config.suffix_ept << ','
                       << config.prefix_units_per_cta << ',' << config.suffix_units_per_cta << ',' << config.local_stages << ','
@@ -305,11 +454,20 @@ int main(int argc, char** argv) {
                       << "direction: " << (config.inverse ? "inverse" : "forward") << "\n"
                       << "normalization: " << (config.normalize_inverse ? "inverse" : "none") << "\n"
                       << "placement: " << cuntt::butterfly_placement_name(config.placement) << "\n"
+                      << "auto_select: " << (config.auto_select ? "yes" : "no") << "\n"
                       << "backend: " << cuntt::butterfly_backend_name(config.backend) << "\n"
                       << "compute_unit: " << cuntt::compute_unit_name(config.compute_unit) << "\n"
                       << "complex_multiply: " << cuntt::complex_multiply_name(config.complex_multiply) << "\n"
                       << "cross_twiddle: " << cuntt::cross_twiddle_mode_name(config.cross_twiddle) << "\n"
+                      << "direct_boundary: " << cuntt::direct_boundary_name(config.direct_boundary) << "\n"
+                      << "stage_partition: " << format_stage_partition(config.stage_partition) << "\n"
+                      << "segment_threads: " << format_mapping_list(config.segment_mappings, [](const auto& mapping) { return std::to_string(mapping.threads); }) << "\n"
+                      << "segment_ept: " << format_mapping_list(config.segment_mappings, [](const auto& mapping) { return std::to_string(mapping.ept); }) << "\n"
+                      << "boundary_residencies: " << format_mapping_list(config.boundaries, [](const auto& boundary) { return std::string(cuntt::fft_boundary_residency_name(boundary.residency)); }) << "\n"
+                      << "group_threads: " << format_mapping_list(config.execution_group_mappings, [](const auto& mapping) { return std::to_string(mapping.threads); }) << "\n"
+                      << "group_ept: " << format_mapping_list(config.execution_group_mappings, [](const auto& mapping) { return std::to_string(mapping.ept); }) << "\n"
                       << "local_exchange: " << cuntt::local_exchange_name(config.local_exchange) << "\n"
+                      << "shared_layout: " << cuntt::shared_layout_name(config.shared_layout) << "\n"
                       << "fft_core: " << cuntt::fft_core_name(config.fft_core) << "\n"
                       << "stage_space: " << config.stage_space << "\n"
                       << "stage_handoff: " << cuntt::stage_handoff_name(config.stage_handoff) << "\n"
diff --git a/config/butterfly_architecture_space.json b/config/butterfly_architecture_space.json
index a173637..a4d00bd 100644
--- a/config/butterfly_architecture_space.json
+++ b/config/butterfly_architecture_space.json
@@ -160,7 +160,7 @@
       "thread-dft8": {"stage_group": "full-codelet", "arithmetic_core": "scalar", "precision": ["fp32"], "coefficient": ["generated"], "exchange": ["thread-register"]},
       "cta-dft8": {"stage_group": "full-codelet", "arithmetic_core": "scalar", "precision": ["fp32"], "coefficient": ["generated"], "exchange": ["shared"]},
       "wmma-dft8": {"stage_group": "matrix-tile", "arithmetic_core": "tensor", "precision": ["fp16-fp32"], "coefficient": ["generated"], "exchange": ["tensor-fragment", "shared"]},
-      "cufftdx-block": {"stage_group": "full-codelet", "arithmetic_core": "imported-codelet", "precision": ["fp32"], "coefficient": ["native-table", "recurrence"], "exchange": ["thread-register", "shared", "imported-codelet"]},
+      "cufftdx-block": {"stage_group": "full-codelet", "arithmetic_core": "imported-codelet", "precision": ["fp32", "fp64"], "coefficient": ["native-table", "recurrence"], "exchange": ["thread-register", "shared", "imported-codelet"]},
       "cufftdx-direct": {"stage_group": "full-codelet", "arithmetic_core": "imported-codelet", "precision": ["fp32"], "coefficient": ["native-table", "generated"], "exchange": ["imported-codelet"]},
       "turbofft-generated": {"stage_group": "full-codelet", "arithmetic_core": "generated-codelet", "precision": ["fp32"], "coefficient": ["generated"], "exchange": ["imported-codelet"]}
     },
diff --git a/config/fft_architecture_space.json b/config/fft_architecture_space.json
index be5e812..5592568 100644
--- a/config/fft_architecture_space.json
+++ b/config/fft_architecture_space.json
@@ -1,6 +1,6 @@
 {
   "schema_version": 1,
-  "model": "two-dimensional-space-time-butterfly",
+  "model": "parameterized-factorization-two-axis-space-time-butterfly",
   "hardware_profiles": {
     "v100-sm70": {
       "sm_count": 80,
@@ -14,7 +14,11 @@
   },
   "axes": {
     "log_n": {"min": 1, "max": 20},
-    "decomposition": ["single-unit", "two-dimensional", "multi-dimensional"],
+    "decomposition": {
+      "decomposition_count": {"min": 1, "max": 8},
+      "stage_partition": "ordered-composition",
+      "constraint": "sum(stages_per_decomposition)=log_n"
+    },
     "precision": ["fp16-fp32", "fp32", "fp64"],
     "direction": ["forward", "inverse"],
     "placement": ["out-of-place", "in-place"],
@@ -40,7 +44,7 @@
   "families": [
     {
       "name": "cufftdx-online",
-      "decomposition": "two-dimensional",
+      "decomposition_count": "parameterized",
       "prefix_core": "cufftdx-block",
       "suffix_core": "cufftdx-block",
       "boundary": "global-scratch",
@@ -51,19 +55,19 @@
     },
     {
       "name": "cufftdx-large-online",
-      "decomposition": "two-dimensional",
+      "decomposition_count": "parameterized",
       "prefix_core": "cufftdx-block-or-direct",
       "suffix_core": "cufftdx-block-or-direct",
       "boundary": "global-scratch",
       "reorder": "direct-strided-or-transpose",
       "precision": ["fp32"],
       "cross_twiddle": ["table", "recurrence"],
-      "dimension_log_n": {"min": 3, "max": 14},
-      "status": "requires-new-kernel"
+      "dimension_log_n": {"min": 3, "max": 12},
+      "status": "compiled-direct-strided-and-directional-transpose"
     },
     {
       "name": "resident-composition",
-      "decomposition": "two-dimensional",
+      "decomposition_count": "parameterized",
       "boundary": "shared-resident",
       "reorder": "online-tiled",
       "precision": ["fp32"],
@@ -71,7 +75,7 @@
     },
     {
       "name": "mixed-core-composition",
-      "decomposition": "two-dimensional",
+      "decomposition_count": "parameterized",
       "boundary": "global-scratch",
       "reorder": "online-tiled-or-transpose",
       "precision": ["fp16-fp32", "fp32", "fp64"],
@@ -79,7 +83,7 @@
     },
     {
       "name": "single-whole-transform",
-      "decomposition": "single-unit",
+      "decomposition_count": 1,
       "boundary": "none",
       "reorder": "direct-strided",
       "precision": ["fp32"],
diff --git a/config/v100_comprehensive_suite.json b/config/v100_comprehensive_suite.json
index 3f9ee2a..f31472c 100644
--- a/config/v100_comprehensive_suite.json
+++ b/config/v100_comprehensive_suite.json
@@ -19,11 +19,11 @@
     {"id": "fft14_cufft", "tier": "quick", "group": "fft-fp32-fwd-log14", "runner": "fft-library", "implementation": "cuFFT", "reference": true, "operator": "fft", "precision": "fp32", "logN": 14, "args": ["--library", "cufft"]},
     {"id": "fft14_vkfft", "tier": "quick", "group": "fft-fp32-fwd-log14", "runner": "fft-library", "implementation": "VkFFT", "operator": "fft", "precision": "fp32", "logN": 14, "args": ["--library", "vkfft"]},
 
-    {"id": "fft18_cub", "tier": "quick", "group": "fft-fp32-fwd-log18", "runner": "butterfly", "implementation": "cuButterfly-cuFFTDx-online", "operator": "fft", "precision": "fp32", "logN": 18, "args": ["--backend", "online-reorder", "--fft-core", "cufftdx-block", "--local-stages", "9", "--reorder-columns", "1", "--cross-twiddle", "recurrence", "--prefix-threads", "256", "--suffix-threads", "256", "--prefix-ept", "8", "--suffix-ept", "8", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
+    {"id": "fft18_cub", "tier": "quick", "group": "fft-fp32-fwd-log18", "runner": "butterfly", "implementation": "cuButterfly-auto-vectorized", "operator": "fft", "precision": "fp32", "logN": 18, "args": ["--auto-select", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
     {"id": "fft18_cufft", "tier": "quick", "group": "fft-fp32-fwd-log18", "runner": "fft-library", "implementation": "cuFFT", "reference": true, "operator": "fft", "precision": "fp32", "logN": 18, "args": ["--library", "cufft"]},
     {"id": "fft18_vkfft", "tier": "quick", "group": "fft-fp32-fwd-log18", "runner": "fft-library", "implementation": "VkFFT", "operator": "fft", "precision": "fp32", "logN": 18, "args": ["--library", "vkfft"]},
 
-    {"id": "fft20_cub", "tier": "quick", "group": "fft-fp32-fwd-log20", "runner": "butterfly", "implementation": "cuButterfly-cuFFTDx-online", "operator": "fft", "precision": "fp32", "logN": 20, "args": ["--backend", "online-reorder", "--fft-core", "cufftdx-block", "--local-stages", "10", "--reorder-columns", "1", "--cross-twiddle", "recurrence", "--prefix-threads", "512", "--suffix-threads", "512", "--prefix-ept", "8", "--suffix-ept", "8", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
+    {"id": "fft20_cub", "tier": "quick", "group": "fft-fp32-fwd-log20", "runner": "butterfly", "implementation": "cuButterfly-auto-vectorized", "operator": "fft", "precision": "fp32", "logN": 20, "args": ["--auto-select", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
     {"id": "fft20_cufft", "tier": "quick", "group": "fft-fp32-fwd-log20", "runner": "fft-library", "implementation": "cuFFT", "reference": true, "operator": "fft", "precision": "fp32", "logN": 20, "args": ["--library", "cufft"]},
     {"id": "fft20_vkfft", "tier": "quick", "group": "fft-fp32-fwd-log20", "runner": "fft-library", "implementation": "VkFFT", "operator": "fft", "precision": "fp32", "logN": 20, "args": ["--library", "vkfft"]},
 
@@ -57,7 +57,7 @@
     {"id": "ntt16_60_inverse", "tier": "full", "group": "ntt-u60-inverse-log16", "runner": "ntt", "implementation": "cuNTT-Hybrid2D-radix2", "operator": "ntt", "precision": "uint64", "direction": "inverse", "modulus_bits": 60, "logN": 16, "args": ["--backend", "hybrid2d", "--compute-unit", "radix2", "--word-bits", "64", "--cross-twiddle", "fused", "--output-order", "natural", "--inverse"]}
   ],
   "external_evidence": [
-    {"operator": "fwht", "implementation": "Dao-AILab FHT", "status": "not-runnable", "reason": "PyTorch is not installed in the active Python environment", "existing_result": "results/external_dao_fht_v100_summary.csv"},
-    {"operator": "ntt", "implementation": "GPU-NTT", "status": "not-runnable", "reason": "the external comparator harness binary is not present", "existing_result": "results/compact_stage_logN20.csv"}
+    {"operator": "fwht", "implementation": "Dao-AILab FHT", "status": "measured-matching-protocol", "reason": "five-trial correctness-checked refresh is archived separately", "existing_result": "results/v100_external_baselines_summary.csv"},
+    {"operator": "ntt", "implementation": "GPU-NTT", "status": "measured-matching-protocol", "reason": "natural and native bit-reversed contracts are archived separately", "existing_result": "results/v100_external_baselines_summary.csv"}
   ]
 }
diff --git a/config/v100_external_baseline_suite.json b/config/v100_external_baseline_suite.json
new file mode 100644
index 0000000..d7c8451
--- /dev/null
+++ b/config/v100_external_baseline_suite.json
@@ -0,0 +1,47 @@
+{
+  "schema_version": 1,
+  "hardware": "v100-sm70",
+  "protocol": {"warmup": 1000, "repeat": 100, "trials": 5, "seed": 20260724},
+  "workloads": [
+    {
+      "id": "fwht8", "operator": "fwht", "precision": "fp32", "logN": 8,
+      "direction": "forward", "normalization": "none", "placement": "out-of-place",
+      "batches": [4096, 65536],
+      "implementations": [
+        {"id": "warp", "name": "cuButterfly-warp-register", "runner": "butterfly", "reference": true,
+         "args": ["--backend", "temporal-tile", "--local-exchange", "warp-register", "--compute-unit", "radix2", "--tile-threads", "32"]},
+        {"id": "dao", "name": "Dao-AILab-FHT", "runner": "dao-fht", "args": []}
+      ]
+    },
+    {
+      "id": "fwht15", "operator": "fwht", "precision": "fp32", "logN": 15,
+      "direction": "forward", "normalization": "none", "placement": "out-of-place",
+      "batches": [4, 16, 256, 512],
+      "implementations": [
+        {"id": "warp", "name": "cuButterfly-warp-register", "runner": "butterfly", "reference": true,
+         "args": ["--backend", "temporal-tile", "--local-exchange", "warp-register", "--compute-unit", "radix2", "--tile-threads", "256"]},
+        {"id": "dao", "name": "Dao-AILab-FHT", "runner": "dao-fht", "args": []}
+      ]
+    },
+    {
+      "id": "ntt16", "operator": "ntt", "precision": "uint64", "modulus": "576460756061519873",
+      "modulus_bits": 60, "logN": 16, "direction": "forward", "normalization": "none",
+      "placement": "out-of-place", "output_order": "natural", "batches": [4, 64, 256],
+      "implementations": [
+        {"id": "cub", "name": "cuNTT-Hybrid2D-radix4", "runner": "ntt", "reference": true,
+         "args": ["--backend", "hybrid2d", "--compute-unit", "radix4", "--word-bits", "64", "--cross-twiddle", "fused", "--output-order", "natural"]},
+        {"id": "gpuntt", "name": "GPU-NTT-Merge-natural", "runner": "gpuntt", "naturalize": true, "args": []}
+      ]
+    },
+    {
+      "id": "ntt20", "operator": "ntt", "precision": "uint64", "modulus": "576460756061519873",
+      "modulus_bits": 60, "logN": 20, "direction": "forward", "normalization": "none",
+      "placement": "out-of-place", "output_order": "bit-reversed", "batches": [2, 4, 16],
+      "implementations": [
+        {"id": "cub", "name": "cuNTT-compact-stage", "runner": "ntt", "reference": true,
+         "args": ["--backend", "compact-stage", "--compute-unit", "radix2", "--word-bits", "64", "--output-order", "bit-reversed"]},
+        {"id": "gpuntt", "name": "GPU-NTT-Merge-native", "runner": "gpuntt", "naturalize": false, "args": []}
+      ]
+    }
+  ]
+}
diff --git a/config/v100_fft_codegen.json b/config/v100_fft_codegen.json
index c28a1ff..9710c39 100644
--- a/config/v100_fft_codegen.json
+++ b/config/v100_fft_codegen.json
@@ -9,6 +9,12 @@
         [128, 8], [256, 8], [512, 8], [1024, 8],
         [128, 16], [256, 16], [512, 16]
       ]
+    },
+    "cufftdx-online-direct": {
+      "points": [
+        [11, 256, 8], [11, 512, 4], [11, 1024, 2],
+        [12, 256, 16], [12, 512, 8], [12, 1024, 4]
+      ]
     }
   }
 }
diff --git a/config/v100_fft_dispatch.json b/config/v100_fft_dispatch.json
new file mode 100644
index 0000000..718c9b8
--- /dev/null
+++ b/config/v100_fft_dispatch.json
@@ -0,0 +1,102 @@
+{
+  "schema_version": 1,
+  "target": "v100-sm70",
+  "entries": [
+    {
+      "logN": 18,
+      "max_batch": 4,
+      "candidate_id": "fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8",
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "prefix_log_n": 9,
+      "suffix_log_n": 9,
+      "prefix_threads": 256,
+      "suffix_threads": 256,
+      "prefix_ept": 8,
+      "suffix_ept": 8,
+      "median_kernel_ms": 0.025866,
+      "cufft_median_ms": 0.028058,
+      "throughput_vs_cufft": 1.084744
+    },
+    {
+      "logN": 18,
+      "max_batch": 32,
+      "candidate_id": "fft18-fp32_b16_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8",
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "prefix_log_n": 9,
+      "suffix_log_n": 9,
+      "prefix_threads": 256,
+      "suffix_threads": 256,
+      "prefix_ept": 8,
+      "suffix_ept": 8,
+      "median_kernel_ms": 0.195441,
+      "cufft_median_ms": 0.211108,
+      "throughput_vs_cufft": 1.080162
+    },
+    {
+      "logN": 18,
+      "max_batch": null,
+      "candidate_id": "fft18-fp32_b64_p8s10_t128x128_e16x16_rec",
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "prefix_log_n": 8,
+      "suffix_log_n": 10,
+      "prefix_threads": 128,
+      "suffix_threads": 128,
+      "prefix_ept": 16,
+      "suffix_ept": 16,
+      "median_kernel_ms": 0.767201,
+      "cufft_median_ms": 0.706273,
+      "throughput_vs_cufft": 0.920584
+    },
+    {
+      "logN": 20,
+      "max_batch": 4,
+      "candidate_id": "fft20-fp32_b2_p10s10_t512x512_e8x8_rec",
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "prefix_log_n": 10,
+      "suffix_log_n": 10,
+      "prefix_threads": 512,
+      "suffix_threads": 512,
+      "prefix_ept": 8,
+      "suffix_ept": 8,
+      "median_kernel_ms": 0.119869,
+      "cufft_median_ms": 0.123453,
+      "throughput_vs_cufft": 1.029899
+    },
+    {
+      "logN": 20,
+      "max_batch": 8,
+      "candidate_id": "fft20-fp32_b8_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16",
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "prefix_log_n": 10,
+      "suffix_log_n": 10,
+      "prefix_threads": 256,
+      "suffix_threads": 128,
+      "prefix_ept": 16,
+      "suffix_ept": 16,
+      "median_kernel_ms": 0.397332,
+      "cufft_median_ms": 0.3823,
+      "throughput_vs_cufft": 0.962168
+    },
+    {
+      "logN": 20,
+      "max_batch": null,
+      "candidate_id": "fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt256x128_ge16x16",
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "prefix_log_n": 10,
+      "suffix_log_n": 10,
+      "prefix_threads": 256,
+      "suffix_threads": 128,
+      "prefix_ept": 16,
+      "suffix_ept": 16,
+      "median_kernel_ms": 0.764334,
+      "cufft_median_ms": 0.729416,
+      "throughput_vs_cufft": 0.954316
+    }
+  ]
+}
diff --git a/config/v100_fft_pipeline.json b/config/v100_fft_pipeline.json
new file mode 100644
index 0000000..8afd888
--- /dev/null
+++ b/config/v100_fft_pipeline.json
@@ -0,0 +1,78 @@
+{
+  "schema_version": 2,
+  "target": "v100-sm70",
+  "processing_units": [
+    {
+      "id": "cufftdx-online-shared",
+      "family": "cufftdx-online",
+      "core": "cufftdx-block",
+      "exchange": "shared",
+      "status": "compiled",
+      "dimension_log_n": {"min": 3, "max": 10},
+      "threads": [128, 256, 512],
+      "elements_per_thread": [4, 8, 16],
+      "cross_twiddle": ["recurrence", "table"],
+      "estimated_registers_per_thread": {"default": 48, "logN10": 52}
+    },
+    {
+      "id": "cufftdx-large-online",
+      "family": "cufftdx-large-online",
+      "core": "cufftdx-direct",
+      "exchange": "direct-strided",
+      "direct_boundaries": ["direct-strided", "tiled-transpose", "prefix-tiled-transpose"],
+      "status": "compiled",
+      "dimension_log_n": {"min": 11, "max": 12},
+      "threads": [256, 512, 1024],
+      "elements_per_thread": [2, 4, 8, 16],
+      "cross_twiddle": ["recurrence", "table"]
+    }
+  ],
+  "mapping_spaces": [
+    {
+      "id": "fft18-fp32",
+      "operator": "fft", "precision": "fp32", "logN": 18,
+      "direction": "forward", "placement": "in-place", "normalization": "none",
+      "batches": [2, 16, 64],
+      "decomposition_space": {
+        "decomposition_count": {"min": 2, "max": 4},
+        "stages_per_decomposition": {"min": 3, "max": 12},
+        "compiled_decomposition_counts": [2, 3, 4]
+      },
+      "max_runnable_candidates_per_shape": 48,
+      "required_candidates": [
+        {"stage_partition": [9, 9],
+         "segment_mappings": [{"threads": 256, "ept": 8}, {"threads": 256, "ept": 8}],
+         "cross_twiddle": "recurrence"}
+      ]
+    },
+    {
+      "id": "fft20-fp32",
+      "operator": "fft", "precision": "fp32", "logN": 20,
+      "direction": "forward", "placement": "in-place", "normalization": "none",
+      "batches": [2, 8, 16],
+      "decomposition_space": {
+        "decomposition_count": {"min": 2, "max": 4},
+        "stages_per_decomposition": {"min": 3, "max": 12},
+        "compiled_decomposition_counts": [2, 3, 4]
+      },
+      "max_runnable_candidates_per_shape": 48,
+      "required_candidates": [
+        {"stage_partition": [10, 10],
+         "segment_mappings": [{"threads": 512, "ept": 8}, {"threads": 512, "ept": 8}],
+         "cross_twiddle": "recurrence"},
+        {"stage_partition": [10, 10],
+         "segment_mappings": [{"threads": 256, "ept": 16}, {"threads": 128, "ept": 16}],
+         "cross_twiddle": "recurrence"}
+      ]
+    }
+  ],
+  "selection": {
+    "max_runnable_candidates_per_shape": 12,
+    "retain_per_factorization_twiddle": 1,
+    "prefix_work_weight": 1.25,
+    "suffix_work_weight": 1.0,
+    "underfill_penalty": 0.5,
+    "imbalance_penalty": 0.1
+  },
+  "protocol": {"warmup": 100, "repeat": 50, "trials": 3, "seed": 20260724}
+}
diff --git a/config/v100_fft_pipeline_candidates.json b/config/v100_fft_pipeline_candidates.json
new file mode 100644
index 0000000..8f3100f
--- /dev/null
+++ b/config/v100_fft_pipeline_candidates.json
@@ -0,0 +1,50746 @@
+{
+  "schema_version": 2,
+  "target": "v100-sm70",
+  "protocol": {
+    "warmup": 100,
+    "repeat": 50,
+    "trials": 3,
+    "seed": 20260724
+  },
+  "processing_units": [
+    {
+      "id": "cufftdx-online-shared",
+      "family": "cufftdx-online",
+      "core": "cufftdx-block",
+      "exchange": "shared",
+      "status": "compiled",
+      "dimension_log_n": {
+        "min": 3,
+        "max": 10
+      },
+      "threads": [
+        128,
+        256,
+        512
+      ],
+      "elements_per_thread": [
+        4,
+        8,
+        16
+      ],
+      "cross_twiddle": [
+        "recurrence",
+        "table"
+      ],
+      "estimated_registers_per_thread": {
+        "default": 48,
+        "logN10": 52
+      }
+    },
+    {
+      "id": "cufftdx-large-online",
+      "family": "cufftdx-large-online",
+      "core": "cufftdx-direct",
+      "exchange": "direct-strided",
+      "direct_boundaries": [
+        "direct-strided",
+        "tiled-transpose",
+        "prefix-tiled-transpose"
+      ],
+      "status": "compiled",
+      "dimension_log_n": {
+        "min": 11,
+        "max": 12
+      },
+      "threads": [
+        256,
+        512,
+        1024
+      ],
+      "elements_per_thread": [
+        2,
+        4,
+        8,
+        16
+      ],
+      "cross_twiddle": [
+        "recurrence",
+        "table"
+      ]
+    }
+  ],
+  "runnable_candidates": [
+    {
+      "id": "fft18-fp32_b2_p8s10_t512x512_e16x16_rec",
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 18,
+      "direction": "forward",
+      "placement": "in-place",
+      "normalization": "none",
+      "max_runnable_candidates_per_shape": 48,
+      "mapping_id": "fft18-fp32",
+      "batch": 2,
+      "decomposition_count": 2,
+      "stages_per_decomposition": [
+        8,
+        10
+      ],
+      "processing_unit": "cufftdx-online-shared+cufftdx-online-shared",
+      "prefix_processing_unit": "cufftdx-online-shared",
+      "suffix_processing_unit": "cufftdx-online-shared",
+      "prefix_log_n": 8,
+      "suffix_log_n": 10,
+      "prefix_threads": 512,
+      "suffix_threads": 512,
+      "prefix_ept": 16,
+      "suffix_ept": 16,
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "segment_mappings": [
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16
+        },
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16
+        }
+      ],
+      "boundaries": [
+        {
+          "cross_twiddle": "recurrence",
+          "layout": "direct-strided",
+          "residency": "global-scratch"
+        }
+      ],
+      "prefix_units_per_cta": 32,
+      "prefix_tile_shared_bytes": 65536,
+      "suffix_units_per_cta": 8,
+      "suffix_tile_shared_bytes": 65536,
+      "status": "compiled",
+      "reason": "",
+      "prefix_resources": {
+        "units_per_cta": 32,
+        "blocks": 64,
+        "threads": 512,
+        "ept": 16,
+        "tile_shared_bytes": 65536,
+        "estimated_registers_per_thread": 48,
+        "estimated_resident_ctas_per_sm": 1,
+        "estimated_waves_per_sm": 0.8,
+        "issued_thread_slots": 32768
+      },
+      "suffix_resources": {
+        "units_per_cta": 8,
+        "blocks": 64,
+        "threads": 512,
+        "ept": 16,
+        "tile_shared_bytes": 65536,
+        "estimated_registers_per_thread": 52,
+        "estimated_resident_ctas_per_sm": 1,
+        "estimated_waves_per_sm": 0.8,
+        "issued_thread_slots": 32768
+      },
+      "estimated_work_imbalance": 1.25,
+      "static_score": 81804.82522882584,
+      "args": [
+        "--operator",
+        "fft",
+        "--precision",
+        "fp32",
+        "--backend",
+        "online-reorder",
+        "--fft-core",
+        "cufftdx-block",
+        "--stage-partition",
+        "8,10",
+        "--reorder-columns",
+        "1",
+        "--cross-twiddle",
+        "recurrence",
+        "--direct-boundary",
+        "direct-strided",
+        "--prefix-threads",
+        "512",
+        "--suffix-threads",
+        "512",
+        "--prefix-ept",
+        "16",
+        "--suffix-ept",
+        "16",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "selection_pool_size": 3987,
+      "selection_limit": 48
+    },
+    {
+      "id": "fft18-fp32_b2_p9s9_t512x512_e16x16_rec",
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 18,
+      "direction": "forward",
+      "placement": "in-place",
+      "normalization": "none",
+      "max_runnable_candidates_per_shape": 48,
+      "mapping_id": "fft18-fp32",
+      "batch": 2,
+      "decomposition_count": 2,
+      "stages_per_decomposition": [
+        9,
+        9
+      ],
+      "processing_unit": "cufftdx-online-shared+cufftdx-online-shared",
+      "prefix_processing_unit": "cufftdx-online-shared",
+      "suffix_processing_unit": "cufftdx-online-shared",
+      "prefix_log_n": 9,
+      "suffix_log_n": 9,
+      "prefix_threads": 512,
+      "suffix_threads": 512,
+      "prefix_ept": 16,
+      "suffix_ept": 16,
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "segment_mappings": [
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16
+        },
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16
+        }
+      ],
+      "boundaries": [
+        {
+          "cross_twiddle": "recurrence",
+          "layout": "direct-strided",
+          "residency": "global-scratch"
+        }
+      ],
+      "prefix_units_per_cta": 16,
+      "prefix_tile_shared_bytes": 65536,
+      "suffix_units_per_cta": 16,
+      "suffix_tile_shared_bytes": 65536,
+      "status": "compiled",
+      "reason": "",
+      "prefix_resources": {
+        "units_per_cta": 16,
+        "blocks": 64,
+        "threads": 512,
+        "ept": 16,
+        "tile_shared_bytes": 65536,
+        "estimated_registers_per_thread": 48,
+        "estimated_resident_ctas_per_sm": 1,
+        "estimated_waves_per_sm": 0.8,
+        "issued_thread_slots": 32768
+      },
+      "suffix_resources": {
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+        "blocks": 64,
+        "threads": 512,
+        "ept": 16,
+        "tile_shared_bytes": 65536,
+        "estimated_registers_per_thread": 48,
+        "estimated_resident_ctas_per_sm": 1,
+        "estimated_waves_per_sm": 0.8,
+        "issued_thread_slots": 32768
+      },
+      "estimated_work_imbalance": 1.25,
+      "static_score": 81804.82522882584,
+      "args": [
+        "--operator",
+        "fft",
+        "--precision",
+        "fp32",
+        "--backend",
+        "online-reorder",
+        "--fft-core",
+        "cufftdx-block",
+        "--stage-partition",
+        "9,9",
+        "--reorder-columns",
+        "1",
+        "--cross-twiddle",
+        "recurrence",
+        "--direct-boundary",
+        "direct-strided",
+        "--prefix-threads",
+        "512",
+        "--suffix-threads",
+        "512",
+        "--prefix-ept",
+        "16",
+        "--suffix-ept",
+        "16",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "selection_pool_size": 3987,
+      "selection_limit": 48
+    },
+    {
+      "id": "fft18-fp32_b2_p10s8_t512x512_e16x16_rec",
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 18,
+      "direction": "forward",
+      "placement": "in-place",
+      "normalization": "none",
+      "max_runnable_candidates_per_shape": 48,
+      "mapping_id": "fft18-fp32",
+      "batch": 2,
+      "decomposition_count": 2,
+      "stages_per_decomposition": [
+        10,
+        8
+      ],
+      "processing_unit": "cufftdx-online-shared+cufftdx-online-shared",
+      "prefix_processing_unit": "cufftdx-online-shared",
+      "suffix_processing_unit": "cufftdx-online-shared",
+      "prefix_log_n": 10,
+      "suffix_log_n": 8,
+      "prefix_threads": 512,
+      "suffix_threads": 512,
+      "prefix_ept": 16,
+      "suffix_ept": 16,
+      "cross_twiddle": "recurrence",
+      "direct_boundary": "direct-strided",
+      "segment_mappings": [
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16
+        },
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16
+        }
+      ],
+      "boundaries": [
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+          "layout": "direct-strided",
+          "residency": "global-scratch"
+        }
+      ],
+      "prefix_units_per_cta": 8,
+      "prefix_tile_shared_bytes": 65536,
+      "suffix_units_per_cta": 32,
+      "suffix_tile_shared_bytes": 65536,
+      "status": "compiled",
+      "reason": "",
+      "prefix_resources": {
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+        "blocks": 64,
+        "threads": 512,
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+        "estimated_registers_per_thread": 52,
+        "estimated_resident_ctas_per_sm": 1,
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+      },
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+        "blocks": 64,
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+      },
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+      "args": [
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+        "fft",
+        "--precision",
+        "fp32",
+        "--backend",
+        "online-reorder",
+        "--fft-core",
+        "cufftdx-block",
+        "--stage-partition",
+        "10,8",
+        "--reorder-columns",
+        "1",
+        "--cross-twiddle",
+        "recurrence",
+        "--direct-boundary",
+        "direct-strided",
+        "--prefix-threads",
+        "512",
+        "--suffix-threads",
+        "512",
+        "--prefix-ept",
+        "16",
+        "--suffix-ept",
+        "16",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "selection_pool_size": 3987,
+      "selection_limit": 48
+    },
+    {
+      "id": "fft18-fp32_b2_d3_3x5x10_t512x512x512_e8x16x16_tt_fg_gt512x512_ge16x16",
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 18,
+      "direction": "forward",
+      "placement": "in-place",
+      "normalization": "none",
+      "max_runnable_candidates_per_shape": 48,
+      "mapping_id": "fft18-fp32",
+      "batch": 2,
+      "decomposition_count": 3,
+      "stages_per_decomposition": [
+        3,
+        5,
+        10
+      ],
+      "segment_mappings": [
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 8,
+          "resources": {
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+            "blocks": 128,
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+            "estimated_waves_per_sm": 0.8,
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+          }
+        },
+        {
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+            "estimated_resident_ctas_per_sm": 1,
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+          }
+        },
+        {
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+          "core": "cufftdx-block",
+          "exchange": "shared",
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+          }
+        }
+      ],
+      "boundaries": [
+        {
+          "cross_twiddle": "table",
+          "layout": "direct-strided",
+          "residency": "fused"
+        },
+        {
+          "cross_twiddle": "table",
+          "layout": "direct-strided",
+          "residency": "global-scratch"
+        }
+      ],
+      "processing_unit": "cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared",
+      "prefix_log_n": 3,
+      "suffix_log_n": 10,
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+      "suffix_threads": 512,
+      "prefix_ept": 8,
+      "suffix_ept": 16,
+      "cross_twiddle": "table",
+      "direct_boundary": "direct-strided",
+      "status": "compiled",
+      "reason": "",
+      "estimated_work_imbalance": 1.25,
+      "static_score": 83474.31145798555,
+      "args": [
+        "--operator",
+        "fft",
+        "--precision",
+        "fp32",
+        "--backend",
+        "online-reorder",
+        "--fft-core",
+        "cufftdx-block",
+        "--stage-partition",
+        "3,5,10",
+        "--segment-threads",
+        "512,512,512",
+        "--segment-ept",
+        "8,16,16",
+        "--boundary-twiddle",
+        "table,table",
+        "--boundary-layout",
+        "direct-strided,direct-strided",
+        "--boundary-residency",
+        "fused,global-scratch",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none",
+        "--group-threads",
+        "512,512",
+        "--group-ept",
+        "16,16"
+      ],
+      "execution_group_count": 2,
+      "execution_group_stages": [
+        8,
+        10
+      ],
+      "execution_group_mappings": [
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
+          "threads": 512,
+          "ept": 16,
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+            "estimated_resident_ctas_per_sm": 1,
+            "estimated_waves_per_sm": 0.8,
+            "issued_thread_slots": 32768
+          }
+        },
+        {
+          "processing_unit": "cufftdx-online-shared",
+          "core": "cufftdx-block",
+          "exchange": "shared",
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+          "ept": 16,
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+          }
+        }
+      ],
+      "physical_processing_unit": "cufftdx-online-shared+cufftdx-online-shared",
+      "selection_pool_size": 3987,
+      "selection_limit": 48
+    },
+    {
+      "id": "fft18-fp32_b2_d3_6x3x9_t512x512x512_e16x8x16_tt_gf_gt512x256_ge16x16",
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 18,
+      "direction": "forward",
+      "placement": "in-place",
+      "normalization": "none",
+      "max_runnable_candidates_per_shape": 48,
+      "mapping_id": "fft18-fp32",
+      "batch": 2,
+      "decomposition_count": 3,
+      "stages_per_decomposition": [
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+        3,
+        9
+      ],
+      "segment_mappings": [
+        {
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+          "core": "cufftdx-block",
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+    {
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+    }
+  ]
+}
diff --git a/config/v100_scaling_space.json b/config/v100_scaling_space.json
new file mode 100644
index 0000000..fd0cb51
--- /dev/null
+++ b/config/v100_scaling_space.json
@@ -0,0 +1,116 @@
+{
+  "schema_version": 1,
+  "hardware": "v100-sm70",
+  "max_points": 16777216,
+  "protocols": {
+    "quick": {"target_points": 4194304, "warmup": 1000, "repeat": 100, "trials": 3, "verify_batch": 1},
+    "full": {"target_points": 4194304, "warmup": 1000, "repeat": 100, "trials": 5, "verify_batch": 1}
+  },
+  "binaries": {
+    "butterfly": "build/cubutterfly_bench",
+    "ntt": "build/cuntt_bench",
+    "fft-library": "build/vkfft_bench"
+  },
+  "workloads": [
+    {
+      "id": "fft8", "operator": "fft", "precision": "fp32", "logN": 8,
+      "batches": {"quick": [1, 64, 16384], "full": [4, 16, 256, 1024, 4096, 65536]},
+      "implementations": [
+        {"id": "cub", "name": "cuButterfly-cuFFTDx", "runner": "butterfly", "args": ["--backend", "temporal-tile", "--fft-core", "cufftdx-block", "--tile-threads", "32", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
+        {"id": "cufft", "name": "cuFFT", "runner": "fft-library", "reference": true, "args": ["--library", "cufft"]},
+        {"id": "vkfft", "name": "VkFFT", "runner": "fft-library", "args": ["--library", "vkfft"]}
+      ]
+    },
+    {
+      "id": "fft14", "operator": "fft", "precision": "fp32", "logN": 14,
+      "batches": {"quick": [1, 16, 256], "full": [4, 64, 1024]},
+      "implementations": [
+        {"id": "cub", "name": "cuButterfly-cuFFTDx-direct", "runner": "butterfly", "args": ["--backend", "temporal-tile", "--fft-core", "cufftdx-direct", "--tile-threads", "1024", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
+        {"id": "cufft", "name": "cuFFT", "runner": "fft-library", "reference": true, "args": ["--library", "cufft"]},
+        {"id": "vkfft", "name": "VkFFT", "runner": "fft-library", "args": ["--library", "vkfft"]}
+      ]
+    },
+    {
+      "id": "fft18", "operator": "fft", "precision": "fp32", "logN": 18,
+      "batches": {"quick": [1, 4, 16], "full": [2, 8, 32, 64]},
+      "implementations": [
+        {"id": "cub", "name": "cuButterfly-cuFFTDx-online", "runner": "butterfly", "args": ["--backend", "online-reorder", "--fft-core", "cufftdx-block", "--local-stages", "9", "--reorder-columns", "1", "--cross-twiddle", "recurrence", "--prefix-threads", "256", "--suffix-threads", "256", "--prefix-ept", "8", "--suffix-ept", "8", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
+        {"id": "cufft", "name": "cuFFT", "runner": "fft-library", "reference": true, "args": ["--library", "cufft"]},
+        {"id": "vkfft", "name": "VkFFT", "runner": "fft-library", "args": ["--library", "vkfft"]}
+      ]
+    },
+    {
+      "id": "fft20", "operator": "fft", "precision": "fp32", "logN": 20,
+      "batches": {"quick": [1, 4], "full": [2, 8, 16]},
+      "implementations": [
+        {"id": "cub", "name": "cuButterfly-cuFFTDx-online", "runner": "butterfly", "args": ["--backend", "online-reorder", "--fft-core", "cufftdx-block", "--local-stages", "10", "--reorder-columns", "1", "--cross-twiddle", "recurrence", "--prefix-threads", "512", "--suffix-threads", "512", "--prefix-ept", "8", "--suffix-ept", "8", "--precision", "fp32", "--operator", "fft", "--placement", "in-place", "--normalization", "none"]},
+        {"id": "cufft", "name": "cuFFT", "runner": "fft-library", "reference": true, "args": ["--library", "cufft"]},
+        {"id": "vkfft", "name": "VkFFT", "runner": "fft-library", "args": ["--library", "vkfft"]}
+      ]
+    },
+    {
+      "id": "fwht8", "operator": "fwht", "precision": "fp32", "logN": 8,
+      "batches": {"quick": [1, 64, 16384], "full": [4, 16, 256, 1024, 4096, 65536]},
+      "implementations": [
+        {"id": "warp", "name": "cuButterfly-warp-register", "runner": "butterfly", "args": ["--operator", "fwht", "--precision", "fp32", "--backend", "temporal-tile", "--local-exchange", "warp-register", "--compute-unit", "radix2", "--tile-threads", "32", "--normalization", "none"]},
+        {"id": "shared", "name": "cuButterfly-shared-radix4", "runner": "butterfly", "args": ["--operator", "fwht", "--precision", "fp32", "--backend", "temporal-tile", "--local-exchange", "shared", "--compute-unit", "radix4", "--tile-threads", "128", "--normalization", "none"]}
+      ]
+    },
+    {
+      "id": "fwht15", "operator": "fwht", "precision": "fp32", "logN": 15,
+      "batches": {"quick": [1, 16, 128], "full": [4, 32, 256, 512]},
+      "implementations": [
+        {"id": "warp", "name": "cuButterfly-warp-register", "runner": "butterfly", "args": ["--operator", "fwht", "--precision", "fp32", "--backend", "temporal-tile", "--local-exchange", "warp-register", "--compute-unit", "radix2", "--tile-threads", "256", "--normalization", "none"]},
+        {"id": "online", "name": "cuButterfly-online-radix4", "runner": "butterfly", "args": ["--operator", "fwht", "--precision", "fp32", "--backend", "online-reorder", "--compute-unit", "radix4", "--tile-threads", "256", "--local-stages", "8", "--reorder-columns", "1", "--normalization", "none"]}
+      ]
+    },
+    {
+      "id": "fwht20", "operator": "fwht", "precision": "fp32", "logN": 20,
+      "batches": {"quick": [1, 4], "full": [2, 8, 16]},
+      "implementations": [
+        {"id": "online", "name": "cuButterfly-online-radix4", "runner": "butterfly", "args": ["--operator", "fwht", "--precision", "fp32", "--backend", "online-reorder", "--compute-unit", "radix4", "--tile-threads", "256", "--local-stages", "10", "--reorder-columns", "1", "--normalization", "none"]},
+        {"id": "hier", "name": "cuButterfly-hierarchical-radix4", "runner": "butterfly", "args": ["--operator", "fwht", "--precision", "fp32", "--backend", "hierarchical", "--compute-unit", "radix4", "--tile-threads", "256", "--local-stages", "10", "--normalization", "none"]}
+      ]
+    },
+    {
+      "id": "ntt12", "operator": "ntt", "precision": "uint32", "modulus_bits": 30, "logN": 12,
+      "batches": {"quick": [1, 16, 1024], "full": [4, 64, 256, 4096]},
+      "implementations": [
+        {"id": "r4", "name": "cuNTT-Hybrid2D-radix4", "runner": "ntt", "args": ["--backend", "hybrid2d", "--compute-unit", "radix4", "--word-bits", "32", "--cross-twiddle", "fused", "--output-order", "natural"]},
+        {"id": "r2", "name": "cuNTT-Hybrid2D-radix2", "runner": "ntt", "reference": true, "args": ["--backend", "hybrid2d", "--compute-unit", "radix2", "--word-bits", "32", "--cross-twiddle", "fused", "--output-order", "natural"]}
+      ]
+    },
+    {
+      "id": "ntt16", "operator": "ntt", "precision": "uint64", "modulus_bits": 60, "logN": 16,
+      "batches": {"quick": [1, 16, 64], "full": [4, 32, 128, 256]},
+      "implementations": [
+        {"id": "r4", "name": "cuNTT-Hybrid2D-radix4", "runner": "ntt", "args": ["--backend", "hybrid2d", "--compute-unit", "radix4", "--word-bits", "64", "--cross-twiddle", "fused", "--output-order", "natural"]},
+        {"id": "r2", "name": "cuNTT-Hybrid2D-radix2", "runner": "ntt", "args": ["--backend", "hybrid2d", "--compute-unit", "radix2", "--word-bits", "64", "--cross-twiddle", "fused", "--output-order", "natural"]}
+      ]
+    },
+    {
+      "id": "ntt20", "operator": "ntt", "precision": "uint64", "modulus_bits": 60, "logN": 20,
+      "batches": {"quick": [1, 4], "full": [2, 8, 16]},
+      "implementations": [
+        {"id": "compact", "name": "cuNTT-compact-stage", "runner": "ntt", "args": ["--backend", "compact-stage", "--compute-unit", "radix2", "--word-bits", "64", "--output-order", "bit-reversed"]}
+      ]
+    },
+    {
+      "id": "xor8", "operator": "xor-zeta", "precision": "uint32", "logN": 8,
+      "batches": {"quick": [1, 64, 16384], "full": [4, 16, 256, 1024, 4096, 65536]},
+      "implementations": [
+        {"id": "r4", "name": "cuButterfly-radix4", "runner": "butterfly", "args": ["--operator", "xor-zeta", "--precision", "uint32", "--backend", "temporal-tile", "--compute-unit", "radix4", "--tile-threads", "128"]},
+        {"id": "r2", "name": "cuButterfly-radix2", "runner": "butterfly", "args": ["--operator", "xor-zeta", "--precision", "uint32", "--backend", "temporal-tile", "--compute-unit", "radix2", "--tile-threads", "128"]}
+      ]
+    },
+    {
+      "id": "xor20", "operator": "xor-zeta", "precision": "uint32", "logN": 20,
+      "batches": {"quick": [1, 4], "full": [2, 8, 16]},
+      "implementations": [
+        {"id": "online", "name": "cuButterfly-online-radix4", "runner": "butterfly", "args": ["--operator", "xor-zeta", "--precision", "uint32", "--backend", "online-reorder", "--compute-unit", "radix4", "--tile-threads", "256", "--local-stages", "10", "--reorder-columns", "1"]},
+        {"id": "hier", "name": "cuButterfly-hierarchical-radix4", "runner": "butterfly", "args": ["--operator", "xor-zeta", "--precision", "uint32", "--backend", "hierarchical", "--compute-unit", "radix4", "--tile-threads", "256", "--local-stages", "10"]}
+      ]
+    }
+  ],
+  "external_evidence": []
+}
diff --git a/config/v100_scaling_suite.json b/config/v100_scaling_suite.json
new file mode 100644
index 0000000..c7a0f57
--- /dev/null
+++ b/config/v100_scaling_suite.json
@@ -0,0 +1,4509 @@
+{
+  "schema_version": 1,
+  "hardware": "v100-sm70",
+  "protocols": {
+    "quick": {
+      "target_points": 4194304,
+      "warmup": 1000,
+      "repeat": 100,
+      "trials": 3,
+      "verify_batch": 1
+    },
+    "full": {
+      "target_points": 4194304,
+      "warmup": 1000,
+      "repeat": 100,
+      "trials": 5,
+      "verify_batch": 1
+    }
+  },
+  "binaries": {
+    "butterfly": "build/cubutterfly_bench",
+    "ntt": "build/cuntt_bench",
+    "fft-library": "build/vkfft_bench"
+  },
+  "cases": [
+    {
+      "id": "fft8_cub_b1",
+      "tier": "quick",
+      "group": "fft8-batch1",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 1,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b1",
+      "tier": "quick",
+      "group": "fft8-batch1",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 1,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b1",
+      "tier": "quick",
+      "group": "fft8-batch1",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 1,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b64",
+      "tier": "quick",
+      "group": "fft8-batch64",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 64,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b64",
+      "tier": "quick",
+      "group": "fft8-batch64",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 64,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b64",
+      "tier": "quick",
+      "group": "fft8-batch64",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 64,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b16384",
+      "tier": "quick",
+      "group": "fft8-batch16384",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 16384,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b16384",
+      "tier": "quick",
+      "group": "fft8-batch16384",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 16384,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b16384",
+      "tier": "quick",
+      "group": "fft8-batch16384",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 16384,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b4",
+      "tier": "full",
+      "group": "fft8-batch4",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 4,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b4",
+      "tier": "full",
+      "group": "fft8-batch4",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 4,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b4",
+      "tier": "full",
+      "group": "fft8-batch4",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 4,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b16",
+      "tier": "full",
+      "group": "fft8-batch16",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 16,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b16",
+      "tier": "full",
+      "group": "fft8-batch16",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 16,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b16",
+      "tier": "full",
+      "group": "fft8-batch16",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 16,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b256",
+      "tier": "full",
+      "group": "fft8-batch256",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 256,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b256",
+      "tier": "full",
+      "group": "fft8-batch256",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 256,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b256",
+      "tier": "full",
+      "group": "fft8-batch256",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 256,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b1024",
+      "tier": "full",
+      "group": "fft8-batch1024",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 1024,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b1024",
+      "tier": "full",
+      "group": "fft8-batch1024",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 1024,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b1024",
+      "tier": "full",
+      "group": "fft8-batch1024",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 1024,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b4096",
+      "tier": "full",
+      "group": "fft8-batch4096",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 4096,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b4096",
+      "tier": "full",
+      "group": "fft8-batch4096",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 4096,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b4096",
+      "tier": "full",
+      "group": "fft8-batch4096",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 4096,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cub_b65536",
+      "tier": "full",
+      "group": "fft8-batch65536",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx",
+      "reference": false,
+      "batch": 65536,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-block",
+        "--tile-threads",
+        "32",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_cufft_b65536",
+      "tier": "full",
+      "group": "fft8-batch65536",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 65536,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft8_vkfft_b65536",
+      "tier": "full",
+      "group": "fft8-batch65536",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 65536,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 8
+    },
+    {
+      "id": "fft14_cub_b1",
+      "tier": "quick",
+      "group": "fft14-batch1",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx-direct",
+      "reference": false,
+      "batch": 1,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-direct",
+        "--tile-threads",
+        "1024",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 14
+    },
+    {
+      "id": "fft14_cufft_b1",
+      "tier": "quick",
+      "group": "fft14-batch1",
+      "runner": "fft-library",
+      "implementation": "cuFFT",
+      "reference": true,
+      "batch": 1,
+      "args": [
+        "--library",
+        "cufft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 14
+    },
+    {
+      "id": "fft14_vkfft_b1",
+      "tier": "quick",
+      "group": "fft14-batch1",
+      "runner": "fft-library",
+      "implementation": "VkFFT",
+      "reference": false,
+      "batch": 1,
+      "args": [
+        "--library",
+        "vkfft"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 14
+    },
+    {
+      "id": "fft14_cub_b16",
+      "tier": "quick",
+      "group": "fft14-batch16",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-cuFFTDx-direct",
+      "reference": false,
+      "batch": 16,
+      "args": [
+        "--backend",
+        "temporal-tile",
+        "--fft-core",
+        "cufftdx-direct",
+        "--tile-threads",
+        "1024",
+        "--precision",
+        "fp32",
+        "--operator",
+        "fft",
+        "--placement",
+        "in-place",
+        "--normalization",
+        "none"
+      ],
+      "operator": "fft",
+      "precision": "fp32",
+      "logN": 14
+    },
+    {
+      "id": "fft14_cufft_b16",
+      "tier": "quick",
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+    },
+    {
+      "id": "xor8_r2_b1024",
+      "tier": "full",
+      "group": "xor8-batch1024",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-radix2",
+      "reference": false,
+      "batch": 1024,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "temporal-tile",
+        "--compute-unit",
+        "radix2",
+        "--tile-threads",
+        "128"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 8
+    },
+    {
+      "id": "xor8_r4_b4096",
+      "tier": "full",
+      "group": "xor8-batch4096",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-radix4",
+      "reference": false,
+      "batch": 4096,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "temporal-tile",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "128"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 8
+    },
+    {
+      "id": "xor8_r2_b4096",
+      "tier": "full",
+      "group": "xor8-batch4096",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-radix2",
+      "reference": false,
+      "batch": 4096,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "temporal-tile",
+        "--compute-unit",
+        "radix2",
+        "--tile-threads",
+        "128"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 8
+    },
+    {
+      "id": "xor8_r4_b65536",
+      "tier": "full",
+      "group": "xor8-batch65536",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-radix4",
+      "reference": false,
+      "batch": 65536,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "temporal-tile",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "128"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 8
+    },
+    {
+      "id": "xor8_r2_b65536",
+      "tier": "full",
+      "group": "xor8-batch65536",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-radix2",
+      "reference": false,
+      "batch": 65536,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "temporal-tile",
+        "--compute-unit",
+        "radix2",
+        "--tile-threads",
+        "128"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 8
+    },
+    {
+      "id": "xor20_online_b1",
+      "tier": "quick",
+      "group": "xor20-batch1",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-online-radix4",
+      "reference": false,
+      "batch": 1,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "online-reorder",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10",
+        "--reorder-columns",
+        "1"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_hier_b1",
+      "tier": "quick",
+      "group": "xor20-batch1",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-hierarchical-radix4",
+      "reference": false,
+      "batch": 1,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "hierarchical",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_online_b4",
+      "tier": "quick",
+      "group": "xor20-batch4",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-online-radix4",
+      "reference": false,
+      "batch": 4,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "online-reorder",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10",
+        "--reorder-columns",
+        "1"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_hier_b4",
+      "tier": "quick",
+      "group": "xor20-batch4",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-hierarchical-radix4",
+      "reference": false,
+      "batch": 4,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "hierarchical",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_online_b2",
+      "tier": "full",
+      "group": "xor20-batch2",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-online-radix4",
+      "reference": false,
+      "batch": 2,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "online-reorder",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10",
+        "--reorder-columns",
+        "1"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_hier_b2",
+      "tier": "full",
+      "group": "xor20-batch2",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-hierarchical-radix4",
+      "reference": false,
+      "batch": 2,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "hierarchical",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_online_b8",
+      "tier": "full",
+      "group": "xor20-batch8",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-online-radix4",
+      "reference": false,
+      "batch": 8,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "online-reorder",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10",
+        "--reorder-columns",
+        "1"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_hier_b8",
+      "tier": "full",
+      "group": "xor20-batch8",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-hierarchical-radix4",
+      "reference": false,
+      "batch": 8,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "hierarchical",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_online_b16",
+      "tier": "full",
+      "group": "xor20-batch16",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-online-radix4",
+      "reference": false,
+      "batch": 16,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "online-reorder",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10",
+        "--reorder-columns",
+        "1"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    },
+    {
+      "id": "xor20_hier_b16",
+      "tier": "full",
+      "group": "xor20-batch16",
+      "runner": "butterfly",
+      "implementation": "cuButterfly-hierarchical-radix4",
+      "reference": false,
+      "batch": 16,
+      "args": [
+        "--operator",
+        "xor-zeta",
+        "--precision",
+        "uint32",
+        "--backend",
+        "hierarchical",
+        "--compute-unit",
+        "radix4",
+        "--tile-threads",
+        "256",
+        "--local-stages",
+        "10"
+      ],
+      "operator": "xor-zeta",
+      "precision": "uint32",
+      "logN": 20
+    }
+  ],
+  "external_evidence": []
+}
diff --git a/docs/README.md b/docs/README.md
index 7bad431..9ad3452 100644
--- a/docs/README.md
+++ b/docs/README.md
@@ -1,21 +1,55 @@
 # Documentation Index
 
-The documentation is organized by abstraction level. Start with the first row
-for the research idea, then move toward implementation and evidence.
+The repository separates its architecture claim from kernel implementation and
+measurement evidence. The shortest useful reading order is [Design
+Overview](design_overview.md), [Experimental Results](experiments.md), then
+[Getting Started](getting_started.md). The first explains the method, the
+second states what the current V100 data supports, and the third turns one
+mapping into a reproducible command.
+
+## Reading Paths
+
+**Architecture and paper review.** Begin with the [Design
+Overview](design_overview.md) for the `D x S` iteration domain and its four
+space-time factors. Continue with [Hardware Mapping
+Methodology](hardware_mapping_methodology.md) for resource demand and selection,
+then [Complete Butterfly Design Space](butterfly_design_space.md) for the formal
+object boundaries. [Research Positioning](cubutterfly_positioning.md) and
+[V100 Research Status](research_status.md) delimit the contribution and claims.
+
+**Kernel and generator development.** Read [FFT Design
+Space](fft_design_space.md), [FFT Pipeline
+Generator](fft_pipeline_generator.md), and [Processing-Unit Design
+Space](processing_unit_design_space.md). Together they show how a logical stage
+decomposition is lowered into physical execution groups, how online layout
+boundaries are generated, and where operator-specific codelets plug in.
+
+**Experimental reproduction.** Start with
+[Reproducibility](reproducibility.md), regenerate the derived tables, and use
+[Single-GPU Comprehensive Benchmark](comprehensive_benchmark.md) only when new
+timings are needed. The focused NCU reports explain mechanisms; the
+comprehensive and scaling reports define the paper-facing comparison protocol.
 
 ## Primary Documents
 
 | Document | Question answered |
 |:--|:--|
-| [Design Overview](design_overview.md) | What is the reusable space-time parallel paradigm? |
+| [Design Overview](design_overview.md) | Why are data and stage work each unfolded in space and time, and how does that map to a GPU? |
 | [Hardware Mapping Methodology](hardware_mapping_methodology.md) | How do the unfolding factors translate into GPU resource demand? |
 | [Complete Butterfly Design Space](butterfly_design_space.md) | How are graph, architecture, processing unit, layout, realization, selection, and hardware separated? |
-| [FFT Design Space](fft_design_space.md) | Which semantic, two-dimensional, processing-unit, and hardware axes are enumerable? |
+| [FFT Design Space](fft_design_space.md) | Which semantic, factorization, two-axis mapping, processing-unit, and hardware parameters are enumerable? |
+| [FFT Pipeline Generator](fft_pipeline_generator.md) | How are stage partitions, local units, boundaries, measured search, and runtime dispatch separated? |
 | [Candidate Implementations](implementation_candidates.md) | Which processing units and kernel forms are implemented or planned? |
 | [Getting Started](getting_started.md) | How is the project built and used? |
-| [Experimental Results](experiments.md) | What has been measured, and where are the gaps? |
+| [Experimental Results](experiments.md) | Which experiment tests each architecture claim, what has been measured, and where are the gaps? |
 | [Single-GPU Comprehensive Benchmark](comprehensive_benchmark.md) | How are lengths, precision, semantics, implementations, and external baselines compared together? |
 | [V100 Comprehensive Results](comprehensive_v100_results.md) | What does the controlled full-suite comparison currently establish? |
+| [V100 Length/Batch Scaling](v100_scaling_results.md) | How do saturation and the best mapping change when length and batch are swept independently? |
+| [V100 Mapping Selector](v100_mapping_selector.md) | How accurately can the measured V100 mappings be selected with a held-out shape? |
+| [V100 Counter Attribution](v100_ncu_attribution.md) | Which hardware services explain the observed saturation and mapping crossovers? |
+| [V100 External Baselines](v100_external_baselines.md) | What do matching-protocol Dao FHT and GPU-NTT comparisons establish? |
+| [V100 Research Status](research_status.md) | Which claims are closed, what are the current performance boundaries, and what remains? |
+| [v0.3.0 Mapping-Selection Milestone](next_phase_v0.3.md) | Which falsifiable goal, execution order, and definition of done shaped this release? |
 | [Reproducibility](reproducibility.md) | How are sweeps, external baselines, and profiler data reproduced? |
 | [Research Positioning](cubutterfly_positioning.md) | What is the intended contribution relative to prior work? |
 
@@ -38,6 +72,10 @@ Repository maintenance and research priorities are documented in
 ## Measurement Reports
 
 - [V100 Comprehensive Results](comprehensive_v100_results.md)
+- [V100 Length/Batch Scaling](v100_scaling_results.md)
+- [V100 Mapping Selector](v100_mapping_selector.md)
+- [V100 Counter Attribution](v100_ncu_attribution.md)
+- [V100 Matching-Protocol External Baselines](v100_external_baselines.md)
 - [V100 Initial NTT Results](v100_initial_results.md)
 - [V100 NTT Parameter Matrix](v100_matrix_results.md)
 - [GPU-NTT Gap Analysis](gpu_ntt_gap_analysis.md)
diff --git a/docs/comprehensive_v100_results.md b/docs/comprehensive_v100_results.md
index fc95c11..944af2a 100644
--- a/docs/comprehensive_v100_results.md
+++ b/docs/comprehensive_v100_results.md
@@ -12,6 +12,28 @@ The raw samples, machine-readable summary, and generated complete table are:
 - [`comprehensive_v100_full_summary.csv`](../results/comprehensive_v100_full_summary.csv)
 - [`comprehensive_v100_full_report.md`](../results/comprehensive_v100_full_report.md)
 
+The long-FFT processing-unit optimization was subsequently rerun under the
+same full protocol. Its focused records are
+`results/comprehensive_v100_vectorized_fft_raw.csv`,
+`results/comprehensive_v100_vectorized_fft_summary.csv`, and
+`results/comprehensive_v100_vectorized_fft_report.md`. Those rows supersede the
+`logN=18/20` cuButterfly rows below:
+
+| Workload | cuButterfly | cuFFT | VkFFT | cuButterfly/cuFFT |
+|:--|--:|--:|--:|--:|
+| FP32 `logN=18`, batch 16 | 0.195942 ms | 0.211098 ms | 0.201103 ms | 1.077x |
+| FP32 `logN=20`, batch 4 | 0.214733 ms | 0.210330 ms | 0.206520 ms | 0.979x |
+
+The FP64 row was also followed by a focused physical-unit study. The original
+table below intentionally remains the scalar comprehensive baseline; it is not
+the current FP64 ceiling. A generated double-precision cuFFTDx unit, recurrence
+twiddles, XOR-swizzled prefix staging, and strength-reduced addressing reach
+0.339364 ms versus cuFFT's 0.343040 ms at the same `logN=16`, batch-64 shape
+under the focused interleaved five-trial protocol. The expanded `logN=14..18`
+matrix has a higher cuButterfly median on 20 of 25 stable shapes. See [FP64
+robustness](../results/fp64_robustness_batch_analysis.md); focused and
+comprehensive rows must not be mixed as one protocol.
+
 ## FFT Against Runnable Libraries
 
 Each group below has identical precision, transform length, batch, direction,
@@ -28,13 +50,15 @@ than cuFFT.
 | FP32 forward in-place, `logN=20` | 1,048,576 | 4 | 0.235438 ms | 0.210063 ms | 0.206275 ms | 0.892x |
 | FP32 forward stride-2 in-place, `logN=8` | 256 | 16,384 | 0.172636 ms | 0.171428 ms | - | 0.993x |
 
-The FP32 forward result is therefore at library parity for `logN=8` and
-`logN=14`, ahead of cuFFT by 3.1% at `logN=18`, and behind by 10.8% at
-`logN=20`. FP64 remains a clear gap. The inverse result is semantically fair,
-but its 1.963x ratio mainly demonstrates fused normalization: the cuButterfly
-path folds scaling into the transform while the measured cuFFT path launches a
-separate normalization kernel. It must not be presented as a 1.963x raw FFT
-core advantage.
+The original FP32 forward result is therefore at library parity for `logN=8`
+and `logN=14`, ahead of cuFFT by 3.1% at `logN=18`, and behind by 10.8% at
+`logN=20`; the superseding rows above narrow the latter gap to 2.1%. The scalar
+FP64 implementation is a clear processing-unit gap, while the focused
+double-precision unit closes it at the selected shape. The inverse result is
+semantically fair, but its 1.963x ratio mainly demonstrates fused
+normalization: the cuButterfly path folds scaling into the transform while the
+measured cuFFT path launches a separate normalization kernel. It must not be
+presented as a 1.963x raw FFT core advantage.
 
 ## Internal Design-Space Evidence
 
@@ -70,18 +94,16 @@ Short per-process warmups exposed two V100 clock modes near the configured
 1000 warmups to reach the boosted steady state. The full range remains in the
 CSV even when the robust central range is used for the stability decision.
 
-Dao-AILab FHT was not rerun because PyTorch is absent from the active Python
-environment. GPU-NTT was not rerun because its comparator executable is not
-present. Existing same-V100 records remain useful context, but are not merged
-with this suite: the archived GPU-NTT data also uses a different modulus from
-the newly generated full-suite NTT case. Fresh external coverage is therefore
-complete for cuFFT and VkFFT only.
+Dao-AILab FHT and GPU-NTT were subsequently refreshed under the matching
+five-trial protocol. They remain in a separate result table because their
+supported batches and semantic contracts do not coincide with every
+comprehensive-suite row. See [V100 External Baselines](v100_external_baselines.md).
 
 ## Current Conclusion
 
 The defensible statement is: **cuButterfly reaches top-library performance on
-selected V100 FP32 FFT shapes and demonstrates competitive archived FWHT/NTT
-results, while long FP32 FFT, FP64 FFT, and fresh external coverage remain open
-gaps.** The evidence does not support a blanket claim that every butterfly
-operator, length, precision, and semantic mode is already faster than the best
-specialized library.
+selected V100 FP32 and FP64 FFT shapes and on matching-protocol FWHT/NTT
+results.** FP32 `logN=20` at saturated batch and five FP64 crossover shapes
+remain measurable gaps. The evidence does not support a blanket claim that
+every operator, length, precision, and semantic mode is already faster than
+the best specialized library.
diff --git a/docs/cubutterfly_feature_coverage.md b/docs/cubutterfly_feature_coverage.md
index 731dcbc..1cd0963 100644
--- a/docs/cubutterfly_feature_coverage.md
+++ b/docs/cubutterfly_feature_coverage.md
@@ -30,9 +30,16 @@ Generated FFT codelets add FP32 `thread-dft8` and mixed `fp16-fp32`
 Core operands to FP16 and accumulates into FP32. Generated availability is
 controlled by `config/v100_design_points.json`.
 
-When cuFFTDx is enabled, FP32 online-reorder can compose two local FFTs whose
-individual sizes are `logN=3..10`. The first pass fuses the cross twiddle and a
-transposed scratch store; the second pass restores natural order. Cross
+When cuFFTDx is enabled, FP32 online-reorder can compose block FFT dimensions
+at `logN=3..10` with direct-strided dimensions at `logN=11..12`. The first pass
+fuses the cross twiddle and scratch-layout conversion; the second pass restores
+natural order. For suffix-direct `8+12` and `9+11`,
+`--direct-boundary tiled-transpose` instead performs a contiguous in-place
+suffix write and an explicit 32x32 padded transpose to natural order. The
+`--direct-boundary prefix-tiled-transpose` alternative first transposes natural
+input into a dedicated workspace so a direct `11/12`-bit prefix reads a
+contiguous row. The default `direct-strided` remains available as a measured
+alternative. Cross
 twiddles are independently selectable as table lookup or register recurrence,
 so this processing-unit choice remains subordinate to the architecture-level
 space/time schedule.
@@ -43,6 +50,21 @@ processing-unit granularity ceiling independently of the composed schedule.
 The V100-valid CTA choices are 256/512/1024 threads through `logN=13` and
 512/1024 threads at `logN=14`.
 
+The FP64 cuFFTDx adapter provides temporal block FFTs at `logN=3..10` and
+two-segment online compositions at `logN=14..18`, with each segment covering
+`logN=7..9`. These compile independent prefix/suffix mappings at 128/256/512
+threads and EPT 4/8. They support table
+and register-recurrence cross twiddles with a direct-strided global boundary;
+multi-segment, resident, direct whole-transform, and tiled-boundary FP64 forms
+remain outside the compiled matrix and are rejected rather than silently
+falling back.
+The prefix shared staging layout is independently selectable as `linear` or
+`xor-swizzle`. XOR swizzle permutes the physical `FFTsPerBlock` slot using
+element bits without increasing shared capacity or changing logical/global
+layout. Fixed-stride address strength reduction is selected at compile time
+when a mapping step spans a complete swizzle period; other legal mappings use
+the general per-item permutation.
+
 Each temporal length is a compile-time CUDA specialization selected by the
 runtime. This preserves unrolling at performance-critical fixed sizes while
 presenting one plan interface. The FP64 complex stage pipeline is rejected
@@ -70,7 +92,7 @@ normalization
 placement
 element_stride and batch_stride
 logN, N, batch
-backend, compute_unit, FFT complex_multiply, local_exchange, and fft_core
+backend, compute_unit, FFT complex_multiply, local_exchange, fft_core, and direct_boundary
 tile_threads, local_stages, reorder_columns, warp_stages, stage_space, pipeline_warps, handoff
 kernel/H2D/D2H time, transforms/s, points/s, butterflies/s, correctness
 ```
@@ -96,9 +118,11 @@ radix-2/radix-4/radix-8 FFT, FWHT, and XOR are checked in both directions at
 `logN=11`. Online-reorder additionally covers unequal stage groups, multiple
 columns per suffix CTA, FP64, strided/in-place execution, and verified
 `logN=20` execution in the large-length protocol.
-Optional cuFFTDx tests cover local `logN=3..10`, temporal and online-reorder
+Optional cuFFTDx tests cover local `logN=3..12`, temporal and online-reorder
 layouts, unequal long-FFT splits, table/recurrence cross twiddles, and forward
-and normalized inverse execution. Online-reorder also covers independent
+and normalized inverse execution. Both directional tiled boundaries are checked
+in natural order, and manual regressions cover normalized inverse, out-of-place,
+element-stride-two execution. Online-reorder also covers independent
 prefix/suffix EPT 4/8/16 and asymmetric thread/EPT mappings. Direct whole-transform tests cover every
 valid `logN=11..14` CTA shape, normalized inverse, strided layout, and in-place
 execution.
diff --git a/docs/design_overview.md b/docs/design_overview.md
index afc7827..2b4507d 100644
--- a/docs/design_overview.md
+++ b/docs/design_overview.md
@@ -1,14 +1,26 @@
 # Design Overview
 
-## 1. Problem Class
+## 1. Why A Mapping Paradigm Is Needed
 
-cuButterfly targets transforms whose dependency graph is a regular sequence of
-binary stages. For `N=2^m`, stage `s` contains `N/2` independent butterfly
-updates. FFT and NTT attach stage coefficients, FWHT uses add/subtract, and
-XOR-zeta changes the pair operator, but their dependency topology is shared.
+FFT, NTT, FWHT, and XOR-zeta use different arithmetic, but their regular
+power-of-two forms share the same dependency graph. For `N=2^m`, each stage
+contains independent butterfly updates; an element produced at stage `s` is
+consumed by a prescribed partner at stage `s+1`. A GPU implementation must
+therefore answer two different questions:
 
-The project separates seven objects and treats a complete external library as
-a comparison role:
+1. how much independent data work should execute concurrently; and
+2. how many dependent stage groups should remain on chip before ownership or
+   layout changes.
+
+Specialized libraries often answer both questions inside one highly tuned
+kernel. That is effective for one operator and device, but it entangles the
+arithmetic codelet with scheduling, storage, synchronization, and layout.
+cuButterfly separates them. Its contribution is the architecture-level
+organization of the dependency graph; a radix codelet, modular reduction,
+cuFFTDx block, or register FWHT hierarchy remains a replaceable physical
+processing unit.
+
+The separation is represented by seven objects:
 
 ```text
 G: mathematical graph and exact transform semantics
@@ -17,129 +29,198 @@ P: replaceable processing unit
 L: global and intermediate layout
 F: concrete GPU kernel realization
 Q: generation, selection state, and objective
-H: target hardware capacities and rates
-B: complete external library baseline (comparison role)
+H: target hardware capacities and service rates
 ```
 
-This separation is essential. A faster complex multiply belongs to `P`; block
-shape, state residency, and online layout conversion belong to `A` and `F`.
-cuFFT remains `B` unless a local unit can be isolated without importing its
-complete scheduler.
+A complete external library is a baseline, not a processing unit, unless its
+local codelet can be isolated from its scheduler and measured under the same
+contract.
 
-## 2. Three Independent Unfolding Axes
+## 2. Two Logical Dimensions, Four Unfolding Factors
 
-Let `S` be the number of stage positions and `D` the independent data work.
-The logical iteration space is factorized as:
+Let `D` denote independent butterfly data groups and `S` denote the ordered
+stage positions. The core logical iteration domain is the product `D x S`.
+cuButterfly factorizes each dimension into a spatial part and a temporal part:
 
 ```text
-S = Us * Ts
 D = Ud * Td
-Bbatch = Ub * Tb
+S = Us * Ts
+```
+
+`Ud` and `Us` are physical replication: they spend parallel hardware to expose
+work at the same time. `Td` and `Ts` are physical reuse: they let the same
+hardware serve multiple logical positions over time. These are architecture
+factors, not fixed CUDA tile sizes.
+
+```mermaid
+flowchart LR
+    subgraph Logical["Logical butterfly domain D x S"]
+        D["Data dimension D<br/>independent groups"]
+        S["Stage dimension S<br/>ordered dependencies"]
+    end
+
+    subgraph Factors["Two dimensions x two unfoldings"]
+        Ud["Data-space Ud<br/>parallel groups"]
+        Td["Data-time Td<br/>worker reuse"]
+        Us["Stage-space Us<br/>parallel stage service"]
+        Ts["Stage-time Ts<br/>resident stage reuse"]
+    end
+
+    subgraph Hardware["GPU realization selected per device"]
+        Grid["grid / CTA / warp placement"]
+        Resident["register + shared residence"]
+        Transport["shuffle / shared / barrier transport"]
+        Boundary["online reorder or global handoff"]
+    end
+
+    Unit["Replaceable processing unit<br/>radix, cuFFTDx, modular, FWHT, WMMA"]
+
+    D --> Ud
+    D --> Td
+    S --> Us
+    S --> Ts
+    Ud --> Grid
+    Td --> Resident
+    Us --> Transport
+    Ts --> Resident
+    Grid --> Unit
+    Resident --> Unit
+    Transport --> Unit
+    Unit --> Boundary
+    Boundary -. "next stage group" .-> Resident
 ```
 
-| Factor | Meaning | Typical GPU effect |
-|:--|:--|:--|
-| `Us` | stage-space unfolding | more simultaneous stage services, barriers, or warp roles |
-| `Ts` | stage-time folding | more dependent stages retained in registers/shared memory |
-| `Ud` | data-space unfolding | more lanes, warps, CTAs, and memory-level parallelism |
-| `Td` | data-time folding | more independent items reused by each physical worker |
-| `Ub` | batch-space unfolding | more independent transforms resident concurrently |
-| `Tb` | batch-time folding | repeated transforms on the same physical mapping |
+The four factors place different demands on the GPU:
 
-These factors are not fixed tile dimensions. Legal and efficient values depend
-on the current GPU's register file, shared-memory partition, barrier service,
-warp size, SM count, cache, and global-memory system.
+| Factor | Architectural question | Typical GPU realization | Main limiting services |
+|:--|:--|:--|:--|
+| `Ud` | How many independent data groups execute now? | lanes, warps, CTAs, grid waves | thread slots, memory concurrency, transaction shape |
+| `Td` | How many data groups reuse one physical worker? | per-thread items, CTA loops, repeated batch tiles | register lifetime, shared capacity, instruction count |
+| `Us` | How much stage service is physically replicated? | lane roles, warp roles, local pipelines, grouped codelets | shuffles, barriers, shared ports, code size |
+| `Ts` | How many dependent stages reuse that service? | register-resident or CTA-resident stage loops | state capacity, synchronization, coefficient supply |
 
-## 3. Expanded Mapping Descriptor
+Batch does not add a new dependency dimension. It contributes more independent
+points to `D`. The implementation may still expose `Ub` and `Tb` to distinguish
+batch-space and batch-time scheduling, but both refine the data-dimension
+mapping rather than changing the two-dimensional graph model.
 
-The four factors alone cannot distinguish two mappings with different storage
-or handoff costs. cuButterfly uses:
+## 3. What Spatial And Temporal Mean On A GPU
+
+Data-space unfolding is dependency-free: different transforms or independent
+groups can be assigned to different lanes, warps, or CTAs without synchronizing
+with one another. Stage-space unfolding is different. Adjacent stage work may
+be placed in different physical roles, but dependency edges still require an
+explicit transport and, when producer and consumer are not warp-synchronous, a
+synchronization mechanism.
+
+Temporal unfolding means reuse, not a promise that every value stays in a
+register. Thread-private state can remain in registers; values exchanged by a
+CTA normally reside in shared memory; state crossing CTA ownership requires a
+cooperative launch mechanism or a global-memory boundary. `Td` and `Ts`
+describe which logical work reuses a physical resource, while the residence
+fields describe where its live state is held.
+
+This distinction prevents two common but incorrect conclusions:
+
+- a larger temporal factor is not automatically better, because longer live
+  ranges can reduce occupancy or exceed shared-memory capacity;
+- a single source-level CUDA function does not remove grid-wide dependency
+  boundaries, because ordinary CTAs cannot safely synchronize with each other.
+
+## 4. Residence, Transport, And Layout
+
+The four factors alone cannot distinguish mappings with different handoff
+costs. The expanded mapping descriptor is:
 
 ```text
 M = (Us, Ts, Ud, Td, Ub, Tb, Hs, Rs, Rd, Rb, L, F, Q)
 ```
 
-| Field | Role |
-|:--|:--|
-| `Hs` | physical transport for a spatial stage edge: register, shuffle, shared memory, named barrier, or global handoff |
-| `Rs` | residence level across stage-time folds |
-| `Rd` | residence level across data-time folds |
-| `Rb` | residence and ownership across batch-time folds |
-| `L` | bank mapping, input order, intermediate permutation, and output order |
-| `F` | temporal tile, Hybrid2D, online reorder, stage pipeline, or another kernel family |
-| `Q` | threads, rows, local stages, radix, columns, warps, and generated-core selection |
+`Hs` records how spatial stage edges are transported. `Rs`, `Rd`, and `Rb`
+record residence across stage, data, and batch reuse. `L` records input,
+intermediate, bank, and output layouts. `F` selects a kernel family, while `Q`
+contains its concrete threads, rows, radix, segment lengths, and processing-unit
+choices.
 
-This descriptor explains why two kernels with identical `(Us,Ts,Ud,Td)` can
-have very different performance: one may keep a boundary in shared memory,
-while another writes the same boundary to global memory.
+For a long transform, stage groups are chosen independently of physical kernel
+groups. Several logical groups may be fused into one CTA-resident execution
+group when capacity and dependency scope permit. A global pass is introduced
+only when the next group needs a different ownership domain or cannot fit in
+the current resident state.
 
-## 4. Online Reordering
+## 5. Online Reordering
 
-When a long transform is split into prefix and suffix groups, the prefix output
-layout determines whether suffix dependencies are contiguous. cuButterfly can
-write prefix result `(h,l)` directly to physical address `(l,h)` at the
-required boundary store.
+After a resident stage group, the next group often needs a different view of
+the same values. Writing the current result in the consumer's order performs
+the permutation at an already-required handoff:
 
 ```mermaid
 flowchart LR
-    I[Natural global input] --> P[Local prefix<br/>Ts stages resident]
-    P --> R[Boundary store<br/>online permutation]
-    R --> S[Suffix columns<br/>resident per CTA]
-    S --> O[Requested output layout]
+    I["input tile"] --> P["resident prefix<br/>Ts stage groups"]
+    P --> R["fused boundary store<br/>consumer-oriented layout"]
+    R --> X["resident suffix<br/>new ownership view"]
+    X --> O["requested output order"]
 ```
 
-The integer address calculation is small, but the operation is not declared
-free. Destination coalescing, shared-memory bank mapping, cache sectors, and the
-number of eliminated later passes determine whether it wins. The V100 results
-show both positive cases and a CTA DFT8 case where a bit-reversed shared store
-was slower than paying one extra barrier.
+This is an online layout transformation, not a free permutation. It can remove
+a later transpose and expose contiguous suffix work, but its address arithmetic,
+coalescing, and shared-bank behavior must be measured. The V100 FP64 path is a
+concrete example: recurrence reduced coefficient traffic, XOR swizzling reduced
+bank conflicts, and strength-reduced address generation recovered the extra
+integer and warp instructions introduced by the swizzle.
 
-## 5. Replaceable Processing Units
+## 6. Replaceable Processing Units
 
-A local processing unit is described independently:
+A local unit is described independently from the mapping:
 
 ```text
 P = (stage_group, arithmetic_core, coefficient_form, local_exchange)
 ```
 
-- `stage_group`: radix-2, fused radix-4, fused radix-8, or matrix codelet.
-- `arithmetic_core`: modular, complex, add/subtract, or semiring update.
-- `coefficient_form`: native, Shoup, Barrett, generated matrix, or another
-  precomputed representation.
-- `local_exchange`: register, warp shuffle, shared memory, or an imported local
-  hierarchy.
+The unit may use radix-2/4/8 composition, modular arithmetic, complex
+four-multiply or Gauss-3, cuFFTDx, warp shuffles, shared memory, or a validated
+external register hierarchy. Replacing it changes local latency, register use,
+coefficient demand, and legal CTA shapes, so it changes the selected mapping.
+It does not change the meanings of `Ud`, `Td`, `Us`, and `Ts`.
 
-The same architecture search can therefore absorb a validated processing unit
-without claiming it as a new arithmetic invention. This is demonstrated by the
-Dao-derived FWHT register hierarchy and by generated scalar/CTA/WMMA DFT8
-choices.
+This boundary is why importing an established codelet strengthens rather than
+weakens the architecture experiment: the same mapper can test whether a better
+local unit remains efficient once embedded in a long-transform dataflow.
+
+## 7. Hardware-Driven Selection
 
-## 6. Selection Procedure
+Selection proceeds from semantics to hardware rather than from a universal
+tile constant:
 
-1. Fix exact semantics: operator, precision or modulus, length, batch,
-   direction, normalization, placement, strides, and output order.
-2. Enumerate legal `(A,P,F,Q)` candidates from the GPU profile and build-time
-   design specification.
-3. Reject candidates exceeding register, shared-memory, thread, layout, or
+1. Fix operator, precision or modulus, length, batch, direction,
+   normalization, placement, strides, and output order.
+2. Enumerate legal graph factorizations, four-factor mappings, residence and
+   layout choices, and processing units.
+3. Reject candidates that exceed thread, register, shared-memory, layout, or
    numeric constraints.
-4. Predict the dominant demand: arithmetic, global traffic, local exchange,
-   synchronization, or occupancy.
-5. Benchmark the reduced set with identical resident timing and verification.
-6. Use NCU/NSYS counters to classify the remaining gap and update the profile.
-7. Record the selected mapping per GPU rather than promoting it to an
-   architecture constant.
-
-The complete object/axis contract is in
-[Operator-Independent Butterfly Design Space](butterfly_design_space.md). The
-executable resource equations are detailed in
-[Hardware Mapping Methodology](hardware_mapping_methodology.md).
-
-## 7. Current Research Claim
-
-The current artifact supports the following claim: a common layered-transform
-mapping vocabulary survives changes in operator and local processing unit, and
-hardware-dependent choices materially change the selected design point.
-
-It does not yet establish an automatic selector across GPU generations or
-universal superiority over specialized libraries. Those require the same
-prediction-and-measurement protocol on at least one additional GPU family.
+4. Estimate grid waves, state residence, transport, coefficient supply, and
+   useful work per resident warp.
+5. Measure a reduced calibration set and dispatch among the remaining
+   candidates.
+6. Use NCU/NSYS to test the predicted limiting service and update the hardware
+   profile.
+
+Static constraints provide legality and a shortlist, but do not capture every
+launch-limited crossover. On V100, a small measured calibration set reduces
+the FFT selector's top-3 geometric-mean regret to `1.0007x`; this is why the
+current method is counter-calibrated rather than presented as a purely analytic
+cost model.
+
+The full resource equations are in [Hardware Mapping
+Methodology](hardware_mapping_methodology.md), and the complete separation of
+graph, mapping, unit, layout, realization, and selector is specified in
+[Complete Butterfly Design Space](butterfly_design_space.md).
+
+## 8. Current Claim Boundary
+
+The artifact demonstrates on V100 that one mapping vocabulary survives changes
+in operator and processing unit, that the best factorization changes with
+length, batch, and precision, and that counter-guided changes predict measured
+performance improvements. It does not yet establish cross-generation selector
+transfer, non-power-of-two coverage, or universal superiority over specialized
+libraries. Those remain explicit evidence boundaries rather than assumptions.
diff --git a/docs/experiments.md b/docs/experiments.md
index a2c1665..b9971ea 100644
--- a/docs/experiments.md
+++ b/docs/experiments.md
@@ -10,14 +10,57 @@ and external-library revision. Raw and summarized CSV files are retained.
 The reference system is a Tesla V100-SXM2-16GB (`sm_70`, 80 SMs, 6 MiB L2)
 with CUDA 11.8. Cross-GPU rows are placeholders until measured.
 
+Performance is reported only after correctness preflight. Ratios are computed
+from matched resident CUDA-event times; a value above `1.0x` means
+cuButterfly has higher throughput. Rows below the established `0.020 ms`
+timing floor remain useful launch-latency observations but are not counted as
+stable performance claims.
+
 ## 2. What The Results Establish
 
+The experiments test the mapping model in three steps. First, cross-operator
+and processing-unit scans test whether the same four-factor vocabulary remains
+valid when arithmetic changes. Second, orthogonal length/batch and decomposition
+scans test whether hardware-selected factors move as concurrency, residence,
+and local-unit requirements change. Third, NCU fixed-mapping comparisons test
+whether the proposed service bottleneck changes in the direction predicted by
+an optimization. A fast isolated row is not sufficient evidence for the
+architecture claim unless its semantics and mechanism are also controlled.
+
 The controlled full-suite cross-section and its evidence boundaries are
 reported in [V100 Comprehensive Results](comprehensive_v100_results.md). It is
 the current authority for claims spanning multiple lengths, precisions,
 semantics, and runnable FFT libraries; the focused experiments below retain
 their original protocols.
 
+The follow-up [V100 Length/Batch Scaling](v100_scaling_results.md) experiment
+holds transform length fixed while varying batch, exposing saturation points
+and mapping crossovers hidden by constant-total-point comparisons.
+
+The [V100 Mapping Selector](v100_mapping_selector.md) performs
+leave-one-complete-shape-out validation over the internal multi-candidate rows.
+The [matching-protocol external refresh](v100_external_baselines.md) is the
+current authority for Dao FHT and GPU-NTT comparisons with matching semantics.
+Targeted [V100 counter attribution](v100_ncu_attribution.md) explains the
+length/batch saturation and FWHT mapping crossover in hardware-service terms.
+
+The evidence chain is therefore:
+
+```text
+same graph, different operators
+    -> different mapping winners
+    -> hardware services explain the crossover
+    -> a small calibrated candidate set recovers the measured winner
+```
+
+The leave-one-complete-shape-out selector reaches `93.88%` top-1 accuracy,
+`100%` top-3 recall, and `1.0049x` geometric-mean regret across the internal
+NTT/FWHT/XOR-zeta candidate rows. In the separate 48-candidate FFT pipeline
+experiment, static scoring alone has `1.0762x` geometric-mean regret, while a
+small measured calibration set reduces top-3 regret to `1.0007x`. This negative
+static-model result is why the method combines hardware constraints with
+calibration instead of claiming a universal analytic tile rule.
+
 ### Common Mapping Across Operators
 
 At `N=256`, a controlled eight-warp stage pipeline selects the interior
@@ -48,6 +91,14 @@ selected spatial factor changes with length, and it crosses below the existing
 shared radix-8 schedule after `N=64`. This identifies layout synchronization as
 a composition cost rather than presenting the codelet as a universal winner.
 
+The long FFT results make the separation more explicit. Logical stage
+decomposition count and physical execution-group count are independent: adjacent
+segments may be fused when a CTA can retain their state. Segment length,
+prefix/suffix CTA threads, elements per thread, coefficient policy, and boundary
+layout are selected independently. The same architecture can therefore use a
+scalar unit for coverage and a cuFFTDx unit where its local precision and size
+contract is legal.
+
 ### Online Reordering
 
 At `logN=20`, fusing the boundary permutation and retaining the suffix in one
@@ -57,6 +108,47 @@ permuted prefix itself becomes about 25% slower, which confirms that online
 reordering is beneficial only when the eliminated downstream work is larger
 than its transaction cost.
 
+### FFT Against cuFFT And VkFFT
+
+The latest matching-protocol FP32 long-transform comparison uses five process
+trials, 1000 warmups, 100 timed repetitions, randomized execution order, and
+correctness preflight:
+
+| Shape | cuButterfly | cuFFT | VkFFT | cuButterfly/cuFFT |
+|:--|--:|--:|--:|--:|
+| `logN=18`, batch 16 | 0.195942 ms | 0.211098 ms | 0.201103 ms | 1.077x |
+| `logN=20`, batch 4 | 0.214733 ms | 0.210330 ms | 0.206520 ms | 0.979x |
+
+The broader mapping scan finds low-batch points above cuFFT at both lengths,
+but the saturated `logN=20` batch-8/16 rows remain at `0.962x/0.954x`. This is
+a narrow remaining ceiling, not evidence that every FFT shape exceeds cuFFT.
+The counters attribute the long-path gap to useful work per resident warp and
+local exchange rather than missing occupancy alone.
+
+The expanded FP64 experiment covers all two-segment totals `logN=14..18` whose
+segments are each `logN=7..9`. It independently selects decomposition and both
+CTA/EPT dimensions, then alternates cuButterfly and cuFFT execution order over
+five trials. Among 25 stable length/batch shapes, 20 have a higher
+cuButterfly median and 19 have non-overlapping faster trial ranges. All 13
+stable `logN=17/18` shapes are faster.
+
+| Shape with `2^22` total points | Split and physical mappings | cuButterfly | cuFFT | Ratio |
+|:--|:--|--:|--:|--:|
+| `logN=14`, batch 256 | `7+7`, `128/4 + 128/4` | 0.340173 ms | 0.344433 ms | 1.013x |
+| `logN=15`, batch 128 | `7+8`, `128/4 + 128/8` | 0.338852 ms | 0.342753 ms | 1.012x |
+| `logN=16`, batch 64 | `8+8`, `128/8 + 128/8` | 0.339364 ms | 0.343040 ms | 1.011x |
+| `logN=17`, batch 32 | `8+9`, `128/8 + 256/8` | 0.346307 ms | 0.395213 ms | 1.141x |
+| `logN=18`, batch 16 | `9+9`, `256/8 + 256/8` | 0.354877 ms | 0.421970 ms | 1.189x |
+
+At the profiled FP64 `logN=16`, batch-64 point, hoisting invariant global
+addresses and advancing XOR-swizzled shared pointers by compile-time strides
+reduces prefix warp instructions by 26.8% and prefix replay by 8.3% relative
+to the pre-optimization XOR kernel. Total replay becomes 2.5% lower than
+cuFFT, although the complete path still executes 1.83x its warp instructions,
+3.62x its integer instructions, and about 114x its shared-bank conflicts. The
+result validates the predicted address-path mechanism while identifying the
+remaining physical-unit cost.
+
 ### NTT Against GPU-NTT
 
 With the same V100, 60-bit prime, resident timing, and output semantics:
@@ -76,9 +168,10 @@ separately.
 
 | Area | Current boundary | Needed evidence or implementation |
 |:--|:--|:--|
-| FFT | two-pass `logN=16..20` reaches 79.3%-88.8%; direct units at `logN=11,12,14` reach 1.006x-1.029x cuFFT while `logN=13` reaches 0.965x | compose larger units into long FFTs, NCU validation, automatic selection |
+| FP32 FFT | selected direct and long shapes reach parity or advantage; saturated `logN=20` batch 8/16 remains at `0.962x/0.954x` cuFFT | reduce long-path local exchange and excess useful-work cost without losing residence |
+| FP64 FFT | 20/25 stable shapes have higher median throughput; five `logN=14..16` crossover shapes remain 0.1%-3.2% behind | reduce launch and boundary overhead; exhaustive remapping alone did not remove the deficits |
 | cross GPU | only V100 fully measured | predict and validate mappings on another GPU generation |
-| automatic selection | scripts rank measured candidates | calibrated cost model selecting before exhaustive sweep |
+| automatic selection | V100 calibrated selectors meet current regret gates | validate pre/post-calibration regret on another GPU generation |
 | XOR-zeta baseline | internal comparisons only | pinned same-machine external implementation |
 | public API | host-vector plan interface | device-pointer and stream-aware integration contract |
 | numeric coverage | current listed precisions/moduli | additional FFT mixed precision and NTT reduction contracts |
@@ -88,12 +181,18 @@ separately.
 | Topic | Report | Primary records |
 |:--|:--|:--|
 | comprehensive V100 suite | `comprehensive_v100_results.md` | `comprehensive_v100_full_raw.csv`, `comprehensive_v100_full_summary.csv` |
+| orthogonal length/batch scaling | `v100_scaling_results.md` | `v100_scaling_full_raw.csv`, `v100_scaling_full_summary.csv` |
+| calibrated V100 selector | `v100_mapping_selector.md` | `v100_mapping_selector_evaluation.csv`, `v100_mapping_selector_metrics.json` |
+| scaling-crossover counters | `v100_ncu_attribution.md` | `ncu_scaling_crossovers/summary.csv`, `ncu_scaling_crossovers/attribution.csv` |
+| refreshed external baselines | `v100_external_baselines.md` | `v100_external_baselines_raw.csv`, `v100_external_baselines_summary.csv` |
 | V100 NTT baseline | `v100_initial_results.md` | `hybrid2d_matrix*.csv` |
 | NTT vs GPU-NTT | `gpu_ntt_gap_analysis.md` | `fused_vs_gpuntt.csv`, `gpu_ntt_gap_same_modulus.csv` |
 | processing units | `processing_unit_design_space.md` | `processing_units_v100_*.csv` |
 | cross operator | `cubutterfly_cross_operator_results.md` | `cubutterfly_design_sweep_v100_*.csv` |
 | large transforms | `cubutterfly_large_results.md` | `cubutterfly_large_v100_*.csv`, `cubutterfly_online_*.csv` |
 | CTA DFT8 | `fft_cta_space_time_results.md` | `fft_cta_*_v100_raw.csv` |
+| FP64 length/batch robustness | `results/fp64_robustness_batch_analysis.md` | `fp64_robustness_batch_raw.csv`, `fp64_robustness_batch_summary.csv` |
+| FP64 address-path NCU | `results/ncu_fp64_fft/analysis.md` | `ncu_fp64_fft/summary.csv`, `ncu_fp64_fft/analysis.csv` |
 | hardware model | `hardware_mapping_methodology.md` | `hardware_capabilities_v100.json`, `v100_compact_mapping_model.csv` |
 | NCU | `ncu_profiling.md` | `ncu_summary_logN20.csv`, `ncu_fft_units_analysis.md` |
 
diff --git a/docs/fft_design_space.md b/docs/fft_design_space.md
index e8ee274..5eef41a 100644
--- a/docs/fft_design_space.md
+++ b/docs/fft_design_space.md
@@ -7,8 +7,9 @@ the architecture independently of the CUDA specializations currently compiled.
 The model has five layers:
 
 1. Semantic: length, precision, direction, placement, normalization, and layout.
-2. Decomposition: single-unit, two-dimensional, or multi-dimensional stage partition.
-3. Per-dimension mapping: spatial scope, stage fusion, temporal reuse, core,
+2. Factorization: `decomposition_count=D` and ordered stage vector
+   `stages_per_decomposition=S=[s0,...,s(D-1)]`, constrained by `sum(S)=logN`.
+3. Per-segment mapping: spatial scope, stage fusion, temporal reuse, core,
    threads, elements/thread, units/CTA, exchange, padding, and pipeline buffers.
 4. Boundary: residency, permutation, cross-twiddle policy, and global/shared handoff.
 5. Hardware: SM count, thread/shared/register limits, and scheduling capacity.
@@ -25,6 +26,7 @@ The relation must produce an integer and cover at least one unit.
 
 The architectural terms remain independent of a particular codelet:
 
+- `D/S` determines the number of local transform segments and boundaries;
 - `spatial_scope` states whether concurrent work is owned by a thread, warp,
   CTA, or cooperating CTAs;
 - `stage_fusion` states how many equivalent butterfly stages form one operation;
@@ -80,10 +82,19 @@ compiled into this build. The generator validates every selected thread/EPT pair
 against the canonical axes and V100 shared-memory/thread limits, then emits
 availability, dispatch, and a resolved build manifest.
 
+The factorization parameters and the paper's two space/time axes are distinct. `D`
+does not introduce a new parallel axis: the stage/data spatial and temporal
+mapping is applied independently to every decomposition segment `i`, and `D-1` boundary
+descriptors connect them. The optimized `D=2` CUDA path remains unchanged,
+while a generic ping-pong lowering
+executes `D=3/4` with one cuFFTDx processing unit per segment and one explicit
+boundary descriptor per adjacent pair.
+
 The current selection contains EPT 4/8/16 and 128/256/512/1024-thread points;
 1024/16 is excluded because its tiled storage exceeds the V100 per-CTA shared
-memory limit. The public FFT configuration records independent prefix/suffix
-thread and EPT values plus normalized units/CTA. Feasible but unselected values
+memory limit. The public FFT configuration records `segment_mappings[D]` and
+`boundaries[D-1]`; the old prefix/suffix fields remain a `D=2` compatibility
+interface. Feasible but unselected values
 fail explicitly as `awaiting code generation`; they do not fall back to EPT=8.
 
 Regenerate an isolated manifest with:
@@ -106,12 +117,19 @@ Completing the model does not imply every family is implemented. The major
 implementation queues are now explicit:
 
 - optionally emit the remaining cuFFTDx online EPT 1/2/32/64 points selected by a target profile;
-- compose `logN=11..14` direct units using direct-strided or explicit transpose boundaries;
-- allow different cores on the two dimensions;
+- fuse the implemented directional tiled transposes into adjacent work or retain
+  their layouts across multiple dimensions; standalone prefix and suffix
+  transpose kernels are measured but do not win at saturated batch;
+- allow heterogeneous core families across segments; the descriptors are
+  per-segment, but the generic runtime currently validates cuFFTDx-block/shared;
 - add shared-resident and cooperative-grid boundaries beyond selected points;
 - generate padding and multi-buffer pipeline variants;
-- extend the same schema to three or more dimensions for transforms beyond a
-  profitable two-dimensional factorization.
+- fuse adjacent segment/boundary work or keep multiple segments resident; the
+  functional `D=3/4` lowering currently incurs one global read/write pass per
+  segment and is therefore a correctness and exploration baseline.
 
 Fine-grained performance search should operate only on `compiled` points after
 the desired `awaiting-codegen` subset has been emitted.
+
+The bounded candidate search and measured runtime selection built on this
+space are documented in [FFT Pipeline Generator](fft_pipeline_generator.md).
diff --git a/docs/fft_pipeline_generator.md b/docs/fft_pipeline_generator.md
new file mode 100644
index 0000000..b9eeca7
--- /dev/null
+++ b/docs/fft_pipeline_generator.md
@@ -0,0 +1,267 @@
+# FFT Pipeline Generator
+
+The FFT generator separates four decisions that must not be collapsed into one
+kernel implementation.
+
+## Layers
+
+1. **Factorization topology** selects a decomposition count `D` and an ordered
+   stage vector `S=[s0,...,s(D-1)]`, constrained by `sum(S)=logN`. In the
+   machine-readable schema these are `decomposition_count` and
+   `stages_per_decomposition`. Neither `D`
+   nor an individual `si` is fixed by the architecture paradigm.
+2. **Processing unit mapping** describes one decomposition segment: supported stage count,
+   thread and element-per-thread choices, exchange method, twiddle method, and compiled
+   availability. `cufftdx-online-shared` covers local `logN=3..10`, while
+   `cufftdx-large-online` adapts the direct unit for `logN=11..12`. A suffix
+   direct unit independently selects either a strided natural-order store or a
+   contiguous store followed by a padded tiled transpose. A prefix direct unit
+   can instead transpose input into a workspace and consume contiguous rows.
+   Each segment independently selects threads and elements per thread. The model derives
+   units/CTA, grid blocks, shared storage, estimated resident CTAs, waves/SM,
+   issued thread slots, and work imbalance.
+3. **Boundary mapping** describes each of the `D-1` connections: twiddle
+   generation, permutation, residency, synchronization, and physical handoff.
+   A `fused` boundary remains inside one processing group; a `global-scratch`
+   boundary terminates the group and materializes its output.
+4. **Dispatch** is generated only from measured winners. It selects a mapping by
+   `(GPU, semantics, logN, batch regime)` and then reuses the normal runtime
+   validation path.
+
+`config/v100_fft_pipeline.json` is the search specification.
+`scripts/generate_fft_pipeline.py` emits the bounded candidate manifest. The
+specification supplies ranges for `D` and `si`, not a list of splits; the
+generator enumerates ordered integer compositions before lowering supported
+topologies. Known measured incumbents are mandatory candidates so that static
+pruning cannot exclude an existing strong point. Each selected row records the legal pool size
+and shortlist limit so that pruning remains auditable. Prefix and suffix units
+are selected independently. Prefix/suffix names appear only in the current
+`D=2` lowering and are not part of the general architecture abstraction. The
+current runtime accepts the same topology as `--stage-partition s0,s1,...`,
+plus `--segment-threads`, `--segment-ept`, `--boundary-twiddle`, and
+`--boundary-layout`. `--boundary-residency` controls logical-boundary fusion,
+while `--group-threads` and `--group-ept` map the resulting physical groups.
+
+The lowering derives an ordered physical partition `G=[g0,...,g(P-1)]` by
+coalescing logical segments across fused boundaries. Thus `P <= D`,
+`sum(G)=sum(S)=logN`, and the global handoff count is `P-1`, not `D-1`.
+For example, logical `7+3+10` with boundary residency
+`fused,global-scratch` lowers to physical `10+10`. It executes the same
+optimized two-group path as native `D=2`, while preserving the D3 topology in
+the architecture and experiment metadata. This separation is essential: `D`
+expresses the algorithmic space/time decomposition, whereas `P` expresses a
+hardware-dependent residency decision.
+
+For `logN=18/20`, `D=2..4`, and `si=3..12`, the current manifest contains 385
+factorization topologies:
+
+| logN | `D=2` | `D=3` | `D=4` |
+|--:|--:|--:|--:|
+| 18 | 7 | 55 | 84 |
+| 20 | 5 | 69 | 165 |
+
+All 385 topologies have a compiled runtime lowering. The bounded performance
+manifest selects 288 internal candidates from this topology/mapping product;
+it preserves every `D=2` split and directional boundary realization, then
+retains multiple `D=3/4` segment-mapping and physical-lowering classes under a
+per-shape limit. Measured D2 incumbents are also injected as physical-group
+mappings for compatible D3/D4 lowerings, including their boundary twiddle mode.
+
+## V100 Search Result
+
+The physical-unit optimization pairs adjacent FP32 complex values at the
+online cuFFTDx input, global-scratch handoff, and final output. Contiguous,
+aligned boundaries now use one 128-bit transaction for two transforms. Strided
+layouts, odd batch distances, and units with fewer than two transforms per CTA
+retain the scalar path. This changes the processing-unit realization without
+constraining the logical decomposition or physical group partition.
+
+The post-optimization scan contains 882 samples: 294 cases, three randomized
+trials per case, 100 warmups, and 50 timed repetitions. Times are resident
+kernel times on the repository V100. All 294 cases pass verification. A ratio
+above 1 means cuButterfly is faster.
+
+| logN | Batch | New best ms | Previous best ms | Best-point gain | cuFFT ms | Ratio |
+|--:|--:|--:|--:|--:|--:|--:|
+| 18 | 2 | 0.025866 | 0.026010 | 0.6% | 0.028058 | 1.085x |
+| 18 | 16 | 0.195441 | 0.205496 | 5.1% | 0.211108 | 1.080x |
+| 18 | 64 | 0.767201 | 0.836690 | 9.1% | 0.706273 | 0.921x |
+| 20 | 2 | 0.119869 | 0.128573 | 7.3% | 0.123453 | 1.030x |
+| 20 | 8 | 0.397332 | 0.445338 | 12.1% | 0.382300 | 0.962x |
+| 20 | 16 | 0.764334 | 0.867799 | 13.5% | 0.729416 | 0.954x |
+
+Across all 48 internal candidates per shape, the median same-candidate gain is
+3.4--6.0%. The larger best-point gains at saturated batch include mapping
+selection: vectorized boundary traffic changes which physical unit wins. The
+best `logN=20` batch-8/16 points are now within 3.8%/4.6% of cuFFT; `logN=18`
+batch 64 remains 7.9% behind. The next physical-unit target is therefore the
+cuFFTDx internal shared-memory exchange and synchronization, not another
+logical decomposition restriction. The records are
+`results/v100_fft_pipeline_vectorized_raw.csv`,
+`results/v100_fft_pipeline_vectorized_summary.csv`, and
+`results/v100_fft_pipeline_vectorized_report.md`.
+
+### Model validation
+
+Ranking the 48 measured candidates per shape with the static resource score
+alone gives 1.0762x geometric-mean top-1 regret and a 1.4220x worst case. The
+failure is concentrated in low-batch shapes where the score does not model
+launch and service latency accurately enough. A leave-one-batch-out calibrated
+selector interpolates or extrapolates matching physical mappings using only the
+other batches at the same length. Its top-3 geometric-mean regret is 1.0007x,
+worst regret is 1.0020x, and candidate fraction is 6.2%. Top-10 finds the exact
+winner in all six shapes while measuring 20.8% of the shortlist.
+
+This supports a two-level method rather than a universal analytic cost model:
+static constraints reject illegal points and form the candidate classes, then
+a small target-hardware calibration set ranks the surviving physical mappings.
+The complete per-shape ranks, including the static-model failures, are in
+`results/v100_fft_pipeline_model_report.md`.
+
+### Counter attribution
+
+The controlled NCU capture holds the physical mapping at 512/512 threads and
+EPT 8/8 across the code change. Paired boundary I/O reduces CUDA-event time by
+10.5%, NCU replay time by 9.3%, and executed warp instructions by 19.6%; DRAM
+write volume is unchanged. The gain therefore comes from the boundary
+instruction/transaction realization, not from removing a global handoff.
+
+The selected 256/128-thread mapping is 7.8% faster than the post-vector fixed
+point under CUDA-event timing. NCU replay reverses that pairwise ordering by
+2.8%, so replay time is retained only for attribution. The raw counters and
+generated analysis are in `results/ncu_fft_vectorized/`.
+
+The tables below preserve the pre-vectorization scan as a controlled baseline
+for boundary and physical-group experiments.
+
+The complete `D=2` scan confirms that the earlier balanced points were winners
+rather than assumptions. Best recurrence time per `logN=18` partition at batch
+16 is:
+
+| Stages | 6x12 | 7x11 | 8x10 | 9x9 | 10x8 | 11x7 | 12x6 |
+|:--|--:|--:|--:|--:|--:|--:|--:|
+| ms | 0.302141 | 0.305316 | 0.236872 | **0.205722** | 0.243384 | 0.324792 | 0.336261 |
+
+| logN | Batch | Selected mapping | cuButterfly ms | cuFFT ms | Ratio |
+|--:|--:|:--|--:|--:|--:|
+| 18 | 2 | `9+9`, `256/256`, EPT `8/8` | 0.026051 | 0.028099 | 1.079x |
+| 18 | 16 | `9+9`, `256/256`, EPT `8/8` | 0.205722 | 0.216146 | 1.051x |
+| 18 | 64 | `9+9`, `256/256`, EPT `8/8` | 0.842875 | 0.717599 | 0.851x |
+| 20 | 2 | `10+10`, `512/512`, EPT `8/8` | 0.128799 | 0.123556 | 0.959x |
+| 20 | 8 | `10+10`, `256/128`, EPT `16/16` | 0.450109 | 0.382157 | 0.849x |
+| 20 | 16 | `10+10`, `256/128`, EPT `16/16` | 0.883835 | 0.720855 | 0.816x |
+
+The original generic multi-segment baseline is correct but not competitive when
+each logical segment is a separate global-scratch pass. Per-segment mapping still
+matters: the second scan replaced the initially selected uniform
+`512-thread/EPT16` points with smaller codelets and improved `D=3` by roughly
+15--28%. Best measured points by decomposition count are:
+
+| logN | Batch | `D=2` ms / cuFFT | `D=3` stages, mapping, ms / cuFFT | `D=4` ms / cuFFT |
+|--:|--:|:--|:--|:--|
+| 18 | 2 | 0.026051 / 1.079x | `3+3+12`, `128/128/512`, 0.068301 / 0.411x | 0.114934 / 0.244x |
+| 18 | 16 | 0.205722 / 1.051x | `3+3+12`, `128/128/512`, 0.485929 / 0.445x | 0.868803 / 0.249x |
+| 18 | 64 | 0.842875 / 0.851x | `3+5+10`, `128/128/128`, 1.725727 / 0.416x | 3.172168 / 0.226x |
+| 20 | 2 | 0.128799 / 0.959x | `7+3+10`, `128/128/128`, 0.306196 / 0.404x | 0.545915 / 0.226x |
+| 20 | 8 | 0.450109 / 0.849x | `7+3+10`, `128/128/128`, 1.046466 / 0.365x | 1.800069 / 0.212x |
+| 20 | 16 | 0.883835 / 0.816x | `7+3+10`, `128/128/128`, 2.050929 / 0.351x | 3.581092 / 0.201x |
+
+These rows isolate the cost of setting `P=D`. Merely increasing `D` while
+materializing every boundary in global memory is predictably bandwidth-bound.
+
+The controlled fused-boundary scan then holds the physical group partition,
+threads/EPT, recurrence twiddle, and direct-strided global boundary constant.
+Only the logical decomposition metadata and fused internal boundaries change:
+
+| logN | Batch | D2/P2 ms / cuFFT | D3/P2 ms / cuFFT | D4/P2 ms / cuFFT | D3/P3 ms / cuFFT | D4/P4 ms / cuFFT |
+|--:|--:|:--|:--|:--|:--|:--|
+| 18 | 2 | 0.026051 / 1.079x | 0.026030 / 1.079x | 0.026010 / 1.080x | 0.081039 / 0.347x | 0.114913 / 0.245x |
+| 18 | 16 | 0.205722 / 1.051x | 0.205681 / 1.051x | 0.205496 / 1.052x | 0.716513 / 0.302x | 0.868434 / 0.249x |
+| 18 | 64 | 0.842875 / 0.851x | 0.836690 / 0.858x | 0.839721 / 0.855x | 2.613678 / 0.275x | 3.176305 / 0.226x |
+| 20 | 2 | 0.128799 / 0.959x | 0.128655 / 0.960x | 0.128573 / 0.961x | 0.371220 / 0.333x | 0.545833 / 0.226x |
+| 20 | 8 | 0.450109 / 0.849x | 0.445338 / 0.858x | 0.446628 / 0.856x | 1.411707 / 0.271x | 1.799455 / 0.212x |
+| 20 | 16 | 0.883835 / 0.816x | 0.868844 / 0.830x | 0.867799 / 0.831x | 2.792632 / 0.258x | 3.578204 / 0.201x |
+
+The D2/P2, D3/P2, and D4/P2 columns agree within normal run-to-run variation
+(at most 1.8% here). This is the central result of the lowering experiment:
+logical decomposition count has no intrinsic execution penalty when it maps to
+the same physical schedule. The large D3/P3 and D4/P4 loss is attributable to
+extra global handoffs. Fusion does not itself improve the selected arithmetic
+core; it prevents the architecture abstraction from imposing avoidable passes.
+
+The boundary experiment compares the same `9+11`, 128/256-thread, EPT 16/8,
+recurrence point. Both rows include every launched kernel.
+
+| Batch | Direct-strided ms | Tiled-transpose ms | Tiled change | Tiled/cuFFT |
+|--:|--:|--:|--:|--:|
+| 2 | 0.169226 | 0.161690 | 4.66% faster | 0.764x |
+| 8 | 0.579461 | 0.583332 | 0.67% slower | 0.655x |
+| 16 | 1.133466 | 1.150116 | 1.47% slower | 0.627x |
+
+The tiled realization makes the suffix FFT write its contiguous scratch row in
+place, then launches a 32x32 shared-memory transpose with a 33-element pitch.
+It improves the low-batch point but does not change the selected `10+10`
+mapping. At saturated batch, the saved strided stores do not repay an extra
+full global read/write and third launch. The result isolates the next target:
+fuse the tiled permutation into an adjacent pass or retain a transposed layout
+across more work, instead of adding another standalone arithmetic core.
+
+`8+12` tiled recurrence reaches 0.170271, 0.611820, and 1.201418 ms at batch
+2, 8, and 16.
+
+The prefix-side experiment uses the same padded transpose before the direct
+prefix, a dedicated workspace, and the existing twiddle/scratch epilogue. It
+therefore measures the cost of converting strided input into a contiguous
+processing-unit contract without changing arithmetic:
+
+| Split | Batch | Direct-strided ms | Prefix transpose ms | Prefix change |
+|:--|--:|--:|--:|--:|
+| `11+9` | 2 | 0.173691 | 0.197345 | 13.62% slower |
+| `11+9` | 8 | 0.675103 | 0.733348 | 8.63% slower |
+| `11+9` | 16 | 1.370194 | 1.480540 | 8.05% slower |
+| `12+8` | 2 | 0.181473 | 0.213893 | 17.86% slower |
+| `12+8` | 8 | 0.655667 | 0.856842 | 30.68% slower |
+| `12+8` | 16 | 1.314959 | 1.944105 | 47.84% slower |
+
+The negative result is useful: coalescing one direct-unit boundary does not
+justify a standalone full-array pass. A profitable realization must fuse the
+permutation with a producer/consumer or preserve the transposed layout across
+additional work. Neither directional transpose changes the current measured
+dispatch winners.
+
+## Commands
+
+```bash
+python3 scripts/generate_fft_pipeline.py \
+  --output config/v100_fft_pipeline_candidates.json
+
+python3 scripts/run_fft_pipeline.py --resume \
+  --manifest config/v100_fft_pipeline_candidates.json \
+  --binary build/cubutterfly_bench \
+  --output results/v100_fft_pipeline_raw.csv
+
+python3 scripts/summarize_fft_pipeline.py \
+  results/v100_fft_pipeline_raw.csv \
+  --output results/v100_fft_pipeline_summary.csv \
+  --markdown results/v100_fft_pipeline_report.md
+
+# Repeat after a processing-unit change without overwriting the baseline.
+python3 scripts/run_fft_pipeline.py \
+  --manifest config/v100_fft_pipeline_candidates.json \
+  --binary build/cubutterfly_bench \
+  --output results/v100_fft_pipeline_vectorized_raw.csv
+
+python3 scripts/summarize_fft_pipeline.py \
+  results/v100_fft_pipeline_vectorized_raw.csv \
+  --output results/v100_fft_pipeline_vectorized_summary.csv \
+  --markdown results/v100_fft_pipeline_vectorized_report.md
+
+python3 scripts/generate_fft_dispatch.py \
+  --summary results/v100_fft_pipeline_vectorized_summary.csv \
+  --output config/v100_fft_dispatch.json
+```
+
+At runtime, `--auto-select` currently accepts only the calibrated V100 SM70
+semantics: FP32 forward, in-place, contiguous, no normalization, and
+`logN=18/20`. The build must enable cuFFTDx. Unsupported hardware, build
+capability, or semantics fail explicitly.
diff --git a/docs/getting_started.md b/docs/getting_started.md
index 528c87d..3fee716 100644
--- a/docs/getting_started.md
+++ b/docs/getting_started.md
@@ -59,8 +59,9 @@ cmake -S . -B build \
 cmake --build build -j
 ```
 
-The cuFFTDx adapter supports FP32 forward/inverse local FFTs at `logN=3..10`,
-including strided and in-place plan semantics. The current TurboFFT artifact
+The cuFFTDx adapter supports FP32 forward/inverse block FFTs at `logN=3..10`
+and direct-strided online dimensions at `logN=11..12`, including strided and
+in-place plan semantics. The current TurboFFT artifact
 adapter supports the generated FP32 forward, contiguous, out-of-place kernels
 actually present upstream at `logN=7..10`.
 
diff --git a/docs/hardware_mapping_methodology.md b/docs/hardware_mapping_methodology.md
index ef81cfe..111d235 100644
--- a/docs/hardware_mapping_methodology.md
+++ b/docs/hardware_mapping_methodology.md
@@ -459,6 +459,20 @@ This is a pruning and interpretation model, not a cycle-accurate predictor.
 Final selection uses measured steady-state CUDA-event time with correctness and
 output semantics held constant.
 
+The targeted V100 length/batch experiment validates that the categories above
+must remain separate:
+
+| Case | Coverage/residency | Useful-work evidence | Diagnosis |
+|:--|:--|:--|:--|
+| FFT `logN=14`, batch 16 | direct: 0.20 waves/SM, one 1024-thread CTA/SM | strong local cuFFTDx core | `Ub` grid underfill |
+| FFT `logN=18`, batch 64 | online: 60.6% active warps | 1.60x cuFFT warp instructions, 9.50x bank conflicts | exchange/synchronization ceiling |
+| FFT `logN=20`, batch 16 | equal aggregate waves to cuFFT | 2.00x warp instructions; first pass is 61.8% of time | prefix/core/layout imbalance |
+| FWHT `logN=15`, batch 4/16 | warp-register: 0.05/0.20 waves/SM | at batch 16, 0.07x online warp instructions | `Ud` decomposition to `Td` residence crossover |
+
+Thus `active_warps` is not an optimization objective by itself. Grid coverage,
+residency, and useful work per active warp are independent selector features.
+See [V100 Counter Attribution](v100_ncu_attribution.md) for the complete data.
+
 ## 10. Portable architecture-selection procedure
 
 1. Enumerate ordered graph factorizations and per-dimension `(Us, Ud)` points;
diff --git a/docs/ncu_profiling.md b/docs/ncu_profiling.md
index 034d5de..80420b3 100644
--- a/docs/ncu_profiling.md
+++ b/docs/ncu_profiling.md
@@ -40,6 +40,28 @@ sudo chown -R "$USER:$USER" results/ncu_fft_architecture
 Override `LOG_N`, `BATCH`, and `LOCAL_STAGES` to reuse the script for another
 selected split.
 
+The paired 128-bit boundary optimization has a dedicated controlled capture.
+It profiles the pre-existing 512/512-thread mapping, the newly selected
+256/128-thread mapping, and cuFFT at `logN=20`, batch 16. The reducer compares
+the fixed mapping with the archived pre-vector capture before attributing the
+additional mapping-selection gain:
+
+```bash
+sudo -E ./scripts/profile_fft_vectorized_ncu.sh
+sudo chown -R "$USER:$USER" results/ncu_fft_vectorized
+```
+
+The script writes raw CSV, a pivoted summary, `attribution.csv`, and
+`attribution.md`. Override `BATCH` only when a matching archived pre-vector
+label exists.
+
+The archived V100 capture shows that vectorizing the same fixed mapping reduces
+warp instructions by 19.6%, CUDA-event time by 10.5%, and NCU replay time by
+9.3%, while DRAM writes remain unchanged. See
+`results/ncu_fft_vectorized/attribution.md`. The selected mapping is faster in
+CUDA-event timing but not under replay, reinforcing that NCU time is not the
+performance authority.
+
 ## Purpose
 
 The profiling run compares three implementations under the same modulus,
@@ -191,3 +213,28 @@ capacity and bandwidth from modular-arithmetic cost.
 
 The script assumes two cuNTT kernels at all supported Hybrid2D lengths, two
 GPU-NTT kernels through `logN=16`, and three GPU-NTT kernels above it.
+
+## Length/Batch Crossover Targets
+
+The orthogonal V100 scaling sweep selects FFT `logN=14/18/20` and FWHT
+`logN=15` crossover points for counter attribution. Collect all selected
+low/intermediate/saturated batches with administrator-enabled counters:
+
+```bash
+sudo -E ./scripts/profile_scaling_crossovers_ncu.sh
+sudo chown -R "$USER:$USER" results/ncu_scaling_crossovers
+
+python3 scripts/summarize_ncu.py \
+  results/ncu_scaling_crossovers/*.csv \
+  --output results/ncu_scaling_crossovers/summary.csv
+
+python3 scripts/analyze_scaling_ncu.py \
+  results/ncu_scaling_crossovers/summary.csv \
+  --output results/ncu_scaling_crossovers/attribution.csv \
+  --markdown results/ncu_scaling_crossovers/attribution.md
+```
+
+The script requests base profiling clocks. Compare grid waves, active warps,
+DRAM throughput, register/shared-memory limits, barrier stalls, and long
+scoreboard stalls across batch before comparing absolute NCU kernel time with
+the steady-state CUDA-event table.
diff --git a/docs/next_phase_v0.3.md b/docs/next_phase_v0.3.md
new file mode 100644
index 0000000..6161fc5
--- /dev/null
+++ b/docs/next_phase_v0.3.md
@@ -0,0 +1,129 @@
+# v0.3.0 Mapping-Selection Milestone
+
+Status: completed on V100. Cross-GPU transfer remains future work.
+
+## Objective
+
+Turn cuButterfly's measured V100 design space into a counter-calibrated mapping
+selector. The result must predict a small set of efficient mappings from the
+operator contract, shape, and GPU service profile, while keeping the local
+butterfly computation unit replaceable.
+
+This is the next architecture-level step. Adding more isolated fast kernels is
+useful only when it fills a missing candidate class or tests a selector
+hypothesis.
+
+## Starting Point
+
+- `v0.2.0` is the archived V100 comprehensive baseline on `main`.
+- The new orthogonal suite contains 184 cases and 920 process trials.
+- Length and batch are now independent axes; fixed total points are no longer
+  used to infer saturation.
+- The scan establishes real mapping crossovers, including FWHT `logN=15`, and
+  distinct FFT launch-limited and throughput-limited regions.
+- Cross-GPU rows are still placeholders.
+- P1 is implemented over 49 internal multi-candidate shapes; it reaches 93.88%
+  top-1 accuracy and 1.0049x geometric-mean regret.
+- P2 is complete with 120 matching-protocol Dao FHT/GPU-NTT samples.
+- P0 is complete with 22 profiled implementation-shape pairs and 37 kernels;
+  the attribution separates grid coverage, residency, and useful work/warp.
+- The parameterized FFT pipeline now has a separate six-shape evaluation over
+  48 candidates per shape. Leave-one-batch-out top-3 regret is 1.0007x
+  geometric mean and 1.0020x worst case. The post-vector fixed-mapping NCU
+  capture records 19.6% fewer warp instructions and 9.3% lower replay time.
+
+## Work Packages
+
+### P0: Mechanism Attribution
+
+Run `scripts/profile_scaling_crossovers_ncu.sh` and reduce the output with
+`scripts/summarize_ncu.py`. Analyze counters at these boundaries:
+
+| Question | Cases | Required attribution |
+|:--|:--|:--|
+| Why does direct FFT need batch concurrency? | FFT `logN=14`, batch 16/256/1024 | CTA waves, occupancy, registers, launch amortization |
+| Why does cuButterfly saturate early? | FFT `logN=18`, batch 2/16/64 | DRAM/L2 service, active warps, issue stalls, composition cost |
+| Why is the long FFT ceiling lower? | FFT `logN=20`, batch 2/8/16 | the same services plus prefix/suffix imbalance |
+| Why does the preferred unit change? | FWHT `logN=15`, batch 4/16 | occupancy and exchange cost for online versus warp-register |
+
+Output: `results/ncu_scaling_crossovers/summary.csv` plus a counter-attribution
+report. A performance explanation is accepted only when its predicted trend
+matches at least two measured batch points.
+
+### P1: Calibrated Selector
+
+Implement a selector over the existing descriptor
+`M=(Us,Ts,Ud,Td,Ub,Tb,Hs,Rs,Rd,Rb,L,F,Q)`. Its first version should:
+
+1. reject illegal candidates from static resource and semantic constraints;
+2. estimate launch concurrency, residency, data movement, and synchronization;
+3. rank mapping families separately from replaceable processing units;
+4. return top-k candidates with human-readable limiting factors;
+5. fall back to measurement when the model confidence is low.
+
+Evaluate by holding out complete `(operator, logN, batch)` shapes. Report top-1
+accuracy, top-3 recall, geometric-mean regret, worst regret, and search-space
+reduction. The initial V100 gate is top-3 recall at least 90% with geometric
+mean regret at most 5%; otherwise keep the selector labeled experimental.
+
+### P2: Baseline Refresh
+
+Rerun Dao-AILab FHT and GPU-NTT with the comprehensive-suite controls. Every
+paper-facing comparison must record library revision, modulus or precision,
+direction, output order, placement, batch, clock policy, warmups, repetitions,
+process trials, and correctness result.
+
+XOR-zeta remains an internal architecture ablation until a maintained tuned
+external implementation with matching semantics is available.
+
+### Future: Cross-GPU Transfer
+
+This work is deferred until the repository moves to a newer GPU host. After
+P0-P2 are frozen on V100, capture one newer GPU profile, generate a
+reduced candidate set without using its timing results, and then measure it.
+The primary portability metric is prediction regret before recalibration; a
+second result may show regret after a small calibration set.
+
+## Decision Gates
+
+| Gate | Continue when | Reconsider when |
+|:--|:--|:--|
+| G1: counters | bottlenecks explain observed batch trends | counters contradict the proposed resource model |
+| G2: selector | top-3 recall and regret meet the V100 target | exhaustive search remains necessary for common shapes |
+| G3: baselines | matching semantics and protocols are reproducible | library contracts cannot be aligned |
+
+Cross-GPU transfer is intentionally not a `v0.3.0` decision gate.
+
+## Deferred Scope
+
+- production-compatible cuFFT replacement API;
+- broad Tensor Core FFT claims without end-to-end accuracy and composition
+  accounting;
+- universal superiority claims;
+- additional operators that do not test a new dependency or hardware service;
+- large multidimensional or non-power-of-two transforms before the selector is
+  validated on the current regular graph family.
+
+## Immediate Commands
+
+```bash
+# Repository and generated-manifest checks
+cmake --build build -j
+/usr/bin/ctest --test-dir build --output-on-failure
+
+# Recollect counters only when an administrator-enabled run is required
+sudo -E ./scripts/profile_scaling_crossovers_ncu.sh
+sudo chown -R "$USER:$USER" results/ncu_scaling_crossovers
+
+# The profiling script also emits this summary; rerun explicitly if needed
+python3 scripts/summarize_ncu.py results/ncu_scaling_crossovers/*.csv \
+  --output results/ncu_scaling_crossovers/summary.csv
+
+python3 scripts/analyze_scaling_ncu.py \
+  results/ncu_scaling_crossovers/summary.csv \
+  --output results/ncu_scaling_crossovers/attribution.csv \
+  --markdown results/ncu_scaling_crossovers/attribution.md
+
+# Regenerate every derived V100 analysis from immutable raw records
+./scripts/reproduce_v100_analysis.sh
+```
diff --git a/docs/processing_unit_design_space.md b/docs/processing_unit_design_space.md
index 43919a9..7bec5da 100644
--- a/docs/processing_unit_design_space.md
+++ b/docs/processing_unit_design_space.md
@@ -35,7 +35,8 @@ search the product of both spaces.
 | Operator | Stage group | Arithmetic/coefficient choices | Mapping support |
 |:--|:--|:--|:--|
 | FFT FP32/FP64 | radix-2, fused radix-4, fused radix-8 | four-multiply, Gauss three-multiply, FP32 thread-register DFT8 | temporal, hierarchical, online-reorder; generated DFT8 point |
-| FFT FP32 optional | cuFFTDx block FFT, TurboFFT generated FFT | imported local codelet transport and arithmetic | temporal full-local points; cuFFTDx `logN=3..10`, TurboFFT `logN=7..10` |
+| FFT FP32 optional | cuFFTDx block/direct FFT, TurboFFT generated FFT | imported local codelet transport and arithmetic | cuFFTDx online dimensions `logN=3..12`, TurboFFT `logN=7..10` |
+| FFT FP64 optional | cuFFTDx block FFT | imported double-precision local codelet | temporal `logN=3..10`; online `logN=16` with an `8+8` decomposition |
 | FFT mixed | temporally fused DFT8 matrix | FP16 WMMA input with FP32 accumulation/output | generated temporal point |
 | FWHT FP32/FP64 | radix-2, fused radix-4, fused radix-8 | add/subtract; FP32 register-vector/XOR-swizzle exchange | temporal, hierarchical, online-reorder |
 | XOR-zeta uint32 | radix-2, fused radix-4, fused radix-8 | add/subtract modulo `2^32` | temporal, hierarchical, online-reorder |
@@ -154,6 +155,134 @@ Reproduce the constrained search with:
 Primary records are `results/fft_architecture_explore_v100_{search,confirm,summary}.csv`
 and `results/fft_architecture_logN18_confirm_v100_{confirm,summary}.csv`.
 
+### FP64 processing-unit isolation
+
+The FP64 `logN=16`, batch-64 case separates mapping and local-unit effects in
+three ordered experiments. A 264-point scalar scan covers decomposition,
+radix, complex multiplication, CTA width, and reorder columns. It moves the
+original 0.534313 ms point to a 0.521492 ms confirmed result (`8+8`, radix-4,
+128 threads), or 0.658x cuFFT throughput. Replacing both local dimensions with
+`Precision<double>()` cuFFTDx codelets and independently scanning their CTA/EPT
+axes selects prefix `256/4` and suffix `128/8`.
+
+| FP64 implementation | Median ms | Throughput vs cuFFT |
+|:--|--:|--:|
+| scalar comprehensive point | 0.534313 | 0.642x |
+| scalar mapping winner, current build | 0.521226 | 0.658x |
+| cuFFTDx `8+8`, table twiddle, current build | 0.369459 | 0.928x |
+| cuFFTDx `8+8`, recurrence twiddle, current build | 0.345027 | 0.994x |
+| cuFFTDx `8+8`, recurrence + strength-reduced XOR | 0.342098 | 1.002x |
+| cuFFT, current build | 0.342856 | 1.000x |
+
+The five current-build rows use five independent trials, 1000 warmups, and 100 timed
+repetitions; all FP64 cuFFTDx local, online-forward, and normalized-inverse
+paths pass automated correctness tests. The imported table unit reduces the
+selected scalar latency by 29.1%, recurrence raises that reduction to 33.8%,
+and strength-reduced XOR raises it to 34.4%, so the former FP64 deficit is
+primarily a physical-core and mapping maturity issue rather than evidence
+against the architecture-level
+space/time decomposition. `scripts/profile_fp64_fft_ncu.sh` fixes the scalar,
+table, recurrence, and cuFFT mappings for privileged boundary attribution.
+Reproduce the original design sequence with `scripts/benchmark_fp64_fft_units.sh`,
+the focused address-path result with `scripts/benchmark_fp64_fft_address_path.sh`,
+and counters with `scripts/profile_fp64_fft_ncu.sh`. Raw and ranked records are
+`results/fp64_*logN16*.csv`.
+
+The first prefix optimization replaces four EPT4 twiddle-table reads per
+thread with two initial reads and register recurrence. The selected mapping
+remains prefix `256/4`, suffix `128/8` across the full 36-point rescan, while
+latency falls from 0.383949 ms to 0.361708 ms (5.8%). Simple `pitch+1` shared
+padding is a negative result: prefix-only and both-pass variants take 0.398039
+and 0.397609 ms, while suffix-only is statistically neutral at 0.383765 ms.
+The conflict count therefore identifies real exchange overhead, but uniform
+padding is not an efficient realization on V100.
+
+An equal-capacity XOR swizzle succeeds where padding fails. It maps the prefix
+shared slot as `slot XOR ((element >> 1) & (FFTsPerBlock-1))`, spreading the
+fixed-transform access across bank groups without changing logical ownership,
+global layout, or shared allocation. With recurrence and the same selected
+mapping, it lowers latency from 0.361708 ms to 0.353526 ms (2.3%). A full
+36-point scan retains prefix `256/4`, suffix `128/8`, confirming that the gain
+is orthogonal to CTA/EPT selection. NCU confirms that it cuts prefix shared
+conflicts by 53.5% and prefix replay by 5.3%, raising peak DRAM utilization
+from 72.9% to 77.0%. Suffix replay decreases by only 0.5%, while the prefix
+executes 10.0% more warp instructions; strength-reducing the swizzled address
+path is therefore the next local optimization. That optimization is now implemented:
+each staging loop computes the physical slot once and advances its shared
+pointer by the CTA stride, while transform identity, batch identity, and global
+address increments are hoisted out of the loop. Compile-time period checks
+guard all generated CTA/EPT specializations. It reduces current-build linear
+recurrence to 0.345027 ms and XOR to 0.342098 ms, a further 0.8% reduction over
+linear and 3.2% over the former XOR result, without local spills.
+
+The fixed privileged capture below predates address strength reduction, is
+preserved in commit `7892666`, and confirms the recurrence and swizzle
+mechanisms. It reduces prefix replay from
+249.824 us to 206.016 us (17.5%), warp instructions by 6.9%,
+and raises peak DRAM use from 60.2% to 72.9%. This costs 8.4% more prefix FP64
+instructions but does not change registers, shared allocation, or waves/SM.
+The suffix is effectively unchanged, confirming that the measured gain belongs to
+the prefix twiddle policy. Against cuFFT, the recurrence path transfers 1.006x
+the bytes and executes 1.023x the FP64 instructions, but still executes 2.06x
+the warp instructions and incurs about 145x the shared-bank conflicts. With
+XOR swizzle, total replay is 367.648 us versus cuFFT's 361.120 us, a 1.8% gap;
+the authoritative CUDA-event gap is 3.1%. It still executes 2.19x cuFFT's warp
+instructions and incurs about 100x its shared conflicts. The remaining work is
+therefore shared exchange and general address work, not twiddle service,
+occupancy, or FP64 arithmetic throughput.
+
+The refreshed optimized capture validates the address-strength-reduction
+mechanism. Relative to the prior XOR prefix, warp instructions fall from
+22.020M to 16.122M (26.8%), replay falls from 195.008 us to 178.912 us (8.3%),
+and shared conflicts fall from 2.794M to 2.552M (8.6%); suffix replay changes
+by less than 0.4%. Total XOR replay is 350.880 us versus cuFFT's 359.744 us,
+2.5% lower. The optimized path still executes 1.83x cuFFT's warp instructions,
+3.62x its integer instructions, and 113.7x its shared conflicts, but reaches
+85.5% peak DRAM utilization with lower long-scoreboard stall. Prefix registers
+rise from 48 to 64 and the register block limit falls from 5 to 4. The result
+therefore demonstrates an explicit trade: additional induction state reduces
+dynamic address work enough to outweigh lower occupancy. See
+`results/ncu_fp64_fft/analysis.md`.
+
+Recollect and regenerate the current optimized attribution with:
+
+```bash
+./scripts/profile_fp64_fft_ncu.sh
+```
+
+### FP64 length and batch robustness
+
+The physical-unit templates now instantiate segment sizes 128, 256, and 512,
+covering two-segment totals `logN=14..18`. The architecture parameters remain
+shape-dependent: a 648-point scan over split direction, both CTA/EPT mappings,
+and shared layout selects the following equal-`2^22`-point winners.
+
+| logN | Batch | Split | Prefix | Suffix | cuButterfly ms | cuFFT ms | Throughput |
+|--:|--:|:--|:--|:--|--:|--:|--:|
+| 14 | 256 | `7+7` | `128/4` | `128/4` | 0.340173 | 0.344433 | 1.013x |
+| 15 | 128 | `7+8` | `128/4` | `128/8` | 0.338852 | 0.342753 | 1.012x |
+| 16 | 64 | `8+8` | `128/8` | `128/8` | 0.339364 | 0.343040 | 1.011x |
+| 17 | 32 | `8+9` | `128/8` | `256/8` | 0.346307 | 0.395213 | 1.141x |
+| 18 | 16 | `9+9` | `256/8` | `256/8` | 0.354877 | 0.421970 | 1.189x |
+
+The formal length/batch matrix alternates implementation order within each of
+five trials. Of 25 shapes above the 0.020-ms timing floor, 20 have a faster
+median and 19 have non-overlapping faster ranges. All 13 stable `logN=17/18`
+shapes are faster. Remaining deficits occur at five `logN=14..16` medium-batch
+crossovers (0.1%-3.2%); targeted exhaustive remapping does not consistently
+remove them, localizing the next work in launch/boundary overhead rather than
+the mapping selector. Reproduce with:
+
+```bash
+./scripts/benchmark_fp64_fft_robustness_mapping.sh
+python3 scripts/benchmark_fp64_fft_robustness.py \
+  --output results/fp64_robustness_batch_raw.csv
+python3 scripts/analyze_fp64_fft_robustness.py \
+  results/fp64_robustness_batch_raw.csv \
+  --output results/fp64_robustness_batch_summary.csv \
+  --markdown results/fp64_robustness_batch_analysis.md
+```
+
 ### Resident and direct granularity experiment
 
 At `logN=12`, one 4096-value transform fits in a V100 CTA. Three physical
diff --git a/docs/reproducibility.md b/docs/reproducibility.md
index 7ff63c5..2da1a02 100644
--- a/docs/reproducibility.md
+++ b/docs/reproducibility.md
@@ -75,6 +75,56 @@ The current protocol fixes `N * batch = 2^22` for length comparisons. Do not
 use it to infer independent batch scaling; that requires holding `N` fixed and
 sweeping batch separately.
 
+Generate and run the orthogonal length/batch suite with:
+
+```bash
+python3 scripts/generate_scaling_suite.py \
+  --spec config/v100_scaling_space.json \
+  --output config/v100_scaling_suite.json
+
+python3 scripts/run_comprehensive_suite.py \
+  --manifest config/v100_scaling_suite.json --mode full \
+  --output results/v100_scaling_full_raw.csv
+
+python3 scripts/summarize_scaling_suite.py \
+  results/v100_scaling_full_raw.csv \
+  --output results/v100_scaling_full_summary.csv \
+  --markdown results/v100_scaling_full_report.md
+```
+
+Rows below the default 0.020 ms timing floor are retained for transparency but
+cannot define the reported peak or saturation batch.
+
+After all raw records are present, regenerate the V100 scaling, selector,
+external-baseline, and NCU analyses together without modifying raw data:
+
+```bash
+./scripts/reproduce_v100_analysis.sh
+```
+
+Evaluate the V100-calibrated selector without using the target shape's own
+timing:
+
+```bash
+python3 scripts/select_mapping.py --evaluate --top-k 3 \
+  --evaluation-output results/v100_mapping_selector_evaluation.csv \
+  --metrics-output results/v100_mapping_selector_metrics.json
+```
+
+Refresh matching-protocol external baselines with:
+
+```bash
+python3 scripts/run_external_baseline_suite.py --resume \
+  --fht-python /home/wt/.conda/envs/cubutterfly-baselines/bin/python \
+  --gpuntt-binary /tmp/gpuntt_merge_gap_bench \
+  --output results/v100_external_baselines_raw.csv
+
+python3 scripts/summarize_external_baseline_suite.py \
+  results/v100_external_baselines_raw.csv \
+  --output results/v100_external_baselines_summary.csv \
+  --markdown results/v100_external_baselines_report.md
+```
+
 ## 4. Generated Design Points
 
 The build invokes:
diff --git a/docs/research_status.md b/docs/research_status.md
new file mode 100644
index 0000000..b9d1f4d
--- /dev/null
+++ b/docs/research_status.md
@@ -0,0 +1,135 @@
+# Research Status: V100 Evidence Closure
+
+## Scope
+
+cuButterfly is a single-GPU research artifact for hardware-mapped space-time
+parallelism across regular butterfly computations. V100 is the only fully
+measured hardware target. Cross-GPU transfer is explicitly future work and is
+not used to support any current portability claim.
+
+## Research Claims And Evidence
+
+| Claim | Evidence | Current result |
+|:--|:--|:--|
+| Logical factorization is independent of physical execution | controlled `D2/D3/D4 -> P2` FFT lowering | the same physical schedule agrees within 1.8% |
+| Processing units are replaceable mapping parameters | scalar, register, warp, cuFFTDx, TurboFFT, WMMA, radix and reduction alternatives | winners change with operator, length, batch and precision |
+| Boundary realization affects the optimum without changing the paradigm | scalar versus paired 128-bit online cuFFTDx boundaries | best-point gain is 0.6%-13.5% across six long-FFT shapes |
+| The physical-unit gain has a counter-level mechanism | fixed-mapping pre/post NCU capture at `logN=20`, batch 16 | CUDA-event -10.5%, replay -9.3%, warp instructions -19.6%, unchanged DRAM writes |
+| Static hardware constraints are useful but insufficient for final ranking | 48-candidate FFT static-score evaluation | top-1 geomean regret 1.0762x; worst 1.4220x |
+| A small hardware calibration set can replace exhaustive timing | leave-one-batch-out FFT interpolation | top-3 geomean regret 1.0007x, worst 1.0020x using 6.2% of candidates |
+| The selection method extends beyond FFT | leave-one-complete-shape-out selector over NTT/FWHT/XOR-zeta | 93.88% top-1, 100% top-3, 1.0049x geomean regret |
+
+The static-model failure is part of the result, not a row to hide. Resource
+legality, occupancy, waves, and issued work provide a useful shortlist, but do
+not capture launch-limited low-batch behavior accurately enough. The supported
+method is therefore hierarchical: static legality and service constraints,
+then a small measured calibration set, then dispatch.
+
+## Current Performance Boundary
+
+The latest matching-protocol FP32 long-FFT comparison uses five process trials,
+1000 warmups, 100 timed repetitions, correctness preflight, and resident CUDA
+event time.
+
+| Shape | cuButterfly | cuFFT | VkFFT | cuButterfly/cuFFT |
+|:--|--:|--:|--:|--:|
+| `logN=18`, batch 16 | 0.195942 ms | 0.211098 ms | 0.201103 ms | 1.077x |
+| `logN=20`, batch 4 | 0.214733 ms | 0.210330 ms | 0.206520 ms | 0.979x |
+| FP64 `logN=14`, batch 256 | 0.340173 ms | 0.344433 ms | not measured | 1.013x |
+| FP64 `logN=16`, batch 64 | 0.339364 ms | 0.343040 ms | not measured | 1.011x |
+| FP64 `logN=17`, batch 32 | 0.346307 ms | 0.395213 ms | not measured | 1.141x |
+| FP64 `logN=18`, batch 16 | 0.354877 ms | 0.421970 ms | not measured | 1.189x |
+
+The broader design scan reaches 1.085x cuFFT at `logN=18`, batch 2 and 1.030x
+at `logN=20`, batch 2. At saturated `logN=20` batch 8/16 it reaches
+0.962x/0.954x. These focused results use a different batch protocol and must
+not be mixed into the comprehensive rows above.
+
+Matching-protocol external measurements show parity or advantage over Dao FHT
+on the qualified large FWHT shapes and 1.109x-1.425x throughput over GPU-NTT on
+the matched natural-order NTT shapes. XOR-zeta remains an internal architecture
+ablation because no maintained matching external baseline has been identified.
+
+## Semantic Coverage
+
+| Operator | Numeric coverage | Measured lengths | Additional contracts |
+|:--|:--|:--|:--|
+| FFT | FP16/FP32 accumulation, FP32, FP64 | 3, 8, 12, 14, 16, 18, 20 | forward/inverse, normalized inverse, in/out-of-place, stride 2 |
+| NTT | 30-bit/32-bit and 60-bit/64-bit | 12, 16, 20 | forward/inverse, natural and native bit-reversed order |
+| FWHT | FP32, FP64 | 8, 12, 15, 20 | forward, multiple exchange and residency choices |
+| XOR-zeta | uint32 | 8, 12, 20 | forward/inverse, multiple mapping families |
+
+Coverage establishes generality of the abstraction, not universal superiority.
+The original FP64 scalar row remains 0.642x cuFFT in the comprehensive suite.
+A controlled follow-up first scans 264 scalar mappings and confirms the winner
+at 0.658x, then replaces the local unit with double-precision cuFFTDx and reaches
+0.893x with table twiddles. Register recurrence reduces the selected prefix's
+table lookups and raises the final result to 0.948x. This isolates most of the
+former deficit in the physical unit and its precision-specific CTA/EPT mapping.
+The controlled NCU capture shows recurrence reduces prefix replay time by
+17.5% and warp instructions by 6.9%, while spending 8.4% more FP64 instructions
+with unchanged registers, shared allocation, and waves/SM. Prefix DRAM peak
+rises from 60.2% to 72.9%; suffix time is effectively unchanged. The remaining 5.5%
+event-time gap is now localized to shared exchange and address work: total
+shared-bank conflicts remain unchanged and warp instructions are still 2.06x
+cuFFT.
+An XOR-swizzled prefix then redistributes the same-capacity shared slot layout
+and reaches 0.353526 ms, or 0.970x cuFFT. The complete 36-point remap retains
+the same `256/4 + 128/8` winner, so this is a boundary-layout gain rather than
+a mapping-selection artifact. NCU confirms that it cuts prefix shared conflicts
+by 53.5% and prefix replay by 5.3%, raising peak DRAM utilization from 72.9% to
+77.0%; the suffix remains unchanged. Its 10.0% increase in prefix warp
+instructions identifies swizzled address generation as the next optimization
+target. The implemented strength reduction computes each swizzled pointer once,
+advances it by a compile-time stride, and hoists invariant transform/global
+address work out of the staging loops. It lowers linear recurrence from
+0.361708 ms to 0.345027 ms and XOR swizzle from 0.353526 ms to 0.342098 ms.
+The latter matches the 0.342856 ms cuFFT measurement at 1.002x throughput; five
+trial ranges are 0.341893-0.342170 ms and 0.342610-0.343040 ms, respectively.
+This is parity evidence rather than a claim of a robust lead. Updated NCU
+counters confirm the predicted mechanism: versus the pre-optimization XOR
+kernel, prefix warp instructions fall 26.8%, prefix replay falls 8.3%, and
+prefix shared conflicts fall 8.6%; suffix replay changes by less than 0.4%.
+The full XOR path now replays 2.5% below cuFFT while executing 1.83x its warp
+instructions, 3.62x its integer instructions, and about 114x its shared
+conflicts. Prefix registers rise from 48 to 64 and the register block limit
+falls from 5 to 4, so strength reduction exchanges occupancy for substantially
+less dynamic address work.
+
+The FP64 adapter now instantiates 128/256/512-point segments and covers every
+two-segment composition whose dimensions are both `logN=7..9`. A 648-point
+coarse scan selects distinct mappings for `logN=14..18`; a subsequent
+five-trial, execution-order-interleaved matrix covers batch 1..64. Applying the
+existing 0.020-ms timing floor leaves 25 stable shapes: 20 have higher median
+throughput than cuFFT and 19 have completely separated faster trial ranges.
+All 13 stable `logN=17/18` shapes are faster. The five remaining median deficits
+are confined to `logN=14..16` crossover batches and range from 0.1% to 3.2%.
+
+## Remaining Work
+
+1. **FP64 crossover margin:** target `logN=14..16` medium-batch launch and
+   boundary overhead; exhaustive remapping did not remove all five deficits.
+2. **Cross-GPU transfer:** capture a newer GPU profile, predict without its
+   timings, and report pre/post-calibration regret. This is the only deferred
+   architecture-level validation item.
+
+The repository does not currently claim a production cuFFT API replacement,
+non-power-of-two coverage, universal library superiority, or architecture
+portability beyond V100.
+
+## Reproduction Map
+
+- FFT mapping and vectorization: `results/v100_fft_pipeline_vectorized_*`
+- FFT prediction evaluation: `results/v100_fft_pipeline_model_*`
+- latest comprehensive FFT: `results/comprehensive_v100_vectorized_fft_*`
+- cross-operator semantics: `results/comprehensive_v100_full_*`
+- calibrated selector: `results/v100_mapping_selector_*`
+- matching external baselines: `results/v100_external_baselines_*`
+- counter attribution: `results/ncu_scaling_crossovers/`
+- vectorized FFT attribution: `results/ncu_fft_vectorized/`
+- FP64 scalar/core/mapping validation: `results/fp64_*logN16*`
+- FP64 length/batch robustness: `results/fp64_robustness_*`
+- FP64 privileged counter command: `scripts/profile_fp64_fft_ncu.sh`
+
+Run `./scripts/reproduce_v100_analysis.sh` to regenerate derived artifacts from
+the checked-in raw measurements. It does not recollect timings or counters.
diff --git a/docs/v100_external_baselines.md b/docs/v100_external_baselines.md
new file mode 100644
index 0000000..78eb7f1
--- /dev/null
+++ b/docs/v100_external_baselines.md
@@ -0,0 +1,54 @@
+# V100 Matching-Protocol External Baselines
+
+## Protocol
+
+This refresh runs each local/external pair with the same workload semantics,
+1000 warmups, 100 repetitions, five independently launched process trials,
+randomized case order, and correctness verification.
+
+- Dao-AILab `fast-hadamard-transform`: commit
+  `e7706faf8d1c3b9f241e36860640ad1dac644ede`, PyTorch 2.1.2 with CUDA 11.8,
+  plus the recorded `sm_70` build patch.
+- GPU-NTT: commit `d03c5eaeadaa780d153496afcb3b6a9b79a13a63`, built with CUDA 11.8 for
+  `sm_70`.
+- GPU-NTT and cuNTT both use modulus `576460756061519873`.
+- Natural-order `logN=16` includes GPU-NTT's required output permutation;
+  native bit-reversed `logN=20` excludes it for both implementations.
+
+Rows below 0.020 ms are retained but are not used for stable latency claims.
+The complete table is
+[`v100_external_baselines_report.md`](../results/v100_external_baselines_report.md).
+
+## Qualified Results
+
+Ratios are cuButterfly/cuNTT throughput divided by external throughput.
+
+| Operator | Contract | Batch | Ratio | Interpretation |
+|:--|:--|--:|--:|:--|
+| FWHT FP32 | `logN=8`, natural | 65,536 | 1.001x | parity with Dao FHT |
+| FWHT FP32 | `logN=15`, natural | 256 | 1.082x | cuButterfly ahead |
+| FWHT FP32 | `logN=15`, natural | 512 | 1.076x | cuButterfly ahead; one timing outlier |
+| NTT 60-bit | `logN=16`, natural | 4 | 1.109x | cuNTT ahead; one timing outlier in each row |
+| NTT 60-bit | `logN=16`, natural | 64 | 1.393x | cuNTT ahead |
+| NTT 60-bit | `logN=16`, natural | 256 | 1.425x | cuNTT ahead |
+| NTT 60-bit | `logN=20`, bit-reversed | 2 | 1.139x | compact stage ahead |
+| NTT 60-bit | `logN=20`, bit-reversed | 4 | 1.168x | compact stage ahead |
+| NTT 60-bit | `logN=20`, bit-reversed | 16 | 1.192x | compact stage ahead; one local timing outlier |
+
+The low-batch FWHT rows are below the timing floor and do not support a latency
+claim. This refresh supersedes the historical Dao/GPU-NTT performance rows
+when the listed semantics match.
+
+## Reproduction
+
+```bash
+python3 scripts/run_external_baseline_suite.py --resume \
+  --fht-python /home/wt/.conda/envs/cubutterfly-baselines/bin/python \
+  --gpuntt-binary /tmp/gpuntt_merge_gap_bench \
+  --output results/v100_external_baselines_raw.csv
+
+python3 scripts/summarize_external_baseline_suite.py \
+  results/v100_external_baselines_raw.csv \
+  --output results/v100_external_baselines_summary.csv \
+  --markdown results/v100_external_baselines_report.md
+```
diff --git a/docs/v100_mapping_selector.md b/docs/v100_mapping_selector.md
new file mode 100644
index 0000000..6680425
--- /dev/null
+++ b/docs/v100_mapping_selector.md
@@ -0,0 +1,61 @@
+# V100 Calibrated Mapping Selector
+
+## Scope
+
+The first selector ranks already measured internal candidates for a covered
+V100 semantic contract. It is deliberately not a cross-GPU model and does not
+invent support for unseen operators, lengths, precision, layout, or output
+order.
+
+The selector reads the generated scaling manifest, measured scaling summary,
+and V100 hardware profile. It reports the mapping family separately from the
+processing unit, checks basic hardware legality, interpolates log-latency over
+the remaining batch measurements, and attaches resource-oriented explanations
+such as batch concurrency and working-set size relative to L2.
+
+## Validation
+
+Every complete `(operator, precision, logN, batch)` shape is held out before
+its candidates are ranked. Thus the target timing is not used in its own
+prediction.
+
+| Metric | V100 result |
+|:--|--:|
+| evaluated multi-candidate shapes | 49 |
+| operators | FWHT, NTT, XOR-zeta |
+| top-1 accuracy | 93.88% |
+| top-3 recall | 100.00% |
+| geometric-mean regret | 1.0049x |
+| worst regret | 1.1532x |
+| top-1 candidate reduction | 50.00% |
+
+NTT selects the measured winner for all 14 shapes. The three misses are FWHT
+`logN=15`, batch 4 at the online-to-warp crossover, and the extrapolated
+largest-batch points for FWHT and XOR-zeta `logN=8`. These are useful failure
+boundaries rather than rows to hide.
+
+Current groups contain only two internal candidates. Top-3 recall is therefore
+an acceptance check, not evidence of aggressive top-3 pruning. FFT is also
+excluded from the internal validation because the scaling manifest currently
+contains one cuButterfly implementation per FFT length; cuFFT and VkFFT remain
+external baselines rather than architecture candidates.
+
+The separate FFT pipeline evaluation closes that gap over 48 internal
+candidates per shape. Static-only ranking is insufficient, but
+leave-one-batch-out calibration reaches 1.0007x top-3 geometric-mean regret and
+1.0020x worst regret while returning 6.2% of candidates. See
+[`v100_fft_pipeline_model_report.md`](../results/v100_fft_pipeline_model_report.md).
+
+## Commands
+
+```bash
+python3 scripts/select_mapping.py --evaluate --top-k 3 \
+  --evaluation-output results/v100_mapping_selector_evaluation.csv \
+  --metrics-output results/v100_mapping_selector_metrics.json
+
+python3 scripts/select_mapping.py \
+  --operator fwht --precision fp32 --logN 15 --batch 16 --top-k 2
+```
+
+An unseen shape fails with `measurement is required`; it is not silently
+assigned the nearest measured configuration.
diff --git a/docs/v100_ncu_attribution.md b/docs/v100_ncu_attribution.md
new file mode 100644
index 0000000..6efc016
--- /dev/null
+++ b/docs/v100_ncu_attribution.md
@@ -0,0 +1,53 @@
+# V100 Counter Attribution
+
+## Result
+
+The targeted NCU experiment covers 22 FFT/FWHT implementation-shape pairs and
+37 kernels. CUDA-event measurements remain the performance authority; NCU
+replay is used only to attribute grid coverage, residency, data service, and
+stall behavior. The complete counter table and generated analysis are in
+[`attribution.md`](../results/ncu_scaling_crossovers/attribution.md).
+
+## Architecture Findings
+
+| Boundary | Counter evidence | Architecture interpretation |
+|:--|:--|:--|
+| FFT `logN=14`, batch 16 | direct has 0.20 waves/SM and one resident 1024-thread CTA/SM | insufficient `Ub` grid coverage; the local core is not the limiting factor |
+| FFT `logN=18`, batch 64 | online has 1.60x warp instructions, 9.50x bank conflicts, and lower DRAM utilization than cuFFT | extra exchange and synchronization reduce useful work per warp |
+| FFT `logN=20`, batch 16 | equal aggregate waves, but online has 2.00x warp instructions and 9.42x bank conflicts | occupancy cannot close the gap; the prefix/core/layout composition must improve |
+| FWHT `logN=15`, batch 4 to 16 | warp-register has only 0.05 to 0.20 waves/SM but 0.07x the online warp instructions at batch 16 | low batch favors `Ud` decomposition; sufficient `Ub` favors register-resident `Td` reuse |
+
+For FFT `logN=20`, the online first pass consumes 61.8% of profiled time and
+reaches only 56.6% of peak DRAM, while its second pass reaches 85.3%. This
+identifies prefix/suffix imbalance as the next concrete FFT optimization target.
+
+## Post-Optimization Validation
+
+The subsequent paired 128-bit boundary implementation was profiled with the
+same 512/512-thread, EPT 8/8 physical mapping. Relative to the archived
+pre-vector capture, it reduces CUDA-event time by 10.5%, NCU replay time by
+9.3%, and warp instructions by 19.6%, while DRAM writes are unchanged. This
+confirms that the improvement removes boundary instruction/transaction
+overhead rather than a global handoff.
+
+The event-selected 256/128-thread mapping is another 7.8% faster than the
+post-vector fixed point, although NCU replay reverses that ordering by 2.8%.
+The complete controlled table is
+[`attribution.md`](../results/ncu_fft_vectorized/attribution.md).
+
+## Methodological Consequence
+
+The selector must model three quantities independently:
+
+1. **grid coverage**: batch and spatial data unfolding translated to waves/SM;
+2. **residency**: register/shared allocations translated to resident CTAs;
+3. **useful work per resident warp**: instructions, exchange conflicts, barrier
+   stalls, and scoreboard stalls.
+
+Maximizing occupancy alone is incorrect. Both long online FFT mappings expose
+at least as many active warps as cuFFT while reaching a lower saturated
+throughput ceiling.
+
+Small cases may report zero DRAM traffic because the collection uses
+`--cache-control none`, NCU replay, and working sets that fit in V100's L2. The
+report therefore does not interpret those zeros as zero algorithmic traffic.
diff --git a/docs/v100_scaling_results.md b/docs/v100_scaling_results.md
new file mode 100644
index 0000000..deb08c3
--- /dev/null
+++ b/docs/v100_scaling_results.md
@@ -0,0 +1,102 @@
+# V100 Orthogonal Length/Batch Scaling
+
+This experiment separates transform length from batch instead of fixing only
+`N * batch`. It measures 184 cases and 920 independent process trials across
+FFT, NTT, FWHT, and XOR-zeta on the Tesla V100-SXM2-16GB. Every implementation
+passes a batch-1 correctness preflight. The compact source space is
+[`v100_scaling_space.json`](../config/v100_scaling_space.json); its generated
+manifest is [`v100_scaling_suite.json`](../config/v100_scaling_suite.json).
+
+## Protocol
+
+- fixed `logN`, independently swept power-of-two batch;
+- no case exceeds `2^24` resident points;
+- 1000 warmups, 100 measured repetitions, and five process trials;
+- randomized case/trial order and durable per-sample output;
+- peak and `Batch@90%` exclude unstable rows and rows below 0.020 ms;
+- the V100 application clock is 1312 MHz and boost clock is 1530 MHz, so
+  process-level bimodality remains explicit rather than silently filtered.
+
+The complete generated table is
+[`v100_scaling_full_report.md`](../results/v100_scaling_full_report.md), with
+raw samples in [`v100_scaling_full_raw.csv`](../results/v100_scaling_full_raw.csv).
+
+## Saturation Points
+
+`Batch@90%` is the smallest measured batch reaching 90% of an implementation's
+qualified peak measured point throughput.
+
+| Operator | logN | Implementation | Batch@90% | Peak batch | Peak Gpoint/s |
+|:--|--:|:--|--:|--:|--:|
+| FFT | 8 | cuButterfly cuFFTDx | 4,096 | 65,536 | 51.206 |
+| FFT | 14 | cuButterfly cuFFTDx direct | 1,024 | 1,024 | 44.142 |
+| FFT | 18 | cuButterfly online | 2 | 16 | 20.450 |
+| FFT | 20 | cuButterfly online | 4 | 8 | 18.412 |
+| FWHT | 8 | warp-register | 16,384 | 65,536 | 102.056 |
+| FWHT | 15 | warp-register | 256 | 512 | 86.876 |
+| FWHT | 20 | online radix-4 | 2 | 16 | 13.609 |
+| NTT | 12 | Hybrid2D radix-4 | 1,024 | 4,096 | 31.167 |
+| NTT | 16 | Hybrid2D radix-4 | 64 | 256 | 15.687 |
+| NTT | 20 | compact stage | 2 | 16 | 12.769 |
+| XOR-zeta | 8 | radix-4 | 16,384 | 65,536 | 95.802 |
+| XOR-zeta | 20 | online radix-4 | 2 | 16 | 13.617 |
+
+The required batch falls rapidly as a transform exposes more internal
+parallelism. It is therefore incorrect to treat one fixed batch or one fixed
+total-point workload as a hardware-independent mapping property.
+
+## FFT Against cuFFT
+
+Ratios are cuButterfly throughput divided by cuFFT throughput at the same
+length, batch, precision, direction, placement, and stride.
+
+| logN | Batch range | Observed ratio | Interpretation |
+|--:|:--|:--|:--|
+| 8 | 4,096-65,536 | 0.994x-1.000x | parity after timing-floor and saturation filtering |
+| 14 | 1-64 | 0.578x-0.872x | direct core lacks enough independent CTAs |
+| 14 | 256-1,024 | 0.998x-1.069x | catches and then exceeds cuFFT after saturation |
+| 18 | 2-16 | 1.030x-1.150x | online composition wins in the intermediate-batch region |
+| 18 | 32-64 | 0.921x-0.840x | cuFFT reaches a higher large-batch ceiling |
+| 20 | 1-16 | 0.778x-0.959x | gap remains; best ratio occurs at batch 2 |
+
+This exposes two different FFT limitations. At `logN=14`, the local direct
+unit is strong but needs batch concurrency. At `logN=18`, cuButterfly saturates
+early near 20.45 Gpoint/s while cuFFT continues to 23.75 Gpoint/s. At
+`logN=20`, both early saturation and a lower ceiling remain.
+
+## Mapping Crossovers
+
+The best processing unit is not constant over batch:
+
+| Workload | Low-batch choice | Crossover | Saturated choice |
+|:--|:--|:--|:--|
+| FWHT FP32 `logN=15` | online radix-4 | between batch 4 and 16 | warp-register, up to 6.445x at batch 512 |
+| FWHT FP32 `logN=20` | online radix-4 | none in measured range | online, about 1.52x for batch 2-16 |
+| NTT 30-bit `logN=12` | radix-4 | none | radix-4, 1.11x-1.18x |
+| NTT 60-bit `logN=16` | radix-4 | none | radix-4, advantage grows to 1.104x |
+| XOR-zeta `logN=8` | radix-4 | none | radix-4, advantage contracts from 1.165x to 1.022x |
+
+The FWHT crossover is direct evidence that batch unfolding belongs in the
+architecture mapping. The shrinking XOR radix advantage shows the opposite
+effect: once memory throughput dominates, local arithmetic organization has
+less influence.
+
+## Timing Quality
+
+Of 184 cases, 101 are stable, 13 are stable with one reported outlier, and 69
+fall below the 0.020 ms timing floor. One original `fft14_cufft_b64` row is
+unstable because it crosses V100 clock modes; an independent five-trial
+confirmation is stable but lands on the other clock mode, so the original row
+is excluded from saturation selection rather than replaced. No low-duration
+row is used to claim a latency advantage.
+
+## Next Profiling Targets
+
+1. FFT `logN=14`, batch 16/256/1024: attribute the direct-unit concurrency
+   threshold to CTA count, occupancy, and launch amortization.
+2. FFT `logN=18`, batch 2/16/64: explain why cuButterfly saturates early while
+   cuFFT continues scaling.
+3. FFT `logN=20`, batch 2/8/16: separate the intermediate-batch near-parity
+   point from the lower large-batch throughput ceiling.
+4. FWHT `logN=15`, batch 4/16: measure the online-to-warp mapping crossover.
+
diff --git a/figures/cubutterfly_concept.dot b/figures/cubutterfly_concept.dot
index 9155dde..d692d8e 100644
--- a/figures/cubutterfly_concept.dot
+++ b/figures/cubutterfly_concept.dot
@@ -3,9 +3,10 @@ digraph cuButterfly {
     rankdir=LR,
     bgcolor="transparent",
     pad=0.20,
-    nodesep=0.38,
-    ranksep=0.72,
-    fontname="Helvetica"
+    nodesep=0.32,
+    ranksep=0.68,
+    fontname="Helvetica",
+    compound=true
   ];
   node [
     shape=box,
@@ -14,32 +15,58 @@ digraph cuButterfly {
     fillcolor="#f7f8fa",
     fontcolor="#17202a",
     fontname="Helvetica",
-    fontsize=11,
-    margin="0.16,0.10"
+    fontsize=10,
+    margin="0.14,0.09"
   ];
-  edge [color="#596579", penwidth=1.4, arrowsize=0.7, fontname="Helvetica", fontsize=9];
+  edge [color="#596579", penwidth=1.3, arrowsize=0.7, fontname="Helvetica", fontsize=9];
+
+  subgraph cluster_domain {
+    label="Logical domain D x S";
+    color="#89afd0";
+    style="rounded";
+    fontcolor="#274f70";
+    data [label="Data D\nindependent groups", fillcolor="#e8f1fb", color="#27658f"];
+    stage [label="Stages S\nordered dependencies", fillcolor="#e8f1fb", color="#27658f"];
+  }
 
-  graph_model [label="Regular butterfly graph\nstages x independent data", fillcolor="#e8f1fb", color="#27658f"];
-  factorization [label="Space-time factorization\n(Us, Ts, Ud, Td)", fillcolor="#e8f1fb", color="#27658f"];
-  search [label="Hardware-constrained search\nresidency + transport + layout", fillcolor="#eef7ec", color="#3f7d43"];
-  mapping [label="Generated CUDA mapping\n(F, Q, Hs, Rs, Rd, L)", fillcolor="#eef7ec", color="#3f7d43"];
+  subgraph cluster_factors {
+    label="Two dimensions x two unfoldings";
+    color="#8ebc91";
+    style="rounded";
+    fontcolor="#356a39";
+    ud [label="Data-space Ud\nparallel groups", fillcolor="#eef7ec", color="#3f7d43"];
+    td [label="Data-time Td\nworker reuse", fillcolor="#eef7ec", color="#3f7d43"];
+    us [label="Stage-space Us\nparallel service", fillcolor="#eef7ec", color="#3f7d43"];
+    ts [label="Stage-time Ts\nresident reuse", fillcolor="#eef7ec", color="#3f7d43"];
+  }
 
-  hardware [label="GPU profile\nSMs | registers | shared memory\nbarriers | bandwidth | cache", fillcolor="#fff3dc", color="#9a6a16"];
-  units [label="Processing-unit pool\nradix-2/4/8 | Shoup | Barrett\nGauss-3 | register | WMMA", fillcolor="#fff3dc", color="#9a6a16"];
+  subgraph cluster_gpu {
+    label="Hardware-selected GPU realization";
+    color="#ddb66c";
+    style="rounded";
+    fontcolor="#80550f";
+    placement [label="grid / CTA / warp\nplacement", fillcolor="#fff3dc", color="#9a6a16"];
+    residence [label="register / shared\nresidence", fillcolor="#fff3dc", color="#9a6a16"];
+    transport [label="shuffle / shared / barrier\ntransport", fillcolor="#fff3dc", color="#9a6a16"];
+  }
 
-  fft [label="FFT", fillcolor="#f5ebf8", color="#7d4b8f"];
-  ntt [label="NTT", fillcolor="#f5ebf8", color="#7d4b8f"];
-  fwht [label="FWHT", fillcolor="#f5ebf8", color="#7d4b8f"];
-  xor [label="XOR-zeta", fillcolor="#f5ebf8", color="#7d4b8f"];
-  counters [label="Measured counters and timing\nNCU | NSYS | verified sweeps", fillcolor="#fbeaea", color="#9b4444"];
+  unit [label="Replaceable processing unit\nradix | cuFFTDx | modular | FWHT | WMMA", fillcolor="#f5ebf8", color="#7d4b8f"];
+  boundary [label="Online reorder or global handoff\nonly when ownership/layout requires it", fillcolor="#fbeaea", color="#9b4444"];
+  measure [label="Verified timing + NCU counters\ncalibrate selection", fillcolor="#fbeaea", color="#9b4444"];
 
-  graph_model -> factorization -> search -> mapping;
-  hardware -> search;
-  units -> search;
-  mapping -> fft;
-  mapping -> ntt;
-  mapping -> fwht;
-  mapping -> xor;
-  mapping -> counters [label="measure", color="#9b4444"];
-  counters -> search [label="calibrate", color="#9b4444"];
+  data -> ud;
+  data -> td;
+  stage -> us;
+  stage -> ts;
+  ud -> placement;
+  td -> residence;
+  us -> transport;
+  ts -> residence;
+  placement -> unit;
+  residence -> unit;
+  transport -> unit;
+  unit -> boundary;
+  boundary -> residence [label="next group", style=dashed, color="#9b4444", constraint=false];
+  boundary -> measure;
+  measure -> placement [label="reselect", style=dashed, color="#9b4444", constraint=false];
 }
diff --git a/figures/cubutterfly_concept.svg b/figures/cubutterfly_concept.svg
index 1a809ad..dd48750 100644
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-<path fill="#eef7ec" stroke="#3f7d43" d="M667,-121C667,-121 495,-121 495,-121 489,-121 483,-115 483,-109 483,-109 483,-95 483,-95 483,-89 489,-83 495,-83 495,-83 667,-83 667,-83 673,-83 679,-89 679,-95 679,-95 679,-109 679,-109 679,-115 673,-121 667,-121"/>
-<text text-anchor="middle" x="581" y="-105.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">Hardware&#45;constrained search</text>
-<text text-anchor="middle" x="581" y="-93.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">residency + transport + layout</text>
+<!-- td -->
+<g id="node4" class="node">
+<title>td</title>
+<path fill="#eef7ec" stroke="#3f7d43" d="M350.5,-111C350.5,-111 289.5,-111 289.5,-111 283.5,-111 277.5,-105 277.5,-99 277.5,-99 277.5,-87 277.5,-87 277.5,-81 283.5,-75 289.5,-75 289.5,-75 350.5,-75 350.5,-75 356.5,-75 362.5,-81 362.5,-87 362.5,-87 362.5,-99 362.5,-99 362.5,-105 356.5,-111 350.5,-111"/>
+<text text-anchor="middle" x="320" y="-96" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Data&#45;time Td</text>
+<text text-anchor="middle" x="320" y="-85" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">worker reuse</text>
 </g>
-<!-- factorization&#45;&gt;search -->
+<!-- data&#45;&gt;td -->
 <g id="edge2" class="edge">
-<title>factorization&#45;&gt;search</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M395.9,-153.97C429.73,-144.42 470.8,-132.83 505.55,-123.02"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="506.35,-125.34 512.42,-121.08 505.01,-120.62 506.35,-125.34"/>
+<title>data&#45;&gt;td</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M139.3,-93C179.33,-93 232.04,-93 270.01,-93"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="270.4,-95.45 277.4,-93 270.4,-90.55 270.4,-95.45"/>
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-<!-- mapping -->
-<g id="node4" class="node">
-<title>mapping</title>
-<path fill="#eef7ec" stroke="#3f7d43" d="M889,-206C889,-206 744,-206 744,-206 738,-206 732,-200 732,-194 732,-194 732,-180 732,-180 732,-174 738,-168 744,-168 744,-168 889,-168 889,-168 895,-168 901,-174 901,-180 901,-180 901,-194 901,-194 901,-200 895,-206 889,-206"/>
-<text text-anchor="middle" x="816.5" y="-190.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">Generated CUDA mapping</text>
-<text text-anchor="middle" x="816.5" y="-178.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">(F, Q, Hs, Rs, Rd, L)</text>
+<!-- stage -->
+<g id="node2" class="node">
+<title>stage</title>
+<path fill="#e8f1fb" stroke="#27658f" d="M133,-170C133,-170 28,-170 28,-170 22,-170 16,-164 16,-158 16,-158 16,-146 16,-146 16,-140 22,-134 28,-134 28,-134 133,-134 133,-134 139,-134 145,-140 145,-146 145,-146 145,-158 145,-158 145,-164 139,-170 133,-170"/>
+<text text-anchor="middle" x="80.5" y="-155" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Stages S</text>
+<text text-anchor="middle" x="80.5" y="-144" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">ordered dependencies</text>
+</g>
+<!-- us -->
+<g id="node5" class="node">
+<title>us</title>
+<path fill="#eef7ec" stroke="#3f7d43" d="M356,-229C356,-229 284,-229 284,-229 278,-229 272,-223 272,-217 272,-217 272,-205 272,-205 272,-199 278,-193 284,-193 284,-193 356,-193 356,-193 362,-193 368,-199 368,-205 368,-205 368,-217 368,-217 368,-223 362,-229 356,-229"/>
+<text text-anchor="middle" x="320" y="-214" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Stage&#45;space Us</text>
+<text text-anchor="middle" x="320" y="-203" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">parallel service</text>
 </g>
-<!-- search&#45;&gt;mapping -->
+<!-- stage&#45;&gt;us -->
 <g id="edge3" class="edge">
-<title>search&#45;&gt;mapping</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M634.4,-121.08C670.6,-134.25 718.81,-151.8 756.39,-165.48"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="755.86,-167.9 763.27,-167.99 757.53,-163.29 755.86,-167.9"/>
+<title>stage&#45;&gt;us</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M145.29,-168.82C162.09,-173.18 180.21,-177.82 197,-182 219.11,-187.5 243.54,-193.35 264.69,-198.34"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="264.35,-200.78 271.73,-200 265.48,-196.01 264.35,-200.78"/>
 </g>
-<!-- fft -->
+<!-- ts -->
+<g id="node6" class="node">
+<title>ts</title>
+<path fill="#eef7ec" stroke="#3f7d43" d="M353,-170C353,-170 287,-170 287,-170 281,-170 275,-164 275,-158 275,-158 275,-146 275,-146 275,-140 281,-134 287,-134 287,-134 353,-134 353,-134 359,-134 365,-140 365,-146 365,-146 365,-158 365,-158 365,-164 359,-170 353,-170"/>
+<text text-anchor="middle" x="320" y="-155" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Stage&#45;time Ts</text>
+<text text-anchor="middle" x="320" y="-144" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">resident reuse</text>
+</g>
+<!-- stage&#45;&gt;ts -->
+<g id="edge4" class="edge">
+<title>stage&#45;&gt;ts</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M145.15,-152C183.53,-152 231.79,-152 267.72,-152"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="267.73,-154.45 274.73,-152 267.73,-149.55 267.73,-154.45"/>
+</g>
+<!-- placement -->
 <g id="node7" class="node">
-<title>fft</title>
-<path fill="#f5ebf8" stroke="#7d4b8f" d="M1104.5,-357C1104.5,-357 1074.5,-357 1074.5,-357 1068.5,-357 1062.5,-351 1062.5,-345 1062.5,-345 1062.5,-333 1062.5,-333 1062.5,-327 1068.5,-321 1074.5,-321 1074.5,-321 1104.5,-321 1104.5,-321 1110.5,-321 1116.5,-327 1116.5,-333 1116.5,-333 1116.5,-345 1116.5,-345 1116.5,-351 1110.5,-357 1104.5,-357"/>
-<text text-anchor="middle" x="1089.5" y="-336.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">FFT</text>
+<title>placement</title>
+<path fill="#fff3dc" stroke="#9a6a16" d="M643.5,-70C643.5,-70 567.5,-70 567.5,-70 561.5,-70 555.5,-64 555.5,-58 555.5,-58 555.5,-46 555.5,-46 555.5,-40 561.5,-34 567.5,-34 567.5,-34 643.5,-34 643.5,-34 649.5,-34 655.5,-40 655.5,-46 655.5,-46 655.5,-58 655.5,-58 655.5,-64 649.5,-70 643.5,-70"/>
+<text text-anchor="middle" x="605.5" y="-55" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">grid / CTA / warp</text>
+<text text-anchor="middle" x="605.5" y="-44" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">placement</text>
 </g>
-<!-- mapping&#45;&gt;fft -->
-<g id="edge6" class="edge">
-<title>mapping&#45;&gt;fft</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M840.54,-206.17C872.85,-232.25 934.27,-278.99 993,-308 1012.73,-317.74 1036.23,-325.42 1054.97,-330.69"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="1054.77,-333.18 1062.17,-332.66 1056.07,-328.45 1054.77,-333.18"/>
+<!-- ud&#45;&gt;placement -->
+<g id="edge5" class="edge">
+<title>ud&#45;&gt;placement</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M366.55,-36.89C415.98,-40.03 494.97,-45.05 548.24,-48.43"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="548.11,-50.87 555.25,-48.87 548.42,-45.98 548.11,-50.87"/>
 </g>
-<!-- ntt -->
+<!-- residence -->
 <g id="node8" class="node">
-<title>ntt</title>
-<path fill="#f5ebf8" stroke="#7d4b8f" d="M1104.5,-294C1104.5,-294 1074.5,-294 1074.5,-294 1068.5,-294 1062.5,-288 1062.5,-282 1062.5,-282 1062.5,-270 1062.5,-270 1062.5,-264 1068.5,-258 1074.5,-258 1074.5,-258 1104.5,-258 1104.5,-258 1110.5,-258 1116.5,-264 1116.5,-270 1116.5,-270 1116.5,-282 1116.5,-282 1116.5,-288 1110.5,-294 1104.5,-294"/>
-<text text-anchor="middle" x="1089.5" y="-273.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">NTT</text>
+<title>residence</title>
+<path fill="#fff3dc" stroke="#9a6a16" d="M643.5,-129C643.5,-129 567.5,-129 567.5,-129 561.5,-129 555.5,-123 555.5,-117 555.5,-117 555.5,-105 555.5,-105 555.5,-99 561.5,-93 567.5,-93 567.5,-93 643.5,-93 643.5,-93 649.5,-93 655.5,-99 655.5,-105 655.5,-105 655.5,-117 655.5,-117 655.5,-123 649.5,-129 643.5,-129"/>
+<text text-anchor="middle" x="605.5" y="-114" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">register / shared</text>
+<text text-anchor="middle" x="605.5" y="-103" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">residence</text>
 </g>
-<!-- mapping&#45;&gt;ntt -->
-<g id="edge7" class="edge">
-<title>mapping&#45;&gt;ntt</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M874.78,-206.01C909.06,-217.37 953.51,-232.06 993,-245 1013.62,-251.75 1036.77,-259.27 1055.11,-265.21"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="1054.73,-267.66 1062.14,-267.48 1056.23,-263 1054.73,-267.66"/>
+<!-- td&#45;&gt;residence -->
+<g id="edge6" class="edge">
+<title>td&#45;&gt;residence</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M362.53,-95.64C411.54,-98.75 493.29,-103.94 548.03,-107.41"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="548.09,-109.87 555.23,-107.87 548.4,-104.98 548.09,-109.87"/>
 </g>
-<!-- fwht -->
+<!-- transport -->
 <g id="node9" class="node">
-<title>fwht</title>
-<path fill="#f5ebf8" stroke="#7d4b8f" d="M1106,-231C1106,-231 1073,-231 1073,-231 1067,-231 1061,-225 1061,-219 1061,-219 1061,-207 1061,-207 1061,-201 1067,-195 1073,-195 1073,-195 1106,-195 1106,-195 1112,-195 1118,-201 1118,-207 1118,-207 1118,-219 1118,-219 1118,-225 1112,-231 1106,-231"/>
-<text text-anchor="middle" x="1089.5" y="-210.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">FWHT</text>
+<title>transport</title>
+<path fill="#fff3dc" stroke="#9a6a16" d="M662,-188C662,-188 549,-188 549,-188 543,-188 537,-182 537,-176 537,-176 537,-164 537,-164 537,-158 543,-152 549,-152 549,-152 662,-152 662,-152 668,-152 674,-158 674,-164 674,-164 674,-176 674,-176 674,-182 668,-188 662,-188"/>
+<text text-anchor="middle" x="605.5" y="-173" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">shuffle / shared / barrier</text>
+<text text-anchor="middle" x="605.5" y="-162" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">transport</text>
+</g>
+<!-- us&#45;&gt;transport -->
+<g id="edge7" class="edge">
+<title>us&#45;&gt;transport</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M368.13,-204.18C412.12,-197.82 478.47,-188.23 529.69,-180.82"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="530.24,-183.22 536.81,-179.79 529.54,-178.37 530.24,-183.22"/>
 </g>
-<!-- mapping&#45;&gt;fwht -->
+<!-- ts&#45;&gt;residence -->
 <g id="edge8" class="edge">
-<title>mapping&#45;&gt;fwht</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M901.02,-195.01C952.2,-199.92 1015.03,-205.95 1053.4,-209.63"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="1053.54,-212.11 1060.74,-210.34 1054,-207.23 1053.54,-212.11"/>
+<title>ts&#45;&gt;residence</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M365.3,-145.59C414.63,-138.46 494.48,-126.91 548.21,-119.14"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="548.7,-121.55 555.28,-118.12 548,-116.7 548.7,-121.55"/>
 </g>
-<!-- xor -->
+<!-- unit -->
 <g id="node10" class="node">
-<title>xor</title>
-<path fill="#f5ebf8" stroke="#7d4b8f" d="M1115.5,-168C1115.5,-168 1063.5,-168 1063.5,-168 1057.5,-168 1051.5,-162 1051.5,-156 1051.5,-156 1051.5,-144 1051.5,-144 1051.5,-138 1057.5,-132 1063.5,-132 1063.5,-132 1115.5,-132 1115.5,-132 1121.5,-132 1127.5,-138 1127.5,-144 1127.5,-144 1127.5,-156 1127.5,-156 1127.5,-162 1121.5,-168 1115.5,-168"/>
-<text text-anchor="middle" x="1089.5" y="-147.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">XOR&#45;zeta</text>
+<title>unit</title>
+<path fill="#f5ebf8" stroke="#7d4b8f" d="M992,-129C992,-129 788,-129 788,-129 782,-129 776,-123 776,-117 776,-117 776,-105 776,-105 776,-99 782,-93 788,-93 788,-93 992,-93 992,-93 998,-93 1004,-99 1004,-105 1004,-105 1004,-117 1004,-117 1004,-123 998,-129 992,-129"/>
+<text text-anchor="middle" x="890" y="-114" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Replaceable processing unit</text>
+<text text-anchor="middle" x="890" y="-103" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">radix | cuFFTDx | modular | FWHT | WMMA</text>
 </g>
-<!-- mapping&#45;&gt;xor -->
+<!-- placement&#45;&gt;unit -->
 <g id="edge9" class="edge">
-<title>mapping&#45;&gt;xor</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M901.02,-175.6C948.31,-169.14 1005.56,-161.32 1044.25,-156.04"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="1044.65,-158.46 1051.26,-155.09 1043.99,-153.6 1044.65,-158.46"/>
-</g>
-<!-- counters -->
-<g id="node11" class="node">
-<title>counters</title>
-<path fill="#fbeaea" stroke="#9b4444" d="M1174,-105C1174,-105 1005,-105 1005,-105 999,-105 993,-99 993,-93 993,-93 993,-79 993,-79 993,-73 999,-67 1005,-67 1005,-67 1174,-67 1174,-67 1180,-67 1186,-73 1186,-79 1186,-79 1186,-93 1186,-93 1186,-99 1180,-105 1174,-105"/>
-<text text-anchor="middle" x="1089.5" y="-89.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">Measured counters and timing</text>
-<text text-anchor="middle" x="1089.5" y="-77.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">NCU | NSYS | verified sweeps</text>
+<title>placement&#45;&gt;unit</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M655.71,-62.28C694.2,-70.32 748.85,-81.73 795.58,-91.49"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="795.35,-93.94 802.71,-92.98 796.35,-89.15 795.35,-93.94"/>
 </g>
-<!-- mapping&#45;&gt;counters -->
+<!-- residence&#45;&gt;unit -->
 <g id="edge10" class="edge">
-<title>mapping&#45;&gt;counters</title>
-<path fill="none" stroke="#9b4444" stroke-width="1.4" d="M864.18,-167.89C899.4,-153.66 949,-134.01 993,-118 1002.77,-114.44 1013.16,-110.81 1023.35,-107.33"/>
-<polygon fill="#9b4444" stroke="#9b4444" stroke-width="1.4" points="1024.16,-109.64 1030,-105.07 1022.59,-105.01 1024.16,-109.64"/>
-<text text-anchor="middle" x="947" y="-144.8" font-family="Helvetica,sans-Serif" font-size="9.00">measure</text>
-</g>
-<!-- hardware -->
-<g id="node5" class="node">
-<title>hardware</title>
-<path fill="#fff3dc" stroke="#9a6a16" d="M418,-127C418,-127 237,-127 237,-127 231,-127 225,-121 225,-115 225,-115 225,-89 225,-89 225,-83 231,-77 237,-77 237,-77 418,-77 418,-77 424,-77 430,-83 430,-89 430,-89 430,-115 430,-115 430,-121 424,-127 418,-127"/>
-<text text-anchor="middle" x="327.5" y="-111.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">GPU profile</text>
-<text text-anchor="middle" x="327.5" y="-99.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">SMs | registers | shared memory</text>
-<text text-anchor="middle" x="327.5" y="-87.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">barriers | bandwidth | cache</text>
+<title>residence&#45;&gt;unit</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M655.71,-111C686.96,-111 728.86,-111 768.52,-111"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="768.9,-113.45 775.9,-111 768.9,-108.55 768.9,-113.45"/>
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-<!-- hardware&#45;&gt;search -->
-<g id="edge4" class="edge">
-<title>hardware&#45;&gt;search</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M430.07,-102C445.07,-102 460.54,-102 475.59,-102"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="475.94,-104.45 482.94,-102 475.94,-99.55 475.94,-104.45"/>
-</g>
-<!-- units -->
-<g id="node6" class="node">
-<title>units</title>
-<path fill="#fff3dc" stroke="#9a6a16" d="M405,-50C405,-50 250,-50 250,-50 244,-50 238,-44 238,-38 238,-38 238,-12 238,-12 238,-6 244,0 250,0 250,0 405,0 405,0 411,0 417,-6 417,-12 417,-12 417,-38 417,-38 417,-44 411,-50 405,-50"/>
-<text text-anchor="middle" x="327.5" y="-34.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">Processing&#45;unit pool</text>
-<text text-anchor="middle" x="327.5" y="-22.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">radix&#45;2/4/8 | Shoup | Barrett</text>
-<text text-anchor="middle" x="327.5" y="-10.2" font-family="Helvetica,sans-Serif" font-size="11.00" fill="#17202a">Gauss&#45;3 | register | WMMA</text>
-</g>
-<!-- units&#45;&gt;search -->
-<g id="edge5" class="edge">
-<title>units&#45;&gt;search</title>
-<path fill="none" stroke="#596579" stroke-width="1.4" d="M410.5,-50.11C442.89,-60.02 479.69,-71.29 510.71,-80.79"/>
-<polygon fill="#596579" stroke="#596579" stroke-width="1.4" points="510.24,-83.2 517.65,-82.91 511.67,-78.52 510.24,-83.2"/>
-</g>
-<!-- counters&#45;&gt;search -->
+<!-- transport&#45;&gt;unit -->
 <g id="edge11" class="edge">
-<title>counters&#45;&gt;search</title>
-<path fill="none" stroke="#9b4444" stroke-width="1.4" d="M992.63,-89.03C905.18,-91.79 776.27,-95.86 686.28,-98.71"/>
-<polygon fill="#9b4444" stroke="#9b4444" stroke-width="1.4" points="685.98,-96.26 679.06,-98.93 686.13,-101.16 685.98,-96.26"/>
-<text text-anchor="middle" x="816.5" y="-100.8" font-family="Helvetica,sans-Serif" font-size="9.00">calibrate</text>
+<title>transport&#45;&gt;unit</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M674.17,-155.87C710.43,-148.29 755.68,-138.84 795.28,-130.57"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="796.25,-132.87 802.6,-129.04 795.25,-128.08 796.25,-132.87"/>
+</g>
+<!-- boundary -->
+<g id="node11" class="node">
+<title>boundary</title>
+<path fill="#fbeaea" stroke="#9b4444" d="M1288,-129C1288,-129 1102,-129 1102,-129 1096,-129 1090,-123 1090,-117 1090,-117 1090,-105 1090,-105 1090,-99 1096,-93 1102,-93 1102,-93 1288,-93 1288,-93 1294,-93 1300,-99 1300,-105 1300,-105 1300,-117 1300,-117 1300,-123 1294,-129 1288,-129"/>
+<text text-anchor="middle" x="1195" y="-114" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Online reorder or global handoff</text>
+<text text-anchor="middle" x="1195" y="-103" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">only when ownership/layout requires it</text>
+</g>
+<!-- unit&#45;&gt;boundary -->
+<g id="edge12" class="edge">
+<title>unit&#45;&gt;boundary</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M1004.26,-111C1029.92,-111 1057.14,-111 1082.72,-111"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="1082.88,-113.45 1089.88,-111 1082.88,-108.55 1082.88,-113.45"/>
+</g>
+<!-- boundary&#45;&gt;residence -->
+<g id="edge13" class="edge">
+<title>boundary&#45;&gt;residence</title>
+<path fill="none" stroke="#9b4444" stroke-width="1.3" stroke-dasharray="5,2" d="M1125.5,-92.99C1089.6,-84.47 1044.74,-75.24 1004,-71 903.21,-60.51 876.65,-59.28 776,-71 774.53,-71.17 711.66,-86.05 662.92,-97.61"/>
+<polygon fill="#9b4444" stroke="#9b4444" stroke-width="1.3" points="662.09,-95.29 655.84,-99.28 663.22,-100.05 662.09,-95.29"/>
+<text text-anchor="middle" x="890" y="-73.8" font-family="Helvetica,sans-Serif" font-size="9.00">next group</text>
+</g>
+<!-- measure -->
+<g id="node12" class="node">
+<title>measure</title>
+<path fill="#fbeaea" stroke="#9b4444" d="M1512,-129C1512,-129 1363,-129 1363,-129 1357,-129 1351,-123 1351,-117 1351,-117 1351,-105 1351,-105 1351,-99 1357,-93 1363,-93 1363,-93 1512,-93 1512,-93 1518,-93 1524,-99 1524,-105 1524,-105 1524,-117 1524,-117 1524,-123 1518,-129 1512,-129"/>
+<text text-anchor="middle" x="1437.5" y="-114" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">Verified timing + NCU counters</text>
+<text text-anchor="middle" x="1437.5" y="-103" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#17202a">calibrate selection</text>
+</g>
+<!-- boundary&#45;&gt;measure -->
+<g id="edge14" class="edge">
+<title>boundary&#45;&gt;measure</title>
+<path fill="none" stroke="#596579" stroke-width="1.3" d="M1300.09,-111C1314.47,-111 1329.16,-111 1343.32,-111"/>
+<polygon fill="#596579" stroke="#596579" stroke-width="1.3" points="1343.68,-113.45 1350.68,-111 1343.68,-108.55 1343.68,-113.45"/>
+</g>
+<!-- measure&#45;&gt;placement -->
+<g id="edge15" class="edge">
+<title>measure&#45;&gt;placement</title>
+<path fill="none" stroke="#9b4444" stroke-width="1.3" stroke-dasharray="5,2" d="M1362.44,-92.93C1342.28,-88.5 1320.38,-84.14 1300,-81 1065.51,-44.91 781.53,-47.18 662.86,-50.15"/>
+<polygon fill="#9b4444" stroke="#9b4444" stroke-width="1.3" points="662.56,-47.71 655.63,-50.34 662.69,-52.61 662.56,-47.71"/>
+<text text-anchor="middle" x="1047" y="-59.8" font-family="Helvetica,sans-Serif" font-size="9.00">reselect</text>
 </g>
 </g>
 </svg>
diff --git a/include/cuntt/butterfly.hpp b/include/cuntt/butterfly.hpp
index fa32e41..4263c14 100644
--- a/include/cuntt/butterfly.hpp
+++ b/include/cuntt/butterfly.hpp
@@ -97,6 +97,23 @@ enum class CrossTwiddleMode {
 const char*      cross_twiddle_mode_name(CrossTwiddleMode mode) noexcept;
 CrossTwiddleMode parse_cross_twiddle_mode(const std::string& name);
 
+enum class DirectBoundary {
+    Strided,
+    TiledTranspose,
+    PrefixTiledTranspose,
+};
+
+const char*    direct_boundary_name(DirectBoundary boundary) noexcept;
+DirectBoundary parse_direct_boundary(const std::string& name);
+
+enum class FftBoundaryResidency {
+    GlobalScratch,
+    Fused,
+};
+
+const char*          fft_boundary_residency_name(FftBoundaryResidency residency) noexcept;
+FftBoundaryResidency parse_fft_boundary_residency(const std::string& name);
+
 enum class LocalExchange {
     SharedMemory,
     WarpRegister,
@@ -105,6 +122,14 @@ enum class LocalExchange {
 const char*   local_exchange_name(LocalExchange exchange) noexcept;
 LocalExchange parse_local_exchange(const std::string& name);
 
+enum class SharedLayout {
+    Linear,
+    XorSwizzle,
+};
+
+const char*  shared_layout_name(SharedLayout layout) noexcept;
+SharedLayout parse_shared_layout(const std::string& name);
+
 enum class FftCore {
     Scalar,
     ThreadDft8,
@@ -119,6 +144,19 @@ enum class FftCore {
 const char* fft_core_name(FftCore core) noexcept;
 FftCore     parse_fft_core(const std::string& name);
 
+struct FftSegmentMapping {
+    FftCore         core     = FftCore::CufftDxBlock;
+    LocalExchange   exchange = LocalExchange::SharedMemory;
+    std::uint32_t   threads  = 0;
+    std::uint32_t   ept      = 8;
+};
+
+struct FftBoundaryMapping {
+    CrossTwiddleMode cross_twiddle = CrossTwiddleMode::Table;
+    DirectBoundary   layout        = DirectBoundary::Strided;
+    FftBoundaryResidency residency = FftBoundaryResidency::GlobalScratch;
+};
+
 std::vector<ButterflyCapability> butterfly_capabilities();
 
 struct ButterflyConfig {
@@ -127,11 +165,18 @@ struct ButterflyConfig {
     ButterflyPrecision precision         = ButterflyPrecision::Fp32;
     ButterflyPlacement placement         = ButterflyPlacement::OutOfPlace;
     std::uint32_t      log_n             = 8;
+    // Ordered stage counts for each algorithmic decomposition segment.
+    std::vector<std::uint32_t> stage_partition;
+    std::vector<FftSegmentMapping> segment_mappings;
+    std::vector<FftBoundaryMapping> boundaries;
+    // Physical processing groups after fused logical boundaries are lowered.
+    std::vector<FftSegmentMapping> execution_group_mappings;
     std::size_t        batch             = 1;
     std::size_t        batch_stride      = 0;
     std::size_t        element_stride    = 1;
     bool               inverse           = false;
     bool               normalize_inverse = true;
+    bool               auto_select       = false;
     std::uint32_t      stage_space       = 0;
     StageHandoff       stage_handoff     = StageHandoff::NamedBarrier;
     std::uint32_t      tile_threads      = 128;
@@ -148,7 +193,9 @@ struct ButterflyConfig {
     ComputeUnit        compute_unit      = ComputeUnit::Radix2;
     ComplexMultiply    complex_multiply  = ComplexMultiply::FourMul;
     CrossTwiddleMode   cross_twiddle     = CrossTwiddleMode::Table;
+    DirectBoundary     direct_boundary   = DirectBoundary::Strided;
     LocalExchange      local_exchange    = LocalExchange::SharedMemory;
+    SharedLayout       shared_layout     = SharedLayout::Linear;
     FftCore            fft_core          = FftCore::Scalar;
 };
 
diff --git a/results/README.md b/results/README.md
new file mode 100644
index 0000000..ec22043
--- /dev/null
+++ b/results/README.md
@@ -0,0 +1,43 @@
+# Result Inventory
+
+This directory stores measured records and reduced reports. Raw measurements
+are immutable evidence; summaries and Markdown tables are reproducible derived
+artifacts.
+
+## Canonical V100 Evidence
+
+| Dataset | Purpose | Raw record | Reduced report |
+|:--|:--|:--|:--|
+| comprehensive suite | controlled cross-operator baseline for `v0.2.0` | `comprehensive_v100_full_raw.csv` | `comprehensive_v100_full_summary.csv`, `comprehensive_v100_full_report.md` |
+| orthogonal scaling | independent length/batch saturation and crossover scan | `v100_scaling_full_raw.csv` | `v100_scaling_full_summary.csv`, `v100_scaling_full_report.md` |
+| calibrated selector | held-out-shape mapping prediction | `v100_mapping_selector_evaluation.csv` | `v100_mapping_selector_metrics.json` |
+| external baseline refresh | matching-protocol Dao FHT and GPU-NTT pairs | `v100_external_baselines_raw.csv` | `v100_external_baselines_summary.csv`, `v100_external_baselines_report.md` |
+| crossover counters | NCU mechanism attribution for FFT/FWHT scaling boundaries | `ncu_scaling_crossovers/*.csv` | `ncu_scaling_crossovers/summary.csv`, `ncu_scaling_crossovers/attribution.md` |
+| hardware capabilities | V100 service and resource profile | `hardware_capabilities_raw.csv` | `hardware_capabilities_v100.json` |
+
+The `quick` files are protocol smoke tests. Files containing `confirm` retain
+independent reruns used to investigate instability; they do not silently
+replace rows in the canonical full raw data.
+
+## Focused Evidence
+
+Files prefixed with `fft_`, `cubutterfly_`, `processing_units_`, `ntt_`, or
+`stage_pipeline_` are focused design-space experiments. Their protocol and
+interpretation live in the matching document under `docs/`; they must not be
+mixed directly with the comprehensive suite unless their contracts and clock
+policy are explicitly aligned.
+
+Profiler exports are grouped in `ncu*` and `nsys*` directories. Binary
+`.ncu-rep`, `.nsys-rep`, and `.sqlite` files are machine artifacts and are not
+versioned; reduced CSV and analysis documents may be versioned.
+
+## Naming Policy
+
+- `*_raw.csv`: append-only trial or counter records;
+- `*_summary.csv`: deterministic reduction of raw records;
+- `*_report.md`: human-readable table generated from the summary;
+- `*_search.csv`: explored candidates, including rejected or nonselected rows;
+- `*_confirm_*`: an explicitly separate rerun for a suspected unstable case.
+
+New paper-facing datasets must include the GPU, workload family, and protocol
+scope in the basename and be linked from `docs/experiments.md`.
diff --git a/results/comprehensive_v100_full_report.md b/results/comprehensive_v100_full_report.md
index f022bfa..ed28edc 100644
--- a/results/comprehensive_v100_full_report.md
+++ b/results/comprehensive_v100_full_report.md
@@ -62,7 +62,7 @@ their fastest internal implementation as the basis.
 | uint32 | forward | 20 | 1,048,576 | 4 | out-of-place, es=1, bs=1048576 | cuButterfly-online-radix4 | online-reorder / radix4 | 0.319304 | 0.013 | 13.136 | 1.000x | cuButterfly-online-radix4 | stable |
 | uint32 | forward | 20 | 1,048,576 | 4 | out-of-place, es=1, bs=1048576 | cuButterfly-hierarchical-radix4 | hierarchical / radix4 | 0.486994 | 0.008 | 8.613 | 0.656x | cuButterfly-online-radix4 | stable |
 
-## External Coverage Gaps
+## External Evidence
 
-- **fwht / Dao-AILab FHT**: not-runnable; PyTorch is not installed in the active Python environment. Existing evidence: `results/external_dao_fht_v100_summary.csv`.
-- **ntt / GPU-NTT**: not-runnable; the external comparator harness binary is not present. Existing evidence: `results/compact_stage_logN20.csv`.
+- **fwht / Dao-AILab FHT**: measured-matching-protocol; five-trial correctness-checked refresh is archived separately. Existing evidence: `results/v100_external_baselines_summary.csv`.
+- **ntt / GPU-NTT**: measured-matching-protocol; natural and native bit-reversed contracts are archived separately. Existing evidence: `results/v100_external_baselines_summary.csv`.
diff --git a/results/comprehensive_v100_full_summary.csv b/results/comprehensive_v100_full_summary.csv
index c2fd764..130d99b 100644
--- a/results/comprehensive_v100_full_summary.csv
+++ b/results/comprehensive_v100_full_summary.csv
@@ -1,38 +1,38 @@
-case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class
-fft14_cub,fft-fp32-fwd-log14,cuButterfly-cuFFTDx-direct,0,5,0.121129000,0.120934000,0.121252000,0.002625,0.000083,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,temporal-tile,auto,cufftdx-direct,shared,table,2.113449,34.626753,declared-reference,cuFFT,0.121610239,1.003973,parity
-fft14_cufft,fft-fp32-fwd-log14,cuFFT,1,5,0.121610239,0.120698884,0.125224963,0.037218,0.002863,stable-with-outlier,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,,,,,,2.105086,34.489727,declared-reference,cuFFT,0.121610239,1.000000,parity
-fft14_vkfft,fft-fp32-fwd-log14,VkFFT,0,5,0.171765760,0.171509758,0.172052473,0.003160,0.001550,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,,,,,,1.490402,24.418743,declared-reference,cuFFT,0.121610239,0.708000,slower
-fft18_vkfft,fft-fp32-fwd-log18,VkFFT,0,5,0.201082885,0.201011196,0.201205775,0.000968,0.000357,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,0.079569,20.858583,declared-reference,cuFFT,0.211343363,1.051026,faster
-fft18_cub,fft-fp32-fwd-log18,cuButterfly-cuFFTDx-online,0,5,0.205087000,0.204933000,0.207206000,0.011083,0.002345,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,online-reorder,auto,cufftdx-block,shared,recurrence,0.078016,20.451340,declared-reference,cuFFT,0.211343363,1.030506,faster
-fft18_cufft,fft-fp32-fwd-log18,cuFFT,1,5,0.211343363,0.211046398,0.211384311,0.001599,0.000291,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,0.075706,19.845922,declared-reference,cuFFT,0.211343363,1.000000,parity
-fft20_vkfft,fft-fp32-fwd-log20,VkFFT,0,5,0.206274569,0.205854714,0.206807047,0.004617,0.002383,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,0.019392,20.333597,declared-reference,cuFFT,0.210063368,1.018368,parity
-fft20_cufft,fft-fp32-fwd-log20,cuFFT,1,5,0.210063368,0.209879041,0.210984960,0.005265,0.002876,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,0.019042,19.966851,declared-reference,cuFFT,0.210063368,1.000000,parity
-fft20_cub,fft-fp32-fwd-log20,cuButterfly-cuFFTDx-online,0,5,0.235438000,0.235397000,0.235479000,0.000348,0.000221,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,online-reorder,auto,cufftdx-block,shared,recurrence,0.016990,17.814898,declared-reference,cuFFT,0.210063368,0.892224,slower
-fft8_vkfft,fft-fp32-fwd-log8,VkFFT,0,5,0.083548166,0.083517440,0.083578885,0.000735,0.000490,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,,,,,,196.102449,50.202227,declared-reference,cuFFT,0.083824642,1.003309,parity
-fft8_cufft,fft-fp32-fwd-log8,cuFFT,1,5,0.083824642,0.083742723,0.083834879,0.001099,0.000855,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,,,,,,195.455651,50.036647,declared-reference,cuFFT,0.083824642,1.000000,parity
-fft8_cub,fft-fp32-fwd-log8,cuButterfly-cuFFTDx,0,5,0.084234000,0.084183000,0.084306000,0.001460,0.001092,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,temporal-tile,auto,cufftdx-block,shared,table,194.505782,49.793480,declared-reference,cuFFT,0.083824642,0.995140,parity
-fft12_inverse_cub,fft-fp32-inverse-log12,cuButterfly-cuFFTDx-direct,0,5,0.088064000,0.087818000,0.088125000,0.003486,0.000920,stable,1,fft,fp32,inverse,inverse,out-of-place,12,4096,1024,1,4096,,,,,temporal-tile,auto,cufftdx-direct,shared,table,11.627907,47.627907,declared-reference,cuFFT,0.172892000,1.963254,faster
-fft12_inverse_cufft,fft-fp32-inverse-log12,cuFFT,1,5,0.172892000,0.172861000,0.172933000,0.000416,0.000237,stable,1,fft,fp32,inverse,inverse,out-of-place,12,4096,1024,1,4096,,,,,cufft,auto,scalar,shared,table,5.922773,24.259677,declared-reference,cuFFT,0.172892000,1.000000,parity
-fft8_stride_cufft,fft-fp32-stride2-log8,cuFFT,1,5,0.171428000,0.171039000,0.171643000,0.003523,0.001079,stable,1,fft,fp32,forward,none,in-place,8,256,16384,2,518,,,,,cufft,auto,scalar,shared,table,95.573652,24.466855,declared-reference,cuFFT,0.171428000,1.000000,parity
-fft8_stride_cub,fft-fp32-stride2-log8,cuButterfly-scalar,0,5,0.172636000,0.172564000,0.172892000,0.001900,0.000475,stable,1,fft,fp32,forward,none,in-place,8,256,16384,2,518,,,,,temporal-tile,radix4,scalar,shared,table,94.904887,24.295651,declared-reference,cuFFT,0.171428000,0.993003,parity
-fft16_fp64_cufft,fft-fp64-fwd-log16,cuFFT,1,5,0.342804000,0.342712000,0.342989000,0.000808,0.000449,stable,1,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,,,,,cufft,auto,scalar,shared,table,0.186696,12.235283,declared-reference,cuFFT,0.342804000,1.000000,parity
-fft16_fp64_cub,fft-fp64-fwd-log16,cuButterfly-scalar-online,0,5,0.534313000,0.533668000,0.535828000,0.004043,0.002682,stable,1,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,,,,,online-reorder,radix4,scalar,shared,table,0.119780,7.849901,declared-reference,cuFFT,0.342804000,0.641579,slower
-fft3_mixed,fft-mixed-fwd-log3,cuButterfly-WMMA,0,5,0.087020000,0.086948000,0.087593000,0.007412,0.003884,stable,1,fft,fp16-fp32,forward,none,out-of-place,3,8,524288,1,8,,,,,temporal-tile,radix8,wmma-dft8,shared,table,6024.913813,48.199311,group-fastest,cuButterfly-WMMA,0.087020000,1.000000,parity
-fwht15_warp,fwht-fp32-fwd-log15,cuButterfly-warp-register,0,5,0.064707000,0.064666000,0.064829000,0.002519,0.000804,stable,1,fwht,fp32,forward,none,out-of-place,15,32768,128,1,32768,,,,,temporal-tile,radix2,scalar,warp-register,table,1.978148,64.819942,group-fastest,cuButterfly-warp-register,0.064707000,1.000000,parity
-fwht15_online,fwht-fp32-fwd-log15,cuButterfly-online-radix4,0,5,0.316396000,0.316006000,0.318188000,0.006896,0.001650,stable,1,fwht,fp32,forward,none,out-of-place,15,32768,128,1,32768,,,,,online-reorder,radix4,scalar,shared,table,0.404556,13.256501,group-fastest,cuButterfly-warp-register,0.064707000,0.204513,slower
-fwht20_online,fwht-fp32-fwd-log20,cuButterfly-online-radix4,0,5,0.319560000,0.319160000,0.319703000,0.001699,0.000451,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,table,0.012517,13.125247,group-fastest,cuButterfly-online-radix4,0.319560000,1.000000,parity
-fwht20_hier,fwht-fp32-fwd-log20,cuButterfly-hierarchical-radix4,0,5,0.488079000,0.488008000,0.488202000,0.000397,0.000148,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,table,0.008195,8.593494,group-fastest,cuButterfly-online-radix4,0.319560000,0.654730,slower
-fwht8_warp,fwht-fp32-fwd-log8,cuButterfly-warp-register,0,5,0.042742000,0.042732000,0.043121000,0.009101,0.001895,stable,1,fwht,fp32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix2,scalar,warp-register,table,383.323195,98.130738,group-fastest,cuButterfly-warp-register,0.042742000,1.000000,parity
-fwht8_shared,fwht-fp32-fwd-log8,cuButterfly-shared-radix4,0,5,0.048466000,0.048394000,0.049101000,0.014588,0.001486,stable,1,fwht,fp32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix4,scalar,shared,table,338.051417,86.541163,group-fastest,cuButterfly-warp-register,0.042742000,0.881897,slower
-fwht12_fp64,fwht-fp64-fwd-log12,cuButterfly-online-radix4,0,5,0.373197000,0.372603000,0.374241000,0.004389,0.003786,stable,1,fwht,fp64,forward,none,out-of-place,12,4096,1024,1,4096,,,,,online-reorder,radix4,scalar,shared,table,2.743859,11.238847,group-fastest,cuButterfly-online-radix4,0.373197000,1.000000,parity
-ntt12_30_hybrid,ntt-u30-natural-log12,cuNTT-Hybrid2D-radix4,0,5,0.140012000,0.139776000,0.141087000,0.009363,0.008192,stable,1,ntt,uint32,forward,,,12,4096,1024,1,4096,32,30,0,natural,hybrid2d,radix4,,,fused,7.313659,29.956747,declared-reference,cuNTT-Hybrid2D-radix2,0.164291000,1.173407,faster
-ntt12_30_r2,ntt-u30-natural-log12,cuNTT-Hybrid2D-radix2,1,5,0.164291000,0.163359000,0.164823000,0.008911,0.000560,stable,1,ntt,uint32,forward,,,12,4096,1024,1,4096,32,30,0,natural,hybrid2d,radix2,,,fused,6.232843,25.529725,declared-reference,cuNTT-Hybrid2D-radix2,0.164291000,1.000000,parity
-ntt20_60_compact,ntt-u60-bitrev-log20,cuNTT-compact-stage,0,5,0.341924000,0.341801000,0.342088000,0.000839,0.000298,stable,1,ntt,uint64,forward,,,20,1048576,4,1,1048576,64,60,0,bit-reversed,compact-stage,radix2,,,fused,0.011699,12.266773,group-fastest,cuNTT-compact-stage,0.341924000,1.000000,parity
-ntt16_60_inverse,ntt-u60-inverse-log16,cuNTT-Hybrid2D-radix2,0,5,0.307671000,0.306493000,0.309002000,0.008155,0.003159,stable,1,ntt,uint64,inverse,,,16,65536,64,1,65536,64,60,1,natural,hybrid2d,radix2,,,fused,0.208014,13.632432,group-fastest,cuNTT-Hybrid2D-radix2,0.307671000,1.000000,parity
-ntt16_60_r4,ntt-u60-natural-log16,cuNTT-Hybrid2D-radix4,0,5,0.277780000,0.276982000,0.279603000,0.009436,0.006930,stable,1,ntt,uint64,forward,,,16,65536,64,1,65536,64,60,0,natural,hybrid2d,radix4,,,fused,0.230398,15.099374,group-fastest,cuNTT-Hybrid2D-radix4,0.277780000,1.000000,parity
-ntt16_60_r2,ntt-u60-natural-log16,cuNTT-Hybrid2D-radix2,0,5,0.304835000,0.303421000,0.305428000,0.006584,0.004366,stable,1,ntt,uint64,forward,,,16,65536,64,1,65536,64,60,0,natural,hybrid2d,radix2,,,fused,0.209950,13.759260,group-fastest,cuNTT-Hybrid2D-radix4,0.277780000,0.911247,slower
-xor20_online,xor-u32-fwd-log20,cuButterfly-online-radix4,0,5,0.319304000,0.318884000,0.319345000,0.001444,0.000163,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,table,0.012527,13.135770,group-fastest,cuButterfly-online-radix4,0.319304000,1.000000,parity
-xor20_hier,xor-u32-fwd-log20,cuButterfly-hierarchical-radix4,0,5,0.486994000,0.486830000,0.487066000,0.000485,0.000314,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,table,0.008214,8.612640,group-fastest,cuButterfly-online-radix4,0.319304000,0.655663,slower
-xor8_r4,xor-u32-fwd-log8,cuButterfly-radix4,0,5,0.047759000,0.047718000,0.047780000,0.001298,0.000440,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix4,scalar,shared,table,343.055759,87.822274,group-fastest,cuButterfly-radix4,0.047759000,1.000000,parity
-xor8_r2,xor-u32-fwd-log8,cuButterfly-radix2,0,5,0.049766000,0.049705000,0.050145000,0.008841,0.001648,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix2,scalar,shared,table,329.220753,84.280513,group-fastest,cuButterfly-radix4,0.047759000,0.959671,slower
-xor12_inverse,xor-u32-inverse-log12,cuButterfly-online-radix4,0,5,0.354243000,0.354130000,0.355000000,0.002456,0.000319,stable,1,xor-zeta,uint32,inverse,none,out-of-place,12,4096,1024,1,4096,,,,,online-reorder,radix4,scalar,shared,table,2.890671,11.840189,group-fastest,cuButterfly-online-radix4,0.354243000,1.000000,parity
+case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,shared_layout,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class
+fft14_cub,fft-fp32-fwd-log14,cuButterfly-cuFFTDx-direct,0,5,0.121129000,0.120934000,0.121252000,0.002625,0.000083,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,temporal-tile,auto,cufftdx-direct,shared,,table,2.113449,34.626753,declared-reference,cuFFT,0.121610239,1.003973,parity
+fft14_cufft,fft-fp32-fwd-log14,cuFFT,1,5,0.121610239,0.120698884,0.125224963,0.037218,0.002863,stable-with-outlier,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,,,,,,,2.105086,34.489727,declared-reference,cuFFT,0.121610239,1.000000,parity
+fft14_vkfft,fft-fp32-fwd-log14,VkFFT,0,5,0.171765760,0.171509758,0.172052473,0.003160,0.001550,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,,,,,,,1.490402,24.418743,declared-reference,cuFFT,0.121610239,0.708000,slower
+fft18_vkfft,fft-fp32-fwd-log18,VkFFT,0,5,0.201082885,0.201011196,0.201205775,0.000968,0.000357,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,,0.079569,20.858583,declared-reference,cuFFT,0.211343363,1.051026,faster
+fft18_cub,fft-fp32-fwd-log18,cuButterfly-cuFFTDx-online,0,5,0.205087000,0.204933000,0.207206000,0.011083,0.002345,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,online-reorder,auto,cufftdx-block,shared,,recurrence,0.078016,20.451340,declared-reference,cuFFT,0.211343363,1.030506,faster
+fft18_cufft,fft-fp32-fwd-log18,cuFFT,1,5,0.211343363,0.211046398,0.211384311,0.001599,0.000291,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,,0.075706,19.845922,declared-reference,cuFFT,0.211343363,1.000000,parity
+fft20_vkfft,fft-fp32-fwd-log20,VkFFT,0,5,0.206274569,0.205854714,0.206807047,0.004617,0.002383,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,,0.019392,20.333597,declared-reference,cuFFT,0.210063368,1.018368,parity
+fft20_cufft,fft-fp32-fwd-log20,cuFFT,1,5,0.210063368,0.209879041,0.210984960,0.005265,0.002876,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,,0.019042,19.966851,declared-reference,cuFFT,0.210063368,1.000000,parity
+fft20_cub,fft-fp32-fwd-log20,cuButterfly-cuFFTDx-online,0,5,0.235438000,0.235397000,0.235479000,0.000348,0.000221,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,online-reorder,auto,cufftdx-block,shared,,recurrence,0.016990,17.814898,declared-reference,cuFFT,0.210063368,0.892224,slower
+fft8_vkfft,fft-fp32-fwd-log8,VkFFT,0,5,0.083548166,0.083517440,0.083578885,0.000735,0.000490,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,,,,,,,196.102449,50.202227,declared-reference,cuFFT,0.083824642,1.003309,parity
+fft8_cufft,fft-fp32-fwd-log8,cuFFT,1,5,0.083824642,0.083742723,0.083834879,0.001099,0.000855,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,,,,,,,195.455651,50.036647,declared-reference,cuFFT,0.083824642,1.000000,parity
+fft8_cub,fft-fp32-fwd-log8,cuButterfly-cuFFTDx,0,5,0.084234000,0.084183000,0.084306000,0.001460,0.001092,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,temporal-tile,auto,cufftdx-block,shared,,table,194.505782,49.793480,declared-reference,cuFFT,0.083824642,0.995140,parity
+fft12_inverse_cub,fft-fp32-inverse-log12,cuButterfly-cuFFTDx-direct,0,5,0.088064000,0.087818000,0.088125000,0.003486,0.000920,stable,1,fft,fp32,inverse,inverse,out-of-place,12,4096,1024,1,4096,,,,,temporal-tile,auto,cufftdx-direct,shared,,table,11.627907,47.627907,declared-reference,cuFFT,0.172892000,1.963254,faster
+fft12_inverse_cufft,fft-fp32-inverse-log12,cuFFT,1,5,0.172892000,0.172861000,0.172933000,0.000416,0.000237,stable,1,fft,fp32,inverse,inverse,out-of-place,12,4096,1024,1,4096,,,,,cufft,auto,scalar,shared,,table,5.922773,24.259677,declared-reference,cuFFT,0.172892000,1.000000,parity
+fft8_stride_cufft,fft-fp32-stride2-log8,cuFFT,1,5,0.171428000,0.171039000,0.171643000,0.003523,0.001079,stable,1,fft,fp32,forward,none,in-place,8,256,16384,2,518,,,,,cufft,auto,scalar,shared,,table,95.573652,24.466855,declared-reference,cuFFT,0.171428000,1.000000,parity
+fft8_stride_cub,fft-fp32-stride2-log8,cuButterfly-scalar,0,5,0.172636000,0.172564000,0.172892000,0.001900,0.000475,stable,1,fft,fp32,forward,none,in-place,8,256,16384,2,518,,,,,temporal-tile,radix4,scalar,shared,,table,94.904887,24.295651,declared-reference,cuFFT,0.171428000,0.993003,parity
+fft16_fp64_cufft,fft-fp64-fwd-log16,cuFFT,1,5,0.342804000,0.342712000,0.342989000,0.000808,0.000449,stable,1,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,,,,,cufft,auto,scalar,shared,,table,0.186696,12.235283,declared-reference,cuFFT,0.342804000,1.000000,parity
+fft16_fp64_cub,fft-fp64-fwd-log16,cuButterfly-scalar-online,0,5,0.534313000,0.533668000,0.535828000,0.004043,0.002682,stable,1,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,,,,,online-reorder,radix4,scalar,shared,,table,0.119780,7.849901,declared-reference,cuFFT,0.342804000,0.641579,slower
+fft3_mixed,fft-mixed-fwd-log3,cuButterfly-WMMA,0,5,0.087020000,0.086948000,0.087593000,0.007412,0.003884,stable,1,fft,fp16-fp32,forward,none,out-of-place,3,8,524288,1,8,,,,,temporal-tile,radix8,wmma-dft8,shared,,table,6024.913813,48.199311,group-fastest,cuButterfly-WMMA,0.087020000,1.000000,parity
+fwht15_warp,fwht-fp32-fwd-log15,cuButterfly-warp-register,0,5,0.064707000,0.064666000,0.064829000,0.002519,0.000804,stable,1,fwht,fp32,forward,none,out-of-place,15,32768,128,1,32768,,,,,temporal-tile,radix2,scalar,warp-register,,table,1.978148,64.819942,group-fastest,cuButterfly-warp-register,0.064707000,1.000000,parity
+fwht15_online,fwht-fp32-fwd-log15,cuButterfly-online-radix4,0,5,0.316396000,0.316006000,0.318188000,0.006896,0.001650,stable,1,fwht,fp32,forward,none,out-of-place,15,32768,128,1,32768,,,,,online-reorder,radix4,scalar,shared,,table,0.404556,13.256501,group-fastest,cuButterfly-warp-register,0.064707000,0.204513,slower
+fwht20_online,fwht-fp32-fwd-log20,cuButterfly-online-radix4,0,5,0.319560000,0.319160000,0.319703000,0.001699,0.000451,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.012517,13.125247,group-fastest,cuButterfly-online-radix4,0.319560000,1.000000,parity
+fwht20_hier,fwht-fp32-fwd-log20,cuButterfly-hierarchical-radix4,0,5,0.488079000,0.488008000,0.488202000,0.000397,0.000148,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.008195,8.593494,group-fastest,cuButterfly-online-radix4,0.319560000,0.654730,slower
+fwht8_warp,fwht-fp32-fwd-log8,cuButterfly-warp-register,0,5,0.042742000,0.042732000,0.043121000,0.009101,0.001895,stable,1,fwht,fp32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix2,scalar,warp-register,,table,383.323195,98.130738,group-fastest,cuButterfly-warp-register,0.042742000,1.000000,parity
+fwht8_shared,fwht-fp32-fwd-log8,cuButterfly-shared-radix4,0,5,0.048466000,0.048394000,0.049101000,0.014588,0.001486,stable,1,fwht,fp32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,338.051417,86.541163,group-fastest,cuButterfly-warp-register,0.042742000,0.881897,slower
+fwht12_fp64,fwht-fp64-fwd-log12,cuButterfly-online-radix4,0,5,0.373197000,0.372603000,0.374241000,0.004389,0.003786,stable,1,fwht,fp64,forward,none,out-of-place,12,4096,1024,1,4096,,,,,online-reorder,radix4,scalar,shared,,table,2.743859,11.238847,group-fastest,cuButterfly-online-radix4,0.373197000,1.000000,parity
+ntt12_30_hybrid,ntt-u30-natural-log12,cuNTT-Hybrid2D-radix4,0,5,0.140012000,0.139776000,0.141087000,0.009363,0.008192,stable,1,ntt,uint32,forward,,,12,4096,1024,1,4096,32,30,0,natural,hybrid2d,radix4,,,,fused,7.313659,29.956747,declared-reference,cuNTT-Hybrid2D-radix2,0.164291000,1.173407,faster
+ntt12_30_r2,ntt-u30-natural-log12,cuNTT-Hybrid2D-radix2,1,5,0.164291000,0.163359000,0.164823000,0.008911,0.000560,stable,1,ntt,uint32,forward,,,12,4096,1024,1,4096,32,30,0,natural,hybrid2d,radix2,,,,fused,6.232843,25.529725,declared-reference,cuNTT-Hybrid2D-radix2,0.164291000,1.000000,parity
+ntt20_60_compact,ntt-u60-bitrev-log20,cuNTT-compact-stage,0,5,0.341924000,0.341801000,0.342088000,0.000839,0.000298,stable,1,ntt,uint64,forward,,,20,1048576,4,1,1048576,64,60,0,bit-reversed,compact-stage,radix2,,,,fused,0.011699,12.266773,group-fastest,cuNTT-compact-stage,0.341924000,1.000000,parity
+ntt16_60_inverse,ntt-u60-inverse-log16,cuNTT-Hybrid2D-radix2,0,5,0.307671000,0.306493000,0.309002000,0.008155,0.003159,stable,1,ntt,uint64,inverse,,,16,65536,64,1,65536,64,60,1,natural,hybrid2d,radix2,,,,fused,0.208014,13.632432,group-fastest,cuNTT-Hybrid2D-radix2,0.307671000,1.000000,parity
+ntt16_60_r4,ntt-u60-natural-log16,cuNTT-Hybrid2D-radix4,0,5,0.277780000,0.276982000,0.279603000,0.009436,0.006930,stable,1,ntt,uint64,forward,,,16,65536,64,1,65536,64,60,0,natural,hybrid2d,radix4,,,,fused,0.230398,15.099374,group-fastest,cuNTT-Hybrid2D-radix4,0.277780000,1.000000,parity
+ntt16_60_r2,ntt-u60-natural-log16,cuNTT-Hybrid2D-radix2,0,5,0.304835000,0.303421000,0.305428000,0.006584,0.004366,stable,1,ntt,uint64,forward,,,16,65536,64,1,65536,64,60,0,natural,hybrid2d,radix2,,,,fused,0.209950,13.759260,group-fastest,cuNTT-Hybrid2D-radix4,0.277780000,0.911247,slower
+xor20_online,xor-u32-fwd-log20,cuButterfly-online-radix4,0,5,0.319304000,0.318884000,0.319345000,0.001444,0.000163,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.012527,13.135770,group-fastest,cuButterfly-online-radix4,0.319304000,1.000000,parity
+xor20_hier,xor-u32-fwd-log20,cuButterfly-hierarchical-radix4,0,5,0.486994000,0.486830000,0.487066000,0.000485,0.000314,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.008214,8.612640,group-fastest,cuButterfly-online-radix4,0.319304000,0.655663,slower
+xor8_r4,xor-u32-fwd-log8,cuButterfly-radix4,0,5,0.047759000,0.047718000,0.047780000,0.001298,0.000440,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,343.055759,87.822274,group-fastest,cuButterfly-radix4,0.047759000,1.000000,parity
+xor8_r2,xor-u32-fwd-log8,cuButterfly-radix2,0,5,0.049766000,0.049705000,0.050145000,0.008841,0.001648,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,329.220753,84.280513,group-fastest,cuButterfly-radix4,0.047759000,0.959671,slower
+xor12_inverse,xor-u32-inverse-log12,cuButterfly-online-radix4,0,5,0.354243000,0.354130000,0.355000000,0.002456,0.000319,stable,1,xor-zeta,uint32,inverse,none,out-of-place,12,4096,1024,1,4096,,,,,online-reorder,radix4,scalar,shared,,table,2.890671,11.840189,group-fastest,cuButterfly-online-radix4,0.354243000,1.000000,parity
diff --git a/results/comprehensive_v100_vectorized_fft_raw.csv b/results/comprehensive_v100_vectorized_fft_raw.csv
new file mode 100644
index 0000000..44cc8ca
--- /dev/null
+++ b/results/comprehensive_v100_vectorized_fft_raw.csv
@@ -0,0 +1,31 @@
+suite_case_id,suite_group,suite_tier,suite_runner,implementation,reference,trial,performance_batch,preflight_correct,preflight_max_error,device,compute_capability,operator,precision,direction,normalization,placement,auto_select,backend,compute_unit,complex_multiply,cross_twiddle,direct_boundary,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,group_threads,group_ept,local_exchange,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_stride,warmup,repeat,h2d_ms,kernel_ms,d2h_ms,transforms_s,Gbutterfly_s,points_s,max_error,correct,output_order,library,library_version,plan_ms,max_abs_error,relative_l2_error
+fft20_cub,fft-fp32-fwd-log20,quick,butterfly,cuButterfly-auto-vectorized,0,2,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,1,online-reorder,auto,four-mul,recurrence,direct-strided,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,512x512,8x8,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,4,1,1048576,1000,100,5.465248,0.218593,5.098752,18298.825062,191.877088,19187708788.714798,0.000000,-1,,,,,,
+fft20_cufft,fft-fp32-fwd-log20,quick,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.210216954,,19027.960957570,199.522631890,19952263189.044689178,,-1,,cufft,10900,1.956618000,0.000000000,0.000000000
+fft18_cufft,fft-fp32-fwd-log18,quick,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.211097598,,75794.325211837,178.821248295,19869027588.331924438,,-1,,cufft,10900,2.179070000,0.000000000,0.000000000
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+fft20_cub,fft-fp32-fwd-log20,quick,butterfly,cuButterfly-auto-vectorized,0,1,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,1,online-reorder,auto,four-mul,recurrence,direct-strided,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,512x512,8x8,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,4,1,1048576,1000,100,5.459776,0.214170,5.091712,18676.787722,195.840314,19584031362.189842,0.000000,-1,,,,,,
+fft18_cufft,fft-fp32-fwd-log18,quick,fft-library,cuFFT,1,4,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.211097598,,75794.325211837,178.821248295,19869027588.331924438,,-1,,cufft,10900,1.964931000,0.000000000,0.000000000
+fft18_vkfft,fft-fp32-fwd-log18,quick,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201215997,,79516.540492056,187.603055917,20844783990.749572754,,-1,,vkfft,10304,402.465863000,0.000000000,0.000000000
+fft18_vkfft,fft-fp32-fwd-log18,quick,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201103359,,79561.077661243,187.708132282,20856459142.428863525,,-1,,vkfft,10304,441.035882000,0.000000000,0.000000000
+fft20_vkfft,fft-fp32-fwd-log20,quick,fft-library,VkFFT,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.206520334,,19368.552842865,203.093996658,20309399665.760250092,,-1,,vkfft,10304,980.510309000,0.000000000,0.000000000
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+fft18_cub,fft-fp32-fwd-log18,quick,butterfly,cuButterfly-auto-vectorized,0,5,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,1,online-reorder,auto,four-mul,recurrence,direct-strided,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,256x256,8x8,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.513280,0.195758,5.112288,81733.537884,192.833609,21425956555.003986,0.000000,-1,,,,,,
+fft18_cub,fft-fp32-fwd-log18,quick,butterfly,cuButterfly-auto-vectorized,0,3,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,1,online-reorder,auto,four-mul,recurrence,direct-strided,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,256x256,8x8,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.497792,0.196137,5.107552,81575.653552,192.461113,21384568124.805202,0.000000,-1,,,,,,
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+fft20_cufft,fft-fp32-fwd-log20,quick,fft-library,cuFFT,1,5,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.210421756,,19009.441218200,199.328438348,19932843834.815044403,,-1,,cufft,10900,2.361036000,0.000000000,0.000000000
+fft18_cufft,fft-fp32-fwd-log18,quick,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.211077124,,75801.677158852,178.838593714,19870954857.130027771,,-1,,cufft,10900,2.333650000,0.000000000,0.000000000
+fft18_vkfft,fft-fp32-fwd-log18,quick,fft-library,VkFFT,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201287687,,79488.220329773,187.536240271,20837360030.128097534,,-1,,vkfft,10304,382.376958000,0.000000000,0.000000000
+fft18_vkfft,fft-fp32-fwd-log18,quick,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201052144,,79581.344760424,187.755948368,20861772040.876701355,,-1,,vkfft,10304,440.183302000,0.000000000,0.000000000
+fft20_vkfft,fft-fp32-fwd-log20,quick,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.206653446,,19356.076940482,202.963177339,20296317733.943321228,,-1,,vkfft,10304,964.038935000,0.000000000,0.000000000
+fft20_vkfft,fft-fp32-fwd-log20,quick,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.206059515,,19411.867444003,203.548183170,20354818316.962890625,,-1,,vkfft,10304,792.400092000,0.000000000,0.000000000
+fft20_cufft,fft-fp32-fwd-log20,quick,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.210257918,,19024.253853781,199.483760090,19948376008.981891632,,-1,,cufft,10900,2.309559000,0.000000000,0.000000000
+fft20_cufft,fft-fp32-fwd-log20,quick,fft-library,cuFFT,1,4,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.210462719,,19005.741326377,199.289642170,19928964217.047481537,,-1,,cufft,10900,2.080110000,0.000000000,0.000000000
+fft18_cufft,fft-fp32-fwd-log18,quick,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.211527675,,75640.220460429,178.457669571,19828629952.378597260,,-1,,cufft,10900,2.305685000,0.000000000,0.000000000
+fft18_cub,fft-fp32-fwd-log18,quick,butterfly,cuButterfly-auto-vectorized,0,4,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,1,online-reorder,auto,four-mul,recurrence,direct-strided,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,256x256,8x8,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.523456,0.195389,5.117408,81887.737711,193.197412,21466379114.449234,0.000000,-1,,,,,,
+fft18_cub,fft-fp32-fwd-log18,quick,butterfly,cuButterfly-auto-vectorized,0,1,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,1,online-reorder,auto,four-mul,recurrence,direct-strided,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,256x256,8x8,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.531936,0.195983,5.124160,81639.588146,192.611954,21401328194.833725,0.000000,-1,,,,,,
+fft18_vkfft,fft-fp32-fwd-log18,quick,fft-library,VkFFT,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201072633,,79573.235502406,187.736816228,20859646247.542640686,,-1,,vkfft,10304,336.182779000,0.000000000,0.000000000
diff --git a/results/comprehensive_v100_vectorized_fft_report.md b/results/comprehensive_v100_vectorized_fft_report.md
new file mode 100644
index 0000000..6714ecb
--- /dev/null
+++ b/results/comprehensive_v100_vectorized_fft_report.md
@@ -0,0 +1,22 @@
+# Single-GPU Comprehensive Summary
+
+Every row uses the listed transform length and batch. `Mtransform/s` and
+`Gpoint/s` are derived from the median resident kernel time. Ratios above one
+mean higher throughput than `Basis`; groups without a declared reference use
+their fastest internal implementation as the basis.
+
+## FFT Results
+
+| Numeric | Semantics | logN | N | Batch | Layout | Implementation | Design point | Median ms | Mtransform/s | Gpoint/s | vs basis | Basis | Stability |
+|:--|:--|--:|--:|--:|:--|:--|:--|--:|--:|--:|--:|:--|:--|
+| fp32 | forward | 18 | 262,144 | 16 | in-place, es=1, bs=262144 | cuButterfly-auto-vectorized | online-reorder / cufftdx-block | 0.195942 | 0.082 | 21.406 | 1.077x | cuFFT | stable |
+| fp32 | forward | 18 | 262,144 | 16 | in-place, es=1, bs=262144 | VkFFT | library | 0.201103 | 0.080 | 20.856 | 1.050x | cuFFT | stable |
+| fp32 | forward | 18 | 262,144 | 16 | in-place, es=1, bs=262144 | cuFFT | library | 0.211098 | 0.076 | 19.869 | 1.000x | cuFFT | stable |
+| fp32 | forward | 20 | 1,048,576 | 4 | in-place, es=1, bs=1048576 | VkFFT | library | 0.206520 | 0.019 | 20.309 | 1.018x | cuFFT | stable |
+| fp32 | forward | 20 | 1,048,576 | 4 | in-place, es=1, bs=1048576 | cuFFT | library | 0.210330 | 0.019 | 19.942 | 1.000x | cuFFT | stable |
+| fp32 | forward | 20 | 1,048,576 | 4 | in-place, es=1, bs=1048576 | cuButterfly-auto-vectorized | online-reorder / cufftdx-block | 0.214733 | 0.019 | 19.533 | 0.979x | cuFFT | stable |
+
+## External Evidence
+
+- **fwht / Dao-AILab FHT**: measured-matching-protocol; five-trial correctness-checked refresh is archived separately. Existing evidence: `results/v100_external_baselines_summary.csv`.
+- **ntt / GPU-NTT**: measured-matching-protocol; natural and native bit-reversed contracts are archived separately. Existing evidence: `results/v100_external_baselines_summary.csv`.
diff --git a/results/comprehensive_v100_vectorized_fft_summary.csv b/results/comprehensive_v100_vectorized_fft_summary.csv
new file mode 100644
index 0000000..5b4789f
--- /dev/null
+++ b/results/comprehensive_v100_vectorized_fft_summary.csv
@@ -0,0 +1,7 @@
+case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,shared_layout,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class
+fft18_cub,fft-fp32-fwd-log18,cuButterfly-auto-vectorized,0,5,0.195942000,0.195389000,0.196137000,0.003817,0.001148,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,online-reorder,auto,cufftdx-block,shared,,recurrence,0.081657,21.405845,declared-reference,cuFFT,0.211097598,1.077347,faster
+fft18_vkfft,fft-fp32-fwd-log18,VkFFT,0,5,0.201103359,0.201052144,0.201287687,0.001171,0.000713,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,,0.079561,20.856459,declared-reference,cuFFT,0.211097598,1.049697,faster
+fft18_cufft,fft-fp32-fwd-log18,cuFFT,1,5,0.211097598,0.211077124,0.211527675,0.002134,0.001940,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,,0.075794,19.869028,declared-reference,cuFFT,0.211097598,1.000000,parity
+fft20_vkfft,fft-fp32-fwd-log20,VkFFT,0,5,0.206520334,0.206059515,0.206653446,0.002876,0.001140,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,,0.019369,20.309400,declared-reference,cuFFT,0.210329607,1.018445,parity
+fft20_cufft,fft-fp32-fwd-log20,cuFFT,1,5,0.210329607,0.210216954,0.210462719,0.001168,0.000779,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,,0.019018,19.941577,declared-reference,cuFFT,0.210329607,1.000000,parity
+fft20_cub,fft-fp32-fwd-log20,cuButterfly-auto-vectorized,0,5,0.214733000,0.213985000,0.218593000,0.021459,0.003861,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,online-reorder,auto,cufftdx-block,shared,,recurrence,0.018628,19.532648,declared-reference,cuFFT,0.210329607,0.979494,parity
diff --git a/results/fp64_address_cufft_logN16_raw.csv b/results/fp64_address_cufft_logN16_raw.csv
new file mode 100644
index 0000000..b142f73
--- /dev/null
+++ b/results/fp64_address_cufft_logN16_raw.csv
@@ -0,0 +1,6 @@
+trial,device,compute_capability,operator,precision,direction,normalization,placement,auto_select,backend,compute_unit,complex_multiply,cross_twiddle,direct_boundary,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,group_threads,group_ept,local_exchange,shared_layout,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_stride,warmup,repeat,h2d_ms,kernel_ms,d2h_ms,transforms_s,Gbutterfly_s,points_s,max_error,correct
+1,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,cufft,auto,four-mul,table,direct-strided,1,16,,,,,,0,,,shared,linear,scalar,0,named-barrier,0,0,0,8,8,0,0,0,0,0,0,16,65536,64,1,65536,1000,100,10.974528,0.343040,10.146848,186567.153697,97.814920,12226864984.673401,0.000000,-1
+2,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,cufft,auto,four-mul,table,direct-strided,1,16,,,,,,0,,,shared,linear,scalar,0,named-barrier,0,0,0,8,8,0,0,0,0,0,0,16,65536,64,1,65536,1000,100,10.939680,0.342856,10.109120,186667.456630,97.867508,12233438437.719091,0.000000,-1
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diff --git a/results/fp64_address_logN16_summary.csv b/results/fp64_address_logN16_summary.csv
new file mode 100644
index 0000000..92f92f1
--- /dev/null
+++ b/results/fp64_address_logN16_summary.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_address_recurrence_logN16_raw.csv b/results/fp64_address_recurrence_logN16_raw.csv
new file mode 100644
index 0000000..5b4f837
--- /dev/null
+++ b/results/fp64_address_recurrence_logN16_raw.csv
@@ -0,0 +1,11 @@
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diff --git a/results/fp64_address_scalar_logN16_raw.csv b/results/fp64_address_scalar_logN16_raw.csv
new file mode 100644
index 0000000..1fbae2b
--- /dev/null
+++ b/results/fp64_address_scalar_logN16_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_address_table_logN16_raw.csv b/results/fp64_address_table_logN16_raw.csv
new file mode 100644
index 0000000..c2b51c9
--- /dev/null
+++ b/results/fp64_address_table_logN16_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufft_logN16_confirm_raw.csv b/results/fp64_cufft_logN16_confirm_raw.csv
new file mode 100644
index 0000000..1b5224d
--- /dev/null
+++ b/results/fp64_cufft_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufftdx_logN16_confirm_raw.csv b/results/fp64_cufftdx_logN16_confirm_raw.csv
new file mode 100644
index 0000000..c97b5af
--- /dev/null
+++ b/results/fp64_cufftdx_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufftdx_logN16_mapping_raw.csv b/results/fp64_cufftdx_logN16_mapping_raw.csv
new file mode 100644
index 0000000..4ced7c7
--- /dev/null
+++ b/results/fp64_cufftdx_logN16_mapping_raw.csv
@@ -0,0 +1,109 @@
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diff --git a/results/fp64_cufftdx_logN16_mapping_summary.csv b/results/fp64_cufftdx_logN16_mapping_summary.csv
new file mode 100644
index 0000000..22a72ac
--- /dev/null
+++ b/results/fp64_cufftdx_logN16_mapping_summary.csv
@@ -0,0 +1,37 @@
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diff --git a/results/fp64_cufftdx_padded_logN16_confirm_raw.csv b/results/fp64_cufftdx_padded_logN16_confirm_raw.csv
new file mode 100644
index 0000000..a819ab7
--- /dev/null
+++ b/results/fp64_cufftdx_padded_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufftdx_padded_logN16_confirm_summary.csv b/results/fp64_cufftdx_padded_logN16_confirm_summary.csv
new file mode 100644
index 0000000..7c11a62
--- /dev/null
+++ b/results/fp64_cufftdx_padded_logN16_confirm_summary.csv
@@ -0,0 +1,2 @@
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diff --git a/results/fp64_cufftdx_prefix_padded_logN16_confirm_raw.csv b/results/fp64_cufftdx_prefix_padded_logN16_confirm_raw.csv
new file mode 100644
index 0000000..d5b7a63
--- /dev/null
+++ b/results/fp64_cufftdx_prefix_padded_logN16_confirm_raw.csv
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diff --git a/results/fp64_cufftdx_prefix_padded_logN16_confirm_summary.csv b/results/fp64_cufftdx_prefix_padded_logN16_confirm_summary.csv
new file mode 100644
index 0000000..ee62e89
--- /dev/null
+++ b/results/fp64_cufftdx_prefix_padded_logN16_confirm_summary.csv
@@ -0,0 +1,2 @@
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diff --git a/results/fp64_cufftdx_recurrence_logN16_confirm_raw.csv b/results/fp64_cufftdx_recurrence_logN16_confirm_raw.csv
new file mode 100644
index 0000000..2d041c3
--- /dev/null
+++ b/results/fp64_cufftdx_recurrence_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufftdx_recurrence_logN16_confirm_summary.csv b/results/fp64_cufftdx_recurrence_logN16_confirm_summary.csv
new file mode 100644
index 0000000..e253a64
--- /dev/null
+++ b/results/fp64_cufftdx_recurrence_logN16_confirm_summary.csv
@@ -0,0 +1,2 @@
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diff --git a/results/fp64_cufftdx_recurrence_mapping_raw.csv b/results/fp64_cufftdx_recurrence_mapping_raw.csv
new file mode 100644
index 0000000..99068d8
--- /dev/null
+++ b/results/fp64_cufftdx_recurrence_mapping_raw.csv
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diff --git a/results/fp64_cufftdx_recurrence_mapping_summary.csv b/results/fp64_cufftdx_recurrence_mapping_summary.csv
new file mode 100644
index 0000000..3d70a44
--- /dev/null
+++ b/results/fp64_cufftdx_recurrence_mapping_summary.csv
@@ -0,0 +1,37 @@
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diff --git a/results/fp64_cufftdx_suffix_padded_logN16_confirm_raw.csv b/results/fp64_cufftdx_suffix_padded_logN16_confirm_raw.csv
new file mode 100644
index 0000000..5c0b434
--- /dev/null
+++ b/results/fp64_cufftdx_suffix_padded_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufftdx_suffix_padded_logN16_confirm_summary.csv b/results/fp64_cufftdx_suffix_padded_logN16_confirm_summary.csv
new file mode 100644
index 0000000..883131b
--- /dev/null
+++ b/results/fp64_cufftdx_suffix_padded_logN16_confirm_summary.csv
@@ -0,0 +1,2 @@
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diff --git a/results/fp64_cufftdx_xor_swizzle_logN16_confirm_raw.csv b/results/fp64_cufftdx_xor_swizzle_logN16_confirm_raw.csv
new file mode 100644
index 0000000..854f2af
--- /dev/null
+++ b/results/fp64_cufftdx_xor_swizzle_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_cufftdx_xor_swizzle_logN16_confirm_summary.csv b/results/fp64_cufftdx_xor_swizzle_logN16_confirm_summary.csv
new file mode 100644
index 0000000..1c32a15
--- /dev/null
+++ b/results/fp64_cufftdx_xor_swizzle_logN16_confirm_summary.csv
@@ -0,0 +1,2 @@
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diff --git a/results/fp64_cufftdx_xor_swizzle_mapping_raw.csv b/results/fp64_cufftdx_xor_swizzle_mapping_raw.csv
new file mode 100644
index 0000000..27497d5
--- /dev/null
+++ b/results/fp64_cufftdx_xor_swizzle_mapping_raw.csv
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diff --git a/results/fp64_cufftdx_xor_swizzle_mapping_summary.csv b/results/fp64_cufftdx_xor_swizzle_mapping_summary.csv
new file mode 100644
index 0000000..4ec4e0e
--- /dev/null
+++ b/results/fp64_cufftdx_xor_swizzle_mapping_summary.csv
@@ -0,0 +1,37 @@
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+19,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,512,4,4,2,8,8,1,0,0,named-barrier,3,0.382300,0.381829,0.382464,87.769866,1.081456
+20,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,512,8,4,8,8,8,1,0,0,named-barrier,3,0.382546,0.382484,0.382976,87.713475,1.082152
+21,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,256,8,8,8,8,8,1,0,0,named-barrier,3,0.382996,0.382812,0.383099,87.610291,1.083425
+22,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,256,4,8,2,8,8,1,0,0,named-barrier,3,0.383263,0.383058,0.383590,87.549427,1.084180
+23,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,128,4,4,8,2,8,1,0,0,named-barrier,3,0.384778,0.383140,0.385659,87.204594,1.088466
+24,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,512,4,8,8,16,8,1,0,0,named-barrier,3,0.385147,0.385126,0.385331,87.121137,1.089509
+25,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,128,8,4,4,2,8,1,0,0,named-barrier,3,0.388977,0.385843,0.389120,86.263362,1.100344
+26,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,512,8,8,4,16,8,1,0,0,named-barrier,3,0.389202,0.389181,0.389571,86.213425,1.100980
+27,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,128,4,4,2,2,8,1,0,0,named-barrier,3,0.395837,0.395448,0.396902,84.768215,1.119749
+28,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,128,8,4,8,2,8,1,0,0,named-barrier,3,0.397046,0.396452,0.398090,84.510245,1.123169
+29,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,512,8,8,8,16,8,1,0,0,named-barrier,3,0.398459,0.398438,0.398684,84.210529,1.127167
+30,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,512,4,8,2,16,8,1,0,0,named-barrier,3,0.398582,0.398418,0.398602,84.184562,1.127514
+31,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,128,8,8,16,4,8,1,0,0,named-barrier,3,0.426435,0.426312,0.426496,78.686008,1.206305
+32,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,256,8,4,16,4,8,1,0,0,named-barrier,3,0.428093,0.428073,0.428134,78.381089,1.210996
+33,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,512,8,4,16,8,8,1,0,0,named-barrier,3,0.432353,0.432148,0.432394,77.608828,1.223046
+34,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,256,8,8,16,8,8,1,0,0,named-barrier,3,0.433275,0.433172,0.433275,77.443754,1.225655
+35,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,128,8,4,16,2,8,1,0,0,named-barrier,3,0.447836,0.447529,0.448123,74.925687,1.266845
+36,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,512,8,8,16,16,8,1,0,0,named-barrier,3,0.448389,0.448307,0.448553,74.833284,1.268409
diff --git a/results/fp64_logN16_confirm_summary.csv b/results/fp64_logN16_confirm_summary.csv
new file mode 100644
index 0000000..d65aff1
--- /dev/null
+++ b/results/fp64_logN16_confirm_summary.csv
@@ -0,0 +1,4 @@
+rank,operator,precision,direction,normalization,placement,logN,N,batch,element_stride,batch_stride,backend,compute_unit,complex_multiply,cross_twiddle,local_exchange,fft_core,stage_space,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,stage_handoff,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,median_Gbutterfly_s,slowdown_vs_best
+1,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,cufft,auto,four-mul,table,shared,scalar,0,0,0,0,8,8,0,0,0,0,0,0,named-barrier,5,0.342927,0.342743,0.343204,97.847052,1.000000
+2,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,table,shared,cufftdx-block,0,32,256,128,4,8,4,4,8,1,0,0,named-barrier,5,0.383949,0.383734,0.384492,87.392992,1.119623
+3,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,radix4,four-mul,table,shared,scalar,0,128,0,0,8,8,0,0,8,1,0,0,named-barrier,5,0.521492,0.520755,0.522916,64.343079,1.520708
diff --git a/results/fp64_logN16_twiddle_summary.csv b/results/fp64_logN16_twiddle_summary.csv
new file mode 100644
index 0000000..9c8a880
--- /dev/null
+++ b/results/fp64_logN16_twiddle_summary.csv
@@ -0,0 +1,6 @@
+rank,operator,precision,direction,normalization,placement,logN,N,batch,element_stride,batch_stride,backend,compute_unit,complex_multiply,cross_twiddle,local_exchange,shared_layout,fft_core,stage_space,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,stage_handoff,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,median_Gbutterfly_s,slowdown_vs_best
+1,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,cufft,auto,four-mul,table,shared,linear,scalar,0,0,0,0,8,8,0,0,0,0,0,0,named-barrier,5,0.342927,0.342743,0.343204,97.847052,1.000000
+2,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,128,4,8,4,4,8,1,0,0,named-barrier,5,0.353526,0.353208,0.353700,94.913684,1.030907
+3,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,256,128,4,8,4,4,8,1,0,0,named-barrier,5,0.361708,0.361605,0.362086,92.766748,1.054767
+4,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,table,shared,linear,cufftdx-block,0,32,256,128,4,8,4,4,8,1,0,0,named-barrier,5,0.383949,0.383734,0.384492,87.392992,1.119623
+5,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,radix4,four-mul,table,shared,linear,scalar,0,128,0,0,8,8,0,0,8,1,0,0,named-barrier,5,0.521492,0.520755,0.522916,64.343079,1.520708
diff --git a/results/fp64_robustness_batch_analysis.md b/results/fp64_robustness_batch_analysis.md
new file mode 100644
index 0000000..7e4c425
--- /dev/null
+++ b/results/fp64_robustness_batch_analysis.md
@@ -0,0 +1,46 @@
+# FP64 FFT Length/Batch Robustness
+
+All rows use the per-length mapping selected by the V100 coarse scan, recurrence twiddles,
+and XOR-swizzled prefix staging. Trials alternate cuButterfly/cuFFT execution order.
+
+Among 25 stable shapes with both medians at least 0.020 ms, cuButterfly has
+higher median throughput in 20/25 and non-overlapping faster trial ranges in
+19/25. Short rows remain measurements, not stable performance claims.
+
+| logN | Batch | Points | Split | Prefix | Suffix | cuButterfly ms | cuFFT ms | Throughput | Quality | Trial ranges |
+|--:|--:|--:|:--|:--|:--|--:|--:|--:|:--|:--|
+| 14 | 1 | 16384 | `7+7` | `128/4` | `128/4` | 0.009339 | 0.014264 | 1.527x | short | faster |
+| 14 | 2 | 32768 | `7+7` | `128/4` | `128/4` | 0.010578 | 0.014285 | 1.350x | short | faster |
+| 14 | 4 | 65536 | `7+7` | `128/4` | `128/4` | 0.012892 | 0.014397 | 1.117x | short | faster |
+| 14 | 8 | 131072 | `7+7` | `128/4` | `128/4` | 0.017029 | 0.016722 | 0.982x | short | slower |
+| 14 | 16 | 262144 | `7+7` | `128/4` | `128/4` | 0.025969 | 0.028058 | 1.080x | stable | overlap |
+| 14 | 32 | 524288 | `7+7` | `128/4` | `128/4` | 0.050883 | 0.049500 | 0.973x | stable | slower |
+| 14 | 64 | 1048576 | `7+7` | `128/4` | `128/4` | 0.092856 | 0.095519 | 1.029x | stable | faster |
+| 15 | 1 | 32768 | `7+8` | `128/4` | `128/8` | 0.009738 | 0.012319 | 1.265x | short | faster |
+| 15 | 2 | 65536 | `7+8` | `128/4` | `128/8` | 0.010854 | 0.012462 | 1.148x | short | faster |
+| 15 | 4 | 131072 | `7+8` | `128/4` | `128/8` | 0.017295 | 0.016927 | 0.979x | short | overlap |
+| 15 | 8 | 262144 | `7+8` | `128/4` | `128/8` | 0.029112 | 0.028436 | 0.977x | stable | overlap |
+| 15 | 16 | 524288 | `7+8` | `128/4` | `128/8` | 0.049889 | 0.049828 | 0.999x | stable | overlap |
+| 15 | 32 | 1048576 | `7+8` | `128/4` | `128/8` | 0.092006 | 0.093788 | 1.019x | stable | faster |
+| 15 | 64 | 2097152 | `7+8` | `128/4` | `128/8` | 0.174141 | 0.178084 | 1.023x | stable | faster |
+| 16 | 1 | 65536 | `8+8` | `128/8` | `128/8` | 0.011018 | 0.012206 | 1.108x | short | faster |
+| 16 | 2 | 131072 | `8+8` | `128/8` | `128/8` | 0.015237 | 0.014377 | 0.944x | short | slower |
+| 16 | 4 | 262144 | `8+8` | `128/8` | `128/8` | 0.026081 | 0.025242 | 0.968x | stable | slower |
+| 16 | 8 | 524288 | `8+8` | `128/8` | `128/8` | 0.048916 | 0.050760 | 1.038x | stable | faster |
+| 16 | 16 | 1048576 | `8+8` | `128/8` | `128/8` | 0.093327 | 0.092365 | 0.990x | stable | slower |
+| 16 | 32 | 2097152 | `8+8` | `128/8` | `128/8` | 0.174776 | 0.178012 | 1.019x | stable | faster |
+| 16 | 64 | 4194304 | `8+8` | `128/8` | `128/8` | 0.339364 | 0.343040 | 1.011x | stable | faster |
+| 17 | 1 | 131072 | `8+9` | `128/8` | `256/8` | 0.017664 | 0.026685 | 1.511x | short | faster |
+| 17 | 2 | 262144 | `8+9` | `128/8` | `256/8` | 0.027290 | 0.035011 | 1.283x | stable | faster |
+| 17 | 4 | 524288 | `8+9` | `128/8` | `256/8` | 0.052357 | 0.053842 | 1.028x | stable | faster |
+| 17 | 8 | 1048576 | `8+9` | `128/8` | `256/8` | 0.096276 | 0.109230 | 1.135x | stable | faster |
+| 17 | 16 | 2097152 | `8+9` | `128/8` | `256/8` | 0.179753 | 0.203725 | 1.133x | stable | faster |
+| 17 | 32 | 4194304 | `8+9` | `128/8` | `256/8` | 0.346307 | 0.395213 | 1.141x | stable | faster |
+| 17 | 64 | 8388608 | `8+9` | `128/8` | `256/8` | 0.678134 | 0.754668 | 1.113x | stable | faster |
+| 18 | 1 | 262144 | `9+9` | `256/8` | `256/8` | 0.029194 | 0.042455 | 1.454x | stable | faster |
+| 18 | 2 | 524288 | `9+9` | `256/8` | `256/8` | 0.055306 | 0.059341 | 1.073x | stable | faster |
+| 18 | 4 | 1048576 | `9+9` | `256/8` | `256/8` | 0.100506 | 0.128379 | 1.277x | stable | faster |
+| 18 | 8 | 2097152 | `9+9` | `256/8` | `256/8` | 0.185283 | 0.225044 | 1.215x | stable | faster |
+| 18 | 16 | 4194304 | `9+9` | `256/8` | `256/8` | 0.354877 | 0.421970 | 1.189x | stable | faster |
+| 18 | 32 | 8388608 | `9+9` | `256/8` | `256/8` | 0.693135 | 0.780964 | 1.127x | stable | faster |
+| 18 | 64 | 16777216 | `9+9` | `256/8` | `256/8` | 1.370327 | 1.485660 | 1.084x | stable | faster |
diff --git a/results/fp64_robustness_batch_raw.csv b/results/fp64_robustness_batch_raw.csv
new file mode 100644
index 0000000..0918fe1
--- /dev/null
+++ b/results/fp64_robustness_batch_raw.csv
@@ -0,0 +1,351 @@
+trial,device,compute_capability,operator,precision,direction,normalization,placement,auto_select,backend,compute_unit,complex_multiply,cross_twiddle,direct_boundary,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,group_threads,group_ept,local_exchange,shared_layout,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_stride,warmup,repeat,h2d_ms,kernel_ms,d2h_ms,transforms_s,Gbutterfly_s,points_s,max_error,correct
+1,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,online-reorder,auto,four-mul,recurrence,direct-strided,2,7x7,128x128,4x4,recurrence,direct-strided,global-scratch,2,128x128,4x4,shared,xor-swizzle,cufftdx-block,0,named-barrier,128,128,128,4,4,4,4,7,1,0,0,14,16384,1,1,16384,1000,100,0.067040,0.009329,0.081696,107196.761041,12.294182,1756311732.892490,0.000000,-1
+1,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,cufft,auto,four-mul,table,direct-strided,1,14,,,,,,0,,,shared,linear,scalar,0,named-barrier,0,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.066208,0.014264,0.095328,70104.989117,8.040201,1148600141.694182,0.000000,-1
+2,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,cufft,auto,four-mul,table,direct-strided,1,14,,,,,,0,,,shared,linear,scalar,0,named-barrier,0,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.066464,0.014264,0.094080,70104.989117,8.040201,1148600141.694182,0.000000,-1
+2,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,online-reorder,auto,four-mul,recurrence,direct-strided,2,7x7,128x128,4x4,recurrence,direct-strided,global-scratch,2,128x128,4x4,shared,xor-swizzle,cufftdx-block,0,named-barrier,128,128,128,4,4,4,4,7,1,0,0,14,16384,1,1,16384,1000,100,0.067840,0.009339,0.087904,107079.221975,12.280702,1754385972.840813,0.000000,-1
+3,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,online-reorder,auto,four-mul,recurrence,direct-strided,2,7x7,128x128,4x4,recurrence,direct-strided,global-scratch,2,128x128,4x4,shared,xor-swizzle,cufftdx-block,0,named-barrier,128,128,128,4,4,4,4,7,1,0,0,14,16384,1,1,16384,1000,100,0.066464,0.009318,0.082208,107314.558431,12.307692,1758241725.339002,0.000000,-1
+3,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,cufft,auto,four-mul,table,direct-strided,1,14,,,,,,0,,,shared,linear,scalar,0,named-barrier,0,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.065760,0.014275,0.098272,70054.699126,8.034433,1147776190.473506,0.000000,-1
+4,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,cufft,auto,four-mul,table,direct-strided,1,14,,,,,,0,,,shared,linear,scalar,0,named-barrier,0,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.065696,0.014254,0.096416,70155.351364,8.045977,1149425276.740288,0.000000,-1
+4,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,online-reorder,auto,four-mul,recurrence,direct-strided,2,7x7,128x128,4x4,recurrence,direct-strided,global-scratch,2,128x128,4x4,shared,xor-swizzle,cufftdx-block,0,named-barrier,128,128,128,4,4,4,4,7,1,0,0,14,16384,1,1,16384,1000,100,0.074496,0.009349,0.082560,106961.940386,12.267251,1752464431.277015,0.000000,-1
+5,Tesla V100-SXM2-16GB,7.0,fft,fp64,forward,none,out-of-place,0,online-reorder,auto,four-mul,recurrence,direct-strided,2,7x7,128x128,4x4,recurrence,direct-strided,global-scratch,2,128x128,4x4,shared,xor-swizzle,cufftdx-block,0,named-barrier,128,128,128,4,4,4,4,7,1,0,0,14,16384,1,1,16384,1000,100,0.066176,0.009339,0.084032,107079.221975,12.280702,1754385972.840813,0.000000,-1
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diff --git a/results/fp64_robustness_batch_summary.csv b/results/fp64_robustness_batch_summary.csv
new file mode 100644
index 0000000..e118522
--- /dev/null
+++ b/results/fp64_robustness_batch_summary.csv
@@ -0,0 +1,36 @@
+logN,batch,total_points,local_stages,prefix_threads,prefix_ept,suffix_threads,suffix_ept,trials,cuntt_median_ms,cuntt_min_ms,cuntt_max_ms,cufft_median_ms,cufft_min_ms,cufft_max_ms,throughput_vs_cufft,timing_quality,range_separation
+14,1,16384,7,128,4,128,4,5,0.009339,0.009318,0.009349,0.014264,0.014254,0.014275,1.5273583895492022,short,faster
+14,2,32768,7,128,4,128,4,5,0.010578,0.010568,0.010598,0.014285,0.014275,0.014295,1.3504443183966723,short,faster
+14,4,65536,7,128,4,128,4,5,0.012892,0.012872,0.012913,0.014397,0.014377,0.014418,1.1167390629847966,short,faster
+14,8,131072,7,128,4,128,4,5,0.017029,0.017019,0.01705,0.016722,0.016722,0.016773,0.9819719302366552,short,slower
+14,16,262144,7,128,4,128,4,5,0.025969,0.025876,0.028887,0.028058,0.026798,0.029716,1.080442065539682,stable,overlap
+14,32,524288,7,128,4,128,4,5,0.050883,0.050719,0.050954,0.0495,0.04949,0.049674,0.9728199988208244,stable,slower
+14,64,1048576,7,128,4,128,4,5,0.092856,0.092795,0.092938,0.095519,0.095468,0.095652,1.0286788145084864,stable,faster
+15,1,32768,7,128,4,128,8,5,0.009738,0.009718,0.009779,0.012319,0.012268,0.012329,1.26504415691107,short,faster
+15,2,65536,7,128,4,128,8,5,0.010854,0.010854,0.010865,0.012462,0.012442,0.012472,1.1481481481481481,short,faster
+15,4,131072,7,128,4,128,8,5,0.017295,0.015002,0.017357,0.016927,0.014725,0.016968,0.9787221740387395,short,overlap
+15,8,262144,7,128,4,128,8,5,0.029112,0.028068,0.029215,0.028436,0.028109,0.029215,0.976779334982138,stable,overlap
+15,16,524288,7,128,4,128,8,5,0.049889,0.049879,0.052019,0.049828,0.049644,0.050104,0.9987772855739742,stable,overlap
+15,32,1048576,7,128,4,128,8,5,0.092006,0.091996,0.09215,0.093788,0.093676,0.093952,1.0193683020672564,stable,faster
+15,64,2097152,7,128,4,128,8,5,0.174141,0.17409,0.174203,0.178084,0.177961,0.178115,1.0226425712497345,stable,faster
+16,1,65536,8,128,8,128,8,5,0.011018,0.011018,0.011039,0.012206,0.012196,0.012247,1.1078235614449083,short,faster
+16,2,131072,8,128,8,128,8,5,0.015237,0.015206,0.015258,0.014377,0.014356,0.014387,0.9435584432631094,short,slower
+16,4,262144,8,128,8,128,8,5,0.026081,0.026061,0.026112,0.025242,0.025201,0.025272,0.9678309880756106,stable,slower
+16,8,524288,8,128,8,128,8,5,0.048916,0.048794,0.049009,0.05076,0.050606,0.050821,1.0376972769645922,stable,faster
+16,16,1048576,8,128,8,128,8,5,0.093327,0.093235,0.093522,0.092365,0.092303,0.092488,0.9896921576821285,stable,slower
+16,32,2097152,8,128,8,128,8,5,0.174776,0.174684,0.174807,0.178012,0.177848,0.178063,1.0185151279351856,stable,faster
+16,64,4194304,8,128,8,128,8,5,0.339364,0.339251,0.339548,0.34304,0.342446,0.34305,1.0108320269680933,stable,faster
+17,1,131072,8,128,8,256,8,5,0.017664,0.017623,0.017746,0.026685,0.026655,0.026767,1.5106997282608696,short,faster
+17,2,262144,8,128,8,256,8,5,0.02729,0.027259,0.027331,0.035011,0.03499,0.035021,1.282924148039575,stable,faster
+17,4,524288,8,128,8,256,8,5,0.052357,0.052081,0.052603,0.053842,0.053576,0.053996,1.0283629696124683,stable,faster
+17,8,1048576,8,128,8,256,8,5,0.096276,0.096133,0.096819,0.10923,0.109199,0.109292,1.1345506668328555,stable,faster
+17,16,2097152,8,128,8,256,8,5,0.179753,0.179558,0.179784,0.203725,0.203346,0.204073,1.1333607784014732,stable,faster
+17,32,4194304,8,128,8,256,8,5,0.346307,0.345979,0.350413,0.395213,0.394885,0.39593,1.141221517324224,stable,faster
+17,64,8388608,8,128,8,256,8,5,0.678134,0.678031,0.678369,0.754668,0.754043,0.755026,1.1128597002952219,stable,faster
+18,1,262144,9,256,8,256,8,5,0.029194,0.029174,0.029276,0.042455,0.042424,0.042465,1.4542371720216483,stable,faster
+18,2,524288,9,256,8,256,8,5,0.055306,0.054989,0.055726,0.059341,0.05932,0.059617,1.0729577261056666,stable,faster
+18,4,1048576,9,256,8,256,8,5,0.100506,0.100311,0.100782,0.128379,0.128317,0.128399,1.2773267267625812,stable,faster
+18,8,2097152,9,256,8,256,8,5,0.185283,0.185129,0.185815,0.225044,0.224676,0.225413,1.2145960503661966,stable,faster
+18,16,4194304,9,256,8,256,8,5,0.354877,0.354642,0.355154,0.42197,0.421018,0.422246,1.1890598714484173,stable,faster
+18,32,8388608,9,256,8,256,8,5,0.693135,0.6929,0.693565,0.780964,0.779796,0.781619,1.1267126894472217,stable,faster
+18,64,16777216,9,256,8,256,8,5,1.370327,1.369907,1.370675,1.48566,1.484984,1.488405,1.0841645826142228,stable,faster
diff --git a/results/fp64_robustness_confirm_summary.csv b/results/fp64_robustness_confirm_summary.csv
new file mode 100644
index 0000000..02ad6fa
--- /dev/null
+++ b/results/fp64_robustness_confirm_summary.csv
@@ -0,0 +1,11 @@
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+1,fft,fp64,forward,none,out-of-place,17,131072,32,1,131072,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,256,8,8,4,4,8,1,0,0,named-barrier,5,0.346143,0.345917,0.346296,102.996770,1.000000
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+1,fft,fp64,forward,none,out-of-place,18,262144,16,1,262144,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,256,8,8,4,4,9,1,0,0,named-barrier,5,0.354970,0.354447,0.355103,106.343577,1.000000
+2,fft,fp64,forward,none,out-of-place,18,262144,16,1,262144,cufft,auto,four-mul,table,shared,linear,scalar,0,0,0,0,8,8,0,0,0,0,0,0,named-barrier,5,0.422154,0.421612,0.423066,89.419297,1.189267
diff --git a/results/fp64_robustness_crossover_logN14_b32_raw.csv b/results/fp64_robustness_crossover_logN14_b32_raw.csv
new file mode 100644
index 0000000..31b5967
--- /dev/null
+++ b/results/fp64_robustness_crossover_logN14_b32_raw.csv
@@ -0,0 +1,73 @@
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diff --git a/results/fp64_robustness_crossover_logN15_b16_raw.csv b/results/fp64_robustness_crossover_logN15_b16_raw.csv
new file mode 100644
index 0000000..2622cb4
--- /dev/null
+++ b/results/fp64_robustness_crossover_logN15_b16_raw.csv
@@ -0,0 +1,145 @@
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diff --git a/results/fp64_robustness_crossover_logN15_b8_raw.csv b/results/fp64_robustness_crossover_logN15_b8_raw.csv
new file mode 100644
index 0000000..ba9e6f3
--- /dev/null
+++ b/results/fp64_robustness_crossover_logN15_b8_raw.csv
@@ -0,0 +1,145 @@
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diff --git a/results/fp64_robustness_crossover_logN16_b16_raw.csv b/results/fp64_robustness_crossover_logN16_b16_raw.csv
new file mode 100644
index 0000000..25a676c
--- /dev/null
+++ b/results/fp64_robustness_crossover_logN16_b16_raw.csv
@@ -0,0 +1,217 @@
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diff --git a/results/fp64_robustness_crossover_logN16_b4_raw.csv b/results/fp64_robustness_crossover_logN16_b4_raw.csv
new file mode 100644
index 0000000..0e4f8ce
--- /dev/null
+++ b/results/fp64_robustness_crossover_logN16_b4_raw.csv
@@ -0,0 +1,217 @@
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diff --git a/results/fp64_robustness_crossover_summary.csv b/results/fp64_robustness_crossover_summary.csv
new file mode 100644
index 0000000..c3eb953
--- /dev/null
+++ b/results/fp64_robustness_crossover_summary.csv
@@ -0,0 +1,793 @@
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+59,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,512,8,4,32,16,7,1,0,0,named-barrier,1,0.074260,0.074260,0.074260,49.420849,1.379221
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+61,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,512,4,8,16,32,7,1,0,0,named-barrier,1,0.075203,0.075203,0.075203,48.801742,1.396735
+62,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,128,512,8,8,8,32,7,1,0,0,named-barrier,1,0.075264,0.075264,0.075264,48.761905,1.397868
+63,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,512,128,8,8,32,8,7,1,0,0,named-barrier,1,0.075694,0.075694,0.075694,48.484851,1.405854
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+68,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,512,256,8,8,32,16,7,1,0,0,named-barrier,1,0.078275,0.078275,0.078275,46.886445,1.453791
+69,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,512,512,8,8,32,32,7,1,0,0,named-barrier,1,0.081285,0.081285,0.081285,45.149908,1.509695
+70,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,512,512,8,4,32,16,7,1,0,0,named-barrier,1,0.082043,0.082043,0.082043,44.732905,1.523773
+71,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,512,512,4,8,16,32,7,1,0,0,named-barrier,1,0.082350,0.082350,0.082350,44.566027,1.529475
+72,fft,fp64,forward,none,out-of-place,14,16384,32,1,16384,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,512,512,8,8,32,32,7,1,0,0,named-barrier,1,0.089006,0.089006,0.089006,41.233317,1.653096
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diff --git a/results/fp64_robustness_cufft_confirm_raw.csv b/results/fp64_robustness_cufft_confirm_raw.csv
new file mode 100644
index 0000000..8427882
--- /dev/null
+++ b/results/fp64_robustness_cufft_confirm_raw.csv
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diff --git a/results/fp64_robustness_logN14_confirm_raw.csv b/results/fp64_robustness_logN14_confirm_raw.csv
new file mode 100644
index 0000000..7ac313d
--- /dev/null
+++ b/results/fp64_robustness_logN14_confirm_raw.csv
@@ -0,0 +1,6 @@
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diff --git a/results/fp64_robustness_logN15_confirm_raw.csv b/results/fp64_robustness_logN15_confirm_raw.csv
new file mode 100644
index 0000000..f6d2e2c
--- /dev/null
+++ b/results/fp64_robustness_logN15_confirm_raw.csv
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diff --git a/results/fp64_robustness_logN16_confirm_raw.csv b/results/fp64_robustness_logN16_confirm_raw.csv
new file mode 100644
index 0000000..7e4befc
--- /dev/null
+++ b/results/fp64_robustness_logN16_confirm_raw.csv
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diff --git a/results/fp64_robustness_logN17_confirm_raw.csv b/results/fp64_robustness_logN17_confirm_raw.csv
new file mode 100644
index 0000000..cd09408
--- /dev/null
+++ b/results/fp64_robustness_logN17_confirm_raw.csv
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diff --git a/results/fp64_robustness_logN18_confirm_raw.csv b/results/fp64_robustness_logN18_confirm_raw.csv
new file mode 100644
index 0000000..afae5fa
--- /dev/null
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diff --git a/results/fp64_robustness_mapping_coarse_raw.csv b/results/fp64_robustness_mapping_coarse_raw.csv
new file mode 100644
index 0000000..c2446b4
--- /dev/null
+++ b/results/fp64_robustness_mapping_coarse_raw.csv
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diff --git a/results/fp64_robustness_mapping_coarse_summary.csv b/results/fp64_robustness_mapping_coarse_summary.csv
new file mode 100644
index 0000000..dcab9e3
--- /dev/null
+++ b/results/fp64_robustness_mapping_coarse_summary.csv
@@ -0,0 +1,649 @@
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+13,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,128,8,4,4,4,9,1,0,0,named-barrier,1,0.351181,0.351181,0.351181,95.547458,1.025262
+14,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,linear,cufftdx-block,0,32,128,256,8,4,4,4,8,1,0,0,named-barrier,1,0.351232,0.351232,0.351232,95.533530,1.025411
+15,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,256,256,4,4,8,2,7,1,0,0,named-barrier,1,0.351898,0.351898,0.351898,95.352831,1.027355
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+17,fft,fp64,forward,none,out-of-place,16,65536,64,1,65536,online-reorder,auto,four-mul,recurrence,shared,xor-swizzle,cufftdx-block,0,32,128,128,8,4,4,2,8,1,0,0,named-barrier,1,0.352051,0.352051,0.352051,95.311228,1.027802
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diff --git a/results/fp64_scalar_logN16_coarse_raw.csv b/results/fp64_scalar_logN16_coarse_raw.csv
new file mode 100644
index 0000000..95d877d
--- /dev/null
+++ b/results/fp64_scalar_logN16_coarse_raw.csv
@@ -0,0 +1,796 @@
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diff --git a/results/fp64_scalar_logN16_coarse_summary.csv b/results/fp64_scalar_logN16_coarse_summary.csv
new file mode 100644
index 0000000..dcd36bb
--- /dev/null
+++ b/results/fp64_scalar_logN16_coarse_summary.csv
@@ -0,0 +1,266 @@
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diff --git a/results/fp64_scalar_logN16_confirm_raw.csv b/results/fp64_scalar_logN16_confirm_raw.csv
new file mode 100644
index 0000000..7c3bb7f
--- /dev/null
+++ b/results/fp64_scalar_logN16_confirm_raw.csv
@@ -0,0 +1,6 @@
+trial,device,compute_capability,operator,precision,direction,normalization,placement,auto_select,backend,compute_unit,complex_multiply,cross_twiddle,direct_boundary,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,group_threads,group_ept,local_exchange,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_stride,warmup,repeat,h2d_ms,kernel_ms,d2h_ms,transforms_s,Gbutterfly_s,points_s,max_error,correct
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diff --git a/results/ncu_fft_vectorized/attribution.csv b/results/ncu_fft_vectorized/attribution.csv
new file mode 100644
index 0000000..1bb12de
--- /dev/null
+++ b/results/ncu_fft_vectorized/attribution.csv
@@ -0,0 +1,5 @@
+configuration,label,time_us,dram_read_mib,dram_write_mib,shared_load_bank_conflicts,shared_store_bank_conflicts,warp_instructions,fp32_thread_instructions,dram_peak_pct,l2_hit_pct,l1_hit_pct,active_warps_pct,barrier_stall_pct,long_scoreboard_stall_pct,kernel_count,shared_bank_conflicts,time_us_vs_pre_vector,dram_read_mib_vs_pre_vector,dram_write_mib_vs_pre_vector,warp_instructions_vs_pre_vector,shared_bank_conflicts_vs_pre_vector,cuda_event_ms,cuda_event_ms_vs_pre_vector
+pre-vector fixed,fft20_online_b16,917.6,274.488037109375,256.626708984375,5085525.0,14680064.0,138739712.0,1572864000.0,67.55001987794246,66.82936878814299,6.65994106364429,48.59744481255449,11.92259912816042,32.78359511769835,2,19765589.0,1.0,1.0,1.0,1.0,1.0,0.926618,1.0
+post-vector fixed,post_vector_fixed_b16,832.3520000000001,268.849365234375,256.66021728515625,5193417.0,14680064.0,111607808.0,1572864000.0,73.67827649840451,66.19297374187843,6.675425781400176,48.21416516089346,13.33954980585137,27.862626581061857,2,19873481.0,0.9070967741935485,0.9794574949991239,1.000130572148604,0.8044402456306093,1.0054585775308795,0.829174,0.8948390814769408
+post-vector selected,post_vector_selected_b16,855.552,263.101806640625,259.73687744140625,5061796.0,13049427.0,94928896.0,1459617792.0,71.31516943447038,72.15325291741472,4.225166068222621,36.177709829443444,10.578160906642728,25.90875561041293,2,18111223.0,0.9323801220575414,0.9585182997821762,1.0121194261865416,0.6842229570146434,0.9163006981476747,0.764334,0.8248641835146737
+cuFFT,post_vector_cufft_b16,773.568,256.01446533203125,257.27374267578125,0.0,2097152.0,69468160.0,1608515584.0,77.44232026143791,62.2724183006536,1.6847058823529413,24.105032679738564,4.7003594771241834,21.34699346405229,2,2097152.0,0.8430340017436792,0.9326980804996517,1.0025213030006384,0.5007085498346717,0.10610116399769316,0.729416,0.7871809095010025
diff --git a/results/ncu_fft_vectorized/attribution.md b/results/ncu_fft_vectorized/attribution.md
new file mode 100644
index 0000000..d5129e3
--- /dev/null
+++ b/results/ncu_fft_vectorized/attribution.md
@@ -0,0 +1,17 @@
+# FFT Vectorized-Boundary NCU Attribution
+
+All cuButterfly rows use FP32 forward `logN=20`, batch 16. The fixed
+rows use the same 512/512-thread, EPT 8/8 mapping, isolating the code change.
+NCU replay time is attribution-only; CUDA-event scans remain authoritative.
+
+| Configuration | CUDA-event ms | NCU time us | Kernels | DRAM read MiB | DRAM write MiB | Warp inst. | Bank conflicts | DRAM peak | Barrier stall | Scoreboard stall |
+|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|
+| pre-vector fixed | 0.926618 | 917.600 | 2 | 274.49 | 256.63 | 138739712 | 19765589 | 67.6% | 11.9% | 32.8% |
+| post-vector fixed | 0.829174 | 832.352 | 2 | 268.85 | 256.66 | 111607808 | 19873481 | 73.7% | 13.3% | 27.9% |
+| post-vector selected | 0.764334 | 855.552 | 2 | 263.10 | 259.74 | 94928896 | 18111223 | 71.3% | 10.6% | 25.9% |
+| cuFFT | 0.729416 | 773.568 | 2 | 256.01 | 257.27 | 69468160 | 2097152 | 77.4% | 4.7% | 21.3% |
+
+## Controlled Changes
+
+- Vectorizing the same fixed mapping changes replay time by -9.3%, warp instructions by -19.6%, and DRAM writes by +0.0%. The matching CUDA-event change is -10.5%.
+- CUDA-event timing selects the 256/128 mapping: it is -7.8% versus the post-vector fixed point. NCU replay reverses that ordering by +2.8%; replay time must not be used as the mapping-performance result.
diff --git a/results/ncu_fft_vectorized/post_vector_cufft_b16.csv b/results/ncu_fft_vectorized/post_vector_cufft_b16.csv
new file mode 100644
index 0000000..f09625a
--- /dev/null
+++ b/results/ncu_fft_vectorized/post_vector_cufft_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 1493868 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 1493868
+"ID","Process ID","Process Name","Host Name","Kernel Name","Kernel 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diff --git a/results/ncu_fft_vectorized/post_vector_fixed_b16.csv b/results/ncu_fft_vectorized/post_vector_fixed_b16.csv
new file mode 100644
index 0000000..3d2f2e5
--- /dev/null
+++ b/results/ncu_fft_vectorized/post_vector_fixed_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 1491920 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 1491920
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diff --git a/results/ncu_fft_vectorized/post_vector_selected_b16.csv b/results/ncu_fft_vectorized/post_vector_selected_b16.csv
new file mode 100644
index 0000000..30074f7
--- /dev/null
+++ b/results/ncu_fft_vectorized/post_vector_selected_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 1492989 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 1492989
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+"0","1492989","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)1024>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<float>, cufftdx::ElementsPerThread<(unsigned int)16>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex32 *, cuntt::Complex32 *, const cuntt::Complex32 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Aug-01 17:57:35","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","141,663,296","134,538,976","68.17","450,912","4,199,215","7,656,010","5.19","64","4","1","256","1","0","cudaFuncCachePreferNone","125,869,303,903,488","4,096","1","1","4,096","32","3","3","8","831","3,736","2,072","80","20,480","98,304","32,768","32,768","0","32,768","0","7","1,048,576","17.07","76.67","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","285,914,846","285,914,846","285,914,846","1,143,659,384","285,914,846","285,914,846","285,914,846","1,143,659,384","4","0","24","37.50","36.40","53,673,984","6","778,043,392","8.01","41.89"
+"1","1492989","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)1024>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<float>, cufftdx::ElementsPerThread<(unsigned int)16>, cufftdx::FFTsPerBlock<(unsigned int)2>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex32 *, cuntt::Complex32 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Aug-01 17:57:36","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","134,218,944","137,814,880","74.82","404,640","862,581","5,393,417","3.15","64","2","1","128","1","0","cudaFuncCachePreferNone","125,869,312,529,664","8,192","1","1","8,192","32","8","6","16","1,588","3,960","1,732","64","8,192","98,304","16,384","16,384","0","16,384","0","7","1,048,576","17.07","67.12","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","285,914,846","285,914,846","285,914,846","1,143,659,384","285,914,846","285,914,846","285,914,846","1,143,659,384","4","0","24","37.50","35.93","41,254,912","6","681,574,400","13.44","8.10"
diff --git a/results/ncu_fft_vectorized/summary.csv b/results/ncu_fft_vectorized/summary.csv
new file mode 100644
index 0000000..40a0292
--- /dev/null
+++ b/results/ncu_fft_vectorized/summary.csv
@@ -0,0 +1,7 @@
+label,kernel_id,kernel_name,grid_size,block_size,time_us,dram_read_mib,dram_write_mib,dram_peak_pct,l2_hit_pct,l1_hit_pct,shared_load_bank_conflicts,shared_store_bank_conflicts,warp_instructions,integer_thread_instructions,fp32_thread_instructions,fp64_thread_instructions,tensor_warp_instructions,tensor_active_pct,active_warps_pct,barrier_stall_pct,long_scoreboard_stall_pct,registers_per_thread,shared_mem_bytes,waves_per_sm,occupancy_register_block_limit,occupancy_shared_block_limit,occupancy_warp_block_limit
+post_vector_cufft_b16,0,void regular_fft<,2048,512,396.896,128.011962890625,128.6556396484375,75.48,50.07,1.86,0.0,1048576.0,38141952.0,,882900992.0,,,,23.92,4.9,17.51,64.0,65536.0,25.6,2.0,1.0,4.0
+post_vector_cufft_b16,1,void regular_fft<,2048,512,376.672,128.00250244140625,128.61810302734375,79.51,75.13,1.5,0.0,1048576.0,31326208.0,,725614592.0,,,,24.3,4.49,25.39,64.0,65536.0,25.6,2.0,1.0,4.0
+post_vector_fixed_b16,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,512,480.096,140.84649658203125,128.3350830078125,65.43,77.92,6.54,4394474.0,7340032.0,59899904.0,,832569344.0,,,,48.43,12.29,33.14,51.0,32768.0,25.6,2.0,2.0,4.0
+post_vector_fixed_b16,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,512,352.25600000000003,128.00286865234375,128.32513427734375,84.92,50.21,6.86,798943.0,7340032.0,51707904.0,,740294656.0,,,,47.92,14.77,20.67,50.0,32768.0,25.6,2.0,2.0,4.0
+post_vector_selected_b16,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,256,450.91200000000003,135.10064697265625,128.30636596679688,68.17,76.67,5.19,4199215.0,7656010.0,53673984.0,,778043392.0,,,,36.4,8.01,41.89,80.0,32768.0,17.07,3.0,3.0,8.0
+post_vector_selected_b16,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",8192,128,404.64,128.00115966796875,131.43051147460938,74.82,67.12,3.15,862581.0,5393417.0,41254912.0,,681574400.0,,,,35.93,13.44,8.1,64.0,16384.0,17.07,8.0,6.0,16.0
diff --git a/results/ncu_fp64_fft/analysis.csv b/results/ncu_fp64_fft/analysis.csv
new file mode 100644
index 0000000..f90c183
--- /dev/null
+++ b/results/ncu_fp64_fft/analysis.csv
@@ -0,0 +1,6 @@
+implementation,label,cuda_event_ms,time_us,dram_read_mib,dram_write_mib,shared_load_bank_conflicts,shared_store_bank_conflicts,warp_instructions,integer_thread_instructions,fp64_thread_instructions,dram_peak_pct,l2_hit_pct,l1_hit_pct,active_warps_pct,barrier_stall_pct,long_scoreboard_stall_pct,kernel_count,shared_bank_conflicts,dram_total_mib,cuda_event_ms_vs_cufft,time_us_vs_cufft,dram_total_mib_vs_cufft,warp_instructions_vs_cufft,integer_thread_instructions_vs_cufft,fp64_thread_instructions_vs_cufft,shared_bank_conflicts_vs_cufft
+scalar,fp64_scalar_b64,0.521226,597.6320000000001,130.94012451171875,129.1727294921875,5051402.0,4194304.0,38076416.0,512769792.0,285212672.0,50.793611587063616,83.36955718569287,16.139459734418505,56.91732705076033,34.87696776611694,24.289221996144786,2,9245706.0,260.11285400390625,1.5202475674918916,1.6612702366127023,1.0184619862748527,2.342741935483871,4.724392761833385,1.0421455938697317,154.02835437976876
+cufftdx,fp64_cufftdx_b64,0.369459,387.616,128.50518798828125,128.82125854492188,2487689.0,7398945.0,30507008.0,409993216.0,268656384.0,77.48858581689095,63.823377363163544,13.821574341616445,42.53328737719805,18.433020721538842,23.801044332535295,2,9886634.0,257.3264465332031,1.0775923419744733,1.0774773172033445,1.0075519138063052,1.877016129032258,3.7774631272959063,0.9816501661278736,164.7058607936561
+cufft,fp64_cufft_b64,0.342856,359.744,128.0013427734375,127.3963623046875,46550.0,13476.0,16252928.0,108536656.0,273678336.0,82.85999644191423,50.245001779042866,0.5849839886141256,18.195001779042872,4.019839886141256,39.78024550791674,2,60026.0,255.397705078125,1.0,1.0,1.0,1.0,1.0,1.0,1.0
+recurrence,fp64_recurrence_b64,0.345027,362.656,128.2322998046875,128.76986694335938,2716488.0,7398132.0,29392896.0,381681664.0,279969792.0,82.71430689137917,55.3118591723286,16.849328509662048,42.183833053913354,19.089824406600197,19.72007588458484,2,10114620.0,257.0021667480469,1.0063321044403482,1.0080946450809465,1.006282208641738,1.8084677419354838,3.516615289861151,1.0229885057471264,168.50398160796988
+xor_swizzle,fp64_xor_swizzle_b64,0.342098,350.88,128.328857421875,128.76119995117188,1002389.0,5824136.0,29753344.0,393216000.0,279969792.0,85.51303875968993,55.22118650250799,16.645330597355223,42.030871865025084,17.683655266757867,24.196005471956227,2,6826525.0,257.0900573730469,0.9977891592971977,0.9753602561821739,1.006626341040943,1.8306451612903225,3.6228866310382735,1.0229885057471264,113.72613534135208
diff --git a/results/ncu_fp64_fft/analysis.md b/results/ncu_fp64_fft/analysis.md
new file mode 100644
index 0000000..6d28f60
--- /dev/null
+++ b/results/ncu_fp64_fft/analysis.md
@@ -0,0 +1,38 @@
+# FP64 FFT NCU Attribution
+
+All rows are FP64 forward `logN=16`, batch 64 on V100. CUDA-event medians use
+five process trials, 1000 warmups, and 100 repetitions. NCU replay time is
+attribution-only and is not used to rank the implementations.
+
+| Implementation | CUDA-event ms | NCU us | DRAM MiB | Warp inst. | Integer inst. | FP64 inst. | Shared conflicts | DRAM peak | Barrier stall | Scoreboard stall |
+|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|
+| scalar | 0.521226 | 597.632 | 260.11 | 38076416 | 512769792 | 285212672 | 9245706 | 50.8% | 34.9% | 24.3% |
+| cufftdx | 0.369459 | 387.616 | 257.33 | 30507008 | 409993216 | 268656384 | 9886634 | 77.5% | 18.4% | 23.8% |
+| cufft | 0.342856 | 359.744 | 255.40 | 16252928 | 108536656 | 273678336 | 60026 | 82.9% | 4.0% | 39.8% |
+| recurrence | 0.345027 | 362.656 | 257.00 | 29392896 | 381681664 | 279969792 | 10114620 | 82.7% | 19.1% | 19.7% |
+| xor_swizzle | 0.342098 | 350.880 | 257.09 | 29753344 | 393216000 | 279969792 | 6826525 | 85.5% | 17.7% | 24.2% |
+
+## Attribution
+
+- Replacing the scalar unit with cuFFTDx reduces CUDA-event time by 29.1% and NCU replay time by 35.1%. It also reduces FP64 instructions by 5.8%.
+- Against cuFFT, cuFFTDx transfers 1.008x the DRAM bytes and executes 0.982x the FP64 instructions. The remaining gap is therefore not explained by external traffic volume or double-precision arithmetic work.
+- cuFFTDx executes 1.88x the warp instructions and incurs 164.7x the shared-memory bank conflicts of cuFFT. Its weighted barrier and long-scoreboard stalls are 18.4% and 23.8%.
+- Twiddle recurrence changes CUDA-event time by -6.6%, replay time by -6.4%, and FP64 instructions by +4.2%.
+- XOR swizzle changes CUDA-event time by -0.8% and replay time by -3.2% versus linear recurrence. It finishes 2.5% below cuFFT replay while still executing 1.83x its warp instructions, 3.62x its integer instructions, and incurring 113.7x its shared conflicts.
+
+## Prefix/Suffix Split
+
+| cuFFTDx pass | NCU us | Warp inst. | Integer inst. | FP64 inst. | Shared conflicts | DRAM peak | Barrier stall | Scoreboard stall |
+|:--|--:|--:|--:|--:|--:|--:|--:|--:|
+| table prefix + twiddle/reorder | 214.464 | 16875520 | 207618048 | 135487232 | 5607036 | 70.1% | 19.6% | 29.5% |
+| table suffix + natural-order store | 173.152 | 13631488 | 202375168 | 133169152 | 4279598 | 86.6% | 17.0% | 16.7% |
+| recurrence prefix + twiddle/reorder | 189.344 | 15761408 | 179306496 | 146800640 | 5828681 | 79.2% | 21.1% | 22.1% |
+| recurrence suffix + natural-order store | 173.312 | 13631488 | 202375168 | 133169152 | 4285939 | 86.5% | 16.9% | 17.1% |
+| XOR-swizzle prefix + twiddle/reorder | 178.912 | 16121856 | 190840832 | 146800640 | 2552475 | 83.9% | 18.4% | 31.2% |
+| XOR-swizzle suffix + natural-order store | 171.968 | 13631488 | 202375168 | 133169152 | 4274050 | 87.2% | 17.0% | 16.9% |
+
+Recurrence reduces prefix replay time by 11.7%, warp instructions by 6.6%, and raises DRAM peak from 70.1% to 79.2%. It spends 8.4% more FP64 instructions while registers, shared allocation, and waves/SM remain unchanged. The suffix changes by only +0.1%.
+
+The recurrence result confirms a useful architecture trade: idle FP64 capacity replaces dependent twiddle-table service in the prefix. Shared conflicts remain essentially unchanged, so the next target is the local exchange/address path rather than another twiddle change.
+
+XOR swizzle changes prefix replay time by -5.5%, shared conflicts by -56.2%, and warp instructions by +2.3%. Integer instructions change by +6.4%. The suffix changes by -0.8%.
diff --git a/results/ncu_fp64_fft/fp64_cufft_b64.csv b/results/ncu_fp64_fft/fp64_cufft_b64.csv
new file mode 100644
index 0000000..f195d7c
--- /dev/null
+++ b/results/ncu_fp64_fft/fp64_cufft_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 2232917 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 2232917
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diff --git a/results/ncu_fp64_fft/fp64_cufftdx_b64.csv b/results/ncu_fp64_fft/fp64_cufftdx_b64.csv
new file mode 100644
index 0000000..33ecd56
--- /dev/null
+++ b/results/ncu_fp64_fft/fp64_cufftdx_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 2232831 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 2232831
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+"1","2232831","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::fp64_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)256>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<double>, cufftdx::ElementsPerThread<(unsigned int)8>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex64 *, cuntt::Complex64 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Aug-02 18:05:16","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","67,111,168","67,640,832","86.64","173,152","550,669","3,728,929","10.95","32","4","1","128","1","0","cudaFuncCachePreferNone","132,485,768,743,424","4,096","1","1","4,096","32","8","6","16","1,588","3,960","1,732","60","8,192","98,304","16,384","16,384","0","16,384","0","7","524,288","8.53","50.81","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","211,465,122","211,465,122","211,465,122","845,860,488","211,465,122","211,465,122","211,465,122","845,860,488","4","0","24","37.50","36.01","13,631,488","6","133,169,152","202,375,168","17.00","16.73"
diff --git a/results/ncu_fp64_fft/fp64_recurrence_b64.csv b/results/ncu_fp64_fft/fp64_recurrence_b64.csv
new file mode 100644
index 0000000..bb224e3
--- /dev/null
+++ b/results/ncu_fp64_fft/fp64_recurrence_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 2232856 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 2232856
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diff --git a/results/ncu_fp64_fft/fp64_scalar_b64.csv b/results/ncu_fp64_fft/fp64_scalar_b64.csv
new file mode 100644
index 0000000..0153d57
--- /dev/null
+++ b/results/ncu_fp64_fft/fp64_scalar_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 2232806 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 2232806
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diff --git a/results/ncu_fp64_fft/fp64_xor_swizzle_b64.csv b/results/ncu_fp64_fft/fp64_xor_swizzle_b64.csv
new file mode 100644
index 0000000..7920456
--- /dev/null
+++ b/results/ncu_fp64_fft/fp64_xor_swizzle_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 2232890 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 2232890
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+"0","2232890","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::fp64_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)256>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<double>, cufftdx::ElementsPerThread<(unsigned int)4>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>, (bool)1>(const cuntt::Complex64 *, cuntt::Complex64 *, const cuntt::Complex64 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Aug-02 18:05:17","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","67,452,416","67,463,776","83.93","178,912","455,323","2,097,152","22.11","64","4","1","256","1","0","cudaFuncCachePreferNone","135,034,965,439,744","4,096","1","1","4,096","32","4","4","8","1,514","4,256","1,904","64","16,384","65,536","16,384","16,384","0","16,384","0","7","1,048,576","12.80","59.49","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","211,465,122","211,465,122","211,465,122","845,860,488","211,465,122","211,465,122","211,465,122","845,860,488","4","0","32","50","47.77","16,121,856","8","146,800,640","190,840,832","18.36","31.18"
+"1","2232890","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::fp64_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)256>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<double>, cufftdx::ElementsPerThread<(unsigned int)8>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex64 *, cuntt::Complex64 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Aug-02 18:05:17","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","67,110,144","67,552,128","87.16","171,968","547,066","3,726,984","10.96","32","4","1","128","1","0","cudaFuncCachePreferNone","135,034,966,051,328","4,096","1","1","4,096","32","8","6","16","1,588","3,960","1,732","60","8,192","98,304","16,384","16,384","0","16,384","0","7","524,288","8.53","50.78","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","211,465,122","211,465,122","211,465,122","845,860,488","211,465,122","211,465,122","211,465,122","845,860,488","4","0","24","37.50","36.06","13,631,488","6","133,169,152","202,375,168","16.98","16.93"
diff --git a/results/ncu_fp64_fft/summary.csv b/results/ncu_fp64_fft/summary.csv
new file mode 100644
index 0000000..3789851
--- /dev/null
+++ b/results/ncu_fp64_fft/summary.csv
@@ -0,0 +1,11 @@
+label,kernel_id,kernel_name,grid_size,block_size,time_us,dram_read_mib,dram_write_mib,dram_peak_pct,l2_hit_pct,l1_hit_pct,shared_load_bank_conflicts,shared_store_bank_conflicts,warp_instructions,integer_thread_instructions,fp32_thread_instructions,fp64_thread_instructions,tensor_warp_instructions,tensor_active_pct,active_warps_pct,barrier_stall_pct,long_scoreboard_stall_pct,registers_per_thread,shared_mem_bytes,waves_per_sm,occupancy_register_block_limit,occupancy_shared_block_limit,occupancy_warp_block_limit
+fp64_cufft_b64,0,void regular_fft<,2048,128,179.808,64.00067138671875,63.685791015625,82.87,50.24,0.63,23600.0,6479.0,9101312.0,61870992.0,,157810688.0,,,18.19,4.47,39.09,134.0,32768.0,8.53,3.0,3.0,16.0
+fp64_cufft_b64,1,void regular_fft<,2048,128,179.936,64.00067138671875,63.7105712890625,82.85,50.25,0.54,22950.0,6997.0,7151616.0,46665664.0,,115867648.0,,,18.2,3.57,40.47,134.0,32768.0,8.53,3.0,3.0,16.0
+fp64_cufftdx_b64,0,"void cuntt::detail::<unnamed>::fp64_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,256,214.464,64.50299072265625,64.31393432617188,70.1,74.33,16.14,1937020.0,3670016.0,16875520.0,207618048.0,,135487232.0,,,47.8,19.59,29.51,63.0,16384.0,12.8,4.0,4.0,8.0
+fp64_cufftdx_b64,1,"void cuntt::detail::<unnamed>::fp64_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,128,173.15200000000002,64.002197265625,64.50732421875,86.64,50.81,10.95,550669.0,3728929.0,13631488.0,202375168.0,,133169152.0,,,36.01,17.0,16.73,60.0,16384.0,8.53,8.0,6.0,16.0
+fp64_recurrence_b64,0,"void cuntt::detail::<unnamed>::fp64_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,256,189.344,64.2310791015625,64.31307983398438,79.24,59.46,22.24,2158665.0,3670016.0,15761408.0,179306496.0,,146800640.0,,,47.78,21.14,22.1,63.0,16384.0,12.8,4.0,4.0,8.0
+fp64_recurrence_b64,1,"void cuntt::detail::<unnamed>::fp64_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,128,173.312,64.001220703125,64.456787109375,86.51,50.78,10.96,557823.0,3728116.0,13631488.0,202375168.0,,133169152.0,,,36.07,16.85,17.12,60.0,16384.0,8.53,8.0,6.0,16.0
+fp64_scalar_b64,0,"void cuntt::detail::hierarchical_prefix_kernel<cuntt::<unnamed>::FftOperator<cuntt::Complex64, double>,",16384,128,273.37600000000003,64.00613403320312,64.57000732421875,54.89,87.9,24.24,2571679.0,2097152.0,14680064.0,170917888.0,,134217728.0,,,53.51,32.94,25.51,50.0,4096.0,22.76,9.0,16.0,16.0
+fp64_scalar_b64,1,"void cuntt::detail::online_reorder_suffix_kernel<cuntt::<unnamed>::FftOperator<cuntt::Complex64, double>,",16384,128,324.25600000000003,66.93399047851562,64.60272216796875,47.34,79.55,9.31,2479723.0,2097152.0,23396352.0,341851904.0,,150994944.0,,,59.79,36.51,23.26,44.0,4096.0,20.48,10.0,16.0,16.0
+fp64_xor_swizzle_b64,0,"void cuntt::detail::<unnamed>::fp64_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,256,178.912,64.32763671875,64.33847045898438,83.93,59.49,22.11,455323.0,2097152.0,16121856.0,190840832.0,,146800640.0,,,47.77,18.36,31.18,64.0,16384.0,12.8,4.0,4.0,8.0
+fp64_xor_swizzle_b64,1,"void cuntt::detail::<unnamed>::fp64_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,128,171.96800000000002,64.001220703125,64.4227294921875,87.16,50.78,10.96,547066.0,3726984.0,13631488.0,202375168.0,,133169152.0,,,36.06,16.98,16.93,60.0,16384.0,8.53,8.0,6.0,16.0
diff --git a/results/ncu_scaling_crossovers/attribution.csv b/results/ncu_scaling_crossovers/attribution.csv
new file mode 100644
index 0000000..db39d6a
--- /dev/null
+++ b/results/ncu_scaling_crossovers/attribution.csv
@@ -0,0 +1,23 @@
+label,operator,logN,implementation,batch,kernels,time_us,dram_read_mib,dram_write_mib,warp_instructions,fp32_thread_instructions,shared_load_bank_conflicts,shared_store_bank_conflicts,dram_peak_pct,l2_hit_pct,l1_hit_pct,active_warps_pct,barrier_stall_pct,long_scoreboard_stall_pct,registers_per_thread,shared_mem_bytes,total_waves_per_sm,dram_bytes_per_point,profiled_gpoint_s
+fft14_cufft_b1024,fft,14,cufft,1024,1,438.944000,128.032471,127.825562,41811968.000000,1018167296.000000,74619.000000,1048644.000000,68.020000,51.650000,2.120000,46.920000,5.950000,15.070000,61.000000,67584.000000,12.800000,15.991127,38.221769
+fft14_cufft_b16,fft,14,cufft,16,2,27.872000,3.101624,0.697845,785920.000000,17432576.000000,0.000000,0.000000,15.946785,64.790344,29.292227,12.420000,0.414466,18.791986,64.000000,32768.000000,0.540000,15.197876,9.405281
+fft14_cufft_b256,fft,14,cufft,256,1,137.984000,32.019226,31.808014,10452992.000000,254541824.000000,17299.000000,262154.000000,53.990000,51.740000,2.100000,46.480000,5.090000,15.890000,61.000000,67584.000000,3.200000,15.956810,30.397032
+fft14_direct_b1024,fft,14,direct,1024,1,413.792000,128.037201,127.885803,38436864.000000,938475520.000000,3847.000000,4194304.000000,72.180000,53.140000,2.250000,47.440000,6.990000,6.520000,63.000000,65536.000000,12.800000,15.995188,40.545047
+fft14_direct_b16,fft,14,direct,16,1,24.416000,0.000000,0.000427,600576.000000,14663680.000000,27.000000,65536.000000,0.000000,101.790000,2.190000,48.590000,8.340000,3.470000,63.000000,65536.000000,0.200000,0.001709,10.736566
+fft14_direct_b256,fft,14,direct,256,1,129.312000,32.036957,31.511047,9609216.000000,234618880.000000,977.000000,1048576.000000,57.350000,53.210000,2.110000,47.290000,6.180000,7.500000,63.000000,65536.000000,3.200000,15.887001,32.435536
+fft18_cufft_b16,fft,18,cufft,16,2,229.696000,64.231995,64.158508,19611648.000000,362807296.000000,0.000000,524288.000000,65.237423,63.093926,19.492536,46.982067,8.306952,26.608579,39.000000,32768.000000,12.800000,32.097626,18.260240
+fft18_cufft_b2,fft,18,cufft,2,2,39.520000,8.001465,5.944916,2451456.000000,45350912.000000,0.000000,65536.000000,41.249595,63.184089,18.143036,48.128300,3.543158,31.559190,39.000000,32768.000000,1.600000,27.892761,13.266397
+fft18_cufft_b64,fft,18,cufft,64,2,754.496000,256.176025,256.185333,78446592.000000,1451229184.000000,0.000000,2097152.000000,79.251944,63.284765,19.780215,46.872504,9.498500,24.944413,39.000000,32768.000000,51.200000,32.022585,22.236322
+fft18_online_b16,fft,18,online,16,2,221.504000,64.604675,64.965088,31342592.000000,321912832.000000,1199959.000000,3777939.000000,68.299073,66.944080,5.751872,58.728136,12.297746,33.284701,48.000000,16384.000000,10.240000,32.392441,18.935568
+fft18_online_b2,fft,18,online,2,2,41.568000,8.226013,8.475647,3917824.000000,40239104.000000,168970.000000,458752.000000,46.929330,66.724573,6.186490,37.716467,7.139400,38.024665,48.000000,16384.000000,1.280000,33.403320,12.612779
+fft18_online_b64,fft,18,online,64,2,857.184000,257.208252,257.520538,125370368.000000,1287651328.000000,4749278.000000,15183693.000000,70.081875,65.650812,5.628486,60.612720,13.435873,30.784459,48.000000,16384.000000,40.960000,32.170549,19.572479
+fft20_cufft_b16,fft,20,cufft,16,2,772.864000,256.012390,257.219147,69468160.000000,1608515584.000000,0.000000,2097152.000000,77.494423,62.200499,1.670329,24.099025,4.700329,21.382762,64.000000,65536.000000,51.200000,32.076971,21.707850
+fft20_cufft_b2,fft,20,cufft,2,2,146.304000,32.004333,33.368195,8683520.000000,201064448.000000,0.000000,262144.000000,52.159477,62.738681,1.626039,24.204180,2.755055,18.242843,64.000000,65536.000000,6.400000,32.686264,14.334208
+fft20_cufft_b8,fft,20,cufft,8,2,425.696000,128.012634,129.218323,34734080.000000,804257792.000000,0.000000,1048576.000000,70.524922,62.381186,1.677997,24.066692,4.277584,19.801757,64.000000,65536.000000,25.600000,32.153870,19.705630
+fft20_online_b16,fft,20,online,16,2,917.600000,274.488037,256.626709,138739712.000000,1572864000.000000,5085525.000000,14680064.000000,67.550020,66.829369,6.659941,48.597445,11.922599,32.783595,52.000000,32768.000000,51.200000,33.194672,18.283801
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+fft20_online_b8,fft,20,online,8,2,470.560000,137.558228,128.603333,69369856.000000,786432000.000000,2566184.000000,7340032.000000,66.016875,66.605906,6.651094,48.343045,11.796232,33.342609,52.000000,32768.000000,25.600000,33.270195,17.826862
+fwht15_online_b16,fwht,15,online,16,2,56.224000,1.799194,0.496643,5758976.000000,9961472.000000,170571.000000,131517.000000,4.771264,89.000353,4.676369,80.652880,27.952402,11.754917,25.000000,1024.000000,9.600000,4.591675,9.324986
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+fwht15_warp_b4,fwht,15,warp,4,1,42.560000,0.000244,0.000000,106752.000000,2102272.000000,0.000000,0.000000,0.000000,115.850000,0.000000,12.480000,1.280000,6.380000,255.000000,32768.000000,0.050000,0.001953,3.079699
diff --git a/results/ncu_scaling_crossovers/attribution.md b/results/ncu_scaling_crossovers/attribution.md
new file mode 100644
index 0000000..853accd
--- /dev/null
+++ b/results/ncu_scaling_crossovers/attribution.md
@@ -0,0 +1,60 @@
+# V100 Scaling-Crossover Counter Attribution
+
+NCU replay time is used only for attribution; CUDA-event time remains the performance authority.
+
+| Workload | Batch | Impl | Kernels | Waves/SM | Active warps | DRAM peak | B/point | Barrier stall | Scoreboard stall | Reg/thread | Shared B |
+|:--|--:|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|
+| fft logN=14 | 1024 | cufft | 1 | 12.80 | 46.9% | 68.0% | 16.0 | 6.0% | 15.1% | 61 | 67584 |
+| fft logN=14 | 16 | cufft | 2 | 0.54 | 12.4% | 15.9% | 15.2 | 0.4% | 18.8% | 64 | 32768 |
+| fft logN=14 | 256 | cufft | 1 | 3.20 | 46.5% | 54.0% | 16.0 | 5.1% | 15.9% | 61 | 67584 |
+| fft logN=14 | 1024 | direct | 1 | 12.80 | 47.4% | 72.2% | 16.0 | 7.0% | 6.5% | 63 | 65536 |
+| fft logN=14 | 16 | direct | 1 | 0.20 | 48.6% | 0.0% | 0.0 | 8.3% | 3.5% | 63 | 65536 |
+| fft logN=14 | 256 | direct | 1 | 3.20 | 47.3% | 57.4% | 15.9 | 6.2% | 7.5% | 63 | 65536 |
+| fft logN=18 | 16 | cufft | 2 | 12.80 | 47.0% | 65.2% | 32.1 | 8.3% | 26.6% | 39 | 32768 |
+| fft logN=18 | 2 | cufft | 2 | 1.60 | 48.1% | 41.2% | 27.9 | 3.5% | 31.6% | 39 | 32768 |
+| fft logN=18 | 64 | cufft | 2 | 51.20 | 46.9% | 79.3% | 32.0 | 9.5% | 24.9% | 39 | 32768 |
+| fft logN=18 | 16 | online | 2 | 10.24 | 58.7% | 68.3% | 32.4 | 12.3% | 33.3% | 48 | 16384 |
+| fft logN=18 | 2 | online | 2 | 1.28 | 37.7% | 46.9% | 33.4 | 7.1% | 38.0% | 48 | 16384 |
+| fft logN=18 | 64 | online | 2 | 40.96 | 60.6% | 70.1% | 32.2 | 13.4% | 30.8% | 48 | 16384 |
+| fft logN=20 | 16 | cufft | 2 | 51.20 | 24.1% | 77.5% | 32.1 | 4.7% | 21.4% | 64 | 65536 |
+| fft logN=20 | 2 | cufft | 2 | 6.40 | 24.2% | 52.2% | 32.7 | 2.8% | 18.2% | 64 | 65536 |
+| fft logN=20 | 8 | cufft | 2 | 25.60 | 24.1% | 70.5% | 32.2 | 4.3% | 19.8% | 64 | 65536 |
+| fft logN=20 | 16 | online | 2 | 51.20 | 48.6% | 67.6% | 33.2 | 11.9% | 32.8% | 52 | 32768 |
+| fft logN=20 | 2 | online | 2 | 6.40 | 47.0% | 56.9% | 34.0 | 11.4% | 35.1% | 52 | 32768 |
+| fft logN=20 | 8 | online | 2 | 25.60 | 48.3% | 66.0% | 33.3 | 11.8% | 33.3% | 52 | 32768 |
+| fwht logN=15 | 16 | online | 2 | 9.60 | 80.7% | 4.8% | 4.6 | 28.0% | 11.8% | 25 | 1024 |
+| fwht logN=15 | 4 | online | 2 | 2.40 | 56.6% | 0.0% | 0.0 | 17.2% | 4.3% | 25 | 1024 |
+| fwht logN=15 | 16 | warp | 1 | 0.20 | 12.5% | 5.2% | 3.8 | 1.5% | 4.8% | 255 | 32768 |
+| fwht logN=15 | 4 | warp | 1 | 0.05 | 12.5% | 0.0% | 0.0 | 1.3% | 6.4% | 255 | 32768 |
+
+## Measured Trends
+
+- FFT logN=14 direct: waves/SM change 64.00x from batch 16 to 1024; active warps 48.6% -> 47.4%, DRAM peak 0.0% -> 72.2%, the low-batch DRAM count is cache-resident/replay-sensitive, barrier stalls 8.3% -> 7.0%, and long-scoreboard stalls 3.5% -> 6.5%.
+- FFT logN=18 online: waves/SM change 32.00x from batch 2 to 64; active warps 37.7% -> 60.6%, DRAM peak 46.9% -> 70.1%, bytes/point changes 0.96x, barrier stalls 7.1% -> 13.4%, and long-scoreboard stalls 38.0% -> 30.8%.
+- FFT logN=20 online: waves/SM change 8.00x from batch 2 to 16; active warps 47.0% -> 48.6%, DRAM peak 56.9% -> 67.6%, bytes/point changes 0.98x, barrier stalls 11.4% -> 11.9%, and long-scoreboard stalls 35.1% -> 32.8%.
+- FWHT logN=15 online: waves/SM change 4.00x from batch 4 to 16; active warps 56.6% -> 80.7%, DRAM peak 0.0% -> 4.8%, the low-batch DRAM count is cache-resident/replay-sensitive, barrier stalls 17.2% -> 28.0%, and long-scoreboard stalls 4.3% -> 11.8%.
+- FWHT logN=15 warp: waves/SM change 4.00x from batch 4 to 16; active warps 12.5% -> 12.5%, DRAM peak 0.0% -> 5.2%, the low-batch DRAM count is cache-resident/replay-sensitive, barrier stalls 1.3% -> 1.5%, and long-scoreboard stalls 6.4% -> 4.8%.
+
+Counts reported as zero for the smallest cases are not zero algorithmic traffic. `--cache-control none`, NCU replay, and a working set that fits in the 6 MiB L2 make those DRAM counters unsuitable for traffic ratios.
+
+## Architecture Attribution
+
+### FFT logN=14: grid concurrency threshold
+
+The direct unit launches one 1024-thread CTA per transform and is limited to one resident CTA per SM by its register and 65536-byte shared allocations. At batch 16 it exposes only 0.20 waves/SM, whereas cuFFT exposes 0.54 waves/SM across two kernels. The direct grid therefore leaves most of the 80 SMs without work even though active CTAs individually report 48.6% active warps. At batch 1024 it reaches 12.8 waves/SM and the grid-level deficit disappears. This attributes the low-batch gap to `Ub`/grid coverage, not to the local cuFFTDx arithmetic core.
+
+### FFT logN=18: useful-work ceiling
+
+At batch 64, online composition has 60.6% active warps versus cuFFT's 46.9%, but executes 1.60x as many warp instructions and 9.50x as many shared-memory bank conflicts. Its barrier and long-scoreboard stalls are 13.4% and 30.8%, and it reaches only 70.1% of peak DRAM versus cuFFT's 79.3%. The early saturation is therefore caused by less useful work per active warp and exchange/synchronization overhead, not a lack of resident warps.
+
+### FFT logN=20: prefix/suffix imbalance
+
+At batch 16, online and cuFFT both expose 51.2 aggregate waves/SM. Online nevertheless executes 2.00x the warp instructions, incurs 9.42x the shared bank conflicts, and has 11.9% barrier plus 32.8% scoreboard stalls. The first pass consumes 61.8% of profiled time and reaches only 56.6% DRAM, while the second reaches 85.3%. The remaining gap is a prefix-core/layout imbalance and synchronization problem; increasing occupancy alone cannot close it.
+
+### FWHT logN=15: mapping crossover
+
+The warp-register unit uses 255 registers/thread and 32768 shared bytes, limiting it to one CTA/SM. It launches only 0.05 waves/SM at batch 4 and 0.20 at batch 16, with nearly fixed NCU time. Online decomposition exposes 2.40 and 9.60 waves/SM, so it wins when four transforms cannot cover the GPU. By batch 16, the register unit's single-kernel path executes only 0.07x the online warp instructions and avoids its shared exchanges and 28.0% barrier stalls. The crossover is the expected tradeoff between `Ud` spatial decomposition at low batch and `Td` register residence once `Ub` supplies enough independent transforms.
+
+## Methodological Result
+
+The counters support separating three quantities in the selector: grid coverage (`Ub` and waves/SM), residency (register/shared limits), and useful work per resident warp (instruction, exchange, and stall costs). Occupancy is not a sufficient objective: both long online FFTs expose at least as many active warps as cuFFT while delivering a lower saturated ceiling.
diff --git a/results/ncu_scaling_crossovers/fft14_cufft_b1024.csv b/results/ncu_scaling_crossovers/fft14_cufft_b1024.csv
new file mode 100644
index 0000000..121504e
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft14_cufft_b1024.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097249 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097249
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diff --git a/results/ncu_scaling_crossovers/fft14_cufft_b16.csv b/results/ncu_scaling_crossovers/fft14_cufft_b16.csv
new file mode 100644
index 0000000..40c576a
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft14_cufft_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4096751 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4096751
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diff --git a/results/ncu_scaling_crossovers/fft14_cufft_b256.csv b/results/ncu_scaling_crossovers/fft14_cufft_b256.csv
new file mode 100644
index 0000000..57830da
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft14_cufft_b256.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097070 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097070
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diff --git a/results/ncu_scaling_crossovers/fft14_direct_b1024.csv b/results/ncu_scaling_crossovers/fft14_direct_b1024.csv
new file mode 100644
index 0000000..6e67afd
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft14_direct_b1024.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097096 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097096
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diff --git a/results/ncu_scaling_crossovers/fft14_direct_b16.csv b/results/ncu_scaling_crossovers/fft14_direct_b16.csv
new file mode 100644
index 0000000..556e8bc
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft14_direct_b16.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4096732 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4096732
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diff --git a/results/ncu_scaling_crossovers/fft14_direct_b256.csv b/results/ncu_scaling_crossovers/fft14_direct_b256.csv
new file mode 100644
index 0000000..b39a89b
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft14_direct_b256.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4096808 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4096808
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diff --git a/results/ncu_scaling_crossovers/fft18_cufft_b16.csv b/results/ncu_scaling_crossovers/fft18_cufft_b16.csv
new file mode 100644
index 0000000..d44f867
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft18_cufft_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097414 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097414
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diff --git a/results/ncu_scaling_crossovers/fft18_cufft_b2.csv b/results/ncu_scaling_crossovers/fft18_cufft_b2.csv
new file mode 100644
index 0000000..553273b
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft18_cufft_b2.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097345 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097345
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diff --git a/results/ncu_scaling_crossovers/fft18_cufft_b64.csv b/results/ncu_scaling_crossovers/fft18_cufft_b64.csv
new file mode 100644
index 0000000..0a8356f
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft18_cufft_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097477 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097477
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diff --git a/results/ncu_scaling_crossovers/fft18_online_b16.csv b/results/ncu_scaling_crossovers/fft18_online_b16.csv
new file mode 100644
index 0000000..6039251
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft18_online_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097389 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097389
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diff --git a/results/ncu_scaling_crossovers/fft18_online_b2.csv b/results/ncu_scaling_crossovers/fft18_online_b2.csv
new file mode 100644
index 0000000..66fb2bc
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft18_online_b2.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097293 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097293
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diff --git a/results/ncu_scaling_crossovers/fft18_online_b64.csv b/results/ncu_scaling_crossovers/fft18_online_b64.csv
new file mode 100644
index 0000000..2235dd6
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft18_online_b64.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097445 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097445
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diff --git a/results/ncu_scaling_crossovers/fft20_cufft_b16.csv b/results/ncu_scaling_crossovers/fft20_cufft_b16.csv
new file mode 100644
index 0000000..3986c79
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft20_cufft_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097920 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097920
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diff --git a/results/ncu_scaling_crossovers/fft20_cufft_b2.csv b/results/ncu_scaling_crossovers/fft20_cufft_b2.csv
new file mode 100644
index 0000000..71f2881
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft20_cufft_b2.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097552 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097552
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diff --git a/results/ncu_scaling_crossovers/fft20_cufft_b8.csv b/results/ncu_scaling_crossovers/fft20_cufft_b8.csv
new file mode 100644
index 0000000..4685366
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft20_cufft_b8.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097632 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097632
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diff --git a/results/ncu_scaling_crossovers/fft20_online_b16.csv b/results/ncu_scaling_crossovers/fft20_online_b16.csv
new file mode 100644
index 0000000..2919825
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft20_online_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097870 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097870
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diff --git a/results/ncu_scaling_crossovers/fft20_online_b2.csv b/results/ncu_scaling_crossovers/fft20_online_b2.csv
new file mode 100644
index 0000000..ce39f3e
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft20_online_b2.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097521 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097521
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+"0","4097521","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)1024>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<float>, cufftdx::ElementsPerThread<(unsigned int)8>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex32 *, cuntt::Complex32 *, const cuntt::Complex32 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Jul-24 20:17:35","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","19,646,208","17,746,656","50.43","82,560","540,492","917,504","6.46","128","4","1","512","1","0","cudaFuncCachePreferNone","127,917,365,769,472","512","1","1","512","32","2","2","4","1,400","3,104","2,592","52","28,672","65,536","32,768","32,768","0","32,768","0","7","262,144","3.20","77.25","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","51,033,822","51,033,822","51,033,822","204,135,288","51,033,822","51,033,822","51,033,822","204,135,288","4","0","32","50","47.04","9,740,288","8","104,071,168","10.12","42.03"
+"1","4097521","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)1024>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<float>, cufftdx::ElementsPerThread<(unsigned int)8>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex32 *, cuntt::Complex32 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Jul-24 20:17:36","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","16,779,840","17,093,248","66.26","56,928","129,180","917,504","6.83","128","4","1","512","1","0","cudaFuncCachePreferNone","127,917,010,773,760","512","1","1","512","32","2","2","4","1,400","3,104","2,592","51","28,672","65,536","32,768","32,768","0","32,768","0","7","262,144","3.20","50.40","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","51,033,822","51,033,822","51,033,822","204,135,288","51,033,822","51,033,822","51,033,822","204,135,288","4","0","32","50","47.02","7,602,176","8","92,536,832","13.16","24.98"
diff --git a/results/ncu_scaling_crossovers/fft20_online_b8.csv b/results/ncu_scaling_crossovers/fft20_online_b8.csv
new file mode 100644
index 0000000..85db8a9
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fft20_online_b8.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097593 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097593
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+"1","4097593","cubutterfly_bench","127.0.0.1","void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<(unsigned int)1024>, cufftdx::Type<(cufftdx::fft_type)0>, cufftdx::Direction<(cufftdx::fft_direction)0>, cufftdx::Precision<float>, cufftdx::ElementsPerThread<(unsigned int)8>, cufftdx::FFTsPerBlock<(unsigned int)4>, cufftdx::SM<(unsigned int)700>>>(const cuntt::Complex32 *, cuntt::Complex32 *, unsigned long, unsigned int, unsigned int, unsigned long, unsigned long, bool)","2026-Jul-24 20:17:37","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","67,111,808","67,430,912","82.14","182,304","404,868","3,670,016","6.89","128","4","1","512","1","0","cudaFuncCachePreferNone","128,144,342,050,560","2,048","1","1","2,048","32","2","2","4","1,400","3,104","2,592","51","28,672","65,536","32,768","32,768","0","32,768","0","7","1,048,576","12.80","50.25","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","151,697,118","151,697,118","151,697,118","606,788,472","151,697,118","151,697,118","151,697,118","606,788,472","4","0","32","50","48.00","30,408,704","8","370,147,328","13.83","21.14"
diff --git a/results/ncu_scaling_crossovers/fwht15_online_b16.csv b/results/ncu_scaling_crossovers/fwht15_online_b16.csv
new file mode 100644
index 0000000..e655edb
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fwht15_online_b16.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4098041 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4098041
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diff --git a/results/ncu_scaling_crossovers/fwht15_online_b4.csv b/results/ncu_scaling_crossovers/fwht15_online_b4.csv
new file mode 100644
index 0000000..b268f4f
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fwht15_online_b4.csv
@@ -0,0 +1,7 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4097965 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4097965
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diff --git a/results/ncu_scaling_crossovers/fwht15_warp_b16.csv b/results/ncu_scaling_crossovers/fwht15_warp_b16.csv
new file mode 100644
index 0000000..272c48a
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fwht15_warp_b16.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4098062 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4098062
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diff --git a/results/ncu_scaling_crossovers/fwht15_warp_b4.csv b/results/ncu_scaling_crossovers/fwht15_warp_b4.csv
new file mode 100644
index 0000000..57b0250
--- /dev/null
+++ b/results/ncu_scaling_crossovers/fwht15_warp_b4.csv
@@ -0,0 +1,6 @@
+==WARNING== Note: Running with uncontrolled GPU caches. Profiling results may be inconsistent.
+==PROF== Connected to process 4098000 (/home/wt/git/Hermes/cuNTT/build/cubutterfly_bench)
+==PROF== Disconnected from process 4098000
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ce__attribute_maximum_texture2d_mipmapped_height","device__attribute_maximum_texture2d_mipmapped_width","device__attribute_maximum_texture2d_width","device__attribute_maximum_texture3d_depth","device__attribute_maximum_texture3d_depth_alternate","device__attribute_maximum_texture3d_height","device__attribute_maximum_texture3d_height_alternate","device__attribute_maximum_texture3d_width","device__attribute_maximum_texture3d_width_alternate","device__attribute_maximum_texturecubemap_layered_layers","device__attribute_maximum_texturecubemap_layered_width","device__attribute_maximum_texturecubemap_width","device__attribute_memory_clock_rate","device__attribute_memory_pools_supported","device__attribute_mempool_supported_handle_types","device__attribute_multi_gpu_board","device__attribute_multi_gpu_board_group_id","device__attribute_multiprocessor_count","device__attribute_num_l2s_per_fbp","device__attribute_num_schedulers_per_multiprocessor","device__attribute_num_tex_per_multiprocessor","device__attribute_pageable_memory_access","device__attribute_pageable_memory_access_uses_host_page_tables","device__attribute_pci_bus_id","device__attribute_pci_device_id","device__attribute_pci_domain_id","device__attribute_ram_location","device__attribute_ram_type","device__attribute_reserved_shared_memory_per_block","device__attribute_sass_level","device__attribute_single_to_double_precision_perf_ratio","device__attribute_sparse_cuda_array_supported","device__attribute_stream_priorities_supported","device__attribute_surface_alignment","device__attribute_tcc_driver","device__attribute_texture_alignment","device__attribute_texture_pitch_alignment","device__attribute_total_constant_memory","device__attribute_total_memory","device__attribute_unified_addressing","device__attribute_virtual_address_management_supported","device__attribute_warp_size","dram__bytes_read.sum","dram__bytes_write.sum","dram__throughput.avg.pct_of_peak_sustained_elapsed","gpu__time_duration.sum","l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_ld.sum","l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_st.sum","l1tex__t_sector_hit_rate.pct","launch__block_dim_x","launch__block_dim_y","launch__block_dim_z","launch__block_size","launch__context_id","launch__device_id","launch__func_cache_config","launch__function_pcs","launch__grid_dim_x","launch__grid_dim_y","launch__grid_dim_z","launch__grid_size","launch__occupancy_limit_blocks","launch__occupancy_limit_registers","launch__occupancy_limit_shared_mem","launch__occupancy_limit_warps","launch__occupancy_per_block_size","launch__occupancy_per_register_count","launch__occupancy_per_shared_mem_size","launch__registers_per_thread","launch__registers_per_thread_allocated","launch__shared_mem_config_size","launch__shared_mem_per_block","launch__shared_mem_per_block_allocated","launch__shared_mem_per_block_driver","launch__shared_mem_per_block_dynamic","launch__shared_mem_per_block_static","launch__stream_id","launch__thread_count","launch__waves_per_multiprocessor","lts__t_sector_hit_rate.pct","nvlink__bandwidth","nvlink__count_logical","nvlink__count_physical","nvlink__destination_ports","nvlink__dev0Id","nvlink__dev0type","nvlink__dev1Id","nvlink__dev1type","nvlink__dev_display_name_all","nvlink__enabled_mask","nvlink__is_direct_link","nvlink__is_nvswitch_connected","nvlink__max_count","nvlink__peer_access","nvlink__peer_atomic","nvlink__source_ports","nvlink__system_access","nvlink__system_atomic","profiler__perfworks_session_reuse","profiler__replayer_bytes_mem_accessible.avg","profiler__replayer_bytes_mem_accessible.max","profiler__replayer_bytes_mem_accessible.min","profiler__replayer_bytes_mem_accessible.sum","profiler__replayer_bytes_mem_backed_up.avg","profiler__replayer_bytes_mem_backed_up.max","profiler__replayer_bytes_mem_backed_up.min","profiler__replayer_bytes_mem_backed_up.sum","profiler__replayer_passes","profiler__replayer_passes_type_warmup","sm__maximum_warps_avg_per_active_cycle","sm__maximum_warps_per_active_cycle_pct","sm__warps_active.avg.pct_of_peak_sustained_active","smsp__inst_executed.sum","smsp__maximum_warps_avg_per_active_cycle","smsp__sass_thread_inst_executed_op_fp32_pred_on.sum","smsp__warp_issue_stalled_barrier_per_warp_active.pct","smsp__warp_issue_stalled_long_scoreboard_per_warp_active.pct"
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+"0","4098000","cubutterfly_bench","127.0.0.1","void cuntt::detail::register_fwht_kernel<(unsigned int)15>(const float *, float *, unsigned long, unsigned long, unsigned long, float)","2026-Jul-24 20:17:41","1","7","320","2","0","1","1","0","1","1","0","0","1","320","1,530,000","7","0","0","1","1","1","1","1","0","0","Tesla V100-SXM2-16GB","0","4,096","8","0","1","4,096","1","1","1","0","1","498,143,454","7,601","32,000","16","2","2","8,000","16","161","303,173,854","1","0","0","0","1","320","0","1","6,291,456","64","32","1","1","0","1,024","1,024","64","32","1,530,000","2,147,483,647","65,535","65,535","4","1","877,000","0","2,147,483,647","65,536","65,536","255","49,152","98,304","98,304","1,024","2,048","64","16","2,048","32,768","32,768","65,536","32,768","2,048","32,768","131,072","16,384","16,384","16,384","2,046","32,768","32,768","2,048","32,768","268,435,456","32,768","131,072","32,768","32,768","65,536","32,768","2,048","32,768","65,000","2,097,120","131,072","32,768","32,768","131,072","16,384","32,768","16,384","8,192","16,384","8,192","2,046","32,768","32,768","877,000","1","9","0","0","80","8","4","1","0","0","168","0","0","1","15","0","7","2","1","1","512","0","512","32","65,536","16,928,342,016","1","1","32","256","0","0.00","42,560","0","0","0","256","1","1","256","1","0","cudaFuncCachePreferNone","124,120,044,254,464","4","1","1","4","32","1","1","8","73","2,056","776","255","65,536","32,768","32,768","32,768","0","32,768","0","7","1,024","0.05","115.85","0","0","0","no data","0","0","0","0","","0","0","0","6","0","0","no data","0","0","0","9,437,520","9,437,520","9,437,520","37,750,080","9,437,520","9,437,520","9,437,520","37,750,080","4","0","8","12.50","12.48","106,752","2","2,102,272","1.28","6.38"
diff --git a/results/ncu_scaling_crossovers/summary.csv b/results/ncu_scaling_crossovers/summary.csv
new file mode 100644
index 0000000..98f8fc7
--- /dev/null
+++ b/results/ncu_scaling_crossovers/summary.csv
@@ -0,0 +1,38 @@
+label,kernel_id,kernel_name,grid_size,block_size,time_us,dram_read_mib,dram_write_mib,dram_peak_pct,l2_hit_pct,l1_hit_pct,shared_load_bank_conflicts,shared_store_bank_conflicts,warp_instructions,integer_thread_instructions,fp32_thread_instructions,fp64_thread_instructions,tensor_warp_instructions,tensor_active_pct,active_warps_pct,barrier_stall_pct,long_scoreboard_stall_pct,registers_per_thread,shared_mem_bytes,waves_per_sm,occupancy_register_block_limit,occupancy_shared_block_limit,occupancy_warp_block_limit
+fft14_cufft_b1024,0,void vector_fft<,1024,1024,438.944,128.032470703125,127.8255615234375,68.02,51.65,2.12,74619.0,1048644.0,41811968.0,,1018167296.0,,,,46.92,5.95,15.07,61.0,67584.0,12.8,1.0,1.0,2.0
+fft14_cufft_b16,0,void regular_fft<,64,256,14.432,1.773193359375,0.365234375,17.35,53.69,0.63,0.0,0.0,445952.0,,9945088.0,,,,12.42,0.4,21.42,64.0,32768.0,0.27,4.0,3.0,8.0
+fft14_cufft_b16,1,void regular_fft<,64,256,13.44,1.32843017578125,0.332611083984375,14.44,76.71,60.07,0.0,0.0,339968.0,,7487488.0,,,,12.42,0.43,15.97,64.0,32768.0,0.27,4.0,3.0,8.0
+fft14_cufft_b256,0,void vector_fft<,256,1024,137.984,32.01922607421875,31.808013916015625,53.99,51.74,2.1,17299.0,262154.0,10452992.0,,254541824.0,,,,46.48,5.09,15.89,61.0,67584.0,3.2,1.0,1.0,2.0
+fft14_direct_b1024,0,"void cuntt::detail::<unnamed>::cufftdx_contiguous_block_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",1024,1024,413.79200000000003,128.03720092773438,127.88580322265625,72.18,53.14,2.25,3847.0,4194304.0,38436864.0,,938475520.0,,,,47.44,6.99,6.52,63.0,65536.0,12.8,1.0,1.0,2.0
+fft14_direct_b16,0,"void cuntt::detail::<unnamed>::cufftdx_contiguous_block_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",16,1024,24.416,0.0,0.00042724609375,0.0,101.79,2.19,27.0,65536.0,600576.0,,14663680.0,,,,48.59,8.34,3.47,63.0,65536.0,0.2,1.0,1.0,2.0
+fft14_direct_b256,0,"void cuntt::detail::<unnamed>::cufftdx_contiguous_block_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",256,1024,129.312,32.036956787109375,31.51104736328125,57.35,53.21,2.11,977.0,1048576.0,9609216.0,,234618880.0,,,,47.29,6.18,7.5,63.0,65536.0,3.2,1.0,1.0,2.0
+fft18_cufft_b16,0,void regular_fft<,512,1024,109.568,32.00079345703125,31.973052978515625,68.14,50.15,2.94,0.0,262144.0,10911744.0,,203948032.0,,,,46.48,7.58,31.76,39.0,32768.0,6.4,1.0,1.0,2.0
+fft18_cufft_b16,1,void regular_fft<,512,1024,120.128,32.231201171875,32.185455322265625,62.59,74.9,34.59,0.0,262144.0,8699904.0,,158859264.0,,,,47.44,8.97,21.91,39.0,32768.0,6.4,1.0,1.0,2.0
+fft18_cufft_b2,0,void regular_fft<,64,1024,20.16,4.000732421875,2.90185546875,40.02,51.04,2.56,0.0,32768.0,1363968.0,,25493504.0,,,,48.53,2.97,36.36,39.0,32768.0,0.8,1.0,1.0,2.0
+fft18_cufft_b2,1,void regular_fft<,64,1024,19.36,4.000732421875,3.043060302734375,42.53,75.83,34.37,0.0,32768.0,1087488.0,,19857408.0,,,,47.71,4.14,26.56,39.0,32768.0,0.8,1.0,1.0,2.0
+fft18_cufft_b64,0,void regular_fft<,2048,1024,354.112,128.00079345703125,128.1094970703125,84.41,50.05,2.99,0.0,1048576.0,43646976.0,,815792128.0,,,,46.31,8.14,27.81,39.0,32768.0,25.6,1.0,1.0,2.0
+fft18_cufft_b64,1,void regular_fft<,2048,1024,400.384,128.17523193359375,128.07583618164062,74.69,74.99,34.63,0.0,1048576.0,34799616.0,,635437056.0,,,,47.37,10.7,22.41,39.0,32768.0,25.6,1.0,1.0,2.0
+fft18_online_b16,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",2048,256,124.608,32.60400390625,32.296844482421875,60.81,79.7,5.73,1000918.0,1902870.0,17727488.0,,172490752.0,,,,58.82,9.24,46.01,48.0,16384.0,5.12,5.0,6.0,8.0
+fft18_online_b16,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",2048,256,96.896,32.00067138671875,32.668243408203125,77.93,50.54,5.78,199041.0,1875069.0,13615104.0,,149422080.0,,,,58.61,16.23,16.92,48.0,16384.0,5.12,5.0,6.0,8.0
+fft18_online_b2,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",256,256,23.232,4.22528076171875,4.250579833984375,42.58,79.23,6.31,129211.0,229376.0,2215936.0,,21561344.0,,,,37.69,7.06,47.31,48.0,16384.0,0.64,5.0,6.0,8.0
+fft18_online_b2,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",256,256,18.336000000000002,4.000732421875,4.225067138671875,52.44,50.88,6.03,39759.0,229376.0,1701888.0,,18677760.0,,,,37.75,7.24,26.26,48.0,16384.0,0.64,5.0,6.0,8.0
+fft18_online_b64,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",8192,256,441.568,129.20758056640625,128.30136108398438,68.06,79.93,5.58,4023705.0,7653495.0,70909952.0,,689963008.0,,,,60.86,9.3,44.7,48.0,16384.0,20.48,5.0,6.0,8.0
+fft18_online_b64,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",8192,256,415.616,128.00067138671875,129.21917724609375,72.23,50.48,5.68,725573.0,7530198.0,54460416.0,,597688320.0,,,,60.35,17.83,16.0,48.0,16384.0,20.48,5.0,6.0,8.0
+fft20_cufft_b16,0,void regular_fft<,2048,512,398.91200000000003,128.00933837890625,128.62646484375,75.08,50.08,1.83,0.0,1048576.0,38141952.0,,882900992.0,,,,23.92,4.86,17.72,64.0,65536.0,25.6,2.0,1.0,4.0
+fft20_cufft_b16,1,void regular_fft<,2048,512,373.952,128.0030517578125,128.59268188476562,80.07,75.13,1.5,0.0,1048576.0,31326208.0,,725614592.0,,,,24.29,4.53,25.29,64.0,65536.0,25.6,2.0,1.0,4.0
+fft20_cufft_b2,0,void regular_fft<,256,512,73.952,16.0020751953125,16.718292236328125,51.66,50.41,1.72,0.0,131072.0,4767744.0,,110362624.0,,,,24.13,2.76,18.5,64.0,65536.0,3.2,2.0,1.0,4.0
+fft20_cufft_b2,1,void regular_fft<,256,512,72.352,16.00225830078125,16.64990234375,52.67,75.34,1.53,0.0,131072.0,3915776.0,,90701824.0,,,,24.28,2.75,17.98,64.0,65536.0,3.2,2.0,1.0,4.0
+fft20_cufft_b8,0,void regular_fft<,1024,512,217.248,64.0098876953125,64.61993408203125,69.1,50.12,1.82,0.0,524288.0,19070976.0,,441450496.0,,,,23.91,4.4,17.99,64.0,65536.0,12.8,2.0,1.0,4.0
+fft20_cufft_b8,1,void regular_fft<,1024,512,208.448,64.00274658203125,64.598388671875,72.01,75.16,1.53,0.0,524288.0,15663104.0,,362807296.0,,,,24.23,4.15,21.69,64.0,65536.0,12.8,2.0,1.0,4.0
+fft20_online_b16,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,512,566.912,146.48565673828125,128.32916259765625,56.57,77.11,6.53,4313727.0,7340032.0,77922304.0,,832569344.0,,,,48.8,10.52,40.71,52.0,32768.0,25.6,2.0,2.0,4.0
+fft20_online_b16,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",4096,512,350.688,128.00238037109375,128.29754638671875,85.3,50.21,6.87,771798.0,7340032.0,60817408.0,,740294656.0,,,,48.27,14.19,19.97,51.0,32768.0,25.6,2.0,2.0,4.0
+fft20_online_b2,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",512,512,82.56,18.736083984375,16.924530029296875,50.43,77.25,6.46,540492.0,917504.0,9740288.0,,104071168.0,,,,47.04,10.12,42.03,52.0,32768.0,3.2,2.0,2.0,4.0
+fft20_online_b2,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",512,512,56.928000000000004,16.00250244140625,16.3013916015625,66.26,50.4,6.83,129180.0,917504.0,7602176.0,,92536832.0,,,,47.02,13.16,24.98,51.0,32768.0,3.2,2.0,2.0,4.0
+fft20_online_b8,0,"void cuntt::detail::<unnamed>::cufftdx_online_first_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",2048,512,288.25600000000003,73.555419921875,64.29620361328125,55.82,76.95,6.5,2161316.0,3670016.0,38961152.0,,416284672.0,,,,48.56,10.51,41.06,52.0,32768.0,12.8,2.0,2.0,4.0
+fft20_online_b8,1,"void cuntt::detail::<unnamed>::cufftdx_online_second_kernel<cufftdx::detail::fft_block_execution<cufftdx::Block, cufftdx::Size<",2048,512,182.304,64.0028076171875,64.30712890625,82.14,50.25,6.89,404868.0,3670016.0,30408704.0,,370147328.0,,,,48.0,13.83,21.14,51.0,32768.0,12.8,2.0,2.0,4.0
+fwht15_online_b16,0,"void cuntt::detail::hierarchical_prefix_kernel<cuntt::<unnamed>::FwhtOperator<float>,",2048,256,27.616,0.793212890625,0.24884033203125,4.41,88.98,0.56,80088.0,65670.0,1593344.0,,4194304.0,,,,79.91,24.93,13.49,18.0,1024.0,3.2,10.0,8.0,8.0
+fwht15_online_b16,1,"void cuntt::detail::online_reorder_suffix_kernel<cuntt::<unnamed>::FwhtOperator<float>,",4096,256,28.608,1.0059814453125,0.247802734375,5.12,89.02,8.65,90483.0,65847.0,4165632.0,,5767168.0,,,,81.37,30.87,10.08,25.0,512.0,6.4,8.0,16.0,8.0
+fwht15_online_b4,0,"void cuntt::detail::hierarchical_prefix_kernel<cuntt::<unnamed>::FwhtOperator<float>,",512,256,9.312,0.0,0.0,0.0,100.36,0.0,16920.0,16384.0,398336.0,,1048576.0,,,,48.62,11.6,3.79,18.0,1024.0,0.8,10.0,8.0,8.0
+fwht15_online_b4,1,"void cuntt::detail::online_reorder_suffix_kernel<cuntt::<unnamed>::FwhtOperator<float>,",1024,256,10.144,0.0,0.0,0.0,100.52,2.08,18993.0,16423.0,1041408.0,,1441792.0,,,,63.84,22.29,4.78,25.0,512.0,1.6,8.0,16.0,8.0
+fwht15_warp_b16,0,void cuntt::detail::register_fwht_kernel<,16,256,42.592,1.49609375,0.4140625,5.24,59.01,0.0,0.0,0.0,427008.0,,8409088.0,,,,12.47,1.46,4.75,255.0,32768.0,0.2,1.0,1.0,8.0
+fwht15_warp_b4,0,void cuntt::detail::register_fwht_kernel<,4,256,42.56,0.000244140625,0.0,0.0,115.85,0.0,0.0,0.0,106752.0,,2102272.0,,,,12.48,1.28,6.38,255.0,32768.0,0.05,1.0,1.0,8.0
diff --git a/results/v100_external_baselines_raw.csv b/results/v100_external_baselines_raw.csv
new file mode 100644
index 0000000..f554f12
--- /dev/null
+++ b/results/v100_external_baselines_raw.csv
@@ -0,0 +1,121 @@
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+ntt20_gpuntt_b16,ntt20-batch16,5,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,16,576460756061519873,60,1000,100,GPU-NTT-Merge,1.5689,10198.2,1
+ntt16_cub_b4,ntt16-batch4,4,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,hybrid2d,0.031232,128073.770492,1
+ntt20_cub_b16,ntt20-batch16,3,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,16,576460756061519873,60,1000,100,compact-stage,1.460828,10952.692583,1
+ntt16_gpuntt_b4,ntt16-batch4,4,GPU-NTT-Merge-natural,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.0345907,115638,1
+ntt20_cub_b4,ntt20-batch4,5,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,compact-stage,0.342159,11690.471389,1
+ntt20_gpuntt_b2,ntt20-batch2,5,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,GPU-NTT-Merge,0.204759,9767.58,1
+ntt20_cub_b2,ntt20-batch2,1,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,compact-stage,0.179405,11147.961317,1
+fwht8_warp_b4096,fwht8-batch4096,2,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,temporal-tile,0.011305,362318821.794491,1
+ntt20_gpuntt_b16,ntt20-batch16,1,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,16,576460756061519873,60,1000,100,GPU-NTT-Merge,1.56915,10196.6,1
+ntt16_cub_b64,ntt16-batch64,3,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,64,576460756061519873,60,1000,100,hybrid2d,0.281539,227321.969603,1
+ntt20_cub_b2,ntt20-batch2,2,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,compact-stage,0.179855,11120.068944,1
+ntt20_gpuntt_b16,ntt20-batch16,3,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,16,576460756061519873,60,1000,100,GPU-NTT-Merge,1.57787,10140.2,1
+fwht15_dao_b4,fwht15-batch4,5,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.017828,224368.181078,1
+ntt20_cub_b2,ntt20-batch2,5,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,compact-stage,0.180480,11081.560284,1
+fwht8_warp_b65536,fwht8-batch65536,5,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,65536,,,1000,100,temporal-tile,0.164321,398828420.904083,1
+fwht8_warp_b65536,fwht8-batch65536,4,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,65536,,,1000,100,temporal-tile,0.164280,398927868.753938,1
+fwht15_warp_b512,fwht15-batch512,1,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,temporal-tile,0.193270,2649146.778421,1
+ntt16_cub_b4,ntt16-batch4,5,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,hybrid2d,0.029512,135538.086202,1
+fwht15_dao_b256,fwht15-batch256,2,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.115712,2212389.309637,1
+fwht8_dao_b4096,fwht8-batch4096,5,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.011479,356824252.104277,1
+fwht8_dao_b4096,fwht8-batch4096,2,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.011858,345423152.293764,1
+fwht15_warp_b512,fwht15-batch512,2,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,temporal-tile,0.200448,2554278.524784,1
+fwht15_dao_b512,fwht15-batch512,3,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.207800,2463903.903551,1
+fwht15_dao_b16,fwht15-batch16,4,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,16,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.015483,1033399.479103,1
+fwht15_warp_b16,fwht15-batch16,5,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,16,,,1000,100,temporal-tile,0.017592,909487.765179,1
+fwht8_dao_b4096,fwht8-batch4096,1,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.011448,357781748.431074,1
+ntt16_gpuntt_b4,ntt16-batch4,1,GPU-NTT-Merge-natural,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.0327168,122261,1
+fwht8_warp_b65536,fwht8-batch65536,3,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,65536,,,1000,100,temporal-tile,0.164280,398927868.753938,1
+ntt20_cub_b2,ntt20-batch2,4,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,compact-stage,0.179323,11153.059005,1
+ntt16_cub_b256,ntt16-batch256,2,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,256,576460756061519873,60,1000,100,hybrid2d,1.066762,239978.551917,1
+ntt20_gpuntt_b4,ntt20-batch4,2,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.399002,10025,1
+fwht8_dao_b65536,fwht8-batch65536,5,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,65536,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.164628,398084203.652902,1
+ntt16_gpuntt_b4,ntt16-batch4,5,GPU-NTT-Merge-natural,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.0326656,122453,1
+fwht15_dao_b16,fwht15-batch16,1,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,16,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.015462,1034768.230582,1
+fwht15_warp_b512,fwht15-batch512,5,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,temporal-tile,0.193249,2649427.652031,1
+ntt20_gpuntt_b4,ntt20-batch4,5,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.399094,10022.7,1
+fwht15_warp_b4,fwht15-batch4,2,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,temporal-tile,0.018534,215814.922145,1
+ntt16_cub_b256,ntt16-batch256,1,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,256,576460756061519873,60,1000,100,hybrid2d,1.068636,239557.716566,1
+fwht15_dao_b256,fwht15-batch256,3,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.117658,2175804.969874,1
+ntt16_gpuntt_b256,ntt16-batch256,5,GPU-NTT-Merge-natural,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,256,576460756061519873,60,1000,100,GPU-NTT-Merge,1.52389,167992,1
+ntt20_cub_b2,ntt20-batch2,3,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,compact-stage,0.180285,11093.546329,1
+fwht15_warp_b4,fwht15-batch4,5,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,temporal-tile,0.017838,224239.386531,1
+fwht15_warp_b256,fwht15-batch256,4,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,temporal-tile,0.107551,2380272.349843,1
+fwht15_warp_b256,fwht15-batch256,5,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,temporal-tile,0.107059,2391200.313614,1
+ntt20_gpuntt_b4,ntt20-batch4,4,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.402104,9947.67,1
+ntt20_cub_b4,ntt20-batch4,4,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,compact-stage,0.342221,11688.353432,1
+ntt16_gpuntt_b64,ntt16-batch64,5,GPU-NTT-Merge-natural,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,64,576460756061519873,60,1000,100,GPU-NTT-Merge,0.386836,165445,1
+fwht15_dao_b4,fwht15-batch4,3,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.015790,253323.608401,1
+fwht8_warp_b4096,fwht8-batch4096,4,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,temporal-tile,0.011325,361663641.001895,1
+fwht15_dao_b16,fwht15-batch16,5,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,16,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.015790,1013294.433604,1
+ntt16_cub_b64,ntt16-batch64,2,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,64,576460756061519873,60,1000,100,hybrid2d,0.277617,230533.432751,1
+ntt20_cub_b4,ntt20-batch4,1,cuNTT-compact-stage,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,compact-stage,0.341914,11698.848248,1
+fwht15_dao_b4,fwht15-batch4,4,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.015606,256315.623028,1
+fwht15_dao_b512,fwht15-batch512,5,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.208118,2460145.734300,1
+ntt20_gpuntt_b2,ntt20-batch2,1,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,GPU-NTT-Merge,0.204872,9762.21,1
+fwht15_warp_b4,fwht15-batch4,4,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,temporal-tile,0.017818,224497.130231,1
+fwht15_dao_b512,fwht15-batch512,1,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.207882,2462932.947341,1
+fwht15_dao_b256,fwht15-batch256,4,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.115558,2215330.172641,1
+ntt16_gpuntt_b256,ntt16-batch256,1,GPU-NTT-Merge-natural,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,256,576460756061519873,60,1000,100,GPU-NTT-Merge,1.52208,168190,1
+fwht8_warp_b4096,fwht8-batch4096,3,cuButterfly-warp-register,1,butterfly,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,temporal-tile,0.011284,362976410.670370,1
+ntt16_cub_b64,ntt16-batch64,1,cuNTT-Hybrid2D-radix4,1,ntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,natural,16,65536,64,576460756061519873,60,1000,100,hybrid2d,0.281549,227313.895627,1
+ntt20_gpuntt_b4,ntt20-batch4,1,GPU-NTT-Merge-native,0,gpuntt,Tesla V100-SXM2-16GB,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,GPU-NTT-Merge,0.401388,9965.43,1
+fwht15_dao_b512,fwht15-batch512,4,Dao-AILab-FHT,0,dao-fht,Tesla V100-SXM2-16GB,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,dao-fast-hadamard-transform-sm70-local,0.208159,2459661.527838,1
diff --git a/results/v100_external_baselines_report.md b/results/v100_external_baselines_report.md
new file mode 100644
index 0000000..21f5518
--- /dev/null
+++ b/results/v100_external_baselines_report.md
@@ -0,0 +1,32 @@
+# V100 Matching-Protocol External Baselines
+
+All rows use 1000 warmups, 100 repetitions, five independent process trials, and correctness checks.
+
+Rows below 0.020 ms are retained but are not used for stable latency claims.
+
+| Operator | logN | Batch | Output | Implementation | Median ms | vs cuButterfly/cuNTT | Timing quality |
+|:--|--:|--:|:--|:--|--:|--:|:--|
+| fwht | 15 | 16 | natural | Dao-AILab-FHT | 0.015483 | 1.148x | below-timing-floor |
+| fwht | 15 | 16 | natural | cuButterfly-warp-register | 0.017777 | 1.000x | below-timing-floor |
+| fwht | 15 | 256 | natural | Dao-AILab-FHT | 0.116429 | 0.924x | stable |
+| fwht | 15 | 256 | natural | cuButterfly-warp-register | 0.107551 | 1.000x | stable |
+| fwht | 15 | 4 | natural | Dao-AILab-FHT | 0.015606 | 1.142x | below-timing-floor |
+| fwht | 15 | 4 | natural | cuButterfly-warp-register | 0.017818 | 1.000x | below-timing-floor |
+| fwht | 15 | 512 | natural | Dao-AILab-FHT | 0.207882 | 0.930x | stable |
+| fwht | 15 | 512 | natural | cuButterfly-warp-register | 0.193270 | 1.000x | stable-with-outlier |
+| fwht | 8 | 4,096 | natural | Dao-AILab-FHT | 0.011561 | 0.978x | below-timing-floor |
+| fwht | 8 | 4,096 | natural | cuButterfly-warp-register | 0.011305 | 1.000x | below-timing-floor |
+| fwht | 8 | 65,536 | natural | Dao-AILab-FHT | 0.164506 | 0.999x | stable |
+| fwht | 8 | 65,536 | natural | cuButterfly-warp-register | 0.164280 | 1.000x | stable |
+| ntt | 16 | 256 | natural | GPU-NTT-Merge-natural | 1.522080 | 0.702x | stable |
+| ntt | 16 | 256 | natural | cuNTT-Hybrid2D-radix4 | 1.068636 | 1.000x | stable |
+| ntt | 16 | 4 | natural | GPU-NTT-Merge-natural | 0.032881 | 0.902x | stable-with-outlier |
+| ntt | 16 | 4 | natural | cuNTT-Hybrid2D-radix4 | 0.029645 | 1.000x | stable-with-outlier |
+| ntt | 16 | 64 | natural | GPU-NTT-Merge-natural | 0.386632 | 0.718x | stable |
+| ntt | 16 | 64 | natural | cuNTT-Hybrid2D-radix4 | 0.277678 | 1.000x | stable |
+| ntt | 20 | 16 | bit-reversed | GPU-NTT-Merge-native | 1.568900 | 0.839x | stable |
+| ntt | 20 | 16 | bit-reversed | cuNTT-compact-stage | 1.315605 | 1.000x | stable-with-outlier |
+| ntt | 20 | 2 | bit-reversed | GPU-NTT-Merge-native | 0.204872 | 0.878x | stable |
+| ntt | 20 | 2 | bit-reversed | cuNTT-compact-stage | 0.179855 | 1.000x | stable |
+| ntt | 20 | 4 | bit-reversed | GPU-NTT-Merge-native | 0.399534 | 0.856x | stable |
+| ntt | 20 | 4 | bit-reversed | cuNTT-compact-stage | 0.341914 | 1.000x | stable |
diff --git a/results/v100_external_baselines_summary.csv b/results/v100_external_baselines_summary.csv
new file mode 100644
index 0000000..a1caf98
--- /dev/null
+++ b/results/v100_external_baselines_summary.csv
@@ -0,0 +1,25 @@
+group,implementation,reference,runner,operator,precision,direction,normalization,placement,output_order,logN,N,batch,modulus,modulus_bits,warmup,repeat,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,timing_quality,correct,throughput_vs_reference
+fwht15-batch16,Dao-AILab-FHT,0,dao-fht,fwht,fp32,forward,none,out-of-place,natural,15,32768,16,,,1000,100,5,0.015483,0.015462,0.015790,0.021185,0.008655,stable,below-timing-floor,1,1.148163
+fwht15-batch16,cuButterfly-warp-register,1,butterfly,fwht,fp32,forward,none,out-of-place,natural,15,32768,16,,,1000,100,5,0.017777,0.017592,0.018872,0.072003,0.002306,stable-with-outlier,below-timing-floor,1,1.000000
+fwht15-batch256,Dao-AILab-FHT,0,dao-fht,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,5,0.116429,0.115558,0.117658,0.018037,0.016267,stable,stable,1,0.923748
+fwht15-batch256,cuButterfly-warp-register,1,butterfly,fwht,fp32,forward,none,out-of-place,natural,15,32768,256,,,1000,100,5,0.107551,0.107059,0.108851,0.016662,0.003803,stable,stable,1,1.000000
+fwht15-batch4,Dao-AILab-FHT,0,dao-fht,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,5,0.015606,0.015401,0.017828,0.155517,0.011790,stable-with-outlier,below-timing-floor,1,1.141740
+fwht15-batch4,cuButterfly-warp-register,1,butterfly,fwht,fp32,forward,none,out-of-place,natural,15,32768,4,,,1000,100,5,0.017818,0.017766,0.018534,0.043102,0.001740,stable-with-outlier,below-timing-floor,1,1.000000
+fwht15-batch512,Dao-AILab-FHT,0,dao-fht,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,5,0.207882,0.207800,0.208159,0.001727,0.001381,stable,stable,1,0.929710
+fwht15-batch512,cuButterfly-warp-register,1,butterfly,fwht,fp32,forward,none,out-of-place,natural,15,32768,512,,,1000,100,5,0.193270,0.192891,0.200448,0.039101,0.006468,stable-with-outlier,stable-with-outlier,1,1.000000
+fwht8-batch4096,Dao-AILab-FHT,0,dao-fht,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,5,0.011561,0.011448,0.011919,0.040740,0.032783,unstable,below-timing-floor,1,0.977857
+fwht8-batch4096,cuButterfly-warp-register,1,butterfly,fwht,fp32,forward,none,out-of-place,natural,8,256,4096,,,1000,100,5,0.011305,0.011233,0.011397,0.014507,0.003627,stable,below-timing-floor,1,1.000000
+fwht8-batch65536,Dao-AILab-FHT,0,dao-fht,fwht,fp32,forward,none,out-of-place,natural,8,256,65536,,,1000,100,5,0.164506,0.164454,0.164628,0.001058,0.000626,stable,stable,1,0.998626
+fwht8-batch65536,cuButterfly-warp-register,1,butterfly,fwht,fp32,forward,none,out-of-place,natural,8,256,65536,,,1000,100,5,0.164280,0.164260,0.164321,0.000371,0.000250,stable,stable,1,1.000000
+ntt16-batch256,GPU-NTT-Merge-natural,0,gpuntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,256,576460756061519873,60,1000,100,5,1.522080,1.521590,1.524910,0.002181,0.001347,stable,stable,1,0.702089
+ntt16-batch256,cuNTT-Hybrid2D-radix4,1,ntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,256,576460756061519873,60,1000,100,5,1.068636,1.066465,1.075866,0.008797,0.002214,stable,stable,1,1.000000
+ntt16-batch4,GPU-NTT-Merge-natural,0,gpuntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,5,0.032881,0.032666,0.034591,0.058548,0.011524,stable-with-outlier,stable-with-outlier,1,0.901595
+ntt16-batch4,cuNTT-Hybrid2D-radix4,1,ntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,576460756061519873,60,1000,100,5,0.029645,0.029512,0.031232,0.058020,0.003812,stable-with-outlier,stable-with-outlier,1,1.000000
+ntt16-batch64,GPU-NTT-Merge-natural,0,gpuntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,64,576460756061519873,60,1000,100,5,0.386632,0.385198,0.388762,0.009218,0.001324,stable,stable,1,0.718197
+ntt16-batch64,cuNTT-Hybrid2D-radix4,1,ntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,64,576460756061519873,60,1000,100,5,0.277678,0.276931,0.281549,0.016631,0.014124,stable,stable,1,1.000000
+ntt20-batch16,GPU-NTT-Merge-native,0,gpuntt,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,16,576460756061519873,60,1000,100,5,1.568900,1.560020,1.577870,0.011377,0.000701,stable,stable,1,0.838552
+ntt20-batch16,cuNTT-compact-stage,1,ntt,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,16,576460756061519873,60,1000,100,5,1.315605,1.311406,1.460828,0.113577,0.001168,stable-with-outlier,stable-with-outlier,1,1.000000
+ntt20-batch2,GPU-NTT-Merge-native,0,gpuntt,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,5,0.204872,0.203930,0.206234,0.011246,0.002899,stable,stable,1,0.877890
+ntt20-batch2,cuNTT-compact-stage,1,ntt,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,2,576460756061519873,60,1000,100,5,0.179855,0.179323,0.180480,0.006433,0.004893,stable,stable,1,1.000000
+ntt20-batch4,GPU-NTT-Merge-native,0,gpuntt,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,5,0.399534,0.399002,0.402104,0.007764,0.005742,stable,stable,1,0.855782
+ntt20-batch4,cuNTT-compact-stage,1,ntt,ntt,uint64,forward,none,out-of-place,bit-reversed,20,1048576,4,576460756061519873,60,1000,100,5,0.341914,0.341617,0.342221,0.001767,0.001167,stable,stable,1,1.000000
diff --git a/results/v100_fft_pipeline_model_calibrated_evaluation.csv b/results/v100_fft_pipeline_model_calibrated_evaluation.csv
new file mode 100644
index 0000000..44396fe
--- /dev/null
+++ b/results/v100_fft_pipeline_model_calibrated_evaluation.csv
@@ -0,0 +1,7 @@
+group,logN,batch,candidate_count,calibrated_coverage,measured_winner,measured_winner_ms,winner_calibrated_rank,top1_regret,top1_recall,top3_regret,top3_recall,top10_regret,top10_recall
+fft18-fp32-batch16,18,16,48,48,fft18-fp32_b16_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,0.195441,5,1.0042928556444144,0,1.0019903704954436,0,1.0,1
+fft18-fp32-batch2,18,2,48,44,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8,0.025866,5,1.0023969689940462,0,1.0015850923992886,0,1.0,1
+fft18-fp32-batch64,18,64,48,48,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,0.767201,2,1.0799764338159101,0,1.0,1,1.0,1
+fft20-fp32-batch16,20,16,48,48,fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt256x128_ge16x16,0.764334,2,1.0017152187394516,0,1.0,1,1.0,1
+fft20-fp32-batch2,20,2,48,48,fft20-fp32_b2_p10s10_t512x512_e8x8_rec,0.119869,3,1.0029115117336427,0,1.0,1,1.0,1
+fft20-fp32-batch8,20,8,48,48,fft20-fp32_b8_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,0.397332,5,1.000722317860127,0,1.000722317860127,0,1.0,1
diff --git a/results/v100_fft_pipeline_model_evaluation.csv b/results/v100_fft_pipeline_model_evaluation.csv
new file mode 100644
index 0000000..63ef579
--- /dev/null
+++ b/results/v100_fft_pipeline_model_evaluation.csv
@@ -0,0 +1,7 @@
+group,logN,batch,candidate_count,measured_winner,measured_winner_ms,winner_static_rank,spearman,top1_candidate,top1_regret,top1_recall,top3_candidate,top3_regret,top3_recall,top10_candidate,top10_regret,top10_recall
+fft18-fp32-batch16,18,16,48,fft18-fp32_b16_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,0.195441,32,0.341670209219245,fft18-fp32_b16_p9s9_t128x128_e16x16_rec,1.025250587133713,0,fft18-fp32_b16_p9s9_t128x128_e16x16_rec,1.025250587133713,0,fft18-fp32_b16_p9s9_t128x128_e16x16_rec,1.025250587133713,0
+fft18-fp32-batch2,18,2,48,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8,0.025866,31,0.3419927441059366,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,1.4220211861130443,0,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,1.4220211861130443,0,fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,1.296914868939921,0
+fft18-fp32-batch64,18,64,48,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,0.767201,1,0.3653491344734382,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,1.0,1,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,1.0,1,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,1.0,1
+fft20-fp32-batch16,20,16,48,fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt256x128_ge16x16,0.764334,7,0.34038907750224084,fft20-fp32_b16_p10s10_t256x128_e16x16_rec,1.0004827732378778,0,fft20-fp32_b16_p10s10_t256x128_e16x16_rec,1.0004827732378778,0,fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt256x128_ge16x16,1.0,1
+fft20-fp32-batch2,20,2,48,fft20-fp32_b2_p10s10_t512x512_e8x8_rec,0.119869,32,0.3208459865207856,fft20-fp32_b2_p10s10_t256x128_e16x16_rec,1.0642451342715797,0,fft20-fp32_b2_p10s10_t256x128_e16x16_rec,1.0642451342715797,0,fft20-fp32_b2_p10s10_t256x128_e16x16_rec,1.0642451342715797,0
+fft20-fp32-batch8,20,8,48,fft20-fp32_b8_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,0.397332,7,0.3656948315982306,fft20-fp32_b8_p10s10_t256x128_e16x16_rec,1.000722317860127,0,fft20-fp32_b8_p10s10_t256x128_e16x16_rec,1.000722317860127,0,fft20-fp32_b8_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,1.0,1
diff --git a/results/v100_fft_pipeline_model_metrics.json b/results/v100_fft_pipeline_model_metrics.json
new file mode 100644
index 0000000..07505f7
--- /dev/null
+++ b/results/v100_fft_pipeline_model_metrics.json
@@ -0,0 +1,34 @@
+{
+  "static": {
+    "evaluated_shapes": 6,
+    "top1_exact_recall": 0.16666666666666666,
+    "top1_geomean_regret": 1.076176475816476,
+    "top1_worst_regret": 1.4220211861130443,
+    "top1_candidate_fraction": 0.020833333333333332,
+    "top3_exact_recall": 0.16666666666666666,
+    "top3_geomean_regret": 1.076176475816476,
+    "top3_worst_regret": 1.4220211861130443,
+    "top3_candidate_fraction": 0.0625,
+    "top10_exact_recall": 0.5,
+    "top10_geomean_regret": 1.0595721342083242,
+    "top10_worst_regret": 1.296914868939921,
+    "top10_candidate_fraction": 0.20833333333333334,
+    "mean_spearman": 0.34599033056997947
+  },
+  "calibrated": {
+    "evaluated_shapes": 6,
+    "mean_candidate_coverage": 0.9861111111111112,
+    "top1_exact_recall": 0,
+    "top1_geomean_regret": 1.0149371399354197,
+    "top1_worst_regret": 1.0799764338159101,
+    "top1_candidate_fraction": 0.020833333333333332,
+    "top3_exact_recall": 0.5,
+    "top3_geomean_regret": 1.0007159706702138,
+    "top3_worst_regret": 1.0019903704954436,
+    "top3_candidate_fraction": 0.0625,
+    "top10_exact_recall": 1,
+    "top10_geomean_regret": 1.0,
+    "top10_worst_regret": 1.0,
+    "top10_candidate_fraction": 0.20833333333333334
+  }
+}
diff --git a/results/v100_fft_pipeline_model_report.md b/results/v100_fft_pipeline_model_report.md
new file mode 100644
index 0000000..e26ec32
--- /dev/null
+++ b/results/v100_fft_pipeline_model_report.md
@@ -0,0 +1,46 @@
+# V100 FFT Static-Model Evaluation
+
+Candidates are ordered only by the generator's static resource score; measured
+latency is then used to compute selection regret. Lower regret is better.
+
+| logN | Batch | Candidates | Winner static rank | Top-1 regret | Top-3 regret | Top-10 regret | Spearman |
+|--:|--:|--:|--:|--:|--:|--:|--:|
+| 18 | 16 | 48 | 32 | 1.0253x | 1.0253x | 1.0253x | 0.342 |
+| 18 | 2 | 48 | 31 | 1.4220x | 1.4220x | 1.2969x | 0.342 |
+| 18 | 64 | 48 | 1 | 1.0000x | 1.0000x | 1.0000x | 0.365 |
+| 20 | 16 | 48 | 7 | 1.0005x | 1.0005x | 1.0000x | 0.340 |
+| 20 | 2 | 48 | 32 | 1.0642x | 1.0642x | 1.0642x | 0.321 |
+| 20 | 8 | 48 | 7 | 1.0007x | 1.0007x | 1.0000x | 0.366 |
+
+## Aggregate
+
+| Budget | Exact recall | Geomean regret | Worst regret | Candidate fraction |
+|:--|--:|--:|--:|--:|
+| Top-1 | 16.7% | 1.0762x | 1.4220x | 2.1% |
+| Top-3 | 16.7% | 1.0762x | 1.4220x | 6.2% |
+| Top-10 | 50.0% | 1.0596x | 1.2969x | 20.8% |
+
+Mean per-shape Spearman correlation: 0.346.
+
+## Leave-One-Batch-Out Calibration
+
+For each held-out shape, the calibrated selector sees only the other batches
+at the same length and interpolates or extrapolates log-latency for matching
+physical mappings. It never consumes timing from the target shape.
+
+| logN | Batch | Covered | Winner rank | Top-1 regret | Top-3 regret | Top-10 regret |
+|--:|--:|--:|--:|--:|--:|--:|
+| 18 | 16 | 48/48 | 5 | 1.0043x | 1.0020x | 1.0000x |
+| 18 | 2 | 44/48 | 5 | 1.0024x | 1.0016x | 1.0000x |
+| 18 | 64 | 48/48 | 2 | 1.0800x | 1.0000x | 1.0000x |
+| 20 | 16 | 48/48 | 2 | 1.0017x | 1.0000x | 1.0000x |
+| 20 | 2 | 48/48 | 3 | 1.0029x | 1.0000x | 1.0000x |
+| 20 | 8 | 48/48 | 5 | 1.0007x | 1.0007x | 1.0000x |
+
+| Budget | Exact recall | Geomean regret | Worst regret | Candidate fraction |
+|:--|--:|--:|--:|--:|
+| Top-1 | 0.0% | 1.0149x | 1.0800x | 2.1% |
+| Top-3 | 50.0% | 1.0007x | 1.0020x | 6.2% |
+| Top-10 | 100.0% | 1.0000x | 1.0000x | 20.8% |
+
+Mean mapping coverage: 98.6%.
diff --git a/results/v100_fft_pipeline_raw.csv b/results/v100_fft_pipeline_raw.csv
new file mode 100644
index 0000000..dca21b2
--- /dev/null
+++ b/results/v100_fft_pipeline_raw.csv
@@ -0,0 +1,883 @@
+candidate_id,group,trial,implementation,reference,static_score,mapping_id,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,execution_group_stages,group_threads,group_ept,processing_unit,prefix_log_n,suffix_log_n,prefix_threads,suffix_threads,prefix_ept,suffix_ept,cross_twiddle,direct_boundary,device,compute_capability,operator,precision,direction,normalization,placement,backend,fft_core,logN,N,batch,warmup,repeat,kernel_ms,points_s,max_error,correct
+fft20-fp32_b16_p8s12_t128x256_e16x16_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p8s12_t128x256_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.646653,10188674714.226828,0.001339,1
+fft20-fp32_b16_p10s10_t512x512_e8x8_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p10s10_t512x512_e8x8_rec,0,4773086.798644853,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.916357,18308600435.156132,0.001466,1
+fft20-fp32_b2_p11s9_t256x128_e8x16_rec,fft20-fp32-batch2,1,fft20-fp32_b2_p11s9_t256x128_e8x16_rec,0,509007.80142380524,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.175247,11966810033.604259,0.001485,1
+fft20-fp32_b16_cufft,fft20-fp32-batch16,2,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,16,100,50,0.720855,23274051029.743492,0.002107,1
+fft20-fp32_b16_p9s11_t128x256_e16x8_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p9s11_t128x256_e16x8_rec,0,3566171.2214231617,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.134285,14791007692.462622,0.001748,1
+fft20-fp32_b8_p8s12_t128x256_e16x16_rec,fft20-fp32-batch8,1,fft20-fp32_b8_p8s12_t128x256_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.821432,10212171433.108576,0.001371,1
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+fft20-fp32_b8_p8s12_t128x256_e16x16_rec,fft20-fp32-batch8,3,fft20-fp32_b8_p8s12_t128x256_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.775967,10810525706.745008,0.001371,1
+fft18-fp32_b2_p10s8_t512x512_e16x16_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,10x8,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.038666,13559321728.476145,0.000637,1
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+fft20-fp32_b2_p10s10_t512x512_e8x8_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p10s10_t512x512_e8x8_rec,0,596635.8498306066,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.128369,16336948833.505247,0.001288,1
+fft18-fp32_b2_p9s9_t256x256_e8x8_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p9s9_t256x256_e8x8_rec,0,175170.20085765165,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.026030,20141620466.983376,0.000553,1
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+fft20-fp32_b8_p12s8_t256x128_e16x16_rec,fft20-fp32-batch8,3,fft20-fp32_b8_p12s8_t256x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.655667,12794003088.590370,0.001355,1
+fft18-fp32_b16_p10s8_t128x128_e16x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p10s8_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,10x8,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.256082,16378757598.362514,0.000671,1
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+fft20-fp32_b2_cufft,fft20-fp32-batch2,3,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,2,100,50,0.132915,15778120326.999699,0.002033,1
+fft18-fp32_b16_p10s8_t128x128_e16x16_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p10s8_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,10x8,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.243036,17257942836.529514,0.000671,1
+fft18-fp32_b16_cufft,fft18-fp32-batch16,2,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,16,100,50,0.216146,19404965142.113571,0.000601,1
+fft20-fp32_b8_p9s11_t128x256_e16x8_rec,fft20-fp32-batch8,1,fft20-fp32_b8_p9s11_t128x256_e16x8_rec,0,1783085.6107115808,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.579727,14469919309.310482,0.001716,1
+fft20-fp32_b2_p9s11_t128x256_e16x8_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p9s11_t128x256_e16x8_rec,0,445771.4026778952,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.169411,12379110503.197569,0.001638,1
+fft18-fp32_b2_cufft,fft18-fp32-batch2,1,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,2,100,50,0.028099,18658892787.650810,0.000583,1
+fft18-fp32_b64_p9s9_t256x256_e8x8_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p9s9_t256x256_e8x8_rec,0,4773086.798644853,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.842875,19904752539.701385,0.000666,1
+fft20-fp32_b8_p8s12_t128x256_e16x16_rec,fft20-fp32-batch8,2,fft20-fp32_b8_p8s12_t128x256_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.791183,10602608538.011602,0.001371,1
+fft20-fp32_b16_p10s10_t128x128_e16x16_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p10s10_t128x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.896819,18707466751.294586,0.001451,1
+fft20-fp32_b16_p10s10_t512x512_e8x8_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p10s10_t512x512_e8x8_rec,0,4773086.798644853,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.934072,17961367356.824551,0.001466,1
+fft18-fp32_b16_p9s9_t256x256_e8x8_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p9s9_t256x256_e8x8_rec,0,1193271.6996612132,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.205722,20388252679.385384,0.000629,1
+fft20-fp32_b16_p11s9_t256x128_e8x16_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p11s9_t256x128_e8x16_rec,0,4072062.411390442,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.371341,12234170084.888609,0.001713,1
+fft20-fp32_b16_p9s11_t128x256_e16x8_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p9s11_t128x256_e16x8_rec,0,3566171.2214231617,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.133466,14801699370.935270,0.001748,1
+fft20-fp32_b8_p11s9_t256x128_e8x16_rec,fft20-fp32-batch8,2,fft20-fp32_b8_p11s9_t256x128_e8x16_rec,0,2036031.205695221,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.674120,12443796859.510174,0.001587,1
+fft20-fp32_b8_p10s10_t512x512_e8x8_rec,fft20-fp32-batch8,2,fft20-fp32_b8_p10s10_t512x512_e8x8_rec,0,2386543.3993224264,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.455332,18423065130.353367,0.001485,1
+fft20-fp32_b16_p12s8_t256x128_e16x16_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p12s8_t256x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.326674,12646074094.460869,0.001377,1
+fft20-fp32_b2_p10s10_t128x128_e16x16_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p10s10_t128x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.156488,13401386531.711643,0.001320,1
+fft18-fp32_b2_p8s10_t512x512_e16x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p8s10_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,8x10,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.047862,10954214268.638493,0.000593,1
+fft20-fp32_b8_cufft,fft20-fp32-batch8,3,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,8,100,50,0.382075,21955402367.982166,0.002079,1
+fft20-fp32_b2_p10s10_t128x128_e16x16_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p10s10_t128x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.141189,14853496502.582733,0.001320,1
+fft20-fp32_b2_p11s9_t256x128_e8x16_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p11s9_t256x128_e8x16_rec,0,509007.80142380524,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.173404,12094012244.725166,0.001485,1
+fft18-fp32_b64_p9s9_t128x128_e16x16_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p9s9_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,9x9,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.905216,18533937089.280807,0.000984,1
+fft20-fp32_b16_p10s10_t128x128_e16x16_rec,fft20-fp32-batch16,1,fft20-fp32_b16_p10s10_t128x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.896307,18718153149.428429,0.001451,1
+fft20-fp32_b8_p11s9_t256x128_e8x16_rec,fft20-fp32-batch8,1,fft20-fp32_b8_p11s9_t256x128_e8x16_rec,0,2036031.205695221,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.675103,12425676666.303619,0.001587,1
+fft20-fp32_b8_cufft,fft20-fp32-batch8,1,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,8,100,50,0.382157,21950697291.819561,0.002079,1
+fft20-fp32_b16_cufft,fft20-fp32-batch16,3,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,16,100,50,0.720753,23277355760.860184,0.002107,1
+fft18-fp32_b64_p8s10_t128x128_e16x16_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,8x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.860140,19505225662.306740,0.000674,1
+fft18-fp32_b64_cufft,fft18-fp32-batch64,1,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,64,100,50,0.717599,23379662130.995724,0.000678,1
+fft18-fp32_b64_p9s9_t128x128_e16x16_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p9s9_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,9x9,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.910643,18423478737.327480,0.000984,1
+fft18-fp32_b16_p8s10_t128x128_e16x16_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p8s10_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,8x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.236585,17728531749.972099,0.000626,1
+fft18-fp32_b64_p10s8_t128x128_e16x16_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p10s8_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,10x8,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.860795,19490375656.250889,0.000739,1
+fft20-fp32_b2_p11s9_t256x128_e8x16_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p11s9_t256x128_e8x16_rec,0,509007.80142380524,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.173691,12074048538.758224,0.001485,1
+fft18-fp32_b2_p9s9_t256x256_e8x8_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p9s9_t256x256_e8x8_rec,0,175170.20085765165,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.026051,20125786027.262531,0.000553,1
+fft18-fp32_b2_p9s9_t512x512_e16x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p9s9_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,9x9,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.045384,11552346414.651926,0.000725,1
+fft18-fp32_b64_p9s9_t256x256_e8x8_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p9s9_t256x256_e8x8_rec,0,4773086.798644853,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.845148,19851213158.755203,0.000666,1
+fft20-fp32_b8_p12s8_t256x128_e16x16_rec,fft20-fp32-batch8,1,fft20-fp32_b8_p12s8_t256x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.655503,12797199983.353340,0.001355,1
+fft18-fp32_b16_p8s10_t128x128_e16x16_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p8s10_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,8x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.256061,16380069119.600151,0.000626,1
+fft18-fp32_b2_cufft,fft18-fp32-batch2,3,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,2,100,50,0.031703,16537467698.288412,0.000583,1
+fft18-fp32_b64_p8s10_t128x128_e16x16_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,8x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.876032,19151372276.013020,0.000674,1
+fft18-fp32_b16_p9s9_t128x128_e16x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p9s9_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,9x9,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.221348,18948925561.710960,0.000916,1
+fft18-fp32_b16_p8s10_t128x128_e16x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p8s10_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,8x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.236872,17707072853.163483,0.000626,1
+fft18-fp32_b64_cufft,fft18-fp32-batch64,3,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,64,100,50,0.706683,23740797342.570267,0.000678,1
+fft18-fp32_b64_p9s9_t256x256_e8x8_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p9s9_t256x256_e8x8_rec,0,4773086.798644853,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.838513,20008303772.718445,0.000666,1
+fft20-fp32_b8_cufft,fft20-fp32-batch8,2,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,8,100,50,0.382321,21941289766.035637,0.002079,1
+fft20-fp32_b2_p12s8_t256x128_e16x16_rec,fft20-fp32-batch2,1,fft20-fp32_b2_p12s8_t256x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.181473,11556258391.786486,0.001315,1
+fft20-fp32_b2_cufft,fft20-fp32-batch2,1,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,2,100,50,0.123392,16995850512.985561,0.002033,1
+fft20-fp32_b16_cufft,fft20-fp32-batch16,1,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,16,100,50,0.721674,23247629642.715019,0.002107,1
+fft20-fp32_b16_p11s9_t256x128_e8x16_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p11s9_t256x128_e8x16_rec,0,4072062.411390442,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.369354,12251918029.194801,0.001713,1
+fft20-fp32_b16_p8s12_t128x256_e16x16_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p8s12_t128x256_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.788641,9379866607.793947,0.001339,1
+fft20-fp32_b16_p12s8_t256x128_e16x16_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p12s8_t256x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.313587,12772061225.977135,0.001377,1
+fft20-fp32_b2_p8s12_t128x256_e16x16_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p8s12_t128x256_e16x16_rec,0,298317.9249153033,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.194560,10778947847.107462,0.001274,1
+fft18-fp32_b64_p8s10_t128x128_e16x16_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p8s10_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,8x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.860426,19498726423.279408,0.000674,1
+fft18-fp32_b2_p9s9_t256x256_e8x8_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p9s9_t256x256_e8x8_rec,0,175170.20085765165,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.026051,20125786027.262531,0.000553,1
+fft18-fp32_b2_p10s8_t512x512_e16x16_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,10x8,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.038769,13523508383.478348,0.000637,1
+fft20-fp32_b8_p12s8_t256x128_e16x16_rec,fft20-fp32-batch8,2,fft20-fp32_b8_p12s8_t256x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.655831,12790805465.711050,0.001355,1
+fft18-fp32_b2_p8s10_t512x512_e16x16_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p8s10_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,8x10,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.041595,12604627787.881304,0.000593,1
+fft20-fp32_b2_p12s8_t256x128_e16x16_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p12s8_t256x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.181228,11571929976.103218,0.001315,1
+fft20-fp32_b2_cufft,fft20-fp32-batch2,2,cuFFT,1,0.0,fft20-fp32,0,,,,,,,2,9x11,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,20,1048576,2,100,50,0.123556,16973313571.624226,0.002033,1
+fft20-fp32_b16_p10s10_t512x512_e8x8_rec,fft20-fp32-batch16,1,fft20-fp32_b16_p10s10_t512x512_e8x8_rec,0,4773086.798644853,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.926618,18105868779.166531,0.001466,1
+fft20-fp32_b8_p11s9_t256x128_e8x16_rec,fft20-fp32-batch8,3,fft20-fp32_b8_p11s9_t256x128_e8x16_rec,0,2036031.205695221,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.675840,12412120841.510597,0.001587,1
+fft18-fp32_b16_p9s9_t128x128_e16x16_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p9s9_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,9x9,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.220467,19024615966.705112,0.000916,1
+fft20-fp32_b8_p10s10_t128x128_e16x16_rec,fft20-fp32-batch8,3,fft20-fp32_b8_p10s10_t128x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.466207,17993323577.335499,0.001451,1
+fft18-fp32_b2_p9s9_t512x512_e16x16_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p9s9_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,9x9,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.045486,11526340078.090260,0.000725,1
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+fft18-fp32_b16_p9s9_t256x256_e8x8_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p9s9_t256x256_e8x8_rec,0,1193271.6996612132,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.205373,20422816491.512276,0.000629,1
+fft18-fp32_b2_p8s10_t512x512_e16x16_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p8s10_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,8x10,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.041636,12592227892.016632,0.000593,1
+fft20-fp32_b8_p10s10_t128x128_e16x16_rec,fft20-fp32-batch8,1,fft20-fp32_b8_p10s10_t128x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.466104,17997275469.665531,0.001451,1
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+fft20-fp32_b2_p12s8_t256x128_e16x16_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p12s8_t256x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,12x8,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.181862,11531531596.077833,0.001315,1
+fft18-fp32_b64_p9s9_t128x128_e16x16_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p9s9_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,9x9,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.910377,18428866971.143589,0.000984,1
+fft20-fp32_b2_p9s11_t128x256_e16x8_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p9s11_t128x256_e16x8_rec,0,445771.4026778952,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.168673,12433219139.736277,0.001638,1
+fft20-fp32_b16_p11s9_t256x128_e8x16_rec,fft20-fp32-batch16,1,fft20-fp32_b16_p11s9_t256x128_e8x16_rec,0,4072062.411390442,fft20-fp32,2,11x9,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.370194,12244409558.651194,0.001713,1
+fft18-fp32_b64_p10s8_t128x128_e16x16_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p10s8_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,10x8,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.860877,19488521501.222866,0.000739,1
+fft18-fp32_b16_p9s9_t128x128_e16x16_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p9s9_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,9x9,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.228188,18380901330.037231,0.000916,1
+fft18-fp32_b16_p9s9_t256x256_e8x8_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p9s9_t256x256_e8x8_rec,0,1193271.6996612132,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.212255,19760710341.741566,0.000629,1
+fft20-fp32_b2_p8s12_t128x256_e16x16_rec,fft20-fp32-batch2,1,fft20-fp32_b2_p8s12_t128x256_e16x16_rec,0,298317.9249153033,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.212234,9881308326.778183,0.001274,1
+fft18-fp32_b64_cufft,fft18-fp32-batch64,2,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,64,100,50,0.749076,22397200181.505543,0.000678,1
+fft18-fp32_b16_p10s8_t128x128_e16x16_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p10s8_t128x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,10x8,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.243384,17233255039.684765,0.000671,1
+fft20-fp32_b8_p10s10_t512x512_e8x8_rec,fft20-fp32-batch8,3,fft20-fp32_b8_p10s10_t512x512_e8x8_rec,0,2386543.3993224264,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.456458,18377602267.106907,0.001485,1
+fft20-fp32_b16_p10s10_t128x128_e16x16_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p10s10_t128x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.897208,18699353742.751347,0.001451,1
+fft20-fp32_b16_p9s11_t128x256_e16x8_rec,fft20-fp32-batch16,1,fft20-fp32_b16_p9s11_t128x256_e16x8_rec,0,3566171.2214231617,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.132995,14807852568.996576,0.001748,1
+fft18-fp32_b2_cufft,fft18-fp32-batch2,2,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,2,100,50,0.028037,18699781090.844635,0.000583,1
+fft18-fp32_b2_p10s8_t512x512_e16x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,10x8,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.038728,13537811255.969238,0.000637,1
+fft18-fp32_b64_p10s8_t128x128_e16x16_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p10s8_t128x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,10x8,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.861348,19477864930.391479,0.000739,1
+fft20-fp32_b2_p10s10_t512x512_e8x8_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p10s10_t512x512_e8x8_rec,0,596635.8498306066,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.128942,16264295750.050962,0.001288,1
+fft20-fp32_b2_p10s10_t128x128_e16x16_rec,fft20-fp32-batch2,1,fft20-fp32_b2_p10s10_t128x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,10x10,128x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,128,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.156508,13399633379.652552,0.001320,1
+fft18-fp32_b2_p9s9_t512x512_e16x16_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p9s9_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,9x9,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.045404,11547136142.239889,0.000725,1
+fft20-fp32_b2_p10s10_t512x512_e8x8_rec,fft20-fp32-batch2,1,fft20-fp32_b2_p10s10_t512x512_e8x8_rec,0,596635.8498306066,fft20-fp32,2,10x10,512x512,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,512,512,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.128799,16282397430.325737,0.001288,1
+fft20-fp32_b16_p10s10_t256x128_e16x16_rec,fft20-fp32-batch16,3,fft20-fp32_b16_p10s10_t256x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.888463,18883407483.448952,0.001451,1
+fft20-fp32_b8_p10s10_t256x128_e16x16_rec,fft20-fp32-batch8,2,fft20-fp32_b8_p10s10_t256x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.474644,17673455219.058941,0.001451,1
+fft20-fp32_b2_p10s10_t256x128_e16x16_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p10s10_t256x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.137032,15304140516.497099,0.001320,1
+fft20-fp32_b2_p10s10_t256x128_e16x16_rec,fft20-fp32-batch2,2,fft20-fp32_b2_p10s10_t256x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.136704,15340824211.261984,0.001320,1
+fft20-fp32_b16_p10s10_t256x128_e16x16_rec,fft20-fp32-batch16,1,fft20-fp32_b16_p10s10_t256x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.883835,18982296387.038044,0.001451,1
+fft20-fp32_b8_p10s10_t256x128_e16x16_rec,fft20-fp32-batch8,1,fft20-fp32_b8_p10s10_t256x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.450109,18636818139.576687,0.001451,1
+fft20-fp32_b8_p10s10_t256x128_e16x16_rec,fft20-fp32-batch8,3,fft20-fp32_b8_p10s10_t256x128_e16x16_rec,0,1193271.6996612132,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.449864,18647000229.922119,0.001451,1
+fft20-fp32_b2_p10s10_t256x128_e16x16_rec,fft20-fp32-batch2,1,fft20-fp32_b2_p10s10_t256x128_e16x16_rec,0,298317.9249153033,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.134205,15626431719.949450,0.001320,1
+fft20-fp32_b16_p10s10_t256x128_e16x16_rec,fft20-fp32-batch16,2,fft20-fp32_b16_p10s10_t256x128_e16x16_rec,0,2386543.3993224264,fft20-fp32,2,10x10,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,10,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.871465,19251738877.979771,0.001451,1
+fft20-fp32_b8_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch8,1,fft20-fp32_b8_p8s12_t128x256_e16x16_rec_tx,0,1193271.6996612132,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.611983,13707248536.342630,0.001371,1
+fft20-fp32_b16_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch16,3,fft20-fp32_b16_p8s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.202012,13957608967.078634,0.001339,1
+fft20-fp32_b8_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch8,2,fft20-fp32_b8_p8s12_t128x256_e16x16_rec_tx,0,1193271.6996612132,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.611820,13710919514.601795,0.001371,1
+fft20-fp32_b2_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch2,3,fft20-fp32_b2_p8s12_t128x256_e16x16_rec_tx,0,298317.9249153033,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.170086,12329921826.631407,0.001274,1
+fft20-fp32_b2_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch2,1,fft20-fp32_b2_p8s12_t128x256_e16x16_rec_tx,0,298317.9249153033,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.170271,12316574012.591415,0.001274,1
+fft20-fp32_b16_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch16,2,fft20-fp32_b16_p8s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.201418,13964508673.532358,0.001339,1
+fft20-fp32_b8_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch8,3,fft20-fp32_b8_p8s12_t128x256_e16x16_rec_tx,0,1193271.6996612132,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.611656,13714591123.198479,0.001371,1
+fft20-fp32_b16_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch16,1,fft20-fp32_b16_p8s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.200947,13969986758.881210,0.001339,1
+fft20-fp32_b2_p8s12_t128x256_e16x16_rec_tx,fft20-fp32-batch2,2,fft20-fp32_b2_p8s12_t128x256_e16x16_rec_tx,0,298317.9249153033,fft20-fp32,2,8x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.170701,12285542646.785393,0.001274,1
+fft20-fp32_b8_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch8,1,fft20-fp32_b8_p12s8_t256x128_e16x16_rec_ptx,0,1193271.6996612132,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.861737,9734533708.989103,0.001355,1
+fft20-fp32_b16_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch16,3,fft20-fp32_b16_p12s8_t256x128_e16x16_rec_ptx,0,2386543.3993224264,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.990226,8429804325.819130,0.001377,1
+fft20-fp32_b8_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch8,2,fft20-fp32_b8_p12s8_t256x128_e16x16_rec_ptx,0,1193271.6996612132,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.856842,9790142481.693623,0.001355,1
+fft20-fp32_b2_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch2,3,fft20-fp32_b2_p12s8_t256x128_e16x16_rec_ptx,0,298317.9249153033,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.213094,9841421779.742336,0.001315,1
+fft20-fp32_b2_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch2,1,fft20-fp32_b2_p12s8_t256x128_e16x16_rec_ptx,0,298317.9249153033,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.215347,9738468825.433344,0.001315,1
+fft20-fp32_b16_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch16,2,fft20-fp32_b16_p12s8_t256x128_e16x16_rec_ptx,0,2386543.3993224264,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.944105,8629789428.848341,0.001377,1
+fft20-fp32_b8_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch8,3,fft20-fp32_b8_p12s8_t256x128_e16x16_rec_ptx,0,1193271.6996612132,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.816742,10270812183.333693,0.001355,1
+fft20-fp32_b16_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch16,1,fft20-fp32_b16_p12s8_t256x128_e16x16_rec_ptx,0,2386543.3993224264,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.932104,8683392893.973288,0.001377,1
+fft20-fp32_b2_p12s8_t256x128_e16x16_rec_ptx,fft20-fp32-batch2,2,fft20-fp32_b2_p12s8_t256x128_e16x16_rec_ptx,0,298317.9249153033,fft20-fp32,2,12x8,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,8,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.213893,9804672061.538269,0.001315,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p6s12_t128x256_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.229906,13641055906.290844,0.000637,1
+fft18-fp32_b64_p7s11_t128x256_e16x8_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p7s11_t128x256_e16x8_rec,0,3566171.2214231617,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.244570,13480335050.380514,0.000672,1
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p7s11_t128x256_e16x8_rec,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.045609,11495285113.750792,0.000682,1
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch2,1,fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.036229,14471453315.550766,0.000549,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p12s6_t256x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.336056,12480955504.105425,0.000675,1
+fft18-fp32_b16_p11s7_t256x128_e8x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p11s7_t256x128_e8x16_rec,0,1018015.6028476105,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.324792,12913802669.401302,0.000633,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p6s12_t128x256_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.200599,13974037093.849636,0.000637,1
+fft18-fp32_b16_p11s7_t256x128_e8x16_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p11s7_t256x128_e8x16_rec,0,1018015.6028476105,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.324588,12921950754.987030,0.000633,1
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p11s7_t256x128_e8x16_rec,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.047206,11106290243.093365,0.000546,1
+fft18-fp32_b64_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch64,3,fft18-fp32_b64_p12s6_t256x128_e16x16_rec_ptx,0,2386543.3993224264,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.397248,12007329460.955475,0.000793,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch16,1,fft18-fp32_b16_p12s6_t256x128_e16x16_rec_ptx,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.371589,11287477826.481567,0.000675,1
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p12s6_t256x128_e16x16_rec,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.052675,9953343372.805685,0.000579,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch16,3,fft18-fp32_b16_p12s6_t256x128_e16x16_rec_ptx,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.371261,11297440190.315414,0.000675,1
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch2,2,fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.056320,9309090836.383095,0.000579,1
+fft18-fp32_b64_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch64,2,fft18-fp32_b64_p12s6_t256x128_e16x16_rec_ptx,0,2386543.3993224264,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.390674,12064089829.897757,0.000793,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p6s12_t128x256_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.192264,14071732356.286142,0.000637,1
+fft18-fp32_b64_p12s6_t256x128_e16x16_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p12s6_t256x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.262858,13285113917.620819,0.000793,1
+fft18-fp32_b64_p7s11_t128x256_e16x8_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p7s11_t128x256_e16x8_rec,0,3566171.2214231617,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.132524,14814010885.063791,0.000672,1
+fft18-fp32_b64_p12s6_t256x128_e16x16_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p12s6_t256x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.263800,13275210413.607248,0.000793,1
+fft18-fp32_b16_p6s12_t128x256_e16x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p6s12_t128x256_e16x16_rec,0,596635.8498306066,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.322806,12993274872.892593,0.000644,1
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p7s11_t128x256_e16x8_rec,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.045548,11510791650.161873,0.000682,1
+fft18-fp32_b16_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch16,3,fft18-fp32_b16_p6s12_t128x256_e16x16_rec_tx,0,596635.8498306066,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.300810,13943354764.779016,0.000644,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch64,2,fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.139651,14721368326.686737,0.000637,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch64,1,fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.139200,14727191371.236280,0.000637,1
+fft18-fp32_b16_p6s12_t128x256_e16x16_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p6s12_t128x256_e16x16_rec,0,596635.8498306066,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.322560,13003174105.697348,0.000644,1
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch2,2,fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.036106,14520703344.838606,0.000549,1
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p6s12_t128x256_e16x16_rec,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.050012,10483210463.801924,0.000549,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p12s6_t256x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.336978,12446821113.713036,0.000675,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch16,2,fft18-fp32_b16_p12s6_t256x128_e16x16_rec_ptx,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.372511,11259552137.627239,0.000675,1
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p12s6_t256x128_e16x16_rec,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.052777,9934031345.860666,0.000579,1
+fft18-fp32_b64_p7s11_t128x256_e16x8_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p7s11_t128x256_e16x8_rec,0,3566171.2214231617,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.131827,14823126043.406815,0.000672,1
+fft18-fp32_b16_p7s11_t128x256_e16x8_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p7s11_t128x256_e16x8_rec,0,891542.8053557904,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.309596,13547661961.928600,0.000712,1
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p11s7_t256x128_e8x16_rec,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.047063,11140121495.137054,0.000546,1
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p6s12_t128x256_e16x16_rec,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.050115,10461789764.771149,0.000549,1
+fft18-fp32_b16_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch16,2,fft18-fp32_b16_p6s12_t128x256_e16x16_rec_tx,0,596635.8498306066,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.302141,13881922872.511292,0.000644,1
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec,fft18-fp32-batch2,2,fft18-fp32_b2_p6s12_t128x256_e16x16_rec,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.050115,10461789764.771149,0.000549,1
+fft18-fp32_b64_p11s7_t256x128_e8x16_rec,fft18-fp32-batch64,3,fft18-fp32_b64_p11s7_t256x128_e8x16_rec,0,4072062.411390442,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.380659,12151598110.047232,0.000697,1
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec,fft18-fp32-batch2,3,fft18-fp32_b2_p7s11_t128x256_e16x8_rec,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.045568,11505617844.909451,0.000682,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch64,3,fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.139282,14726132713.486225,0.000637,1
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch2,1,fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.053453,9808428942.736332,0.000579,1
+fft18-fp32_b16_p11s7_t256x128_e8x16_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p11s7_t256x128_e8x16_rec,0,1018015.6028476105,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.324895,12909732478.796162,0.000633,1
+fft18-fp32_b16_p6s12_t128x256_e16x16_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p6s12_t128x256_e16x16_rec,0,596635.8498306066,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.324280,12934192180.797392,0.000644,1
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch2,3,fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.053617,9778456978.317270,0.000579,1
+fft18-fp32_b16_p7s11_t128x256_e16x8_rec,fft18-fp32-batch16,2,fft18-fp32_b16_p7s11_t128x256_e16x8_rec,0,891542.8053557904,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.309084,13570102618.894115,0.000712,1
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p11s7_t256x128_e8x16_rec,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.047124,11125596930.890581,0.000546,1
+fft18-fp32_b64_p12s6_t256x128_e16x16_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p12s6_t256x128_e16x16_rec,0,2386543.3993224264,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.264148,13271555002.055553,0.000793,1
+fft18-fp32_b16_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch16,1,fft18-fp32_b16_p6s12_t128x256_e16x16_rec_tx,0,596635.8498306066,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.302264,13876278294.381121,0.000644,1
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p12s6_t256x128_e16x16_rec,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.052572,9972730632.215231,0.000579,1
+fft18-fp32_b16_p7s11_t128x256_e16x8_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p7s11_t128x256_e16x8_rec,0,891542.8053557904,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.309391,13556628528.969551,0.000712,1
+fft18-fp32_b64_p11s7_t256x128_e8x16_rec,fft18-fp32-batch64,2,fft18-fp32_b64_p11s7_t256x128_e8x16_rec,0,4072062.411390442,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.233387,13602551026.939215,0.000697,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec,fft18-fp32-batch16,1,fft18-fp32_b16_p12s6_t256x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.336261,12473352808.737211,0.000675,1
+fft18-fp32_b64_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch64,1,fft18-fp32_b64_p12s6_t256x128_e16x16_rec_ptx,0,2386543.3993224264,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.391329,12058407839.812408,0.000793,1
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch2,3,fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.036209,14479637695.522373,0.000549,1
+fft18-fp32_b64_p11s7_t256x128_e8x16_rec,fft18-fp32-batch64,1,fft18-fp32_b64_p11s7_t256x128_e8x16_rec,0,4072062.411390442,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.233408,13602324900.075930,0.000697,1
+fft20-fp32_b8_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch8,3,fft20-fp32_b8_p9s11_t128x256_e16x8_rec_tx,0,1783085.6107115808,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.596910,14053385479.972321,0.001716,1
+fft18-fp32_b16_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch16,1,fft18-fp32_b16_p11s7_t256x128_e8x16_rec_ptx,0,1018015.6028476105,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.369930,11338094522.865309,0.000633,1
+fft20-fp32_b16_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch16,3,fft20-fp32_b16_p9s11_t128x256_e16x8_rec_tx,0,3566171.2214231617,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.150423,14583518646.525839,0.001748,1
+fft18-fp32_b64_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch64,1,fft18-fp32_b64_p7s11_t128x256_e16x8_rec_tx,0,3566171.2214231617,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.148293,14610568896.885269,0.000672,1
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch2,1,fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.036209,14479637695.522373,0.000682,1
+fft20-fp32_b2_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch2,3,fft20-fp32_b2_p9s11_t128x256_e16x8_rec_tx,0,445771.4026778952,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.161976,12947275053.670696,0.001638,1
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch2,3,fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.036209,14479637695.522373,0.000682,1
+fft20-fp32_b2_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch2,2,fft20-fp32_b2_p9s11_t128x256_e16x8_rec_tx,0,445771.4026778952,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.161874,12955466639.430428,0.001638,1
+fft20-fp32_b16_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch16,3,fft20-fp32_b16_p11s9_t256x128_e8x16_rec_ptx,0,4072062.411390442,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.472430,11394235886.859064,0.001713,1
+fft18-fp32_b64_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch64,3,fft18-fp32_b64_p7s11_t128x256_e16x8_rec_tx,0,3566171.2214231617,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.148744,14604839208.511097,0.000672,1
+fft20-fp32_b8_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch8,2,fft20-fp32_b8_p9s11_t128x256_e16x8_rec_tx,0,1783085.6107115808,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.582820,14393141276.339542,0.001716,1
+fft20-fp32_b8_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch8,2,fft20-fp32_b8_p11s9_t256x128_e8x16_rec_ptx,0,2036031.205695221,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.735150,11410741852.154230,0.001587,1
+fft18-fp32_b64_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch64,3,fft18-fp32_b64_p11s7_t256x128_e8x16_rec_ptx,0,4072062.411390442,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.333310,12583136629.009985,0.000697,1
+fft20-fp32_b8_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch8,1,fft20-fp32_b8_p11s9_t256x128_e8x16_rec_ptx,0,2036031.205695221,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.733676,11433675444.312157,0.001587,1
+fft20-fp32_b2_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch2,2,fft20-fp32_b2_p11s9_t256x128_e8x16_rec_ptx,0,509007.80142380524,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.196751,10658893958.723427,0.001485,1
+fft18-fp32_b16_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch16,3,fft18-fp32_b16_p7s11_t128x256_e16x8_rec_tx,0,891542.8053557904,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.305316,13737590008.036154,0.000712,1
+fft18-fp32_b64_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch64,1,fft18-fp32_b64_p11s7_t256x128_e8x16_rec_ptx,0,4072062.411390442,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.333432,12581977944.342037,0.000697,1
+fft18-fp32_b64_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch64,2,fft18-fp32_b64_p11s7_t256x128_e8x16_rec_ptx,0,4072062.411390442,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.333924,12577341966.758907,0.000697,1
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch2,1,fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.049295,10635646386.281420,0.000546,1
+fft18-fp32_b16_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch16,2,fft18-fp32_b16_p11s7_t256x128_e8x16_rec_ptx,0,1018015.6028476105,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.358113,11712226633.992794,0.000633,1
+fft20-fp32_b16_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch16,1,fft20-fp32_b16_p11s9_t256x128_e8x16_rec_ptx,0,4072062.411390442,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.474621,11377303915.274517,0.001713,1
+fft20-fp32_b8_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch8,3,fft20-fp32_b8_p11s9_t256x128_e8x16_rec_ptx,0,2036031.205695221,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.734904,11414557572.184578,0.001587,1
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch2,2,fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.049295,10635646386.281420,0.000546,1
+fft20-fp32_b8_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch8,1,fft20-fp32_b8_p9s11_t128x256_e16x8_rec_tx,0,1783085.6107115808,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.583598,14373947287.231911,0.001716,1
+fft20-fp32_b2_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch2,1,fft20-fp32_b2_p9s11_t128x256_e16x8_rec_tx,0,445771.4026778952,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.161567,12980098919.021608,0.001638,1
+fft18-fp32_b16_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch16,1,fft18-fp32_b16_p7s11_t128x256_e16x8_rec_tx,0,891542.8053557904,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.305275,13739434056.356504,0.000712,1
+fft18-fp32_b64_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch64,2,fft18-fp32_b64_p7s11_t128x256_e16x8_rec_tx,0,3566171.2214231617,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.148682,14605619782.730835,0.000672,1
+fft18-fp32_b16_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch16,3,fft18-fp32_b16_p11s7_t256x128_e8x16_rec_ptx,0,1018015.6028476105,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.359096,11680163332.274460,0.000633,1
+fft18-fp32_b16_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch16,2,fft18-fp32_b16_p7s11_t128x256_e16x8_rec_tx,0,891542.8053557904,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.305275,13739434056.356504,0.000712,1
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch2,3,fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.049254,10644490905.342285,0.000546,1
+fft20-fp32_b16_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch16,2,fft20-fp32_b16_p9s11_t128x256_e16x8_rec_tx,0,3566171.2214231617,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.149747,14592092047.668489,0.001748,1
+fft20-fp32_b2_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch2,3,fft20-fp32_b2_p11s9_t256x128_e8x16_rec_ptx,0,509007.80142380524,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.196813,10655566656.652042,0.001485,1
+fft20-fp32_b16_p9s11_t128x256_e16x8_rec_tx,fft20-fp32-batch16,1,fft20-fp32_b16_p9s11_t128x256_e16x8_rec_tx,0,3566171.2214231617,fft20-fp32,2,9x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.149215,14598852024.221622,0.001748,1
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch2,2,fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.036229,14471453315.550766,0.000682,1
+fft20-fp32_b16_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch16,2,fft20-fp32_b16_p11s9_t256x128_e8x16_rec_ptx,0,4072062.411390442,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.476731,11361052219.418655,0.001713,1
+fft20-fp32_b2_p11s9_t256x128_e8x16_rec_ptx,fft20-fp32-batch2,1,fft20-fp32_b2_p11s9_t256x128_e8x16_rec_ptx,0,509007.80142380524,fft20-fp32,2,11x9,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,9,256,128,8,16,recurrence,prefix-tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.197284,10630125921.377962,0.001485,1
+fft18-fp32_b2_d3_3x5x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,1,fft18-fp32_b2_d3_3x5x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,3x5x10,256x256x256,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,256,256,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.042865,12231246147.169355,0.000501,1
+fft20-fp32_b8_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_ttt_ffg_gt512x512_ge16x16,fft20-fp32-batch8,3,fft20-fp32_b8_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_ttt_ffg_gt512x512_ge16x16,0,1217624.1833277687,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,512x512,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.662200,12667779822.184185,0.001343,1
+fft18-fp32_b16_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch16,1,fft18-fp32_b16_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,0,608812.0916638843,fft18-fp32,3,3x5x10,128x128x128,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,128,128,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.284467,14744420938.554352,0.000610,1
+fft20-fp32_b16_d3_3x11x6_t128x512x128_e8x4x16_tt_gg,fft20-fp32-batch16,2,fft20-fp32_b16_d3_3x11x6_t128x512x128_e8x4x16_tt_gg,0,9437184.0,fft20-fp32,3,3x11x6,128x512x128,8x4x16,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,3,6,128,128,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,2.792018,6008992914.920296,0.001274,1
+fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_ttt_ffg_gt512x512_ge16x16,fft20-fp32-batch16,3,fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_ttt_ffg_gt512x512_ge16x16,0,2435248.3666555374,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,512x512,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.343037,12491994946.601227,0.001468,1
+fft18-fp32_b64_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_fgf_gt512x256_ge16x16,fft18-fp32-batch64,1,fft18-fp32_b64_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_fgf_gt512x256_ge16x16,0,2435248.3666555374,fft18-fp32,4,3x3x3x9,512x512x512x512,8x8x8x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,6x12,512x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.440625,11645792160.963377,0.000617,1
+fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_fgf_gt512x256_ge16x16,fft18-fp32-batch2,1,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_fgf_gt512x256_ge16x16,0,83474.31145798555,fft18-fp32,4,3x3x3x9,512x512x512x512,8x8x8x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,6x12,512x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.060129,8719345884.690075,0.000497,1
+fft20-fp32_b16_d3_5x3x12_t128x128x512_e16x8x8_tt_fg_gt128x512_ge16x8,fft20-fp32-batch16,1,fft20-fp32_b16_d3_5x3x12_t128x128x512_e16x8x8_tt_fg_gt128x512_ge16x8,0,3638950.2259420017,fft20-fp32,3,5x3x12,128x128x512,16x8x8,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x12,128x512,16x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,5,12,128,512,16,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.823723,9199429954.302582,0.001152,1
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+fft20-fp32_b16_d3_3x6x11_t128x128x512_e8x16x4_tt_fg_gt128x512_ge16x4,fft20-fp32-batch16,1,fft20-fp32_b16_d3_3x6x11_t128x128x512_e8x16x4_tt_fg_gt128x512_ge16x4,0,6428806.61113708,fft20-fp32,3,3x6x11,128x128x512,8x16x4,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,9x11,128x512,16x4,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,3,11,128,512,8,4,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.494897,11222993908.289421,0.001485,1
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+fft20-fp32_b16_d4_3x7x3x7_t512x512x512x512_e8x16x8x16_rrr_fgf_gt512x512_ge8x8,fft20-fp32-batch16,2,fft20-fp32_b16_d4_3x7x3x7_t512x512x512x512_e8x16x8x16_rrr_fgf_gt512x512_ge8x8,0,4870496.733311075,fft20-fp32,4,3x7x3x7,512x512x512x512,8x16x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,7,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.924856,18140347668.961491,0.001466,1
+fft20-fp32_b8_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,fft20-fp32-batch8,3,fft20-fp32_b8_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,0,1217624.1833277687,fft20-fp32,4,10x3x3x4,512x512x512x512,16x8x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,4,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.475034,17658977816.950275,0.001451,1
+fft20-fp32_b8_d3_3x7x10_t512x512x512_e8x16x16_rr_fg_gt512x512_ge8x8,fft20-fp32-batch8,3,fft20-fp32_b8_d3_3x7x10_t512x512x512_e8x16x16_rr_fg_gt512x512_ge8x8,0,2435248.3666555374,fft20-fp32,3,3x7x10,512x512x512,8x16x16,recurrencexrecurrence,direct-stridedxdirect-strided,fusedxglobal-scratch,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.455291,18424722081.767349,0.001485,1
+fft18-fp32_b16_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,fft18-fp32-batch16,1,fft18-fp32_b16_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,0,1217624.1833277687,fft18-fp32,4,3x6x3x6,512x512x512x512,8x16x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,6,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.205394,20420779210.905476,0.000629,1
+fft18-fp32_b64_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,fft18-fp32-batch64,2,fft18-fp32_b64_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,0,4870496.733311075,fft18-fp32,4,9x3x3x3,512x512x512x512,16x8x8x8,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,3,512,512,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.845926,19832948514.842037,0.000666,1
+fft18-fp32_b64_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,fft18-fp32-batch64,3,fft18-fp32_b64_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,0,4870496.733311075,fft18-fp32,4,9x3x3x3,512x512x512x512,16x8x8x8,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,3,512,512,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.841359,19940607603.640411,0.000666,1
+fft20-fp32_b16_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt256x128_ge16x16,fft20-fp32-batch16,1,fft20-fp32_b16_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt256x128_ge16x16,0,2435248.3666555374,fft20-fp32,3,10x3x7,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,7,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.872919,19219670504.637066,0.001451,1
+fft20-fp32_b8_d4_3x7x3x7_t512x512x512x512_e8x16x8x16_rrr_fgf_gt512x512_ge8x8,fft20-fp32-batch8,2,fft20-fp32_b8_d4_3x7x3x7_t512x512x512x512_e8x16x8x16_rrr_fgf_gt512x512_ge8x8,0,2435248.3666555374,fft20-fp32,4,3x7x3x7,512x512x512x512,8x16x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,7,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.456602,18371832655.037361,0.001485,1
+fft20-fp32_b16_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt512x512_ge8x8,fft20-fp32-batch16,2,fft20-fp32_b16_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt512x512_ge8x8,0,4870496.733311075,fft20-fp32,3,10x3x7,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,7,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.923320,18170526651.957840,0.001466,1
+fft20-fp32_b8_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt256x128_ge16x16,fft20-fp32-batch8,2,fft20-fp32_b8_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt256x128_ge16x16,0,1217624.1833277687,fft20-fp32,3,10x3x7,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,7,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.445338,18836514413.768005,0.001451,1
+fft18-fp32_b16_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,fft18-fp32-batch16,1,fft18-fp32_b16_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,0,1217624.1833277687,fft18-fp32,4,9x3x3x3,512x512x512x512,16x8x8x8,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,3,512,512,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.205578,20402470832.793159,0.000629,1
+fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,fft18-fp32-batch2,1,fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,3,9x3x6,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,6,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.026051,20125786027.262531,0.000553,1
+fft20-fp32_b8_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt256x128_ge16x16,fft20-fp32-batch8,1,fft20-fp32_b8_d3_10x3x7_t512x512x512_e16x8x16_rr_gf_gt256x128_ge16x16,0,1217624.1833277687,fft20-fp32,3,10x3x7,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,7,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.449475,18663142480.972908,0.001451,1
+fft20-fp32_b2_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,fft20-fp32-batch2,1,fft20-fp32_b2_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,0,304406.0458319422,fft20-fp32,4,10x3x3x4,512x512x512x512,16x8x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,4,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.134021,15647921960.831467,0.001320,1
+fft20-fp32_b16_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,fft20-fp32-batch16,2,fft20-fp32_b16_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,0,2435248.3666555374,fft20-fp32,4,10x3x3x4,512x512x512x512,16x8x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,4,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.870523,19272573799.338989,0.001451,1
+fft20-fp32_b2_d3_3x7x10_t512x512x512_e8x16x16_rr_fg_gt256x128_ge16x16,fft20-fp32-batch2,3,fft20-fp32_b2_d3_3x7x10_t512x512x512_e8x16x16_rr_fg_gt256x128_ge16x16,0,304406.0458319422,fft20-fp32,3,3x7x10,512x512x512,8x16x16,recurrencexrecurrence,direct-stridedxdirect-strided,fusedxglobal-scratch,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.134267,15619279684.133774,0.001320,1
+fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt256x128_ge16x16,fft20-fp32-batch16,1,fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt256x128_ge16x16,0,2435248.3666555374,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.867799,19333065785.979664,0.001451,1
+fft20-fp32_b8_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt512x512_ge8x8,fft20-fp32-batch8,1,fft20-fp32_b8_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt512x512_ge8x8,0,2435248.3666555374,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.456274,18385026524.515854,0.001485,1
+fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,fft18-fp32-batch2,3,fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,3,9x3x6,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,6,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.026071,20109976464.638767,0.000553,1
+fft20-fp32_b16_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,fft20-fp32-batch16,1,fft20-fp32_b16_d4_10x3x3x4_t512x512x512x512_e16x8x8x16_rrr_gff_gt256x128_ge16x16,0,2435248.3666555374,fft20-fp32,4,10x3x3x4,512x512x512x512,16x8x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,10x10,256x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,10,4,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.870093,19282100681.561672,0.001451,1
diff --git a/results/v100_fft_pipeline_report.md b/results/v100_fft_pipeline_report.md
new file mode 100644
index 0000000..69c6783
--- /dev/null
+++ b/results/v100_fft_pipeline_report.md
@@ -0,0 +1,10 @@
+# Generated V100 FFT Pipeline Search
+
+| logN | Batch | Logical stages | Physical groups | Threads/EPT | Residency | Median ms | cuFFT ms | Throughput ratio |
+|--:|--:|:--|:--|:--|:--|--:|--:|--:|
+| 18 | 2 | 3x6x3x6 | 9x9 | 256x256 / 8x8 | fusedxglobal-scratchxfused | 0.026010 | 0.028099 | 1.080x |
+| 18 | 16 | 3x6x3x6 | 9x9 | 256x256 / 8x8 | fusedxglobal-scratchxfused | 0.205496 | 0.216146 | 1.052x |
+| 18 | 64 | 9x3x6 | 9x9 | 256x256 / 8x8 | global-scratchxfused | 0.836690 | 0.717599 | 0.858x |
+| 20 | 2 | 10x3x3x4 | 10x10 | 512x512 / 8x8 | global-scratchxfusedxfused | 0.128573 | 0.123556 | 0.961x |
+| 20 | 8 | 10x3x7 | 10x10 | 256x128 / 16x16 | global-scratchxfused | 0.445338 | 0.382157 | 0.858x |
+| 20 | 16 | 3x3x4x10 | 10x10 | 256x128 / 16x16 | fusedxfusedxglobal-scratch | 0.867799 | 0.720855 | 0.831x |
diff --git a/results/v100_fft_pipeline_summary.csv b/results/v100_fft_pipeline_summary.csv
new file mode 100644
index 0000000..e64d533
--- /dev/null
+++ b/results/v100_fft_pipeline_summary.csv
@@ -0,0 +1,289 @@
+candidate_id,group,implementation,reference,static_score,mapping_id,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,execution_group_stages,group_threads,group_ept,processing_unit,prefix_log_n,suffix_log_n,prefix_threads,suffix_threads,prefix_ept,suffix_ept,cross_twiddle,direct_boundary,operator,precision,direction,normalization,placement,backend,fft_core,logN,N,batch,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,correct,rank,cufft_median_ms,throughput_vs_cufft,slowdown_vs_internal_best
+fft18-fp32_b2_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,4,3x6x3x6,512x512x512x512,8x16x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,6,512,512,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.026010,0.025969,0.026153,1,1,0.028099,1.080315,1.000000
+fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,4,3x3x3x9,512x512x512x512,8x8x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.026010,0.025989,0.026071,1,2,0.028099,1.080315,1.000000
+fft18-fp32_b2_d3_3x6x9_t512x512x512_e8x16x16_rr_fg_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d3_3x6x9_t512x512x512_e8x16x16_rr_fg_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,3,3x6x9,512x512x512,8x16x16,recurrencexrecurrence,direct-stridedxdirect-strided,fusedxglobal-scratch,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.026030,0.025969,0.026071,1,3,0.028099,1.079485,1.000769
+fft18-fp32_b2_p9s9_t256x256_e8x8_rec,fft18-fp32-batch2,fft18-fp32_b2_p9s9_t256x256_e8x8_rec,0,175170.20085765165,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.026051,0.026030,0.026051,1,4,0.028099,1.078615,1.001576
+fft18-fp32_b2_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,4,9x3x3x3,512x512x512x512,16x8x8x8,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,3,512,512,16,8,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.026051,0.025969,0.026092,1,5,0.028099,1.078615,1.001576
+fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,3,9x3x6,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,6,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.026071,0.026051,0.026092,1,6,0.028099,1.077788,1.002345
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch2,fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.036209,0.036106,0.036229,1,7,0.028099,0.776023,1.392118
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch2,fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.036209,0.036209,0.036229,1,8,0.028099,0.776023,1.392118
+fft18-fp32_b2_p10s8_t512x512_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,10x8,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.038728,0.038666,0.038769,1,9,0.028099,0.725547,1.488966
+fft18-fp32_b2_p8s10_t512x512_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p8s10_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,8x10,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.041636,0.041595,0.047862,1,10,0.028099,0.674873,1.600769
+fft18-fp32_b2_d3_8x7x3_t128x128x128_e16x16x8_tt_gf_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_8x7x3_t128x128x128_e16x16x8_tt_gf_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,8x7x3,128x128x128,16x16x8,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,8,3,128,128,16,8,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042619,0.041759,0.042824,1,11,0.028099,0.659307,1.638562
+fft18-fp32_b2_d3_4x4x10_t128x128x128_e16x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_4x4x10_t128x128x128_e16x16x16_tt_fg_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,4x4x10,128x128x128,16x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,10,128,128,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042680,0.042496,0.044483,1,12,0.028099,0.658365,1.640907
+fft18-fp32_b2_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,3x5x10,128x128x128,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,128,128,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042783,0.042598,0.042844,1,13,0.028099,0.656780,1.644867
+fft18-fp32_b2_d3_5x3x10_t256x256x256_e16x8x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_5x3x10_t256x256x256_e16x8x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,5x3x10,256x256x256,16x8x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,5,10,256,256,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042824,0.042824,0.042947,1,14,0.028099,0.656151,1.646444
+fft18-fp32_b2_d3_5x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_5x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,5x3x10,128x128x128,16x8x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,5,10,128,128,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042865,0.042598,0.047800,1,15,0.028099,0.655523,1.648020
+fft18-fp32_b2_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,4x4x10,256x256x256,16x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,10,256,256,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042947,0.042885,0.049910,1,16,0.028099,0.654272,1.651173
+fft18-fp32_b2_d3_3x5x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_3x5x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,3x5x10,256x256x256,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,256,256,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042967,0.042865,0.045404,1,17,0.028099,0.653967,1.651942
+fft18-fp32_b2_d3_8x7x3_t256x256x256_e16x16x8_tt_gf_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_8x7x3_t256x256x256_e16x16x8_tt_gf_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,8x7x3,256x256x256,16x16x8,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,8,3,256,256,16,8,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042967,0.042865,0.043028,1,18,0.028099,0.653967,1.651942
+fft18-fp32_b2_p9s9_t512x512_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p9s9_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,9x9,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.045404,0.045384,0.045486,1,19,0.028099,0.618866,1.745636
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec,fft18-fp32-batch2,fft18-fp32_b2_p7s11_t128x256_e16x8_rec,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.045568,0.045548,0.045609,1,20,0.028099,0.616639,1.751942
+fft18-fp32_b2_d3_3x5x10_t512x512x512_e8x16x16_tt_fg_gt512x512_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_3x5x10_t512x512x512_e8x16x16_tt_fg_gt512x512_ge16x16,0,83474.31145798555,fft18-fp32,3,3x5x10,512x512x512,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,512x512,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.045711,0.045691,0.048108,1,21,0.028099,0.614710,1.757439
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p11s7_t256x128_e8x16_rec,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.047124,0.047063,0.047206,1,22,0.028099,0.596278,1.811765
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,fft18-fp32-batch2,fft18-fp32_b2_p11s7_t256x128_e8x16_rec_ptx,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,prefix-tiled-transpose,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.049295,0.049254,0.049295,1,23,0.028099,0.570017,1.895233
+fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_ffg_gt512x512_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_ffg_gt512x512_ge16x16,0,83474.31145798555,fft18-fp32,4,3x3x3x9,512x512x512x512,8x8x8x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,9x9,512x512,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.049336,0.049336,0.049377,1,24,0.028099,0.569544,1.896809
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p6s12_t128x256_e16x16_rec,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.050115,0.050012,0.050115,1,25,0.028099,0.560690,1.926759
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p12s6_t256x128_e16x16_rec,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.052675,0.052572,0.052777,1,26,0.028099,0.533441,2.025183
+fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,fft18-fp32-batch2,fft18-fp32_b2_p12s6_t256x128_e16x16_rec_ptx,0,91438.61722882584,fft18-fp32,2,12x6,256x128,16x16,recurrence,prefix-tiled-transpose,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,prefix-tiled-transpose,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.053617,0.053453,0.056320,1,27,0.028099,0.524069,2.061399
+fft18-fp32_b2_d3_11x3x4_t512x128x128_e4x8x16_tt_gf_gt512x128_ge4x16,fft18-fp32-batch2,fft18-fp32_b2_d3_11x3x4_t512x128x128_e4x8x16_tt_gf_gt512x128_ge4x16,0,288134.1638879615,fft18-fp32,3,11x3x4,512x128x128,4x8x16,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,11x7,512x128,4x16,cufftdx-large-online+cufftdx-online-shared+cufftdx-online-shared,11,4,512,128,4,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.054866,0.054804,0.058143,1,28,0.028099,0.512139,2.109419
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diff --git a/results/v100_fft_pipeline_vectorized_raw.csv b/results/v100_fft_pipeline_vectorized_raw.csv
new file mode 100644
index 0000000..03cff9e
--- /dev/null
+++ b/results/v100_fft_pipeline_vectorized_raw.csv
@@ -0,0 +1,883 @@
+candidate_id,group,trial,implementation,reference,static_score,mapping_id,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,execution_group_stages,group_threads,group_ept,processing_unit,prefix_log_n,suffix_log_n,prefix_threads,suffix_threads,prefix_ept,suffix_ept,cross_twiddle,direct_boundary,device,compute_capability,operator,precision,direction,normalization,placement,backend,fft_core,logN,N,batch,warmup,repeat,kernel_ms,points_s,max_error,correct
+fft20-fp32_b8_d3_3x5x12_t256x256x1024_e8x16x4_tt_fg_gt256x1024_ge16x4,fft20-fp32-batch8,1,fft20-fp32_b8_d3_3x5x12_t256x256x1024_e8x16x4_tt_fg_gt256x1024_ge16x4,0,3214403.30556854,fft20-fp32,3,3x5x12,256x256x1024,8x16x4,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x12,256x1024,16x4,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,3,12,256,1024,8,4,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.839619,9990975615.190218,0.001050,1
+fft18-fp32_b16_p12s6_t256x128_e16x16_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p12s6_t256x128_e16x16_rec,0,596635.8498306066,fft18-fp32,2,12x6,256x128,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,12,6,256,128,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.346788,12094726269.676991,0.000675,1
+fft18-fp32_b16_d3_5x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch16,3,fft18-fp32_b16_d3_5x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,0,608812.0916638843,fft18-fp32,3,5x3x10,128x128x128,16x8x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,5,10,128,128,16,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.265687,15786633276.641626,0.000610,1
+fft18-fp32_b16_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch16,2,fft18-fp32_b16_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,0,608812.0916638843,fft18-fp32,3,4x4x10,256x256x256,16x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,10,256,256,16,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.288338,14546487871.628933,0.000610,1
+fft18-fp32_b16_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch16,1,fft18-fp32_b16_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,0,608812.0916638843,fft18-fp32,3,3x5x10,128x128x128,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,128,128,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.265708,15785416831.535055,0.000610,1
+fft20-fp32_b16_d3_7x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,fft20-fp32-batch16,2,fft20-fp32_b16_d3_7x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,0,2435248.3666555374,fft20-fp32,3,7x3x10,128x128x128,16x8x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,10x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,7,10,128,128,16,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.297326,12932150332.758234,0.001468,1
+fft18-fp32_b64_cufft,fft18-fp32-batch64,2,cuFFT,1,0.0,fft18-fp32,0,,,,,,,0,,,,vendor-baseline,0,0,0,0,0,0,none,none,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,cufft,scalar,18,262144,64,100,50,0.706560,23744929012.434086,0.000678,1
+fft18-fp32_b64_d3_4x11x3_t256x1024x256_e16x2x8_tt_gg,fft18-fp32-batch64,3,fft18-fp32_b64_d3_4x11x3_t256x1024x256_e16x2x8_tt_gg,0,14955662.166722313,fft18-fp32,3,4x11x3,256x1024x256,16x2x8,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,4,3,256,256,16,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,3.288863,5101221152.624272,0.000401,1
+fft20-fp32_b2_p8s12_t128x256_e16x16_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p8s12_t128x256_e16x16_rec,0,298317.9249153033,fft20-fp32,2,8x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,8,12,128,256,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.176128,11906976742.767656,0.001274,1
+fft18-fp32_b2_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,1,fft18-fp32_b2_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,4x4x10,256x256x256,16x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,10,256,256,16,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.039506,13271124497.074245,0.000501,1
+fft20-fp32_b8_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt512x512_ge8x8,fft20-fp32-batch8,1,fft20-fp32_b8_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt512x512_ge8x8,0,2435248.3666555374,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,8,100,50,0.414618,20232154728.477669,0.001485,1
+fft20-fp32_b16_d3_3x5x12_t128x128x512_e8x16x8_tt_fg_gt128x512_ge16x8,fft20-fp32-batch16,1,fft20-fp32_b16_d3_3x5x12_t128x128x512_e8x16x8_tt_fg_gt128x512_ge16x8,0,3638950.2259420017,fft20-fp32,3,3x5x12,128x128x512,8x16x8,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x12,128x512,16x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,3,12,128,512,8,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.757082,9548341826.651150,0.001152,1
+fft18-fp32_b64_d3_3x12x3_t256x1024x256_e8x4x8_tt_gg,fft18-fp32-batch64,1,fft18-fp32_b64_d3_3x12x3_t256x1024x256_e8x4x8_tt_gg,0,9804185.600000001,fft18-fp32,3,3x12x3,256x1024x256,8x4x8,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,3,3,256,256,8,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,3.048182,5504007717.923839,0.000489,1
+fft18-fp32_b64_d3_12x3x3_t256x512x512_e16x8x8_tt_gf_gt256x512_ge16x16,fft18-fp32-batch64,2,fft18-fp32_b64_d3_12x3x3_t256x512x512_e16x8x8_tt_gf_gt256x512_ge16x16,0,2435248.3666555374,fft18-fp32,3,12x3x3,256x512x512,16x8x8,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,12x6,256x512,16x16,cufftdx-large-online+cufftdx-online-shared+cufftdx-online-shared,12,3,256,512,16,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.551565,10813093892.761606,0.000657,1
+fft18-fp32_b2_d3_6x3x9_t512x512x512_e16x8x16_tt_gf_gt512x256_ge16x16,fft18-fp32-batch2,3,fft18-fp32_b2_d3_6x3x9_t512x512x512_e16x8x16_tt_gf_gt512x256_ge16x16,0,83474.31145798555,fft18-fp32,3,6x3x9,512x512x512,16x8x16,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,6x12,512x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,6,9,512,512,16,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.057344,9142857611.407455,0.000497,1
+fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch64,3,fft18-fp32_b64_p6s12_t128x256_e16x16_rec_tx,0,2386543.3993224264,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,1.070387,15673968547.854292,0.000637,1
+fft18-fp32_b2_d3_4x3x11_t128x128x512_e16x8x4_tt_fg_gt128x512_ge16x4,fft18-fp32-batch2,1,fft18-fp32_b2_d3_4x3x11_t128x128x512_e16x8x4_tt_fg_gt128x512_ge16x4,0,241041.00659803377,fft18-fp32,3,4x3x11,128x128x512,16x8x4,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,7x11,128x512,16x4,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,4,11,128,512,16,4,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.053494,9800918739.736185,0.000516,1
+fft20-fp32_b16_d4_3x7x3x7_t512x512x512x512_e8x16x8x16_rrr_fgf_gt512x512_ge8x8,fft20-fp32-batch16,3,fft20-fp32_b16_d4_3x7x3x7_t512x512x512x512_e8x16x8x16_rrr_fgf_gt512x512_ge8x8,0,4870496.733311075,fft20-fp32,4,3x7x3x7,512x512x512x512,8x16x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,7,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.829931,20215181673.481499,0.001466,1
+fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_fgf_gt512x256_ge16x16,fft18-fp32-batch2,3,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_ttt_fgf_gt512x256_ge16x16,0,83474.31145798555,fft18-fp32,4,3x3x3x9,512x512x512x512,8x8x8x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,6x12,512x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.057324,9146123752.715437,0.000497,1
+fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt512x512_ge8x8,fft20-fp32-batch16,1,fft20-fp32_b16_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_rrr_ffg_gt512x512_ge8x8,0,4870496.733311075,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,512x512,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,0.832819,20145087347.320728,0.001466,1
+fft18-fp32_b64_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch64,1,fft18-fp32_b64_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,0,2435248.3666555374,fft18-fp32,3,3x5x10,128x128x128,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,128,128,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,64,100,50,0.939541,17856830975.788807,0.000610,1
+fft20-fp32_b2_p9s11_t128x256_e16x8_rec,fft20-fp32-batch2,3,fft20-fp32_b2_p9s11_t128x256_e16x8_rec,0,445771.4026778952,fft20-fp32,2,9x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,9,11,128,256,16,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.157716,13296974176.286972,0.001638,1
+fft18-fp32_b2_d3_6x3x9_t512x512x512_e16x8x16_tt_gf_gt512x256_ge16x16,fft18-fp32-batch2,1,fft18-fp32_b2_d3_6x3x9_t512x512x512_e16x8x16_tt_gf_gt512x256_ge16x16,0,83474.31145798555,fft18-fp32,3,6x3x9,512x512x512,16x8x16,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,6x12,512x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,6,9,512,512,16,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.057283,9152663041.000748,0.000497,1
+fft18-fp32_b16_p9s9_t256x256_e8x8_rec,fft18-fp32-batch16,3,fft18-fp32_b16_p9s9_t256x256_e8x8_rec,0,1193271.6996612132,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,16,100,50,0.195830,21418114556.744560,0.000629,1
+fft18-fp32_b2_d3_12x3x3_t256x512x512_e16x8x8_tt_gf_gt256x512_ge16x16,fft18-fp32-batch2,3,fft18-fp32_b2_d3_12x3x3_t256x512x512_e16x8x8_tt_gf_gt256x512_ge16x16,0,93304.71145798556,fft18-fp32,3,12x3x3,256x512x512,16x8x8,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,12x6,256x512,16x16,cufftdx-large-online+cufftdx-online-shared+cufftdx-online-shared,12,3,256,512,16,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.061911,8468408994.708865,0.000503,1
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+fft20-fp32_b16_d3_3x7x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,fft20-fp32-batch16,1,fft20-fp32_b16_d3_3x7x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,0,2435248.3666555374,fft20-fp32,3,3x7x10,256x256x256,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,10x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,256,256,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.278300,13124629445.047678,0.001468,1
+fft18-fp32_b2_p8s10_t512x512_e16x16_rec,fft18-fp32-batch2,1,fft18-fp32_b2_p8s10_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,8x10,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,512,512,16,16,recurrence,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,100,50,0.044974,11657559848.385071,0.000593,1
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+fft20-fp32_b2_d3_6x11x3_t128x512x128_e16x4x8_tt_gg,fft20-fp32-batch2,1,fft20-fp32_b2_d3_6x11x3_t128x512x128_e16x4x8_tt_gg,0,1109734.4745415198,fft20-fp32,3,6x11x3,128x512x128,16x4x8,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,6,3,128,128,16,8,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.420516,4987094002.245473,0.001152,1
+fft20-fp32_b16_d3_3x5x12_t256x256x1024_e8x16x4_tt_fg_gt256x1024_ge16x4,fft20-fp32-batch16,1,fft20-fp32_b16_d3_3x5x12_t256x256x1024_e8x16x4_tt_fg_gt256x1024_ge16x4,0,6428806.61113708,fft20-fp32,3,3x5x12,256x256x1024,8x16x4,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x12,256x1024,16x4,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,3,12,256,1024,8,4,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,100,50,1.451377,11559518814.764973,0.001221,1
+fft20-fp32_b2_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_ttt_ffg_gt512x512_ge16x16,fft20-fp32-batch2,1,fft20-fp32_b2_d4_3x3x4x10_t512x512x512x512_e8x8x16x16_ttt_ffg_gt512x512_ge16x16,0,304406.0458319422,fft20-fp32,4,3x3x4x10,512x512x512x512,8x8x16x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,10x10,512x512,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,table,direct-strided,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,2,100,50,0.197345,10626816552.859238,0.001125,1
diff --git a/results/v100_fft_pipeline_vectorized_report.md b/results/v100_fft_pipeline_vectorized_report.md
new file mode 100644
index 0000000..2b4c91b
--- /dev/null
+++ b/results/v100_fft_pipeline_vectorized_report.md
@@ -0,0 +1,10 @@
+# Generated V100 FFT Pipeline Search
+
+| logN | Batch | Logical stages | Physical groups | Threads/EPT | Residency | Median ms | cuFFT ms | Throughput ratio |
+|--:|--:|:--|:--|:--|:--|--:|--:|--:|
+| 18 | 2 | 3x3x3x9 | 9x9 | 256x256 / 8x8 | fusedxfusedxglobal-scratch | 0.025866 | 0.028058 | 1.085x |
+| 18 | 16 | 3x6x3x6 | 9x9 | 256x256 / 8x8 | fusedxglobal-scratchxfused | 0.195441 | 0.211108 | 1.080x |
+| 18 | 64 | 8x10 | 8x10 | 128x128 / 16x16 | global-scratch | 0.767201 | 0.706273 | 0.921x |
+| 20 | 2 | 10x10 | 10x10 | 512x512 / 8x8 | global-scratch | 0.119869 | 0.123453 | 1.030x |
+| 20 | 8 | 10x3x3x4 | 10x10 | 256x128 / 16x16 | global-scratchxfusedxfused | 0.397332 | 0.382300 | 0.962x |
+| 20 | 16 | 3x3x4x10 | 10x10 | 256x128 / 16x16 | fusedxfusedxglobal-scratch | 0.764334 | 0.729416 | 0.954x |
diff --git a/results/v100_fft_pipeline_vectorized_summary.csv b/results/v100_fft_pipeline_vectorized_summary.csv
new file mode 100644
index 0000000..cd05b33
--- /dev/null
+++ b/results/v100_fft_pipeline_vectorized_summary.csv
@@ -0,0 +1,289 @@
+candidate_id,group,implementation,reference,static_score,mapping_id,decomposition_count,stages_per_decomposition,segment_threads,segment_ept,boundary_twiddles,boundary_layouts,boundary_residencies,execution_group_count,execution_group_stages,group_threads,group_ept,processing_unit,prefix_log_n,suffix_log_n,prefix_threads,suffix_threads,prefix_ept,suffix_ept,cross_twiddle,direct_boundary,operator,precision,direction,normalization,placement,backend,fft_core,logN,N,batch,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,correct,rank,cufft_median_ms,throughput_vs_cufft,slowdown_vs_internal_best
+fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d4_3x3x3x9_t512x512x512x512_e8x8x8x16_rrr_ffg_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,4,3x3x3x9,512x512x512x512,8x8x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxfusedxglobal-scratch,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.025866,0.025866,0.025928,1,1,0.028058,1.084744,1.000000
+fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d3_9x3x6_t512x512x512_e16x8x16_rr_gf_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,3,9x3x6,512x512x512,16x8x16,recurrencexrecurrence,direct-stridedxdirect-strided,global-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,6,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.025907,0.025846,0.029860,1,2,0.028058,1.083028,1.001585
+fft18-fp32_b2_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d4_9x3x3x3_t512x512x512x512_e16x8x8x8_rrr_gff_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,4,9x3x3x3,512x512x512x512,16x8x8x8,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,global-scratchxfusedxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,9,3,512,512,16,8,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.025907,0.025846,0.026010,1,3,0.028058,1.083028,1.001585
+fft18-fp32_b2_d3_3x6x9_t512x512x512_e8x16x16_rr_fg_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d3_3x6x9_t512x512x512_e8x16x16_rr_fg_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,3,3x6x9,512x512x512,8x16x16,recurrencexrecurrence,direct-stridedxdirect-strided,fusedxglobal-scratch,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,9,512,512,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.025907,0.025887,0.025928,1,4,0.028058,1.083028,1.001585
+fft18-fp32_b2_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,fft18-fp32-batch2,fft18-fp32_b2_d4_3x6x3x6_t512x512x512x512_e8x16x8x16_rrr_fgf_gt256x256_ge8x8,0,166948.6229159711,fft18-fp32,4,3x6x3x6,512x512x512x512,8x16x8x16,recurrencexrecurrencexrecurrence,direct-stridedxdirect-stridedxdirect-strided,fusedxglobal-scratchxfused,2,9x9,256x256,8x8,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,6,512,512,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.025928,0.025887,0.029901,1,5,0.028058,1.082151,1.002397
+fft18-fp32_b2_p9s9_t256x256_e8x8_rec,fft18-fp32-batch2,fft18-fp32_b2_p9s9_t256x256_e8x8_rec,0,175170.20085765165,fft18-fp32,2,9x9,256x256,8x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,256,256,8,8,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.025928,0.025887,0.025928,1,6,0.028058,1.082151,1.002397
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,fft18-fp32-batch2,fft18-fp32_b2_p7s11_t128x256_e16x8_rec_tx,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,tiled-transpose,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.033075,0.033034,0.033096,1,7,0.028058,0.848314,1.278706
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,fft18-fp32-batch2,fft18-fp32_b2_p6s12_t128x256_e16x16_rec_tx,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,tiled-transpose,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,tiled-transpose,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.033546,0.033505,0.038011,1,8,0.028058,0.836404,1.296915
+fft18-fp32_b2_p10s8_t512x512_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p10s8_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,10x8,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,10,8,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.036782,0.036782,0.036782,1,9,0.028058,0.762819,1.422021
+fft18-fp32_b2_d3_5x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_5x3x10_t128x128x128_e16x8x16_tt_fg_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,5x3x10,128x128x128,16x8x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,5,10,128,128,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.038953,0.038953,0.039035,1,10,0.028058,0.720304,1.505954
+fft18-fp32_b2_d3_4x4x10_t128x128x128_e16x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_4x4x10_t128x128x128_e16x16x16_tt_fg_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,4x4x10,128x128x128,16x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,10,128,128,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.038973,0.038973,0.039096,1,11,0.028058,0.719934,1.506727
+fft18-fp32_b2_d3_8x7x3_t128x128x128_e16x16x8_tt_gf_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_8x7x3_t128x128x128_e16x16x8_tt_gf_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,8x7x3,128x128x128,16x16x8,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,8,3,128,128,16,8,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.038973,0.038932,0.039035,1,12,0.028058,0.719934,1.506727
+fft18-fp32_b2_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_3x5x10_t128x128x128_e8x16x16_tt_fg_gt128x128_ge16x16,0,93304.71145798556,fft18-fp32,3,3x5x10,128x128x128,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,128x128,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,128,128,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.038994,0.038994,0.039014,1,13,0.028058,0.719547,1.507539
+fft18-fp32_b2_d3_5x3x10_t256x256x256_e16x8x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_5x3x10_t256x256x256_e16x8x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,5x3x10,256x256x256,16x8x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,5,10,256,256,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.039424,0.039342,0.039444,1,14,0.028058,0.711698,1.524163
+fft18-fp32_b2_d3_3x5x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_3x5x10_t256x256x256_e8x16x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,3x5x10,256x256x256,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,256,256,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.039444,0.039404,0.039444,1,15,0.028058,0.711338,1.524936
+fft18-fp32_b2_d3_8x7x3_t256x256x256_e16x16x8_tt_gf_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_8x7x3_t256x256x256_e16x16x8_tt_gf_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,8x7x3,256x256x256,16x16x8,tablextable,direct-stridedxdirect-strided,global-scratchxfused,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,8,3,256,256,16,8,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.039444,0.039444,0.039465,1,16,0.028058,0.711338,1.524936
+fft18-fp32_b2_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_4x4x10_t256x256x256_e16x16x16_tt_fg_gt256x256_ge16x16,0,93304.71145798556,fft18-fp32,3,4x4x10,256x256x256,16x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,256x256,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,10,256,256,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.039506,0.039444,0.041718,1,17,0.028058,0.710221,1.527333
+fft18-fp32_b2_p8s10_t512x512_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p8s10_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,8x10,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,8,10,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.039690,0.039629,0.044974,1,18,0.028058,0.706929,1.534447
+fft18-fp32_b2_p7s11_t128x256_e16x8_rec,fft18-fp32-batch2,fft18-fp32_b2_p7s11_t128x256_e16x8_rec,0,135794.93600280714,fft18-fp32,2,7x11,128x256,16x8,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,7,11,128,256,16,8,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.042803,0.042721,0.042885,1,19,0.028058,0.655515,1.654798
+fft18-fp32_b2_p9s9_t512x512_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p9s9_t512x512_e16x16_rec,0,81804.82522882584,fft18-fp32,2,9x9,512x512,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-online-shared,9,9,512,512,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.043418,0.043418,0.043438,1,20,0.028058,0.646230,1.678574
+fft18-fp32_b2_d3_3x5x10_t512x512x512_e8x16x16_tt_fg_gt512x512_ge16x16,fft18-fp32-batch2,fft18-fp32_b2_d3_3x5x10_t512x512x512_e8x16x16_tt_fg_gt512x512_ge16x16,0,83474.31145798555,fft18-fp32,3,3x5x10,512x512x512,8x16x16,tablextable,direct-stridedxdirect-strided,fusedxglobal-scratch,2,8x10,512x512,16x16,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,3,10,512,512,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.043704,0.043684,0.043745,1,21,0.028058,0.642001,1.689631
+fft18-fp32_b2_p11s7_t256x128_e8x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p11s7_t256x128_e8x16_rec,0,153477.27302261797,fft18-fp32,2,11x7,256x128,8x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-large-online+cufftdx-online-shared,11,7,256,128,8,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.045998,0.045957,0.053617,1,22,0.028058,0.609983,1.778319
+fft18-fp32_b2_p6s12_t128x256_e16x16_rec,fft18-fp32-batch2,fft18-fp32_b2_p6s12_t128x256_e16x16_rec,0,91438.61722882584,fft18-fp32,2,6x12,128x256,16x16,recurrence,direct-strided,global-scratch,2,,,,cufftdx-online-shared+cufftdx-large-online,6,12,128,256,16,16,recurrence,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,18,262144,2,3,0.047309,0.047145,0.047329,1,23,0.028058,0.593080,1.829003
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+fft20-fp32_b16_d3_3x12x5_t128x512x128_e8x8x16_tt_gg,fft20-fp32-batch16,fft20-fp32_b16_d3_3x12x5_t128x512x128_e8x8x16_tt_gg,0,6529546.140713537,fft20-fp32,3,3x12x5,128x512x128,8x8x16,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,3,5,128,128,8,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,2.944532,2.943386,2.946724,1,42,0.729416,0.247719,3.852415
+fft20-fp32_b16_d3_4x4x12_t512x512x256_e16x16x16_tt_gg,fft20-fp32-batch16,fft20-fp32_b16_d3_4x4x12_t512x512x256_e16x16x16_tt_gg,0,3517580.9740579985,fft20-fp32,3,4x4x12,512x512x256,16x16x16,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-online-shared+cufftdx-large-online,4,12,512,256,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,3.258266,3.253330,3.259617,1,43,0.729416,0.223866,4.262882
+fft20-fp32_b16_d3_4x11x5_t128x512x128_e16x4x16_tt_gg,fft20-fp32-batch16,fft20-fp32_b16_d3_4x11x5_t128x512x128_e16x4x16_tt_gg,0,7864320.0,fft20-fp32,3,4x11x5,128x512x128,16x4x16,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,4,5,128,128,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,3.334349,3.332465,3.340288,1,44,0.729416,0.218758,4.362424
+fft20-fp32_b16_d3_6x11x3_t128x512x128_e16x4x8_tt_gg,fft20-fp32-batch16,fft20-fp32_b16_d3_6x11x3_t128x512x128_e16x4x8_tt_gg,0,8877875.796332158,fft20-fp32,3,6x11x3,128x512x128,16x4x8,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,6,3,128,128,16,8,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,3.357266,3.349995,3.361014,1,45,0.729416,0.217265,4.392407
+fft20-fp32_b16_d3_5x12x3_t128x512x128_e16x8x8_tt_gg,fft20-fp32-batch16,fft20-fp32_b16_d3_5x12x3_t128x512x128_e16x8x8_tt_gg,0,5878304.21113708,fft20-fp32,3,5x12x3,128x512x128,16x8x8,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,5,3,128,128,16,8,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,3.420508,3.417784,3.422597,1,46,0.729416,0.213248,4.475148
+fft20-fp32_b16_d4_4x4x4x8_t512x512x512x512_e16x16x16x16_ttt_ggg,fft20-fp32-batch16,fft20-fp32_b16_d4_4x4x4x8_t512x512x512x512_e16x16x16x16_ttt_ggg,0,4599913.58146046,fft20-fp32,4,4x4x4x8,512x512x512x512,16x16x16x16,tablextablextable,direct-stridedxdirect-stridedxdirect-strided,global-scratchxglobal-scratchxglobal-scratch,4,,,,cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared+cufftdx-online-shared,4,8,512,512,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,3.583713,3.578696,3.585474,1,47,0.729416,0.203536,4.688674
+fft20-fp32_b16_d3_4x12x4_t128x512x128_e16x8x16_tt_gg,fft20-fp32-batch16,fft20-fp32_b16_d3_4x12x4_t128x512x128_e16x8x16_tt_gg,0,4902092.800000001,fft20-fp32,3,4x12x4,128x512x128,16x8x16,tablextable,direct-stridedxdirect-strided,global-scratchxglobal-scratch,3,,,,cufftdx-online-shared+cufftdx-large-online+cufftdx-online-shared,4,4,128,128,16,16,table,direct-strided,fft,fp32,forward,none,in-place,online-reorder,cufftdx-block,20,1048576,16,3,4.096655,4.094894,4.103086,1,48,0.729416,0.178052,5.359771
diff --git a/results/v100_mapping_selector_evaluation.csv b/results/v100_mapping_selector_evaluation.csv
new file mode 100644
index 0000000..383872e
--- /dev/null
+++ b/results/v100_mapping_selector_evaluation.csv
@@ -0,0 +1,50 @@
+operator,precision,logN,batch,candidates,measured_winner,predicted_winner,top1_correct,topk_contains_winner,top3_contains_winner,regret,confidence
+fwht,fp32,15,1,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,extrapolated-low
+fwht,fp32,15,4,2,cuButterfly-online-radix4,cuButterfly-warp-register,0,1,1,1.153178,interpolated
+fwht,fp32,15,16,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,15,32,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,15,128,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,15,256,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,15,512,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,extrapolated-high
+fwht,fp32,20,1,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,extrapolated-low
+fwht,fp32,20,2,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,interpolated
+fwht,fp32,20,4,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,interpolated
+fwht,fp32,20,8,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,interpolated
+fwht,fp32,20,16,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,extrapolated-high
+fwht,fp32,8,1,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,extrapolated-low
+fwht,fp32,8,4,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,16,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,64,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,256,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,1024,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,4096,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,16384,2,cuButterfly-warp-register,cuButterfly-warp-register,1,1,1,1.000000,interpolated
+fwht,fp32,8,65536,2,cuButterfly-warp-register,cuButterfly-shared-radix4,0,1,1,1.078732,extrapolated-high
+ntt,uint32,12,1,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,extrapolated-low
+ntt,uint32,12,4,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint32,12,16,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint32,12,64,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint32,12,256,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint32,12,1024,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint32,12,4096,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,extrapolated-high
+ntt,uint64,16,1,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,extrapolated-low
+ntt,uint64,16,4,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint64,16,16,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint64,16,32,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint64,16,64,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint64,16,128,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,interpolated
+ntt,uint64,16,256,2,cuNTT-Hybrid2D-radix4,cuNTT-Hybrid2D-radix4,1,1,1,1.000000,extrapolated-high
+xor-zeta,uint32,20,1,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,extrapolated-low
+xor-zeta,uint32,20,2,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,20,4,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,20,8,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,20,16,2,cuButterfly-online-radix4,cuButterfly-online-radix4,1,1,1,1.000000,extrapolated-high
+xor-zeta,uint32,8,1,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,extrapolated-low
+xor-zeta,uint32,8,4,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,16,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,64,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,256,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,1024,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,4096,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,16384,2,cuButterfly-radix4,cuButterfly-radix4,1,1,1,1.000000,interpolated
+xor-zeta,uint32,8,65536,2,cuButterfly-radix4,cuButterfly-radix2,0,1,1,1.022458,extrapolated-high
diff --git a/results/v100_mapping_selector_metrics.json b/results/v100_mapping_selector_metrics.json
new file mode 100644
index 0000000..51a0399
--- /dev/null
+++ b/results/v100_mapping_selector_metrics.json
@@ -0,0 +1,15 @@
+{
+  "method": "leave-one-complete-shape-out log-latency interpolation",
+  "scope": "V100 calibrated internal candidates",
+  "evaluated_shapes": 49,
+  "top_k": 3,
+  "top1_accuracy": 0.9387755102040817,
+  "topk_recall": 1,
+  "top3_recall": 1,
+  "geomean_regret": 1.0049205916018493,
+  "worst_regret": 1.1531778692272519,
+  "mean_candidates": 2,
+  "mean_returned": 2,
+  "search_space_reduction": 0.0,
+  "top1_search_space_reduction": 0.5
+}
diff --git a/results/v100_scaling_full_fft14_cufft_b64_confirm_raw.csv b/results/v100_scaling_full_fft14_cufft_b64_confirm_raw.csv
new file mode 100644
index 0000000..d313517
--- /dev/null
+++ b/results/v100_scaling_full_fft14_cufft_b64_confirm_raw.csv
@@ -0,0 +1,6 @@
+suite_case_id,suite_group,suite_tier,suite_runner,implementation,reference,trial,performance_batch,preflight_correct,preflight_max_error,device,compute_capability,library,library_version,precision,direction,placement,logN,N,batch,warmup,repeat,plan_ms,kernel_ms,transforms_s,Gbutterfly_s,points_s,max_abs_error,relative_l2_error,correct,operator,normalization,element_stride,output_order,batch_stride
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,4,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,1.831170000,0.029419519,2175426.456983337,249.495309499,35642187071.214988708,0.000000000,0.000000000,-1,fft,none,1,,16384
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,5,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,1.707759000,0.029409280,2176183.840546579,249.582172305,35654596043.515144348,0.000000000,0.000000000,-1,fft,none,1,,16384
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,3,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,1.758108000,0.029419519,2175426.456983337,249.495309499,35642187071.214988708,0.000000000,0.000000000,-1,fft,none,1,,16384
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,2,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,2.195733000,0.029583361,2163378.258487389,248.113525709,35444789387.057380676,0.000000000,0.000000000,-1,fft,none,1,,16384
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,1,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,2.118368000,0.029511681,2168632.833086015,248.716162361,35530880337.281272888,0.000000000,0.000000000,-1,fft,none,1,,16384
diff --git a/results/v100_scaling_full_fft14_cufft_b64_confirm_summary.csv b/results/v100_scaling_full_fft14_cufft_b64_confirm_summary.csv
new file mode 100644
index 0000000..cf6d9db
--- /dev/null
+++ b/results/v100_scaling_full_fft14_cufft_b64_confirm_summary.csv
@@ -0,0 +1,2 @@
+case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class,peak_billion_points_s,peak_batch,fraction_of_peak,saturation_fraction,saturation_batch,throughput_speedup_vs_batch1,batch_efficiency_vs_batch1,scaling_region,timing_floor_ms,timing_quality,eligible_for_saturation
+fft14_cufft_b64,fft14-batch64,cuFFT,1,5,0.029419519,0.029409280,0.029583361,0.005917,0.003133,stable,1,fft,fp32,forward,none,in-place,14,16384,64,1,16384,,,,,,,,,,2.175426458,35.642187080,declared-reference,cuFFT,0.029419519,1.000000,parity,35.642187080,64,1.000000,0.900000,64,0.000000,0.000000,saturated,0.020000,stable,1
diff --git a/results/v100_scaling_full_raw.csv b/results/v100_scaling_full_raw.csv
new file mode 100644
index 0000000..6cb66b5
--- /dev/null
+++ b/results/v100_scaling_full_raw.csv
@@ -0,0 +1,921 @@
+suite_case_id,suite_group,suite_tier,suite_runner,implementation,reference,trial,performance_batch,preflight_correct,preflight_max_error,device,compute_capability,library,library_version,precision,direction,placement,logN,N,batch,warmup,repeat,plan_ms,kernel_ms,transforms_s,Gbutterfly_s,points_s,max_abs_error,relative_l2_error,correct,operator,normalization,element_stride,output_order,batch_stride,backend,compute_unit,complex_multiply,cross_twiddle,local_exchange,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,h2d_ms,d2h_ms,max_error,word_bits,modulus,modulus_bits,n1_log,rows_per_block,threads_per_block,inverse,kernel_ntt_s,end_to_end_ntt_s,kernel_points_s,mod_multiply
+fft18_vkfft_b8,fft18-batch8,full,fft-library,VkFFT,0,4,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,8,1000,100,342.160588000,0.111779839,71569.256905828,168.853061541,18761451282.321289062,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002836,352549.634236,0.361011,90252706.364468,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.019488,0.000000,,,,,,,,,,,
+xor20_hier_b2,xor20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,3,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.256860,7786.337699,81.645668,8164566838.929377,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.428576,1.350464,0.000000,,,,,,,,,,,
+fft8_cub_b65536,fft8-batch65536,full,butterfly,cuButterfly-cuFFTDx,0,3,65536,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,65536,1000,100,,0.327598,200050021.578792,204.851222,51212805524.170723,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,21.625919,20.140160,0.000000,,,,,,,,,,,
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,4,1000,100,794.356296000,0.206817284,19340.743279565,202.802392251,20280239225.113304138,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b256,fwht8-batch256,full,butterfly,cuButterfly-warp-register,0,1,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002417,105932201.003720,108.474574,27118643456.952290,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.076000,0.085504,0.000000,,,,,,,,,,,
+fft20_vkfft_b8,fft20-batch8,full,fft-library,VkFFT,0,1,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,8,1000,100,801.016047000,0.383057952,20884.568404732,218.990571996,21899057199.560703278,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b65536,fft8-batch65536,full,fft-library,cuFFT,1,4,65536,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,65536,1000,100,1.874314000,0.327086061,200363169.716561556,205.171885790,51292971447.439758301,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002079,481065.239552,0.492611,123152701.325208,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.010240,0.016128,0.000000,,,,,,,,,,,
+xor20_online_b8,xor20-batch8,full,butterfly,cuButterfly-online-radix4,0,1,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.623821,12824.196042,134.471442,13447144189.450462,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.465184,5.105664,0.000000,,,,,,,,,,,
+fft18_vkfft_b8,fft18-batch8,full,fft-library,VkFFT,0,3,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,8,1000,100,329.137789000,0.111626245,71667.733642429,169.085397312,18787266367.960800171,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b4096,fft8-batch4096,full,butterfly,cuButterfly-cuFFTDx,0,4,4096,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4096,1000,100,,0.022057,185701009.298548,190.157834,47539458380.428352,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,1.422496,1.349664,0.000000,,,,,,,,,,,
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002519,396976.604636,0.406504,101626010.786939,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.008192,0.016512,0.000000,,,,,,,,,,,
+fwht15_online_b512,fwht15-batch512,full,butterfly,cuButterfly-online-radix4,0,3,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,1.244969,411255.255968,101.070092,13476012227.571527,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,10.857024,10.113024,0.000000,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.048497,337837829.348379,345.945937,86486484313.185104,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.785600,2.611712,0.000000,,,,,,,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,1,1000,100,,0.095058,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.415296,1.341536,,64,1152921504577486849,60,0,0,256,0,10519.902013,350.644670,11030916773.432024,shoup
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,16,1000,100,430.144365000,0.010670080,1499520.174678847,171.976969794,24568138541.938224792,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.090153,11092.259625,116.310772,11631077228.981354,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.744608,0.740256,0.000000,,,,,,,,,,,
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,64,1000,100,150.344919000,0.002457600,26041668.212713014,26.666668250,6666667062.454531670,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b1024,fft8-batch1024,full,fft-library,cuFFT,1,4,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1024,1000,100,1.804721000,0.004546560,225225231.099434704,230.630636646,57657659161.455284119,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b4096,fft8-batch4096,full,fft-library,cuFFT,1,2,4096,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4096,1000,100,1.663890000,0.022118399,185185194.229929537,189.629638891,47407409722.861961365,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_online_b8,xor20-batch8,full,butterfly,cuButterfly-online-radix4,0,3,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.623892,12822.722149,134.455987,13445598700.024906,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.449728,5.096032,0.000000,,,,,,,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1,1000,100,307.401633000,0.008263680,121011.459971133,13.878562321,1982651760.167040586,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,5,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.318167,402304.411219,98.870332,13182710946.840523,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,2.768224,2.601600,0.000000,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,4,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016527,60505.729986,142.750927,15861214081.336325,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.411712,0.413120,0.000000,,,,,,,,,,,
+fft20_vkfft_b8,fft20-batch8,full,fft-library,VkFFT,0,5,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,8,1000,100,804.072603000,0.382341117,20923.724002647,219.401148198,21940114819.799991608,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b65536,fft8-batch65536,full,fft-library,VkFFT,0,5,65536,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,65536,1000,100,204.734541000,0.326215655,200897777.508658201,205.719324169,51429831042.216499329,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b256,xor8-batch256,full,butterfly,cuButterfly-radix4,0,3,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.002939,87108010.396126,89.198603,22299650661.408287,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.073024,0.075712,0.000000,,,,,,,,,,,
+xor8_r2_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix2,0,2,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004823,212314215.493464,217.409757,54352439166.326683,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.255616,0.257344,0.000000,,,,,,,,,,,
+ntt20_compact_b16,ntt20-batch16,full,ntt,cuNTT-compact-stage,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,16,1000,100,,1.311857,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.702496,37.135391,,64,1152921504577486849,60,0,0,256,0,12196.453645,266.002797,12788908577.511402,shoup
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,2,16384,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16384,1000,100,270.164420000,0.083681278,195790509.002038985,200.489481218,50122370304.521980286,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,4,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.139889,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.807328,2.620160,,32,1073692673,30,6,4,256,0,7320108.116860,183928.634461,29983162846.659184,shoup
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,4,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,16,1000,100,,0.205271,77945.726567,183.897041,20433004545.216415,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,5.467296,5.098208,0.000000,,,,,,,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.017592,56842.985324,13.969732,1862630943.086279,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.041248,0.049792,0.000000,,,,,,,,,,,
+fft8_vkfft_b1024,fft8-batch1024,full,fft-library,VkFFT,0,1,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1024,1000,100,204.545774000,0.005765120,177619906.752715975,181.882784515,45470696128.695289612,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b65536,fft8-batch65536,full,fft-library,cuFFT,1,3,65536,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,65536,1000,100,1.941154000,0.327116817,200344331.281290948,205.152595232,51288148808.010482788,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b4,fft14-batch4,full,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,4,1000,100,2.208379000,0.011939840,335012.853515353,38.421954144,5488850591.995541573,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b256,xor8-batch256,full,butterfly,cuButterfly-radix4,0,4,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.002939,87108010.396126,89.198603,22299650661.408287,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.069024,0.075584,0.000000,,,,,,,,,,,
+xor8_r2_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix2,0,4,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.179057,366007082.312275,374.791252,93697813071.942352,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.855584,10.116448,0.000000,,,,,,,,,,,
+xor8_r2_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix2,0,3,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.016005,255918087.474414,262.060122,65515030393.450058,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.747584,0.734880,0.000000,,,,,,,,,,,
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,16,1000,100,,0.205322,77926.283896,183.851170,20427907765.541668,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,5.454240,5.095520,0.000000,,,,,,,,,,,
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,4,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1,1000,100,,0.020552,48657.823435,5.580468,797209779.167070,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.038336,0.046368,0.000000,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002048,488281.251233,0.500000,125000000.315595,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.010240,0.016128,0.000000,,,,,,,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.005970,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.010240,0.020000,,32,1073692673,30,6,4,256,0,167506.426758,27616.741879,686106323.999443,shoup
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,16,1000,100,445.361846000,0.201256961,79500.355912569,187.564871703,20840541300.344451904,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix4,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.013855,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.253696,0.252448,,32,1073692673,30,6,4,256,0,4619364.165494,123077.228922,18920915621.861832,shoup
+fft18_cub_b2,fft18-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,3,2,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,2,1000,100,,0.025938,77107.183859,181.918670,20213185605.543285,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.744704,0.717312,0.000000,,,,,,,,,,,
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015514,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.117696,0.129472,,64,1152921504606584833,60,8,4,256,0,64459.571579,3806.890103,4224422483.025257,shoup
+fwht15_online_b4,fwht15-batch4,full,butterfly,cuButterfly-online-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.015309,261287.622799,64.214046,8561872823.886603,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.131296,0.140800,0.000000,,,,,,,,,,,
+fwht15_warp_b4,fwht15-batch4,full,butterfly,cuButterfly-warp-register,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.017633,226843.789054,55.749130,7433217279.730257,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.133088,0.163264,0.000000,,,,,,,,,,,
+ntt16_r4_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix4,0,5,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.539699,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.851552,10.117760,,64,1152921504606584833,60,8,4,256,0,237169.150437,5950.994238,15543117443.007517,shoup
+fwht15_warp_b256,fwht15-batch256,full,butterfly,cuButterfly-warp-register,0,3,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.108913,2350507.724343,577.660778,77021437111.271332,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,5.459392,5.107584,0.000000,,,,,,,,,,,
+fft20_vkfft_b2,fft20-batch2,full,fft-library,VkFFT,0,2,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,2,1000,100,811.191866000,0.117483519,17023.664397546,178.506059193,17850605919.321407318,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b32,fwht15-batch32,full,butterfly,cuButterfly-warp-register,0,5,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.022385,1429551.584530,351.326597,46843546321.885712,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.751616,0.722144,0.000000,,,,,,,,,,,
+ntt12_r4_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,4,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.042711,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.789152,0.736544,,32,1073692673,30,6,4,256,0,5993766.743534,163222.930895,24550468581.516678,shoup
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,5,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.006830,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.011264,0.021312,,32,1073692673,30,6,4,256,0,146411.170559,25376.794477,599700154.607828,shoup
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1,1000,100,1.923272000,0.011868160,84259.057986368,9.663502842,1380500406.048649788,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,2,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,2.078648000,0.027648000,2314814.810912346,265.481481034,37925925861.987884521,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix4,0,2,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.148562,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.761824,2.591264,,64,1152921504606584833,60,8,4,256,0,215398.415679,5816.437086,14116350569.917755,shoup
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.319601,12515.619425,131.235782,13123578154.692392,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.775616,2.596288,0.000000,,,,,,,,,,,
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002478,403538.244254,0.413223,103305790.529078,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.017504,0.000000,,,,,,,,,,,
+fft18_cub_b2,fft18-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,4,2,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,2,1000,100,,0.025969,77015.972463,181.703476,20189275085.407219,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.741856,0.723232,0.000000,,,,,,,,,,,
+fft8_vkfft_b4096,fft8-batch4096,full,fft-library,VkFFT,0,5,4096,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4096,1000,100,203.472669000,0.020142080,203355360.849485606,208.235889510,52058972377.468315125,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b4,fwht15-batch4,full,butterfly,cuButterfly-warp-register,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.017674,226318.084771,55.619933,7415991001.763029,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.124704,0.148736,0.000000,,,,,,,,,,,
+fwht8_shared_b4096,fwht8-batch4096,full,butterfly,cuButterfly-shared-radix4,0,1,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.014961,273785093.742328,280.355936,70088983998.035843,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.748960,0.730112,0.000000,,,,,,,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1,1000,100,150.716398000,0.002314240,432107.305888526,0.442477881,110619470.307462543,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,1.772496000,0.002682880,372733.806415253,0.381679418,95419854.442304835,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002109,30339805.198601,31.067961,7766990130.841847,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.032768,0.033504,0.000000,,,,,,,,,,,
+fwht8_warp_b4,fwht8-batch4,full,butterfly,cuButterfly-warp-register,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002673,1496647.430564,1.532567,383141742.224474,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.015360,0.019424,0.000000,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,2,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,256,1000,100,1.837162000,0.121425927,2108281.212985148,241.794555755,34542079393.548660278,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,4,16384,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16384,1000,100,1.814035000,0.083804160,195503420.478157699,200.195502570,50048875642.408370972,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,16,1000,100,369.127246000,0.010680321,1498082.360102851,171.812069715,24544581387.925106049,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix2,1,5,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.007137,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.027648,0.032256,,32,1073692673,30,6,4,256,0,560437.593005,59664.732162,2295552380.947012,shoup
+ntt16_r2_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix2,0,1,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.591575,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.868864,10.118560,,64,1152921504606584833,60,8,4,256,0,216371.540825,5931.693145,14180125299.504623,shoup
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,2,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,16,1000,100,,0.021053,759970.785757,87.159529,12451361353.848986,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.508096,0.403872,0.000000,,,,,,,,,,,
+xor8_r2_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix2,0,4,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004874,210084047.591033,215.126065,53781516183.304466,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.255040,0.249504,0.000000,,,,,,,,,,,
+fft18_cufft_b8,fft18-batch8,full,fft-library,cuFFT,1,1,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,8,1000,100,1.997462000,0.123361282,64850.169088855,153.000744531,17000082725.628879547,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,4,1000,100,,0.342497,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.464192,5.099168,,64,1152921504577486849,60,0,0,256,0,11678.924553,366.775393,12246239992.242460,shoup
+fwht8_warp_b16,fwht8-batch16,full,butterfly,cuButterfly-warp-register,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002161,7405213.380607,7.582939,1895734625.435377,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.015360,0.020064,0.000000,,,,,,,,,,,
+xor8_r2_b16,xor8-batch16,full,butterfly,cuButterfly-radix2,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.003011,5314625.744562,5.442177,1360544190.607812,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.015360,0.020192,0.000000,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,4,1000,100,,0.060334,66297.519105,156.415472,17379496848.206203,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,1.433408,1.350592,0.000000,,,,,,,,,,,
+ntt16_r2_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix2,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.031529,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.409984,0.430816,,64,1152921504606584833,60,8,4,256,0,126867.485769,4585.426184,8314387547.368338,shoup
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002570,24900400.082036,25.498010,6374502421.001141,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.036864,0.034432,0.000000,,,,,,,,,,,
+xor8_r2_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix2,0,2,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.179036,366048968.569643,374.834144,93708535953.828705,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.856864,10.116416,0.000000,,,,,,,,,,,
+fft14_cub_b1024,fft14-batch1024,full,butterfly,cuButterfly-cuFFTDx-direct,0,5,1024,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1024,1000,100,,0.380160,2693602.877128,308.923927,44131989538.872375,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,21.676352,20.140257,0.000000,,,,,,,,,,,
+fwht15_warp_b512,fwht15-batch512,full,butterfly,cuButterfly-warp-register,0,3,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,0.193341,2648164.699834,650.812957,86775060884.176529,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,10.855072,10.111072,0.000000,,,,,,,,,,,
+fwht20_online_b2,fwht20-batch2,full,butterfly,cuButterfly-online-radix4,0,1,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.167066,11971.344992,125.528650,12552865046.383547,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.419168,1.364128,0.000000,,,,,,,,,,,
+fft8_vkfft_b1024,fft8-batch1024,full,fft-library,VkFFT,0,3,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1024,1000,100,202.613305000,0.005754880,177935953.084311932,182.206415958,45551603989.583854675,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.488110,8194.872507,85.929466,8592946633.779652,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.762752,2.608640,0.000000,,,,,,,,,,,
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.098591,10142.942797,106.356464,10635646386.281420,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.746624,0.729120,0.000000,,,,,,,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1,1000,100,306.781125000,0.008253440,121161.596666420,13.895781198,1985111599.782624006,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,1,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.042824,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.790880,0.735520,,32,1073692673,30,6,4,256,0,5978000.472015,163137.988458,24485889933.373840,shoup
+fwht8_shared_b256,fwht8-batch256,full,butterfly,cuButterfly-shared-radix4,0,5,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002949,86805555.226460,88.888889,22222222137.973820,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.071456,0.078048,0.000000,,,,,,,,,,,
+fwht15_online_b32,fwht15-batch32,full,butterfly,cuButterfly-online-radix4,0,2,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.084255,379800.683682,93.339816,12445308802.885481,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.747424,0.736000,0.000000,,,,,,,,,,,
+fwht20_online_b16,fwht20-batch16,full,butterfly,cuButterfly-online-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.232824,12978.329246,136.087646,13608764567.780863,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.846656,10.113856,0.000000,,,,,,,,,,,
+xor8_r2_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix2,0,1,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004884,209643604.450651,214.675051,53668762739.366753,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.274592,0.263392,0.000000,,,,,,,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,4,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.065075,1966955.039279,483.398870,64453182727.085091,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,2.774464,2.617472,0.000000,,,,,,,,,,,
+fft8_cub_b65536,fft8-batch65536,full,butterfly,cuButterfly-cuFFTDx,0,4,65536,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,65536,1000,100,,0.327660,200012502.291115,204.812802,51203200586.525414,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,21.612513,20.138752,0.000000,,,,,,,,,,,
+fft20_cub_b16,fft20-batch16,full,butterfly,cuButterfly-cuFFTDx-online,0,5,16,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,16,1000,100,,0.926781,17264.048130,181.026665,18102666532.207699,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,21.586624,37.808224,0.000000,,,,,,,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.049725,329489270.892755,337.397013,84349253348.545319,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.777472,2.620512,0.000000,,,,,,,,,,,
+xor20_online_b16,xor20-batch16,full,butterfly,cuButterfly-online-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.232108,12985.879673,136.166818,13616681763.772770,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.866912,10.125248,0.000000,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,16,1000,100,2.235674000,0.013496321,1185508.284958062,135.963574185,19423367740.752895355,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b256,fft8-batch256,full,fft-library,cuFFT,1,5,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,256,1000,100,2.020455000,0.003164160,80906147.196269244,82.847894729,20711973682.244926453,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,4,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,256,1000,100,365.722907000,0.171878397,1489425.103887758,170.819186315,24402740902.097034454,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4,xor8-batch4,full,butterfly,cuButterfly-radix2,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002877,1390124.633471,1.423488,355871906.168624,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.013312,0.018720,0.000000,,,,,,,,,,,
+fwht20_hier_b16,fwht20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.868257,8564.130934,89.801422,8980142158.259295,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.914368,17.597055,0.000000,,,,,,,,,,,
+xor8_r4_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix4,0,2,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004332,236406628.813911,242.080388,60520096976.361305,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.265472,0.263424,0.000000,,,,,,,,,,,
+xor8_r2_b16,xor8-batch16,full,butterfly,cuButterfly-radix2,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002898,5521201.247711,5.653710,1413427519.414016,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.017408,0.024288,0.000000,,,,,,,,,,,
+xor20_online_b8,xor20-batch8,full,butterfly,cuButterfly-online-radix4,0,5,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.623677,12827.143620,134.502349,13450234948.979464,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.471232,5.100352,0.000000,,,,,,,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,4,1000,100,2.334622000,0.210032642,19044.658792319,199.697721378,19969772137.815170288,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b256,fwht8-batch256,full,butterfly,cuButterfly-warp-register,0,5,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002642,96899233.334323,99.224815,24806203733.586769,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.074304,0.092576,0.000000,,,,,,,,,,,
+xor20_online_b2,xor20-batch2,full,butterfly,cuButterfly-online-radix4,0,4,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.166902,11983.096602,125.651875,12565187502.238991,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.424864,1.339392,0.000000,,,,,,,,,,,
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.098314,10171.466454,106.655556,10665555608.923458,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.747232,0.706240,0.000000,,,,,,,,,,,
+xor8_r4_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix4,0,1,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004332,236406628.813911,242.080388,60520096976.361305,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.264704,0.250432,0.000000,,,,,,,,,,,
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002560,24999998.357816,25.599998,6399999579.601017,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.033792,0.034400,0.000000,,,,,,,,,,,
+ntt16_r2_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix2,0,5,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.160707,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.768736,2.603904,,64,1152921504606584833,60,8,4,256,0,199120.677136,5783.118812,13049572696.784698,shoup
+xor8_r2_b256,xor8-batch256,full,butterfly,cuButterfly-radix2,0,1,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.003369,75987842.058366,77.811550,19452887566.941746,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.074880,0.079488,0.000000,,,,,,,,,,,
+fft18_vkfft_b8,fft18-batch8,full,fft-library,VkFFT,0,2,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,8,1000,100,357.396938000,0.113059834,70758.993198782,166.941409618,18549045513.101402283,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b4,fwht15-batch4,full,butterfly,cuButterfly-online-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.015319,261112.967145,64.171123,8556149707.407044,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.136768,0.151520,0.000000,,,,,,,,,,,
+fft14_cub_b64,fft14-batch64,full,butterfly,cuButterfly-cuFFTDx-direct,0,3,64,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,64,1000,100,,0.031642,2022653.798974,231.974119,33139159842.393803,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,1.482144,1.343488,0.000000,,,,,,,,,,,
+fwht15_warp_b256,fwht15-batch256,full,butterfly,cuButterfly-warp-register,0,5,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.107049,2391429.150658,587.717628,78362350408.747070,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,5.483936,5.109088,0.000000,,,,,,,,,,,
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.042742,383325341.904111,392.525150,98131287527.452530,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,2.777504,2.601568,0.000000,,,,,,,,,,,
+fwht20_hier_b8,fwht20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,2,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.947681,8441.656955,88.517189,8851718883.368378,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.503168,5.108608,0.000000,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.098294,10173.585901,106.677780,10667778009.790064,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.755648,0.711488,0.000000,,,,,,,,,,,
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002847,351281.483464,0.359712,89928059.766890,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.011264,0.019360,0.000000,,,,,,,,,,,
+fwht20_hier_b8,fwht20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,3,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.947814,8440.471002,88.504753,8850475320.972424,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.465344,5.105312,0.000000,,,,,,,,,,,
+fft8_cub_b16,fft8-batch16,full,butterfly,cuButterfly-cuFFTDx,0,3,16,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16,1000,100,,0.003103,5156765.648956,5.280528,1320132006.132636,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.019456,0.025216,0.000000,,,,,,,,,,,
+fwht8_warp_b4096,fwht8-batch4096,full,butterfly,cuButterfly-warp-register,0,5,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.011223,364963516.988258,373.722641,93430660348.994034,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.746592,0.736256,0.000000,,,,,,,,,,,
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002888,346298.763369,0.354610,88652483.422564,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.009216,0.017152,0.000000,,,,,,,,,,,
+xor8_r4_b256,xor8-batch256,full,butterfly,cuButterfly-radix4,0,2,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.002939,87108010.396126,89.198603,22299650661.408287,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.071424,0.093504,0.000000,,,,,,,,,,,
+fwht8_warp_b4,fwht8-batch4,full,butterfly,cuButterfly-warp-register,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002079,1924260.958206,1.970443,492610805.300830,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.008192,0.015936,0.000000,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,4,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,4,1000,100,,0.059628,67083.120852,158.268939,17585437632.724442,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,1.417888,1.345088,0.000000,,,,,,,,,,,
+fwht15_warp_b4,fwht15-batch4,full,butterfly,cuButterfly-warp-register,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.017654,226580.631983,55.684456,7424594148.811483,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.123584,0.150048,0.000000,,,,,,,,,,,
+fft8_cufft_b4,fft8-batch4,full,fft-library,cuFFT,1,4,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4,1000,100,1.715987000,0.002682880,1490935.225661013,1.526717671,381679417.769219339,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b256,fwht15-batch256,full,butterfly,cuButterfly-warp-register,0,1,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.111043,2305422.371087,566.580602,75544080255.787354,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,5.513984,5.122016,0.000000,,,,,,,,,,,
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,1,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,16,1000,100,,0.020746,771224.072286,88.450146,12635735200.337797,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.481984,0.406496,0.000000,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016435,60845.014286,143.551399,15950155425.028454,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.426912,0.409280,0.000000,,,,,,,,,,,
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.006871,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.016384,0.022208,,32,1073692673,30,6,4,256,0,145538.376000,21995.889631,596125188.097195,shoup
+xor20_online_b16,xor20-batch16,full,butterfly,cuButterfly-online-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.232067,12986.310637,136.171337,13617133662.701624,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.922272,10.115776,0.000000,,,,,,,,,,,
+fwht20_online_b2,fwht20-batch2,full,butterfly,cuButterfly-online-radix4,0,4,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.167301,11954.492710,125.351941,12535194148.035856,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.432192,1.349312,0.000000,,,,,,,,,,,
+fwht15_warp_b512,fwht15-batch512,full,butterfly,cuButterfly-warp-register,0,4,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,0.193116,2651253.862654,651.572149,86876286571.445389,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,10.871424,10.134816,0.000000,,,,,,,,,,,
+fft20_cub_b2,fft20-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,5,2,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,2,1000,100,,0.128317,15586.345192,163.434675,16343467496.233179,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,2.763136,2.620096,0.000000,,,,,,,,,,,
+xor8_r4_b4,xor8-batch4,full,butterfly,cuButterfly-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002509,1594387.748030,1.632653,408163263.495648,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.010240,0.018080,0.000000,,,,,,,,,,,
+fft18_cub_b32,fft18-batch32,full,butterfly,cuButterfly-cuFFTDx-online,0,1,32,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,32,1000,100,,0.410010,78046.948750,184.135854,20459539333.101898,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,10.869952,10.121312,0.000000,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,5,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,1,1000,100,1.928530000,0.063518718,15743.390819226,165.081417717,16508141771.660902023,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002929,21853146.890947,22.377622,5594405604.082486,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.031744,0.032704,0.000000,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,5,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,16,1000,100,1.732209000,0.013496321,1185508.284958062,135.963574185,19423367740.752895355,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,3,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.064799,1975347.655671,485.461440,64728191981.029152,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,2.773376,2.607264,0.000000,,,,,,,,,,,
+fft8_cub_b1024,fft8-batch1024,full,butterfly,cuButterfly-cuFFTDx,0,1,1024,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1024,1000,100,,0.005192,197238657.107943,201.972385,50493096219.633461,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.423360,0.424800,0.000000,,,,,,,,,,,
+fft14_cufft_b4,fft14-batch4,full,fft-library,cuFFT,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,4,1000,100,1.904172000,0.011909120,335877.048200874,38.521066904,5503009557.723119736,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix2,0,3,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004803,213219617.621664,218.336888,54584222111.145874,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.250304,0.268352,0.000000,,,,,,,,,,,
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,1,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16384,1000,100,,0.084265,194434325.929846,199.100750,49775187438.040695,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,5.479232,5.111168,0.000000,,,,,,,,,,,
+fwht8_shared_b16,fwht8-batch16,full,butterfly,cuButterfly-shared-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002540,6300403.426558,6.451613,1612903277.198866,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.013312,0.020928,0.000000,,,,,,,,,,,
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,3,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,16,1000,100,,0.020777,770083.748097,88.319365,12617052128.820662,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.492224,0.424128,0.000000,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.487014,8213.309789,86.122795,8612279525.492992,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.768768,2.601472,0.000000,,,,,,,,,,,
+fft20_cufft_b8,fft20-batch8,full,fft-library,cuFFT,1,1,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,8,1000,100,1.978573000,0.381409258,20974.844840639,219.937189036,21993718903.618083954,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1,1000,100,151.613821000,0.002314240,432107.305888526,0.442477881,110619470.307462543,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b64,fft14-batch64,full,fft-library,VkFFT,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,64,1000,100,362.354258000,0.047237121,1354866.664805485,155.386948053,22198135436.173069000,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b8,fft18-batch8,full,fft-library,cuFFT,1,2,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,8,1000,100,1.838562000,0.122664958,65218.299625870,153.869273434,17096585937.124158859,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002499,400230.550953,0.409836,102459021.044087,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.019616,0.000000,,,,,,,,,,,
+fft8_cufft_b256,fft8-batch256,full,fft-library,cuFFT,1,4,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,256,1000,100,1.999969000,0.003143680,81433223.483656451,83.387620847,20846905211.816051483,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015862,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.124800,0.142976,,64,1152921504606584833,60,8,4,256,0,63044.702983,3525.623689,4131697654.717077,shoup
+ntt12_r4_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.006380,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.026624,0.030720,,32,1073692673,30,6,4,256,0,627006.369382,62771.172008,2568218088.989159,shoup
+ntt12_r2_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix2,1,3,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.048220,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.770272,0.750688,,32,1073692673,30,6,4,256,0,5308983.060569,163142.513231,21745594616.088997,shoup
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,1,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,256,1000,100,364.927285000,0.171796471,1490135.383386651,170.900646850,24414378121.406883240,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b65536,fft8-batch65536,full,fft-library,VkFFT,0,2,65536,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,65536,1000,100,204.952883000,0.326113284,200960841.796050012,205.783901999,51445975499.788803101,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,3,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.042844,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.828096,0.751808,,32,1073692673,30,6,4,256,0,5975143.209414,157757.076770,24474186585.758392,shoup
+xor8_r2_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix2,0,5,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004823,212314215.493464,217.409757,54352439166.326683,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.254656,0.247456,0.000000,,,,,,,,,,,
+xor20_hier_b2,xor20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,1,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.257004,7781.994704,81.600129,8160012878.330842,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.416480,1.350272,0.000000,,,,,,,,,,,
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002550,25100401.177010,25.702811,6425702701.314640,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.031744,0.032320,0.000000,,,,,,,,,,,
+fwht8_shared_b256,fwht8-batch256,full,butterfly,cuButterfly-shared-radix4,0,2,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002949,86805555.226460,88.888889,22222222137.973820,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.067040,0.079264,0.000000,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002918,21929825.535294,22.456141,5614035337.035136,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.030720,0.032352,0.000000,,,,,,,,,,,
+fft18_cufft_b64,fft18-batch64,full,fft-library,cuFFT,1,3,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,64,1000,100,2.040869000,0.706355214,90605.970934649,213.766304802,23751811644.692611694,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix2,1,1,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.048230,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.799328,0.746976,,32,1073692673,30,6,4,256,0,5307855.797313,160548.428862,21740977345.792061,shoup
+xor20_online_b2,xor20-batch2,full,butterfly,cuButterfly-online-radix4,0,3,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.166922,11981.626790,125.636463,12563646292.973320,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.428704,1.361696,0.000000,,,,,,,,,,,
+fwht8_shared_b1024,fwht8-batch1024,full,butterfly,cuButterfly-shared-radix4,0,2,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.004342,235849046.575243,241.509424,60377355923.262245,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.175616,0.257824,0.000000,,,,,,,,,,,
+fft18_cub_b8,fft18-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,4,8,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,8,1000,100,,0.108861,73487.913430,173.379740,19264415578.300797,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,2.765248,2.606848,0.000000,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002488,401877.572843,0.411523,102880658.647830,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.009216,0.018016,0.000000,,,,,,,,,,,
+fft8_cub_b4096,fft8-batch4096,full,butterfly,cuButterfly-cuFFTDx,0,1,4096,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4096,1000,100,,0.022108,185270959.118150,189.717462,47429365534.246376,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,1.417920,1.350752,0.000000,,,,,,,,,,,
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.086856,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.414272,1.349984,,64,1152921504606584833,60,8,4,256,0,184213.629390,5611.846113,12072624415.729794,shoup
+ntt12_r4_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix4,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.013855,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.275744,0.273792,,32,1073692673,30,6,4,256,0,4619364.165494,113597.897196,18920915621.861832,shoup
+fwht8_shared_b16,fwht8-batch16,full,butterfly,cuButterfly-shared-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002540,6300403.426558,6.451613,1612903277.198866,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.015360,0.021472,0.000000,,,,,,,,,,,
+fwht15_online_b512,fwht15-batch512,full,butterfly,cuButterfly-online-radix4,0,2,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,1.244600,411377.051441,101.100024,13480003221.631529,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,10.849408,10.116416,0.000000,,,,,,,,,,,
+fwht8_shared_b4096,fwht8-batch4096,full,butterfly,cuButterfly-shared-radix4,0,4,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.014971,273597811.184919,280.164159,70041039663.339142,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.749472,0.741792,0.000000,,,,,,,,,,,
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,5,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,1,1000,100,2.214248000,0.023050239,43383.497523193,102.354512172,11372723574.719779968,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b4,fft8-batch4,full,fft-library,VkFFT,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4,1000,100,152.137767000,0.002396160,1669337.580233027,1.709401682,427350420.539654911,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,4,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,256,1000,100,1.895281000,0.121098243,2113986.085115905,242.448836130,34635548018.538986206,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b4096,fft8-batch4096,full,fft-library,cuFFT,1,5,4096,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4096,1000,100,1.774563000,0.022097919,185356819.107649952,189.805382766,47451345691.558387756,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cub_b4,fft14-batch4,full,butterfly,cuButterfly-cuFFTDx-direct,0,4,4,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,4,1000,100,,0.020603,194147.613883,22.266402,3180914505.855709,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.138400,0.157344,0.000000,,,,,,,,,,,
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,5,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,16,1000,100,,0.205036,78035.264141,184.108287,20456476282.960819,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,5.447616,5.097280,0.000000,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,1,1000,100,,0.070717,14140.783566,148.276863,14827686268.134108,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,1.417248,1.350496,0.000000,,,,,,,,,,,
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015872,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.124064,0.136096,,64,1152921504606584833,60,8,4,256,0,63004.033110,3622.768389,4129032313.916736,shoup
+fwht15_online_b32,fwht15-batch32,full,butterfly,cuButterfly-online-radix4,0,5,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.084255,379800.683682,93.339816,12445308802.885481,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.747808,0.717440,0.000000,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.319273,12528.464468,131.370472,13137047157.961670,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.783488,2.600512,0.000000,,,,,,,,,,,
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,4,1000,100,329.433224000,0.063805439,62690.580758285,147.905636421,16433959602.299955368,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_online_b2,xor20-batch2,full,butterfly,cuButterfly-online-radix4,0,5,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.167137,11966.211241,125.474819,12547481918.235926,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.436064,1.345248,0.000000,,,,,,,,,,,
+fft8_cufft_b1024,fft8-batch1024,full,fft-library,cuFFT,1,5,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1024,1000,100,1.814674000,0.004526080,226244338.992537081,231.674203128,57918550782.089492798,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,4,1000,100,797.632656000,0.206551030,19365.674403136,203.063814029,20306381402.942630768,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b16,fwht8-batch16,full,butterfly,cuButterfly-warp-register,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002089,7659313.625312,7.843137,1960784288.079768,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.019456,0.021312,0.000000,,,,,,,,,,,
+ntt16_r2_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix2,0,3,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.160010,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.763680,2.606464,,64,1152921504606584833,60,8,4,256,0,199987.190292,5786.457158,13106360502.990751,shoup
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,3,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,256,1000,100,367.628766000,0.171724796,1490757.336872766,170.971977451,24424568207.323406219,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix2,0,3,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.178593,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.638048,34.903358,,64,1152921504606584833,60,8,4,256,0,217208.094424,4435.204442,14234949676.150431,shoup
+fft14_cub_b64,fft14-batch64,full,butterfly,cuButterfly-cuFFTDx-direct,0,2,64,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,64,1000,100,,0.031836,2010292.728465,230.556452,32936636063.177502,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,1.489408,1.342720,0.000000,,,,,,,,,,,
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,4,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16384,1000,100,,0.084204,194576191.218150,199.246020,49811504951.846397,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,5.488384,5.100160,0.000000,,,,,,,,,,,
+ntt20_compact_b2,ntt20-batch2,full,ntt,cuNTT-compact-stage,0,1,2,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,2,1000,100,,0.179866,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.763488,2.587680,,64,1152921504577486849,60,0,0,256,0,11119.412767,361.596057,11659549361.669125,shoup
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,3,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,2.158395000,0.026296319,2433800.674881916,279.127731801,39875390257.265319824,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b8,ntt20-batch8,full,ntt,cuNTT-compact-stage,0,4,8,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,8,1000,100,,0.664955,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.866112,10.144832,,64,1152921504577486849,60,0,0,256,0,12030.891104,369.073516,12615303670.436563,shoup
+xor8_r2_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix2,0,5,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.179241,365630719.298422,374.405857,93601464140.396057,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.906912,10.124160,0.000000,,,,,,,,,,,
+fft18_cufft_b8,fft18-batch8,full,fft-library,cuFFT,1,4,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,8,1000,100,1.942296000,0.122736648,65180.206142812,153.779399632,17086599959.101179123,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,16,1000,100,2.001088000,0.211425290,75676.850375631,178.544090384,19838232264.869510651,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,4,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002550,25100401.177010,25.702811,6425702701.314640,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.035840,0.033152,0.000000,,,,,,,,,,,
+fft20_vkfft_b2,fft20-batch2,full,fft-library,VkFFT,0,1,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,2,1000,100,801.031408000,0.117268473,17054.882274592,178.833402360,17883340235.962650299,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix2,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.007148,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.027648,0.033376,,32,1073692673,30,6,4,256,0,559634.645831,58675.528000,2292263509.323721,shoup
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015862,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.120064,0.133216,,64,1152921504606584833,60,8,4,256,0,63044.702983,3715.514191,4131697654.717077,shoup
+fwht8_shared_b65536,fwht8-batch65536,full,butterfly,cuButterfly-shared-radix4,0,3,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.177326,369579019.755714,378.448916,94612229057.462799,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.886112,10.126304,0.000000,,,,,,,,,,,
+fft8_cufft_b4,fft8-batch4,full,fft-library,cuFFT,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4,1000,100,2.074090000,0.002734080,1463015.004278372,1.498127364,374531841.095263302,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b16,fft20-batch16,full,butterfly,cuButterfly-cuFFTDx-online,0,3,16,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,16,1000,100,,0.927017,17259.662398,180.980678,18098067758.930569,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,21.611776,20.135809,0.000000,,,,,,,,,,,
+fwht8_shared_b4096,fwht8-batch4096,full,butterfly,cuButterfly-shared-radix4,0,3,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.014991,273224047.630686,279.781425,69945356193.455490,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.763712,0.722560,0.000000,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,4,1000,100,,0.059628,67083.120852,158.268939,17585437632.724442,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,1.438112,1.346528,0.000000,,,,,,,,,,,
+fwht20_hier_b8,fwht20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,1,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.947896,8439.741227,88.497101,8849710097.044708,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.476000,5.105664,0.000000,,,,,,,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1,1000,100,199.913208000,0.002334720,428316.887900589,0.438596493,109649123.302550793,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b8,fft18-batch8,full,fft-library,cuFFT,1,5,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,8,1000,100,1.957007000,0.122869760,65109.592573054,153.612801319,17068089035.470582962,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.488233,8192.810080,85.907840,8590784022.549105,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.779328,2.601536,0.000000,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,5,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,1,1000,100,,0.071516,13982.852952,146.620840,14662084017.441879,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,1.415712,1.344096,0.000000,,,,,,,,,,,
+fft20_vkfft_b2,fft20-batch2,full,fft-library,VkFFT,0,4,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,2,1000,100,792.556539000,0.125327364,15958.206910180,167.333927690,16733392769.048784256,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b1024,fwht8-batch1024,full,butterfly,cuButterfly-shared-radix4,0,1,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.004526,226244338.992537,231.674203,57918550782.089493,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.261312,0.276960,0.000000,,,,,,,,,,,
+fft8_vkfft_b1024,fft8-batch1024,full,fft-library,VkFFT,0,5,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1024,1000,100,205.155248000,0.006154240,166389360.723703593,170.382705381,42595676345.268119812,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4,xor8-batch4,full,butterfly,cuButterfly-radix2,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.003011,1328656.436140,1.360544,340136047.651953,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.019456,0.022688,0.000000,,,,,,,,,,,
+xor20_hier_b16,xor20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.863752,8584.834788,90.018517,9001851722.728809,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.863168,18.224833,0.000000,,,,,,,,,,,
+ntt12_r4_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix4,0,4,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.013875,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.284704,0.266112,,32,1073692673,30,6,4,256,0,4612546.297712,113336.280279,18892989635.428600,shoup
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,5,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1,1000,100,,0.002898,345075.077982,0.353357,88339219.963376,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.008192,0.015136,0.000000,,,,,,,,,,,
+fft8_vkfft_b16,fft8-batch16,full,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16,1000,100,151.953044000,0.002324480,6883260.311922644,7.048458559,1762114639.852196932,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,16,1000,100,366.756576000,0.010680321,1498082.360102851,171.812069715,24544581387.925106049,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b2,fwht20-batch2,full,butterfly,cuButterfly-online-radix4,0,5,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.167332,11952.297575,125.328924,12532892381.668558,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.423424,1.337312,0.000000,,,,,,,,,,,
+fwht20_hier_b2,fwht20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,3,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.257331,7772.085384,81.496222,8149622203.509089,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.418848,1.336128,0.000000,,,,,,,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,4,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.279716,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,5.460640,5.100800,,64,1152921504606584833,60,8,4,256,0,228803.634804,5903.429581,14994875010.502993,shoup
+fwht8_warp_b65536,fwht8-batch65536,full,butterfly,cuButterfly-warp-register,0,3,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.164393,398654533.523745,408.222242,102055560582.078766,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,10.913568,10.129632,0.000000,,,,,,,,,,,
+fft20_cub_b8,fft20-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,2,8,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,8,1000,100,,0.455598,17559.337423,184.122998,18412299797.378403,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,10.825024,10.107776,0.000000,,,,,,,,,,,
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,5,16384,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16384,1000,100,2.165221000,0.083773442,195575109.301850498,200.268911925,50067227981.273727417,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.305172,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.462336,5.104960,,64,1152921504606584833,60,8,4,256,0,209717.473305,5886.427723,13744044330.493036,shoup
+ntt16_r4_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix4,0,4,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.149914,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.768832,2.594304,,64,1152921504606584833,60,8,4,256,0,213456.292516,5804.409909,13989071586.313683,shoup
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,4,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002161,29620853.522428,30.331754,7582938501.741509,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.037888,0.036576,0.000000,,,,,,,,,,,
+xor8_r2_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix2,0,5,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.016220,252525255.192733,258.585861,64646465329.339523,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.747872,0.717152,0.000000,,,,,,,,,,,
+fft8_vkfft_b256,fft8-batch256,full,fft-library,VkFFT,0,5,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,256,1000,100,199.524669000,0.002775040,92250922.858236462,94.464945007,23616236251.708534241,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b512,fwht15-batch512,full,butterfly,cuButterfly-warp-register,0,1,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,0.193403,2647323.468408,650.606216,86747495412.808701,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,10.847648,10.112928,0.000000,,,,,,,,,,,
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,5,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,1.864942000,0.027658241,2313957.720653476,265.383183066,37911883295.186546326,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix4,0,2,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.014735,277970818.751544,284.642118,71160529600.395203,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.746592,0.713184,0.000000,,,,,,,,,,,
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,4,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.008468,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.067232,0.087136,,32,1073692673,30,6,4,256,0,1889359.162983,98258.081896,7738815131.579692,shoup
+fft8_vkfft_b4096,fft8-batch4096,full,fft-library,VkFFT,0,1,4096,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4096,1000,100,203.179423000,0.020193281,202839750.041346967,207.707904042,51926976010.584823608,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b4096,fft8-batch4096,full,fft-library,cuFFT,1,1,4096,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4096,1000,100,1.809081000,0.022067200,185614845.886610895,190.069602188,47517400546.972389221,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b64,fft18-batch64,full,butterfly,cuButterfly-cuFFTDx-online,0,4,64,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,64,1000,100,,0.840888,76109.993334,179.566003,19951778092.591854,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,21.583839,20.136703,0.000000,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,4,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,16,1000,100,1.936912000,0.013506561,1184609.501261122,135.860494481,19408642068.662227631,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix4,0,1,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.540559,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.829184,10.115840,,64,1152921504606584833,60,8,4,256,0,236791.759606,5957.483242,15518384757.543570,shoup
+xor8_r4_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix4,0,5,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004536,225733634.823505,231.151242,57787810514.817314,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.257088,0.247808,0.000000,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,1,1000,100,1.921802000,0.065392643,15292.240087904,160.350759424,16035075942.413976669,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b256,xor8-batch256,full,butterfly,cuButterfly-radix2,0,2,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.003308,77399382.062821,79.256967,19814241808.082253,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.067520,0.081312,0.000000,,,,,,,,,,,
+ntt12_r4_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix4,0,4,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.538163,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.888224,10.111488,,32,1073692673,30,6,4,256,0,7611074.323283,190176.605939,31174960428.165623,shoup
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,16,1000,100,330.550625000,0.201410562,79439.726780007,187.421829633,20824647737.018211365,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,4,1000,100,2.028546000,0.210237443,19026.106550835,199.503187026,19950318702.648757935,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,5,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1,1000,100,1.711991000,0.011878400,84186.421636252,9.655172325,1379310332.088345051,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b4,fft14-batch4,full,fft-library,VkFFT,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,4,1000,100,309.610948000,0.008478720,471769.338076766,54.106281845,7729468835.049730301,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4,xor8-batch4,full,butterfly,cuButterfly-radix2,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002867,1395089.198606,1.428571,357142834.843162,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.018752,0.000000,,,,,,,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1,1000,100,306.368527000,0.008243200,121312.106368169,13.913042855,1987577550.736074924,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b4,fwht15-batch4,full,butterfly,cuButterfly-warp-register,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.017644,226712.146120,55.716777,7428903604.076395,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.124736,0.145920,0.000000,,,,,,,,,,,
+xor20_hier_b2,xor20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,4,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.256696,7791.307837,81.697784,8169778406.353244,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.418400,1.359168,0.000000,,,,,,,,,,,
+ntt20_compact_b16,ntt20-batch16,full,ntt,cuNTT-compact-stage,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,16,1000,100,,1.313854,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.587872,39.611137,,64,1152921504577486849,60,0,0,256,0,12177.917837,255.947326,12769472373.417465,shoup
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002570,24900400.082036,25.498010,6374502421.001141,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.035840,0.030688,0.000000,,,,,,,,,,,
+fft14_cufft_b1024,fft14-batch1024,full,fft-library,cuFFT,1,3,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1024,1000,100,11.794440000,0.405821443,2523277.216278229,289.389617381,41341373911.502502441,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,376.836928000,0.018534400,53953.730536310,127.292820639,14143646737.710565567,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b256,fft8-batch256,full,butterfly,cuButterfly-cuFFTDx,0,2,256,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,256,1000,100,,0.003348,76452599.873783,78.287462,19571865567.688519,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.128800,0.135872,0.000000,,,,,,,,,,,
+fft20_cufft_b16,fft20-batch16,full,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,16,1000,100,2.011746000,0.721008599,22191.136175810,232.690928067,23269092806.686088562,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b256,fwht15-batch256,full,butterfly,cuButterfly-online-radix4,0,1,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.625746,409111.715591,100.543295,13405772696.498045,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,5.456320,5.105312,0.000000,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.486984,8213.827505,86.128224,8612822389.486319,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.761792,2.618560,0.000000,,,,,,,,,,,
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.047759,343053161.999721,351.286438,87821609471.928665,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.774400,2.601280,0.000000,,,,,,,,,,,
+fft14_cub_b64,fft14-batch64,full,butterfly,cuButterfly-cuFFTDx-direct,0,4,64,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,64,1000,100,,0.031693,2019386.158824,231.599360,33085622826.179016,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,1.483680,1.340864,0.000000,,,,,,,,,,,
+ntt16_r2_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix2,0,2,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.160543,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.763040,2.596192,,64,1152921504606584833,60,8,4,256,0,199323.903764,5797.338110,13062891357.048124,shoup
+fft8_cub_b1024,fft8-batch1024,full,butterfly,cuButterfly-cuFFTDx,0,5,1024,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1024,1000,100,,0.005294,193423601.612462,198.065768,49516442012.790276,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.422720,0.411264,0.000000,,,,,,,,,,,
+fft8_vkfft_b256,fft8-batch256,full,fft-library,VkFFT,0,1,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,256,1000,100,151.902470000,0.002795520,91575083.759790808,93.772885770,23443221442.506446838,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b64,fft18-batch64,full,fft-library,VkFFT,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,64,1000,100,331.121535000,0.713666558,89677.734312687,211.576319853,23508479983.665039062,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,5,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.047749,343126763.877919,351.361806,87840451552.747177,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.764928,2.598112,0.000000,,,,,,,,,,,
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,4,1000,100,,0.235571,16980.005016,178.048257,17804825739.821865,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,5.519552,5.098560,0.000000,,,,,,,,,,,
+ntt12_r2_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix2,1,5,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.015473,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.265504,0.261408,,32,1073692673,30,6,4,256,0,4136333.727147,117997.441139,16942422946.393141,shoup
+fwht15_warp_b256,fwht15-batch256,full,butterfly,cuButterfly-warp-register,0,2,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.106988,2392802.426693,588.055124,78407349917.889481,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,5.450784,5.099712,0.000000,,,,,,,,,,,
+fft18_cub_b64,fft18-batch64,full,butterfly,cuButterfly-cuFFTDx-online,0,5,64,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,64,1000,100,,0.840612,76135.017716,179.625043,19958338084.217491,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,21.583809,20.139809,0.000000,,,,,,,,,,,
+ntt16_r4_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,2,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.069466,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,21.612415,36.639874,,64,1152921504606584833,60,8,4,256,0,239371.879838,4315.448900,15687475517.039173,shoup
+xor8_r4_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix4,0,3,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.014909,274725262.719901,281.318669,70329667256.294724,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.747904,0.718976,0.000000,,,,,,,,,,,
+fft8_vkfft_b256,fft8-batch256,full,fft-library,VkFFT,0,3,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,256,1000,100,199.361735000,0.002775040,92250922.858236462,94.464945007,23616236251.708534241,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b2,ntt20-batch2,full,ntt,cuNTT-compact-stage,0,2,2,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,2,1000,100,,0.179743,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.760128,2.593504,,64,1152921504577486849,60,0,0,256,0,11127.015096,361.443081,11667520981.048271,shoup
+fwht15_online_b256,fwht15-batch256,full,butterfly,cuButterfly-online-radix4,0,3,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.625777,409091.647323,100.538363,13405115099.485559,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,5.458400,5.117888,0.000000,,,,,,,,,,,
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015534,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.118976,0.137984,,64,1152921504606584833,60,8,4,256,0,64374.585661,3669.804628,4218852845.900787,shoup
+fwht8_shared_b4096,fwht8-batch4096,full,butterfly,cuButterfly-shared-radix4,0,2,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.014920,274536709.289986,281.125590,70281397578.236298,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.760096,0.740704,0.000000,,,,,,,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.319140,12533.690630,131.425272,13142527186.235754,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.759584,2.595040,0.000000,,,,,,,,,,,
+xor8_r4_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix4,0,1,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.175114,374247142.873165,383.229074,95807268575.530197,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.850400,10.111456,0.000000,,,,,,,,,,,
+ntt16_r2_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix2,0,4,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.160625,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.766432,2.618944,,64,1152921504606584833,60,8,4,256,0,199222.238622,5769.923630,13056228630.325594,shoup
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.007066,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.010240,0.021376,,32,1073692673,30,6,4,256,0,141530.792095,25852.084239,579710124.422693,shoup
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.306033,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.449632,5.110496,,64,1152921504606584833,60,8,4,256,0,209128.028131,5889.844715,13705414451.604485,shoup
+fft18_cufft_b64,fft18-batch64,full,fft-library,cuFFT,1,2,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,64,1000,100,2.026120000,0.706201613,90625.678030826,213.812799675,23756977741.712951660,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b2,fft20-batch2,full,fft-library,cuFFT,1,3,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,2,1000,100,1.895780000,0.123269118,16224.663780098,170.127930479,17012793047.879583359,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4,xor8-batch4,full,butterfly,cuButterfly-radix2,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002867,1395089.198606,1.428571,357142834.843162,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.011264,0.018048,0.000000,,,,,,,,,,,
+fft14_vkfft_b1024,fft14-batch1024,full,fft-library,VkFFT,0,5,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1024,1000,100,367.277106000,0.657070100,1558433.414518233,178.733611444,25533373063.466728210,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b64,fft18-batch64,full,butterfly,cuButterfly-cuFFTDx-online,0,1,64,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,64,1000,100,,0.840202,76172.133946,179.712611,19968067881.196533,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,21.617376,20.136127,0.000000,,,,,,,,,,,
+fft14_vkfft_b4,fft14-batch4,full,fft-library,VkFFT,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,4,1000,100,309.991559000,0.008478720,471769.338076766,54.106281845,7729468835.049730301,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix2,0,5,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.180631,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.588800,20.149759,,64,1152921504606584833,60,8,4,256,0,216833.194280,5964.697736,14210380220.313087,shoup
+fwht20_hier_b2,fwht20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,5,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.257311,7772.703808,81.502707,8150270668.365856,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.420256,1.341472,0.000000,,,,,,,,,,,
+fwht8_shared_b16,fwht8-batch16,full,butterfly,cuButterfly-shared-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002519,6351625.674184,6.504065,1626016172.591029,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.019328,0.000000,,,,,,,,,,,
+fft8_vkfft_b256,fft8-batch256,full,fft-library,VkFFT,0,2,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,256,1000,100,153.458441000,0.002734080,93632960.273815826,95.880151320,23970037830.096851349,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,5,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,256,1000,100,365.801683000,0.171663359,1491290.871728651,171.033167497,24433309642.402217865,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix4,0,5,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.013865,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.246304,0.274240,,32,1073692673,30,6,4,256,0,4615952.869097,119758.472884,18906942951.819283,shoup
+fft18_cub_b64,fft18-batch64,full,butterfly,cuButterfly-cuFFTDx-online,0,3,64,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,64,1000,100,,0.846182,75633.810807,178.442547,19826949700.273411,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,21.601601,20.135489,0.000000,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,4,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002929,21853146.890947,22.377622,5594405604.082486,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.033792,0.031296,0.000000,,,,,,,,,,,
+fft20_cufft_b16,fft20-batch16,full,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,16,1000,100,2.015873000,0.720691204,22200.909223838,232.793405903,23279340590.295482635,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.008458,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.068160,0.088640,,32,1073692673,30,6,4,256,0,1891646.498566,96818.171036,7748184058.128383,shoup
+ntt12_r2_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix2,1,2,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.640614,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.877056,10.114240,,32,1073692673,30,6,4,256,0,6393861.988666,189349.898423,26189258705.576973,shoup
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,2,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.065659,1949469.677119,479.101668,63880222379.822678,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,2.771296,2.596864,0.000000,,,,,,,,,,,
+xor8_r2_b256,xor8-batch256,full,butterfly,cuButterfly-radix2,0,4,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.003297,77639750.268576,79.503104,19875776068.755539,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.071968,0.082336,0.000000,,,,,,,,,,,
+fwht8_shared_b4,fwht8-batch4,full,butterfly,cuButterfly-shared-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002509,1594387.748030,1.632653,408163263.495648,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.020320,0.000000,,,,,,,,,,,
+fft18_vkfft_b8,fft18-batch8,full,fft-library,VkFFT,0,5,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,8,1000,100,330.592211000,0.111503363,71746.715161468,169.271738094,18807970899.287761688,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b8,fft20-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,5,8,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,8,1000,100,,0.457257,17495.632601,183.455004,18345500449.824474,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,10.821088,10.107264,0.000000,,,,,,,,,,,
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,16,1000,100,2.009549000,0.210943997,75849.515675521,178.951458935,19883495437.243804932,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix2,0,1,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.016077,254777078.271001,260.891728,65222932037.376183,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.750496,0.715264,0.000000,,,,,,,,,,,
+fft14_cufft_b1024,fft14-batch1024,full,fft-library,cuFFT,1,2,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1024,1000,100,2.205244000,0.406661123,2518067.112862372,288.792081040,41256011577.137100220,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,1,1000,100,2.243594000,0.023009282,43460.722379170,102.536708466,11392967607.365135193,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,4,1000,100,2.100291000,0.068608001,58302.238062814,137.552237053,15283581894.738397598,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b1024,fwht8-batch1024,full,butterfly,cuButterfly-warp-register,0,1,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.003533,289855062.211347,296.811584,74202895926.104736,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.267712,0.276192,0.000000,,,,,,,,,,,
+fft8_cub_b4096,fft8-batch4096,full,butterfly,cuButterfly-cuFFTDx,0,5,4096,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4096,1000,100,,0.022159,184842880.636303,189.279110,47319777442.893654,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,1.433184,1.348288,0.000000,,,,,,,,,,,
+fft8_cufft_b4096,fft8-batch4096,full,fft-library,cuFFT,1,3,4096,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4096,1000,100,2.152950000,0.022128640,185099493.128369719,189.541880963,47385470240.862648010,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b64,fft14-batch64,full,fft-library,VkFFT,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,64,1000,100,449.239941000,0.047185920,1356336.800413441,155.555554966,22222222137.973819733,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b1024,fft14-batch1024,full,fft-library,cuFFT,1,1,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1024,1000,100,1.931934000,0.406333417,2520097.924299232,289.024990742,41289284391.718612671,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,4,1000,100,794.380917000,0.206376955,19382.009012021,203.235094818,20323509481.789348602,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b1024,fft8-batch1024,full,fft-library,VkFFT,0,2,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1024,1000,100,286.513597000,0.005785600,176991156.053279012,181.238943799,45309735949.639427185,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b16,fwht8-batch16,full,butterfly,cuButterfly-warp-register,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002386,6706008.826393,6.866953,1716738259.556526,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.021504,0.023712,0.000000,,,,,,,,,,,
+fft20_cufft_b2,fft20-batch2,full,fft-library,cuFFT,1,2,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,2,1000,100,2.311287000,0.123197444,16234.103067254,170.226908578,17022690857.848501205,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,4,1000,100,2.028107000,0.210186228,19030.742570962,199.551799221,19955179922.088901520,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b2,fft18-batch2,full,fft-library,VkFFT,0,4,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,2,1000,100,333.863905000,0.023592960,84771.050025840,199.999999242,22222222137.973819733,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_hier_b2,xor20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,2,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.256809,7787.890073,81.661946,8166194620.899263,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.435904,1.341152,0.000000,,,,,,,,,,,
+fft8_vkfft_b4,fft8-batch4,full,fft-library,VkFFT,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4,1000,100,153.806448000,0.002355200,1698369.561110481,1.739130431,434782607.644283175,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016394,60997.037126,143.910066,15990007300.422764,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.426720,0.402464,0.000000,,,,,,,,,,,
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,3,16384,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16384,1000,100,1.858130000,0.083752960,195622936.867212325,200.317887352,50079471838.006355286,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b1024,fft8-batch1024,full,butterfly,cuButterfly-cuFFTDx,0,3,1024,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1024,1000,100,,0.005161,198412702.136058,203.174607,50793651746.830963,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.442080,0.408896,0.000000,,,,,,,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,4,1000,100,1.957991000,0.068495363,58398.113755116,137.778436190,15308715132.221189499,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b8,ntt20-batch8,full,ntt,cuNTT-compact-stage,0,3,8,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,8,1000,100,,0.665539,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.853152,10.116896,,64,1152921504577486849,60,0,0,256,0,12020.340530,369.761180,12604240591.728161,shoup
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,5,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,64,1000,100,152.502486000,0.002478080,25826447.632269472,26.446282375,6611570593.860984802,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b16,fft8-batch16,full,fft-library,cuFFT,1,5,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16,1000,100,1.756464000,0.002703360,5918560.498664911,6.060605951,1515151487.658217192,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,5,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.164413,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.840512,2.620896,,32,1073692673,30,6,4,256,0,6228201.399743,182017.859303,25510712933.346226,shoup
+ntt16_r4_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix4,0,5,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.149668,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.770624,2.603232,,64,1152921504606584833,60,8,4,256,0,213806.802404,5793.403265,14012042602.320700,shoup
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,2,16384,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16384,1000,100,1.907535000,0.083793916,195527322.502769470,200.219978243,50054994560.708984375,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b65536,fwht8-batch65536,full,butterfly,cuButterfly-shared-radix4,0,2,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.177408,369408349.069895,378.274149,94568537361.893219,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.905472,10.114464,0.000000,,,,,,,,,,,
+fwht8_warp_b1024,fwht8-batch1024,full,butterfly,cuButterfly-warp-register,0,4,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.003523,290697674.383976,297.674419,74418604642.297852,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.255232,0.250624,0.000000,,,,,,,,,,,
+ntt16_r2_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix2,0,4,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.180733,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.649343,20.147648,,64,1152921504606584833,60,8,4,256,0,216814.389114,5956.574045,14209147804.966326,shoup
+fft8_cufft_b65536,fft8-batch65536,full,fft-library,cuFFT,1,1,65536,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,65536,1000,100,1.879631000,0.327024639,200400802.428770065,205.210421687,51302605421.765136719,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b8,fft20-batch8,full,fft-library,VkFFT,0,3,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,8,1000,100,803.854927000,0.384286731,20817.788761942,218.290336688,21829033668.841880798,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b8,fft20-batch8,full,fft-library,VkFFT,0,2,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,8,1000,100,802.906926000,0.384266257,20818.897960235,218.301967476,21830196747.551002502,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_hier_b16,xor20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.863956,8583.891532,90.008626,9000862647.437197,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.894240,18.663584,0.000000,,,,,,,,,,,
+xor20_online_b16,xor20-batch16,full,butterfly,cuButterfly-online-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.233715,12968.957749,135.989378,13598937841.128448,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.881024,10.125472,0.000000,,,,,,,,,,,
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,4,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.047831,342539071.752609,350.760009,87690002368.667984,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.794560,2.596768,0.000000,,,,,,,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.007629,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.069344,0.081888,,32,1073692673,30,6,4,256,0,2097315.340721,100717.107656,8590603635.593691,shoup
+fft8_cufft_b256,fft8-batch256,full,fft-library,cuFFT,1,1,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,256,1000,100,2.088290000,0.003164160,80906147.196269244,82.847894729,20711973682.244926453,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b4,xor8-batch4,full,butterfly,cuButterfly-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002499,1600922.203814,1.639344,409836084.176348,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.009216,0.017856,0.000000,,,,,,,,,,,
+fwht15_online_b32,fwht15-batch32,full,butterfly,cuButterfly-online-radix4,0,4,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.084419,379063.538770,93.158655,12421154038.414652,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.745792,0.707840,0.000000,,,,,,,,,,,
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015872,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.118400,0.136736,,64,1152921504606584833,60,8,4,256,0,63004.033110,3689.927900,4129032313.916736,shoup
+fwht20_hier_b16,fwht20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.868196,8564.412916,89.804378,8980437837.359671,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.882624,17.038944,0.000000,,,,,,,,,,,
+fft18_cufft_b32,fft18-batch32,full,fft-library,cuFFT,1,1,32,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,32,1000,100,14.282198000,0.378664970,84507.420811517,199.378019891,22153113321.214225769,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b4,fwht15-batch4,full,butterfly,cuButterfly-online-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.015299,261462.528177,64.257031,8567604123.318477,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.124800,0.138944,0.000000,,,,,,,,,,,
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,5,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,64,1000,100,1.697094000,0.002723840,23496242.046643574,24.060151856,6015037963.940754890,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b8,fft20-batch8,full,fft-library,VkFFT,0,4,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,8,1000,100,791.670710000,0.385034263,20777.371693843,217.866533012,21786653301.242778778,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b256,fwht8-batch256,full,butterfly,cuButterfly-shared-radix4,0,3,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002959,86505193.150089,88.581318,22145329446.422657,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.072576,0.073504,0.000000,,,,,,,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,4,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,4,1000,100,1.995647000,0.210339829,19016.845325127,199.406076036,19940607603.640411377,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,5,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,4,1000,100,1.907869000,0.068567045,58337.062623541,137.634398499,15292710944.385543823,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.042762,383141742.224474,392.337144,98084286009.465363,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,2.772576,2.595040,0.000000,,,,,,,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.049715,329557167.006086,337.466539,84366634753.558136,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.777216,2.595168,0.000000,,,,,,,,,,,
+fft8_vkfft_b65536,fft8-batch65536,full,fft-library,VkFFT,0,4,65536,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,65536,1000,100,204.330152000,0.326215655,200897777.508658201,205.719324169,51429831042.216499329,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,2,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.316180,404832.091525,99.491535,13265537975.078365,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,2.769952,2.593760,0.000000,,,,,,,,,,,
+fft8_cub_b4,fft8-batch4,full,butterfly,cuButterfly-cuFFTDx,0,2,4,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4,1000,100,,0.003072,1302083.287278,1.333333,333333321.543049,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.009216,0.018048,0.000000,,,,,,,,,,,
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,1,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,256,1000,100,,0.121211,2112021.617038,242.223535,34603362173.546928,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,5.564672,5.103712,0.000000,,,,,,,,,,,
+fwht15_warp_b4,fwht15-batch4,full,butterfly,cuButterfly-warp-register,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.017654,226580.631983,55.684456,7424594148.811483,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.133632,0.146752,0.000000,,,,,,,,,,,
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,4,1000,100,,0.341576,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.499840,5.096288,,64,1152921504577486849,60,0,0,256,0,11710.434495,365.707475,12279280560.858164,shoup
+fft8_vkfft_b256,fft8-batch256,full,fft-library,VkFFT,0,4,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,256,1000,100,153.188041000,0.002836480,90252706.364468172,92.418771317,23104692829.303852081,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,1,1000,100,777.185150000,0.062126078,16096.300246773,168.781941276,16878194127.560600281,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b4,fft8-batch4,full,butterfly,cuButterfly-cuFFTDx,0,1,4,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4,1000,100,,0.003082,1297757.474928,1.328904,332225913.581687,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.009216,0.016384,0.000000,,,,,,,,,,,
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,16,1000,100,,0.205097,78011.888412,184.053136,20450348475.903534,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,5.488896,5.092736,0.000000,,,,,,,,,,,
+xor8_r4_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix4,0,5,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.175176,374115855.352586,383.094636,95773658970.262009,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.850080,10.113728,0.000000,,,,,,,,,,,
+fwht8_shared_b4,fwht8-batch4,full,butterfly,cuButterfly-shared-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002488,1607510.291372,1.646091,411522634.591321,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.012288,0.018176,0.000000,,,,,,,,,,,
+xor20_online_b16,xor20-batch16,full,butterfly,cuButterfly-online-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.231851,12988.579012,136.195122,13619512225.731428,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.872192,10.116800,0.000000,,,,,,,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,1,1000,100,778.775030000,0.060897280,16421.094796112,172.187658969,17218765896.927928925,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b256,fft8-batch256,full,butterfly,cuButterfly-cuFFTDx,0,5,256,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,256,1000,100,,0.003348,76452599.873783,78.287462,19571865567.688519,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.123360,0.143264,0.000000,,,,,,,,,,,
+xor8_r4_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix4,0,1,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.014807,276625175.285544,283.264179,70816044873.099319,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.762656,0.723520,0.000000,,,,,,,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.005990,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.011264,0.020608,,32,1073692673,30,6,4,256,0,166933.774244,26411.426599,683760739.303273,shoup
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.087163,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.428992,1.347264,,64,1152921504606584833,60,8,4,256,0,183564.390989,5587.725802,12030075927.881510,shoup
+fwht8_warp_b4096,fwht8-batch4096,full,butterfly,cuButterfly-warp-register,0,4,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.011254,363967236.600450,372.702450,93175612569.715088,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.750240,0.719040,0.000000,,,,,,,,,,,
+fft18_vkfft_b2,fft18-batch2,full,fft-library,VkFFT,0,5,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,2,1000,100,333.265976000,0.023572480,84844.699159148,200.173759347,22241528816.375705719,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.047790,342832652.594307,351.060636,87765159064.142548,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.805152,2.592160,0.000000,,,,,,,,,,,
+fft18_cub_b32,fft18-batch32,full,butterfly,cuButterfly-cuFFTDx-online,0,2,32,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,32,1000,100,,0.411003,77858.336268,183.690861,20410095702.539227,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,10.876608,10.131296,0.000000,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002058,485851.961873,0.497512,124378102.239416,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.014336,0.015360,0.000000,,,,,,,,,,,
+xor8_r4_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix4,0,3,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.175124,374225265.835313,383.206672,95801668053.840210,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.880640,10.113984,0.000000,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,4,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.048415,338409460.891576,346.531288,86632821988.243362,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.761824,2.591968,0.000000,,,,,,,,,,,
+fwht20_hier_b16,fwht20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.867960,8565.492377,89.815697,8981569734.756124,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.852704,17.565536,0.000000,,,,,,,,,,,
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.082299,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,1.412512,1.340608,,64,1152921504606584833,60,8,4,256,0,194413.332864,5642.905324,12741072182.560717,shoup
+fwht20_hier_b16,fwht20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.868360,8563.661552,89.796500,8979649975.963535,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.872320,18.362623,0.000000,,,,,,,,,,,
+fwht20_hier_b2,fwht20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,4,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.257454,7768.376005,81.457326,8145732637.358406,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.419584,1.345632,0.000000,,,,,,,,,,,
+fft14_vkfft_b1024,fft14-batch1024,full,fft-library,VkFFT,0,1,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1024,1000,100,365.568420000,0.656998396,1558603.500951318,178.753118317,25536159759.586391449,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.007629,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.067584,0.079104,,32,1073692673,30,6,4,256,0,2097315.340721,103682.813728,8590603635.593691,shoup
+fft8_cufft_b16,fft8-batch16,full,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16,1000,100,1.758002000,0.002693120,5941064.805303289,6.083650361,1520912590.157641888,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix2,1,4,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.640307,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.881152,18.234016,,32,1073692673,30,6,4,256,0,6396928.997923,137655.335270,26201821175.490826,shoup
+fft18_cub_b32,fft18-batch32,full,butterfly,cuButterfly-cuFFTDx-online,0,3,32,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,32,1000,100,,0.411238,77813.744617,183.585656,20398406268.937222,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,10.854944,10.108576,0.000000,,,,,,,,,,,
+fft14_cub_b1024,fft14-batch1024,full,butterfly,cuButterfly-cuFFTDx-direct,0,2,1024,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1024,1000,100,,0.379679,2697017.055074,309.315492,44187927430.325378,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,21.667744,20.134720,0.000000,,,,,,,,,,,
+xor8_r4_b16,xor8-batch16,full,butterfly,cuButterfly-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002519,6351625.674184,6.504065,1626016172.591029,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.016384,0.020864,0.000000,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.098120,10191.635762,106.867047,10686704660.449831,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.743840,0.719744,0.000000,,,,,,,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,1,1000,100,778.720222000,0.061040640,16382.528132238,171.783258188,17178325818.789716721,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,4,1000,100,,0.059709,66991.081119,158.051790,17561309968.745327,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,1.420704,1.336288,0.000000,,,,,,,,,,,
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,16,1000,100,329.649475000,0.201134071,79548.929428098,187.679471004,20853274555.999202728,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,1,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,64,1000,100,1.779375000,0.002734080,23408240.068453956,23.970037830,5992509457.524212837,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b8,fft20-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,1,8,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,8,1000,100,,0.454349,17607.617660,184.629253,18462925295.751591,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,10.820064,10.108736,0.000000,,,,,,,,,,,
+xor20_online_b16,xor20-batch16,full,butterfly,cuButterfly-online-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.231995,12987.067093,136.179269,13617926863.957056,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.857408,10.111168,0.000000,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,4,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,1,1000,100,,0.071066,14071.504836,147.550423,14755042254.578821,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,1.413408,1.342336,0.000000,,,,,,,,,,,
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.006871,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.010240,0.020000,,32,1073692673,30,6,4,256,0,145538.376000,26946.159945,596125188.097195,shoup
+xor8_r2_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix2,0,3,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.178954,366216518.030852,375.005714,93751428615.898071,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.838816,10.110848,0.000000,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,5,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,256,1000,100,1.862628000,0.121425927,2108281.212985148,241.794555755,34542079393.548660278,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,5,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002908,22007042.414798,22.535211,5633802858.188319,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.033792,0.031904,0.000000,,,,,,,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.007608,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.069728,0.074048,,32,1073692673,30,6,4,256,0,2102960.941855,105691.263386,8613728017.836378,shoup
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002550,25100401.177010,25.702811,6425702701.314640,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.032768,0.031200,0.000000,,,,,,,,,,,
+fft8_vkfft_b16,fft8-batch16,full,fft-library,VkFFT,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16,1000,100,151.912052000,0.002355200,6793478.244441925,6.956521722,1739130430.577132702,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,2,256,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,256,1000,100,365.318591000,0.171622396,1491646.817020254,171.073990150,24439141450.059841156,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b2,fft18-batch2,full,fft-library,cuFFT,1,5,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,2,1000,100,1.956012000,0.028098559,71178.027296642,167.930035089,18658892787.650810242,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix4,0,4,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.014817,276434005.793990,283.068422,70767105483.261551,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.744928,0.714304,0.000000,,,,,,,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.005990,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.013312,0.021248,,32,1073692673,30,6,4,256,0,166933.774244,24660.669736,683760739.303273,shoup
+fft20_cub_b8,fft20-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,3,8,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,8,1000,100,,0.456919,17508.573176,183.590696,18359069626.432838,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,10.835840,10.107776,0.000000,,,,,,,,,,,
+fwht8_warp_b256,fwht8-batch256,full,butterfly,cuButterfly-warp-register,0,4,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002417,105932201.003720,108.474574,27118643456.952290,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.076736,0.091424,0.000000,,,,,,,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1,1000,100,2.183056000,0.011898880,84041.523990662,9.638554303,1376936329.063012838,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.099645,10035.581832,105.230703,10523070254.772758,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.751680,0.725856,0.000000,,,,,,,,,,,
+fft14_cub_b4,fft14-batch4,full,butterfly,cuButterfly-cuFFTDx-direct,0,2,4,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,4,1000,100,,0.020572,194437.536409,22.299652,3185664596.528583,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.138304,0.127136,0.000000,,,,,,,,,,,
+fft18_vkfft_b2,fft18-batch2,full,fft-library,VkFFT,0,1,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,2,1000,100,330.274125000,0.023582721,84807.855253629,200.086833668,22231870407.607307434,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,4,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,256,1000,100,,0.121211,2112021.617038,242.223535,34603362173.546928,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,5.518208,5.099776,0.000000,,,,,,,,,,,
+fft18_cufft_b32,fft18-batch32,full,fft-library,cuFFT,1,4,32,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,32,1000,100,2.017614000,0.378296316,84589.774402967,199.572316390,22174701821.091362000,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,5,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002540,25201613.706232,25.806452,6451613108.795465,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.040960,0.032864,0.000000,,,,,,,,,,,
+fwht15_online_b4,fwht15-batch4,full,butterfly,cuButterfly-online-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.015299,261462.528177,64.257031,8567604123.318477,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.127392,0.135552,0.000000,,,,,,,,,,,
+fwht15_warp_b512,fwht15-batch512,full,butterfly,cuButterfly-warp-register,0,2,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,0.193004,2652801.353155,651.952461,86926994740.188644,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,10.915808,10.128736,0.000000,,,,,,,,,,,
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.007690,130034.950633,31.957389,4260985262.351007,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.054656,0.051552,0.000000,,,,,,,,,,,
+fft8_cufft_b4,fft8-batch4,full,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4,1000,100,2.069370000,0.002682880,1490935.225661013,1.526717671,381679417.769219339,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b4,fwht8-batch4,full,butterfly,cuButterfly-warp-register,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002130,1878004.754952,1.923077,480769217.267675,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.015360,0.017024,0.000000,,,,,,,,,,,
+xor8_r4_b16,xor8-batch16,full,butterfly,cuButterfly-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002540,6300403.426558,6.451613,1612903277.198866,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.022528,0.025056,0.000000,,,,,,,,,,,
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.095283,10495.029243,110.048358,11004835783.113758,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.765952,0.719456,0.000000,,,,,,,,,,,
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,5,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.008919,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.071520,0.092832,,32,1073692673,30,6,4,256,0,1793915.092245,92340.878465,7347876217.836832,shoup
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.008909,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.068960,0.082176,,32,1073692673,30,6,4,256,0,1795977.041844,99972.005786,7356321963.394614,shoup
+fwht20_online_b16,fwht20-batch16,full,butterfly,cuButterfly-online-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.232763,12978.975580,136.094423,13609442297.393764,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.892480,10.119360,0.000000,,,,,,,,,,,
+fft8_cub_b1024,fft8-batch1024,full,butterfly,cuButterfly-cuFFTDx,0,4,1024,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1024,1000,100,,0.005161,198412702.136058,203.174607,50793651746.830963,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.430016,0.400928,0.000000,,,,,,,,,,,
+ntt16_r2_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix2,0,3,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.591196,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.859936,10.119424,,64,1152921504606584833,60,8,4,256,0,216510.194860,5934.014921,14189212130.322083,shoup
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.279286,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,5.489024,5.103680,,64,1152921504606584833,60,8,4,256,0,229155.973760,5886.686768,15017965896.351137,shoup
+fft18_cufft_b2,fft18-batch2,full,fft-library,cuFFT,1,4,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,2,1000,100,2.008493000,0.028866561,69284.317969659,163.462214249,18162468249.838409424,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix2,1,5,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.637164,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.890080,17.806593,,32,1073692673,30,6,4,256,0,6428491.073852,139633.966471,26331099438.499584,shoup
+ntt12_r2_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix2,1,5,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.050463,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.797248,0.721536,,32,1073692673,30,6,4,256,0,5073052.043251,163135.598171,20779221169.158119,shoup
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,1,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,64,1000,100,,0.003103,20627062.595822,21.122112,5280528024.530542,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.038432,0.041696,0.000000,,,,,,,,,,,
+fft20_vkfft_b2,fft20-batch2,full,fft-library,VkFFT,0,3,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,2,1000,100,789.587485000,0.117831677,16973.364442843,177.978625940,17797862594.018119812,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b4,fft14-batch4,full,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,4,1000,100,310.490018000,0.008488961,471200.209940766,54.041009678,7720144239.669502258,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix2,0,5,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.591391,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.839584,10.113536,,64,1152921504606584833,60,8,4,256,0,216438.969591,5941.188465,14184544311.147171,shoup
+fft18_vkfft_b32,fft18-batch32,full,fft-library,VkFFT,0,2,32,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,32,1000,100,333.825680000,0.372490227,85908.294127916,202.683094703,22520343855.868507385,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.007639,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.067872,0.075264,,32,1073692673,30,6,4,256,0,2094504.083552,106118.358839,8579088726.229346,shoup
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,4,16384,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16384,1000,100,205.230538000,0.083548166,196102449.787914634,200.808908583,50202227145.706146240,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix2,0,1,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.182228,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.613567,35.357601,,64,1152921504606584833,60,8,4,256,0,216540.213412,4402.150405,14191179426.166384,shoup
+fft18_vkfft_b2,fft18-batch2,full,fft-library,VkFFT,0,2,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,2,1000,100,330.931013000,0.023695359,84404.713996920,199.135704114,22126189346.008510590,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b16,fft20-batch16,full,fft-library,cuFFT,1,5,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,16,1000,100,2.025095000,0.721612751,22172.557188184,232.496113262,23249611326.157279968,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b8,fft20-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,4,8,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,8,1000,100,,0.455567,17560.520581,184.135404,18413540428.782261,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,10.859424,10.106624,0.000000,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.098181,10185.257505,106.800166,10680016573.165754,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.758336,0.719680,0.000000,,,,,,,,,,,
+fft20_cufft_b2,fft20-batch2,full,fft-library,cuFFT,1,1,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,2,1000,100,1.999634000,0.123228163,16230.056173729,170.184473824,17018447382.424180984,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b8,fwht20-batch8,full,butterfly,cuButterfly-online-radix4,0,3,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.624742,12805.278054,134.273072,13427307241.175114,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.466112,5.100416,0.000000,,,,,,,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.319857,12505.602366,131.130745,13113074506.711510,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.793280,2.596480,0.000000,,,,,,,,,,,
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,1,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.165765,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.804480,2.591616,,32,1073692673,30,6,4,256,0,6177415.865868,184111.034417,25302695386.594471,shoup
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,2,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16384,1000,100,,0.084275,194410690.366544,199.076547,49769136733.835213,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,5.489440,5.094752,0.000000,,,,,,,,,,,
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,5,16384,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16384,1000,100,205.479400000,0.083568640,196054404.972436339,200.759710692,50189927672.943702698,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.090030,11107.398578,116.469516,11646951571.214386,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.765248,0.728832,0.000000,,,,,,,,,,,
+fft20_cub_b2,fft20-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,1,2,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,2,1000,100,,0.128788,15529.338532,162.836917,16283691680.292921,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,2.758848,2.588064,0.000000,,,,,,,,,,,
+xor8_r2_b16,xor8-batch16,full,butterfly,cuButterfly-radix2,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002898,5521201.247711,5.653710,1413427519.414016,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.017408,0.023712,0.000000,,,,,,,,,,,
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.042772,383050041.684253,392.243243,98060810671.168701,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,2.779296,2.602848,0.000000,,,,,,,,,,,
+xor20_hier_b8,xor20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,3,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.945766,8458.748471,88.696406,8869640636.720224,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.463520,5.107904,0.000000,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,5,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,4,1000,100,,0.059505,67221.649324,158.595768,17621752040.261051,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,1.417344,1.341024,0.000000,,,,,,,,,,,
+xor8_r4_b4,xor8-batch4,full,butterfly,cuButterfly-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002499,1600922.203814,1.639344,409836084.176348,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.009216,0.017056,0.000000,,,,,,,,,,,
+ntt12_r2_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix2,1,2,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.015452,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.257248,0.272288,,32,1073692673,30,6,4,256,0,4141815.887649,117433.742071,16964877875.811838,shoup
+fft18_vkfft_b32,fft18-batch32,full,fft-library,VkFFT,0,5,32,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,32,1000,100,332.874404000,0.372121572,85993.402063441,202.883889515,22542654390.518653870,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix2,0,4,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.594565,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.870240,10.118720,,64,1152921504606584833,60,8,4,256,0,215283.387074,5930.449151,14108812055.252514,shoup
+ntt16_r4_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix4,0,3,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.149043,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.762560,2.611936,,64,1152921504606584833,60,8,4,256,0,214702.847796,5793.386980,14070765833.176165,shoup
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,4,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.042762,383141742.224474,392.337144,98084286009.465363,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,2.768672,2.599136,0.000000,,,,,,,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.017746,56350.982464,13.848817,1846508993.387821,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.041408,0.051040,0.000000,,,,,,,,,,,
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.007731,129346.031004,31.788081,4238410743.943443,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.043200,0.048064,0.000000,,,,,,,,,,,
+fft14_cub_b1024,fft14-batch1024,full,butterfly,cuButterfly-cuFFTDx-direct,0,4,1024,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1024,1000,100,,0.380150,2693675.307895,308.932234,44133176244.559357,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,21.683456,20.133600,0.000000,,,,,,,,,,,
+fft14_cub_b1024,fft14-batch1024,full,butterfly,cuButterfly-cuFFTDx-direct,0,1,1024,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1024,1000,100,,0.380078,2694183.277369,308.990492,44141498816.409615,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,21.701696,20.134176,0.000000,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.487014,8213.309789,86.122795,8612279525.492992,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.798336,2.604512,0.000000,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.098212,10182.071755,106.766761,10676676072.737425,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.752608,0.711360,0.000000,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.320901,12464.899782,130.703948,13070394754.078093,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.796768,2.592736,0.000000,,,,,,,,,,,
+fft8_vkfft_b4096,fft8-batch4096,full,fft-library,VkFFT,0,3,4096,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4096,1000,100,204.810619000,0.020244479,202326765.915099829,207.182608297,51795652074.265556335,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix4,0,4,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004342,235849046.575243,241.509424,60377355923.262245,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.241568,0.304864,0.000000,,,,,,,,,,,
+fwht20_online_b8,fwht20-batch8,full,butterfly,cuButterfly-online-radix4,0,1,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.625510,12789.555648,134.108211,13410821103.498339,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.492896,5.102528,0.000000,,,,,,,,,,,
+fft18_cub_b2,fft18-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,5,2,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,2,1000,100,,0.025969,77015.972463,181.703476,20189275085.407219,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.743040,0.713920,0.000000,,,,,,,,,,,
+fft20_vkfft_b16,fft20-batch16,full,fft-library,VkFFT,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,16,1000,100,795.823178000,0.737474620,21695.661869116,227.495503401,22749550340.069816589,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.029430,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.411264,0.416224,,64,1152921504606584833,60,8,4,256,0,135916.841424,4667.892490,8907446119.579630,shoup
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,16,1000,100,,0.205087,78015.776781,184.062310,20451367788.510426,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,5.479360,5.090688,0.000000,,,,,,,,,,,
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.487977,8197.108684,85.952914,8595291435.313353,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.769024,2.595296,0.000000,,,,,,,,,,,
+fft8_vkfft_b4096,fft8-batch4096,full,fft-library,VkFFT,0,4,4096,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4096,1000,100,204.261096000,0.020223999,202531651.618665755,207.392411258,51848102814.378433228,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b4,fft14-batch4,full,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,4,1000,100,311.645146000,0.009973761,401052.333479375,45.995890022,6570841431.726085663,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b65536,fft8-batch65536,full,butterfly,cuButterfly-cuFFTDx,0,5,65536,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,65536,1000,100,,0.327608,200043743.122898,204.844793,51211198239.461929,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,21.642048,20.141665,0.000000,,,,,,,,,,,
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002560,24999998.357816,25.599998,6399999579.601017,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.039936,0.035456,0.000000,,,,,,,,,,,
+fft18_cub_b8,fft18-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,3,8,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,8,1000,100,,0.108780,73543.255339,173.510308,19278923127.494396,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,2.771872,2.592352,0.000000,,,,,,,,,,,
+fft8_cufft_b4096,fft8-batch4096,full,fft-library,cuFFT,1,4,4096,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4096,1000,100,1.860599000,0.022026241,185960011.625295311,190.423051904,47605762976.075599670,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b4,fft8-batch4,full,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4,1000,100,2.063129000,0.002682880,1490935.225661013,1.526717671,381679417.769219339,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b1024,fwht8-batch1024,full,butterfly,cuButterfly-shared-radix4,0,3,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.004352,235294113.520559,240.941172,60235293061.263023,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.257888,0.249760,0.000000,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,3,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,256,1000,100,1.895813000,0.121016324,2115417.097921162,242.612956126,34658993732.340316772,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.082258,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,1.415552,1.332768,,64,1152921504606584833,60,8,4,256,0,194510.147982,5652.555962,12747417058.142538,shoup
+fwht8_shared_b256,fwht8-batch256,full,butterfly,cuButterfly-shared-radix4,0,1,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002970,86206895.755522,88.275861,22068965313.413521,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.073760,0.075808,0.000000,,,,,,,,,,,
+ntt12_r4_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.006349,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.028672,0.037376,,32,1073692673,30,6,4,256,0,630040.331103,55251.059458,2580645196.197960,shoup
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.017613,56776.889528,13.953488,1860465116.057446,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.045152,0.051456,0.000000,,,,,,,,,,,
+ntt16_r4_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,4,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.068646,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,21.616064,35.929630,,64,1152921504606584833,60,8,4,256,0,239555.378263,4367.531846,15699501269.829201,shoup
+fft14_cufft_b4,fft14-batch4,full,fft-library,cuFFT,1,4,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,4,1000,100,1.909570000,0.012687360,315274.416427750,36.158192271,5165456038.752255440,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,5,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16384,1000,100,,0.084429,194057016.468198,198.714385,49678596215.858658,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,5.477280,5.096800,0.000000,,,,,,,,,,,
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.098499,10152.432635,106.455972,10645597202.665335,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.746400,0.709632,0.000000,,,,,,,,,,,
+fft20_cufft_b2,fft20-batch2,full,fft-library,cuFFT,1,5,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,2,1000,100,1.967163000,0.123135999,16242.203894540,170.311851909,17031185190.921493530,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002099,30487802.672495,31.219510,7804877484.158601,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.035840,0.034112,0.000000,,,,,,,,,,,
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,1,1000,100,1.929007000,0.022958081,43557.647113803,102.765382605,11418375845.000692368,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,5,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.049633,330101097.165784,338.023523,84505880874.440720,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.781600,2.592448,0.000000,,,,,,,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.049705,329625041.697651,337.536043,84384010674.598770,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.802464,2.591808,0.000000,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,1.798099000,0.002672640,374161.857641088,0.383141742,95785435.556118518,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b16,fft8-batch16,full,butterfly,cuButterfly-cuFFTDx,0,4,16,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16,1000,100,,0.003103,5156765.648956,5.280528,1320132006.132636,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.018432,0.023520,0.000000,,,,,,,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.005990,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.011264,0.020672,,32,1073692673,30,6,4,256,0,166933.774244,26366.858830,683760739.303273,shoup
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,1,1000,100,1.943633000,0.023183361,43134.384747742,101.766781398,11307420155.312124252,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b65536,fft8-batch65536,full,fft-library,VkFFT,0,3,65536,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,65536,1000,100,204.051509000,0.326072305,200986096.968231261,205.809763295,51452440823.867202759,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,4,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,4,1000,100,,0.235581,16979.266083,178.040509,17804050912.009365,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,5.448352,5.095168,0.000000,,,,,,,,,,,
+xor8_r4_b4,xor8-batch4,full,butterfly,cuButterfly-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002488,1607510.291372,1.646091,411522634.591321,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.014336,0.018240,0.000000,,,,,,,,,,,
+fwht8_shared_b4,fwht8-batch4,full,butterfly,cuButterfly-shared-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002488,1607510.291372,1.646091,411522634.591321,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.014336,0.019072,0.000000,,,,,,,,,,,
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.303698,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.453568,5.095584,,64,1152921504606584833,60,8,4,256,0,210735.704111,5897.068598,13810775104.610884,shoup
+fft8_cub_b16,fft8-batch16,full,butterfly,cuButterfly-cuFFTDx,0,1,16,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16,1000,100,,0.003103,5156765.648956,5.280528,1320132006.132636,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.019456,0.024992,0.000000,,,,,,,,,,,
+fwht20_online_b8,fwht20-batch8,full,butterfly,cuButterfly-online-radix4,0,5,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.627507,12748.857504,133.681460,13368146005.796450,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.472736,5.102240,0.000000,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,5,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.048507,337766530.617160,345.872927,86468231837.992966,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.766944,2.595104,0.000000,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,5,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016538,60468.268939,142.662545,15851393892.805090,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.437120,0.425568,0.000000,,,,,,,,,,,
+xor20_hier_b8,xor20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,1,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.945623,8460.030752,88.709852,8870985205.935963,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.493376,5.101760,0.000000,,,,,,,,,,,
+ntt16_r2_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix2,0,1,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.159222,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.764576,2.598592,,64,1152921504606584833,60,8,4,256,0,200977.544250,5794.592800,13171264339.969559,shoup
+xor20_hier_b16,xor20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.863813,8584.551460,90.015546,9001554631.874872,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.884864,17.916128,0.000000,,,,,,,,,,,
+fft14_vkfft_b64,fft14-batch64,full,fft-library,VkFFT,0,5,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,64,1000,100,367.300432000,0.047124483,1358105.094102854,155.758357032,22251193861.781162262,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b2,fft20-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,3,2,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,2,1000,100,,0.128553,15557.790543,163.135258,16313525776.483089,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,2.761952,2.587776,0.000000,,,,,,,,,,,
+fft8_cufft_b1024,fft8-batch1024,full,fft-library,cuFFT,1,3,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1024,1000,100,1.877949000,0.004526080,226244338.992537081,231.674203128,57918550782.089492798,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b16,xor8-batch16,full,butterfly,cuButterfly-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002529,6325911.445034,6.477733,1619433329.928803,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.019456,0.023136,0.000000,,,,,,,,,,,
+fft20_cufft_b16,fft20-batch16,full,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,16,1000,100,2.156916000,0.721326053,22181.369895478,232.588521195,23258852119.520637512,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b32,fft18-batch32,full,fft-library,cuFFT,1,5,32,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,32,1000,100,2.064544000,0.378736645,84491.428077713,199.340288298,22148920922.003925323,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b8,fft18-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,1,8,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,8,1000,100,,0.108585,73675.031457,173.821207,19313467446.171429,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,2.791584,2.585152,0.000000,,,,,,,,,,,
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,5,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1,1000,100,,0.020490,48803.722410,5.597201,799600187.972053,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.036320,0.043616,0.000000,,,,,,,,,,,
+fwht15_online_b32,fwht15-batch32,full,butterfly,cuButterfly-online-radix4,0,1,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.084255,379800.683682,93.339816,12445308802.885481,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.752192,0.712896,0.000000,,,,,,,,,,,
+xor8_r4_b256,xor8-batch256,full,butterfly,cuButterfly-radix4,0,5,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.002918,87719302.141174,89.824565,22456141348.140545,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.071040,0.076032,0.000000,,,,,,,,,,,
+fft8_cufft_b65536,fft8-batch65536,full,fft-library,cuFFT,1,5,65536,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,65536,1000,100,1.928911000,0.327004164,200413349.807823032,205.223270203,51305817550.802696228,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,3,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.316518,404399.875525,99.385313,13251375121.198767,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,2.764000,2.591424,0.000000,,,,,,,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,4,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.049715,329557167.006086,337.466539,84366634753.558136,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.779328,2.588864,0.000000,,,,,,,,,,,
+ntt16_r2_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix2,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.031549,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.419104,0.394720,,64,1152921504606584833,60,8,4,256,0,126785.139381,4731.636725,8308990894.504043,shoup
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1,1000,100,152.750610000,0.002314240,432107.305888526,0.442477881,110619470.307462543,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,4,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,1.800211000,0.002703360,369910.031166557,0.378787872,94696967.978638574,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b16,fft20-batch16,full,butterfly,cuButterfly-cuFFTDx-online,0,4,16,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,16,1000,100,,0.925174,17294.047530,181.341232,18134123182.337456,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,21.621857,20.142015,0.000000,,,,,,,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,5,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,4,1000,100,2.024669000,0.210319370,19018.695231940,199.425473715,19942547371.526767731,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix2,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.007158,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.027648,0.030432,,32,1073692673,30,6,4,256,0,558834.032510,61314.182739,2288984197.161271,shoup
+ntt16_r2_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix2,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.031478,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.416640,0.411104,,64,1152921504606584833,60,8,4,256,0,127073.843039,4655.375539,8327911377.425147,shoup
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.007690,130034.950633,31.957389,4260985262.351007,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.040480,0.048832,0.000000,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,1,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.317020,403759.788641,99.228006,13230400754.179016,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,2.759200,2.586304,0.000000,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.048456,338123403.520029,346.238365,86559591301.127380,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.769248,2.591712,0.000000,,,,,,,,,,,
+fft18_cufft_b8,fft18-batch8,full,fft-library,cuFFT,1,3,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,8,1000,100,1.973289000,0.122931205,65077.048721398,153.536020740,17059557860.022218704,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b8,fft20-batch8,full,fft-library,cuFFT,1,2,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,8,1000,100,2.033430000,0.381562889,20966.399612095,219.848634397,21984863439.651847839,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002038,490734.899789,0.502513,125628134.346072,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.011264,0.017216,0.000000,,,,,,,,,,,
+xor20_online_b8,xor20-batch8,full,butterfly,cuButterfly-online-radix4,0,2,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.623114,12838.737486,134.623920,13462391997.656811,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.455552,5.106880,0.000000,,,,,,,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1,1000,100,308.322928000,0.008263680,121011.459971133,13.878562321,1982651760.167040586,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,5,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.064840,1974099.931584,485.154799,64687306558.142281,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,2.766944,2.593952,0.000000,,,,,,,,,,,
+fft18_vkfft_b64,fft18-batch64,full,fft-library,VkFFT,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,64,1000,100,331.227481000,0.713953257,89641.722910754,211.491358296,23499039810.716648102,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b2,fft18-batch2,full,fft-library,cuFFT,1,2,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,2,1000,100,1.981419000,0.028047359,71307.962624846,168.236590989,18692954554.327716827,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b4,fft8-batch4,full,butterfly,cuButterfly-cuFFTDx,0,3,4,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4,1000,100,,0.003092,1293460.310041,1.324503,331125839.370581,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.009216,0.017952,0.000000,,,,,,,,,,,
+fwht20_hier_b2,fwht20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,1,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.257423,7769.302343,81.467040,8146703973.416983,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.425984,1.334656,0.000000,,,,,,,,,,,
+ntt12_r4_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix4,0,1,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.538552,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.882144,17.682465,,32,1073692673,30,6,4,256,0,7605574.549641,140740.726122,31152433355.330788,shoup
+fft8_cufft_b16,fft8-batch16,full,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16,1000,100,1.800817000,0.002703360,5918560.498664911,6.060605951,1515151487.658217192,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,4,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.184801,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.815456,2.615104,,32,1073692673,30,6,4,256,0,5541087.146354,182356.926278,22696292951.465446,shoup
+xor8_r4_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix4,0,4,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.175176,374115855.352586,383.094636,95773658970.262009,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.861888,10.112384,0.000000,,,,,,,,,,,
+fwht8_shared_b65536,fwht8-batch65536,full,butterfly,cuButterfly-shared-radix4,0,5,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.177336,369557716.112428,378.427101,94606775324.781662,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.867136,10.116064,0.000000,,,,,,,,,,,
+fwht8_warp_b1024,fwht8-batch1024,full,butterfly,cuButterfly-warp-register,0,5,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.003543,289017358.673715,295.953775,73988443820.470993,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.258528,0.249920,0.000000,,,,,,,,,,,
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,4,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,2.151710000,0.026163198,2446184.134993942,280.547966074,40078280867.740737915,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b4,fft8-batch4,full,butterfly,cuButterfly-cuFFTDx,0,5,4,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4,1000,100,,0.003082,1297757.474928,1.328904,332225913.581687,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.011264,0.019264,0.000000,,,,,,,,,,,
+xor8_r4_b1024,xor8-batch1024,full,butterfly,cuButterfly-radix4,0,3,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1024,1000,100,,0.004342,235849046.575243,241.509424,60377355923.262245,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.269568,0.280800,0.000000,,,,,,,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1,1000,100,388.347032000,0.008243200,121312.106368169,13.913042855,1987577550.736074924,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,1,16384,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16384,1000,100,204.546672000,0.083558396,196078441.920646042,200.784324527,50196081131.685386658,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b1024,fwht8-batch1024,full,butterfly,cuButterfly-warp-register,0,2,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.003553,288184445.471565,295.100872,73775218040.720596,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.261920,0.295392,0.000000,,,,,,,,,,,
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002898,345075.077982,0.353357,88339219.963376,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.011264,0.018560,0.000000,,,,,,,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,4,1000,100,2.217594000,0.068679683,58241.387124864,137.408671678,15267630186.460426331,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,16,1000,100,2.252269000,0.211118087,75786.969341599,178.803893620,19867099291.084243774,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_hier_b8,fwht20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,4,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.947692,8441.565634,88.516231,8851623126.666698,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.516032,5.109824,0.000000,,,,,,,,,,,
+fft18_cufft_b32,fft18-batch32,full,fft-library,cuFFT,1,3,32,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,32,1000,100,2.009781000,0.379176974,84393.310167013,199.108799104,22123199900.421504974,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,16,1000,100,1.988153000,0.013506561,1184609.501261122,135.860494481,19408642068.662227631,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b32,fft18-batch32,full,butterfly,cuButterfly-cuFFTDx-online,0,5,32,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,32,1000,100,,0.411300,77802.118451,183.558227,20395358539.212963,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,10.879648,10.109760,0.000000,,,,,,,,,,,
+fwht15_online_b512,fwht15-batch512,full,butterfly,cuButterfly-online-radix4,0,4,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,1.244232,411498.919077,101.129974,13483996580.300865,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,10.869472,10.125984,0.000000,,,,,,,,,,,
+ntt12_r2_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix2,1,1,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.636928,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.901568,10.125216,,32,1073692673,30,6,4,256,0,6430868.547816,189071.938266,26340837571.854740,shoup
+fft14_cub_b4,fft14-batch4,full,butterfly,cuButterfly-cuFFTDx-direct,0,5,4,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,4,1000,100,,0.020777,192520.937024,22.079841,3154263032.205165,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.141920,0.145728,0.000000,,,,,,,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.090819,11010.965867,115.458345,11545834545.199543,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.755072,0.716672,0.000000,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,1,1000,100,2.004512000,0.063580163,15728.176141680,164.921880259,16492188025.938455582,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b65536,fwht8-batch65536,full,butterfly,cuButterfly-warp-register,0,1,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.164332,398803611.891476,408.374899,102093724644.217896,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,10.894464,10.120800,0.000000,,,,,,,,,,,
+xor20_hier_b8,xor20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,2,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.945746,8458.931326,88.698324,8869832373.646309,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.515680,5.103360,0.000000,,,,,,,,,,,
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,4,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.006861,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.013312,0.022592,,32,1073692673,30,6,4,256,0,145755.605050,23383.717376,597014958.284258,shoup
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002478,403538.244254,0.413223,103305790.529078,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.011264,0.018816,0.000000,,,,,,,,,,,
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,2,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.164239,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.825312,2.598336,,32,1073692673,30,6,4,256,0,6234802.597044,183253.518830,25537751437.490955,shoup
+fft18_cub_b8,fft18-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,5,8,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,8,1000,100,,0.108943,73432.654750,173.249369,19249929846.790859,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,2.775392,2.586528,0.000000,,,,,,,,,,,
+xor20_hier_b2,xor20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,5,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.256819,7787.580091,81.658696,8165869581.142016,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.428736,1.340704,0.000000,,,,,,,,,,,
+fft14_vkfft_b1024,fft14-batch1024,full,fft-library,VkFFT,0,4,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1024,1000,100,371.862839000,0.657274842,1557947.960514515,178.677935695,25525419385.069812775,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,5,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.303780,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.474688,5.098720,,64,1152921504606584833,60,8,4,256,0,210678.891335,5883.873681,13807051822.528833,shoup
+fwht8_shared_b1024,fwht8-batch1024,full,butterfly,cuButterfly-shared-radix4,0,4,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.004536,225733634.823505,231.151242,57787810514.817314,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.263904,0.272064,0.000000,,,,,,,,,,,
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002959,337910.910743,0.346021,86505193.150089,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.013312,0.019168,0.000000,,,,,,,,,,,
+fft20_cufft_b2,fft20-batch2,full,fft-library,cuFFT,1,4,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,2,1000,100,2.025984000,0.124979198,16002.663101875,167.800084647,16780008464.711278915,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,4,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,64,1000,100,153.126018000,0.002457600,26041668.212713014,26.666668250,6666667062.454531670,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b4,xor8-batch4,full,butterfly,cuButterfly-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002499,1600922.203814,1.639344,409836084.176348,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.014336,0.017920,0.000000,,,,,,,,,,,
+fwht8_warp_b4096,fwht8-batch4096,full,butterfly,cuButterfly-warp-register,0,3,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.011203,365630719.298422,374.405857,93601464140.396057,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.750080,0.713184,0.000000,,,,,,,,,,,
+fft14_cub_b4,fft14-batch4,full,butterfly,cuButterfly-cuFFTDx-direct,0,1,4,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,4,1000,100,,0.020603,194147.613883,22.266402,3180914505.855709,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.138144,0.165408,0.000000,,,,,,,,,,,
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.017592,909487.765179,223.515713,29802095089.380459,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.432416,0.431616,0.000000,,,,,,,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.321167,12454.564983,130.595579,13059557932.043989,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.807904,2.607840,0.000000,,,,,,,,,,,
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,5,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,16,1000,100,1.994970000,0.211148798,75775.946234413,178.777886847,19864209649.673999786,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b32,ntt16-batch32,full,ntt,cuNTT-Hybrid2D-radix4,0,1,32,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,32,1000,100,,0.148070,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.766720,2.592960,,64,1152921504606584833,60,8,4,256,0,216113.423629,5809.994656,14163209330.950819,shoup
+fft18_cufft_b2,fft18-batch2,full,fft-library,cuFFT,1,3,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,2,1000,100,2.323307000,0.028047359,71307.962624846,168.236590989,18692954554.327716827,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix2,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.031549,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.432992,0.414880,,64,1152921504606584833,60,8,4,256,0,126785.139381,4548.444850,8308990894.504043,shoup
+fft8_cub_b4096,fft8-batch4096,full,butterfly,cuButterfly-cuFFTDx,0,3,4096,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4096,1000,100,,0.022098,185356819.107650,189.805383,47451345691.558388,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,1.441504,1.360896,0.000000,,,,,,,,,,,
+fft8_cub_b1024,fft8-batch1024,full,butterfly,cuButterfly-cuFFTDx,0,2,1024,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1024,1000,100,,0.005181,197628452.691808,202.371536,50592883889.102760,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.444736,0.419168,0.000000,,,,,,,,,,,
+fft20_vkfft_b16,fft20-batch16,full,fft-library,VkFFT,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,16,1000,100,797.262546000,0.738385916,21668.885685087,227.214734761,22721473476.125885010,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.017592,56842.985324,13.969732,1862630943.086279,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.051392,0.057472,0.000000,,,,,,,,,,,
+fft14_cufft_b4,fft14-batch4,full,fft-library,cuFFT,1,5,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,4,1000,100,1.914553000,0.011888640,336455.641648120,38.587424629,5512489232.762804031,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,4,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,16,1000,100,1.933599000,0.211333126,75709.853517681,178.621954565,19846883840.538993835,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b512,fwht15-batch512,full,butterfly,cuButterfly-online-radix4,0,1,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,1.244232,411498.919077,101.129974,13483996580.300865,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,10.873536,10.125984,0.000000,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.487014,8213.309789,86.122795,8612279525.492992,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.776032,2.594112,0.000000,,,,,,,,,,,
+fft8_cub_b4096,fft8-batch4096,full,butterfly,cuButterfly-cuFFTDx,0,2,4096,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4096,1000,100,,0.022036,185873592.041618,190.334558,47583639562.654121,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,1.419072,1.340192,0.000000,,,,,,,,,,,
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.017633,907375.156217,222.996518,29732869118.921028,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.415872,0.411200,0.000000,,,,,,,,,,,
+ntt20_compact_b8,ntt20-batch8,full,ntt,cuNTT-compact-stage,0,2,8,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,8,1000,100,,0.664791,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.873088,10.119488,,64,1152921504577486849,60,0,0,256,0,12033.856396,369.389322,12618413004.542942,shoup
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015995,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.119168,0.132576,,64,1152921504606584833,60,8,4,256,0,62520.005040,3734.982349,4097311050.305886,shoup
+fwht15_online_b32,fwht15-batch32,full,butterfly,cuButterfly-online-radix4,0,3,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.086723,368992.764594,90.683662,12091154910.212337,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.770880,0.708256,0.000000,,,,,,,,,,,
+fft8_vkfft_b1024,fft8-batch1024,full,fft-library,VkFFT,0,4,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1024,1000,100,204.493792000,0.005928960,172711580.487614870,176.856658419,44214164604.829406738,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.092611,10797.904647,113.224237,11322423662.608603,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.750080,0.725696,0.000000,,,,,,,,,,,
+fwht15_warp_b512,fwht15-batch512,full,butterfly,cuButterfly-warp-register,0,5,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,0.193024,2652519.763816,651.883257,86917767620.718292,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,10.882752,10.163136,0.000000,,,,,,,,,,,
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.082381,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,1.424256,1.344544,,64,1152921504606584833,60,8,4,256,0,194220.009037,5611.710025,12728402512.238260,shoup
+fwht15_online_b256,fwht15-batch256,full,butterfly,cuButterfly-online-radix4,0,4,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.625736,409118.457413,100.544952,13405993612.495667,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,5.496416,5.102944,0.000000,,,,,,,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,1,1000,100,,0.095181,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.418048,1.335744,,64,1152921504577486849,60,0,0,256,0,10506.321199,351.003697,11016676257.466995,shoup
+ntt12_r4_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix4,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.013844,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.272960,0.249728,,32,1073692673,30,6,4,256,0,4622780.818650,119284.483477,18934910233.190933,shoup
+xor8_r2_b256,xor8-batch256,full,butterfly,cuButterfly-radix2,0,3,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.003318,77160497.595804,79.012350,19753087384.525818,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.068064,0.077024,0.000000,,,,,,,,,,,
+fft14_vkfft_b64,fft14-batch64,full,fft-library,VkFFT,0,4,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,64,1000,100,366.367547000,0.047226883,1355160.351397806,155.420630381,22202947197.301647186,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b256,fft8-batch256,full,butterfly,cuButterfly-cuFFTDx,0,1,256,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,256,1000,100,,0.003338,76687114.565083,78.527605,19631901328.661247,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.123232,0.148000,0.000000,,,,,,,,,,,
+fwht8_warp_b65536,fwht8-batch65536,full,butterfly,cuButterfly-warp-register,0,5,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.164424,398580072.249713,408.145994,102036498495.926605,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,10.862144,10.114368,0.000000,,,,,,,,,,,
+fft8_cufft_b65536,fft8-batch65536,full,fft-library,cuFFT,1,2,65536,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,65536,1000,100,1.867305000,0.327075839,200369431.725134343,205.178298087,51294574521.634391785,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,5,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.042721,383509084.186330,392.713302,98178325551.700424,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,2.766336,2.600768,0.000000,,,,,,,,,,,
+fft8_vkfft_b16,fft8-batch16,full,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16,1000,100,153.074782000,0.002344960,6823144.450602620,6.986899917,1746724979.354270697,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,4,1000,100,,0.342262,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.460256,5.096352,,64,1152921504577486849,60,0,0,256,0,11686.961416,367.010526,12254667253.839579,shoup
+ntt12_r4_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.006605,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.026624,0.035168,,32,1073692673,30,6,4,256,0,605620.154967,58482.268804,2480620154.743261,shoup
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,4,1000,100,,0.342077,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.451712,5.093984,,64,1152921504577486849,60,0,0,256,0,11693.258899,367.384565,12261270643.266277,shoup
+fwht8_warp_b1024,fwht8-batch1024,full,butterfly,cuButterfly-warp-register,0,3,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.003553,288184445.471565,295.100872,73775218040.720596,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.266592,0.252768,0.000000,,,,,,,,,,,
+fft18_vkfft_b64,fft18-batch64,full,fft-library,VkFFT,0,5,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,64,1000,100,330.166357000,0.713728011,89670.013008619,211.558103011,23506455890.131328583,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4,xor8-batch4,full,butterfly,cuButterfly-radix2,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4,1000,100,,0.002857,1400089.579033,1.433692,358422932.232378,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.015360,0.019616,0.000000,,,,,,,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.279132,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,5.449024,5.097440,,64,1152921504606584833,60,8,4,256,0,229282.073977,5911.914620,15026230000.159939,shoup
+fwht8_shared_b65536,fwht8-batch65536,full,butterfly,cuButterfly-shared-radix4,0,4,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.178115,367942962.174224,376.773593,94193398316.601273,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.877664,10.112192,0.000000,,,,,,,,,,,
+fft8_cufft_b1024,fft8-batch1024,full,fft-library,cuFFT,1,2,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1024,1000,100,1.824210000,0.004536320,225733634.823505133,231.151242059,57787810514.817314148,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b4096,fwht8-batch4096,full,butterfly,cuButterfly-warp-register,0,2,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.011233,364630828.133019,373.381968,93345492002.052795,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.745760,0.714624,0.000000,,,,,,,,,,,
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,64,1000,100,152.567956000,0.002447360,26150628.016946666,26.778243089,6694560772.338346481,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b256,fwht8-batch256,full,butterfly,cuButterfly-warp-register,0,2,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002386,107296141.222283,109.871249,27467812152.904411,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.068032,0.085280,0.000000,,,,,,,,,,,
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,3,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16384,1000,100,,0.084316,194316257.060635,198.979847,49744961807.522552,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,5.453024,5.098336,0.000000,,,,,,,,,,,
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.017613,908430.232450,223.255814,29767441856.919144,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.425568,0.406656,0.000000,,,,,,,,,,,
+fft14_cufft_b64,fft14-batch64,full,fft-library,cuFFT,1,1,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,64,1000,100,1.827963000,0.027688961,2311390.409325065,265.088743265,37869820466.381866455,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,2,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,64,1000,100,1.594933000,0.002734080,23408240.068453956,23.970037830,5992509457.524212837,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.139827,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.807680,2.612032,,32,1073692673,30,6,4,256,0,7323324.436933,184187.932410,29996336893.675751,shoup
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.082749,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,1.411936,1.349664,,64,1152921504606584833,60,8,4,256,0,193354.779866,5625.187844,12671698853.271643,shoup
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.008448,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.068000,0.079296,,32,1073692673,30,6,4,256,0,1893939.379147,102732.686862,7757575696.985913,shoup
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002478,403538.244254,0.413223,103305790.529078,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.010240,0.017440,0.000000,,,,,,,,,,,
+fft8_cub_b65536,fft8-batch65536,full,butterfly,cuButterfly-cuFFTDx,0,1,65536,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,65536,1000,100,,0.327660,200012502.291115,204.812802,51203200586.525414,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,21.627359,20.137793,0.000000,,,,,,,,,,,
+ntt16_r4_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,1,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.069169,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,21.617409,20.149759,,64,1152921504606584833,60,8,4,256,0,239438.389552,5976.234670,15691834297.709091,shoup
+fft8_vkfft_b4,fft8-batch4,full,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4,1000,100,153.039393000,0.002539520,1575100.856639518,1.612903277,403225819.299716532,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.008172,122376.250199,30.075187,4010024966.521593,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.047264,0.051744,0.000000,,,,,,,,,,,
+fft8_cufft_b256,fft8-batch256,full,fft-library,cuFFT,1,3,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,256,1000,100,2.085006000,0.003338240,76687114.565082997,78.527605315,19631901328.661247253,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,1,1000,100,,0.073236,13654.397305,143.176733,14317673308.622478,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,1.431136,1.374208,0.000000,,,,,,,,,,,
+fwht8_shared_b4,fwht8-batch4,full,butterfly,cuButterfly-shared-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002488,1607510.291372,1.646091,411522634.591321,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.014336,0.020160,0.000000,,,,,,,,,,,
+fft18_vkfft_b32,fft18-batch32,full,fft-library,VkFFT,0,4,32,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,32,1000,100,332.275721000,0.372162551,85983.933474395,202.861550310,22540172256.711742401,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002918,21929825.535294,22.456141,5614035337.035136,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.039936,0.034464,0.000000,,,,,,,,,,,
+ntt16_r2_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix2,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.031549,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.434208,0.418368,,64,1152921504606584833,60,8,4,256,0,126785.139381,4524.244802,8308990894.504043,shoup
+ntt16_r4_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix4,0,4,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.539853,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.942080,10.141184,,64,1152921504606584833,60,8,4,256,0,237101.670081,5919.590814,15538695050.408695,shoup
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16384,1000,100,,0.048527,337623971.563120,345.726947,86431736720.158600,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.769920,2.599200,0.000000,,,,,,,,,,,
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,4,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,1,1000,100,1.957215000,0.023255041,43001.429480523,101.453100568,11272566729.742156982,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,16,1000,100,366.543809000,0.010762240,1486679.379747102,170.504284704,24357754957.776512146,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,64,1000,100,149.011495000,0.002457600,26041668.212713014,26.666668250,6666667062.454531670,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b2,ntt20-batch2,full,ntt,cuNTT-compact-stage,0,3,2,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,2,1000,100,,0.179825,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.756800,2.594528,,64,1152921504577486849,60,0,0,256,0,11121.946644,361.588293,11662206323.916311,shoup
+fft8_cufft_b4,fft8-batch4,full,fft-library,cuFFT,1,5,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,4,1000,100,1.765423000,0.002693120,1485266.201325822,1.520912590,380228147.539410472,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002478,403538.244254,0.413223,103305790.529078,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.010240,0.016896,0.000000,,,,,,,,,,,
+fft14_vkfft_b1024,fft14-batch1024,full,fft-library,VkFFT,0,2,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1024,1000,100,366.332662000,0.657070100,1558433.414518233,178.733611444,25533373063.466728210,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b16,fft20-batch16,full,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,16,1000,100,794.102763000,0.737710118,21688.735999726,227.422880396,22742288039.648624420,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,16,1000,100,331.463910000,0.201185286,79528.678833974,187.631693858,20847965984.253387451,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.318945,12541.335904,131.505438,13150543836.675442,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.767648,2.593696,0.000000,,,,,,,,,,,
+fft8_cub_b256,fft8-batch256,full,butterfly,cuButterfly-cuFFTDx,0,4,256,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,256,1000,100,,0.003348,76452599.873783,78.287462,19571865567.688519,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.121472,0.134624,0.000000,,,,,,,,,,,
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,4,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002550,25100401.177010,25.702811,6425702701.314640,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.032768,0.031936,0.000000,,,,,,,,,,,
+fwht8_shared_b256,fwht8-batch256,full,butterfly,cuButterfly-shared-radix4,0,4,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002949,86805555.226460,88.888889,22222222137.973820,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.070560,0.076864,0.000000,,,,,,,,,,,
+ntt12_r2_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix2,1,4,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.048148,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.789696,0.710880,,32,1073692673,30,6,4,256,0,5316886.507207,165297.320527,21777967133.519161,shoup
+fft18_cufft_b64,fft18-batch64,full,fft-library,cuFFT,1,5,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,64,1000,100,2.030208000,0.706047952,90645.401353879,213.859332833,23762148092.511268616,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,5,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002089,30637254.501246,31.372549,7843137152.319073,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.034816,0.034624,0.000000,,,,,,,,,,,
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,3,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,64,1000,100,1.827239000,0.002754560,23234199.005202208,23.791819781,5947954945.331765175,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b64,fft18-batch64,full,butterfly,cuButterfly-cuFFTDx-online,0,2,64,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,64,1000,100,,0.842342,75978.606526,179.256022,19917335829.105812,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,21.623903,20.137568,0.000000,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.044698,357961.072875,87.972513,11729668435.954735,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.430304,0.401152,0.000000,,,,,,,,,,,
+fft8_cufft_b256,fft8-batch256,full,fft-library,cuFFT,1,2,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,256,1000,100,1.799538000,0.003133440,81699348.371997014,83.660132733,20915033183.231235504,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,4,1000,100,,0.235489,16985.911276,178.110189,17811018901.775299,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,5.447712,5.091232,0.000000,,,,,,,,,,,
+ntt12_r4_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix4,0,5,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.538819,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.974848,10.122624,,32,1073692673,30,6,4,256,0,7601817.141941,189311.562286,31137043013.388569,shoup
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,4,1000,100,800.568051000,0.206704631,19351.283868113,202.912918333,20291291833.290958405,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cub_b4,fft14-batch4,full,butterfly,cuButterfly-cuFFTDx-direct,0,3,4,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,4,1000,100,,0.020603,194147.613883,22.266402,3180914505.855709,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.139296,0.128896,0.000000,,,,,,,,,,,
+fft18_cub_b2,fft18-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,2,2,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,2,1000,100,,0.025907,77198.617108,182.134389,20237154283.134544,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.742368,0.709856,0.000000,,,,,,,,,,,
+ntt20_compact_b16,ntt20-batch16,full,ntt,cuNTT-compact-stage,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,16,1000,100,,1.318257,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.627296,20.155712,,64,1152921504577486849,60,0,0,256,0,12137.241226,371.218800,12726819855.615568,shoup
+ntt12_r2_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix2,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.007229,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.027648,0.036960,,32,1073692673,30,6,4,256,0,553293.172059,55681.272473,2266288832.753917,shoup
+xor20_hier_b8,xor20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,5,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.945746,8458.931326,88.698324,8869832373.646309,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.494400,5.107328,0.000000,,,,,,,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,1,1000,100,,0.094976,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.417632,1.344096,,64,1152921504577486849,60,0,0,256,0,10528.976513,350.053778,11040432076.230391,shoup
+fwht15_online_b256,fwht15-batch256,full,butterfly,cuButterfly-online-radix4,0,2,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.626893,408363.276652,100.359359,13381247849.333246,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,5.474784,5.109120,0.000000,,,,,,,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,16,1000,100,,0.007639,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.069440,0.076064,,32,1073692673,30,6,4,256,0,2094504.083552,104477.488845,8579088726.229346,shoup
+fwht8_warp_b16,fwht8-batch16,full,butterfly,cuButterfly-warp-register,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002130,7512019.019807,7.692307,1923076869.070699,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.014336,0.019744,0.000000,,,,,,,,,,,
+fft14_cub_b1024,fft14-batch1024,full,butterfly,cuButterfly-cuFFTDx-direct,0,3,1024,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1024,1000,100,,0.379761,2696435.433378,309.248787,44178398140.458672,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,21.683231,20.136703,0.000000,,,,,,,,,,,
+ntt16_r4_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.029430,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.427904,0.420896,,64,1152921504606584833,60,8,4,256,0,135916.841424,4554.616761,8907446119.579630,shoup
+xor8_r4_b16,xor8-batch16,full,butterfly,cuButterfly-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002509,6377550.992120,6.530612,1632653053.982594,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.017408,0.020864,0.000000,,,,,,,,,,,
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,4,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,16,1000,100,,0.020756,770843.566113,88.406507,12629500987.192324,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.488576,0.396992,0.000000,,,,,,,,,,,
+fwht20_online_b2,fwht20-batch2,full,butterfly,cuButterfly-online-radix4,0,2,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.167260,11957.420457,125.382641,12538264113.022078,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.425664,1.351104,0.000000,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002478,403538.244254,0.413223,103305790.529078,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.010240,0.016512,0.000000,,,,,,,,,,,
+fft8_cub_b16,fft8-batch16,full,butterfly,cuButterfly-cuFFTDx,0,5,16,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16,1000,100,,0.003092,5173841.240165,5.298013,1324503357.482326,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.017408,0.022944,0.000000,,,,,,,,,,,
+fft8_cub_b256,fft8-batch256,full,butterfly,cuButterfly-cuFFTDx,0,3,256,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,256,1000,100,,0.003338,76687114.565083,78.527605,19631901328.661247,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.122784,0.125824,0.000000,,,,,,,,,,,
+ntt12_r4_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,5,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.042824,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.800864,0.746720,,32,1073692673,30,6,4,256,0,5978000.472015,160965.017400,24485889933.373840,shoup
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,2,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1,1000,100,,0.002888,346298.763369,0.354610,88652483.422564,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.007168,0.015808,0.000000,,,,,,,,,,,
+fwht20_online_b16,fwht20-batch16,full,butterfly,cuButterfly-online-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.233644,12969.710932,135.997276,13599727609.749460,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.899744,10.119520,0.000000,,,,,,,,,,,
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.098468,10155.600630,106.489191,10648919086.317030,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.752160,0.710816,0.000000,,,,,,,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,1,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.064707,1978161.208470,486.152899,64820386479.143539,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,2.805408,2.598240,0.000000,,,,,,,,,,,
+fwht15_warp_b256,fwht15-batch256,full,butterfly,cuButterfly-warp-register,0,4,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.107244,2387090.712986,586.651414,78220188483.132217,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,5.502816,5.098464,0.000000,,,,,,,,,,,
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.140052,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.815008,2.592064,,32,1073692673,30,6,4,256,0,7311544.799672,184600.153616,29948087499.456680,shoup
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,5,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,64,1000,100,,0.003123,20491803.063089,20.983606,5245901584.150699,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.040032,0.044480,0.000000,,,,,,,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,1,1000,100,152.532761000,0.002334720,428316.887900589,0.438596493,109649123.302550793,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b32,fft18-batch32,full,fft-library,VkFFT,0,3,32,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,32,1000,100,405.461107000,0.372377574,85934.283362244,202.744410999,22527156777.712028503,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b65536,fft8-batch65536,full,fft-library,VkFFT,0,1,65536,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,65536,1000,100,204.484924000,0.326092809,200973459.405024320,205.796822431,51449205607.686225891,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,1,1000,100,,0.095068,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.413440,1.338560,,64,1152921504577486849,60,0,0,256,0,10518.769213,351.238521,11029728945.908379,shoup
+fwht20_online_b16,fwht20-batch16,full,butterfly,cuButterfly-online-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.233613,12970.034288,136.000667,13600066673.340359,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.851584,10.113472,0.000000,,,,,,,,,,,
+fwht15_warp_b32,fwht15-batch32,full,butterfly,cuButterfly-warp-register,0,2,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.022436,1426289.470060,350.524900,46736653354.915909,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.746880,0.712608,0.000000,,,,,,,,,,,
+fwht8_shared_b1024,fwht8-batch1024,full,butterfly,cuButterfly-shared-radix4,0,5,1024,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1024,1000,100,,0.004332,236406628.813911,242.080388,60520096976.361305,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.239424,0.273600,0.000000,,,,,,,,,,,
+ntt12_r2_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix2,1,4,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.007178,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.025600,0.033472,,32,1073692673,30,6,4,256,0,557239.658406,60377.138949,2282453640.831979,shoup
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,327.507621000,0.018493440,54073.228122019,127.574750815,14174972312.818637848,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.086948,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.415872,1.338912,,64,1152921504606584833,60,8,4,256,0,184018.365130,5630.369419,12059827577.148886,shoup
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,5,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.488090,8195.216763,85.933076,8593307612.096033,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.791136,2.608576,0.000000,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.044564,359030.316182,88.235291,11764705400.661909,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.430528,0.400160,0.000000,,,,,,,,,,,
+fwht20_online_b8,fwht20-batch8,full,butterfly,cuButterfly-online-radix4,0,2,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.624558,12809.056697,134.312694,13431269434.634817,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.459584,5.102400,0.000000,,,,,,,,,,,
+fwht8_shared_b16,fwht8-batch16,full,butterfly,cuButterfly-shared-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002540,6300403.426558,6.451613,1612903277.198866,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.014336,0.020864,0.000000,,,,,,,,,,,
+fft18_vkfft_b64,fft18-batch64,full,fft-library,VkFFT,0,4,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,64,1000,100,330.985019000,0.713062346,89753.722603173,211.755598723,23528399858.086143494,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.017592,56842.985324,13.969732,1862630943.086279,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.044640,0.057536,0.000000,,,,,,,,,,,
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,4,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.306033,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.451936,5.097152,,64,1152921504606584833,60,8,4,256,0,209128.028131,5895.834988,13705414451.604485,shoup
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002120,30193237.636913,30.917875,7729468835.049730,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.031744,0.034080,0.000000,,,,,,,,,,,
+fft8_vkfft_b4096,fft8-batch4096,full,fft-library,VkFFT,0,2,4096,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4096,1000,100,204.409179000,0.020275200,202020204.154185981,206.868689054,51717172263.471611023,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b4,fwht8-batch4,full,butterfly,cuButterfly-shared-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002519,1587906.418546,1.626016,406504043.147757,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.011264,0.017856,0.000000,,,,,,,,,,,
+ntt12_r2_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix2,1,3,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.636723,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.885472,18.428640,,32,1073692673,30,6,4,256,0,6432936.429991,136757.451976,26349307617.242237,shoup
+fwht8_warp_b4096,fwht8-batch4096,full,butterfly,cuButterfly-warp-register,0,1,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.011325,361663641.001895,370.343568,92585892096.485046,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.748320,0.714272,0.000000,,,,,,,,,,,
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,1,16384,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16384,1000,100,1.828912000,0.083865605,195360183.026480138,200.048827419,50012206854.778915405,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b8,fft20-batch8,full,fft-library,cuFFT,1,4,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,8,1000,100,1.951430000,0.382248968,20928.768086004,219.454039246,21945403924.550060272,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,4,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,128,1000,100,,0.317809,402758.064717,98.981822,13197576264.656170,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,2.761888,2.613024,0.000000,,,,,,,,,,,
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,2,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,256,1000,100,,0.121528,2106504.886840,241.590832,34512976065.993210,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,5.524064,5.099840,0.000000,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.052449,305056.627038,74.970717,9996095554.785250,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.432192,0.399744,0.000000,,,,,,,,,,,
+fft8_cub_b4,fft8-batch4,full,butterfly,cuButterfly-cuFFTDx,0,4,4,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,4,1000,100,,0.003308,1209365.344732,1.238390,309597528.251285,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.008192,0.016640,0.000000,,,,,,,,,,,
+fwht8_shared_b4096,fwht8-batch4096,full,butterfly,cuButterfly-shared-radix4,0,5,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4096,1000,100,,0.015421,265604267.541714,271.978770,67994692490.678825,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.744704,0.741504,0.000000,,,,,,,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.279552,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,5.454848,5.099968,,64,1152921504606584833,60,8,4,256,0,228937.718552,5907.128250,15003662323.017323,shoup
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,4,1000,100,,0.342743,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,5.449888,5.102016,,64,1152921504577486849,60,0,0,256,0,11670.550655,367.152778,12237459324.140728,shoup
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,5,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,256,1000,100,,0.121395,2108814.837528,241.855756,34550822298.058083,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,5.551168,5.093024,0.000000,,,,,,,,,,,
+fwht8_warp_b256,fwht8-batch256,full,butterfly,cuButterfly-warp-register,0,3,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,256,1000,100,,0.002406,106382981.822587,108.936173,27234043346.582222,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.069376,0.085280,0.000000,,,,,,,,,,,
+xor20_online_b2,xor20-batch2,full,butterfly,cuButterfly-online-radix4,0,2,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.167086,11969.878062,125.513269,12551326858.323633,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.424512,1.340288,0.000000,,,,,,,,,,,
+xor20_hier_b16,xor20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.863885,8584.222033,90.012092,9001209202.050886,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.876512,19.053473,0.000000,,,,,,,,,,,
+fft18_cub_b2,fft18-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,1,2,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,2,1000,100,,0.026030,76834.184521,181.274584,20141620466.983376,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.742368,0.704832,0.000000,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.319529,12518.426845,131.265219,13126521947.334604,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.776128,2.596384,0.000000,,,,,,,,,,,
+ntt16_r4_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.029471,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.424224,0.400416,,64,1152921504606584833,60,8,4,256,0,135727.938844,4683.233709,8895066200.049400,shoup
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,5,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,4,1000,100,,0.236513,16912.370149,177.339054,17733905441.381710,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,5.451744,5.090784,0.000000,,,,,,,,,,,
+ntt16_r4_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix4,0,3,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.540836,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.857120,10.117760,,64,1152921504606584833,60,8,4,256,0,236670.698236,5949.139932,15510450879.609247,shoup
+ntt16_r4_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,3,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.075712,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,21.619232,35.444481,,64,1152921504606584833,60,8,4,256,0,237981.920994,4403.208319,15596383174.237337,shoup
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.092396,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.422656,1.350560,,64,1152921504606584833,60,8,4,256,0,173168.579989,5583.450468,11348776058.165089,shoup
+fft8_cufft_b16,fft8-batch16,full,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16,1000,100,1.817588000,0.002693120,5941064.805303289,6.083650361,1520912590.157641888,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,4,1000,100,342.862307000,0.063815683,62680.516826468,147.881892627,16431321402.957736969,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.044626,358536.001296,88.113808,11748507690.453604,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.436192,0.405600,0.000000,,,,,,,,,,,
+fft14_vkfft_b1024,fft14-batch1024,full,fft-library,VkFFT,0,3,1024,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,1024,1000,100,367.210024000,0.657029092,1558530.683012675,178.744766973,25534966710.479671478,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.017592,909487.765179,223.515713,29802095089.380459,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.431296,0.405408,0.000000,,,,,,,,,,,
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,3,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.163891,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.815456,2.600512,,32,1073692673,30,6,4,256,0,6248047.628088,183517.177542,25592003084.647507,shoup
+xor20_online_b2,xor20-batch2,full,butterfly,cuButterfly-online-radix4,0,1,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,2,1000,100,,0.167076,11970.611482,125.520959,12552095905.229538,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.424992,1.343904,0.000000,,,,,,,,,,,
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,4,1000,100,331.002732000,0.063825920,62670.463441027,147.858173715,16428685968.284624100,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b32,fft18-batch32,full,fft-library,cuFFT,1,2,32,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,32,1000,100,2.038659000,0.379146218,84400.156075647,199.124950629,22124994514.294410706,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_vkfft_b64,fft14-batch64,full,fft-library,VkFFT,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,64,1000,100,378.634577000,0.047298562,1353106.682090205,155.185099156,22169299879.365917206,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002488,401877.572843,0.411523,102880658.647830,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.014336,0.018304,0.000000,,,,,,,,,,,
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,331.501990000,0.018503681,54043.301408242,127.504144839,14167127204.362192154,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b16,ntt20-batch16,full,ntt,cuNTT-compact-stage,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,16,1000,100,,1.316475,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.618080,20.152449,,64,1152921504577486849,60,0,0,256,0,12153.668728,371.341672,12744045339.994089,shoup
+fft14_cufft_b1024,fft14-batch1024,full,fft-library,cuFFT,1,5,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1024,1000,100,1.960367000,0.405841917,2523149.920233048,289.375018052,41339288293.098258972,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix4,0,2,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.175114,374247142.873165,383.229074,95807268575.530197,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.894976,10.124640,0.000000,,,,,,,,,,,
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.098621,10139.782693,106.323328,10632332776.902119,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,0.768256,0.722688,0.000000,,,,,,,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1,1000,100,1.989473000,0.011868160,84259.057986368,9.663502842,1380500406.048649788,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b2,ntt20-batch2,full,ntt,cuNTT-compact-stage,0,4,2,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,2,1000,100,,0.179988,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.773920,2.602784,,64,1152921504577486849,60,0,0,256,0,11111.822660,359.926344,11651590557.036770,shoup
+fft20_cufft_b8,fft20-batch8,full,fft-library,cuFFT,1,3,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,8,1000,100,2.112101000,0.381429762,20973.717324604,219.925366174,21992536617.364055634,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix2,0,2,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.180621,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.622080,20.146496,,64,1152921504606584833,60,8,4,256,0,216835.077165,5960.530606,14210503617.091885,shoup
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,4,1000,100,,0.235817,16962.308713,177.862698,17786269820.699474,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,5.450304,5.097920,0.000000,,,,,,,,,,,
+fft8_cub_b65536,fft8-batch65536,full,butterfly,cuButterfly-cuFFTDx,0,2,65536,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,65536,1000,100,,0.327639,200025001.091712,204.825601,51206400279.478271,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,21.629185,20.134560,0.000000,,,,,,,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,1,1000,100,782.155528000,0.061050881,16379.780087174,171.754442847,17175444284.688129425,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b32,fft18-batch32,full,butterfly,cuButterfly-cuFFTDx-online,0,4,32,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,32,1000,100,,0.412303,77612.756129,183.111465,20345718342.566051,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,10.868384,10.108960,0.000000,,,,,,,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,1,1000,100,,0.095048,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.417824,1.336032,,64,1152921504577486849,60,0,0,256,0,10521.035058,351.012210,11032104856.825274,shoup
+fwht15_warp_b32,fwht15-batch32,full,butterfly,cuButterfly-warp-register,0,4,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.022364,1430860.683747,351.648322,46886442885.012894,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.757280,0.712288,0.000000,,,,,,,,,,,
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,2,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,64,1000,100,,0.003103,20627062.595822,21.122112,5280528024.530542,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.039392,0.043840,0.000000,,,,,,,,,,,
+fft14_cufft_b4,fft14-batch4,full,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,4,1000,100,2.237466000,0.011980799,333867.548487926,38.290601401,5470085914.426180840,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_shared_b65536,fwht8-batch65536,full,butterfly,cuButterfly-shared-radix4,0,1,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.177203,369835321.683448,378.711369,94677842350.962601,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.906240,10.114272,0.000000,,,,,,,,,,,
+ntt12_r4_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix4,0,2,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.538307,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.884832,10.116512,,32,1073692673,30,6,4,256,0,7609047.520480,190160.925035,31166658643.886890,shoup
+xor8_r2_b65536,xor8-batch65536,full,butterfly,cuButterfly-radix2,0,1,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,65536,1000,100,,0.179128,365860631.957580,374.641287,93660321781.140457,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,10.880320,10.113088,0.000000,,,,,,,,,,,
+ntt16_r4_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix4,0,2,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.543990,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.875264,10.124448,,64,1152921504606584833,60,8,4,256,0,235298.539199,5941.411619,15420525064.917471,shoup
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,332.192038000,0.019107841,52334.536504756,123.472662638,13719184737.502882004,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b16,xor8-batch16,full,butterfly,cuButterfly-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002580,6200396.941752,6.349206,1587301617.088468,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.019456,0.022912,0.000000,,,,,,,,,,,
+xor8_r2_b16,xor8-batch16,full,butterfly,cuButterfly-radix2,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002949,5425347.201654,5.555556,1388888883.623364,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.019456,0.022880,0.000000,,,,,,,,,,,
+fft18_vkfft_b8,fft18-batch8,full,fft-library,VkFFT,0,1,8,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,8,1000,100,336.247801000,0.113192961,70675.773088593,166.745068745,18527229860.536205292,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.090020,11108.662636,116.482770,11648277031.936249,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.753984,0.720800,0.000000,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,5,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,1.842450000,0.002682880,372733.806415253,0.381679418,95419854.442304835,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.006339,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.027648,0.033344,,32,1073692673,30,6,4,256,0,631058.156088,59408.386943,2584814207.338050,shoup
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.090071,11102.347977,116.416556,11641655632.401009,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.754432,0.711968,0.000000,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,16,1000,100,2.034432000,0.013496321,1185508.284958062,135.963574185,19423367740.752895355,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b256,xor8-batch256,full,butterfly,cuButterfly-radix2,0,5,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.003287,77881621.596221,79.750781,19937695128.632660,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.072448,0.076096,0.000000,,,,,,,,,,,
+xor20_hier_b8,xor20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,4,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.945613,8460.122473,88.710814,8871081382.015348,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.484128,5.105120,0.000000,,,,,,,,,,,
+fft18_vkfft_b32,fft18-batch32,full,fft-library,VkFFT,0,1,32,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,32,1000,100,332.581385000,0.371855348,86054.967723631,203.029141130,22558793458.943634033,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cub_b64,fft14-batch64,full,butterfly,cuButterfly-cuFFTDx-direct,0,5,64,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,64,1000,100,,0.034427,1859012.539124,213.206430,30458061441.011448,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,1.491680,1.339296,0.000000,,,,,,,,,,,
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,5,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,16,1000,100,,0.024279,659004.656951,75.579926,10797132299.477934,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.494240,0.399456,0.000000,,,,,,,,,,,
+fwht8_warp_b65536,fwht8-batch65536,full,butterfly,cuButterfly-warp-register,0,2,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.164485,398431197.023412,407.993546,101998386437.993378,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,10.913312,10.117632,0.000000,,,,,,,,,,,
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,4,1000,100,331.978113000,0.063805439,62690.580758285,147.905636421,16433959602.299955368,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b64,fft18-batch64,full,fft-library,VkFFT,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,64,1000,100,331.612505000,0.714547217,89567.209117899,211.315558203,23479506467.002437592,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_cufft_b16,fft20-batch16,full,fft-library,cuFFT,1,4,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,16,1000,100,2.006145000,0.721960962,22161.863100872,232.383977629,23238397762.860252380,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_vkfft_b2,fft18-batch2,full,fft-library,VkFFT,0,3,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,2,1000,100,330.137455000,0.023582721,84807.855253629,200.086833668,22231870407.607307434,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cub_b64,fft14-batch64,full,butterfly,cuButterfly-cuFFTDx-direct,0,1,64,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,64,1000,100,,0.031662,2021345.379608,231.824059,33117722699.499775,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,1.485504,1.350080,0.000000,,,,,,,,,,,
+fwht20_hier_b8,fwht20-batch8,full,butterfly,cuButterfly-hierarchical-radix4,0,5,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.947989,8438.920846,88.488499,8848849865.103748,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,5.465952,5.104832,0.000000,,,,,,,,,,,
+ntt20_compact_b2,ntt20-batch2,full,ntt,cuNTT-compact-stage,0,5,2,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,2,1000,100,,0.179927,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,2.763296,2.588128,,64,1152921504577486849,60,0,0,256,0,11115.615957,361.575317,11655568118.075645,shoup
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,5,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.140626,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.807264,2.597088,,32,1073692673,30,6,4,256,0,7281730.710181,184671.604120,29825968988.900467,shoup
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,5,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,4,1000,100,792.280763000,0.207575038,19270.139786972,202.062060973,20206206097.264453888,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt20_compact_b16,ntt20-batch16,full,ntt,cuNTT-compact-stage,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,16,1000,100,,1.313536,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,21.620352,35.778847,,64,1152921504577486849,60,0,0,256,0,12180.860986,272.513282,12772558489.254353,shoup
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,1,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1,1000,100,,0.020818,48035.537308,5.509100,787014243.251040,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.037056,0.046240,0.000000,,,,,,,,,,,
+fft18_cufft_b64,fft18-batch64,full,fft-library,cuFFT,1,1,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,64,1000,100,2.034775000,0.706478059,90590.216013435,213.729134280,23747681586.625869751,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r4_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix4,0,5,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.014725,278164120.478070,284.840059,71210014842.386017,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.753056,0.723104,0.000000,,,,,,,,,,,
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,3,16384,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16384,1000,100,207.224046000,0.083548166,196102449.787914634,200.808908583,50202227145.706146240,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_warp_b32,fwht15-batch32,full,butterfly,cuButterfly-warp-register,0,1,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.022385,1429551.584530,351.326597,46843546321.885712,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.758336,0.708512,0.000000,,,,,,,,,,,
+fft8_cub_b16,fft8-batch16,full,butterfly,cuButterfly-cuFFTDx,0,2,16,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,16,1000,100,,0.003133,5106209.273250,5.228758,1307189573.951952,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.020480,0.023712,0.000000,,,,,,,,,,,
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.007690,130034.950633,31.957389,4260985262.351007,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.047616,0.047136,0.000000,,,,,,,,,,,
+fwht15_warp_b32,fwht15-batch32,full,butterfly,cuButterfly-warp-register,0,3,32,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,32,1000,100,,0.022415,1427592.598865,350.845157,46779354279.603867,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.749856,0.711648,0.000000,,,,,,,,,,,
+ntt12_r2_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix2,1,3,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.015483,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.283168,0.251712,,32,1073692673,30,6,4,256,0,4133597.836846,116286.916040,16931216739.722347,shoup
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,4,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015534,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.121504,0.137856,,64,1152921504606584833,60,8,4,256,0,64374.585661,3637.764658,4218852845.900787,shoup
+fft14_cufft_b1024,fft14-batch1024,full,fft-library,cuFFT,1,4,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1024,1000,100,1.933998000,0.407111675,2515280.361681915,288.472474121,41210353445.796501160,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b4,ntt12-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4,1000,100,,0.006369,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.027648,0.035872,,32,1073692673,30,6,4,256,0,628014.453362,57233.382849,2572347200.970323,shoup
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.090112,11097.301050,116.363635,11636363545.478868,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.753056,0.711488,0.000000,,,,,,,,,,,
+xor8_r4_b256,xor8-batch256,full,butterfly,cuButterfly-radix4,0,1,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,256,1000,100,,0.002939,87108010.396126,89.198603,22299650661.408287,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.070752,0.075616,0.000000,,,,,,,,,,,
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,1024,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1024,1000,100,,0.139489,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,2.819872,2.598144,,32,1073692673,30,6,4,256,0,7341066.017645,184255.337006,30069006408.275555,shoup
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,16,1000,100,370.303977000,0.010762240,1486679.379747102,170.504284704,24357754957.776512146,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,1,1000,100,806.428446000,0.065515518,15263.559346706,160.050020055,16005002005.531457901,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.033526,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.436896,0.402016,,64,1152921504606584833,60,8,4,256,0,119311.235743,4584.854222,7819181145.632597,shoup
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.091167,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,1.419872,1.336160,,64,1152921504606584833,60,8,4,256,0,175502.654299,5619.558616,11501741952.116627,shoup
+ntt20_compact_b8,ntt20-batch8,full,ntt,cuNTT-compact-stage,0,1,8,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,8,1000,100,,0.665016,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.867104,10.122880,,64,1152921504577486849,60,0,0,256,0,12029.779362,369.429694,12614137923.847214,shoup
+ntt12_r4_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,2,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.043602,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.791264,0.739744,,32,1073692673,30,6,4,256,0,5871301.219611,162579.948266,24048849795.528671,shoup
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,16,1000,100,333.150678000,0.201379836,79451.847559028,187.450426139,20827825126.513908386,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,1,256,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,256,1000,100,1.893935000,0.120954879,2116491.727355599,242.736203227,34676600460.994132996,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b2,fft20-batch2,full,fft-library,VkFFT,0,5,2,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,2,1000,100,879.674754000,0.117196798,17065.312607439,178.942772327,17894277232.657726288,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft20_vkfft_b16,fft20-batch16,full,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,16,1000,100,788.409606000,0.738856971,21655.070767798,227.069874854,22706987485.414081573,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b4,fft8-batch4,full,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4,1000,100,153.435189000,0.002355200,1698369.561110481,1.739130431,434782607.644283175,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.321423,12444.645379,130.491565,13049156472.537729,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.766304,2.594016,0.000000,,,,,,,,,,,
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,3,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1,1000,100,,0.002888,346298.763369,0.354610,88652483.422564,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.007168,0.015744,0.000000,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.319242,12529.670298,131.383116,13138311562.903334,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,2.770752,2.611392,0.000000,,,,,,,,,,,
+fft8_cufft_b16,fft8-batch16,full,fft-library,cuFFT,1,4,16,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,16,1000,100,1.785446000,0.002693120,5941064.805303289,6.083650361,1520912590.157641888,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.090071,11102.347977,116.416556,11641655632.401009,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.748224,0.728864,0.000000,,,,,,,,,,,
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,2,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1,1000,100,,0.020531,48706.359405,5.586035,798004992.487075,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.035424,0.042816,0.000000,,,,,,,,,,,
+fft8_cufft_b1024,fft8-batch1024,full,fft-library,cuFFT,1,1,1024,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1024,1000,100,1.865452000,0.004556800,224719089.347732902,230.112347492,57528086873.019622803,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r2_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix2,1,4,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.015483,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.279136,0.256960,,32,1073692673,30,6,4,256,0,4133597.836846,116030.547091,16931216739.722347,shoup
+fft20_cufft_b8,fft20-batch8,full,fft-library,cuFFT,1,5,8,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,8,1000,100,2.382374000,0.381511688,20969.213386527,219.878138960,21987813895.991443634,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_hier_b2,fwht20-batch2,full,butterfly,cuButterfly-hierarchical-radix4,0,2,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.257270,7773.940952,81.515679,8151567907.718481,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,1.425344,1.339232,0.000000,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,4,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,1,1000,100,2.004861000,0.063508481,15745.928537474,165.108027621,16510802762.110210419,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,1,1000,100,,0.089887,11125.113309,116.655268,11665526812.733540,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.753216,0.713952,0.000000,,,,,,,,,,,
+xor20_hier_b16,xor20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,16,1000,100,,1.863741,8584.882011,90.019012,9001901239.777729,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.889024,18.183168,0.000000,,,,,,,,,,,
+fwht15_online_b256,fwht15-batch256,full,butterfly,cuButterfly-online-radix4,0,5,256,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,256,1000,100,,0.625777,409091.647323,100.538363,13405115099.485559,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,5.480320,5.105984,0.000000,,,,,,,,,,,
+fwht8_warp_b4,fwht8-batch4,full,butterfly,cuButterfly-warp-register,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002068,1933787.118358,1.980198,495049502.299738,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.014336,0.017024,0.000000,,,,,,,,,,,
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,3,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,64,1000,100,,0.003123,20491803.063089,20.983606,5245901584.150699,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.040288,0.043456,0.000000,,,,,,,,,,,
+fwht8_shared_b16,fwht8-batch16,full,butterfly,cuButterfly-shared-radix4,0,4,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002509,6377550.992120,6.530612,1632653053.982594,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.019456,0.021088,0.000000,,,,,,,,,,,
+fwht20_online_b16,fwht20-batch16,full,butterfly,cuButterfly-online-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.232650,12980.161737,136.106861,13610686073.925701,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,10.891840,10.118752,0.000000,,,,,,,,,,,
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,4,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,4,1000,100,332.441359000,0.063825920,62670.463441027,147.858173715,16428685968.284624100,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b16,xor8-batch16,full,butterfly,cuButterfly-radix2,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,16,1000,100,,0.002888,5540780.213910,5.673759,1418439734.761025,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.020480,0.021568,0.000000,,,,,,,,,,,
+fft18_cub_b8,fft18-batch8,full,butterfly,cuButterfly-cuFFTDx-online,0,2,8,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,8,1000,100,,0.108851,73494.824727,173.396046,19266227333.264111,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,2.789216,2.588000,0.000000,,,,,,,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,4,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,14,16384,1,1000,100,1.934502000,0.011878400,84186.421636252,9.655172325,1379310332.088345051,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r4_b4,ntt16-batch4,full,ntt,cuNTT-Hybrid2D-radix4,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,4,1000,100,,0.029379,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.422624,0.410848,,64,1152921504606584833,60,8,4,256,0,136153.714688,4635.797047,8922969845.816900,shoup
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,4,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,4,1000,100,,0.487055,8212.618766,86.115549,8611554935.060228,,,-1,xor-zeta,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.802016,2.598112,0.000000,,,,,,,,,,,
+fft20_vkfft_b16,fft20-batch16,full,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,20,1048576,16,1000,100,797.237328000,0.738242567,21673.093267978,227.258854466,22725885446.563461304,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002068,483446.779590,0.495050,123762375.574935,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.015360,0.016320,0.000000,,,,,,,,,,,
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002529,395369.465315,0.404858,101214583.120550,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.013312,0.017344,0.000000,,,,,,,,,,,
+fft14_vkfft_b4,fft14-batch4,full,fft-library,VkFFT,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,14,16384,4,1000,100,314.885686000,0.008488961,471200.209940766,54.041009678,7720144239.669502258,0.000000000,0.000000000,-1,fft,none,1,,16384,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor8_r2_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix2,0,2,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.016118,254129621.094546,260.228732,65057183000.203850,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.758464,0.720320,0.000000,,,,,,,,,,,
+fft8_vkfft_b16,fft8-batch16,full,fft-library,VkFFT,0,4,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16,1000,100,152.815359000,0.002355200,6793478.244441925,6.956521722,1739130430.577132702,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b2,fft18-batch2,full,fft-library,cuFFT,1,1,2,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,2,1000,100,1.999370000,0.028088320,71203.973633076,167.991250177,18665694464.068958282,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt16_r2_b128,ntt16-batch128,full,ntt,cuNTT-Hybrid2D-radix2,0,2,128,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,128,1000,100,,0.591452,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.870752,10.127264,,64,1152921504606584833,60,8,4,256,0,216416.481397,5928.816625,14183070524.831146,shoup
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.044995,355598.550273,87.391900,11652253295.341375,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.433728,0.414592,0.000000,,,,,,,,,,,
+fwht15_online_b4,fwht15-batch4,full,butterfly,cuButterfly-online-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,4,1000,100,,0.018043,221694.084816,54.483538,7264471771.254147,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.129024,0.135872,0.000000,,,,,,,,,,,
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,4,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1,1000,100,,0.003348,298642.968257,0.305810,76452599.873783,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.007168,0.015744,0.000000,,,,,,,,,,,
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.018115,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.122560,0.133440,,64,1152921504606584833,60,8,4,256,0,55204.213392,3648.109700,3617863328.887691,shoup
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,16,1000,100,,0.020593,776976.657870,190.949783,25459971125.071312,,,-1,fwht,none,1,,32768,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,0.444224,0.411968,0.000000,,,,,,,,,,,
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,5,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.003000,21331058.479890,21.843004,5460750970.851781,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.037888,0.036096,0.000000,,,,,,,,,,,
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,4,1000,100,,0.488335,8191.092601,85.889831,8588983114.683524,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,2.799712,2.596256,0.000000,,,,,,,,,,,
+fwht8_warp_b16,fwht8-batch16,full,butterfly,cuButterfly-warp-register,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16,1000,100,,0.002427,6592827.150528,6.751055,1687763750.535192,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.019456,0.022592,0.000000,,,,,,,,,,,
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,5,16,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,16,1000,100,,0.087245,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,1.426016,1.343328,,64,1152921504606584833,60,8,4,256,0,183392.031869,5601.086229,12018780200.591675,shoup
+fft20_cub_b16,fft20-batch16,full,butterfly,cuButterfly-cuFFTDx-online,0,1,16,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,16,1000,100,,0.927037,17259.281763,180.976686,18097668633.711323,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,21.691744,20.207745,0.000000,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,16384,1000,100,,0.048486,337909184.148800,346.019005,86504751142.092850,,,-1,fwht,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,2.779552,2.601120,0.000000,,,,,,,,,,,
+ntt16_r4_b256,ntt16-batch256,full,ntt,cuNTT-Hybrid2D-radix4,0,5,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,256,1000,100,,1.069629,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,21.603617,36.736862,,64,1152921504606584833,60,8,4,256,0,239335.224551,4309.031025,15685073276.180130,shoup
+fft18_cufft_b64,fft18-batch64,full,fft-library,cuFFT,1,4,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,64,1000,100,2.013464000,0.707194924,90498.387072577,213.512482627,23723609180.753562927,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+ntt12_r4_b4096,ntt12-batch4096,full,ntt,cuNTT-Hybrid2D-radix4,0,3,4096,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,4096,1000,100,,0.535142,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,10.808672,18.928640,,32,1073692673,30,6,4,256,0,7654037.194092,135304.521400,31350936347.002293,shoup
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,434.407323000,0.018677760,53539.610987574,126.315790045,14035087782.726501465,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,3,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,1,1000,100,,0.020716,48272.986164,5.536332,790904605.307889,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,0.038560,0.047808,0.000000,,,,,,,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,5,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,64,1000,100,,0.279675,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,5.470112,5.124992,,64,1152921504606584833,60,8,4,256,0,228837.134918,5885.177270,14997070473.990902,shoup
+ntt12_r2_b256,ntt12-batch256,full,ntt,cuNTT-Hybrid2D-radix2,1,2,256,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,256,1000,100,,0.048568,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.804704,0.733536,,32,1073692673,30,6,4,256,0,5270925.625615,161330.133166,21589711362.517494,shoup
+ntt12_r2_b64,ntt12-batch64,full,ntt,cuNTT-Hybrid2D-radix2,1,1,64,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,64,1000,100,,0.015585,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.281888,0.263232,,32,1073692673,30,6,4,256,0,4106439.135380,114141.960653,16819974698.516592,shoup
+fwht20_online_b2,fwht20-batch2,full,butterfly,cuButterfly-online-radix4,0,3,2,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,2,1000,100,,0.167721,11924.567085,125.038149,12503814855.952843,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,1.438112,1.350560,0.000000,,,,,,,,,,,
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,3,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,14,16384,256,1000,100,,0.121702,2103491.747466,241.245262,34463608790.489891,,,-1,fft,none,1,,16384,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,5.575744,5.102880,0.000000,,,,,,,,,,,
+fft20_cub_b2,fft20-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,2,2,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,2,1000,100,,0.128758,15533.044386,162.875775,16287577549.976408,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,2.774496,2.608576,0.000000,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016425,60882.950637,143.640902,15960100211.727196,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.431520,0.414976,0.000000,,,,,,,,,,,
+fwht20_hier_b16,fwht20-batch16,full,butterfly,cuButterfly-hierarchical-radix4,0,5,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,16,1000,100,,1.867837,8566.055991,89.821607,8982160727.212385,,,-1,fwht,none,1,,1048576,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,10.897664,18.592224,0.000000,,,,,,,,,,,
+ntt20_compact_b8,ntt20-batch8,full,ntt,cuNTT-compact-stage,0,5,8,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,20,1048576,8,1000,100,,0.665344,,,,,,-1,ntt,,1,bit-reversed,1048576,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,10.947392,10.129024,,64,1152921504577486849,60,0,0,256,0,12023.855331,367.955492,12607926128.035173,shoup
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,4,64,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,64,1000,100,2.099075000,0.002826240,22644926.362155665,23.188404595,5797101148.711850166,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b4,fwht8-batch4,full,butterfly,cuButterfly-warp-register,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,4,1000,100,,0.002335,1713267.551602,1.754386,438596493.210203,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.014336,0.018816,0.000000,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,2.086026000,0.002764800,361689.832480331,0.370370388,92592597.114964768,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+xor20_online_b8,xor20-batch8,full,butterfly,cuButterfly-online-radix4,0,4,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,8,1000,100,,0.624271,12814.940514,134.374391,13437439064.778797,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.572768,5.113440,0.000000,,,,,,,,,,,
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,1,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,1,1000,100,,0.002898,345075.077982,0.353357,88339219.963376,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.009216,0.018656,0.000000,,,,,,,,,,,
+fwht20_online_b8,fwht20-batch8,full,butterfly,cuButterfly-online-radix4,0,4,8,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,20,1048576,8,1000,100,,0.624620,12807.796494,134.299480,13429948016.502125,,,-1,fwht,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,5.514176,5.122976,0.000000,,,,,,,,,,,
+fft20_cub_b2,fft20-batch2,full,butterfly,cuButterfly-cuFFTDx-online,0,4,2,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,2,1000,100,,0.128553,15557.790543,163.135258,16313525776.483089,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,2.774368,2.601280,0.000000,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,1,1000,100,,0.071404,14004.912132,146.852147,14685214744.090176,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,1.427776,1.356576,0.000000,,,,,,,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,,12,4096,1,1000,100,,0.005990,,,,,,-1,ntt,,1,natural,4096,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,0.012288,0.023744,,32,1073692673,30,6,4,256,0,166933.774244,23796.832126,683760739.303273,shoup
+fwht8_warp_b65536,fwht8-batch65536,full,butterfly,cuButterfly-warp-register,0,4,65536,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,65536,1000,100,,0.164342,398778769.807163,408.349460,102087365070.633682,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,10.873760,10.113600,0.000000,,,,,,,,,,,
+fft20_cub_b16,fft20-batch16,full,butterfly,cuButterfly-cuFFTDx-online,0,2,16,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,16,1000,100,,0.930765,17190.164580,180.251940,18025194014.479584,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,21.618496,20.150751,0.000000,,,,,,,,,,,
+fft8_vkfft_b16,fft8-batch16,full,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,16,1000,100,200.588983000,0.002375680,6734913.730900121,6.896551660,1724137915.110430956,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,4,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,8,256,64,1000,100,,0.003103,20627062.595822,21.122112,5280528024.530542,,,-1,fft,none,1,,256,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.040352,0.049504,0.000000,,,,,,,,,,,
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,,,uint64,forward,,16,65536,1,1000,100,,0.015882,,,,,,-1,ntt,,1,natural,65536,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,0.124416,0.141472,,64,1152921504606584833,60,8,4,256,0,62963.408291,3548.990854,4126369925.765298,shoup
+xor8_r2_b4096,xor8-batch4096,full,butterfly,cuButterfly-radix2,0,4,4096,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,4096,1000,100,,0.016026,255591039.083629,261.725224,65431306005.409081,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.761312,0.726016,0.000000,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,20,1048576,1,1000,100,2.352250000,0.063569918,15730.710800601,164.948458085,16494845808.451505661,0.000000000,0.000000000,-1,fft,none,1,,1048576,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,4,4,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,18,262144,4,1000,100,1.958447000,0.068597764,58310.938721213,137.572764481,15285862720.133602142,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fft8_vkfft_b4,fft8-batch4,full,fft-library,VkFFT,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,8,256,4,1000,100,200.679865000,0.002355200,1698369.561110481,1.739130431,434782607.644283175,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b512,fwht15-batch512,full,butterfly,cuButterfly-online-radix4,0,5,512,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,512,1000,100,,1.244590,411380.440057,101.100857,13480114259.783314,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,10.907840,10.117632,0.000000,,,,,,,,,,,
diff --git a/results/v100_scaling_full_report.md b/results/v100_scaling_full_report.md
new file mode 100644
index 0000000..52d4aa9
--- /dev/null
+++ b/results/v100_scaling_full_report.md
@@ -0,0 +1,227 @@
+# V100 Orthogonal Length/Batch Scaling
+
+`Batch@90%` is the smallest measured batch reaching 90% of that
+implementation's peak measured `Gpoint/s` at fixed transform length.
+Rows below the configured 0.020 ms timing floor are retained but are not
+used as stable latency claims or peak/saturation references.
+
+## Saturation Summary
+
+| Operator | Numeric | logN | Implementation | Batch@90% | Peak batch | Peak Gpoint/s | Batch-1 ms |
+|:--|:--|--:|:--|--:|--:|--:|--:|
+| fft | fp32 | 8 | VkFFT | 4096 | 4096 | 51.848 | 0.002314 |
+| fft | fp32 | 8 | cuButterfly-cuFFTDx | 4096 | 65536 | 51.206 | 0.002898 |
+| fft | fp32 | 8 | cuFFT | 4096 | 65536 | 51.295 | 0.002683 |
+| fft | fp32 | 14 | VkFFT | 256 | 1024 | 25.533 | 0.008253 |
+| fft | fp32 | 14 | cuButterfly-cuFFTDx-direct | 1024 | 1024 | 44.142 | 0.020552 |
+| fft | fp32 | 14 | cuFFT | 1024 | 1024 | 41.289 | 0.011878 |
+| fft | fp32 | 18 | VkFFT | 2 | 64 | 23.506 | 0.018534 |
+| fft | fp32 | 18 | cuButterfly-cuFFTDx-online | 2 | 16 | 20.450 | 0.016435 |
+| fft | fp32 | 18 | cuFFT | 32 | 64 | 23.752 | 0.023050 |
+| fft | fp32 | 20 | VkFFT | 8 | 16 | 22.726 | 0.061051 |
+| fft | fp32 | 20 | cuButterfly-cuFFTDx-online | 4 | 8 | 18.412 | 0.071404 |
+| fft | fp32 | 20 | cuFFT | 8 | 16 | 23.259 | 0.063570 |
+| fwht | fp32 | 8 | cuButterfly-shared-radix4 | 16384 | 65536 | 94.607 | 0.002488 |
+| fwht | fp32 | 8 | cuButterfly-warp-register | 16384 | 65536 | 102.056 | 0.002058 |
+| fwht | fp32 | 15 | cuButterfly-online-radix4 | 32 | 512 | 13.480 | 0.007690 |
+| fwht | fp32 | 15 | cuButterfly-warp-register | 256 | 512 | 86.876 | 0.017592 |
+| fwht | fp32 | 20 | cuButterfly-hierarchical-radix4 | 1 | 1 | 10.646 | 0.098499 |
+| fwht | fp32 | 20 | cuButterfly-online-radix4 | 2 | 16 | 13.609 | 0.090071 |
+| ntt | uint32 | 12 | cuNTT-Hybrid2D-radix2 | 1024 | 4096 | 26.331 | 0.006871 |
+| ntt | uint32 | 12 | cuNTT-Hybrid2D-radix4 | 1024 | 4096 | 31.167 | 0.005990 |
+| ntt | uint64 | 16 | cuNTT-Hybrid2D-radix2 | 32 | 256 | 14.210 | 0.015872 |
+| ntt | uint64 | 16 | cuNTT-Hybrid2D-radix4 | 64 | 256 | 15.687 | 0.015534 |
+| ntt | uint64 | 20 | cuNTT-compact-stage | 2 | 16 | 12.769 | 0.095058 |
+| xor-zeta | uint32 | 8 | cuButterfly-radix2 | 16384 | 65536 | 93.698 | 0.002888 |
+| xor-zeta | uint32 | 8 | cuButterfly-radix4 | 16384 | 65536 | 95.802 | 0.002478 |
+| xor-zeta | uint32 | 20 | cuButterfly-hierarchical-radix4 | 1 | 1 | 10.677 | 0.098212 |
+| xor-zeta | uint32 | 20 | cuButterfly-online-radix4 | 2 | 16 | 13.617 | 0.090112 |
+
+## Detailed Scaling
+
+| Operator | logN | Batch | Implementation | Median ms | Gpoint/s | Peak fraction | vs basis | Region | Timing quality |
+|:--|--:|--:|:--|--:|--:|--:|--:|:--|:--|
+| fft | 8 | 1 | VkFFT | 0.002314 | 0.111 | 0.002 | 1.159x | launch-limited | below-timing-floor |
+| fft | 8 | 4 | VkFFT | 0.002355 | 0.435 | 0.008 | 1.139x | launch-limited | below-timing-floor |
+| fft | 8 | 16 | VkFFT | 0.002355 | 1.739 | 0.034 | 1.143x | launch-limited | below-timing-floor |
+| fft | 8 | 64 | VkFFT | 0.002458 | 6.667 | 0.129 | 1.113x | launch-limited | below-timing-floor |
+| fft | 8 | 256 | VkFFT | 0.002775 | 23.616 | 0.455 | 1.140x | launch-limited | below-timing-floor |
+| fft | 8 | 1,024 | VkFFT | 0.005786 | 45.310 | 0.874 | 0.784x | ramp | below-timing-floor |
+| fft | 8 | 4,096 | VkFFT | 0.020224 | 51.848 | 1.000 | 1.093x | saturated | stable |
+| fft | 8 | 16,384 | VkFFT | 0.083558 | 50.196 | 0.968 | 1.003x | saturated | stable |
+| fft | 8 | 65,536 | VkFFT | 0.326113 | 51.446 | 0.992 | 1.003x | saturated | stable |
+| fft | 8 | 1 | cuButterfly-cuFFTDx | 0.002898 | 0.088 | 0.002 | 0.926x | launch-limited | below-timing-floor |
+| fft | 8 | 4 | cuButterfly-cuFFTDx | 0.003082 | 0.332 | 0.006 | 0.870x | launch-limited | below-timing-floor |
+| fft | 8 | 16 | cuButterfly-cuFFTDx | 0.003103 | 1.320 | 0.026 | 0.868x | launch-limited | below-timing-floor |
+| fft | 8 | 64 | cuButterfly-cuFFTDx | 0.003103 | 5.280 | 0.103 | 0.881x | launch-limited | below-timing-floor |
+| fft | 8 | 256 | cuButterfly-cuFFTDx | 0.003348 | 19.575 | 0.382 | 0.945x | launch-limited | below-timing-floor |
+| fft | 8 | 1,024 | cuButterfly-cuFFTDx | 0.005181 | 50.597 | 0.988 | 0.876x | saturated | below-timing-floor |
+| fft | 8 | 4,096 | cuButterfly-cuFFTDx | 0.022098 | 47.451 | 0.927 | 1.000x | saturated | stable |
+| fft | 8 | 16,384 | cuButterfly-cuFFTDx | 0.084275 | 49.769 | 0.972 | 0.994x | saturated | stable |
+| fft | 8 | 65,536 | cuButterfly-cuFFTDx | 0.327639 | 51.206 | 1.000 | 0.998x | saturated | stable |
+| fft | 8 | 1 | cuFFT | 0.002683 | 0.095 | 0.002 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 4 | cuFFT | 0.002683 | 0.382 | 0.007 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 16 | cuFFT | 0.002693 | 1.521 | 0.030 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 64 | cuFFT | 0.002734 | 5.993 | 0.117 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 256 | cuFFT | 0.003164 | 20.712 | 0.404 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 1,024 | cuFFT | 0.004536 | 57.788 | 1.127 | 1.000x | saturated | below-timing-floor |
+| fft | 8 | 4,096 | cuFFT | 0.022098 | 47.451 | 0.925 | 1.000x | saturated | stable |
+| fft | 8 | 16,384 | cuFFT | 0.083794 | 50.055 | 0.976 | 1.000x | saturated | stable |
+| fft | 8 | 65,536 | cuFFT | 0.327076 | 51.295 | 1.000 | 1.000x | saturated | stable |
+| fft | 14 | 1 | VkFFT | 0.008253 | 1.985 | 0.078 | 1.439x | launch-limited | below-timing-floor |
+| fft | 14 | 4 | VkFFT | 0.008489 | 7.720 | 0.302 | 1.407x | launch-limited | below-timing-floor |
+| fft | 14 | 16 | VkFFT | 0.010680 | 24.545 | 0.961 | 1.264x | saturated | below-timing-floor |
+| fft | 14 | 64 | VkFFT | 0.047227 | 22.203 | 0.870 | 0.585x | ramp | stable |
+| fft | 14 | 256 | VkFFT | 0.171725 | 24.425 | 0.957 | 0.705x | saturated | stable |
+| fft | 14 | 1,024 | VkFFT | 0.657070 | 25.533 | 1.000 | 0.618x | saturated | stable |
+| fft | 14 | 1 | cuButterfly-cuFFTDx-direct | 0.020552 | 0.797 | 0.018 | 0.578x | launch-limited | stable |
+| fft | 14 | 4 | cuButterfly-cuFFTDx-direct | 0.020603 | 3.181 | 0.072 | 0.580x | launch-limited | stable |
+| fft | 14 | 16 | cuButterfly-cuFFTDx-direct | 0.020777 | 12.617 | 0.286 | 0.650x | launch-limited | stable-with-outlier |
+| fft | 14 | 64 | cuButterfly-cuFFTDx-direct | 0.031693 | 33.085 | 0.750 | 0.872x | ramp | stable-with-outlier |
+| fft | 14 | 256 | cuButterfly-cuFFTDx-direct | 0.121395 | 34.551 | 0.783 | 0.998x | ramp | stable |
+| fft | 14 | 1,024 | cuButterfly-cuFFTDx-direct | 0.380078 | 44.142 | 1.000 | 1.069x | saturated | stable |
+| fft | 14 | 1 | cuFFT | 0.011878 | 1.379 | 0.033 | 1.000x | launch-limited | below-timing-floor |
+| fft | 14 | 4 | cuFFT | 0.011940 | 5.489 | 0.133 | 1.000x | launch-limited | below-timing-floor |
+| fft | 14 | 16 | cuFFT | 0.013496 | 19.423 | 0.470 | 1.000x | launch-limited | below-timing-floor |
+| fft | 14 | 64 | cuFFT | 0.027648 | 37.926 | 0.919 | 1.000x | saturated | unstable |
+| fft | 14 | 256 | cuFFT | 0.121098 | 34.636 | 0.839 | 1.000x | ramp | stable |
+| fft | 14 | 1,024 | cuFFT | 0.406333 | 41.289 | 1.000 | 1.000x | saturated | stable |
+| fft | 18 | 1 | VkFFT | 0.018534 | 14.144 | 0.602 | 1.244x | ramp | below-timing-floor |
+| fft | 18 | 2 | VkFFT | 0.023583 | 22.232 | 0.946 | 1.191x | saturated | stable |
+| fft | 18 | 4 | VkFFT | 0.063816 | 16.431 | 0.699 | 1.075x | ramp | stable |
+| fft | 18 | 8 | VkFFT | 0.111780 | 18.761 | 0.798 | 1.099x | ramp | stable |
+| fft | 18 | 16 | VkFFT | 0.201257 | 20.841 | 0.887 | 1.049x | ramp | stable |
+| fft | 18 | 32 | VkFFT | 0.372163 | 22.540 | 0.959 | 1.018x | saturated | stable |
+| fft | 18 | 64 | VkFFT | 0.713728 | 23.506 | 1.000 | 0.990x | saturated | stable |
+| fft | 18 | 1 | cuButterfly-cuFFTDx-online | 0.016435 | 15.950 | 0.780 | 1.403x | ramp | below-timing-floor |
+| fft | 18 | 2 | cuButterfly-cuFFTDx-online | 0.025969 | 20.189 | 0.987 | 1.082x | saturated | stable |
+| fft | 18 | 4 | cuButterfly-cuFFTDx-online | 0.059628 | 17.585 | 0.860 | 1.150x | ramp | stable |
+| fft | 18 | 8 | cuButterfly-cuFFTDx-online | 0.108851 | 19.266 | 0.942 | 1.129x | saturated | stable |
+| fft | 18 | 16 | cuButterfly-cuFFTDx-online | 0.205097 | 20.450 | 1.000 | 1.030x | saturated | stable |
+| fft | 18 | 32 | cuButterfly-cuFFTDx-online | 0.411238 | 20.398 | 0.997 | 0.921x | saturated | stable |
+| fft | 18 | 64 | cuButterfly-cuFFTDx-online | 0.840888 | 19.952 | 0.976 | 0.840x | saturated | stable |
+| fft | 18 | 1 | cuFFT | 0.023050 | 11.373 | 0.479 | 1.000x | launch-limited | stable |
+| fft | 18 | 2 | cuFFT | 0.028088 | 18.666 | 0.786 | 1.000x | ramp | stable |
+| fft | 18 | 4 | cuFFT | 0.068598 | 15.286 | 0.644 | 1.000x | ramp | stable |
+| fft | 18 | 8 | cuFFT | 0.122870 | 17.068 | 0.719 | 1.000x | ramp | stable |
+| fft | 18 | 16 | cuFFT | 0.211149 | 19.864 | 0.836 | 1.000x | ramp | stable |
+| fft | 18 | 32 | cuFFT | 0.378737 | 22.149 | 0.933 | 1.000x | saturated | stable |
+| fft | 18 | 64 | cuFFT | 0.706355 | 23.752 | 1.000 | 1.000x | saturated | stable |
+| fft | 20 | 1 | VkFFT | 0.061051 | 17.175 | 0.756 | 1.041x | ramp | stable-with-outlier |
+| fft | 20 | 2 | VkFFT | 0.117484 | 17.851 | 0.785 | 1.049x | ramp | stable-with-outlier |
+| fft | 20 | 4 | VkFFT | 0.206705 | 20.291 | 0.893 | 1.017x | ramp | stable |
+| fft | 20 | 8 | VkFFT | 0.384266 | 21.830 | 0.961 | 0.993x | saturated | stable |
+| fft | 20 | 16 | VkFFT | 0.738243 | 22.726 | 1.000 | 0.977x | saturated | stable |
+| fft | 20 | 1 | cuButterfly-cuFFTDx-online | 0.071404 | 14.685 | 0.798 | 0.890x | ramp | stable-with-outlier |
+| fft | 20 | 2 | cuButterfly-cuFFTDx-online | 0.128553 | 16.314 | 0.886 | 0.959x | ramp | stable |
+| fft | 20 | 4 | cuButterfly-cuFFTDx-online | 0.235581 | 17.804 | 0.967 | 0.892x | saturated | stable |
+| fft | 20 | 8 | cuButterfly-cuFFTDx-online | 0.455598 | 18.412 | 1.000 | 0.837x | saturated | stable |
+| fft | 20 | 16 | cuButterfly-cuFFTDx-online | 0.927017 | 18.098 | 0.983 | 0.778x | saturated | stable |
+| fft | 20 | 1 | cuFFT | 0.063570 | 16.495 | 0.709 | 1.000x | ramp | stable |
+| fft | 20 | 2 | cuFFT | 0.123228 | 17.018 | 0.732 | 1.000x | ramp | stable |
+| fft | 20 | 4 | cuFFT | 0.210237 | 19.950 | 0.858 | 1.000x | ramp | stable |
+| fft | 20 | 8 | cuFFT | 0.381512 | 21.988 | 0.945 | 1.000x | saturated | stable |
+| fft | 20 | 16 | cuFFT | 0.721326 | 23.259 | 1.000 | 1.000x | saturated | stable |
+| fwht | 8 | 1 | cuButterfly-shared-radix4 | 0.002488 | 0.103 | 0.001 | 0.827x | launch-limited | below-timing-floor |
+| fwht | 8 | 4 | cuButterfly-shared-radix4 | 0.002488 | 0.412 | 0.004 | 0.856x | launch-limited | below-timing-floor |
+| fwht | 8 | 16 | cuButterfly-shared-radix4 | 0.002540 | 1.613 | 0.017 | 0.851x | launch-limited | below-timing-floor |
+| fwht | 8 | 64 | cuButterfly-shared-radix4 | 0.002550 | 6.425 | 0.068 | 0.827x | launch-limited | below-timing-floor |
+| fwht | 8 | 256 | cuButterfly-shared-radix4 | 0.002949 | 22.223 | 0.235 | 0.820x | launch-limited | below-timing-floor |
+| fwht | 8 | 1,024 | cuButterfly-shared-radix4 | 0.004352 | 60.235 | 0.637 | 0.814x | ramp | below-timing-floor |
+| fwht | 8 | 4,096 | cuButterfly-shared-radix4 | 0.014971 | 70.040 | 0.740 | 0.750x | ramp | below-timing-floor |
+| fwht | 8 | 16,384 | cuButterfly-shared-radix4 | 0.048486 | 86.505 | 0.914 | 0.882x | saturated | stable |
+| fwht | 8 | 65,536 | cuButterfly-shared-radix4 | 0.177336 | 94.607 | 1.000 | 0.927x | saturated | stable |
+| fwht | 8 | 1 | cuButterfly-warp-register | 0.002058 | 0.124 | 0.001 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 4 | cuButterfly-warp-register | 0.002130 | 0.481 | 0.005 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 16 | cuButterfly-warp-register | 0.002161 | 1.895 | 0.019 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 64 | cuButterfly-warp-register | 0.002109 | 7.769 | 0.076 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 256 | cuButterfly-warp-register | 0.002417 | 27.115 | 0.266 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 1,024 | cuButterfly-warp-register | 0.003543 | 73.989 | 0.725 | 1.000x | ramp | below-timing-floor |
+| fwht | 8 | 4,096 | cuButterfly-warp-register | 0.011233 | 93.348 | 0.915 | 1.000x | saturated | below-timing-floor |
+| fwht | 8 | 16,384 | cuButterfly-warp-register | 0.042762 | 98.085 | 0.961 | 1.000x | saturated | stable |
+| fwht | 8 | 65,536 | cuButterfly-warp-register | 0.164393 | 102.056 | 1.000 | 1.000x | saturated | stable |
+| fwht | 15 | 1 | cuButterfly-online-radix4 | 0.007690 | 4.261 | 0.316 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 15 | 4 | cuButterfly-online-radix4 | 0.015309 | 8.562 | 0.635 | 1.000x | ramp | below-timing-floor |
+| fwht | 15 | 16 | cuButterfly-online-radix4 | 0.044698 | 11.730 | 0.870 | 0.394x | ramp | stable-with-outlier |
+| fwht | 15 | 32 | cuButterfly-online-radix4 | 0.084255 | 12.445 | 0.923 | 0.266x | saturated | stable |
+| fwht | 15 | 128 | cuButterfly-online-radix4 | 0.317020 | 13.230 | 0.981 | 0.205x | saturated | stable |
+| fwht | 15 | 256 | cuButterfly-online-radix4 | 0.625777 | 13.405 | 0.994 | 0.171x | saturated | stable |
+| fwht | 15 | 512 | cuButterfly-online-radix4 | 1.244590 | 13.480 | 1.000 | 0.155x | saturated | stable |
+| fwht | 15 | 1 | cuButterfly-warp-register | 0.017592 | 1.863 | 0.021 | 0.437x | launch-limited | below-timing-floor |
+| fwht | 15 | 4 | cuButterfly-warp-register | 0.017654 | 7.424 | 0.085 | 0.867x | launch-limited | below-timing-floor |
+| fwht | 15 | 16 | cuButterfly-warp-register | 0.017613 | 29.767 | 0.343 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 15 | 32 | cuButterfly-warp-register | 0.022385 | 46.843 | 0.539 | 1.000x | ramp | stable |
+| fwht | 15 | 128 | cuButterfly-warp-register | 0.064840 | 64.687 | 0.745 | 1.000x | ramp | stable |
+| fwht | 15 | 256 | cuButterfly-warp-register | 0.107244 | 78.220 | 0.900 | 1.000x | saturated | stable-with-outlier |
+| fwht | 15 | 512 | cuButterfly-warp-register | 0.193116 | 86.876 | 1.000 | 1.000x | saturated | stable |
+| fwht | 20 | 1 | cuButterfly-hierarchical-radix4 | 0.098499 | 10.646 | 1.000 | 0.914x | saturated | stable |
+| fwht | 20 | 2 | cuButterfly-hierarchical-radix4 | 0.257331 | 8.150 | 0.766 | 0.650x | ramp | stable |
+| fwht | 20 | 4 | cuButterfly-hierarchical-radix4 | 0.488110 | 8.593 | 0.807 | 0.655x | ramp | stable |
+| fwht | 20 | 8 | cuButterfly-hierarchical-radix4 | 0.947814 | 8.850 | 0.831 | 0.659x | ramp | stable |
+| fwht | 20 | 16 | cuButterfly-hierarchical-radix4 | 1.868196 | 8.980 | 0.844 | 0.660x | ramp | stable |
+| fwht | 20 | 1 | cuButterfly-online-radix4 | 0.090071 | 11.642 | 0.855 | 1.000x | ramp | stable |
+| fwht | 20 | 2 | cuButterfly-online-radix4 | 0.167301 | 12.535 | 0.921 | 1.000x | saturated | stable |
+| fwht | 20 | 4 | cuButterfly-online-radix4 | 0.319857 | 13.113 | 0.964 | 1.000x | saturated | stable |
+| fwht | 20 | 8 | cuButterfly-online-radix4 | 0.624742 | 13.427 | 0.987 | 1.000x | saturated | stable |
+| fwht | 20 | 16 | cuButterfly-online-radix4 | 1.232824 | 13.609 | 1.000 | 1.000x | saturated | stable |
+| ntt | 12 | 1 | cuNTT-Hybrid2D-radix2 | 0.006871 | 0.596 | 0.023 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 12 | 4 | cuNTT-Hybrid2D-radix2 | 0.007158 | 2.289 | 0.087 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 12 | 16 | cuNTT-Hybrid2D-radix2 | 0.008468 | 7.739 | 0.294 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 12 | 64 | cuNTT-Hybrid2D-radix2 | 0.015483 | 16.931 | 0.643 | 1.000x | ramp | below-timing-floor |
+| ntt | 12 | 256 | cuNTT-Hybrid2D-radix2 | 0.048230 | 21.741 | 0.826 | 1.000x | ramp | stable-with-outlier |
+| ntt | 12 | 1,024 | cuNTT-Hybrid2D-radix2 | 0.164413 | 25.511 | 0.969 | 1.000x | saturated | stable-with-outlier |
+| ntt | 12 | 4,096 | cuNTT-Hybrid2D-radix2 | 0.637164 | 26.331 | 1.000 | 1.000x | saturated | stable |
+| ntt | 12 | 1 | cuNTT-Hybrid2D-radix4 | 0.005990 | 0.684 | 0.022 | 1.147x | launch-limited | below-timing-floor |
+| ntt | 12 | 4 | cuNTT-Hybrid2D-radix4 | 0.006369 | 2.572 | 0.083 | 1.124x | launch-limited | below-timing-floor |
+| ntt | 12 | 16 | cuNTT-Hybrid2D-radix4 | 0.007629 | 8.590 | 0.276 | 1.110x | launch-limited | below-timing-floor |
+| ntt | 12 | 64 | cuNTT-Hybrid2D-radix4 | 0.013855 | 18.921 | 0.607 | 1.118x | ramp | below-timing-floor |
+| ntt | 12 | 256 | cuNTT-Hybrid2D-radix4 | 0.042824 | 24.486 | 0.786 | 1.126x | ramp | stable |
+| ntt | 12 | 1,024 | cuNTT-Hybrid2D-radix4 | 0.139889 | 29.983 | 0.962 | 1.175x | saturated | stable |
+| ntt | 12 | 4,096 | cuNTT-Hybrid2D-radix4 | 0.538307 | 31.167 | 1.000 | 1.184x | saturated | stable |
+| ntt | 16 | 1 | cuNTT-Hybrid2D-radix2 | 0.015872 | 4.129 | 0.291 | 0.979x | launch-limited | below-timing-floor |
+| ntt | 16 | 4 | cuNTT-Hybrid2D-radix2 | 0.031549 | 8.309 | 0.585 | 0.933x | ramp | stable |
+| ntt | 16 | 16 | cuNTT-Hybrid2D-radix2 | 0.087163 | 12.030 | 0.847 | 0.945x | ramp | stable-with-outlier |
+| ntt | 16 | 32 | cuNTT-Hybrid2D-radix2 | 0.160543 | 13.063 | 0.919 | 0.928x | saturated | stable |
+| ntt | 16 | 64 | cuNTT-Hybrid2D-radix2 | 0.305172 | 13.744 | 0.967 | 0.916x | saturated | stable |
+| ntt | 16 | 128 | cuNTT-Hybrid2D-radix2 | 0.591452 | 14.183 | 0.998 | 0.914x | saturated | stable |
+| ntt | 16 | 256 | cuNTT-Hybrid2D-radix2 | 1.180631 | 14.210 | 1.000 | 0.906x | saturated | stable |
+| ntt | 16 | 1 | cuNTT-Hybrid2D-radix4 | 0.015534 | 4.219 | 0.269 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 16 | 4 | cuNTT-Hybrid2D-radix4 | 0.029430 | 8.907 | 0.568 | 1.000x | ramp | stable-with-outlier |
+| ntt | 16 | 16 | cuNTT-Hybrid2D-radix4 | 0.082381 | 12.728 | 0.811 | 1.000x | ramp | stable-with-outlier |
+| ntt | 16 | 32 | cuNTT-Hybrid2D-radix4 | 0.149043 | 14.071 | 0.897 | 1.000x | ramp | stable |
+| ntt | 16 | 64 | cuNTT-Hybrid2D-radix4 | 0.279552 | 15.004 | 0.956 | 1.000x | saturated | stable |
+| ntt | 16 | 128 | cuNTT-Hybrid2D-radix4 | 0.540559 | 15.518 | 0.989 | 1.000x | saturated | stable |
+| ntt | 16 | 256 | cuNTT-Hybrid2D-radix4 | 1.069466 | 15.687 | 1.000 | 1.000x | saturated | stable |
+| ntt | 20 | 1 | cuNTT-compact-stage | 0.095058 | 11.031 | 0.864 | 1.000x | ramp | stable |
+| ntt | 20 | 2 | cuNTT-compact-stage | 0.179866 | 11.660 | 0.913 | 1.000x | saturated | stable |
+| ntt | 20 | 4 | cuNTT-compact-stage | 0.342262 | 12.255 | 0.960 | 1.000x | saturated | stable |
+| ntt | 20 | 8 | cuNTT-compact-stage | 0.665016 | 12.614 | 0.988 | 1.000x | saturated | stable |
+| ntt | 20 | 16 | cuNTT-compact-stage | 1.313854 | 12.769 | 1.000 | 1.000x | saturated | stable |
+| xor-zeta | 8 | 1 | cuButterfly-radix2 | 0.002888 | 0.089 | 0.001 | 0.858x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 4 | cuButterfly-radix2 | 0.002867 | 0.357 | 0.004 | 0.872x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 16 | cuButterfly-radix2 | 0.002898 | 1.413 | 0.015 | 0.873x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 64 | cuButterfly-radix2 | 0.002918 | 5.615 | 0.060 | 0.877x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 256 | cuButterfly-radix2 | 0.003308 | 19.811 | 0.211 | 0.888x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 1,024 | cuButterfly-radix2 | 0.004823 | 54.353 | 0.580 | 0.900x | ramp | below-timing-floor |
+| xor-zeta | 8 | 4,096 | cuButterfly-radix2 | 0.016077 | 65.222 | 0.696 | 0.921x | ramp | below-timing-floor |
+| xor-zeta | 8 | 16,384 | cuButterfly-radix2 | 0.049715 | 84.367 | 0.900 | 0.961x | saturated | stable |
+| xor-zeta | 8 | 65,536 | cuButterfly-radix2 | 0.179057 | 93.698 | 1.000 | 0.978x | saturated | stable |
+| xor-zeta | 8 | 1 | cuButterfly-radix4 | 0.002478 | 0.103 | 0.001 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 4 | cuButterfly-radix4 | 0.002499 | 0.410 | 0.004 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 16 | cuButterfly-radix4 | 0.002529 | 1.620 | 0.017 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 64 | cuButterfly-radix4 | 0.002560 | 6.400 | 0.067 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 256 | cuButterfly-radix4 | 0.002939 | 22.299 | 0.233 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 1,024 | cuButterfly-radix4 | 0.004342 | 60.374 | 0.630 | 1.000x | ramp | below-timing-floor |
+| xor-zeta | 8 | 4,096 | cuButterfly-radix4 | 0.014807 | 70.816 | 0.739 | 1.000x | ramp | below-timing-floor |
+| xor-zeta | 8 | 16,384 | cuButterfly-radix4 | 0.047790 | 87.765 | 0.916 | 1.000x | saturated | stable |
+| xor-zeta | 8 | 65,536 | cuButterfly-radix4 | 0.175124 | 95.802 | 1.000 | 1.000x | saturated | stable |
+| xor-zeta | 20 | 1 | cuButterfly-hierarchical-radix4 | 0.098212 | 10.677 | 1.000 | 0.918x | saturated | stable |
+| xor-zeta | 20 | 2 | cuButterfly-hierarchical-radix4 | 0.256819 | 8.166 | 0.765 | 0.651x | ramp | stable |
+| xor-zeta | 20 | 4 | cuButterfly-hierarchical-radix4 | 0.487014 | 8.612 | 0.807 | 0.656x | ramp | stable |
+| xor-zeta | 20 | 8 | cuButterfly-hierarchical-radix4 | 0.945746 | 8.870 | 0.831 | 0.660x | ramp | stable |
+| xor-zeta | 20 | 16 | cuButterfly-hierarchical-radix4 | 1.863813 | 9.002 | 0.843 | 0.661x | ramp | stable |
+| xor-zeta | 20 | 1 | cuButterfly-online-radix4 | 0.090112 | 11.636 | 0.855 | 1.000x | ramp | stable-with-outlier |
+| xor-zeta | 20 | 2 | cuButterfly-online-radix4 | 0.167076 | 12.552 | 0.922 | 1.000x | saturated | stable |
+| xor-zeta | 20 | 4 | cuButterfly-online-radix4 | 0.319273 | 13.137 | 0.965 | 1.000x | saturated | stable |
+| xor-zeta | 20 | 8 | cuButterfly-online-radix4 | 0.623821 | 13.447 | 0.988 | 1.000x | saturated | stable |
+| xor-zeta | 20 | 16 | cuButterfly-online-radix4 | 1.232067 | 13.617 | 1.000 | 1.000x | saturated | stable |
diff --git a/results/v100_scaling_full_summary.csv b/results/v100_scaling_full_summary.csv
new file mode 100644
index 0000000..fe4c6b5
--- /dev/null
+++ b/results/v100_scaling_full_summary.csv
@@ -0,0 +1,185 @@
+case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,shared_layout,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class,peak_billion_points_s,peak_batch,fraction_of_peak,saturation_fraction,saturation_batch,throughput_speedup_vs_batch1,batch_efficiency_vs_batch1,scaling_region,timing_floor_ms,timing_quality,eligible_for_saturation
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+fft8_vkfft_b4,fft8-batch4,VkFFT,0,5,0.002355200,0.002355200,0.002539520,0.078261,0.017391,stable-with-outlier,1,fft,fp32,forward,none,in-place,8,256,4,1,256,,,,,,,,,,,1.698369565,0.434782609,declared-reference,cuFFT,0.002682880,1.139130,faster,51.848103830,4096,0.008386,0.900000,4096,3.930435,0.982609,launch-limited,0.020000,below-timing-floor,0
+fft8_vkfft_b16,fft8-batch16,VkFFT,0,5,0.002355200,0.002324480,0.002375680,0.021739,0.004348,stable,1,fft,fp32,forward,none,in-place,8,256,16,1,256,,,,,,,,,,,6.793478261,1.739130435,declared-reference,cuFFT,0.002693120,1.143478,faster,51.848103830,4096,0.033543,0.900000,4096,15.721739,0.982609,launch-limited,0.020000,below-timing-floor,0
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+fft14_vkfft_b1,fft14-batch1,VkFFT,0,5,0.008253440,0.008243200,0.008263680,0.002481,0.002481,stable,1,fft,fp32,forward,none,in-place,14,16384,1,1,16384,,,,,,,,,,,0.121161600,1.985111663,declared-reference,cuFFT,0.011878400,1.439206,faster,25.533373075,1024,0.077746,0.900000,256,1.000000,1.000000,launch-limited,0.020000,below-timing-floor,0
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+xor8_r2_b4,xor8-batch4,cuButterfly-radix2,0,5,0.002867000,0.002857000,0.003011000,0.053715,0.003488,stable-with-outlier,1,xor-zeta,uint32,forward,none,out-of-place,8,256,4,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,1.395186606,0.357167771,group-fastest,cuButterfly-radix4,0.002499000,0.871643,slower,93.697627013,65536,0.003812,0.900000,16384,4.029299,1.007325,launch-limited,0.020000,below-timing-floor,0
+xor8_r2_b16,xor8-batch16,cuButterfly-radix2,0,5,0.002898000,0.002888000,0.003011000,0.042443,0.017598,stable-with-outlier,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,5.521048999,1.413388544,group-fastest,cuButterfly-radix4,0.002529000,0.872671,slower,93.697627013,65536,0.015085,0.900000,16384,15.944790,0.996549,launch-limited,0.020000,below-timing-floor,0
+xor8_r2_b64,xor8-batch64,cuButterfly-radix2,0,5,0.002918000,0.002908000,0.002929000,0.007197,0.003770,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,64,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,21.932830706,5.614804661,group-fastest,cuButterfly-radix4,0.002560000,0.877313,slower,93.697627013,65536,0.059925,0.900000,16384,63.342015,0.989719,launch-limited,0.020000,below-timing-floor,0
+xor8_r2_b256,xor8-batch256,cuButterfly-radix2,0,5,0.003308000,0.003287000,0.003369000,0.024788,0.006348,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,256,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,77.388149940,19.811366385,group-fastest,cuButterfly-radix4,0.002939000,0.888452,slower,93.697627013,65536,0.211439,0.900000,16384,223.496977,0.873035,launch-limited,0.020000,below-timing-floor,0
+xor8_r2_b1024,xor8-batch1024,cuButterfly-radix2,0,5,0.004823000,0.004803000,0.004884000,0.016795,0.010574,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,1024,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,212.315985901,54.352892391,group-fastest,cuButterfly-radix4,0.004342000,0.900270,slower,93.697627013,65536,0.580088,0.900000,16384,613.168567,0.598797,ramp,0.020000,below-timing-floor,0
+xor8_r2_b4096,xor8-batch4096,cuButterfly-radix2,0,5,0.016077000,0.016005000,0.016220000,0.013373,0.005722,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,4096,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,254.773900603,65.222118554,group-fastest,cuButterfly-radix4,0.014807000,0.921005,slower,93.697627013,65536,0.696091,0.900000,16384,735.787025,0.179636,ramp,0.020000,below-timing-floor,0
+xor8_r2_b16384,xor8-batch16384,cuButterfly-radix2,0,5,0.049715000,0.049633000,0.049725000,0.001851,0.000201,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,329.558483355,84.366971739,group-fastest,cuButterfly-radix4,0.047790000,0.961279,slower,93.697627013,65536,0.900417,0.900000,16384,951.764900,0.058091,saturated,0.020000,stable,1
+xor8_r2_b65536,xor8-batch65536,cuButterfly-radix2,0,5,0.179057000,0.178954000,0.179241000,0.001603,0.000514,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,65536,1,256,,,,,temporal-tile,radix2,scalar,shared,,table,366.006355518,93.697627013,group-fastest,cuButterfly-radix4,0.175124000,0.978035,parity,93.697627013,65536,1.000000,0.900000,16384,1057.026355,0.016129,saturated,0.020000,stable,1
+xor8_r4_b1,xor8-batch1,cuButterfly-radix4,0,5,0.002478000,0.002478000,0.002499000,0.008475,0.004036,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,1,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,0.403551251,0.103309120,group-fastest,cuButterfly-radix4,0.002478000,1.000000,parity,95.801923209,65536,0.001078,0.900000,16384,1.000000,1.000000,launch-limited,0.020000,below-timing-floor,0
+xor8_r4_b4,xor8-batch4,cuButterfly-radix4,0,5,0.002499000,0.002488000,0.002509000,0.008403,0.000000,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,4,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,1.600640256,0.409763906,group-fastest,cuButterfly-radix4,0.002499000,1.000000,parity,95.801923209,65536,0.004277,0.900000,16384,3.966387,0.991597,launch-limited,0.020000,below-timing-floor,0
+xor8_r4_b16,xor8-batch16,cuButterfly-radix4,0,5,0.002529000,0.002509000,0.002580000,0.028074,0.008304,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,6.326611309,1.619612495,group-fastest,cuButterfly-radix4,0.002529000,1.000000,parity,95.801923209,65536,0.016906,0.900000,16384,15.677343,0.979834,launch-limited,0.020000,below-timing-floor,0
+xor8_r4_b64,xor8-batch64,cuButterfly-radix4,0,5,0.002560000,0.002540000,0.002570000,0.011719,0.007812,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,64,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,25.000000000,6.400000000,group-fastest,cuButterfly-radix4,0.002560000,1.000000,parity,95.801923209,65536,0.066805,0.900000,16384,61.950000,0.967969,launch-limited,0.020000,below-timing-floor,0
+xor8_r4_b256,xor8-batch256,cuButterfly-radix4,0,5,0.002939000,0.002918000,0.002939000,0.007145,0.000000,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,256,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,87.104457298,22.298741068,group-fastest,cuButterfly-radix4,0.002939000,1.000000,parity,95.801923209,65536,0.232759,0.900000,16384,215.844845,0.843144,launch-limited,0.020000,below-timing-floor,0
+xor8_r4_b1024,xor8-batch1024,cuButterfly-radix4,0,5,0.004342000,0.004332000,0.004536000,0.046983,0.002303,stable-with-outlier,1,xor-zeta,uint32,forward,none,out-of-place,8,256,1024,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,235.836020267,60.374021188,group-fastest,cuButterfly-radix4,0.004342000,1.000000,parity,95.801923209,65536,0.630196,0.900000,16384,584.401658,0.570705,ramp,0.020000,below-timing-floor,0
+xor8_r4_b4096,xor8-batch4096,cuButterfly-radix4,0,5,0.014807000,0.014725000,0.014909000,0.012427,0.005538,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,4096,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,276.625920173,70.816235564,group-fastest,cuButterfly-radix4,0.014807000,1.000000,parity,95.801923209,65536,0.739194,0.900000,16384,685.479030,0.167353,ramp,0.020000,below-timing-floor,0
+xor8_r4_b16384,xor8-batch16384,cuButterfly-radix4,0,5,0.047790000,0.047749000,0.048527000,0.016280,0.001507,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,16384,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,342.833228709,87.765306549,group-fastest,cuButterfly-radix4,0.047790000,1.000000,parity,95.801923209,65536,0.916112,0.900000,16384,849.540741,0.051852,saturated,0.020000,stable,1
+xor8_r4_b65536,xor8-batch65536,cuButterfly-radix4,0,5,0.175124000,0.175114000,0.175176000,0.000354,0.000354,stable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,65536,1,256,,,,,temporal-tile,radix4,scalar,shared,,table,374.226262534,95.801923209,group-fastest,cuButterfly-radix4,0.175124000,1.000000,parity,95.801923209,65536,1.000000,0.900000,16384,927.332679,0.014150,saturated,0.020000,stable,1
+xor20_hier_b1,xor20-batch1,cuButterfly-hierarchical-radix4,0,5,0.098212000,0.098120000,0.099645000,0.015528,0.001151,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,1,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.010182055,10.676658657,group-fastest,cuButterfly-online-radix4,0.090112000,0.917525,slower,10.676658657,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,stable,1
+xor20_hier_b2,xor20-batch2,cuButterfly-hierarchical-radix4,0,5,0.256819000,0.256696000,0.257004000,0.001199,0.000199,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,2,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.007787586,8.165875578,group-fastest,cuButterfly-online-radix4,0.167076000,0.650559,slower,10.676658657,1,0.764834,0.900000,1,0.764834,0.382417,ramp,0.020000,stable,1
+xor20_hier_b4,xor20-batch4,cuButterfly-hierarchical-radix4,0,5,0.487014000,0.486984000,0.487055000,0.000146,0.000000,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.008213316,8.612286300,group-fastest,cuButterfly-online-radix4,0.319273000,0.655573,slower,10.676658657,1,0.806646,0.900000,1,0.806646,0.201662,ramp,0.020000,stable,1
+xor20_hier_b8,xor20-batch8,cuButterfly-hierarchical-radix4,0,5,0.945746000,0.945613000,0.945766000,0.000162,0.000130,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,8,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.008458931,8.869831858,group-fastest,cuButterfly-online-radix4,0.623821000,0.659607,slower,10.676658657,1,0.830769,0.900000,1,0.830769,0.103846,ramp,0.020000,stable,1
+xor20_hier_b16,xor20-batch16,cuButterfly-hierarchical-radix4,0,5,1.863813000,1.863741000,1.863956000,0.000115,0.000071,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,16,1,1048576,,,,,hierarchical,radix4,scalar,shared,,table,0.008584552,9.001555414,group-fastest,cuButterfly-online-radix4,1.232067000,0.661046,slower,10.676658657,1,0.843106,0.900000,1,0.843106,0.052694,ramp,0.020000,stable,1
+xor20_online_b1,xor20-batch1,cuButterfly-online-radix4,0,5,0.090112000,0.090030000,0.095283000,0.058294,0.028187,stable-with-outlier,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,1,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.011097301,11.636363636,group-fastest,cuButterfly-online-radix4,0.090112000,1.000000,parity,13.617129588,16,0.854539,0.900000,2,1.000000,1.000000,ramp,0.020000,stable-with-outlier,1
+xor20_online_b2,xor20-batch2,cuButterfly-online-radix4,0,5,0.167076000,0.166902000,0.167137000,0.001407,0.000982,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,2,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.011970600,12.552084081,group-fastest,cuButterfly-online-radix4,0.167076000,1.000000,parity,13.617129588,16,0.921786,0.900000,2,1.078695,0.539347,saturated,0.020000,stable,1
+xor20_online_b4,xor20-batch4,cuButterfly-online-radix4,0,5,0.319273000,0.318945000,0.320901000,0.006126,0.000899,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.012528463,13.137045726,group-fastest,cuButterfly-online-radix4,0.319273000,1.000000,parity,13.617129588,16,0.964744,0.900000,2,1.128965,0.282241,saturated,0.020000,stable,1
+xor20_online_b8,xor20-batch8,cuButterfly-online-radix4,0,5,0.623821000,0.623114000,0.624271000,0.001855,0.000345,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,8,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.012824192,13.447139484,group-fastest,cuButterfly-online-radix4,0.623821000,1.000000,parity,13.617129588,16,0.987516,0.900000,2,1.155614,0.144452,saturated,0.020000,stable,1
+xor20_online_b16,xor20-batch16,cuButterfly-online-radix4,0,5,1.232067000,1.231851000,1.233715000,0.001513,0.000092,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,16,1,1048576,,,,,online-reorder,radix4,scalar,shared,,table,0.012986307,13.617129588,group-fastest,cuButterfly-online-radix4,1.232067000,1.000000,parity,13.617129588,16,1.000000,0.900000,2,1.170222,0.073139,saturated,0.020000,stable,1
diff --git a/results/v100_scaling_quick_raw.csv b/results/v100_scaling_quick_raw.csv
new file mode 100644
index 0000000..e1ce307
--- /dev/null
+++ b/results/v100_scaling_quick_raw.csv
@@ -0,0 +1,220 @@
+suite_case_id,suite_group,suite_tier,suite_runner,implementation,reference,trial,performance_batch,preflight_correct,preflight_max_error,device,compute_capability,operator,precision,direction,normalization,placement,backend,compute_unit,complex_multiply,cross_twiddle,local_exchange,fft_core,stage_space,stage_handoff,tile_threads,prefix_threads,suffix_threads,prefix_ept,suffix_ept,prefix_units_per_cta,suffix_units_per_cta,local_stages,reorder_columns,warp_stages,pipeline_warps,logN,N,batch,element_stride,batch_stride,warmup,repeat,h2d_ms,kernel_ms,d2h_ms,transforms_s,Gbutterfly_s,points_s,max_error,correct,output_order,word_bits,modulus,modulus_bits,n1_log,rows_per_block,threads_per_block,inverse,kernel_ntt_s,end_to_end_ntt_s,kernel_points_s,mod_multiply,library,library_version,plan_ms,max_abs_error,relative_l2_error
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,1,1,32768,1000,100,0.050912,0.009032,0.064544,110721.366824,27.210883,3628117748.090396,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,1,1,1048576,1000,100,1.417504,0.077455,1.367584,12910.662895,135.378113,13537811255.969238,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,1,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,128,1,32768,1000,100,2.784896,0.317297,2.597280,403408.010814,99.141553,13218873698.360846,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,16,1,65536,1000,100,1.416544,0.086764,1.343872,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,184409.308486,5619.596659,12085448440.939711,shoup,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,,0.060917757,,16415.574732796,172.129776910,17212977691.016277313,,-1,,,,,,,,,,,,,vkfft,10304,829.151210000,0.000000000,0.000000000
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,1,1,1048576,1000,100,0.765248,0.100567,0.728160,9943.616179,104.266373,10426637277.999601,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,1,1,262144,1000,100,0.433888,0.017388,0.406976,57512.512997,135.689042,15076560207.082832,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,,0.065310724,,15311.421119464,160.551887118,16055188711.762922287,,-1,,,,,,,,,,,,,cufft,10900,2.392814000,0.000000000,0.000000000
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,1,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.039904,0.020562,0.044544,48633.593910,5.577690,796812802.625143,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.035840,0.002611,0.038560,24509805.240081,25.098041,6274510141.460673,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,4,1,262144,1000,100,1.431488,0.059443,1.349472,67291.126221,158.759685,17639964992.094902,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.037888,0.002929,0.035808,21853146.890947,22.377622,5594405604.082486,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.036864,0.002591,0.035488,24703556.586476,25.296442,6324110486.137845,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.012288,0.002560,0.019392,390624.974341,0.400000,99999993.431266,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.008192,0.002478,0.019264,403538.244254,0.413223,103305790.529078,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,1,1,1048576,1000,100,1.417408,0.071690,1.361280,13948.900349,146.264821,14626482132.678507,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,1,16384,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,16384,1,256,1000,100,,0.083752960,,195622936.867212325,200.317887352,50079471838.006355286,,-1,,,,,,,,,,,,,cufft,10900,1.867097000,0.000000000,0.000000000
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,4,1,1048576,1000,100,5.520064,0.235991,5.097792,16949.795641,177.731489,17773148914.194912,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201093122,,79565.127896869,187.717687987,20857520887.396797180,,-1,,,,,,,,,,,,,vkfft,10304,347.989400000,0.000000000,0.000000000
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.034816,0.002560,0.032256,24999998.357816,25.599998,6399999579.601017,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,2,256,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,256,1,16384,1000,100,,0.171694085,,1491023.991869605,171.002559580,24428937082.791603088,,-1,,,,,,,,,,,,,vkfft,10304,366.255960000,0.000000000,0.000000000
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.770240,0.042762,2.605344,383141742.224474,392.337144,98084286009.465363,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,2,16384,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,16384,1,256,1000,100,,0.083486721,,196246778.164595336,200.956700841,50239175210.136405945,,-1,,,,,,,,,,,,,vkfft,10304,203.837104000,0.000000000,0.000000000
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,1,1,1048576,1000,100,0.752640,0.098079,0.744416,10195.891598,106.911672,10691167228.695623,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,4,1,262144,1000,100,,0.068608001,,58302.238062814,137.552237053,15283581894.738397598,,-1,,,,,,,,,,,,,cufft,10900,1.877021000,0.000000000,0.000000000
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,4,1,262144,1000,100,,0.068597764,,58310.938721213,137.572764481,15285862720.133602142,,-1,,,,,,,,,,,,,cufft,10900,1.807695000,0.000000000,0.000000000
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,16,1,16384,1000,100,,0.010670080,,1499520.174678847,171.976969794,24568138541.938224792,,-1,,,,,,,,,,,,,vkfft,10304,400.132034000,0.000000000,0.000000000
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.012288,0.002550,0.020224,392193.768391,0.401606,100401604.708041,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,1,1,65536,1000,100,0.124512,0.015493,0.140064,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,64544.778307,3570.547118,4230006591.141377,shoup,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1,1,4096,1000,100,0.010240,0.005990,0.021696,,,,,-1,natural,32,1073692673,30,6,4,256,0,166933.774244,26366.858830,683760739.303273,shoup,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.767808,0.049654,2.615296,329964958.744988,337.884118,84471029438.716934,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,16,1,4096,1000,100,0.077088,0.008458,0.077280,,,,,-1,natural,32,1073692673,30,6,4,256,0,1891646.498566,98264.261196,7748184058.128383,shoup,,,,,
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,3,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.038688,0.003123,0.045888,20491803.063089,20.983606,5245901584.150699,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,1,1,256,1000,100,,0.002682880,,372733.806415253,0.381679418,95419854.442304835,,-1,,,,,,,,,,,,,cufft,10900,2.161826000,0.000000000,0.000000000
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,1,64,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,64,1,256,1000,100,,0.002785280,,22977940.235667791,23.529410801,5882352700.330954552,,-1,,,,,,,,,,,,,cufft,10900,2.028573000,0.000000000,0.000000000
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,,0.063549444,,15735.778880309,165.001600752,16500160075.199115753,,-1,,,,,,,,,,,,,cufft,10900,1.847060000,0.000000000,0.000000000
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,3,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.210053116,,19042.802480572,199.678256539,19967825653.868293762,,-1,,,,,,,,,,,,,cufft,10900,2.257240000,0.000000000,0.000000000
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,16,1,32768,1000,100,0.438240,0.017592,0.401632,909487.765179,223.515713,29802095089.380459,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,2,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,16,1,16384,1000,100,0.505600,0.020736,0.407776,771604.884988,88.493821,12641974435.639757,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,4,1,1048576,1000,100,5.471392,0.235366,5.110272,16994.778911,178.203173,17820317291.299896,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1,1,4096,1000,100,0.011264,0.006932,0.020448,,,,,-1,natural,32,1073692673,30,6,4,256,0,144248.527159,25876.917550,590841967.244353,shoup,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,1,1,256,1000,100,,0.002314240,,432107.305888526,0.442477881,110619470.307462543,,-1,,,,,,,,,,,,,vkfft,10304,150.958803000,0.000000000,0.000000000
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,16,1,16384,1000,100,,0.010680321,,1498082.360102851,171.812069715,24544581387.925106049,,-1,,,,,,,,,,,,,vkfft,10304,361.876673000,0.000000000,0.000000000
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,3,16384,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,16384,1,256,1000,100,,0.083773442,,195575109.301850498,200.268911925,50067227981.273727417,,-1,,,,,,,,,,,,,cufft,10900,1.809236000,0.000000000,0.000000000
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,3,256,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,256,1,16384,1000,100,,0.171735033,,1490668.473067502,170.961785839,24423112262.737960815,,-1,,,,,,,,,,,,,vkfft,10304,366.714052000,0.000000000,0.000000000
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,4,1,262144,1000,100,,0.063825920,,62670.463441027,147.858173715,16428685968.284624100,,-1,,,,,,,,,,,,,vkfft,10304,330.701072000,0.000000000,0.000000000
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,16,1,65536,1000,100,1.421120,0.087378,1.352480,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,183112.620022,5592.493153,12000468665.745426,shoup,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,4,1,1048576,1000,100,2.785664,0.319457,2.598304,12521.235524,131.294671,13129467060.936590,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,4,1,1048576,1000,100,2.776096,0.488223,2.606592,8192.982118,85.909644,8590964417.080271,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,2,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,256,1,16384,1000,100,5.556544,0.121375,5.125376,2109170.694164,241.896569,34556652653.177818,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,16,1,16384,1000,100,,0.013506561,,1184609.501261122,135.860494481,19408642068.662227631,,-1,,,,,,,,,,,,,cufft,10900,1.917154000,0.000000000,0.000000000
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.011264,0.002867,0.022080,348772.299652,0.357143,89285708.710791,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,1,1,32768,1000,100,0.044288,0.017603,0.053696,56809.915195,13.961605,1861547301.119975,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,1,1,65536,1000,100,0.120384,0.015862,0.134656,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,63044.702983,3691.375082,4131697654.717077,shoup,,,,,
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,4,1,262144,1000,100,,0.063805439,,62690.580758285,147.905636421,16433959602.299955368,,-1,,,,,,,,,,,,,vkfft,10304,331.433135000,0.000000000,0.000000000
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,1,1,1048576,1000,100,0.755744,0.098550,0.715488,10147.158823,106.400672,10640067210.024492,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,1,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.039616,0.003113,0.049568,20559211.131797,21.052632,5263158049.739938,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,1,256,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,256,1,16384,1000,100,,0.121036798,,2115059.260767617,242.571916499,34653130928.416641235,,-1,,,,,,,,,,,,,cufft,10900,1.861997000,0.000000000,0.000000000
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.206489608,,19371.434934251,203.124217576,20312421757.616989136,,-1,,,,,,,,,,,,,vkfft,10304,859.717125000,0.000000000,0.000000000
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,4,1,1048576,1000,100,2.775776,0.488305,2.601664,8191.607519,85.895230,8589523045.638255,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,1,1,65536,1000,100,0.121056,0.015862,0.139744,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,63044.702983,3614.521969,4131697654.717077,shoup,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,1,1,32768,1000,100,0.043072,0.017562,0.053728,56942.421082,13.994169,1865889254.027232,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.016384,0.002396,0.019296,417334.395058,0.427350,106837605.134914,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,16,1,65536,1000,100,1.419648,0.082217,1.342048,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,194607.059573,5626.051038,12753768256.191294,shoup,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,1.426624,0.094986,1.350624,,,,,-1,bit-reversed,64,1152921504577486849,60,0,0,256,0,10527.840932,348.161031,11039241332.784159,shoup,,,,,
+fwht20_hier_b4,fwht20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,4,1,1048576,1000,100,2.795104,0.488202,2.599936,8193.325715,85.913247,8591324704.414026,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,16,1,4096,1000,100,0.068416,0.008458,0.088000,,,,,-1,natural,32,1073692673,30,6,4,256,0,1891646.498566,97043.662536,7748184058.128383,shoup,,,,,
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.782112,0.042793,2.596672,382866705.565559,392.055506,98013876624.783112,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201103359,,79561.077661243,187.708132282,20856459142.428863525,,-1,,,,,,,,,,,,,vkfft,10304,334.029012000,0.000000000,0.000000000
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,64,1,65536,1000,100,5.471616,0.305193,5.112160,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,209703.383706,5877.507793,13743120954.544653,shoup,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,16,1,4096,1000,100,0.072480,0.007741,0.080256,,,,,-1,natural,32,1073692673,30,6,4,256,0,2066798.918423,99702.487277,8465608369.861174,shoup,,,,,
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,1,1,65536,1000,100,0.121472,0.015821,0.135168,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,63207.931218,3670.252728,4142394980.299225,shoup,,,,,
+ntt16_r2_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,16,1,65536,1000,100,1.420704,0.087859,1.349056,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,182109.560320,5599.066502,11934732145.141279,shoup,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,4,1,1048576,1000,100,2.861088,0.320133,2.595456,12494.802169,131.017497,13101749679.439688,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,1,1,1048576,1000,100,0.777920,0.098150,0.711808,10188.446022,106.833600,10683359975.560677,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1,1,4096,1000,100,0.012288,0.006881,0.028544,,,,,-1,natural,32,1073692673,30,6,4,256,0,145321.803322,20958.525714,595238106.408175,shoup,,,,,
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1,1,4096,1000,100,0.012288,0.005980,0.022880,,,,,-1,natural,32,1073692673,30,6,4,256,0,167219.603722,24302.423448,684931496.845112,shoup,,,,,
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,5.509856,0.341647,5.104448,,,,,-1,bit-reversed,64,1152921504577486849,60,0,0,256,0,11707.977750,365.098368,12276704476.927340,shoup,,,,,
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.771648,0.047852,2.587232,342392483.132327,350.609903,87652475681.875748,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,4,1,1048576,1000,100,2.802560,0.486973,2.645664,8213.999923,86.130032,8613003183.656813,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,4,1,1048576,1000,100,2.910464,0.487178,2.647136,8210.547398,86.093829,8609382948.463964,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,16,1,16384,1000,100,,0.013516800,,1183712.079343213,135.757570956,19393938707.959194183,,-1,,,,,,,,,,,,,cufft,10900,2.299432000,0.000000000,0.000000000
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,3,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,5.563968,0.084316,5.124640,194316257.060635,198.979847,49744961807.522552,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.038912,0.002560,0.042048,24999998.357816,25.599998,6399999579.601017,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,1,1,256,1000,100,,0.002334720,,428316.887900589,0.438596493,109649123.302550793,,-1,,,,,,,,,,,,,vkfft,10304,201.937675000,0.000000000,0.000000000
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,1,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,16,1,16384,1000,100,0.519008,0.020808,0.403744,768946.791073,88.188970,12598424224.938074,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.810144,0.048425,2.602112,338337920.702677,346.458031,86614507699.885284,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.039936,0.002417,0.038016,26483050.250930,27.118643,6779660864.238072,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_vkfft_b16,fft14-batch16,quick,fft-library,VkFFT,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,16,1,16384,1000,100,,0.010659840,,1500960.620713974,172.142171668,24591738809.777744293,,-1,,,,,,,,,,,,,vkfft,10304,484.516994000,0.000000000,0.000000000
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.211445749,,75669.527953858,178.526814623,19836312735.936107635,,-1,,,,,,,,,,,,,cufft,10900,2.329431000,0.000000000,0.000000000
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,1,1,262144,1000,100,,0.022958081,,43557.647113803,102.765382605,11418375845.000692368,,-1,,,,,,,,,,,,,cufft,10900,1.931216000,0.000000000,0.000000000
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,64,1,256,1000,100,,0.002447360,,26150628.016946666,26.778243089,6694560772.338346481,,-1,,,,,,,,,,,,,vkfft,10304,203.628877000,0.000000000,0.000000000
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,,0.060753919,,16459.843470640,172.593968271,17259396827.070243835,,-1,,,,,,,,,,,,,vkfft,10304,914.389171000,0.000000000,0.000000000
+ntt12_r2_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1,1,4096,1000,100,0.012288,0.006861,0.021728,,,,,-1,natural,32,1073692673,30,6,4,256,0,145755.605050,24463.754664,597014958.284258,shoup,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.033792,0.002918,0.033024,21929825.535294,22.456141,5614035337.035136,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,3,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.039136,0.020500,0.048704,48779.342969,5.594405,799200755.199293,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,1,1,262144,1000,100,,0.022978561,,43518.826093677,102.673792328,11408199147.500984192,,-1,,,,,,,,,,,,,cufft,10900,1.935796000,0.000000000,0.000000000
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.517376,0.204995,5.098848,78050.851962,184.145063,20460562536.720055,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r4_b64,xor8-batch64,quick,butterfly,cuButterfly-radix4,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.036864,0.002560,0.034656,24999998.357816,25.599998,6399999579.601017,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,1,1,262144,1000,100,,0.018462719,,54163.201994492,127.787025813,14198558423.644159317,,-1,,,,,,,,,,,,,vkfft,10304,368.396180000,0.000000000,0.000000000
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,4,1,262144,1000,100,1.427616,0.059709,1.359968,66991.081119,158.051790,17561309968.745327,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,1,1,16384,1000,100,,0.011898880,,84041.523990662,9.638554303,1376936329.063012838,,-1,,,,,,,,,,,,,cufft,10900,1.775997000,0.000000000,0.000000000
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.462432,0.205414,5.104768,77891.331860,183.768708,20418745299.147503,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,16,1,32768,1000,100,0.434112,0.044585,0.429760,358865.413165,88.194764,11759301858.605116,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,64,1,65536,1000,100,5.456768,0.278436,5.103744,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,229855.478191,5904.632132,15063808618.712509,shoup,,,,,
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,1,1,262144,1000,100,,0.021657601,,46173.165719129,108.936165188,12104018354.275476456,,-1,,,,,,,,,,,,,vkfft,10304,352.741207000,0.000000000,0.000000000
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,1,1,32768,1000,100,0.045728,0.009052,0.048768,110470.868649,27.149321,3619909423.880593,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.039936,0.003471,0.034240,18436579.002865,18.879057,4719764224.733468,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,3,16384,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,16384,1,256,1000,100,,0.084121600,,194765673.028472334,199.440049181,49860012295.288917542,,-1,,,,,,,,,,,,,vkfft,10304,208.755991000,0.000000000,0.000000000
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,1,1,1048576,1000,100,0.752672,0.095048,0.710208,10521.035058,110.321049,11032104856.825274,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_vkfft_b16384,fft8-batch16384,quick,fft-library,VkFFT,0,1,16384,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,16384,1,256,1000,100,,0.083589122,,196006366.222301126,200.710519012,50177629752.909088135,,-1,,,,,,,,,,,,,vkfft,10304,204.464259000,0.000000000,0.000000000
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,3,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,256,1,16384,1000,100,5.534464,0.120986,5.106464,2115954.211043,242.674557,34667793793.723068,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,16,1,32768,1000,100,0.435680,0.044657,0.428448,358289.398766,88.053203,11740427018.757406,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,64,1,65536,1000,100,5.460576,0.277135,5.103168,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,230934.096875,5903.580104,15134496972.813015,shoup,,,,,
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,16,1,65536,1000,100,1.426912,0.082739,1.349824,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,193378.703129,5595.432521,12673266688.265934,shoup,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.209940478,,19053.019380480,199.785388499,19978538849.905815125,,-1,,,,,,,,,,,,,cufft,10900,2.339535000,0.000000000,0.000000000
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,1,1,1048576,1000,100,0.751520,0.090040,0.741472,11106.135727,116.456274,11645627375.749804,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.011264,0.002048,0.017344,488281.251233,0.500000,125000000.315595,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,1,1,262144,1000,100,0.431232,0.016466,0.430336,60731.495234,143.283574,15920397086.645201,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,2,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,128,1,32768,1000,100,2.777088,0.064707,2.599360,1978161.208470,486.152899,64820386479.143539,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cub_b4,fft20-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,4,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,4,1,1048576,1000,100,5.469504,0.235653,5.096640,16974.101789,177.986358,17798635757.815102,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r2_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix2,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,16,1,4096,1000,100,0.072192,0.008479,0.078272,,,,,-1,natural,32,1073692673,30,6,4,256,0,1887077.352307,100665.196842,7729468835.049730,shoup,,,,,
+fft14_cub_b16,fft14-batch16,quick,butterfly,cuButterfly-cuFFTDx-direct,0,3,16,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,16,1,16384,1000,100,0.503744,0.020777,0.423456,770083.748097,88.319365,12617052128.820662,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,1,1,256,1000,100,,0.002754560,,363034.359456284,0.371747184,92936796.020808831,,-1,,,,,,,,,,,,,cufft,10900,2.047305000,0.000000000,0.000000000
+ntt16_r4_b16,ntt16-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,16,1,65536,1000,100,1.426240,0.082463,1.341888,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,194027.069309,5612.871867,12715758014.221771,shoup,,,,,
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,2,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,5.511584,0.084265,5.128704,194434325.929846,199.100750,49775187438.040695,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,1024,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1024,1,4096,1000,100,2.822240,0.139233,2.597440,,,,,-1,natural,32,1073692673,30,6,4,256,0,7354562.917737,184208.661752,30124289711.052517,shoup,,,,,
+ntt16_r4_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,64,1,65536,1000,100,5.508864,0.279101,5.129664,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,229307.291088,5862.078484,15027882628.724911,shoup,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.036864,0.002109,0.033248,30339805.198601,31.067961,7766990130.841847,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_hier_b4,xor20-batch4,quick,butterfly,cuButterfly-hierarchical-radix4,0,3,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,4,1,1048576,1000,100,2.840224,0.487117,2.604736,8211.582700,86.104685,8610468541.392656,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_hier_b1,xor20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,1,1,1048576,1000,100,0.751168,0.098314,0.711936,10171.466454,106.655556,10665555608.923458,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,3,64,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,64,1,256,1000,100,,0.002734080,,23408240.068453956,23.970037830,5992509457.524212837,,-1,,,,,,,,,,,,,cufft,10900,2.050681000,0.000000000,0.000000000
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,1,64,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,64,1,256,1000,100,,0.002457600,,26041668.212713014,26.666668250,6666667062.454531670,,-1,,,,,,,,,,,,,vkfft,10304,200.734692000,0.000000000,0.000000000
+fft8_cub_b64,fft8-batch64,quick,butterfly,cuButterfly-cuFFTDx,0,2,64,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.041280,0.003144,0.051744,20358305.870914,20.846905,5211726302.954013,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,2,1024,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1024,1,4096,1000,100,2.822624,0.163318,2.628800,,,,,-1,natural,32,1073692673,30,6,4,256,0,6269985.776184,182377.047060,25681861739.251461,shoup,,,,,
+fft14_cub_b256,fft14-batch256,quick,butterfly,cuButterfly-cuFFTDx-direct,0,1,256,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,256,1,16384,1000,100,5.546912,0.121641,5.113856,2104554.291881,241.367123,34481017518.178230,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r4_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,1,1,65536,1000,100,0.119488,0.015514,0.134176,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,64459.571579,3715.019354,4224422483.025257,shoup,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,2,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,128,1,32768,1000,100,2.768704,0.316375,2.621664,404583.108644,99.430345,13257379304.057873,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.206499845,,19370.474607753,203.114147823,20311414782.298995972,,-1,,,,,,,,,,,,,vkfft,10304,828.965365000,0.000000000,0.000000000
+ntt16_r2_b1,ntt16-batch1,quick,ntt,cuNTT-Hybrid2D-radix2,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,1,1,65536,1000,100,0.125056,0.015882,0.142912,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,62963.408291,3522.984520,4126369925.765298,shoup,,,,,
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,1,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,16,1,32768,1000,100,0.426464,0.017592,0.422080,909487.765179,223.515713,29802095089.380459,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,1.418272,0.095089,1.347936,,,,,-1,bit-reversed,64,1152921504577486849,60,0,0,256,0,10516.502695,349.491893,11027352330.063618,shoup,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,1,1,16384,1000,100,,0.011888640,,84113.910412030,9.646856157,1378122308.190701008,,-1,,,,,,,,,,,,,cufft,10900,1.908471000,0.000000000,0.000000000
+fwht8_shared_b64,fwht8-batch64,quick,butterfly,cuButterfly-shared-radix4,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.034816,0.002570,0.034016,24900400.082036,25.498010,6374502421.001141,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_warp_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-warp-register,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.788064,0.042762,2.620512,383141742.224474,392.337144,98084286009.465363,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,64,1,256,1000,100,0.031744,0.002099,0.032992,30487802.672495,31.219510,7804877484.158601,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,1024,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1024,1,4096,1000,100,2.806784,0.139796,2.617984,,,,,-1,natural,32,1073692673,30,6,4,256,0,7324934.047484,184021.590353,30002929858.495735,shoup,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,1,1,1048576,1000,100,0.758048,0.090849,0.735648,11007.242744,115.419306,11541930567.522934,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,1,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.007168,0.002898,0.015520,345075.077982,0.353357,88339219.963376,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,16,1,4096,1000,100,0.074816,0.007639,0.078368,,,,,-1,natural,32,1073692673,30,6,4,256,0,2094504.083552,99488.230118,8579088726.229346,shoup,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,3,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,128,1,32768,1000,100,2.765440,0.064819,2.598560,1974723.710026,485.308099,64707746530.133675,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,1,1,262144,1000,100,0.408608,0.016476,0.430304,60693.754196,143.194532,15910503500.037251,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,4,1,1048576,1000,100,2.774592,0.319406,2.599680,12523.243831,131.315729,13131572923.035238,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,1,1,16384,1000,100,,0.008263680,,121011.459971133,13.878562321,1982651760.167040586,,-1,,,,,,,,,,,,,vkfft,10304,306.966866000,0.000000000,0.000000000
+fft18_vkfft_b16,fft18-batch16,quick,fft-library,VkFFT,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.201349124,,79463.966156492,187.479017497,20831001944.127544403,,-1,,,,,,,,,,,,,vkfft,10304,330.270312000,0.000000000,0.000000000
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.015360,0.002847,0.019360,351281.483464,0.359712,89928059.766890,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,3,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.210851848,,75882.664260452,179.029666259,19892185139.892021179,,-1,,,,,,,,,,,,,cufft,10900,1.987836000,0.000000000,0.000000000
+xor8_r2_b1,xor8-batch1,quick,butterfly,cuButterfly-radix2,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.013312,0.002836,0.018784,352549.634236,0.361011,90252706.364468,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_online_b16,fwht15-batch16,quick,butterfly,cuButterfly-online-radix4,0,3,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,16,1,32768,1000,100,0.432128,0.044780,0.406720,357306.193274,87.811570,11708209341.205387,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b16,fft14-batch16,quick,fft-library,cuFFT,1,2,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,16,1,16384,1000,100,,0.013496321,,1185508.284958062,135.963574185,19423367740.752895355,,-1,,,,,,,,,,,,,cufft,10900,1.907407000,0.000000000,0.000000000
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,1,1,16384,1000,100,,0.008253440,,121161.596666420,13.895781198,1985111599.782624006,,-1,,,,,,,,,,,,,vkfft,10304,307.057470000,0.000000000,0.000000000
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.763200,0.047780,2.593216,342906106.401127,351.135853,87783963238.688507,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_warp_b16,fwht15-batch16,quick,butterfly,cuButterfly-warp-register,0,2,16,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,16,1,32768,1000,100,0.436768,0.017603,0.410688,908958.643125,223.385676,29784756817.919594,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,1,1,262144,1000,100,,0.018483199,,54103.187998257,127.645435032,14182826114.615081787,,-1,,,,,,,,,,,,,vkfft,10304,354.687950000,0.000000000,0.000000000
+fft18_cufft_b16,fft18-batch16,quick,fft-library,cuFFT,1,1,16,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,16,1,262144,1000,100,,0.211353600,,75702.519370827,178.604651142,19844961237.946090698,,-1,,,,,,,,,,,,,cufft,10900,1.953606000,0.000000000,0.000000000
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,1,1,1048576,1000,100,0.749536,0.104591,0.716320,9561.018990,100.254550,10025455048.689434,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_vkfft_b64,fft8-batch64,quick,fft-library,VkFFT,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,64,1,256,1000,100,,0.002457600,,26041668.212713014,26.666668250,6666667062.454531670,,-1,,,,,,,,,,,,,vkfft,10304,182.973539000,0.000000000,0.000000000
+ntt12_r4_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix4,0,3,1024,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1024,1,4096,1000,100,2.843840,0.139510,2.617760,,,,,-1,natural,32,1073692673,30,6,4,256,0,7339987.872265,182820.918390,30064590324.798645,shoup,,,,,
+fft18_cub_b16,fft18-batch16,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,16,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,16,1,262144,1000,100,5.466304,0.205261,5.100320,77949.614002,183.906213,20434023612.989471,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.772640,0.048425,2.603872,338337920.702677,346.458031,86614507699.885284,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cufft_b1,fft20-batch1,quick,fft-library,cuFFT,1,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,,0.063590400,,15725.644141934,164.895330318,16489533031.772968292,,-1,,,,,,,,,,,,,cufft,10900,1.940638000,0.000000000,0.000000000
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,20,1048576,1,1,1048576,1000,100,1.413568,0.071434,1.364032,13998.889624,146.788997,14678899686.102076,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cufft_b16384,fft8-batch16384,quick,fft-library,cuFFT,1,2,16384,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,16384,1,256,1000,100,,0.083834879,,195431784.190846741,200.122147011,50030536752.856765747,,-1,,,,,,,,,,,,,cufft,10900,2.201513000,0.000000000,0.000000000
+fft8_cub_b16384,fft8-batch16384,quick,butterfly,cuButterfly-cuFFTDx,0,1,16384,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,5.481792,0.084234,5.093888,194505232.706111,199.173358,49793339572.764534,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,1,1,32768,1000,100,0.044928,0.007690,0.048160,130034.950633,31.957389,4260985262.351007,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,5.455328,0.341606,5.105952,,,,,-1,bit-reversed,64,1152921504577486849,60,0,0,256,0,11709.382208,366.875333,12278177157.640074,shoup,,,,,
+fft18_cufft_b4,fft18-batch4,quick,fft-library,cuFFT,1,1,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,4,1,262144,1000,100,,0.068894722,,58059.600343596,136.979782852,15219975872.471759796,,-1,,,,,,,,,,,,,cufft,10900,2.242915000,0.000000000,0.000000000
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,2,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,1,1,256,1000,100,,0.002672640,,374161.857641088,0.383141742,95785435.556118518,,-1,,,,,,,,,,,,,cufft,10900,1.811332000,0.000000000,0.000000000
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.014336,0.002560,0.021632,390624.974341,0.400000,99999993.431266,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r4_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix4,0,3,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.779552,0.047770,2.596096,342979645.184681,351.211157,87802789167.278244,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_vkfft_b1,fft20-batch1,quick,fft-library,VkFFT,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,,0.061040640,,16382.528132238,171.783258188,17178325818.789716721,,-1,,,,,,,,,,,,,vkfft,10304,779.599211000,0.000000000,0.000000000
+ntt20_compact_b4,ntt20-batch4,quick,ntt,cuNTT-compact-stage,0,3,4,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,5.457952,0.341565,5.103776,,,,,-1,bit-reversed,64,1152921504577486849,60,0,0,256,0,11710.787002,366.861630,12279650191.712894,shoup,,,,,
+fwht8_shared_b1,fwht8-batch1,quick,butterfly,cuButterfly-shared-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.012288,0.002560,0.018272,390624.974341,0.400000,99999993.431266,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht20_hier_b1,fwht20-batch1,quick,butterfly,cuButterfly-hierarchical-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,hierarchical,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,0,0,0,20,1048576,1,1,1048576,1000,100,0.756608,0.098478,0.722112,10154.544156,106.478113,10647811292.913397,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_vkfft_b256,fft14-batch256,quick,fft-library,VkFFT,0,1,256,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,256,1,16384,1000,100,,0.171458572,,1493072.039449384,171.237446060,24462492294.338710785,,-1,,,,,,,,,,,,,vkfft,10304,368.603180000,0.000000000,0.000000000
+ntt20_compact_b1,ntt20-batch1,quick,ntt,cuNTT-compact-stage,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,compact-stage,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,20,1048576,1,1,1048576,1000,100,1.420384,0.094915,1.339136,,,,,-1,bit-reversed,64,1152921504577486849,60,0,0,256,0,10535.791014,350.332074,11047577598.790255,shoup,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.784128,0.049695,2.611552,329692969.068485,337.605600,84401400081.532104,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_warp_b1,fwht15-batch1,quick,butterfly,cuButterfly-warp-register,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,1,1,32768,1000,100,0.043648,0.017633,0.056768,56710.947264,13.937282,1858304319.932564,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,2,256,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,256,1,16384,1000,100,,0.121026561,,2115238.164210464,242.592434577,34656062082.424247742,,-1,,,,,,,,,,,,,cufft,10900,2.125199000,0.000000000,0.000000000
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,1,1,1048576,1000,100,0.769120,0.090092,0.719872,11099.823022,116.390080,11639008024.833857,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_vkfft_b4,fft20-batch4,quick,fft-library,VkFFT,0,1,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.206520334,,19368.552842865,203.093996658,20309399665.760250092,,-1,,,,,,,,,,,,,vkfft,10304,794.661521000,0.000000000,0.000000000
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,3,1024,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1024,1,4096,1000,100,2.842944,0.164137,2.607872,,,,,-1,natural,32,1073692673,30,6,4,256,0,6238692.328175,182370.185895,25553683776.203911,shoup,,,,,
+xor8_r2_b16384,xor8-batch16384,quick,butterfly,cuButterfly-radix2,0,2,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.784640,0.050176,2.609344,326530598.674974,334.367333,83591833260.793320,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_warp_b128,fwht15-batch128,quick,butterfly,cuButterfly-warp-register,0,1,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,256,0,0,8,8,0,0,0,0,0,0,15,32768,128,1,32768,1000,100,2.784960,0.064788,2.610880,1975659.776376,485.538147,64738419552.293678,0.000000,-1,,,,,,,,,,,,,,,,,
+fft18_cub_b4,fft18-batch4,quick,butterfly,cuButterfly-cuFFTDx-online,0,1,4,1,0.000512,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,18,262144,4,1,262144,1000,100,1.446848,0.059453,1.350176,67279.539577,158.732349,17636927622.871296,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht15_online_b128,fwht15-batch128,quick,butterfly,cuButterfly-online-radix4,0,3,128,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,15,32768,128,1,32768,1000,100,2.781280,0.316303,2.598944,404674.787485,99.452876,13260383436.316048,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,1,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,4,1,1048576,1000,100,2.784992,0.319601,2.603488,12515.619425,131.235782,13123578154.692392,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cub_b1,fft14-batch1,quick,butterfly,cuButterfly-cuFFTDx-direct,0,2,1,1,0.000095,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-direct,0,named-barrier,1024,0,0,8,8,0,0,0,0,0,0,14,16384,1,1,16384,1000,100,0.038784,0.020521,0.045024,48730.665930,5.588823,798403230.595040,0.000000,-1,,,,,,,,,,,,,,,,,
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.013312,0.002499,0.019328,400230.550953,0.409836,102459021.044087,0.000000,-1,,,,,,,,,,,,,,,,,
+xor20_online_b4,xor20-batch4,quick,butterfly,cuButterfly-online-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,xor-zeta,uint32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,4,1,1048576,1000,100,2.787072,0.319252,2.596704,12529.269109,131.378909,13137890885.164440,0.000000,-1,,,,,,,,,,,,,,,,,
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,3,64,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,64,1,65536,1000,100,5.481088,0.303759,5.102752,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,210693.091657,5878.246955,13807982454.829952,shoup,,,,,
+fft18_cufft_b1,fft18-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,1,1,262144,1000,100,,0.023265280,,42982.504716403,101.408451447,11267605716.376638412,,-1,,,,,,,,,,,,,cufft,10900,2.251789000,0.000000000,0.000000000
+ntt16_r2_b64,ntt16-batch64,quick,ntt,cuNTT-Hybrid2D-radix2,0,2,64,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint64,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,16,65536,64,1,65536,1000,100,5.458496,0.301732,5.097280,,,,,-1,natural,64,1152921504606584833,60,8,4,256,0,212108.881874,5894.538630,13900767682.491871,shoup,,,,,
+fwht8_shared_b16384,fwht8-batch16384,quick,butterfly,cuButterfly-shared-radix4,0,1,16384,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,8,256,16384,1,256,1000,100,2.783296,0.048947,2.611552,334728032.248018,342.761505,85690376255.492661,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_vkfft_b1,fft8-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,1,1,256,1000,100,,0.002355200,,424592.390277620,0.434782608,108695651.911070794,,-1,,,,,,,,,,,,,vkfft,10304,182.933752000,0.000000000,0.000000000
+fft14_cufft_b256,fft14-batch256,quick,fft-library,cuFFT,1,3,256,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,256,1,16384,1000,100,,0.123156480,,2078656.348241232,238.396939267,34056705609.584350586,,-1,,,,,,,,,,,,,cufft,10900,1.836037000,0.000000000,0.000000000
+fft8_cufft_b64,fft8-batch64,quick,fft-library,cuFFT,1,2,64,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,8,256,64,1,256,1000,100,,0.002764800,,23148149.278741192,23.703704861,5925926215.357745171,,-1,,,,,,,,,,,,,cufft,10900,1.985735000,0.000000000,0.000000000
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,2,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.009216,0.002888,0.016896,346298.763369,0.354610,88652483.422564,0.000000,-1,,,,,,,,,,,,,,,,,
+fft8_cub_b1,fft8-batch1,quick,butterfly,cuButterfly-cuFFTDx,0,3,1,1,0.000008,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,temporal-tile,auto,four-mul,table,shared,cufftdx-block,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.009216,0.002888,0.018848,346298.763369,0.354610,88652483.422564,0.000000,-1,,,,,,,,,,,,,,,,,
+fft20_cufft_b4,fft20-batch4,quick,fft-library,cuFFT,1,2,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,20,1048576,4,1,1048576,1000,100,,0.210421756,,19009.441218200,199.328438348,19932843834.815044403,,-1,,,,,,,,,,,,,cufft,10900,2.072712000,0.000000000,0.000000000
+ntt12_r4_b16,ntt12-batch16,quick,ntt,cuNTT-Hybrid2D-radix4,0,2,16,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,16,1,4096,1000,100,0.071616,0.007639,0.079680,,,,,-1,natural,32,1073692673,30,6,4,256,0,2094504.083552,100670.057115,8579088726.229346,shoup,,,,,
+fft14_vkfft_b1,fft14-batch1,quick,fft-library,VkFFT,0,3,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,1,1,16384,1000,100,,0.008263680,,121011.459971133,13.878562321,1982651760.167040586,,-1,,,,,,,,,,,,,vkfft,10304,313.106966000,0.000000000,0.000000000
+fft18_vkfft_b4,fft18-batch4,quick,fft-library,VkFFT,0,2,4,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,18,262144,4,1,262144,1000,100,,0.063784964,,62710.703669972,147.953112326,16439234702.861194611,,-1,,,,,,,,,,,,,vkfft,10304,373.385829000,0.000000000,0.000000000
+ntt12_r2_b1024,ntt12-batch1024,quick,ntt,cuNTT-Hybrid2D-radix2,1,1,1024,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix2,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1024,1,4096,1000,100,2.814528,0.162826,2.601728,,,,,-1,natural,32,1073692673,30,6,4,256,0,6288912.644581,183542.734261,25759386192.204250,shoup,,,,,
+fwht20_online_b4,fwht20-batch4,quick,butterfly,cuButterfly-online-radix4,0,2,4,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,4,1,1048576,1000,100,2.790752,0.319652,2.598976,12513.614730,131.214761,13121476079.154661,0.000000,-1,,,,,,,,,,,,,,,,,
+fft14_cufft_b1,fft14-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,fft,fp32,forward,none,in-place,,,,,,,,,,,,,,,,,,,,14,16384,1,1,16384,1000,100,,0.011878400,,84186.421636252,9.655172325,1379310332.088345051,,-1,,,,,,,,,,,,,cufft,10900,1.950454000,0.000000000,0.000000000
+ntt12_r4_b1,ntt12-batch1,quick,ntt,cuNTT-Hybrid2D-radix4,0,1,1,1,,Tesla V100-SXM2-16GB,7.0,ntt,uint32,forward,,,hybrid2d,radix4,,fused,,,0,named-barrier,,,,,,,,,,,,12,4096,1,1,4096,1000,100,0.012288,0.006001,0.023328,,,,,-1,natural,32,1073692673,30,6,4,256,0,166648.894374,24028.849430,682593871.356473,shoup,,,,,
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,8,256,1,1,256,1000,100,0.011264,0.002048,0.016320,488281.251233,0.500000,125000000.315595,0.000000,-1,,,,,,,,,,,,,,,,,
+fwht20_online_b1,fwht20-batch1,quick,butterfly,cuButterfly-online-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,fwht,fp32,forward,none,out-of-place,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,20,1048576,1,1,1048576,1000,100,0.762464,0.090153,0.717920,11092.259625,116.310772,11631077228.981354,0.000000,-1,,,,,,,,,,,,,,,,,
diff --git a/results/v100_scaling_quick_report.md b/results/v100_scaling_quick_report.md
new file mode 100644
index 0000000..e0b0bff
--- /dev/null
+++ b/results/v100_scaling_quick_report.md
@@ -0,0 +1,116 @@
+# V100 Orthogonal Length/Batch Scaling
+
+`Batch@90%` is the smallest measured batch reaching 90% of that
+implementation's peak measured `Gpoint/s` at fixed transform length.
+Rows below the configured 0.020 ms timing floor are retained but are not
+used as stable latency claims.
+
+## Saturation Summary
+
+| Operator | Numeric | logN | Implementation | Batch@90% | Peak batch | Peak Gpoint/s | Batch-1 ms |
+|:--|:--|--:|:--|--:|--:|--:|--:|
+| fft | fp32 | 8 | VkFFT | 16384 | 16384 | 50.178 | 0.002335 |
+| fft | fp32 | 8 | cuButterfly-cuFFTDx | 16384 | 16384 | 49.775 | 0.002888 |
+| fft | fp32 | 8 | cuFFT | 16384 | 16384 | 50.067 | 0.002683 |
+| fft | fp32 | 14 | VkFFT | 16 | 16 | 24.568 | 0.008264 |
+| fft | fp32 | 14 | cuButterfly-cuFFTDx-direct | 256 | 256 | 34.557 | 0.020521 |
+| fft | fp32 | 14 | cuFFT | 256 | 256 | 34.653 | 0.011889 |
+| fft | fp32 | 18 | VkFFT | 16 | 16 | 20.856 | 0.018483 |
+| fft | fp32 | 18 | cuButterfly-cuFFTDx-online | 16 | 16 | 20.434 | 0.016476 |
+| fft | fp32 | 18 | cuFFT | 16 | 16 | 19.845 | 0.022979 |
+| fft | fp32 | 20 | VkFFT | 4 | 4 | 20.311 | 0.060918 |
+| fft | fp32 | 20 | cuButterfly-cuFFTDx-online | 4 | 4 | 17.799 | 0.071690 |
+| fft | fp32 | 20 | cuFFT | 4 | 4 | 19.968 | 0.063590 |
+| fwht | fp32 | 8 | cuButterfly-shared-radix4 | 16384 | 16384 | 86.614 | 0.002560 |
+| fwht | fp32 | 8 | cuButterfly-warp-register | 16384 | 16384 | 98.085 | 0.002048 |
+| fwht | fp32 | 15 | cuButterfly-online-radix4 | 128 | 128 | 13.257 | 0.009032 |
+| fwht | fp32 | 15 | cuButterfly-warp-register | 128 | 128 | 64.739 | 0.017603 |
+| fwht | fp32 | 20 | cuButterfly-hierarchical-radix4 | 1 | 1 | 10.640 | 0.098550 |
+| fwht | fp32 | 20 | cuButterfly-online-radix4 | 4 | 4 | 13.121 | 0.090153 |
+| ntt | uint32 | 12 | cuNTT-Hybrid2D-radix2 | 1024 | 1024 | 25.682 | 0.006881 |
+| ntt | uint32 | 12 | cuNTT-Hybrid2D-radix4 | 1024 | 1024 | 30.065 | 0.005990 |
+| ntt | uint64 | 16 | cuNTT-Hybrid2D-radix2 | 64 | 64 | 13.808 | 0.015862 |
+| ntt | uint64 | 16 | cuNTT-Hybrid2D-radix4 | 64 | 64 | 15.064 | 0.015514 |
+| ntt | uint64 | 20 | cuNTT-compact-stage | 4 | 4 | 12.278 | 0.094986 |
+| xor-zeta | uint32 | 8 | cuButterfly-radix2 | 16384 | 16384 | 84.401 | 0.002847 |
+| xor-zeta | uint32 | 8 | cuButterfly-radix4 | 16384 | 16384 | 87.784 | 0.002499 |
+| xor-zeta | uint32 | 20 | cuButterfly-hierarchical-radix4 | 1 | 1 | 10.683 | 0.098150 |
+| xor-zeta | uint32 | 20 | cuButterfly-online-radix4 | 4 | 4 | 13.132 | 0.095048 |
+
+## Detailed Scaling
+
+| Operator | logN | Batch | Implementation | Median ms | Gpoint/s | Peak fraction | vs basis | Region | Timing quality |
+|:--|--:|--:|:--|--:|--:|--:|--:|:--|:--|
+| fft | 8 | 1 | VkFFT | 0.002335 | 0.110 | 0.002 | 1.149x | launch-limited | below-timing-floor |
+| fft | 8 | 64 | VkFFT | 0.002458 | 6.667 | 0.133 | 1.125x | launch-limited | below-timing-floor |
+| fft | 8 | 16,384 | VkFFT | 0.083589 | 50.178 | 1.000 | 1.002x | saturated | stable |
+| fft | 8 | 1 | cuButterfly-cuFFTDx | 0.002888 | 0.089 | 0.002 | 0.929x | launch-limited | below-timing-floor |
+| fft | 8 | 64 | cuButterfly-cuFFTDx | 0.003123 | 5.246 | 0.105 | 0.885x | launch-limited | below-timing-floor |
+| fft | 8 | 16,384 | cuButterfly-cuFFTDx | 0.084265 | 49.775 | 1.000 | 0.994x | saturated | stable |
+| fft | 8 | 1 | cuFFT | 0.002683 | 0.095 | 0.002 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 64 | cuFFT | 0.002765 | 5.926 | 0.118 | 1.000x | launch-limited | below-timing-floor |
+| fft | 8 | 16,384 | cuFFT | 0.083773 | 50.067 | 1.000 | 1.000x | saturated | stable |
+| fft | 14 | 1 | VkFFT | 0.008264 | 1.983 | 0.081 | 1.439x | launch-limited | below-timing-floor |
+| fft | 14 | 16 | VkFFT | 0.010670 | 24.568 | 1.000 | 1.266x | saturated | below-timing-floor |
+| fft | 14 | 256 | VkFFT | 0.171694 | 24.429 | 0.994 | 0.705x | saturated | stable |
+| fft | 14 | 1 | cuButterfly-cuFFTDx-direct | 0.020521 | 0.798 | 0.023 | 0.579x | launch-limited | stable |
+| fft | 14 | 16 | cuButterfly-cuFFTDx-direct | 0.020777 | 12.617 | 0.365 | 0.650x | launch-limited | stable |
+| fft | 14 | 256 | cuButterfly-cuFFTDx-direct | 0.121375 | 34.557 | 1.000 | 0.997x | saturated | stable |
+| fft | 14 | 1 | cuFFT | 0.011889 | 1.378 | 0.040 | 1.000x | launch-limited | below-timing-floor |
+| fft | 14 | 16 | cuFFT | 0.013507 | 19.409 | 0.560 | 1.000x | ramp | below-timing-floor |
+| fft | 14 | 256 | cuFFT | 0.121037 | 34.653 | 1.000 | 1.000x | saturated | stable |
+| fft | 18 | 1 | VkFFT | 0.018483 | 14.183 | 0.680 | 1.243x | ramp | below-timing-floor |
+| fft | 18 | 4 | VkFFT | 0.063805 | 16.434 | 0.788 | 1.075x | ramp | stable |
+| fft | 18 | 16 | VkFFT | 0.201103 | 20.856 | 1.000 | 1.051x | saturated | stable |
+| fft | 18 | 1 | cuButterfly-cuFFTDx-online | 0.016476 | 15.911 | 0.779 | 1.395x | ramp | below-timing-floor |
+| fft | 18 | 4 | cuButterfly-cuFFTDx-online | 0.059453 | 17.637 | 0.863 | 1.154x | ramp | stable |
+| fft | 18 | 16 | cuButterfly-cuFFTDx-online | 0.205261 | 20.434 | 1.000 | 1.030x | saturated | stable |
+| fft | 18 | 1 | cuFFT | 0.022979 | 11.408 | 0.575 | 1.000x | ramp | stable |
+| fft | 18 | 4 | cuFFT | 0.068608 | 15.284 | 0.770 | 1.000x | ramp | stable |
+| fft | 18 | 16 | cuFFT | 0.211354 | 19.845 | 1.000 | 1.000x | saturated | stable |
+| fft | 20 | 1 | VkFFT | 0.060918 | 17.213 | 0.847 | 1.044x | ramp | stable |
+| fft | 20 | 4 | VkFFT | 0.206500 | 20.311 | 1.000 | 1.017x | saturated | stable |
+| fft | 20 | 1 | cuButterfly-cuFFTDx-online | 0.071690 | 14.627 | 0.822 | 0.887x | ramp | unstable |
+| fft | 20 | 4 | cuButterfly-cuFFTDx-online | 0.235653 | 17.799 | 1.000 | 0.891x | saturated | stable |
+| fft | 20 | 1 | cuFFT | 0.063590 | 16.490 | 0.826 | 1.000x | ramp | stable |
+| fft | 20 | 4 | cuFFT | 0.210053 | 19.968 | 1.000 | 1.000x | saturated | stable |
+| fwht | 8 | 1 | cuButterfly-shared-radix4 | 0.002560 | 0.100 | 0.001 | 0.800x | launch-limited | below-timing-floor |
+| fwht | 8 | 64 | cuButterfly-shared-radix4 | 0.002570 | 6.375 | 0.074 | 0.821x | launch-limited | below-timing-floor |
+| fwht | 8 | 16,384 | cuButterfly-shared-radix4 | 0.048425 | 86.614 | 1.000 | 0.883x | saturated | stable |
+| fwht | 8 | 1 | cuButterfly-warp-register | 0.002048 | 0.125 | 0.001 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 64 | cuButterfly-warp-register | 0.002109 | 7.769 | 0.079 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 16,384 | cuButterfly-warp-register | 0.042762 | 98.085 | 1.000 | 1.000x | saturated | stable |
+| fwht | 15 | 1 | cuButterfly-online-radix4 | 0.009032 | 3.628 | 0.274 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 15 | 16 | cuButterfly-online-radix4 | 0.044657 | 11.740 | 0.886 | 0.394x | ramp | stable |
+| fwht | 15 | 128 | cuButterfly-online-radix4 | 0.316375 | 13.257 | 1.000 | 0.205x | saturated | stable |
+| fwht | 15 | 1 | cuButterfly-warp-register | 0.017603 | 1.862 | 0.029 | 0.513x | launch-limited | below-timing-floor |
+| fwht | 15 | 16 | cuButterfly-warp-register | 0.017592 | 29.803 | 0.460 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 15 | 128 | cuButterfly-warp-register | 0.064788 | 64.739 | 1.000 | 1.000x | saturated | stable |
+| fwht | 20 | 1 | cuButterfly-hierarchical-radix4 | 0.098550 | 10.640 | 1.000 | 0.915x | saturated | stable |
+| fwht | 20 | 4 | cuButterfly-hierarchical-radix4 | 0.488223 | 8.591 | 0.807 | 0.655x | ramp | stable |
+| fwht | 20 | 1 | cuButterfly-online-radix4 | 0.090153 | 11.631 | 0.886 | 1.000x | ramp | stable |
+| fwht | 20 | 4 | cuButterfly-online-radix4 | 0.319652 | 13.121 | 1.000 | 1.000x | saturated | stable |
+| ntt | 12 | 1 | cuNTT-Hybrid2D-radix2 | 0.006881 | 0.595 | 0.023 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 12 | 16 | cuNTT-Hybrid2D-radix2 | 0.008458 | 7.748 | 0.302 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 12 | 1,024 | cuNTT-Hybrid2D-radix2 | 0.163318 | 25.682 | 1.000 | 1.000x | saturated | stable |
+| ntt | 12 | 1 | cuNTT-Hybrid2D-radix4 | 0.005990 | 0.684 | 0.023 | 1.149x | launch-limited | below-timing-floor |
+| ntt | 12 | 16 | cuNTT-Hybrid2D-radix4 | 0.007639 | 8.579 | 0.285 | 1.107x | launch-limited | below-timing-floor |
+| ntt | 12 | 1,024 | cuNTT-Hybrid2D-radix4 | 0.139510 | 30.065 | 1.000 | 1.171x | saturated | stable |
+| ntt | 16 | 1 | cuNTT-Hybrid2D-radix2 | 0.015862 | 4.132 | 0.299 | 0.978x | launch-limited | below-timing-floor |
+| ntt | 16 | 16 | cuNTT-Hybrid2D-radix2 | 0.087378 | 12.000 | 0.869 | 0.944x | ramp | stable |
+| ntt | 16 | 64 | cuNTT-Hybrid2D-radix2 | 0.303759 | 13.808 | 1.000 | 0.917x | saturated | stable |
+| ntt | 16 | 1 | cuNTT-Hybrid2D-radix4 | 0.015514 | 4.224 | 0.280 | 1.000x | launch-limited | below-timing-floor |
+| ntt | 16 | 16 | cuNTT-Hybrid2D-radix4 | 0.082463 | 12.716 | 0.844 | 1.000x | ramp | stable |
+| ntt | 16 | 64 | cuNTT-Hybrid2D-radix4 | 0.278436 | 15.064 | 1.000 | 1.000x | saturated | stable |
+| ntt | 20 | 1 | cuNTT-compact-stage | 0.094986 | 11.039 | 0.899 | 1.000x | ramp | stable |
+| ntt | 20 | 4 | cuNTT-compact-stage | 0.341606 | 12.278 | 1.000 | 1.000x | saturated | stable |
+| xor-zeta | 8 | 1 | cuButterfly-radix2 | 0.002847 | 0.090 | 0.001 | 0.878x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 64 | cuButterfly-radix2 | 0.002929 | 5.594 | 0.066 | 0.874x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 16,384 | cuButterfly-radix2 | 0.049695 | 84.401 | 1.000 | 0.961x | saturated | stable |
+| xor-zeta | 8 | 1 | cuButterfly-radix4 | 0.002499 | 0.102 | 0.001 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 64 | cuButterfly-radix4 | 0.002560 | 6.400 | 0.073 | 1.000x | launch-limited | below-timing-floor |
+| xor-zeta | 8 | 16,384 | cuButterfly-radix4 | 0.047780 | 87.784 | 1.000 | 1.000x | saturated | stable |
+| xor-zeta | 20 | 1 | cuButterfly-hierarchical-radix4 | 0.098150 | 10.683 | 1.000 | 0.968x | saturated | stable |
+| xor-zeta | 20 | 4 | cuButterfly-hierarchical-radix4 | 0.487117 | 8.610 | 0.806 | 0.656x | ramp | stable |
+| xor-zeta | 20 | 1 | cuButterfly-online-radix4 | 0.095048 | 11.032 | 0.840 | 1.000x | ramp | unstable |
+| xor-zeta | 20 | 4 | cuButterfly-online-radix4 | 0.319406 | 13.132 | 1.000 | 1.000x | saturated | stable |
diff --git a/results/v100_scaling_quick_summary.csv b/results/v100_scaling_quick_summary.csv
new file mode 100644
index 0000000..350f2c6
--- /dev/null
+++ b/results/v100_scaling_quick_summary.csv
@@ -0,0 +1,74 @@
+case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class,peak_billion_points_s,peak_batch,fraction_of_peak,saturation_fraction,saturation_batch,throughput_speedup_vs_batch1,batch_efficiency_vs_batch1,scaling_region,timing_floor_ms,timing_quality
+fft8_vkfft_b1,fft8-batch1,VkFFT,0,3,0.002334720,0.002314240,0.002355200,0.017544,0.017544,stable,1,fft,fp32,forward,none,in-place,8,256,1,1,256,,,,,,,,,,0.428316886,0.109649123,declared-reference,cuFFT,0.002682880,1.149123,faster,50.177629572,16384,0.002185,0.900000,16384,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fft8_vkfft_b64,fft8-batch64,VkFFT,0,3,0.002457600,0.002447360,0.002457600,0.004167,0.004167,stable,1,fft,fp32,forward,none,in-place,8,256,64,1,256,,,,,,,,,,26.041666667,6.666666667,declared-reference,cuFFT,0.002764800,1.125000,faster,50.177629572,16384,0.132861,0.900000,16384,60.800000,0.950000,launch-limited,0.020000,below-timing-floor
+fft8_vkfft_b16384,fft8-batch16384,VkFFT,0,3,0.083589122,0.083486721,0.084121600,0.007595,0.007595,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,,,,,,196.006365517,50.177629572,declared-reference,cuFFT,0.083773442,1.002205,parity,50.177629572,16384,1.000000,0.900000,16384,457.619982,0.027931,saturated,0.020000,stable
+fft8_cub_b1,fft8-batch1,cuButterfly-cuFFTDx,0,3,0.002888000,0.002888000,0.002898000,0.003463,0.003463,stable,1,fft,fp32,forward,none,in-place,8,256,1,1,256,,,,,temporal-tile,auto,cufftdx-block,shared,table,0.346260388,0.088642659,declared-reference,cuFFT,0.002682880,0.928975,slower,49.775161692,16384,0.001781,0.900000,16384,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fft8_cub_b64,fft8-batch64,cuButterfly-cuFFTDx,0,3,0.003123000,0.003113000,0.003144000,0.009926,0.009926,stable,1,fft,fp32,forward,none,in-place,8,256,64,1,256,,,,,temporal-tile,auto,cufftdx-block,shared,table,20.493115594,5.246237592,declared-reference,cuFFT,0.002764800,0.885303,slower,49.775161692,16384,0.105399,0.900000,16384,59.184118,0.924752,launch-limited,0.020000,below-timing-floor
+fft8_cub_b16384,fft8-batch16384,cuButterfly-cuFFTDx,0,3,0.084265000,0.084234000,0.084316000,0.000973,0.000973,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,temporal-tile,auto,cufftdx-block,shared,table,194.434225360,49.775161692,declared-reference,cuFFT,0.083773442,0.994167,parity,49.775161692,16384,1.000000,0.900000,16384,561.526043,0.034273,saturated,0.020000,stable
+fft8_cufft_b1,fft8-batch1,cuFFT,1,3,0.002682880,0.002672640,0.002754560,0.030534,0.030534,unstable,1,fft,fp32,forward,none,in-place,8,256,1,1,256,,,,,,,,,,0.372733779,0.095419847,declared-reference,cuFFT,0.002682880,1.000000,parity,50.067227750,16384,0.001906,0.900000,16384,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fft8_cufft_b64,fft8-batch64,cuFFT,1,3,0.002764800,0.002734080,0.002785280,0.018519,0.018519,stable,1,fft,fp32,forward,none,in-place,8,256,64,1,256,,,,,,,,,,23.148148148,5.925925926,declared-reference,cuFFT,0.002764800,1.000000,parity,50.067227750,16384,0.118359,0.900000,16384,62.103704,0.970370,launch-limited,0.020000,below-timing-floor
+fft8_cufft_b16384,fft8-batch16384,cuFFT,1,3,0.083773442,0.083752960,0.083834879,0.000978,0.000978,stable,1,fft,fp32,forward,none,in-place,8,256,16384,1,256,,,,,,,,,,195.575108398,50.067227750,declared-reference,cuFFT,0.083773442,1.000000,parity,50.067227750,16384,1.000000,0.900000,16384,524.704547,0.032025,saturated,0.020000,stable
+fft14_vkfft_b1,fft14-batch1,VkFFT,0,3,0.008263680,0.008253440,0.008263680,0.001239,0.001239,stable,1,fft,fp32,forward,none,in-place,14,16384,1,1,16384,,,,,,,,,,0.121011462,1.982651797,declared-reference,cuFFT,0.011888640,1.438662,faster,24.568138196,16,0.080700,0.900000,16,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fft14_vkfft_b16,fft14-batch16,VkFFT,0,3,0.010670080,0.010659840,0.010680321,0.001919,0.001919,stable,1,fft,fp32,forward,none,in-place,14,16384,16,1,16384,,,,,,,,,,1.499520154,24.568138196,declared-reference,cuFFT,0.013506561,1.265835,faster,24.568138196,16,1.000000,0.900000,16,12.391555,0.774472,saturated,0.020000,below-timing-floor
+fft14_vkfft_b256,fft14-batch256,VkFFT,0,3,0.171694085,0.171458572,0.171735033,0.001610,0.001610,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,,,,,,1.491023992,24.428937083,declared-reference,cuFFT,0.121036798,0.704956,slower,24.568138196,16,0.994334,0.900000,16,12.321345,0.048130,saturated,0.020000,stable
+fft14_cub_b1,fft14-batch1,cuButterfly-cuFFTDx-direct,0,3,0.020521000,0.020500000,0.020562000,0.003021,0.003021,stable,1,fft,fp32,forward,none,in-place,14,16384,1,1,16384,,,,,temporal-tile,auto,cufftdx-direct,shared,table,0.048730569,0.798401637,declared-reference,cuFFT,0.011888640,0.579340,slower,34.556572606,256,0.023104,0.900000,256,1.000000,1.000000,launch-limited,0.020000,stable
+fft14_cub_b16,fft14-batch16,cuButterfly-cuFFTDx-direct,0,3,0.020777000,0.020736000,0.020808000,0.003465,0.003465,stable,1,fft,fp32,forward,none,in-place,14,16384,16,1,16384,,,,,temporal-tile,auto,cufftdx-direct,shared,table,0.770082303,12.617028445,declared-reference,cuFFT,0.013506561,0.650073,slower,34.556572606,256,0.365112,0.900000,256,15.802859,0.987679,launch-limited,0.020000,stable
+fft14_cub_b256,fft14-batch256,cuButterfly-cuFFTDx-direct,0,3,0.121375000,0.120986000,0.121641000,0.005396,0.005396,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,temporal-tile,auto,cufftdx-direct,shared,table,2.109165808,34.556572606,declared-reference,cuFFT,0.121036798,0.997214,parity,34.556572606,256,1.000000,0.900000,256,43.282192,0.169071,saturated,0.020000,stable
+fft14_cufft_b1,fft14-batch1,cuFFT,1,3,0.011888640,0.011878400,0.011898880,0.001723,0.001723,stable,1,fft,fp32,forward,none,in-place,14,16384,1,1,16384,,,,,,,,,,0.084113910,1.378122308,declared-reference,cuFFT,0.011888640,1.000000,parity,34.653130860,256,0.039769,0.900000,256,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fft14_cufft_b16,fft14-batch16,cuFFT,1,3,0.013506561,0.013496321,0.013516800,0.001516,0.001516,stable,1,fft,fp32,forward,none,in-place,14,16384,16,1,16384,,,,,,,,,,1.184609465,19.408641474,declared-reference,cuFFT,0.013506561,1.000000,parity,34.653130860,256,0.560083,0.900000,256,14.083395,0.880212,ramp,0.020000,below-timing-floor
+fft14_cufft_b256,fft14-batch256,cuFFT,1,3,0.121036798,0.121026561,0.123156480,0.017597,0.017597,stable,1,fft,fp32,forward,none,in-place,14,16384,256,1,16384,,,,,,,,,,2.115059257,34.653130860,declared-reference,cuFFT,0.121036798,1.000000,parity,34.653130860,256,1.000000,0.900000,256,25.145178,0.098223,saturated,0.020000,stable
+fft18_vkfft_b1,fft18-batch1,VkFFT,0,3,0.018483199,0.018462719,0.021657601,0.172853,0.172853,unstable,1,fft,fp32,forward,none,in-place,18,262144,1,1,262144,,,,,,,,,,0.054103189,14.182826252,declared-reference,cuFFT,0.022978561,1.243213,faster,20.856459190,16,0.680021,0.900000,16,1.000000,1.000000,ramp,0.020000,below-timing-floor
+fft18_vkfft_b4,fft18-batch4,VkFFT,0,3,0.063805439,0.063784964,0.063825920,0.000642,0.000642,stable,1,fft,fp32,forward,none,in-place,18,262144,4,1,262144,,,,,,,,,,0.062690580,16.433959494,declared-reference,cuFFT,0.068608001,1.075269,faster,20.856459190,16,0.787955,0.900000,16,1.158722,0.289681,ramp,0.020000,stable
+fft18_vkfft_b16,fft18-batch16,VkFFT,0,3,0.201103359,0.201093122,0.201349124,0.001273,0.001273,stable,1,fft,fp32,forward,none,in-place,18,262144,16,1,262144,,,,,,,,,,0.079561078,20.856459190,declared-reference,cuFFT,0.211353600,1.050970,faster,20.856459190,16,1.000000,0.900000,16,1.470543,0.091909,saturated,0.020000,stable
+fft18_cub_b1,fft18-batch1,cuButterfly-cuFFTDx-online,0,3,0.016476000,0.016466000,0.017388000,0.055960,0.055960,unstable,1,fft,fp32,forward,none,in-place,18,262144,1,1,262144,,,,,online-reorder,auto,cufftdx-block,shared,recurrence,0.060694343,15.910657927,declared-reference,cuFFT,0.022978561,1.394669,faster,20.434003537,16,0.778636,0.900000,16,1.000000,1.000000,ramp,0.020000,below-timing-floor
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+fft20_vkfft_b1,fft20-batch1,VkFFT,0,3,0.060917757,0.060753919,0.061040640,0.004707,0.004707,stable,1,fft,fp32,forward,none,in-place,20,1048576,1,1,1048576,,,,,,,,,,0.016415575,17.212977819,declared-reference,cuFFT,0.063590400,1.043873,faster,20.311414762,4,0.847453,0.900000,4,1.000000,1.000000,ramp,0.020000,stable
+fft20_vkfft_b4,fft20-batch4,VkFFT,0,3,0.206499845,0.206489608,0.206520334,0.000149,0.000149,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,0.019370475,20.311414762,declared-reference,cuFFT,0.210053116,1.017207,parity,20.311414762,4,1.000000,0.900000,4,1.180006,0.295001,saturated,0.020000,stable
+fft20_cub_b1,fft20-batch1,cuButterfly-cuFFTDx-online,0,3,0.071690000,0.071434000,0.077455000,0.083987,0.083987,unstable,1,fft,fp32,forward,none,in-place,20,1048576,1,1,1048576,,,,,online-reorder,auto,cufftdx-block,shared,recurrence,0.013948947,14.626530897,declared-reference,cuFFT,0.063590400,0.887019,slower,17.798644617,4,0.821778,0.900000,4,1.000000,1.000000,ramp,0.020000,unstable
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+fft20_cufft_b1,fft20-batch1,cuFFT,1,3,0.063590400,0.063549444,0.065310724,0.027697,0.027697,stable,1,fft,fp32,forward,none,in-place,20,1048576,1,1,1048576,,,,,,,,,,0.015725644,16.489533011,declared-reference,cuFFT,0.063590400,1.000000,parity,19.967825662,4,0.825805,0.900000,4,1.000000,1.000000,ramp,0.020000,stable
+fft20_cufft_b4,fft20-batch4,cuFFT,1,3,0.210053116,0.209940478,0.210421756,0.002291,0.002291,stable,1,fft,fp32,forward,none,in-place,20,1048576,4,1,1048576,,,,,,,,,,0.019042802,19.967825662,declared-reference,cuFFT,0.210053116,1.000000,parity,19.967825662,4,1.000000,0.900000,4,1.210939,0.302735,saturated,0.020000,stable
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+fwht8_warp_b1,fwht8-batch1,cuButterfly-warp-register,0,3,0.002048000,0.002048000,0.002396000,0.169922,0.169922,unstable,1,fwht,fp32,forward,none,out-of-place,8,256,1,1,256,,,,,temporal-tile,radix2,scalar,warp-register,table,0.488281250,0.125000000,group-fastest,cuButterfly-warp-register,0.002048000,1.000000,parity,98.084841682,16384,0.001274,0.900000,16384,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fwht8_warp_b64,fwht8-batch64,cuButterfly-warp-register,0,3,0.002109000,0.002099000,0.002417000,0.150782,0.150782,unstable,1,fwht,fp32,forward,none,out-of-place,8,256,64,1,256,,,,,temporal-tile,radix2,scalar,warp-register,table,30.346135609,7.768610716,group-fastest,cuButterfly-warp-register,0.002109000,1.000000,parity,98.084841682,16384,0.079203,0.900000,16384,62.148886,0.971076,launch-limited,0.020000,below-timing-floor
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+fwht15_online_b1,fwht15-batch1,cuButterfly-online-radix4,0,3,0.009032000,0.007690000,0.009052000,0.150797,0.150797,unstable,1,fwht,fp32,forward,none,out-of-place,15,32768,1,1,32768,,,,,online-reorder,radix4,scalar,shared,table,0.110717449,3.627989371,group-fastest,cuButterfly-online-radix4,0.009032000,1.000000,parity,13.257381272,128,0.273658,0.900000,128,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
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+fwht15_warp_b16,fwht15-batch16,cuButterfly-warp-register,0,3,0.017592000,0.017592000,0.017603000,0.000625,0.000625,stable,1,fwht,fp32,forward,none,out-of-place,15,32768,16,1,32768,,,,,temporal-tile,radix2,scalar,warp-register,table,0.909504320,29.802637563,group-fastest,cuButterfly-warp-register,0.017592000,1.000000,parity,64.738902266,128,0.460351,0.900000,128,16.010005,1.000625,launch-limited,0.020000,below-timing-floor
+fwht15_warp_b128,fwht15-batch128,cuButterfly-warp-register,0,3,0.064788000,0.064707000,0.064819000,0.001729,0.001729,stable,1,fwht,fp32,forward,none,out-of-place,15,32768,128,1,32768,,,,,temporal-tile,radix2,scalar,warp-register,table,1.975674508,64.738902266,group-fastest,cuButterfly-warp-register,0.064788000,1.000000,parity,64.738902266,128,1.000000,0.900000,128,34.777798,0.271702,saturated,0.020000,stable
+fwht20_hier_b1,fwht20-batch1,cuButterfly-hierarchical-radix4,0,3,0.098550000,0.098478000,0.100567000,0.021197,0.021197,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,1,1,1048576,,,,,hierarchical,radix4,scalar,shared,table,0.010147133,10.640040589,group-fastest,cuButterfly-online-radix4,0.090153000,0.914795,slower,10.640040589,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,stable
+fwht20_hier_b4,fwht20-batch4,cuButterfly-hierarchical-radix4,0,3,0.488223000,0.488202000,0.488305000,0.000211,0.000211,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,table,0.008192977,8.590959459,group-fastest,cuButterfly-online-radix4,0.319652000,0.654725,slower,10.640040589,1,0.807418,0.900000,1,0.807418,0.201854,ramp,0.020000,stable
+fwht20_online_b1,fwht20-batch1,cuButterfly-online-radix4,0,3,0.090153000,0.090092000,0.090849000,0.008397,0.008397,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,1,1,1048576,,,,,online-reorder,radix4,scalar,shared,table,0.011092254,11.631071623,group-fastest,cuButterfly-online-radix4,0.090153000,1.000000,parity,13.121469598,4,0.886415,0.900000,4,1.000000,1.000000,ramp,0.020000,stable
+fwht20_online_b4,fwht20-batch4,cuButterfly-online-radix4,0,3,0.319652000,0.319601000,0.320133000,0.001664,0.001664,stable,1,fwht,fp32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,table,0.012513609,13.121469598,group-fastest,cuButterfly-online-radix4,0.319652000,1.000000,parity,13.121469598,4,1.000000,0.900000,4,1.128139,0.282035,saturated,0.020000,stable
+ntt12_r2_b1,ntt12-batch1,cuNTT-Hybrid2D-radix2,1,3,0.006881000,0.006861000,0.006932000,0.010318,0.010318,stable,1,ntt,uint32,forward,,,12,4096,1,1,4096,32,30,0,natural,hybrid2d,radix2,,,fused,0.145327714,0.595262317,declared-reference,cuNTT-Hybrid2D-radix2,0.006881000,1.000000,parity,25.681823192,1024,0.023178,0.900000,1024,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
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+ntt12_r2_b1024,ntt12-batch1024,cuNTT-Hybrid2D-radix2,1,3,0.163318000,0.162826000,0.164137000,0.008027,0.008027,stable,1,ntt,uint32,forward,,,12,4096,1024,1,4096,32,30,0,natural,hybrid2d,radix2,,,fused,6.269976365,25.681823192,declared-reference,cuNTT-Hybrid2D-radix2,0.163318000,1.000000,parity,25.681823192,1024,1.000000,0.900000,1024,43.143707,0.042133,saturated,0.020000,stable
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+ntt12_r4_b16,ntt12-batch16,cuNTT-Hybrid2D-radix4,0,3,0.007639000,0.007639000,0.007741000,0.013353,0.013353,stable,1,ntt,uint32,forward,,,12,4096,16,1,4096,32,30,0,natural,hybrid2d,radix4,,,fused,2.094514989,8.579133394,declared-reference,cuNTT-Hybrid2D-radix2,0.008458000,1.107213,faster,30.064540176,1024,0.285357,0.900000,1024,12.546145,0.784134,launch-limited,0.020000,below-timing-floor
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+ntt16_r2_b1,ntt16-batch1,cuNTT-Hybrid2D-radix2,0,3,0.015862000,0.015862000,0.015882000,0.001261,0.001261,stable,1,ntt,uint64,forward,,,16,65536,1,1,65536,64,60,0,natural,hybrid2d,radix2,,,fused,0.063043752,4.131635355,group-fastest,cuNTT-Hybrid2D-radix4,0.015514000,0.978061,parity,13.807999105,64,0.299220,0.900000,64,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
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+ntt16_r4_b16,ntt16-batch16,cuNTT-Hybrid2D-radix4,0,3,0.082463000,0.082217000,0.082739000,0.006330,0.006330,stable,1,ntt,uint64,forward,,,16,65536,16,1,65536,64,60,0,natural,hybrid2d,radix4,,,fused,0.194026412,12.715714927,group-fastest,cuNTT-Hybrid2D-radix4,0.082463000,1.000000,parity,15.063799221,64,0.844124,0.900000,64,3.010126,0.188133,ramp,0.020000,stable
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+xor20_hier_b4,xor20-batch4,cuButterfly-hierarchical-radix4,0,3,0.487117000,0.486973000,0.487178000,0.000421,0.000421,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,hierarchical,radix4,scalar,shared,table,0.008211580,8.610465248,group-fastest,cuButterfly-online-radix4,0.319406000,0.655707,slower,10.683402955,1,0.805967,0.900000,1,0.805967,0.201492,ramp,0.020000,stable
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+xor20_online_b4,xor20-batch4,cuButterfly-online-radix4,0,3,0.319406000,0.319252000,0.319457000,0.000642,0.000642,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,4,1,1048576,,,,,online-reorder,radix4,scalar,shared,table,0.012523246,13.131575487,group-fastest,cuButterfly-online-radix4,0.319406000,1.000000,parity,13.131575487,4,1.000000,0.900000,4,1.190310,0.297577,saturated,0.020000,stable
diff --git a/results/v100_scaling_quick_unstable_confirm_raw.csv b/results/v100_scaling_quick_unstable_confirm_raw.csv
new file mode 100644
index 0000000..34201a7
--- /dev/null
+++ b/results/v100_scaling_quick_unstable_confirm_raw.csv
@@ -0,0 +1,51 @@
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+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,2,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,328.044557000,0.018462719,54163.201994492,127.787025813,14198558423.644159317,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,5,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016435,60845.014286,143.551399,15950155425.028454,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.437376,0.396544,0.000000
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.089897,11123.847348,116.641994,11664199357.050962,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.761184,0.724384,0.000000
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,1,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002611,382965.706876,0.392157,98039220.960323,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.012288,0.018528,0.000000
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,4,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,2.003535000,0.002682880,372733.806415253,0.381679418,95419854.442304835,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,4,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002468,25933610.183020,26.556017,6639004206.853062,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.036864,0.037248,0.000000
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.007680,130208.328728,31.999999,4266666515.751023,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.045824,0.048192,0.000000
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,3,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002417,26483050.250930,27.118643,6779660864.238072,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.035840,0.039776,0.000000
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002621,381469.728881,0.390625,97656250.593503,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.013312,0.018944,0.000000
+fft18_vkfft_b1,fft18-batch1,quick,fft-library,VkFFT,0,5,1,1,,Tesla V100-SXM2-16GB,7.0,vkfft,10304,fp32,forward,in-place,18,262144,1,1000,100,330.379728000,0.018472960,54133.175633810,127.716184740,14190687193.349597931,0.000000000,0.000000000,-1,fft,none,1,,262144,,,,,,,,,,,,,,,,,,,,,,
+fft18_cub_b1,fft18-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,2,1,1,0.000512,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,18,262144,1,1000,100,,0.016445,60807.132070,143.462023,15940224829.288858,,,-1,fft,none,1,,262144,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,256,256,8,8,4,4,9,1,0,0,0.408416,0.421216,0.000000
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,5,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.089989,11112.454696,116.522533,11652253295.341375,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.756256,0.729728,0.000000
+xor20_online_b1,xor20-batch1,quick,butterfly,cuButterfly-online-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,20,1048576,1,1000,100,,0.090450,11055.841511,115.928901,11592890068.736340,,,-1,xor-zeta,none,1,,1048576,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,10,1,0,0,0.756864,0.749184,0.000000
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,3,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002540,393775.214160,0.403226,100806454.824929,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.008192,0.017088,0.000000
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,5,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,1.760243000,0.002682880,372733.806415253,0.381679418,95419854.442304835,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,
+fwht15_online_b1,fwht15-batch1,quick,butterfly,cuButterfly-online-radix4,0,2,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,15,32768,1,1000,100,,0.007680,130208.328728,31.999999,4266666515.751023,,,-1,fwht,none,1,,32768,online-reorder,radix4,four-mul,table,shared,scalar,0,named-barrier,256,0,0,8,8,0,0,8,1,0,0,0.043424,0.051744,0.000000
+fft20_cub_b1,fft20-batch1,quick,butterfly,cuButterfly-cuFFTDx-online,0,3,1,1,0.001242,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,in-place,20,1048576,1,1000,100,,0.070881,14108.097904,147.934129,14793412867.337908,,,-1,fft,none,1,,1048576,online-reorder,auto,four-mul,recurrence,shared,cufftdx-block,0,named-barrier,128,512,512,8,8,4,4,10,1,0,0,1.427360,1.349472,0.000000
+fwht8_warp_b1,fwht8-batch1,quick,butterfly,cuButterfly-warp-register,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,1,1000,100,,0.002580,387524.808859,0.396825,99206351.068029,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.014336,0.018752,0.000000
+xor8_r2_b64,xor8-batch64,quick,butterfly,cuButterfly-radix2,0,1,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,64,1000,100,,0.002918,21929825.535294,22.456141,5614035337.035136,,,-1,xor-zeta,none,1,,256,temporal-tile,radix2,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.036864,0.034944,0.000000
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,5,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002386,26824035.305571,27.467812,6866953038.226103,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.034816,0.036320,0.000000
+fwht8_warp_b64,fwht8-batch64,quick,butterfly,cuButterfly-warp-register,0,2,64,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,fp32,forward,out-of-place,8,256,64,1000,100,,0.002376,26939654.923600,27.586207,6896551660.441724,,,-1,fwht,none,1,,256,temporal-tile,radix2,four-mul,table,warp-register,scalar,0,named-barrier,32,0,0,8,8,0,0,0,0,0,0,0.035840,0.039584,0.000000
+xor8_r4_b1,xor8-batch1,quick,butterfly,cuButterfly-radix4,0,4,1,1,0.000000,Tesla V100-SXM2-16GB,7.0,,,uint32,forward,out-of-place,8,256,1,1000,100,,0.002621,381469.728881,0.390625,97656250.593503,,,-1,xor-zeta,none,1,,256,temporal-tile,radix4,four-mul,table,shared,scalar,0,named-barrier,128,0,0,8,8,0,0,0,0,0,0,0.011264,0.019296,0.000000
+fft8_cufft_b1,fft8-batch1,quick,fft-library,cuFFT,1,1,1,1,,Tesla V100-SXM2-16GB,7.0,cufft,10900,fp32,forward,in-place,8,256,1,1000,100,2.079633000,0.002703360,369910.031166557,0.378787872,94696967.978638574,0.000000000,0.000000000,-1,fft,none,1,,256,,,,,,,,,,,,,,,,,,,,,,
diff --git a/results/v100_scaling_quick_unstable_confirm_report.md b/results/v100_scaling_quick_unstable_confirm_report.md
new file mode 100644
index 0000000..90f187c
--- /dev/null
+++ b/results/v100_scaling_quick_unstable_confirm_report.md
@@ -0,0 +1,35 @@
+# V100 Orthogonal Length/Batch Scaling
+
+`Batch@90%` is the smallest measured batch reaching 90% of that
+implementation's peak measured `Gpoint/s` at fixed transform length.
+Rows below the configured 0.020 ms timing floor are retained but are not
+used as stable latency claims.
+
+## Saturation Summary
+
+| Operator | Numeric | logN | Implementation | Batch@90% | Peak batch | Peak Gpoint/s | Batch-1 ms |
+|:--|:--|--:|:--|--:|--:|--:|--:|
+| fft | fp32 | 8 | cuFFT | 1 | 1 | 0.095 | 0.002683 |
+| fft | fp32 | 18 | VkFFT | 1 | 1 | 14.191 | 0.018473 |
+| fft | fp32 | 18 | cuButterfly-cuFFTDx-online | 1 | 1 | 15.920 | 0.016466 |
+| fft | fp32 | 20 | cuButterfly-cuFFTDx-online | 1 | 1 | 13.586 | 0.077179 |
+| fwht | fp32 | 8 | cuButterfly-warp-register | 64 | 64 | 6.867 | 0.002580 |
+| fwht | fp32 | 15 | cuButterfly-online-radix4 | 1 | 1 | 4.250 | 0.007711 |
+| xor-zeta | uint32 | 8 | cuButterfly-radix2 | 64 | 64 | 5.333 | - |
+| xor-zeta | uint32 | 8 | cuButterfly-radix4 | 1 | 1 | 0.101 | 0.002540 |
+| xor-zeta | uint32 | 20 | cuButterfly-online-radix4 | 1 | 1 | 11.652 | 0.089989 |
+
+## Detailed Scaling
+
+| Operator | logN | Batch | Implementation | Median ms | Gpoint/s | Peak fraction | vs basis | Region | Timing quality |
+|:--|--:|--:|:--|--:|--:|--:|--:|:--|:--|
+| fft | 8 | 1 | cuFFT | 0.002683 | 0.095 | 1.000 | 1.000x | saturated | below-timing-floor |
+| fft | 18 | 1 | VkFFT | 0.018473 | 14.191 | 1.000 | 0.891x | saturated | below-timing-floor |
+| fft | 18 | 1 | cuButterfly-cuFFTDx-online | 0.016466 | 15.920 | 1.000 | 1.000x | saturated | below-timing-floor |
+| fft | 20 | 1 | cuButterfly-cuFFTDx-online | 0.077179 | 13.586 | 1.000 | 1.000x | saturated | unstable |
+| fwht | 8 | 1 | cuButterfly-warp-register | 0.002580 | 0.099 | 0.014 | 1.000x | launch-limited | below-timing-floor |
+| fwht | 8 | 64 | cuButterfly-warp-register | 0.002386 | 6.867 | 1.000 | 1.000x | saturated | below-timing-floor |
+| fwht | 15 | 1 | cuButterfly-online-radix4 | 0.007711 | 4.250 | 1.000 | 1.000x | saturated | below-timing-floor |
+| xor-zeta | 8 | 64 | cuButterfly-radix2 | 0.003072 | 5.333 | 1.000 | 1.000x | saturated | below-timing-floor |
+| xor-zeta | 8 | 1 | cuButterfly-radix4 | 0.002540 | 0.101 | 1.000 | 1.000x | saturated | below-timing-floor |
+| xor-zeta | 20 | 1 | cuButterfly-online-radix4 | 0.089989 | 11.652 | 1.000 | 1.000x | saturated | stable |
diff --git a/results/v100_scaling_quick_unstable_confirm_summary.csv b/results/v100_scaling_quick_unstable_confirm_summary.csv
new file mode 100644
index 0000000..99083ee
--- /dev/null
+++ b/results/v100_scaling_quick_unstable_confirm_summary.csv
@@ -0,0 +1,11 @@
+case_id,group,implementation,reference,trials,median_kernel_ms,min_kernel_ms,max_kernel_ms,relative_range,central_relative_range,stability_class,correct,operator,precision,direction,normalization,placement,logN,N,performance_batch,element_stride,batch_stride,word_bits,modulus_bits,inverse,output_order,backend,compute_unit,fft_core,local_exchange,cross_twiddle,million_transforms_s,billion_points_s,comparison_basis,basis_implementation,basis_kernel_ms,throughput_vs_basis,performance_class,peak_billion_points_s,peak_batch,fraction_of_peak,saturation_fraction,saturation_batch,throughput_speedup_vs_batch1,batch_efficiency_vs_batch1,scaling_region,timing_floor_ms,timing_quality
+fft8_cufft_b1,fft8-batch1,cuFFT,1,5,0.002682880,0.002672640,0.003051520,0.141221,0.007634,stable-with-outlier,1,fft,fp32,forward,none,in-place,8,256,1,1,256,,,,,,,,,,0.372733779,0.095419847,declared-reference,cuFFT,0.002682880,1.000000,parity,0.095419847,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,below-timing-floor
+fft18_vkfft_b1,fft18-batch1,VkFFT,0,5,0.018472960,0.018462719,0.021575680,0.168514,0.000554,stable-with-outlier,1,fft,fp32,forward,none,in-place,18,262144,1,1,262144,,,,,,,,,,0.054133176,14.190687361,group-fastest,cuButterfly-cuFFTDx-online,0.016466000,0.891357,slower,14.190687361,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,below-timing-floor
+fft18_cub_b1,fft18-batch1,cuButterfly-cuFFTDx-online,0,5,0.016466000,0.016435000,0.019139000,0.164217,0.001275,stable-with-outlier,1,fft,fp32,forward,none,in-place,18,262144,1,1,262144,,,,,online-reorder,auto,cufftdx-block,shared,recurrence,0.060731204,15.920320661,group-fastest,cuButterfly-cuFFTDx-online,0.016466000,1.000000,parity,15.920320661,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,below-timing-floor
+fft20_cub_b1,fft20-batch1,cuButterfly-cuFFTDx-online,0,5,0.077179000,0.070881000,0.077445000,0.085049,0.077081,unstable,1,fft,fp32,forward,none,in-place,20,1048576,1,1,1048576,,,,,online-reorder,auto,cufftdx-block,shared,recurrence,0.012956892,13.586286425,group-fastest,cuButterfly-cuFFTDx-online,0.077179000,1.000000,parity,13.586286425,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,unstable
+fwht8_warp_b1,fwht8-batch1,cuButterfly-warp-register,0,5,0.002580000,0.002365000,0.002621000,0.099225,0.071318,unstable,1,fwht,fp32,forward,none,out-of-place,8,256,1,1,256,,,,,temporal-tile,radix2,scalar,warp-register,table,0.387596899,0.099224806,group-fastest,cuButterfly-warp-register,0.002580000,1.000000,parity,6.866722548,64,0.014450,0.900000,64,1.000000,1.000000,launch-limited,0.020000,below-timing-floor
+fwht8_warp_b64,fwht8-batch64,cuButterfly-warp-register,0,5,0.002386000,0.002376000,0.002468000,0.038558,0.012992,stable-with-outlier,1,fwht,fp32,forward,none,out-of-place,8,256,64,1,256,,,,,temporal-tile,radix2,scalar,warp-register,table,26.823134954,6.866722548,group-fastest,cuButterfly-warp-register,0.002386000,1.000000,parity,6.866722548,64,1.000000,0.900000,64,69.203688,1.081308,saturated,0.020000,below-timing-floor
+fwht15_online_b1,fwht15-batch1,cuButterfly-online-radix4,0,5,0.007711000,0.007680000,0.008980000,0.168590,0.167293,unstable,1,fwht,fp32,forward,none,out-of-place,15,32768,1,1,32768,,,,,online-reorder,radix4,scalar,shared,table,0.129684866,4.249513682,group-fastest,cuButterfly-online-radix4,0.007711000,1.000000,parity,4.249513682,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,below-timing-floor
+xor8_r2_b64,xor8-batch64,cuButterfly-radix2,0,5,0.003072000,0.002918000,0.003420000,0.163411,0.156576,unstable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,64,1,256,,,,,temporal-tile,radix2,scalar,shared,table,20.833333333,5.333333333,group-fastest,cuButterfly-radix2,0.003072000,1.000000,parity,5.333333333,64,1.000000,0.900000,64,0.000000,0.000000,saturated,0.020000,below-timing-floor
+xor8_r4_b1,xor8-batch1,cuButterfly-radix4,0,5,0.002540000,0.002478000,0.002621000,0.056299,0.036220,unstable,1,xor-zeta,uint32,forward,none,out-of-place,8,256,1,1,256,,,,,temporal-tile,radix4,scalar,shared,table,0.393700787,0.100787402,group-fastest,cuButterfly-radix4,0.002540000,1.000000,parity,0.100787402,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,below-timing-floor
+xor20_online_b1,xor20-batch1,cuButterfly-online-radix4,0,5,0.089989000,0.089887000,0.090450000,0.006256,0.002045,stable,1,xor-zeta,uint32,forward,none,out-of-place,20,1048576,1,1,1048576,,,,,online-reorder,radix4,scalar,shared,table,0.011112469,11.652268611,group-fastest,cuButterfly-online-radix4,0.089989000,1.000000,parity,11.652268611,1,1.000000,0.900000,1,1.000000,1.000000,saturated,0.020000,stable
diff --git a/scripts/analyze_fft_pipeline_model.py b/scripts/analyze_fft_pipeline_model.py
new file mode 100755
index 0000000..bda936c
--- /dev/null
+++ b/scripts/analyze_fft_pipeline_model.py
@@ -0,0 +1,243 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import json
+import math
+import pathlib
+import statistics
+
+
+SIGNATURE_FIELDS = (
+    "mapping_id", "decomposition_count", "stages_per_decomposition", "segment_threads",
+    "segment_ept", "boundary_twiddles", "boundary_layouts", "boundary_residencies",
+    "execution_group_stages", "group_threads", "group_ept", "cross_twiddle", "direct_boundary",
+)
+
+
+def rank_values(values):
+    order = sorted(range(len(values)), key=values.__getitem__)
+    ranks = [0.0] * len(values)
+    index = 0
+    while index < len(order):
+        end = index + 1
+        while end < len(order) and values[order[end]] == values[order[index]]:
+            end += 1
+        rank = (index + 1 + end) / 2.0
+        for position in range(index, end):
+            ranks[order[position]] = rank
+        index = end
+    return ranks
+
+
+def pearson(left, right):
+    left_mean = statistics.mean(left)
+    right_mean = statistics.mean(right)
+    numerator = sum((x - left_mean) * (y - right_mean) for x, y in zip(left, right))
+    left_norm = math.sqrt(sum((x - left_mean) ** 2 for x in left))
+    right_norm = math.sqrt(sum((y - right_mean) ** 2 for y in right))
+    return numerator / (left_norm * right_norm) if left_norm and right_norm else 0.0
+
+
+def evaluate(rows, top_k_values=(1, 3, 10)):
+    groups = {}
+    for row in rows:
+        groups.setdefault(row["group"], []).append(row)
+    evaluations = []
+    for group, candidates in sorted(groups.items()):
+        ranked = sorted(candidates, key=lambda row: float(row["static_score"]))
+        measured = sorted(candidates, key=lambda row: float(row["median_kernel_ms"]))
+        winner = measured[0]
+        winner_rank = next(index for index, row in enumerate(ranked, 1)
+                           if row["candidate_id"] == winner["candidate_id"])
+        result = {
+            "group": group,
+            "logN": int(winner["logN"]),
+            "batch": int(winner["batch"]),
+            "candidate_count": len(candidates),
+            "measured_winner": winner["candidate_id"],
+            "measured_winner_ms": float(winner["median_kernel_ms"]),
+            "winner_static_rank": winner_rank,
+            "spearman": pearson(
+                rank_values([float(row["static_score"]) for row in candidates]),
+                rank_values([float(row["median_kernel_ms"]) for row in candidates])),
+        }
+        for top_k in top_k_values:
+            limit = min(top_k, len(ranked))
+            selected = min(ranked[:limit], key=lambda row: float(row["median_kernel_ms"]))
+            result[f"top{top_k}_candidate"] = selected["candidate_id"]
+            result[f"top{top_k}_regret"] = (
+                float(selected["median_kernel_ms"]) / float(winner["median_kernel_ms"]))
+            result[f"top{top_k}_recall"] = int(winner_rank <= limit)
+        evaluations.append(result)
+
+    metrics = {"evaluated_shapes": len(evaluations)}
+    for top_k in top_k_values:
+        regrets = [row[f"top{top_k}_regret"] for row in evaluations]
+        metrics[f"top{top_k}_exact_recall"] = statistics.mean(
+            row[f"top{top_k}_recall"] for row in evaluations)
+        metrics[f"top{top_k}_geomean_regret"] = math.exp(
+            statistics.mean(math.log(value) for value in regrets))
+        metrics[f"top{top_k}_worst_regret"] = max(regrets)
+        metrics[f"top{top_k}_candidate_fraction"] = statistics.mean(
+            min(top_k, row["candidate_count"]) / row["candidate_count"] for row in evaluations)
+    metrics["mean_spearman"] = statistics.mean(row["spearman"] for row in evaluations)
+    return evaluations, metrics
+
+
+def candidate_signature(row):
+    return tuple(row.get(field, "") for field in SIGNATURE_FIELDS)
+
+
+def interpolate_latency(samples, batch):
+    points = sorted((math.log2(int(row["batch"])), math.log(float(row["median_kernel_ms"])))
+                    for row in samples)
+    if len(points) == 1:
+        return math.exp(points[0][1])
+    target = math.log2(batch)
+    if target <= points[0][0]:
+        left, right = points[:2]
+    elif target >= points[-1][0]:
+        left, right = points[-2:]
+    else:
+        left, right = next((left, right) for left, right in zip(points, points[1:])
+                           if left[0] <= target <= right[0])
+    prediction = left[1] + (right[1] - left[1]) * (target - left[0]) / (right[0] - left[0])
+    return math.exp(prediction)
+
+
+def evaluate_calibrated(rows, top_k_values=(1, 3, 10)):
+    groups = {}
+    for row in rows:
+        groups.setdefault(row["group"], []).append(row)
+    evaluations = []
+    for group, held_out in sorted(groups.items()):
+        log_n = held_out[0]["logN"]
+        batch = int(held_out[0]["batch"])
+        training = [row for row in rows if row["logN"] == log_n and row["group"] != group]
+        by_signature = {}
+        for row in training:
+            by_signature.setdefault(candidate_signature(row), []).append(row)
+        predicted = [
+            (interpolate_latency(by_signature[candidate_signature(row)], batch), row)
+            for row in held_out if candidate_signature(row) in by_signature
+        ]
+        predicted.sort(key=lambda item: item[0])
+        winner = min(held_out, key=lambda row: float(row["median_kernel_ms"]))
+        winner_rank = next((index for index, (_, row) in enumerate(predicted, 1)
+                            if row["candidate_id"] == winner["candidate_id"]), None)
+        result = {
+            "group": group, "logN": int(log_n), "batch": batch,
+            "candidate_count": len(held_out), "calibrated_coverage": len(predicted),
+            "measured_winner": winner["candidate_id"],
+            "measured_winner_ms": float(winner["median_kernel_ms"]),
+            "winner_calibrated_rank": winner_rank or 0,
+        }
+        for top_k in top_k_values:
+            limit = min(top_k, len(predicted))
+            selected = min((row for _, row in predicted[:limit]),
+                           key=lambda row: float(row["median_kernel_ms"]))
+            result[f"top{top_k}_regret"] = (
+                float(selected["median_kernel_ms"]) / float(winner["median_kernel_ms"]))
+            result[f"top{top_k}_recall"] = int(winner_rank is not None and winner_rank <= limit)
+        evaluations.append(result)
+
+    metrics = {
+        "evaluated_shapes": len(evaluations),
+        "mean_candidate_coverage": statistics.mean(
+            row["calibrated_coverage"] / row["candidate_count"] for row in evaluations),
+    }
+    for top_k in top_k_values:
+        regrets = [row[f"top{top_k}_regret"] for row in evaluations]
+        metrics[f"top{top_k}_exact_recall"] = statistics.mean(
+            row[f"top{top_k}_recall"] for row in evaluations)
+        metrics[f"top{top_k}_geomean_regret"] = math.exp(
+            statistics.mean(math.log(value) for value in regrets))
+        metrics[f"top{top_k}_worst_regret"] = max(regrets)
+        metrics[f"top{top_k}_candidate_fraction"] = statistics.mean(
+            min(top_k, row["calibrated_coverage"]) / row["candidate_count"] for row in evaluations)
+    return evaluations, metrics
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        writer.writerows(rows)
+
+
+def write_markdown(path, rows, metrics, calibrated_rows, calibrated_metrics):
+    lines = [
+        "# V100 FFT Static-Model Evaluation", "",
+        "Candidates are ordered only by the generator's static resource score; measured",
+        "latency is then used to compute selection regret. Lower regret is better.", "",
+        "| logN | Batch | Candidates | Winner static rank | Top-1 regret | Top-3 regret | Top-10 regret | Spearman |",
+        "|--:|--:|--:|--:|--:|--:|--:|--:|",
+    ]
+    for row in rows:
+        lines.append(
+            f"| {row['logN']} | {row['batch']} | {row['candidate_count']} | "
+            f"{row['winner_static_rank']} | {row['top1_regret']:.4f}x | "
+            f"{row['top3_regret']:.4f}x | {row['top10_regret']:.4f}x | "
+            f"{row['spearman']:.3f} |")
+    lines += ["", "## Aggregate", "",
+              "| Budget | Exact recall | Geomean regret | Worst regret | Candidate fraction |",
+              "|:--|--:|--:|--:|--:|"]
+    for top_k in (1, 3, 10):
+        lines.append(
+            f"| Top-{top_k} | {metrics[f'top{top_k}_exact_recall']:.1%} | "
+            f"{metrics[f'top{top_k}_geomean_regret']:.4f}x | "
+            f"{metrics[f'top{top_k}_worst_regret']:.4f}x | "
+            f"{metrics[f'top{top_k}_candidate_fraction']:.1%} |")
+    lines += ["", f"Mean per-shape Spearman correlation: {metrics['mean_spearman']:.3f}.", ""]
+    lines += [
+        "## Leave-One-Batch-Out Calibration", "",
+        "For each held-out shape, the calibrated selector sees only the other batches",
+        "at the same length and interpolates or extrapolates log-latency for matching",
+        "physical mappings. It never consumes timing from the target shape.", "",
+        "| logN | Batch | Covered | Winner rank | Top-1 regret | Top-3 regret | Top-10 regret |",
+        "|--:|--:|--:|--:|--:|--:|--:|",
+    ]
+    for row in calibrated_rows:
+        lines.append(
+            f"| {row['logN']} | {row['batch']} | {row['calibrated_coverage']}/{row['candidate_count']} | "
+            f"{row['winner_calibrated_rank']} | {row['top1_regret']:.4f}x | "
+            f"{row['top3_regret']:.4f}x | {row['top10_regret']:.4f}x |")
+    lines += ["", "| Budget | Exact recall | Geomean regret | Worst regret | Candidate fraction |",
+              "|:--|--:|--:|--:|--:|"]
+    for top_k in (1, 3, 10):
+        lines.append(
+            f"| Top-{top_k} | {calibrated_metrics[f'top{top_k}_exact_recall']:.1%} | "
+            f"{calibrated_metrics[f'top{top_k}_geomean_regret']:.4f}x | "
+            f"{calibrated_metrics[f'top{top_k}_worst_regret']:.4f}x | "
+            f"{calibrated_metrics[f'top{top_k}_candidate_fraction']:.1%} |")
+    lines += ["", f"Mean mapping coverage: {calibrated_metrics['mean_candidate_coverage']:.1%}.", ""]
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines))
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Evaluate the FFT pipeline static model against measurements.")
+    parser.add_argument("summary", type=pathlib.Path)
+    parser.add_argument("--output", type=pathlib.Path, required=True)
+    parser.add_argument("--calibrated-output", type=pathlib.Path)
+    parser.add_argument("--metrics", type=pathlib.Path, required=True)
+    parser.add_argument("--markdown", type=pathlib.Path)
+    args = parser.parse_args()
+    with args.summary.open(newline="") as source:
+        rows = list(csv.DictReader(source))
+    if not rows:
+        raise ValueError("FFT pipeline summary is empty")
+    evaluations, metrics = evaluate(rows)
+    calibrated_evaluations, calibrated_metrics = evaluate_calibrated(rows)
+    write_csv(args.output, evaluations)
+    if args.calibrated_output:
+        write_csv(args.calibrated_output, calibrated_evaluations)
+    args.metrics.parent.mkdir(parents=True, exist_ok=True)
+    args.metrics.write_text(json.dumps({"static": metrics, "calibrated": calibrated_metrics}, indent=2) + "\n")
+    if args.markdown:
+        write_markdown(args.markdown, evaluations, metrics, calibrated_evaluations, calibrated_metrics)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/analyze_fft_vectorized_ncu.py b/scripts/analyze_fft_vectorized_ncu.py
new file mode 100755
index 0000000..69490ff
--- /dev/null
+++ b/scripts/analyze_fft_vectorized_ncu.py
@@ -0,0 +1,150 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+
+
+SUM_FIELDS = (
+    "time_us", "dram_read_mib", "dram_write_mib", "shared_load_bank_conflicts",
+    "shared_store_bank_conflicts", "warp_instructions", "fp32_thread_instructions",
+)
+WEIGHTED_FIELDS = (
+    "dram_peak_pct", "l2_hit_pct", "l1_hit_pct", "active_warps_pct",
+    "barrier_stall_pct", "long_scoreboard_stall_pct",
+)
+
+
+def number(row, field):
+    value = row.get(field, "")
+    return float(value) if value not in ("", None) else 0.0
+
+
+def aggregate(rows):
+    total_time = sum(number(row, "time_us") for row in rows)
+    result = {field: sum(number(row, field) for row in rows) for field in SUM_FIELDS}
+    for field in WEIGHTED_FIELDS:
+        result[field] = (sum(number(row, field) * number(row, "time_us") for row in rows) / total_time
+                         if total_time else 0.0)
+    result["kernel_count"] = len(rows)
+    result["shared_bank_conflicts"] = (
+        result["shared_load_bank_conflicts"] + result["shared_store_bank_conflicts"])
+    return result
+
+
+def analyze(rows, batch):
+    labels = {
+        "pre-vector fixed": f"fft20_online_b{batch}",
+        "post-vector fixed": f"post_vector_fixed_b{batch}",
+        "post-vector selected": f"post_vector_selected_b{batch}",
+        "cuFFT": f"post_vector_cufft_b{batch}",
+    }
+    output = []
+    for name, label in labels.items():
+        matches = [row for row in rows if row["label"] == label]
+        if not matches:
+            raise ValueError(f"missing NCU label {label}")
+        output.append({"configuration": name, "label": label, **aggregate(matches)})
+    baseline = output[0]
+    for row in output:
+        for field in ("time_us", "dram_read_mib", "dram_write_mib", "warp_instructions",
+                      "shared_bank_conflicts"):
+            row[f"{field}_vs_pre_vector"] = row[field] / baseline[field] if baseline[field] else 0.0
+    return output
+
+
+def attach_event_timings(output, pre_rows, post_rows, batch):
+    group = f"fft20-fp32-batch{batch}"
+
+    def fixed(rows):
+        matches = [row for row in rows if row["group"] == group and
+                   row["candidate_id"].startswith(f"fft20-fp32_b{batch}_p10s10_t512x512_e8x8_rec")]
+        if len(matches) != 1:
+            raise ValueError(f"expected one fixed CUDA-event row for {group}")
+        return float(matches[0]["median_kernel_ms"])
+
+    selected = [row for row in post_rows if row["group"] == group and row["rank"] == "1"]
+    if len(selected) != 1:
+        raise ValueError(f"expected one selected CUDA-event row for {group}")
+    timings = {
+        "pre-vector fixed": fixed(pre_rows),
+        "post-vector fixed": fixed(post_rows),
+        "post-vector selected": float(selected[0]["median_kernel_ms"]),
+        "cuFFT": float(selected[0]["cufft_median_ms"]),
+    }
+    baseline = timings["pre-vector fixed"]
+    for row in output:
+        row["cuda_event_ms"] = timings[row["configuration"]]
+        row["cuda_event_ms_vs_pre_vector"] = row["cuda_event_ms"] / baseline
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        writer.writerows(rows)
+
+
+def write_markdown(path, rows, batch):
+    lines = [
+        "# FFT Vectorized-Boundary NCU Attribution", "",
+        f"All cuButterfly rows use FP32 forward `logN=20`, batch {batch}. The fixed",
+        "rows use the same 512/512-thread, EPT 8/8 mapping, isolating the code change.",
+        "NCU replay time is attribution-only; CUDA-event scans remain authoritative.", "",
+        "| Configuration | CUDA-event ms | NCU time us | Kernels | DRAM read MiB | DRAM write MiB | Warp inst. | Bank conflicts | DRAM peak | Barrier stall | Scoreboard stall |",
+        "|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|",
+    ]
+    for row in rows:
+        lines.append(
+            f"| {row['configuration']} | {row.get('cuda_event_ms', 0.0):.6f} | "
+            f"{row['time_us']:.3f} | {row['kernel_count']} | "
+            f"{row['dram_read_mib']:.2f} | {row['dram_write_mib']:.2f} | "
+            f"{row['warp_instructions']:.0f} | {row['shared_bank_conflicts']:.0f} | "
+            f"{row['dram_peak_pct']:.1f}% | {row['barrier_stall_pct']:.1f}% | "
+            f"{row['long_scoreboard_stall_pct']:.1f}% |")
+    fixed = rows[1]
+    selected = rows[2]
+    lines += ["", "## Controlled Changes", "",
+              f"- Vectorizing the same fixed mapping changes replay time by "
+              f"{(fixed['time_us_vs_pre_vector'] - 1.0):+.1%}, warp instructions by "
+              f"{(fixed['warp_instructions_vs_pre_vector'] - 1.0):+.1%}, and DRAM writes by "
+              f"{(fixed['dram_write_mib_vs_pre_vector'] - 1.0):+.1%}. The matching CUDA-event "
+              f"change is {(fixed.get('cuda_event_ms_vs_pre_vector', 1.0) - 1.0):+.1%}.",
+              f"- CUDA-event timing selects the 256/128 mapping: it is "
+              f"{(selected['cuda_event_ms'] / fixed['cuda_event_ms'] - 1.0):+.1%} versus the "
+              f"post-vector fixed point. NCU replay reverses that ordering by "
+              f"{(selected['time_us'] / fixed['time_us'] - 1.0):+.1%}; replay time must not be "
+              f"used as the mapping-performance result.", ""]
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines))
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Compare pre/post vectorized FFT NCU captures.")
+    parser.add_argument("inputs", nargs="+", type=pathlib.Path)
+    parser.add_argument("--batch", type=int, default=16)
+    parser.add_argument("--pre-timing-summary", type=pathlib.Path)
+    parser.add_argument("--post-timing-summary", type=pathlib.Path)
+    parser.add_argument("--output", type=pathlib.Path, required=True)
+    parser.add_argument("--markdown", type=pathlib.Path)
+    args = parser.parse_args()
+    rows = []
+    for path in args.inputs:
+        with path.open(newline="") as source:
+            rows.extend(csv.DictReader(source))
+    output = analyze(rows, args.batch)
+    if bool(args.pre_timing_summary) != bool(args.post_timing_summary):
+        raise ValueError("CUDA-event attribution requires both timing summaries")
+    if args.pre_timing_summary:
+        with args.pre_timing_summary.open(newline="") as source:
+            pre_rows = list(csv.DictReader(source))
+        with args.post_timing_summary.open(newline="") as source:
+            post_rows = list(csv.DictReader(source))
+        attach_event_timings(output, pre_rows, post_rows, args.batch)
+    write_csv(args.output, output)
+    if args.markdown:
+        write_markdown(args.markdown, output, args.batch)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/analyze_fp64_fft_ncu.py b/scripts/analyze_fp64_fft_ncu.py
new file mode 100644
index 0000000..29e4b84
--- /dev/null
+++ b/scripts/analyze_fp64_fft_ncu.py
@@ -0,0 +1,253 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+
+
+SUM_FIELDS = (
+    "time_us", "dram_read_mib", "dram_write_mib", "shared_load_bank_conflicts",
+    "shared_store_bank_conflicts", "warp_instructions", "integer_thread_instructions",
+    "fp64_thread_instructions",
+)
+WEIGHTED_FIELDS = (
+    "dram_peak_pct", "l2_hit_pct", "l1_hit_pct", "active_warps_pct",
+    "barrier_stall_pct", "long_scoreboard_stall_pct",
+)
+def labels(batch):
+    return {name: f"fp64_{name}_b{batch}" for name in ("scalar", "cufftdx", "cufft")}
+
+
+def number(row, field):
+    value = row.get(field, "")
+    return float(value) if value not in ("", None) else 0.0
+
+
+def aggregate(rows):
+    total_time = sum(number(row, "time_us") for row in rows)
+    result = {field: sum(number(row, field) for row in rows) for field in SUM_FIELDS}
+    for field in WEIGHTED_FIELDS:
+        result[field] = (sum(number(row, field) * number(row, "time_us") for row in rows) / total_time
+                         if total_time else 0.0)
+    result["kernel_count"] = len(rows)
+    result["shared_bank_conflicts"] = (
+        result["shared_load_bank_conflicts"] + result["shared_store_bank_conflicts"])
+    result["dram_total_mib"] = result["dram_read_mib"] + result["dram_write_mib"]
+    return result
+
+
+def event_timings(path):
+    with path.open(newline="") as source:
+        rows = list(csv.DictReader(source))
+    matches = {}
+    for row in rows:
+        if row["backend"] == "cufft":
+            matches["cufft"] = float(row["median_kernel_ms"])
+        elif row["fft_core"] == "cufftdx-block":
+            if row.get("shared_layout") == "xor-swizzle":
+                name = "xor_swizzle"
+            else:
+                name = "recurrence" if row.get("cross_twiddle") == "recurrence" else "cufftdx"
+            matches[name] = float(row["median_kernel_ms"])
+        elif row["fft_core"] == "scalar" and row["backend"] == "online-reorder":
+            matches["scalar"] = float(row["median_kernel_ms"])
+    missing = {"scalar", "cufftdx", "cufft"} - set(matches)
+    if missing:
+        raise ValueError(f"missing CUDA-event configurations: {sorted(missing)}")
+    return matches
+
+
+def analyze(rows, timings, batch):
+    output = []
+    for implementation, label in labels(batch).items():
+        matches = [row for row in rows if row["label"] == label]
+        if not matches:
+            raise ValueError(f"missing NCU label {label}")
+        output.append({
+            "implementation": implementation,
+            "label": label,
+            "cuda_event_ms": timings[implementation],
+            **aggregate(matches),
+        })
+    recurrence_label = f"fp64_recurrence_b{batch}"
+    recurrence_rows = [row for row in rows if row["label"] == recurrence_label]
+    if recurrence_rows:
+        if "recurrence" not in timings:
+            raise ValueError("recurrence NCU rows require a recurrence CUDA-event timing")
+        output.append({
+            "implementation": "recurrence", "label": recurrence_label,
+            "cuda_event_ms": timings["recurrence"], **aggregate(recurrence_rows),
+        })
+    xor_label = f"fp64_xor_swizzle_b{batch}"
+    xor_rows = [row for row in rows if row["label"] == xor_label]
+    if xor_rows:
+        if "xor_swizzle" not in timings:
+            raise ValueError("XOR-swizzle NCU rows require an XOR-swizzle CUDA-event timing")
+        output.append({
+            "implementation": "xor_swizzle", "label": xor_label,
+            "cuda_event_ms": timings["xor_swizzle"], **aggregate(xor_rows),
+        })
+    cufft = next(row for row in output if row["implementation"] == "cufft")
+    for row in output:
+        for field in ("cuda_event_ms", "time_us", "dram_total_mib", "warp_instructions",
+                      "integer_thread_instructions", "fp64_thread_instructions",
+                      "shared_bank_conflicts"):
+            row[f"{field}_vs_cufft"] = row[field] / cufft[field] if cufft[field] else 0.0
+    return output
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        writer.writerows(rows)
+
+
+def write_markdown(path, rows, kernels, batch):
+    by_name = {row["implementation"]: row for row in rows}
+    scalar = by_name["scalar"]
+    cufftdx = by_name["cufftdx"]
+    cufft = by_name["cufft"]
+    recurrence = by_name.get("recurrence")
+    xor_swizzle = by_name.get("xor_swizzle")
+    cufftdx_kernels = [row for row in kernels if row["label"] == labels(batch)["cufftdx"]]
+    first = next(row for row in cufftdx_kernels if "first_kernel" in row["kernel_name"])
+    second = next(row for row in cufftdx_kernels if "second_kernel" in row["kernel_name"])
+    recurrence_first = None
+    recurrence_second = None
+    if recurrence:
+        recurrence_kernels = [row for row in kernels if row["label"] == f"fp64_recurrence_b{batch}"]
+        recurrence_first = next(row for row in recurrence_kernels if "first_kernel" in row["kernel_name"])
+        recurrence_second = next(row for row in recurrence_kernels if "second_kernel" in row["kernel_name"])
+    xor_first = None
+    xor_second = None
+    if xor_swizzle:
+        xor_kernels = [row for row in kernels if row["label"] == f"fp64_xor_swizzle_b{batch}"]
+        xor_first = next(row for row in xor_kernels if "first_kernel" in row["kernel_name"])
+        xor_second = next(row for row in xor_kernels if "second_kernel" in row["kernel_name"])
+
+    def pass_row(name, row):
+        conflicts = number(row, "shared_load_bank_conflicts") + number(row, "shared_store_bank_conflicts")
+        return (f"| {name} | {number(row, 'time_us'):.3f} | {number(row, 'warp_instructions'):.0f} | "
+                f"{number(row, 'integer_thread_instructions'):.0f} | "
+                f"{number(row, 'fp64_thread_instructions'):.0f} | {conflicts:.0f} | "
+                f"{number(row, 'dram_peak_pct'):.1f}% | {number(row, 'barrier_stall_pct'):.1f}% | "
+                f"{number(row, 'long_scoreboard_stall_pct'):.1f}% |")
+
+    lines = [
+        "# FP64 FFT NCU Attribution", "",
+        f"All rows are FP64 forward `logN=16`, batch {batch} on V100. CUDA-event medians use",
+        "five process trials, 1000 warmups, and 100 repetitions. NCU replay time is",
+        "attribution-only and is not used to rank the implementations.", "",
+        "| Implementation | CUDA-event ms | NCU us | DRAM MiB | Warp inst. | Integer inst. | FP64 inst. | Shared conflicts | DRAM peak | Barrier stall | Scoreboard stall |",
+        "|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|",
+    ]
+    for row in rows:
+        lines.append(
+            f"| {row['implementation']} | {row['cuda_event_ms']:.6f} | {row['time_us']:.3f} | "
+            f"{row['dram_total_mib']:.2f} | {row['warp_instructions']:.0f} | "
+            f"{row['integer_thread_instructions']:.0f} | "
+            f"{row['fp64_thread_instructions']:.0f} | {row['shared_bank_conflicts']:.0f} | "
+            f"{row['dram_peak_pct']:.1f}% | {row['barrier_stall_pct']:.1f}% | "
+            f"{row['long_scoreboard_stall_pct']:.1f}% |")
+    lines += [
+        "", "## Attribution", "",
+        f"- Replacing the scalar unit with cuFFTDx reduces CUDA-event time by "
+        f"{1.0 - cufftdx['cuda_event_ms'] / scalar['cuda_event_ms']:.1%} and NCU replay time by "
+        f"{1.0 - cufftdx['time_us'] / scalar['time_us']:.1%}. It also reduces FP64 instructions by "
+        f"{1.0 - cufftdx['fp64_thread_instructions'] / scalar['fp64_thread_instructions']:.1%}.",
+        f"- Against cuFFT, cuFFTDx transfers {cufftdx['dram_total_mib_vs_cufft']:.3f}x the DRAM bytes and "
+        f"executes {cufftdx['fp64_thread_instructions_vs_cufft']:.3f}x the FP64 instructions. The remaining "
+        f"gap is therefore not explained by external traffic volume or double-precision arithmetic work.",
+        f"- cuFFTDx executes {cufftdx['warp_instructions_vs_cufft']:.2f}x the warp instructions and incurs "
+        f"{cufftdx['shared_bank_conflicts_vs_cufft']:.1f}x the shared-memory bank conflicts of cuFFT. "
+        f"Its weighted barrier and long-scoreboard stalls are {cufftdx['barrier_stall_pct']:.1f}% and "
+        f"{cufftdx['long_scoreboard_stall_pct']:.1f}%.",
+    ]
+    if recurrence:
+        lines.append(
+            f"- Twiddle recurrence changes CUDA-event time by "
+            f"{recurrence['cuda_event_ms'] / cufftdx['cuda_event_ms'] - 1.0:+.1%}, replay time by "
+            f"{recurrence['time_us'] / cufftdx['time_us'] - 1.0:+.1%}, and FP64 instructions by "
+            f"{recurrence['fp64_thread_instructions'] / cufftdx['fp64_thread_instructions'] - 1.0:+.1%}.")
+    if xor_swizzle:
+        replay_delta = xor_swizzle['time_us_vs_cufft'] - 1.0
+        replay_position = "below" if replay_delta < 0.0 else "above"
+        lines.append(
+            f"- XOR swizzle changes CUDA-event time by "
+            f"{xor_swizzle['cuda_event_ms'] / recurrence['cuda_event_ms'] - 1.0:+.1%} and replay time by "
+            f"{xor_swizzle['time_us'] / recurrence['time_us'] - 1.0:+.1%} versus linear recurrence. "
+            f"It finishes {abs(replay_delta):.1%} {replay_position} cuFFT replay while still "
+            f"executing {xor_swizzle['warp_instructions_vs_cufft']:.2f}x its warp instructions, "
+            f"{xor_swizzle['integer_thread_instructions_vs_cufft']:.2f}x its integer instructions, and incurring "
+            f"{xor_swizzle['shared_bank_conflicts_vs_cufft']:.1f}x its shared conflicts.")
+    lines += [
+        "", "## Prefix/Suffix Split", "",
+        "| cuFFTDx pass | NCU us | Warp inst. | Integer inst. | FP64 inst. | Shared conflicts | DRAM peak | Barrier stall | Scoreboard stall |",
+        "|:--|--:|--:|--:|--:|--:|--:|--:|--:|",
+        pass_row("table prefix + twiddle/reorder", first),
+        pass_row("table suffix + natural-order store", second),
+    ]
+    if recurrence:
+        lines += [pass_row("recurrence prefix + twiddle/reorder", recurrence_first),
+                  pass_row("recurrence suffix + natural-order store", recurrence_second)]
+    if xor_swizzle:
+        lines += [pass_row("XOR-swizzle prefix + twiddle/reorder", xor_first),
+                  pass_row("XOR-swizzle suffix + natural-order store", xor_second)]
+    if recurrence:
+        lines += ["",
+                  f"Recurrence reduces prefix replay time by "
+                  f"{1.0 - number(recurrence_first, 'time_us') / number(first, 'time_us'):.1%}, warp instructions by "
+                  f"{1.0 - number(recurrence_first, 'warp_instructions') / number(first, 'warp_instructions'):.1%}, "
+                  f"and raises DRAM peak from {number(first, 'dram_peak_pct'):.1f}% to "
+                  f"{number(recurrence_first, 'dram_peak_pct'):.1f}%. It spends "
+                  f"{number(recurrence_first, 'fp64_thread_instructions') / number(first, 'fp64_thread_instructions') - 1.0:.1%} "
+                  f"more FP64 instructions while registers, shared allocation, and waves/SM remain unchanged. "
+                  f"The suffix changes by only "
+                  f"{number(recurrence_second, 'time_us') / number(second, 'time_us') - 1.0:+.1%}.", "",
+                  "The recurrence result confirms a useful architecture trade: idle FP64 capacity replaces "
+                  "dependent twiddle-table service in the prefix. Shared conflicts remain essentially unchanged, "
+                  "so the next target is the local exchange/address path rather than another twiddle change.", ""]
+    if xor_swizzle:
+        recurrence_integer = number(recurrence_first, 'integer_thread_instructions')
+        xor_integer = number(xor_first, 'integer_thread_instructions')
+        integer_delta = xor_integer / recurrence_integer - 1.0 if recurrence_integer else None
+        integer_text = (f"Integer instructions change by {integer_delta:+.1%}. "
+                        if integer_delta is not None else "")
+        xor_summary = (
+            f"XOR swizzle changes prefix replay time by "
+            f"{number(xor_first, 'time_us') / number(recurrence_first, 'time_us') - 1.0:+.1%}, shared conflicts by "
+            f"{(number(xor_first, 'shared_load_bank_conflicts') + number(xor_first, 'shared_store_bank_conflicts')) / (number(recurrence_first, 'shared_load_bank_conflicts') + number(recurrence_first, 'shared_store_bank_conflicts')) - 1.0:+.1%}, "
+            f"and warp instructions by "
+            f"{number(xor_first, 'warp_instructions') / number(recurrence_first, 'warp_instructions') - 1.0:+.1%}. "
+            + integer_text
+            + f"The suffix changes by {number(xor_second, 'time_us') / number(recurrence_second, 'time_us') - 1.0:+.1%}.")
+        lines += [xor_summary, ""]
+    else:
+        lines += ["",
+                  f"The prefix consumes {number(first, 'time_us') / cufftdx['time_us']:.1%} of replay time and is "
+                  f"{number(first, 'time_us') / number(second, 'time_us'):.2f}x slower than the suffix. The suffix "
+                  f"already runs in {number(second, 'time_us'):.3f} us, below either cuFFT pass (about 179 us).", ""]
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines))
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Attribute FP64 scalar/cuFFTDx/cuFFT NCU captures.")
+    parser.add_argument("input", type=pathlib.Path)
+    parser.add_argument("--batch", type=int, default=64)
+    parser.add_argument("--timing-summary", required=True, type=pathlib.Path)
+    parser.add_argument("--output", required=True, type=pathlib.Path)
+    parser.add_argument("--markdown", required=True, type=pathlib.Path)
+    args = parser.parse_args()
+    with args.input.open(newline="") as source:
+        kernels = list(csv.DictReader(source))
+    if not kernels:
+        raise ValueError("FP64 NCU summary is empty")
+    rows = analyze(kernels, event_timings(args.timing_summary), args.batch)
+    write_csv(args.output, rows)
+    write_markdown(args.markdown, rows, kernels, args.batch)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/analyze_fp64_fft_robustness.py b/scripts/analyze_fp64_fft_robustness.py
new file mode 100755
index 0000000..8283eeb
--- /dev/null
+++ b/scripts/analyze_fp64_fft_robustness.py
@@ -0,0 +1,101 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+import statistics
+
+MIN_STABLE_MS = 0.020
+
+
+def analyze(rows):
+    groups = {}
+    for row in rows:
+        key = (int(row["logN"]), int(row["batch"]), row["backend"])
+        groups.setdefault(key, []).append(row)
+
+    output = []
+    shapes = sorted({(log_n, batch) for log_n, batch, _ in groups})
+    for log_n, batch in shapes:
+        ours = groups.get((log_n, batch, "online-reorder"), [])
+        cufft = groups.get((log_n, batch, "cufft"), [])
+        if not ours or not cufft:
+            raise ValueError(f"missing implementation for logN={log_n}, batch={batch}")
+        ours_times = [float(row["kernel_ms"]) for row in ours]
+        cufft_times = [float(row["kernel_ms"]) for row in cufft]
+        ours_median = statistics.median(ours_times)
+        cufft_median = statistics.median(cufft_times)
+        mapping = ours[0]
+        output.append({
+            "logN": log_n,
+            "batch": batch,
+            "total_points": (1 << log_n) * batch,
+            "local_stages": int(mapping["local_stages"]),
+            "prefix_threads": int(mapping["prefix_threads"]),
+            "prefix_ept": int(mapping["prefix_ept"]),
+            "suffix_threads": int(mapping["suffix_threads"]),
+            "suffix_ept": int(mapping["suffix_ept"]),
+            "trials": len(ours_times),
+            "cuntt_median_ms": ours_median,
+            "cuntt_min_ms": min(ours_times),
+            "cuntt_max_ms": max(ours_times),
+            "cufft_median_ms": cufft_median,
+            "cufft_min_ms": min(cufft_times),
+            "cufft_max_ms": max(cufft_times),
+            "throughput_vs_cufft": cufft_median / ours_median,
+            "timing_quality": "stable" if min(ours_median, cufft_median) >= MIN_STABLE_MS else "short",
+            "range_separation": "faster" if max(ours_times) < min(cufft_times)
+                                else "slower" if min(ours_times) > max(cufft_times)
+                                else "overlap",
+        })
+    return output
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        writer.writerows(rows)
+
+
+def write_markdown(path, rows):
+    stable = [row for row in rows if row["timing_quality"] == "stable"]
+    faster = sum(row["throughput_vs_cufft"] > 1.0 for row in stable)
+    separated = sum(row["range_separation"] == "faster" for row in stable)
+    lines = [
+        "# FP64 FFT Length/Batch Robustness", "",
+        "All rows use the per-length mapping selected by the V100 coarse scan, recurrence twiddles,",
+        "and XOR-swizzled prefix staging. Trials alternate cuButterfly/cuFFT execution order.", "",
+        f"Among {len(stable)} stable shapes with both medians at least {MIN_STABLE_MS:.3f} ms, cuButterfly has",
+        f"higher median throughput in {faster}/{len(stable)} and non-overlapping faster trial ranges in",
+        f"{separated}/{len(stable)}. Short rows remain measurements, not stable performance claims.", "",
+        "| logN | Batch | Points | Split | Prefix | Suffix | cuButterfly ms | cuFFT ms | Throughput | Quality | Trial ranges |",
+        "|--:|--:|--:|:--|:--|:--|--:|--:|--:|:--|:--|",
+    ]
+    for row in rows:
+        split = f"{row['local_stages']}+{row['logN'] - row['local_stages']}"
+        prefix = f"{row['prefix_threads']}/{row['prefix_ept']}"
+        suffix = f"{row['suffix_threads']}/{row['suffix_ept']}"
+        lines.append(
+            f"| {row['logN']} | {row['batch']} | {row['total_points']} | `{split}` | `{prefix}` | `{suffix}` | "
+            f"{row['cuntt_median_ms']:.6f} | {row['cufft_median_ms']:.6f} | "
+            f"{row['throughput_vs_cufft']:.3f}x | {row['timing_quality']} | {row['range_separation']} |")
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines) + "\n")
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Summarize FP64 FFT robustness measurements.")
+    parser.add_argument("input", type=pathlib.Path)
+    parser.add_argument("--output", "-o", required=True, type=pathlib.Path)
+    parser.add_argument("--markdown", type=pathlib.Path)
+    args = parser.parse_args()
+    with args.input.open(newline="") as source:
+        rows = analyze(list(csv.DictReader(source)))
+    write_csv(args.output, rows)
+    if args.markdown:
+        write_markdown(args.markdown, rows)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/analyze_scaling_ncu.py b/scripts/analyze_scaling_ncu.py
new file mode 100644
index 0000000..5d7370a
--- /dev/null
+++ b/scripts/analyze_scaling_ncu.py
@@ -0,0 +1,159 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+import re
+
+
+SUM_FIELDS = ("time_us", "dram_read_mib", "dram_write_mib", "warp_instructions",
+              "fp32_thread_instructions", "shared_load_bank_conflicts", "shared_store_bank_conflicts")
+WEIGHTED_FIELDS = ("dram_peak_pct", "l2_hit_pct", "l1_hit_pct", "active_warps_pct",
+                   "barrier_stall_pct", "long_scoreboard_stall_pct")
+MAX_FIELDS = ("registers_per_thread", "shared_mem_bytes")
+LABEL = re.compile(r"^(fft|fwht)(\d+)_([^_]+)_b(\d+)$")
+
+
+def number(row, field):
+    value = row.get(field, "")
+    return None if value in ("", None) else float(value)
+
+
+def aggregate(rows):
+    groups = {}
+    for row in rows:
+        groups.setdefault(row["label"], []).append(row)
+    output = []
+    for label, kernels in sorted(groups.items()):
+        match = LABEL.match(label)
+        if match is None:
+            raise ValueError(f"unsupported crossover label {label}")
+        operator, log_n, implementation, batch = match.groups()
+        total_time = sum(number(row, "time_us") or 0.0 for row in kernels)
+        record = {
+            "label": label, "operator": operator, "logN": int(log_n),
+            "implementation": implementation, "batch": int(batch), "kernels": len(kernels),
+        }
+        for field in SUM_FIELDS:
+            record[field] = sum(number(row, field) or 0.0 for row in kernels)
+        for field in WEIGHTED_FIELDS:
+            values = [(number(row, field), number(row, "time_us")) for row in kernels]
+            values = [(value, weight) for value, weight in values if value is not None and weight is not None]
+            record[field] = sum(value * weight for value, weight in values) / sum(weight for _, weight in values) if values else 0.0
+        for field in MAX_FIELDS:
+            values = [number(row, field) for row in kernels if number(row, field) is not None]
+            record[field] = max(values) if values else 0.0
+        waves = [number(row, "waves_per_sm") for row in kernels if number(row, "waves_per_sm") is not None]
+        record["total_waves_per_sm"] = sum(waves)
+        points = (1 << record["logN"]) * record["batch"]
+        record["dram_bytes_per_point"] = (record["dram_read_mib"] + record["dram_write_mib"]) * 1024 * 1024 / points
+        record["profiled_gpoint_s"] = points / (total_time * 1.0e3) if total_time else 0.0
+        output.append(record)
+    return output
+
+
+def conclusion(rows, operator, log_n, implementation, batches):
+    selected = [row for row in rows if row["operator"] == operator and row["logN"] == log_n
+                and row["implementation"] == implementation and row["batch"] in batches]
+    selected.sort(key=lambda row: row["batch"])
+    if len(selected) < 2:
+        return f"{operator.upper()} logN={log_n} {implementation}: insufficient counter rows."
+    low, high = selected[0], selected[-1]
+    wave_ratio = high["total_waves_per_sm"] / low["total_waves_per_sm"] if low["total_waves_per_sm"] else 0.0
+    if low["dram_bytes_per_point"] < 1.0:
+        traffic = "the low-batch DRAM count is cache-resident/replay-sensitive"
+    else:
+        traffic_change = high["dram_bytes_per_point"] / low["dram_bytes_per_point"]
+        traffic = f"bytes/point changes {traffic_change:.2f}x"
+    return (f"{operator.upper()} logN={log_n} {implementation}: waves/SM change {wave_ratio:.2f}x from "
+            f"batch {low['batch']} to {high['batch']}; active warps {low['active_warps_pct']:.1f}% -> "
+            f"{high['active_warps_pct']:.1f}%, DRAM peak {low['dram_peak_pct']:.1f}% -> "
+            f"{high['dram_peak_pct']:.1f}%, {traffic}, barrier stalls "
+            f"{low['barrier_stall_pct']:.1f}% -> {high['barrier_stall_pct']:.1f}%, and long-scoreboard "
+            f"stalls {low['long_scoreboard_stall_pct']:.1f}% -> {high['long_scoreboard_stall_pct']:.1f}%.")
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        for row in rows:
+            formatted = dict(row)
+            for field, value in row.items():
+                if isinstance(value, float):
+                    formatted[field] = f"{value:.6f}"
+            writer.writerow(formatted)
+
+
+def find_row(rows, label):
+    return next(row for row in rows if row["label"] == label)
+
+
+def safe_ratio(numerator, denominator):
+    return numerator / denominator if denominator else 0.0
+
+
+def write_markdown(path, rows, kernels):
+    lines = ["# V100 Scaling-Crossover Counter Attribution", "",
+             "NCU replay time is used only for attribution; CUDA-event time remains the performance authority.", "",
+             "| Workload | Batch | Impl | Kernels | Waves/SM | Active warps | DRAM peak | B/point | Barrier stall | Scoreboard stall | Reg/thread | Shared B |",
+             "|:--|--:|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|"]
+    for row in rows:
+        lines.append(f"| {row['operator']} logN={row['logN']} | {row['batch']} | {row['implementation']} | "
+                     f"{row['kernels']} | {row['total_waves_per_sm']:.2f} | {row['active_warps_pct']:.1f}% | "
+                     f"{row['dram_peak_pct']:.1f}% | {row['dram_bytes_per_point']:.1f} | "
+                     f"{row['barrier_stall_pct']:.1f}% | {row['long_scoreboard_stall_pct']:.1f}% | "
+                     f"{row['registers_per_thread']:.0f} | {row['shared_mem_bytes']:.0f} |")
+    fft14_low = find_row(rows, "fft14_direct_b16")
+    fft14_high = find_row(rows, "fft14_direct_b1024")
+    cufft14_low = find_row(rows, "fft14_cufft_b16")
+    fft18_online = find_row(rows, "fft18_online_b64")
+    fft18_cufft = find_row(rows, "fft18_cufft_b64")
+    fft20_online = find_row(rows, "fft20_online_b16")
+    fft20_cufft = find_row(rows, "fft20_cufft_b16")
+    fwht_online4 = find_row(rows, "fwht15_online_b4")
+    fwht_online16 = find_row(rows, "fwht15_online_b16")
+    fwht_warp4 = find_row(rows, "fwht15_warp_b4")
+    fwht_warp16 = find_row(rows, "fwht15_warp_b16")
+    fft20_passes = [row for row in kernels if row["label"] == "fft20_online_b16"]
+    fft20_first = next(row for row in fft20_passes if "online_first" in row["kernel_name"])
+    fft20_second = next(row for row in fft20_passes if "online_second" in row["kernel_name"])
+    lines += ["", "## Measured Trends", "",
+              "- " + conclusion(rows, "fft", 14, "direct", {16, 256, 1024}),
+              "- " + conclusion(rows, "fft", 18, "online", {2, 16, 64}),
+              "- " + conclusion(rows, "fft", 20, "online", {2, 8, 16}),
+              "- " + conclusion(rows, "fwht", 15, "online", {4, 16}),
+              "- " + conclusion(rows, "fwht", 15, "warp", {4, 16}), "",
+              "Counts reported as zero for the smallest cases are not zero algorithmic traffic. `--cache-control none`, NCU replay, and a working set that fits in the 6 MiB L2 make those DRAM counters unsuitable for traffic ratios.", "",
+              "## Architecture Attribution", "",
+              "### FFT logN=14: grid concurrency threshold", "",
+              f"The direct unit launches one 1024-thread CTA per transform and is limited to one resident CTA per SM by its register and {fft14_low['shared_mem_bytes']:.0f}-byte shared allocations. At batch 16 it exposes only {fft14_low['total_waves_per_sm']:.2f} waves/SM, whereas cuFFT exposes {cufft14_low['total_waves_per_sm']:.2f} waves/SM across two kernels. The direct grid therefore leaves most of the 80 SMs without work even though active CTAs individually report {fft14_low['active_warps_pct']:.1f}% active warps. At batch 1024 it reaches {fft14_high['total_waves_per_sm']:.1f} waves/SM and the grid-level deficit disappears. This attributes the low-batch gap to `Ub`/grid coverage, not to the local cuFFTDx arithmetic core.", "",
+              "### FFT logN=18: useful-work ceiling", "",
+              f"At batch 64, online composition has {fft18_online['active_warps_pct']:.1f}% active warps versus cuFFT's {fft18_cufft['active_warps_pct']:.1f}%, but executes {safe_ratio(fft18_online['warp_instructions'], fft18_cufft['warp_instructions']):.2f}x as many warp instructions and {safe_ratio(fft18_online['shared_load_bank_conflicts'] + fft18_online['shared_store_bank_conflicts'], fft18_cufft['shared_load_bank_conflicts'] + fft18_cufft['shared_store_bank_conflicts']):.2f}x as many shared-memory bank conflicts. Its barrier and long-scoreboard stalls are {fft18_online['barrier_stall_pct']:.1f}% and {fft18_online['long_scoreboard_stall_pct']:.1f}%, and it reaches only {fft18_online['dram_peak_pct']:.1f}% of peak DRAM versus cuFFT's {fft18_cufft['dram_peak_pct']:.1f}%. The early saturation is therefore caused by less useful work per active warp and exchange/synchronization overhead, not a lack of resident warps.", "",
+              "### FFT logN=20: prefix/suffix imbalance", "",
+              f"At batch 16, online and cuFFT both expose {fft20_online['total_waves_per_sm']:.1f} aggregate waves/SM. Online nevertheless executes {safe_ratio(fft20_online['warp_instructions'], fft20_cufft['warp_instructions']):.2f}x the warp instructions, incurs {safe_ratio(fft20_online['shared_load_bank_conflicts'] + fft20_online['shared_store_bank_conflicts'], fft20_cufft['shared_load_bank_conflicts'] + fft20_cufft['shared_store_bank_conflicts']):.2f}x the shared bank conflicts, and has {fft20_online['barrier_stall_pct']:.1f}% barrier plus {fft20_online['long_scoreboard_stall_pct']:.1f}% scoreboard stalls. The first pass consumes {float(fft20_first['time_us']) / fft20_online['time_us']:.1%} of profiled time and reaches only {float(fft20_first['dram_peak_pct']):.1f}% DRAM, while the second reaches {float(fft20_second['dram_peak_pct']):.1f}%. The remaining gap is a prefix-core/layout imbalance and synchronization problem; increasing occupancy alone cannot close it.", "",
+              "### FWHT logN=15: mapping crossover", "",
+              f"The warp-register unit uses {fwht_warp4['registers_per_thread']:.0f} registers/thread and {fwht_warp4['shared_mem_bytes']:.0f} shared bytes, limiting it to one CTA/SM. It launches only {fwht_warp4['total_waves_per_sm']:.2f} waves/SM at batch 4 and {fwht_warp16['total_waves_per_sm']:.2f} at batch 16, with nearly fixed NCU time. Online decomposition exposes {fwht_online4['total_waves_per_sm']:.2f} and {fwht_online16['total_waves_per_sm']:.2f} waves/SM, so it wins when four transforms cannot cover the GPU. By batch 16, the register unit's single-kernel path executes only {safe_ratio(fwht_warp16['warp_instructions'], fwht_online16['warp_instructions']):.2f}x the online warp instructions and avoids its shared exchanges and {fwht_online16['barrier_stall_pct']:.1f}% barrier stalls. The crossover is the expected tradeoff between `Ud` spatial decomposition at low batch and `Td` register residence once `Ub` supplies enough independent transforms.", "",
+              "## Methodological Result", "",
+              "The counters support separating three quantities in the selector: grid coverage (`Ub` and waves/SM), residency (register/shared limits), and useful work per resident warp (instruction, exchange, and stall costs). Occupancy is not a sufficient objective: both long online FFTs expose at least as many active warps as cuFFT while delivering a lower saturated ceiling.", ""]
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines))
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Aggregate and interpret the selected V100 scaling-crossover counters.")
+    parser.add_argument("input", type=pathlib.Path)
+    parser.add_argument("--output", required=True, type=pathlib.Path)
+    parser.add_argument("--markdown", required=True, type=pathlib.Path)
+    args = parser.parse_args()
+    with args.input.open() as source:
+        rows = list(csv.DictReader(source))
+    if not rows:
+        raise ValueError("NCU summary is empty")
+    aggregated = aggregate(rows)
+    write_csv(args.output, aggregated)
+    write_markdown(args.markdown, aggregated, rows)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/benchmark_external_fht.py b/scripts/benchmark_external_fht.py
index 896819f..a9770f4 100644
--- a/scripts/benchmark_external_fht.py
+++ b/scripts/benchmark_external_fht.py
@@ -10,6 +10,7 @@ def main():
     parser.add_argument("--logNs", nargs="+", type=int, default=(8, 10, 12, 15))
     parser.add_argument("--dtypes", nargs="+", choices=("fp16", "bf16", "fp32"), default=("fp16", "bf16", "fp32"))
     parser.add_argument("--target-points", type=int, default=1 << 24)
+    parser.add_argument("--batch", type=int, help="Use one explicit batch for every requested length.")
     parser.add_argument("--warmup", type=int, default=20)
     parser.add_argument("--repeat", type=int, default=100)
     parser.add_argument("--trials", type=int, default=5)
@@ -35,7 +36,9 @@ def main():
         if not 3 <= log_n <= 15:
             raise ValueError("upstream power-of-two FWHT supports logN in [3, 15]")
         n = 1 << log_n
-        batch = max(1, args.target_points // n)
+        batch = args.batch if args.batch is not None else max(1, args.target_points // n)
+        if batch < 1:
+            raise ValueError("batch must be positive")
         scale = 1.0 / n if args.normalization == "inverse" else 1.0
         for dtype_name in args.dtypes:
             values = torch.randn((batch, n), device="cuda", dtype=dtype_map[dtype_name])
diff --git a/scripts/benchmark_fp64_fft_address_path.sh b/scripts/benchmark_fp64_fft_address_path.sh
new file mode 100755
index 0000000..13b874a
--- /dev/null
+++ b/scripts/benchmark_fp64_fft_address_path.sh
@@ -0,0 +1,43 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+BIN=${BIN:-"$ROOT/build/cubutterfly_bench"}
+OUTPUT_DIR=${OUTPUT_DIR:-"$ROOT/results"}
+SWEEP="$ROOT/scripts/sweep_cubutterfly_designs.py"
+SUMMARY="$ROOT/scripts/summarize_cubutterfly_designs.py"
+
+if [[ ! -x "$BIN" ]]; then
+    echo "benchmark binary is missing: $BIN" >&2
+    exit 1
+fi
+mkdir -p "$OUTPUT_DIR"
+
+COMMON=(--binary "$BIN" --operators fft --precisions fp64 --logNs 16 --batch 64
+        --directions forward --normalizations none --placements out-of-place
+        --warmup 1000 --repeat 100 --trials 5)
+MAPPING=(--hierarchical-local-stages 8
+         --prefix-thread-options 256 --suffix-thread-options 128
+         --prefix-ept-options 4 --suffix-ept-options 8)
+
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores scalar \
+    --tile-thread-options 128 --hierarchical-local-stages 8 --reorder-column-options 1 \
+    --compute-units radix4 --complex-multiplies four-mul \
+    --output "$OUTPUT_DIR/fp64_address_scalar_logN16_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores cufftdx-block \
+    "${MAPPING[@]}" --cross-twiddles table --shared-layouts linear \
+    --output "$OUTPUT_DIR/fp64_address_table_logN16_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores cufftdx-block \
+    "${MAPPING[@]}" --cross-twiddles recurrence --shared-layouts linear xor-swizzle \
+    --output "$OUTPUT_DIR/fp64_address_recurrence_logN16_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends cufft --fft-cores scalar \
+    --output "$OUTPUT_DIR/fp64_address_cufft_logN16_raw.csv"
+
+python3 "$SUMMARY" \
+    "$OUTPUT_DIR/fp64_address_scalar_logN16_raw.csv" \
+    "$OUTPUT_DIR/fp64_address_table_logN16_raw.csv" \
+    "$OUTPUT_DIR/fp64_address_recurrence_logN16_raw.csv" \
+    "$OUTPUT_DIR/fp64_address_cufft_logN16_raw.csv" \
+    --output "$OUTPUT_DIR/fp64_address_logN16_summary.csv"
+
+printf 'FP64 address-path summary: %s\n' "$OUTPUT_DIR/fp64_address_logN16_summary.csv"
diff --git a/scripts/benchmark_fp64_fft_robustness.py b/scripts/benchmark_fp64_fft_robustness.py
new file mode 100755
index 0000000..4e1e2bc
--- /dev/null
+++ b/scripts/benchmark_fp64_fft_robustness.py
@@ -0,0 +1,86 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+import subprocess
+
+
+MAPPINGS = {
+    14: (7, 128, 4, 128, 4),
+    15: (7, 128, 4, 128, 8),
+    16: (8, 128, 8, 128, 8),
+    17: (8, 128, 8, 256, 8),
+    18: (9, 256, 8, 256, 8),
+}
+
+
+def command(binary, log_n, batch, backend, warmup, repeat, verify=False):
+    args = [
+        str(binary), "--operator", "fft", "--precision", "fp64",
+        "--backend", backend, "--logN", str(log_n), "--batch", str(batch),
+        "--placement", "out-of-place", "--normalization", "none",
+        "--warmup", str(warmup), "--repeat", str(repeat), "--csv",
+    ]
+    if backend == "online-reorder":
+        local, prefix_threads, prefix_ept, suffix_threads, suffix_ept = MAPPINGS[log_n]
+        args += [
+            "--fft-core", "cufftdx-block", "--local-stages", str(local),
+            "--prefix-threads", str(prefix_threads), "--prefix-ept", str(prefix_ept),
+            "--suffix-threads", str(suffix_threads), "--suffix-ept", str(suffix_ept),
+            "--cross-twiddle", "recurrence", "--shared-layout", "xor-swizzle",
+        ]
+    if verify:
+        args.append("--verify")
+    return args
+
+
+def run(args):
+    result = subprocess.run(args, check=True, capture_output=True, text=True)
+    rows = list(csv.DictReader(result.stdout.splitlines()))
+    if len(rows) != 1:
+        raise RuntimeError(f"unexpected benchmark output for {' '.join(args)}")
+    return rows[0]
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Measure FP64 FFT length/batch robustness against cuFFT.")
+    parser.add_argument("--binary", type=pathlib.Path, default=pathlib.Path("build/cubutterfly_bench"))
+    parser.add_argument("--lengths", nargs="+", type=int, default=tuple(MAPPINGS))
+    parser.add_argument("--batches", nargs="+", type=int, default=(1, 2, 4, 8, 16, 32, 64))
+    parser.add_argument("--warmup", type=int, default=1000)
+    parser.add_argument("--repeat", type=int, default=100)
+    parser.add_argument("--trials", type=int, default=5)
+    parser.add_argument("--output", "-o", required=True, type=pathlib.Path)
+    args = parser.parse_args()
+
+    if not args.binary.is_file():
+        raise FileNotFoundError(f"benchmark binary not found: {args.binary}")
+    unsupported = set(args.lengths) - set(MAPPINGS)
+    if unsupported:
+        raise ValueError(f"unsupported FP64 robustness lengths: {sorted(unsupported)}")
+    if any(batch < 1 for batch in args.batches):
+        raise ValueError("batches must be positive")
+
+    for log_n in args.lengths:
+        run(command(args.binary, log_n, 1, "online-reorder", 1, 1, verify=True))
+
+    records = []
+    for log_n in args.lengths:
+        for batch in args.batches:
+            for trial in range(1, args.trials + 1):
+                backends = ("online-reorder", "cufft")
+                if (log_n + batch + trial) & 1:
+                    backends = tuple(reversed(backends))
+                for backend in backends:
+                    row = run(command(args.binary, log_n, batch, backend, args.warmup, args.repeat))
+                    records.append({"trial": trial, **row})
+
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    with args.output.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=records[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        writer.writerows(records)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/benchmark_fp64_fft_robustness_mapping.sh b/scripts/benchmark_fp64_fft_robustness_mapping.sh
new file mode 100755
index 0000000..7196083
--- /dev/null
+++ b/scripts/benchmark_fp64_fft_robustness_mapping.sh
@@ -0,0 +1,31 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+BIN=${BIN:-"$ROOT/build/cubutterfly_bench"}
+OUTPUT_DIR=${OUTPUT_DIR:-"$ROOT/results"}
+SWEEP="$ROOT/scripts/sweep_cubutterfly_designs.py"
+SUMMARY="$ROOT/scripts/summarize_cubutterfly_designs.py"
+
+if [[ ! -x "$BIN" ]]; then
+    echo "benchmark binary is missing: $BIN" >&2
+    exit 1
+fi
+mkdir -p "$OUTPUT_DIR"
+
+python3 "$SWEEP" --binary "$BIN" --operators fft --precisions fp64 \
+    --logNs 14 15 16 17 18 --target-points 4194304 \
+    --directions forward --normalizations none --placements out-of-place \
+    --backends online-reorder --fft-cores cufftdx-block \
+    --hierarchical-local-stages 7 8 9 \
+    --prefix-thread-options 128 256 512 --suffix-thread-options 128 256 512 \
+    --prefix-ept-options 4 8 --suffix-ept-options 4 8 \
+    --cross-twiddles recurrence --shared-layouts linear xor-swizzle \
+    --warmup 20 --repeat 20 --trials 1 \
+    --output "$OUTPUT_DIR/fp64_robustness_mapping_coarse_raw.csv"
+
+python3 "$SUMMARY" "$OUTPUT_DIR/fp64_robustness_mapping_coarse_raw.csv" \
+    --output "$OUTPUT_DIR/fp64_robustness_mapping_coarse_summary.csv"
+
+printf 'FP64 robustness mapping summary: %s\n' \
+    "$OUTPUT_DIR/fp64_robustness_mapping_coarse_summary.csv"
diff --git a/scripts/benchmark_fp64_fft_units.sh b/scripts/benchmark_fp64_fft_units.sh
new file mode 100755
index 0000000..8ae2aae
--- /dev/null
+++ b/scripts/benchmark_fp64_fft_units.sh
@@ -0,0 +1,79 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+BIN=${BIN:-"$ROOT/build/cubutterfly_bench"}
+OUTPUT_DIR=${OUTPUT_DIR:-"$ROOT/results"}
+SWEEP="$ROOT/scripts/sweep_cubutterfly_designs.py"
+SUMMARY="$ROOT/scripts/summarize_cubutterfly_designs.py"
+
+if [[ ! -x "$BIN" ]]; then
+    echo "benchmark binary is missing: $BIN" >&2
+    exit 1
+fi
+mkdir -p "$OUTPUT_DIR"
+
+python3 "$SWEEP" --binary "$BIN" --operators fft --precisions fp64 --logNs 16 --batch 64 \
+    --directions forward --normalizations none --placements out-of-place \
+    --backends hierarchical online-reorder cufft --fft-cores scalar \
+    --tile-thread-options 32 64 128 256 --hierarchical-local-stages 5 6 8 10 \
+    --reorder-column-options 1 2 4 --compute-units radix2 radix4 radix8 \
+    --complex-multiplies four-mul gauss3 --warmup 10 --repeat 20 --trials 3 \
+    --output "$OUTPUT_DIR/fp64_scalar_logN16_coarse_raw.csv"
+python3 "$SUMMARY" "$OUTPUT_DIR/fp64_scalar_logN16_coarse_raw.csv" \
+    --output "$OUTPUT_DIR/fp64_scalar_logN16_coarse_summary.csv"
+
+python3 "$SWEEP" --binary "$BIN" --operators fft --precisions fp64 --logNs 16 --batch 64 \
+    --directions forward --normalizations none --placements out-of-place \
+    --backends online-reorder --fft-cores cufftdx-block --hierarchical-local-stages 8 \
+    --prefix-thread-options 128 256 512 --suffix-thread-options 128 256 512 \
+    --prefix-ept-options 4 8 --suffix-ept-options 4 8 --cross-twiddles table \
+    --shared-layouts linear \
+    --warmup 100 --repeat 50 --trials 3 \
+    --output "$OUTPUT_DIR/fp64_cufftdx_logN16_mapping_raw.csv"
+python3 "$SUMMARY" "$OUTPUT_DIR/fp64_cufftdx_logN16_mapping_raw.csv" \
+    --output "$OUTPUT_DIR/fp64_cufftdx_logN16_mapping_summary.csv"
+
+python3 "$SWEEP" --binary "$BIN" --operators fft --precisions fp64 --logNs 16 --batch 64 \
+    --directions forward --normalizations none --placements out-of-place \
+    --backends online-reorder --fft-cores cufftdx-block --hierarchical-local-stages 8 \
+    --prefix-thread-options 128 256 512 --suffix-thread-options 128 256 512 \
+    --prefix-ept-options 4 8 --suffix-ept-options 4 8 --cross-twiddles recurrence \
+    --shared-layouts linear \
+    --warmup 100 --repeat 50 --trials 3 \
+    --output "$OUTPUT_DIR/fp64_cufftdx_recurrence_mapping_raw.csv"
+python3 "$SUMMARY" "$OUTPUT_DIR/fp64_cufftdx_recurrence_mapping_raw.csv" \
+    --output "$OUTPUT_DIR/fp64_cufftdx_recurrence_mapping_summary.csv"
+
+COMMON=(--binary "$BIN" --operators fft --precisions fp64 --logNs 16 --batch 64
+        --directions forward --normalizations none --placements out-of-place
+        --warmup 1000 --repeat 100 --trials 5)
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores scalar \
+    --tile-thread-options 128 --hierarchical-local-stages 8 --reorder-column-options 1 \
+    --compute-units radix4 --complex-multiplies four-mul \
+    --output "$OUTPUT_DIR/fp64_scalar_logN16_confirm_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores cufftdx-block \
+    --hierarchical-local-stages 8 --prefix-thread-options 256 --suffix-thread-options 128 \
+    --prefix-ept-options 4 --suffix-ept-options 8 --cross-twiddles table \
+    --shared-layouts linear \
+    --output "$OUTPUT_DIR/fp64_cufftdx_logN16_confirm_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores cufftdx-block \
+    --hierarchical-local-stages 8 --prefix-thread-options 256 --suffix-thread-options 128 \
+    --prefix-ept-options 4 --suffix-ept-options 8 --cross-twiddles recurrence \
+    --shared-layouts linear \
+    --output "$OUTPUT_DIR/fp64_cufftdx_recurrence_logN16_confirm_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends online-reorder --fft-cores cufftdx-block \
+    --hierarchical-local-stages 8 --prefix-thread-options 256 --suffix-thread-options 128 \
+    --prefix-ept-options 4 --suffix-ept-options 8 --cross-twiddles recurrence \
+    --shared-layouts xor-swizzle \
+    --output "$OUTPUT_DIR/fp64_cufftdx_xor_swizzle_logN16_confirm_raw.csv"
+python3 "$SWEEP" "${COMMON[@]}" --backends cufft --fft-cores scalar \
+    --output "$OUTPUT_DIR/fp64_cufft_logN16_confirm_raw.csv"
+python3 "$SUMMARY" "$OUTPUT_DIR/fp64_scalar_logN16_confirm_raw.csv" \
+    "$OUTPUT_DIR/fp64_cufftdx_logN16_confirm_raw.csv" \
+    "$OUTPUT_DIR/fp64_cufftdx_recurrence_logN16_confirm_raw.csv" \
+    "$OUTPUT_DIR/fp64_cufftdx_xor_swizzle_logN16_confirm_raw.csv" \
+    "$OUTPUT_DIR/fp64_cufft_logN16_confirm_raw.csv" \
+    --output "$OUTPUT_DIR/fp64_logN16_twiddle_summary.csv"
+
+printf 'FP64 confirmation summary: %s\n' "$OUTPUT_DIR/fp64_logN16_twiddle_summary.csv"
diff --git a/scripts/fft_design_space.py b/scripts/fft_design_space.py
index ef2ace8..fb43a66 100755
--- a/scripts/fft_design_space.py
+++ b/scripts/fft_design_space.py
@@ -32,12 +32,18 @@ def load_space(path):
 
 def load_codegen_points(path):
     selection = json.loads(path.read_text())
-    family = selection.get("families", {}).get("cufftdx-online", {})
-    return {
+    expanded = {
         (log_n, threads, ept)
+        for family in selection.get("families", {}).values()
         for log_n in family.get("dimension_log_n", [])
         for threads, ept in family.get("thread_ept_pairs", [])
     }
+    explicit = {
+        tuple(point)
+        for family in selection.get("families", {}).values()
+        for point in family.get("points", [])
+    }
+    return expanded | explicit
 
 
 def classify_online_point(point, hardware, compiled_points=None):
@@ -62,8 +68,11 @@ def classify_online_point(point, hardware, compiled_points=None):
         return "hardware-infeasible", ";".join(reasons)
     if point["prefix_log_n"] < 3 or point["suffix_log_n"] < 3:
         return "requires-new-kernel", "mixed-small-dimension-core"
-    if point["prefix_log_n"] > 10 or point["suffix_log_n"] > 10:
+    if point["prefix_log_n"] > 12 or point["suffix_log_n"] > 12:
         return "requires-new-kernel", "large-dimension-layout"
+    for label in ("prefix", "suffix"):
+        if point[f"{label}_log_n"] >= 11 and point[f"{label}_units_per_cta"] != 1:
+            return "requires-new-kernel", f"{label}-direct-single-unit"
     compiled_points = compiled_points or set()
     prefix_key = (point["prefix_log_n"], point["prefix_threads"], point["prefix_ept"])
     suffix_key = (point["suffix_log_n"], point["suffix_threads"], point["suffix_ept"])
diff --git a/scripts/generate_fft_dispatch.py b/scripts/generate_fft_dispatch.py
new file mode 100755
index 0000000..eb27d58
--- /dev/null
+++ b/scripts/generate_fft_dispatch.py
@@ -0,0 +1,142 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import json
+import math
+import pathlib
+
+
+INTEGER_FIELDS = ("prefix_log_n", "suffix_log_n", "prefix_threads", "suffix_threads", "prefix_ept", "suffix_ept")
+FLOAT_FIELDS = ("median_kernel_ms", "cufft_median_ms", "throughput_vs_cufft")
+
+
+def physical_mapping(row):
+    group_stages = row.get("execution_group_stages", "")
+    group_threads = row.get("group_threads", "")
+    group_ept = row.get("group_ept", "")
+    if group_stages:
+        stages = [int(value) for value in group_stages.split("x")]
+        threads = [int(value) for value in group_threads.split("x")]
+        ept = [int(value) for value in group_ept.split("x")]
+        if len(stages) != 2 or len(threads) != 2 or len(ept) != 2:
+            raise ValueError("generated FFT dispatch currently requires exactly two physical groups")
+        return {
+            "prefix_log_n": stages[0], "suffix_log_n": stages[1],
+            "prefix_threads": threads[0], "suffix_threads": threads[1],
+            "prefix_ept": ept[0], "suffix_ept": ept[1],
+        }
+    return {field: int(row[field]) for field in INTEGER_FIELDS}
+
+
+def select_dispatch(rows):
+    winners = [row for row in rows if int(row["rank"]) == 1]
+    by_log_n = {}
+    for row in winners:
+        by_log_n.setdefault(int(row["logN"]), []).append(row)
+    entries = []
+    for log_n, log_rows in sorted(by_log_n.items()):
+        ordered = sorted(log_rows, key=lambda row: int(row["batch"]))
+        for index, row in enumerate(ordered):
+            if index + 1 == len(ordered):
+                max_batch = None
+            else:
+                left = math.log2(int(row["batch"]))
+                right = math.log2(int(ordered[index + 1]["batch"]))
+                max_batch = 1 << math.floor((left + right) / 2.0)
+            entries.append({
+                "logN": log_n, "max_batch": max_batch,
+                "candidate_id": row["candidate_id"], "cross_twiddle": row["cross_twiddle"],
+                "direct_boundary": row.get("direct_boundary", "direct-strided"),
+                **physical_mapping(row),
+                **{field: float(row[field]) for field in FLOAT_FIELDS},
+            })
+    return entries
+
+
+def validate_dispatch(document):
+    if document.get("schema_version") != 1 or document.get("target") is None:
+        raise ValueError("unsupported generated FFT dispatch schema")
+    previous = {}
+    for entry in document.get("entries", []):
+        log_n = int(entry["logN"])
+        maximum = entry["max_batch"]
+        if maximum is not None and int(maximum) < 1:
+            raise ValueError("dispatch max_batch must be positive or null")
+        if log_n in previous and previous[log_n] is None:
+            raise ValueError("unbounded dispatch entry must be last for a length")
+        if log_n in previous and maximum is not None and int(maximum) <= int(previous[log_n]):
+            raise ValueError("dispatch thresholds must increase")
+        previous[log_n] = maximum
+    if not document.get("entries"):
+        raise ValueError("generated FFT dispatch is empty")
+
+
+def generate_header(path, document):
+    validate_dispatch(document)
+    conditions = []
+    for entry in document["entries"]:
+        threshold = "true" if entry["max_batch"] is None else f"batch <= {int(entry['max_batch'])}ULL"
+        recurrence = "true" if entry["cross_twiddle"] == "recurrence" else "false"
+        suffix_tiled_transpose = "true" if entry.get("direct_boundary") == "tiled-transpose" else "false"
+        prefix_tiled_transpose = "true" if entry.get("direct_boundary") == "prefix-tiled-transpose" else "false"
+        conditions.append(
+            f"    if (log_n == {int(entry['logN'])}U && {threshold}) {{\n"
+            f"        mapping = {{{int(entry['prefix_log_n'])}U, {int(entry['prefix_threads'])}U, "
+            f"{int(entry['suffix_threads'])}U, {int(entry['prefix_ept'])}U, "
+            f"{int(entry['suffix_ept'])}U, {recurrence}, {suffix_tiled_transpose}, "
+            f"{prefix_tiled_transpose}}};\n"
+            f"        return true;\n    }}")
+    body = "\n".join(conditions)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text(f'''// Generated by scripts/generate_fft_dispatch.py for {document["target"]}. Do not edit.
+#pragma once
+#include <cstddef>
+#include <cstdint>
+
+namespace cuntt::detail {{
+struct GeneratedFftMapping {{
+    std::uint32_t local_stages;
+    std::uint32_t prefix_threads;
+    std::uint32_t suffix_threads;
+    std::uint32_t prefix_ept;
+    std::uint32_t suffix_ept;
+    bool recurrence_twiddle;
+    bool suffix_tiled_transpose;
+    bool prefix_tiled_transpose;
+}};
+
+inline bool select_generated_fft_mapping(std::uint32_t log_n, std::size_t batch,
+                                         GeneratedFftMapping& mapping) noexcept {{
+{body}
+    return false;
+}}
+}}  // namespace cuntt::detail
+''')
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Generate measured FFT dispatch data or its C++ header.")
+    parser.add_argument("--summary", type=pathlib.Path)
+    parser.add_argument("--target", default="v100-sm70")
+    parser.add_argument("--output", type=pathlib.Path)
+    parser.add_argument("--dispatch", type=pathlib.Path)
+    parser.add_argument("--header", type=pathlib.Path)
+    args = parser.parse_args()
+    if args.summary:
+        if args.output is None:
+            raise ValueError("--summary requires --output")
+        with args.summary.open() as source:
+            rows = list(csv.DictReader(source))
+        document = {"schema_version": 1, "target": args.target, "entries": select_dispatch(rows)}
+        validate_dispatch(document)
+        args.output.parent.mkdir(parents=True, exist_ok=True)
+        args.output.write_text(json.dumps(document, indent=2) + "\n")
+        return
+    if args.dispatch and args.header:
+        generate_header(args.header, json.loads(args.dispatch.read_text()))
+        return
+    raise ValueError("use --summary/--output or --dispatch/--header")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/generate_fft_pipeline.py b/scripts/generate_fft_pipeline.py
new file mode 100755
index 0000000..86a493b
--- /dev/null
+++ b/scripts/generate_fft_pipeline.py
@@ -0,0 +1,548 @@
+#!/usr/bin/env python3
+import argparse
+import json
+import math
+import pathlib
+
+from fft_design_space import classify_online_point, load_codegen_points, load_space
+
+
+def load_pipeline(path):
+    document = json.loads(path.read_text())
+    if document.get("schema_version") != 2:
+        raise ValueError("unsupported FFT pipeline schema")
+    for field in ("target", "processing_units", "mapping_spaces", "selection", "protocol"):
+        if field not in document:
+            raise ValueError(f"FFT pipeline lacks {field}")
+    ids = [unit["id"] for unit in document["processing_units"]]
+    if len(ids) != len(set(ids)):
+        raise ValueError("duplicate processing-unit id")
+    for mapping in document["mapping_spaces"]:
+        decomposition = mapping.get("decomposition_space", {})
+        for field in ("decomposition_count", "stages_per_decomposition", "compiled_decomposition_counts"):
+            if field not in decomposition:
+                raise ValueError(f"mapping {mapping['id']} lacks decomposition_space.{field}")
+    return document
+
+
+def ceil_div(numerator, denominator):
+    return (numerator + denominator - 1) // denominator
+
+
+def stage_partitions(log_n, decomposition_count, minimum, maximum):
+    def visit(remaining, decompositions_left, prefix):
+        if decompositions_left == 0:
+            if remaining == 0:
+                yield tuple(prefix)
+            return
+        lower = max(minimum, remaining - maximum * (decompositions_left - 1))
+        upper = min(maximum, remaining - minimum * (decompositions_left - 1))
+        for stages in range(lower, upper + 1):
+            yield from visit(remaining - stages, decompositions_left - 1, [*prefix, stages])
+
+    yield from visit(log_n, decomposition_count, [])
+
+
+def mapping_stage_partitions(mapping, compiled_only=False):
+    decomposition = mapping["decomposition_space"]
+    count_range = decomposition["decomposition_count"]
+    stage_range = decomposition["stages_per_decomposition"]
+    compiled_counts = set(decomposition["compiled_decomposition_counts"])
+    for decomposition_count in range(count_range["min"], count_range["max"] + 1):
+        if compiled_only and decomposition_count not in compiled_counts:
+            continue
+        for stages in stage_partitions(mapping["logN"], decomposition_count,
+                                       stage_range["min"], stage_range["max"]):
+            yield stages
+
+
+def enumerate_decomposition_topologies(document):
+    topologies = []
+    for mapping in document["mapping_spaces"]:
+        compiled_counts = set(mapping["decomposition_space"]["compiled_decomposition_counts"])
+        for stages in mapping_stage_partitions(mapping):
+            decomposition_count = len(stages)
+            compiled = decomposition_count in compiled_counts
+            topologies.append({
+                "id": f"{mapping['id']}_d{decomposition_count}_" + "x".join(map(str, stages)),
+                "mapping_id": mapping["id"], "logN": mapping["logN"],
+                "decomposition_count": decomposition_count, "stages_per_decomposition": list(stages),
+                "boundary_count": decomposition_count - 1,
+                "status": "compiled-runtime" if compiled else "requires-multi-pass-runtime",
+                "reason": "" if compiled else "decomposition-count-not-implemented",
+            })
+    return topologies
+
+
+def pass_resources(dimension_log_n, other_log_n, threads, ept, batch, hardware, unit):
+    size = 1 << dimension_log_n
+    units = threads * ept // size
+    blocks = ceil_div(batch * (1 << other_log_n), units)
+    shared = threads * ept * 8
+    register_spec = unit.get("estimated_registers_per_thread", {})
+    registers = int(register_spec.get(f"logN{dimension_log_n}", register_spec.get("default", 0)))
+    limits = [hardware["max_ctas_per_sm"], hardware["max_threads_per_sm"] // threads,
+              hardware["max_shared_bytes_per_cta"] // shared]
+    if registers:
+        limits.append(hardware["registers_per_sm"] // (registers * threads))
+    resident_ctas = max(1, min(limits))
+    waves = blocks / (hardware["sm_count"] * resident_ctas)
+    return {
+        "units_per_cta": units,
+        "blocks": blocks,
+        "threads": threads,
+        "ept": ept,
+        "tile_shared_bytes": shared,
+        "estimated_registers_per_thread": registers,
+        "estimated_resident_ctas_per_sm": resident_ctas,
+        "estimated_waves_per_sm": waves,
+        "issued_thread_slots": blocks * threads,
+    }
+
+
+def score_candidate(point, hardware, prefix_unit, suffix_unit, selection):
+    prefix = pass_resources(point["prefix_log_n"], point["suffix_log_n"], point["prefix_threads"],
+                            point["prefix_ept"], point["batch"], hardware, prefix_unit)
+    suffix = pass_resources(point["suffix_log_n"], point["prefix_log_n"], point["suffix_threads"],
+                            point["suffix_ept"], point["batch"], hardware, suffix_unit)
+    weighted_prefix = selection["prefix_work_weight"] * prefix["issued_thread_slots"]
+    weighted_suffix = selection["suffix_work_weight"] * suffix["issued_thread_slots"]
+    work = weighted_prefix + weighted_suffix
+    imbalance = max(weighted_prefix, weighted_suffix) / min(weighted_prefix, weighted_suffix)
+    underfill = max(0.0, 1.0 - min(prefix["estimated_waves_per_sm"], suffix["estimated_waves_per_sm"]))
+    score = work * (1.0 + selection["imbalance_penalty"] * math.log2(imbalance)
+                    + selection["underfill_penalty"] * underfill)
+    if point["cross_twiddle"] == "recurrence":
+        score *= 0.98
+    point["prefix_resources"] = prefix
+    point["suffix_resources"] = suffix
+    point["estimated_work_imbalance"] = imbalance
+    point["static_score"] = score
+
+
+def compiled_segment_options(stage_log_n, unit, codegen_points, hardware, batch, total_log_n):
+    size = 1 << stage_log_n
+    options = []
+    for threads in unit["threads"]:
+        for ept in unit["elements_per_thread"]:
+            if (threads > hardware["max_threads_per_cta"] or ept > size or
+                    threads * ept < size or (threads * ept) % size or
+                    threads * ept * 8 > hardware["max_shared_bytes_per_cta"]):
+                continue
+            if stage_log_n >= 11:
+                compiled = threads * ept == size
+            else:
+                compiled = (stage_log_n, threads, ept) in codegen_points
+            if not compiled:
+                continue
+            resources = pass_resources(stage_log_n, total_log_n - stage_log_n, threads, ept,
+                                       batch, hardware, unit)
+            options.append({"processing_unit": unit["id"], "core": unit["core"],
+                            "exchange": unit["exchange"], "threads": threads, "ept": ept,
+                            "resources": resources})
+    return sorted(options, key=lambda item: (item["resources"]["issued_thread_slots"],
+                                              -item["resources"]["estimated_waves_per_sm"],
+                                              item["threads"], item["ept"]))
+
+
+def score_multisegment(point, selection):
+    weighted = []
+    mappings = point.get("execution_group_mappings", point["segment_mappings"])
+    for segment, mapping in enumerate(mappings):
+        weight = selection["prefix_work_weight"] if segment == 0 else selection["suffix_work_weight"]
+        weighted.append(weight * mapping["resources"]["issued_thread_slots"])
+    work = sum(weighted)
+    imbalance = max(weighted) / min(weighted)
+    underfill = max(0.0, 1.0 - min(mapping["resources"]["estimated_waves_per_sm"]
+                                   for mapping in point["segment_mappings"]))
+    point["estimated_work_imbalance"] = imbalance
+    point["static_score"] = work * (1.0 + selection["imbalance_penalty"] * math.log2(imbalance)
+                                     + selection["underfill_penalty"] * underfill)
+
+
+def multisegment_runtime_args(point):
+    threads = ",".join(str(mapping["threads"]) for mapping in point["segment_mappings"])
+    ept = ",".join(str(mapping["ept"]) for mapping in point["segment_mappings"])
+    twiddles = ",".join(boundary["cross_twiddle"] for boundary in point["boundaries"])
+    layouts = ",".join(boundary["layout"] for boundary in point["boundaries"])
+    residencies = ",".join(boundary.get("residency", "global-scratch")
+                           for boundary in point["boundaries"])
+    args = [
+        "--operator", "fft", "--precision", point["precision"], "--backend", "online-reorder",
+        "--fft-core", "cufftdx-block", "--stage-partition",
+        ",".join(map(str, point["stages_per_decomposition"])),
+        "--segment-threads", threads, "--segment-ept", ept,
+        "--boundary-twiddle", twiddles, "--boundary-layout", layouts,
+        "--boundary-residency", residencies,
+        "--placement", point["placement"], "--normalization", point["normalization"],
+    ]
+    if point.get("execution_group_mappings"):
+        args.extend([
+            "--group-threads", ",".join(str(item["threads"])
+                                          for item in point["execution_group_mappings"]),
+            "--group-ept", ",".join(str(item["ept"])
+                                      for item in point["execution_group_mappings"]),
+        ])
+    return args
+
+
+def multisegment_candidate_id(point):
+    stages = "x".join(map(str, point["stages_per_decomposition"]))
+    threads = "x".join(str(mapping["threads"]) for mapping in point["segment_mappings"])
+    ept = "x".join(str(mapping["ept"]) for mapping in point["segment_mappings"])
+    twiddles = "".join("r" if boundary["cross_twiddle"] == "recurrence" else "t"
+                       for boundary in point["boundaries"])
+    residencies = "".join("f" if boundary.get("residency") == "fused" else "g"
+                          for boundary in point["boundaries"])
+    group_suffix = ""
+    if point.get("execution_group_mappings"):
+        group_threads = "x".join(str(item["threads"]) for item in point["execution_group_mappings"])
+        group_ept = "x".join(str(item["ept"]) for item in point["execution_group_mappings"])
+        group_suffix = f"_gt{group_threads}_ge{group_ept}"
+    return (f"{point['mapping_id']}_b{point['batch']}_d{point['decomposition_count']}_{stages}_"
+            f"t{threads}_e{ept}_{twiddles}_{residencies}{group_suffix}")
+
+
+def runtime_args(point):
+    return [
+        "--operator", "fft", "--precision", point["precision"], "--backend", "online-reorder",
+        "--fft-core", "cufftdx-block", "--stage-partition",
+        ",".join(map(str, point["stages_per_decomposition"])),
+        "--reorder-columns", "1", "--cross-twiddle", point["cross_twiddle"],
+        "--direct-boundary", point["direct_boundary"],
+        "--prefix-threads", str(point["prefix_threads"]), "--suffix-threads", str(point["suffix_threads"]),
+        "--prefix-ept", str(point["prefix_ept"]), "--suffix-ept", str(point["suffix_ept"]),
+        "--placement", point["placement"], "--normalization", point["normalization"],
+    ]
+
+
+def candidate_id(point):
+    twiddle = "rec" if point["cross_twiddle"] == "recurrence" else "tbl"
+    boundary_suffixes = {"direct-strided": "", "tiled-transpose": "_tx",
+                         "prefix-tiled-transpose": "_ptx"}
+    boundary = boundary_suffixes[point["direct_boundary"]]
+    return (f"{point['mapping_id']}_b{point['batch']}_p{point['prefix_log_n']}s{point['suffix_log_n']}_"
+            f"t{point['prefix_threads']}x{point['suffix_threads']}_e{point['prefix_ept']}x{point['suffix_ept']}_{twiddle}{boundary}")
+
+
+def matches_required(point, required):
+    if len(required["stage_partition"]) != 2 or len(required["segment_mappings"]) != 2:
+        raise ValueError("current runtime incumbent must describe exactly two decomposition segments")
+    prefix, suffix = required["segment_mappings"]
+    fields = {
+        "stages_per_decomposition": required["stage_partition"],
+        "prefix_threads": prefix["threads"], "suffix_threads": suffix["threads"],
+        "prefix_ept": prefix["ept"], "suffix_ept": suffix["ept"],
+        "cross_twiddle": required["cross_twiddle"],
+        "direct_boundary": required.get("direct_boundary", "direct-strided"),
+    }
+    return all(point[field] == value for field, value in fields.items())
+
+
+def enumerate_pipeline(document, architecture, codegen_points):
+    hardware = architecture["hardware_profiles"][document["target"]]
+    compiled_units = [unit for unit in document["processing_units"] if unit["status"] == "compiled"]
+    planned_units = [unit for unit in document["processing_units"] if unit["status"] != "compiled"]
+
+    def find_unit(dimension_log_n):
+        matches = [unit for unit in compiled_units
+                   if unit["dimension_log_n"]["min"] <= dimension_log_n <= unit["dimension_log_n"]["max"]]
+        if len(matches) > 1:
+            raise ValueError(f"multiple compiled processing units cover logN={dimension_log_n}")
+        return matches[0] if matches else None
+
+    runnable = []
+    backlog = []
+    for mapping in document["mapping_spaces"]:
+        for batch in mapping["batches"]:
+            shape = []
+            planned_shape = []
+            for stages in mapping_stage_partitions(mapping, compiled_only=True):
+                if len(stages) != 2:
+                    units = [find_unit(stage) for stage in stages]
+                    if any(unit is None for unit in units):
+                        planned_shape.append({
+                            "mapping_id": mapping["id"], "batch": batch,
+                            "decomposition_count": len(stages), "stages_per_decomposition": list(stages),
+                            "status": "requires-new-kernel", "reason": "segment-processing-unit",
+                        })
+                        continue
+                    options = [compiled_segment_options(stage, unit, codegen_points, hardware,
+                                                        batch, mapping["logN"])
+                               for stage, unit in zip(stages, units)]
+                    if any(not segment_options for segment_options in options):
+                        planned_shape.append({
+                            "mapping_id": mapping["id"], "batch": batch,
+                            "decomposition_count": len(stages), "stages_per_decomposition": list(stages),
+                            "status": "awaiting-codegen", "reason": "segment-specialization-not-selected",
+                        })
+                        continue
+                    mapping_variants = min(3, max(len(segment_options) for segment_options in options))
+                    twiddle_variants = [
+                        ["table"] * (len(stages) - 1),
+                        ["recurrence"] * (len(stages) - 1),
+                        ["recurrence" if boundary % 2 == 0 else "table"
+                         for boundary in range(len(stages) - 1)],
+                    ]
+                    for variant in range(mapping_variants):
+                        segment_mappings = [segment_options[min(variant, len(segment_options) - 1)]
+                                            for segment_options in options]
+                        for twiddles in twiddle_variants:
+                            boundaries = [{"cross_twiddle": twiddle, "layout": "direct-strided",
+                                           "residency": "global-scratch"}
+                                          for twiddle in twiddles]
+                            point = {
+                                **{key: value for key, value in mapping.items()
+                                   if key not in ("batches", "decomposition_space", "required_candidates")},
+                                "mapping_id": mapping["id"], "batch": batch,
+                                "decomposition_count": len(stages),
+                                "stages_per_decomposition": list(stages),
+                                "segment_mappings": segment_mappings, "boundaries": boundaries,
+                                "processing_unit": "+".join(item["id"] for item in units),
+                                "prefix_log_n": stages[0], "suffix_log_n": stages[-1],
+                                "prefix_threads": segment_mappings[0]["threads"],
+                                "suffix_threads": segment_mappings[-1]["threads"],
+                                "prefix_ept": segment_mappings[0]["ept"],
+                                "suffix_ept": segment_mappings[-1]["ept"],
+                                "cross_twiddle": (twiddles[0] if len(set(twiddles)) == 1 else "mixed"),
+                                "direct_boundary": "direct-strided", "status": "compiled", "reason": "",
+                            }
+                            score_multisegment(point, document["selection"])
+                            point["id"] = multisegment_candidate_id(point)
+                            point["args"] = multisegment_runtime_args(point)
+                            shape.append(point)
+                            # Keep the logical decomposition intact while lowering all but one
+                            # boundary into two physical execution groups.
+                            for cut in range(1, len(stages)):
+                                group_stages = [sum(stages[:cut]), sum(stages[cut:])]
+                                group_units = [find_unit(group_stage) for group_stage in group_stages]
+                                if any(unit is None for unit in group_units):
+                                    continue
+                                group_options = [compiled_segment_options(group_stage, unit, codegen_points,
+                                                                          hardware, batch, mapping["logN"])
+                                                 for group_stage, unit in zip(group_stages, group_units)]
+                                if any(not options for options in group_options):
+                                    continue
+                                execution_mapping_variants = [[
+                                    options[min(variant, len(options) - 1)] for options in group_options
+                                ]]
+                                for required in mapping.get("required_candidates", []):
+                                    if required["stage_partition"] != group_stages:
+                                        continue
+                                    incumbent = []
+                                    for required_mapping, group_candidates in zip(required["segment_mappings"],
+                                                                                  group_options):
+                                        match = next((option for option in group_candidates
+                                                      if option["threads"] == required_mapping["threads"] and
+                                                      option["ept"] == required_mapping["ept"]), None)
+                                        if match is None:
+                                            incumbent = []
+                                            break
+                                        incumbent.append(match)
+                                    if incumbent:
+                                        execution_mapping_variants.append(incumbent)
+                                fused_boundaries = [
+                                    {**boundary,
+                                     "residency": ("global-scratch" if boundary_index == cut - 1 else "fused")}
+                                    for boundary_index, boundary in enumerate(boundaries)
+                                ]
+                                unique_execution_mappings = {
+                                    tuple((item["threads"], item["ept"]) for item in execution_mappings): execution_mappings
+                                    for execution_mappings in execution_mapping_variants
+                                }
+                                for execution_mappings in unique_execution_mappings.values():
+                                    fused_point = {
+                                        **point,
+                                        "boundaries": fused_boundaries,
+                                        "execution_group_count": 2,
+                                        "execution_group_stages": group_stages,
+                                        "execution_group_mappings": execution_mappings,
+                                        "physical_processing_unit": "+".join(item["id"] for item in group_units),
+                                    }
+                                    score_multisegment(fused_point, document["selection"])
+                                    fused_point["id"] = multisegment_candidate_id(fused_point)
+                                    fused_point["args"] = multisegment_runtime_args(fused_point)
+                                    shape.append(fused_point)
+                    continue
+                prefix_log_n, suffix_log_n = stages
+                prefix_unit = find_unit(prefix_log_n)
+                suffix_unit = find_unit(suffix_log_n)
+                if prefix_unit is None or suffix_unit is None:
+                    planned = {
+                        **{key: value for key, value in mapping.items() if key not in ("batches", "decomposition_space", "required_candidates")},
+                        "mapping_id": mapping["id"], "batch": batch, "prefix_log_n": prefix_log_n,
+                        "suffix_log_n": suffix_log_n, "status": "requires-new-kernel",
+                        "reason": "large-dimension-processing-unit",
+                        "candidate_processing_units": [item["id"] for item in planned_units],
+                    }
+                    planned_shape.append(planned)
+                    continue
+                twiddles = sorted(set(prefix_unit["cross_twiddle"]) & set(suffix_unit["cross_twiddle"]))
+                boundaries = ["direct-strided"]
+                if suffix_log_n >= 11 and "tiled-transpose" in suffix_unit.get("direct_boundaries", []):
+                    boundaries.append("tiled-transpose")
+                if prefix_log_n >= 11 and "prefix-tiled-transpose" in prefix_unit.get("direct_boundaries", []):
+                    boundaries.append("prefix-tiled-transpose")
+                for twiddle in twiddles:
+                    for boundary in boundaries:
+                        for prefix_threads in prefix_unit["threads"]:
+                            for suffix_threads in suffix_unit["threads"]:
+                                for prefix_ept in prefix_unit["elements_per_thread"]:
+                                    for suffix_ept in suffix_unit["elements_per_thread"]:
+                                        point = {
+                                            **{key: value for key, value in mapping.items() if key not in ("batches", "decomposition_space", "required_candidates")},
+                                            "mapping_id": mapping["id"], "batch": batch,
+                                            "decomposition_count": 2,
+                                            "stages_per_decomposition": [prefix_log_n, suffix_log_n],
+                                            "processing_unit": f"{prefix_unit['id']}+{suffix_unit['id']}",
+                                            "prefix_processing_unit": prefix_unit["id"],
+                                            "suffix_processing_unit": suffix_unit["id"], "prefix_log_n": prefix_log_n,
+                                            "suffix_log_n": suffix_log_n, "prefix_threads": prefix_threads,
+                                            "suffix_threads": suffix_threads, "prefix_ept": prefix_ept,
+                                            "suffix_ept": suffix_ept, "cross_twiddle": twiddle,
+                                            "direct_boundary": boundary,
+                                            "segment_mappings": [
+                                                {"processing_unit": prefix_unit["id"], "core": prefix_unit["core"],
+                                                 "exchange": prefix_unit["exchange"], "threads": prefix_threads,
+                                                 "ept": prefix_ept},
+                                                {"processing_unit": suffix_unit["id"], "core": suffix_unit["core"],
+                                                 "exchange": suffix_unit["exchange"], "threads": suffix_threads,
+                                                 "ept": suffix_ept},
+                                            ],
+                                            "boundaries": [{"cross_twiddle": twiddle, "layout": boundary,
+                                                            "residency": "global-scratch"}],
+                                        }
+                                        status, reason = classify_online_point(point, hardware, codegen_points)
+                                        if status != "compiled":
+                                            continue
+                                        point["status"] = status
+                                        point["reason"] = reason
+                                        score_candidate(point, hardware, prefix_unit, suffix_unit, document["selection"])
+                                        point["id"] = candidate_id(point)
+                                        point["args"] = runtime_args(point)
+                                        shape.append(point)
+            # Preserve factorization/twiddle diversity before filling by score.
+            selected = []
+            for required in mapping.get("required_candidates", []):
+                match = next((point for point in shape if matches_required(point, required)), None)
+                if match is None:
+                    raise ValueError(f"required candidate is not compiled for {mapping['id']} batch={batch}: {required}")
+                selected.append(match)
+            for decomposition_count in sorted({point["decomposition_count"] for point in shape}):
+                selected.append(min((point for point in shape
+                                     if point["decomposition_count"] == decomposition_count),
+                                    key=lambda item: item["static_score"]))
+            for stages in sorted({tuple(point["stages_per_decomposition"]) for point in shape
+                                  if point["decomposition_count"] == 2}):
+                selected.append(min((point for point in shape
+                                     if tuple(point["stages_per_decomposition"]) == stages),
+                                    key=lambda item: item["static_score"]))
+            d2_boundary_keys = {
+                (tuple(point["stages_per_decomposition"]), point["direct_boundary"])
+                for point in shape if point["decomposition_count"] == 2
+            }
+            for stages, boundary in sorted(d2_boundary_keys):
+                selected.append(min((point for point in shape
+                                     if tuple(point["stages_per_decomposition"]) == stages and
+                                     point["direct_boundary"] == boundary),
+                                    key=lambda item: item["static_score"]))
+            multi_mapping_keys = {
+                (point["decomposition_count"],
+                 tuple((item["threads"], item["ept"]) for item in point["segment_mappings"]))
+                for point in shape if point["decomposition_count"] > 2
+            }
+            for decomposition_count, mapping_key in sorted(multi_mapping_keys):
+                selected.append(min(
+                    (point for point in shape
+                     if point["decomposition_count"] == decomposition_count and
+                     tuple((item["threads"], item["ept"]) for item in point["segment_mappings"]) == mapping_key),
+                    key=lambda item: item["static_score"]))
+            lowering_keys = {
+                (point["decomposition_count"],
+                 tuple(boundary.get("residency", "global-scratch") for boundary in point["boundaries"]))
+                for point in shape if point["decomposition_count"] > 2
+            }
+            lowering_selected = []
+            for decomposition_count, residencies in sorted(lowering_keys):
+                lowering_selected.append(min(
+                    (point for point in shape
+                     if point["decomposition_count"] == decomposition_count and
+                     tuple(boundary.get("residency", "global-scratch")
+                           for boundary in point["boundaries"]) == residencies),
+                    key=lambda item: item["static_score"]))
+            incumbent_lowering_selected = []
+            for required in mapping.get("required_candidates", []):
+                required_mapping = tuple((item["threads"], item["ept"])
+                                         for item in required["segment_mappings"])
+                for decomposition_count, residencies in sorted(lowering_keys):
+                    matches = [
+                        point for point in shape
+                        if point["decomposition_count"] == decomposition_count and
+                        point.get("execution_group_stages") == required["stage_partition"] and
+                        tuple(boundary.get("residency", "global-scratch")
+                              for boundary in point["boundaries"]) == residencies and
+                        next(boundary["cross_twiddle"] for boundary in point["boundaries"]
+                             if boundary.get("residency", "global-scratch") == "global-scratch") ==
+                        required["cross_twiddle"] and
+                        tuple((item["threads"], item["ept"])
+                              for item in point.get("execution_group_mappings", [])) == required_mapping
+                    ]
+                    if matches:
+                        incumbent_lowering_selected.append(min(matches, key=lambda item: item["static_score"]))
+            diversity = {}
+            for point in sorted(shape, key=lambda item: item["static_score"]):
+                key = (point["decomposition_count"], tuple(point["stages_per_decomposition"]),
+                       point["cross_twiddle"], point["direct_boundary"],
+                       tuple(boundary.get("residency", "global-scratch")
+                             for boundary in point["boundaries"]))
+                if key not in diversity:
+                    diversity[key] = point
+            selected = list({point["id"]: point
+                             for point in incumbent_lowering_selected + lowering_selected + selected}.values())
+            selected_ids = {point["id"] for point in selected}
+            selected.extend(point for point in diversity.values() if point["id"] not in selected_ids)
+            limit = int(mapping.get("max_runnable_candidates_per_shape",
+                                    document["selection"]["max_runnable_candidates_per_shape"]))
+            selected_ids = {point["id"] for point in selected}
+            selected.extend(point for point in sorted(shape, key=lambda item: item["static_score"])
+                            if point["id"] not in selected_ids)
+            selected = selected[:limit]
+            for point in selected:
+                point["selection_pool_size"] = len(shape)
+                point["selection_limit"] = limit
+            runnable.extend(sorted(selected, key=lambda item: item["static_score"]))
+            backlog.extend(planned_shape)
+    return runnable, backlog
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Generate processing-unit, mapping, and benchmark layers for FFT selection.")
+    parser.add_argument("--pipeline", type=pathlib.Path, default=pathlib.Path("config/v100_fft_pipeline.json"))
+    parser.add_argument("--architecture", type=pathlib.Path, default=pathlib.Path("config/fft_architecture_space.json"))
+    parser.add_argument("--codegen", type=pathlib.Path, default=pathlib.Path("config/v100_fft_codegen.json"))
+    output_group = parser.add_mutually_exclusive_group(required=True)
+    output_group.add_argument("--output", type=pathlib.Path)
+    output_group.add_argument("--check", type=pathlib.Path)
+    args = parser.parse_args()
+    document = load_pipeline(args.pipeline)
+    architecture = load_space(args.architecture)
+    codegen = load_codegen_points(args.codegen)
+    runnable, backlog = enumerate_pipeline(document, architecture, codegen)
+    topologies = enumerate_decomposition_topologies(document)
+    output = {
+        "schema_version": 2, "target": document["target"], "protocol": document["protocol"],
+        "processing_units": document["processing_units"], "runnable_candidates": runnable,
+        "backlog_candidates": backlog, "decomposition_topologies": topologies,
+    }
+    rendered = json.dumps(output, indent=2) + "\n"
+    if args.check:
+        if not args.check.exists() or args.check.read_text() != rendered:
+            raise ValueError(f"generated FFT candidate manifest is stale: {args.check}")
+    else:
+        args.output.parent.mkdir(parents=True, exist_ok=True)
+        args.output.write_text(rendered)
+    print(f"generated runnable={len(runnable)} backlog={len(backlog)}")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/generate_scaling_suite.py b/scripts/generate_scaling_suite.py
new file mode 100755
index 0000000..a9db26b
--- /dev/null
+++ b/scripts/generate_scaling_suite.py
@@ -0,0 +1,91 @@
+#!/usr/bin/env python3
+import argparse
+import json
+import pathlib
+
+
+WORKLOAD_FIELDS = ("operator", "precision", "logN", "modulus_bits", "direction",
+                   "element_stride", "batch_padding")
+
+
+def expand(document):
+    if document.get("schema_version") != 1:
+        raise ValueError("unsupported scaling-space schema")
+    required = {"hardware", "max_points", "protocols", "binaries", "workloads"}
+    missing = required - set(document)
+    if missing:
+        raise ValueError(f"scaling space lacks {sorted(missing)}")
+    cases = []
+    seen = set()
+    for workload in document["workloads"]:
+        for field in ("id", "operator", "precision", "logN", "batches", "implementations"):
+            if field not in workload:
+                raise ValueError(f"scaling workload lacks {field}")
+        quick = [int(value) for value in workload["batches"].get("quick", [])]
+        full = [int(value) for value in workload["batches"].get("full", [])]
+        if not quick or len(set(quick + full)) != len(quick + full):
+            raise ValueError(f"workload {workload['id']} has empty or duplicate batch levels")
+        if any(value <= 0 for value in quick + full):
+            raise ValueError(f"workload {workload['id']} has non-positive batch")
+        if max(quick + full) * (1 << int(workload["logN"])) > int(document["max_points"]):
+            raise ValueError(f"workload {workload['id']} exceeds max_points")
+        references = sum(bool(item.get("reference")) for item in workload["implementations"])
+        if references > 1:
+            raise ValueError(f"workload {workload['id']} has multiple references")
+        for batch in quick + full:
+            tier = "quick" if batch in quick else "full"
+            group = f"{workload['id']}-batch{batch}"
+            for implementation in workload["implementations"]:
+                case_id = f"{workload['id']}_{implementation['id']}_b{batch}"
+                if case_id in seen:
+                    raise ValueError(f"duplicate generated case {case_id}")
+                seen.add(case_id)
+                case = {
+                    "id": case_id,
+                    "tier": tier,
+                    "group": group,
+                    "runner": implementation["runner"],
+                    "implementation": implementation["name"],
+                    "reference": bool(implementation.get("reference")),
+                    "batch": batch,
+                    "args": implementation["args"],
+                }
+                for field in WORKLOAD_FIELDS:
+                    if field in workload:
+                        case[field] = workload[field]
+                cases.append(case)
+    return {
+        "schema_version": 1,
+        "hardware": document["hardware"],
+        "protocols": document["protocols"],
+        "binaries": document["binaries"],
+        "cases": cases,
+        "external_evidence": document.get("external_evidence", []),
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Expand an orthogonal logN/batch scaling space.")
+    parser.add_argument("--spec", type=pathlib.Path, default=pathlib.Path("config/v100_scaling_space.json"))
+    parser.add_argument("--output", type=pathlib.Path)
+    parser.add_argument("--check", type=pathlib.Path, help="Fail if this generated manifest is stale.")
+    parser.add_argument("--validate-only", action="store_true")
+    args = parser.parse_args()
+    suite = expand(json.loads(args.spec.read_text()))
+    rendered = json.dumps(suite, indent=2) + "\n"
+    if args.check:
+        if args.check.read_text() != rendered:
+            raise ValueError(f"generated scaling manifest is stale: {args.check}")
+        print(f"validated generated manifest cases={len(suite['cases'])}")
+        return
+    if args.validate_only:
+        print(f"validated workloads={len(json.loads(args.spec.read_text())['workloads'])} cases={len(suite['cases'])}")
+        return
+    if args.output is None:
+        raise ValueError("--output is required unless --validate-only is used")
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(rendered)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/profile_fft_vectorized_ncu.sh b/scripts/profile_fft_vectorized_ncu.sh
new file mode 100755
index 0000000..5c66ac8
--- /dev/null
+++ b/scripts/profile_fft_vectorized_ncu.sh
@@ -0,0 +1,44 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+NCU=${NCU:-/usr/local/cuda-11.8/bin/ncu}
+BIN=${BIN:-"$ROOT/build/cubutterfly_bench"}
+OUTPUT_DIR=${OUTPUT_DIR:-"$ROOT/results/ncu_fft_vectorized"}
+BATCH=${BATCH:-16}
+
+if [[ ! -x "$NCU" || ! -x "$BIN" ]]; then
+    echo "missing profiler or benchmark: NCU=$NCU BIN=$BIN" >&2
+    exit 1
+fi
+mkdir -p "$OUTPUT_DIR"
+
+METRICS=${METRICS:-gpu__time_duration.sum,dram__bytes_read.sum,dram__bytes_write.sum,dram__throughput.avg.pct_of_peak_sustained_elapsed,lts__t_sector_hit_rate.pct,l1tex__t_sector_hit_rate.pct,l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_ld.sum,l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_st.sum,smsp__inst_executed.sum,smsp__sass_thread_inst_executed_op_fp32_pred_on.sum,sm__warps_active.avg.pct_of_peak_sustained_active,smsp__warp_issue_stalled_barrier_per_warp_active.pct,smsp__warp_issue_stalled_long_scoreboard_per_warp_active.pct,launch__registers_per_thread,launch__shared_mem_per_block,launch__waves_per_multiprocessor}
+COMMON=(--operator fft --precision fp32 --logN 20 --batch "$BATCH" --placement in-place
+        --normalization none --warmup 0 --repeat 1 --csv)
+
+profile() {
+    local label=$1
+    shift
+    "$NCU" --target-processes all --replay-mode kernel --cache-control none --clock-control base \
+        --launch-count 4 --metrics "$METRICS" --page raw --csv --force-overwrite \
+        --log-file "$OUTPUT_DIR/${label}.csv" "$@"
+}
+
+ONLINE=(--backend online-reorder --fft-core cufftdx-block --local-stages 10
+        --reorder-columns 1 --cross-twiddle recurrence)
+profile "post_vector_fixed_b${BATCH}" "$BIN" "${COMMON[@]}" "${ONLINE[@]}" \
+    --prefix-threads 512 --suffix-threads 512 --prefix-ept 8 --suffix-ept 8
+profile "post_vector_selected_b${BATCH}" "$BIN" "${COMMON[@]}" "${ONLINE[@]}" \
+    --prefix-threads 256 --suffix-threads 128 --prefix-ept 16 --suffix-ept 16
+profile "post_vector_cufft_b${BATCH}" "$BIN" "${COMMON[@]}" --backend cufft
+
+python3 "$ROOT/scripts/summarize_ncu.py" "$OUTPUT_DIR"/post_vector_*.csv \
+    --output "$OUTPUT_DIR/summary.csv"
+python3 "$ROOT/scripts/analyze_fft_vectorized_ncu.py" \
+    "$ROOT/results/ncu_scaling_crossovers/summary.csv" "$OUTPUT_DIR/summary.csv" \
+    --pre-timing-summary "$ROOT/results/v100_fft_pipeline_summary.csv" \
+    --post-timing-summary "$ROOT/results/v100_fft_pipeline_vectorized_summary.csv" \
+    --batch "$BATCH" --output "$OUTPUT_DIR/attribution.csv" \
+    --markdown "$OUTPUT_DIR/attribution.md"
+printf 'NCU attribution: %s\n' "$OUTPUT_DIR/attribution.md"
diff --git a/scripts/profile_fp64_fft_ncu.sh b/scripts/profile_fp64_fft_ncu.sh
new file mode 100755
index 0000000..4fffac4
--- /dev/null
+++ b/scripts/profile_fp64_fft_ncu.sh
@@ -0,0 +1,51 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+NCU=${NCU:-/usr/local/cuda-11.8/bin/ncu}
+BIN=${BIN:-"$ROOT/build/cubutterfly_bench"}
+OUTPUT_DIR=${OUTPUT_DIR:-"$ROOT/results/ncu_fp64_fft"}
+BATCH=${BATCH:-64}
+TIMING_SUMMARY=${TIMING_SUMMARY:-"$ROOT/results/fp64_address_logN16_summary.csv"}
+
+if [[ ! -x "$NCU" || ! -x "$BIN" ]]; then
+    echo "missing profiler or benchmark: NCU=$NCU BIN=$BIN" >&2
+    exit 1
+fi
+mkdir -p "$OUTPUT_DIR"
+
+METRICS=${METRICS:-gpu__time_duration.sum,dram__bytes_read.sum,dram__bytes_write.sum,dram__throughput.avg.pct_of_peak_sustained_elapsed,lts__t_sector_hit_rate.pct,l1tex__t_sector_hit_rate.pct,l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_ld.sum,l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_st.sum,smsp__inst_executed.sum,smsp__sass_thread_inst_executed_op_integer_pred_on.sum,smsp__sass_thread_inst_executed_op_fp64_pred_on.sum,sm__warps_active.avg.pct_of_peak_sustained_active,smsp__warp_issue_stalled_barrier_per_warp_active.pct,smsp__warp_issue_stalled_long_scoreboard_per_warp_active.pct,launch__registers_per_thread,launch__shared_mem_per_block,launch__waves_per_multiprocessor,launch__occupancy_limit_registers,launch__occupancy_limit_shared_mem,launch__occupancy_limit_warps}
+COMMON=(--operator fft --precision fp64 --logN 16 --batch "$BATCH" --placement out-of-place
+        --normalization none --warmup 0 --repeat 1 --csv)
+
+profile() {
+    local label=$1
+    shift
+    "$NCU" --target-processes all --replay-mode kernel --cache-control none --clock-control base \
+        --launch-count 4 --metrics "$METRICS" --page raw --csv --force-overwrite \
+        --log-file "$OUTPUT_DIR/${label}.csv" "$@"
+}
+
+profile "fp64_scalar_b${BATCH}" "$BIN" "${COMMON[@]}" \
+    --backend online-reorder --fft-core scalar --compute-unit radix4 \
+    --tile-threads 128 --local-stages 8 --reorder-columns 1 --complex-multiply four-mul
+profile "fp64_cufftdx_b${BATCH}" "$BIN" "${COMMON[@]}" \
+    --backend online-reorder --fft-core cufftdx-block --local-stages 8 \
+    --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8
+profile "fp64_recurrence_b${BATCH}" "$BIN" "${COMMON[@]}" \
+    --backend online-reorder --fft-core cufftdx-block --local-stages 8 \
+    --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8 \
+    --cross-twiddle recurrence
+profile "fp64_xor_swizzle_b${BATCH}" "$BIN" "${COMMON[@]}" \
+    --backend online-reorder --fft-core cufftdx-block --local-stages 8 \
+    --prefix-threads 256 --prefix-ept 4 --suffix-threads 128 --suffix-ept 8 \
+    --cross-twiddle recurrence --shared-layout xor-swizzle
+profile "fp64_cufft_b${BATCH}" "$BIN" "${COMMON[@]}" --backend cufft
+
+python3 "$ROOT/scripts/summarize_ncu.py" "$OUTPUT_DIR"/fp64_*.csv \
+    --output "$OUTPUT_DIR/summary.csv"
+python3 "$ROOT/scripts/analyze_fp64_fft_ncu.py" "$OUTPUT_DIR/summary.csv" \
+    --batch "$BATCH" \
+    --timing-summary "$TIMING_SUMMARY" \
+    --output "$OUTPUT_DIR/analysis.csv" --markdown "$OUTPUT_DIR/analysis.md"
+printf 'FP64 NCU attribution: %s\n' "$OUTPUT_DIR/analysis.md"
diff --git a/scripts/profile_scaling_crossovers_ncu.sh b/scripts/profile_scaling_crossovers_ncu.sh
new file mode 100755
index 0000000..01c75ae
--- /dev/null
+++ b/scripts/profile_scaling_crossovers_ncu.sh
@@ -0,0 +1,69 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+NCU=${NCU:-/usr/local/cuda-11.8/bin/ncu}
+BIN=${BIN:-"$ROOT/build/cubutterfly_bench"}
+OUTPUT_DIR=${OUTPUT_DIR:-"$ROOT/results/ncu_scaling_crossovers"}
+
+if [[ ! -x "$NCU" || ! -x "$BIN" ]]; then
+    echo "missing profiler or benchmark: NCU=$NCU BIN=$BIN" >&2
+    exit 1
+fi
+mkdir -p "$OUTPUT_DIR"
+
+METRICS=${METRICS:-gpu__time_duration.sum,dram__bytes_read.sum,dram__bytes_write.sum,dram__throughput.avg.pct_of_peak_sustained_elapsed,lts__t_sector_hit_rate.pct,l1tex__t_sector_hit_rate.pct,l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_ld.sum,l1tex__data_bank_conflicts_pipe_lsu_mem_shared_op_st.sum,smsp__inst_executed.sum,smsp__sass_thread_inst_executed_op_fp32_pred_on.sum,sm__warps_active.avg.pct_of_peak_sustained_active,smsp__warp_issue_stalled_barrier_per_warp_active.pct,smsp__warp_issue_stalled_long_scoreboard_per_warp_active.pct,launch__registers_per_thread,launch__shared_mem_per_block,launch__waves_per_multiprocessor}
+
+profile() {
+    local label=$1
+    shift
+    "$NCU" --target-processes all --replay-mode kernel --cache-control none \
+        --clock-control base --launch-count 4 --metrics "$METRICS" --page raw --csv \
+        --force-overwrite --log-file "$OUTPUT_DIR/${label}.csv" "$@"
+}
+
+common_fft=(--operator fft --precision fp32 --placement in-place --normalization none \
+            --warmup 0 --repeat 1 --csv)
+
+for batch in 16 256 1024; do
+    profile "fft14_direct_b${batch}" "$BIN" "${common_fft[@]}" --logN 14 --batch "$batch" \
+        --backend temporal-tile --fft-core cufftdx-direct --tile-threads 1024
+    profile "fft14_cufft_b${batch}" "$BIN" "${common_fft[@]}" --logN 14 --batch "$batch" \
+        --backend cufft
+done
+
+for batch in 2 16 64; do
+    profile "fft18_online_b${batch}" "$BIN" "${common_fft[@]}" --logN 18 --batch "$batch" \
+        --backend online-reorder --fft-core cufftdx-block --local-stages 9 \
+        --reorder-columns 1 --cross-twiddle recurrence --prefix-threads 256 \
+        --suffix-threads 256 --prefix-ept 8 --suffix-ept 8
+    profile "fft18_cufft_b${batch}" "$BIN" "${common_fft[@]}" --logN 18 --batch "$batch" \
+        --backend cufft
+done
+
+for batch in 2 8 16; do
+    profile "fft20_online_b${batch}" "$BIN" "${common_fft[@]}" --logN 20 --batch "$batch" \
+        --backend online-reorder --fft-core cufftdx-block --local-stages 10 \
+        --reorder-columns 1 --cross-twiddle recurrence --prefix-threads 512 \
+        --suffix-threads 512 --prefix-ept 8 --suffix-ept 8
+    profile "fft20_cufft_b${batch}" "$BIN" "${common_fft[@]}" --logN 20 --batch "$batch" \
+        --backend cufft
+done
+
+for batch in 4 16; do
+    common_fwht=(--operator fwht --precision fp32 --logN 15 --batch "$batch" \
+                 --normalization none --warmup 0 --repeat 1 --csv)
+    profile "fwht15_online_b${batch}" "$BIN" "${common_fwht[@]}" \
+        --backend online-reorder --compute-unit radix4 --tile-threads 256 \
+        --local-stages 8 --reorder-columns 1
+    profile "fwht15_warp_b${batch}" "$BIN" "${common_fwht[@]}" \
+        --backend temporal-tile --local-exchange warp-register --compute-unit radix2 \
+        --tile-threads 256
+done
+
+python3 "$ROOT/scripts/summarize_ncu.py" "$OUTPUT_DIR"/*.csv \
+    --output "$OUTPUT_DIR/summary.csv"
+python3 "$ROOT/scripts/analyze_scaling_ncu.py" "$OUTPUT_DIR/summary.csv" \
+    --output "$OUTPUT_DIR/attribution.csv" \
+    --markdown "$OUTPUT_DIR/attribution.md"
+printf 'NCU summary: %s\n' "$OUTPUT_DIR/summary.csv"
diff --git a/scripts/reproduce_v100_analysis.sh b/scripts/reproduce_v100_analysis.sh
new file mode 100755
index 0000000..2106641
--- /dev/null
+++ b/scripts/reproduce_v100_analysis.sh
@@ -0,0 +1,107 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)
+cd "$ROOT"
+
+python3 scripts/generate_scaling_suite.py \
+  --spec config/v100_scaling_space.json \
+  --check config/v100_scaling_suite.json
+
+python3 scripts/generate_fft_pipeline.py \
+  --check config/v100_fft_pipeline_candidates.json
+
+python3 scripts/summarize_fft_pipeline.py \
+  results/v100_fft_pipeline_vectorized_raw.csv \
+  --output results/v100_fft_pipeline_vectorized_summary.csv \
+  --markdown results/v100_fft_pipeline_vectorized_report.md
+
+python3 scripts/generate_fft_dispatch.py \
+  --summary results/v100_fft_pipeline_vectorized_summary.csv \
+  --output config/v100_fft_dispatch.json
+
+python3 scripts/analyze_fft_pipeline_model.py \
+  results/v100_fft_pipeline_vectorized_summary.csv \
+  --output results/v100_fft_pipeline_model_evaluation.csv \
+  --calibrated-output results/v100_fft_pipeline_model_calibrated_evaluation.csv \
+  --metrics results/v100_fft_pipeline_model_metrics.json \
+  --markdown results/v100_fft_pipeline_model_report.md
+
+python3 scripts/summarize_scaling_suite.py \
+  results/v100_scaling_full_raw.csv \
+  --output results/v100_scaling_full_summary.csv \
+  --markdown results/v100_scaling_full_report.md
+
+python3 scripts/select_mapping.py --evaluate --top-k 3 \
+  --evaluation-output results/v100_mapping_selector_evaluation.csv \
+  --metrics-output results/v100_mapping_selector_metrics.json
+
+python3 scripts/summarize_external_baseline_suite.py \
+  results/v100_external_baselines_raw.csv \
+  --output results/v100_external_baselines_summary.csv \
+  --markdown results/v100_external_baselines_report.md
+
+python3 scripts/summarize_comprehensive_suite.py \
+  results/comprehensive_v100_full_raw.csv \
+  --output results/comprehensive_v100_full_summary.csv \
+  --markdown results/comprehensive_v100_full_report.md
+
+python3 scripts/summarize_comprehensive_suite.py \
+  results/comprehensive_v100_vectorized_fft_raw.csv \
+  --output results/comprehensive_v100_vectorized_fft_summary.csv \
+  --markdown results/comprehensive_v100_vectorized_fft_report.md \
+  --require-stable
+
+python3 scripts/summarize_ncu.py \
+  results/ncu_scaling_crossovers/fft*.csv \
+  results/ncu_scaling_crossovers/fwht*.csv \
+  --output results/ncu_scaling_crossovers/summary.csv
+
+python3 scripts/analyze_scaling_ncu.py \
+  results/ncu_scaling_crossovers/summary.csv \
+  --output results/ncu_scaling_crossovers/attribution.csv \
+  --markdown results/ncu_scaling_crossovers/attribution.md
+
+python3 scripts/summarize_ncu.py \
+  results/ncu_fft_vectorized/post_vector_*.csv \
+  --output results/ncu_fft_vectorized/summary.csv
+
+python3 scripts/analyze_fft_vectorized_ncu.py \
+  results/ncu_scaling_crossovers/summary.csv \
+  results/ncu_fft_vectorized/summary.csv \
+  --pre-timing-summary results/v100_fft_pipeline_summary.csv \
+  --post-timing-summary results/v100_fft_pipeline_vectorized_summary.csv \
+  --batch 16 \
+  --output results/ncu_fft_vectorized/attribution.csv \
+  --markdown results/ncu_fft_vectorized/attribution.md
+
+python3 scripts/analyze_fp64_fft_robustness.py \
+  results/fp64_robustness_batch_raw.csv \
+  --output results/fp64_robustness_batch_summary.csv \
+  --markdown results/fp64_robustness_batch_analysis.md
+
+python3 scripts/summarize_cubutterfly_designs.py \
+  results/fp64_robustness_mapping_coarse_raw.csv \
+  --output results/fp64_robustness_mapping_coarse_summary.csv
+
+python3 scripts/summarize_cubutterfly_designs.py \
+  results/fp64_robustness_crossover_*_raw.csv \
+  --output results/fp64_robustness_crossover_summary.csv
+
+python3 scripts/summarize_cubutterfly_designs.py \
+  results/fp64_robustness_logN*_confirm_raw.csv \
+  results/fp64_robustness_cufft_confirm_raw.csv \
+  --output results/fp64_robustness_confirm_summary.csv
+
+python3 scripts/summarize_ncu.py \
+  results/ncu_fp64_fft/fp64_*.csv \
+  --output results/ncu_fp64_fft/summary.csv
+
+python3 scripts/analyze_fp64_fft_ncu.py \
+  results/ncu_fp64_fft/summary.csv \
+  --timing-summary results/fp64_address_logN16_summary.csv \
+  --output results/ncu_fp64_fft/analysis.csv \
+  --markdown results/ncu_fp64_fft/analysis.md
+
+python3 scripts/check_repository.py
+printf 'V100 derived analyses reproduced from checked-in raw records.\n'
diff --git a/scripts/run_comprehensive_suite.py b/scripts/run_comprehensive_suite.py
index 92dc1b9..a08dbfd 100644
--- a/scripts/run_comprehensive_suite.py
+++ b/scripts/run_comprehensive_suite.py
@@ -126,17 +126,24 @@ def load_manifest(path):
         groups.setdefault(case["group"], []).append(case)
     comparable_fields = ("operator", "precision", "direction", "normalization", "placement", "logN", "element_stride", "output_order")
     for group, cases in groups.items():
-        contracts = {tuple(expected_semantics(case)[field] for field in comparable_fields) for case in cases}
+        contracts = {
+            tuple(expected_semantics(case)[field] for field in comparable_fields)
+            + (str(case.get("batch", "")),)
+            for case in cases
+        }
         if len(contracts) != 1:
             raise ValueError(f"comparison group {group} mixes semantic contracts")
     return document
 
 
-def selected_cases(document, mode, filters):
+def selected_cases(document, mode, filters, exact=False):
     tiers = {"quick"} if mode == "quick" else {"quick", "full"}
     cases = [case for case in document["cases"] if case["tier"] in tiers]
     if filters:
-        cases = [case for case in cases if any(token in case["id"] or token in case["group"] for token in filters)]
+        if exact:
+            cases = [case for case in cases if case["id"] in filters or case["group"] in filters]
+        else:
+            cases = [case for case in cases if any(token in case["id"] or token in case["group"] for token in filters)]
     if not cases:
         raise ValueError("case selection is empty")
     return cases
@@ -223,6 +230,7 @@ def main():
     parser.add_argument("--manifest", type=pathlib.Path, default=pathlib.Path("config/v100_comprehensive_suite.json"))
     parser.add_argument("--mode", choices=("quick", "full"), default="quick")
     parser.add_argument("--only", nargs="+", help="Run case ids/groups containing any supplied token.")
+    parser.add_argument("--exact", action="store_true", help="Require --only tokens to equal a case id or group.")
     parser.add_argument("--output", "-o", type=pathlib.Path, default=pathlib.Path("results/comprehensive_v100_quick_raw.csv"))
     parser.add_argument("--resume", action="store_true")
     parser.add_argument("--skip-verify", action="store_true")
@@ -234,7 +242,7 @@ def main():
     output_path = args.output if args.output.is_absolute() else root / args.output
     document = load_manifest(manifest_path)
     protocol = document["protocols"][args.mode]
-    cases = selected_cases(document, args.mode, args.only)
+    cases = selected_cases(document, args.mode, args.only, args.exact)
     existing = read_existing(output_path) if args.resume else []
     complete = {(row["suite_case_id"], int(row["trial"])) for row in existing if row.get("trial", "").isdigit()}
     records = list(existing)
@@ -250,6 +258,7 @@ def main():
         return
 
     preflights = {}
+    preflight_cache = {}
     for case, _ in pending:
         if case["id"] in preflights:
             continue
@@ -258,11 +267,16 @@ def main():
             continue
         verify_batch = min(case_batch(case, protocol), int(protocol["verify_batch"]))
         command = build_command(root, document, case, protocol, verify_batch, True)
+        cache_key = tuple(command)
+        if cache_key in preflight_cache:
+            preflights[case["id"]] = preflight_cache[cache_key]
+            continue
         print(f"verify case={case['id']} batch={verify_batch}", flush=True)
         record = execute(command)
         validate_record(case, verify_batch, record)
         if record.get("correct") != "1":
             raise RuntimeError(f"correctness preflight failed for {case['id']}: {record}")
+        preflight_cache[cache_key] = record
         preflights[case["id"]] = record
 
     for run_index, (case, trial) in enumerate(pending, 1):
diff --git a/scripts/run_external_baseline_suite.py b/scripts/run_external_baseline_suite.py
new file mode 100755
index 0000000..8683bb9
--- /dev/null
+++ b/scripts/run_external_baseline_suite.py
@@ -0,0 +1,155 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import json
+import pathlib
+import random
+import subprocess
+import sys
+import tempfile
+
+
+FIELDS = (
+    "case_id", "group", "trial", "implementation", "reference", "runner", "device",
+    "operator", "precision", "direction", "normalization", "placement", "output_order",
+    "logN", "N", "batch", "modulus", "modulus_bits", "warmup", "repeat", "backend",
+    "kernel_ms", "throughput_s", "correct",
+)
+
+
+def read_one_csv(text):
+    lines = [line for line in text.splitlines() if line.strip()]
+    for index, line in enumerate(lines):
+        if "kernel_ms" not in line or "," not in line:
+            continue
+        rows = list(csv.DictReader(lines[index:]))
+        if rows:
+            return rows[0]
+    raise ValueError(f"no benchmark CSV record found in output: {text[-500:]}")
+
+
+def expand(document):
+    cases = []
+    for workload in document["workloads"]:
+        for batch in workload["batches"]:
+            group = f"{workload['id']}-batch{batch}"
+            for implementation in workload["implementations"]:
+                cases.append({
+                    **workload,
+                    **implementation,
+                    "id": f"{workload['id']}_{implementation['id']}_b{batch}",
+                    "group": group,
+                    "batch": int(batch),
+                })
+    return cases
+
+
+def execute(root, case, protocol, fht_python, gpuntt_binary):
+    common = ["--logN", str(case["logN"]), "--batch", str(case["batch"]),
+              "--warmup", str(protocol["warmup"]), "--repeat", str(protocol["repeat"])]
+    if case["runner"] == "butterfly":
+        command = [str(root / "build/cubutterfly_bench"), "--operator", "fwht",
+                   "--precision", case["precision"], "--normalization", case["normalization"],
+                   *common, *case["args"], "--verify", "--csv"]
+        result = subprocess.run(command, cwd=root, text=True, capture_output=True, check=True)
+        row = read_one_csv(result.stdout)
+        correct = row.get("correct") == "1"
+        throughput = row.get("transforms_s", "")
+    elif case["runner"] == "ntt":
+        command = [str(root / "build/cuntt_bench"), *common, "--modulus", case["modulus"],
+                   *case["args"], "--verify", "--csv"]
+        result = subprocess.run(command, cwd=root, text=True, capture_output=True, check=True)
+        row = read_one_csv(result.stdout)
+        correct = row.get("correct") == "1"
+        throughput = row.get("kernel_ntt_s", "")
+    elif case["runner"] == "dao-fht":
+        with tempfile.TemporaryDirectory() as directory:
+            output = pathlib.Path(directory) / "dao.csv"
+            command = [str(fht_python), str(root / "scripts/benchmark_external_fht.py"),
+                       "--logNs", str(case["logN"]), "--dtypes", case["precision"],
+                       "--batch", str(case["batch"]), "--warmup", str(protocol["warmup"]),
+                       "--repeat", str(protocol["repeat"]), "--trials", "1",
+                       "--normalization", case["normalization"], "--sm70-patched",
+                       "--output", str(output)]
+            subprocess.run(command, cwd=root, text=True, capture_output=True, check=True)
+            with output.open() as source:
+                row = next(csv.DictReader(source))
+        correct = row.get("correct") == "1"
+        throughput = row.get("transforms_s", "")
+    elif case["runner"] == "gpuntt":
+        if gpuntt_binary is None:
+            raise ValueError("GPU-NTT cases require --gpuntt-binary")
+        command = [str(gpuntt_binary), str(case["logN"]), str(case["batch"]),
+                   str(protocol["warmup"]), str(protocol["repeat"]), "1",
+                   "1" if case.get("naturalize") else "0"]
+        result = subprocess.run(command, cwd=root, text=True, capture_output=True, check=True)
+        row = read_one_csv(result.stdout)
+        if row.get("modulus") != case["modulus"]:
+            raise RuntimeError(f"GPU-NTT modulus mismatch for {case['id']}: {row.get('modulus')}")
+        expected = "natural_mismatches=0" if case.get("naturalize") else "bit_reversed_mismatches=0"
+        correct = expected in result.stderr
+        throughput = row.get("kernel_ntt_s", "")
+    else:
+        raise ValueError(f"unsupported runner {case['runner']}")
+    if not correct:
+        raise RuntimeError(f"correctness failed for {case['id']}")
+    return {
+        "device": row.get("device", "Tesla V100-SXM2-16GB"),
+        "backend": row.get("backend", row.get("implementation", case["runner"])),
+        "kernel_ms": row["kernel_ms"],
+        "throughput_s": throughput,
+        "correct": 1,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Run matching-protocol Dao FHT and GPU-NTT baselines.")
+    parser.add_argument("--manifest", type=pathlib.Path, default=pathlib.Path("config/v100_external_baseline_suite.json"))
+    parser.add_argument("--output", type=pathlib.Path, default=pathlib.Path("results/v100_external_baselines_raw.csv"))
+    parser.add_argument("--fht-python", type=pathlib.Path, default=pathlib.Path(sys.executable))
+    parser.add_argument("--gpuntt-binary", type=pathlib.Path)
+    parser.add_argument("--resume", action="store_true")
+    parser.add_argument("--only", nargs="+")
+    args = parser.parse_args()
+    root = pathlib.Path(__file__).resolve().parents[1]
+    manifest = args.manifest if args.manifest.is_absolute() else root / args.manifest
+    output = args.output if args.output.is_absolute() else root / args.output
+    document = json.loads(manifest.read_text())
+    if document.get("schema_version") != 1:
+        raise ValueError("unsupported external baseline schema")
+    cases = expand(document)
+    if args.only:
+        cases = [case for case in cases if any(token in case["id"] or token in case["group"] for token in args.only)]
+    existing = []
+    if args.resume and output.exists():
+        with output.open() as source:
+            existing = list(csv.DictReader(source))
+    complete = {(row["case_id"], int(row["trial"])) for row in existing}
+    pending = [(case, trial) for case in cases for trial in range(1, int(document["protocol"]["trials"]) + 1)
+               if (case["id"], trial) not in complete]
+    random.Random(int(document["protocol"]["seed"])).shuffle(pending)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    records = list(existing)
+    for index, (case, trial) in enumerate(pending, 1):
+        print(f"[{index}/{len(pending)}] {case['id']} trial={trial}", flush=True)
+        measured = execute(root, case, document["protocol"], args.fht_python, args.gpuntt_binary)
+        record = {
+            "case_id": case["id"], "group": case["group"], "trial": trial,
+            "implementation": case["name"], "reference": int(case.get("reference", False)),
+            "runner": case["runner"], **measured,
+            "operator": case["operator"], "precision": case["precision"],
+            "direction": case["direction"], "normalization": case["normalization"],
+            "placement": case["placement"], "output_order": case.get("output_order", "natural"),
+            "logN": case["logN"], "N": 1 << int(case["logN"]), "batch": case["batch"],
+            "modulus": case.get("modulus", ""), "modulus_bits": case.get("modulus_bits", ""),
+            "warmup": document["protocol"]["warmup"], "repeat": document["protocol"]["repeat"],
+        }
+        records.append(record)
+        with output.open("w", newline="") as destination:
+            writer = csv.DictWriter(destination, fieldnames=FIELDS, lineterminator="\n")
+            writer.writeheader()
+            writer.writerows({field: row.get(field, "") for field in FIELDS} for row in records)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/run_fft_pipeline.py b/scripts/run_fft_pipeline.py
new file mode 100755
index 0000000..16d7b5e
--- /dev/null
+++ b/scripts/run_fft_pipeline.py
@@ -0,0 +1,142 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import json
+import pathlib
+import random
+import subprocess
+
+
+OUTPUT_FIELDS = (
+    "candidate_id", "group", "trial", "implementation", "reference", "static_score",
+    "mapping_id", "decomposition_count", "stages_per_decomposition", "segment_threads", "segment_ept",
+    "boundary_twiddles", "boundary_layouts", "boundary_residencies", "execution_group_count",
+    "execution_group_stages", "group_threads", "group_ept", "processing_unit",
+    "prefix_log_n", "suffix_log_n", "prefix_threads",
+    "suffix_threads", "prefix_ept", "suffix_ept", "cross_twiddle", "direct_boundary", "device",
+    "compute_capability", "operator", "precision", "direction", "normalization", "placement",
+    "backend", "fft_core", "logN", "N", "batch", "warmup", "repeat", "kernel_ms",
+    "points_s", "max_error", "correct",
+)
+
+
+def parse_record(output):
+    lines = [line for line in output.splitlines() if line.strip()]
+    for index, line in enumerate(lines):
+        if "kernel_ms" in line and "operator" in line:
+            rows = list(csv.DictReader(lines[index:]))
+            if rows:
+                return rows[0]
+    raise ValueError(f"no benchmark CSV row found: {output[-500:]}")
+
+
+def expand(document):
+    cases = []
+    shapes = {}
+    for candidate in document["runnable_candidates"]:
+        group = f"{candidate['mapping_id']}-batch{candidate['batch']}"
+        cases.append({**candidate, "group": group, "implementation": candidate["id"], "reference": False})
+        shapes[(candidate["mapping_id"], candidate["batch"])] = candidate
+    for (mapping_id, batch), seed in shapes.items():
+        cases.append({
+            **seed, "id": f"{mapping_id}_b{batch}_cufft", "group": f"{mapping_id}-batch{batch}",
+            "implementation": "cuFFT", "reference": True, "processing_unit": "vendor-baseline",
+            "prefix_log_n": 0, "suffix_log_n": 0, "prefix_threads": 0, "suffix_threads": 0,
+            "prefix_ept": 0, "suffix_ept": 0, "cross_twiddle": "none", "static_score": 0.0,
+            "direct_boundary": "none", "decomposition_count": 0, "stages_per_decomposition": [],
+            "segment_mappings": [], "boundaries": [], "execution_group_mappings": [],
+            "args": ["--operator", "fft", "--precision", seed["precision"], "--backend", "cufft",
+                     "--placement", seed["placement"], "--normalization", seed["normalization"]],
+        })
+    return cases
+
+
+def execute(binary, case, protocol):
+    command = [str(binary), *case["args"], "--logN", str(case["logN"]), "--batch", str(case["batch"]),
+               "--warmup", str(protocol["warmup"]), "--repeat", str(protocol["repeat"]), "--verify", "--csv"]
+    result = subprocess.run(command, text=True, capture_output=True, check=True)
+    row = parse_record(result.stdout)
+    if row.get("correct") != "1":
+        raise RuntimeError(f"correctness failed for {case['id']}: {row}")
+    return row
+
+
+def filter_existing(rows, cases):
+    valid_ids = {case["id"] for case in cases}
+    return [row for row in rows if row["candidate_id"] in valid_ids]
+
+
+def case_metadata(case, trial):
+    return {
+        "candidate_id": case["id"], "group": case["group"], "trial": trial,
+        "implementation": case["implementation"], "reference": int(case["reference"]),
+        "static_score": case["static_score"], "mapping_id": case["mapping_id"],
+        "decomposition_count": case["decomposition_count"],
+        "stages_per_decomposition": "x".join(map(str, case["stages_per_decomposition"])),
+        "segment_threads": "x".join(str(item["threads"]) for item in case.get("segment_mappings", [])),
+        "segment_ept": "x".join(str(item["ept"]) for item in case.get("segment_mappings", [])),
+        "boundary_twiddles": "x".join(item["cross_twiddle"] for item in case.get("boundaries", [])),
+        "boundary_layouts": "x".join(item["layout"] for item in case.get("boundaries", [])),
+        "boundary_residencies": "x".join(item.get("residency", "global-scratch")
+                                           for item in case.get("boundaries", [])),
+        "execution_group_count": case.get("execution_group_count", case["decomposition_count"]),
+        "execution_group_stages": "x".join(map(str, case.get("execution_group_stages", []))),
+        "group_threads": "x".join(str(item["threads"])
+                                    for item in case.get("execution_group_mappings", [])),
+        "group_ept": "x".join(str(item["ept"])
+                                for item in case.get("execution_group_mappings", [])),
+        "processing_unit": case["processing_unit"], "prefix_log_n": case["prefix_log_n"],
+        "suffix_log_n": case["suffix_log_n"], "prefix_threads": case["prefix_threads"],
+        "suffix_threads": case["suffix_threads"], "prefix_ept": case["prefix_ept"],
+        "suffix_ept": case["suffix_ept"], "cross_twiddle": case["cross_twiddle"],
+        "direct_boundary": case["direct_boundary"],
+    }
+
+
+def write_records(path, records):
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=OUTPUT_FIELDS, extrasaction="ignore", lineterminator="\n")
+        writer.writeheader()
+        writer.writerows(records)
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Benchmark generated FFT mapping candidates and cuFFT.")
+    parser.add_argument("--manifest", type=pathlib.Path, default=pathlib.Path("config/v100_fft_pipeline_candidates.json"))
+    parser.add_argument("--binary", type=pathlib.Path, default=pathlib.Path("build/cubutterfly_bench"))
+    parser.add_argument("--output", type=pathlib.Path, default=pathlib.Path("results/v100_fft_pipeline_raw.csv"))
+    parser.add_argument("--resume", action="store_true")
+    parser.add_argument("--only", nargs="+")
+    args = parser.parse_args()
+    document = json.loads(args.manifest.read_text())
+    cases = expand(document)
+    if args.only:
+        cases = [case for case in cases if any(token in case["id"] or token in case["group"] for token in args.only)]
+    existing = []
+    if args.resume and args.output.exists():
+        with args.output.open() as source:
+            existing = list(csv.DictReader(source))
+        existing = filter_existing(existing, cases)
+        cases_by_id = {case["id"]: case for case in cases}
+        for row in existing:
+            row.update(case_metadata(cases_by_id[row["candidate_id"]], int(row["trial"])))
+    complete = {(row["candidate_id"], int(row["trial"])) for row in existing}
+    pending = [(case, trial) for case in cases for trial in range(1, int(document["protocol"]["trials"]) + 1)
+               if (case["id"], trial) not in complete]
+    random.Random(int(document["protocol"]["seed"])).shuffle(pending)
+    records = list(existing)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    if args.resume:
+        write_records(args.output, records)
+    for index, (case, trial) in enumerate(pending, 1):
+        print(f"[{index}/{len(pending)}] {case['id']} trial={trial}", flush=True)
+        measured = execute(args.binary, case, document["protocol"])
+        record = {field: measured.get(field, "") for field in OUTPUT_FIELDS}
+        # Generated metadata owns these fields; benchmark output owns the timing fields.
+        record.update(case_metadata(case, trial))
+        records.append(record)
+        write_records(args.output, records)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/select_mapping.py b/scripts/select_mapping.py
new file mode 100755
index 0000000..89c98a1
--- /dev/null
+++ b/scripts/select_mapping.py
@@ -0,0 +1,322 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import json
+import math
+import pathlib
+import statistics
+
+
+SEMANTIC_FIELDS = (
+    "operator", "precision", "direction", "normalization", "placement", "logN",
+    "element_stride", "output_order", "modulus_bits",
+)
+EXTERNAL_BACKENDS = {"cufft", "vkfft"}
+
+
+def parse_args_list(values):
+    parsed = {}
+    index = 0
+    while index < len(values):
+        token = values[index]
+        if token.startswith("--"):
+            key = token[2:].replace("-", "_")
+            if index + 1 < len(values) and not values[index + 1].startswith("--"):
+                parsed[key] = values[index + 1]
+                index += 2
+            else:
+                parsed[key] = "1"
+                index += 1
+        else:
+            index += 1
+    return parsed
+
+
+def load_cases(manifest_path):
+    document = json.loads(manifest_path.read_text())
+    return {
+        case["id"]: {**case, "parameters": parse_args_list(case.get("args", []))}
+        for case in document["cases"]
+    }
+
+
+def load_rows(summary_path, cases, internal_only=True):
+    with summary_path.open() as source:
+        rows = list(csv.DictReader(source))
+    output = []
+    for row in rows:
+        case = cases.get(row["case_id"])
+        if case is None or row.get("correct") != "1":
+            continue
+        parameters = case["parameters"]
+        backend = parameters.get("backend", row.get("backend", ""))
+        if internal_only and (backend in EXTERNAL_BACKENDS or not row["implementation"].startswith(("cuButterfly", "cuNTT"))):
+            continue
+        output.append({
+            **row,
+            "batch": int(row["performance_batch"]),
+            "logN_int": int(row["logN"]),
+            "kernel_ms": float(row["median_kernel_ms"]),
+            "throughput": float(row["billion_points_s"]),
+            "parameters": parameters,
+            "mapping_family": backend,
+            "processing_unit": processing_unit(row, parameters),
+        })
+    return output
+
+
+def processing_unit(row, parameters):
+    if parameters.get("fft_core"):
+        return parameters["fft_core"]
+    if parameters.get("local_exchange") == "warp-register":
+        return "warp-register"
+    return parameters.get("compute_unit", row.get("compute_unit", "auto"))
+
+
+def semantic_key(row):
+    return tuple(row.get(field, "") for field in SEMANTIC_FIELDS)
+
+
+def shape_key(row):
+    return semantic_key(row) + (row["batch"],)
+
+
+def interpolate_log_latency(samples, target_batch):
+    points = sorted((math.log2(row["batch"]), math.log(row["kernel_ms"])) for row in samples)
+    if not points:
+        return None, "measurement-required"
+    if len(points) == 1:
+        return math.exp(points[0][1]), "single-point"
+    target = math.log2(target_batch)
+    lower = [point for point in points if point[0] < target]
+    upper = [point for point in points if point[0] > target]
+    if lower and upper:
+        left, right = lower[-1], upper[0]
+        confidence = "interpolated"
+        anchor = left
+    elif lower:
+        left, right = points[-2], points[-1]
+        confidence = "extrapolated-high"
+        anchor = right
+    else:
+        left, right = points[0], points[1]
+        confidence = "extrapolated-low"
+        anchor = left
+    slope = (right[1] - left[1]) / (right[0] - left[0])
+    # Latency cannot improve indefinitely with more work, and a batch doubling
+    # cannot require more than twice the work in this fixed-contract model.
+    slope = min(1.0, max(0.0, slope))
+    predicted = anchor[1] + slope * (target - anchor[0])
+    return math.exp(predicted), confidence
+
+
+def hardware_context(row, hardware):
+    points = (1 << row["logN_int"]) * row["batch"]
+    word_bytes = {"fp16": 2, "bf16": 2, "fp32": 4, "fp64": 8,
+                  "uint32": 4, "uint64": 8}.get(row["precision"], 4)
+    working_set = points * word_bytes * 2
+    sm_count = int(hardware["sm_count"])
+    parameters = row["parameters"]
+    threads = int(parameters.get("tile_threads", parameters.get("prefix_threads", 0)) or 0)
+    return {
+        "total_points": points,
+        "working_set_bytes": working_set,
+        "working_set_over_l2": working_set / int(hardware["l2_bytes"]),
+        "batch_per_sm": row["batch"] / sm_count,
+        "configured_threads": threads,
+        "legal": threads <= int(hardware["threads_per_sm"]),
+    }
+
+
+def explanation(row, context, confidence):
+    factors = [confidence]
+    if context["batch_per_sm"] < 1.0:
+        factors.append("batch concurrency below one transform per SM")
+    else:
+        factors.append("batch concurrency covers all SMs")
+    if context["working_set_over_l2"] <= 1.0:
+        factors.append("estimated two-buffer working set fits L2")
+    else:
+        factors.append(f"estimated working set is {context['working_set_over_l2']:.1f}x L2")
+    if row["mapping_family"] in ("online-reorder", "compact-stage"):
+        factors.append("boundary permutation is fused with the required store")
+    if row["processing_unit"] == "warp-register":
+        factors.append("local exchange is register-resident")
+    return "; ".join(factors)
+
+
+def ncu_implementation(row):
+    if row["operator"] == "fft":
+        return "direct" if row["parameters"].get("fft_core") == "cufftdx-direct" else "online"
+    if row["operator"] == "fwht":
+        return "warp" if row["processing_unit"] == "warp-register" else "online"
+    return ""
+
+
+def counter_evidence(row, ncu_rows):
+    implementation = ncu_implementation(row)
+    match = next((item for item in ncu_rows
+                  if item["operator"] == row["operator"]
+                  and int(item["logN"]) == row["logN_int"]
+                  and item["implementation"] == implementation
+                  and int(item["batch"]) == row["batch"]), None)
+    if match is None:
+        return ""
+    waves = float(match["total_waves_per_sm"])
+    registers = float(match["registers_per_thread"])
+    barrier = float(match["barrier_stall_pct"])
+    scoreboard = float(match["long_scoreboard_stall_pct"])
+    factors = [f"NCU {waves:.2f} waves/SM"]
+    if waves < 1.0:
+        factors.append("grid underfills the GPU")
+    if registers >= 200:
+        factors.append(f"register-limited at {registers:.0f} registers/thread")
+    if barrier >= 10.0:
+        factors.append(f"barrier stalls {barrier:.1f}%")
+    if scoreboard >= 20.0:
+        factors.append(f"scoreboard stalls {scoreboard:.1f}%")
+    return ", ".join(factors)
+
+
+def rank_shape(target_rows, all_rows, hardware, excluded_shape=None, ncu_rows=()):
+    ranked = []
+    for target in target_rows:
+        training = [row for row in all_rows
+                    if semantic_key(row) == semantic_key(target)
+                    and row["implementation"] == target["implementation"]
+                    and (excluded_shape is None or shape_key(row) != excluded_shape)]
+        predicted_ms, confidence = interpolate_log_latency(training, target["batch"])
+        context = hardware_context(target, hardware)
+        if not context["legal"] or predicted_ms is None:
+            continue
+        reason = explanation(target, context, confidence)
+        counters = counter_evidence(target, ncu_rows)
+        if counters:
+            reason += "; " + counters
+        ranked.append({
+            "implementation": target["implementation"],
+            "mapping_family": target["mapping_family"],
+            "processing_unit": target["processing_unit"],
+            "predicted_kernel_ms": predicted_ms,
+            "confidence": confidence,
+            "reason": reason,
+            "parameters": target["parameters"],
+        })
+    ranked.sort(key=lambda row: row["predicted_kernel_ms"])
+    return ranked
+
+
+def evaluate(rows, hardware, top_k=3):
+    groups = {}
+    for row in rows:
+        groups.setdefault(shape_key(row), []).append(row)
+    records = []
+    for key, candidates in sorted(groups.items()):
+        if len(candidates) < 2:
+            continue
+        ranked = rank_shape(candidates, rows, hardware, excluded_shape=key)
+        if len(ranked) != len(candidates):
+            continue
+        actual = sorted(candidates, key=lambda row: row["kernel_ms"])
+        winner = actual[0]["implementation"]
+        predicted = ranked[0]["implementation"]
+        chosen_ms = next(row["kernel_ms"] for row in candidates if row["implementation"] == predicted)
+        regret = chosen_ms / actual[0]["kernel_ms"]
+        top_names = [row["implementation"] for row in ranked[:top_k]]
+        top3_names = [row["implementation"] for row in ranked[:3]]
+        records.append({
+            "operator": candidates[0]["operator"],
+            "precision": candidates[0]["precision"],
+            "logN": candidates[0]["logN_int"],
+            "batch": candidates[0]["batch"],
+            "candidates": len(candidates),
+            "measured_winner": winner,
+            "predicted_winner": predicted,
+            "top1_correct": int(predicted == winner),
+            "topk_contains_winner": int(winner in top_names),
+            "top3_contains_winner": int(winner in top3_names),
+            "regret": regret,
+            "confidence": ranked[0]["confidence"],
+        })
+    if not records:
+        raise ValueError("no multi-candidate shapes can be evaluated")
+    regrets = [row["regret"] for row in records]
+    metrics = {
+        "method": "leave-one-complete-shape-out log-latency interpolation",
+        "scope": "V100 calibrated internal candidates",
+        "evaluated_shapes": len(records),
+        "top_k": top_k,
+        "top1_accuracy": statistics.mean(row["top1_correct"] for row in records),
+        "topk_recall": statistics.mean(row["topk_contains_winner"] for row in records),
+        "top3_recall": statistics.mean(row["top3_contains_winner"] for row in records),
+        "geomean_regret": math.exp(statistics.mean(math.log(value) for value in regrets)),
+        "worst_regret": max(regrets),
+        "mean_candidates": statistics.mean(row["candidates"] for row in records),
+        "mean_returned": statistics.mean(min(top_k, row["candidates"]) for row in records),
+    }
+    metrics["search_space_reduction"] = 1.0 - metrics["mean_returned"] / metrics["mean_candidates"]
+    metrics["top1_search_space_reduction"] = 1.0 - 1.0 / metrics["mean_candidates"]
+    return records, metrics
+
+
+def write_evaluation(path, records):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=records[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        for row in records:
+            formatted = dict(row)
+            formatted["regret"] = f"{row['regret']:.6f}"
+            writer.writerow(formatted)
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Select a calibrated cuButterfly mapping for a covered V100 workload.")
+    parser.add_argument("--summary", type=pathlib.Path, default=pathlib.Path("results/v100_scaling_full_summary.csv"))
+    parser.add_argument("--manifest", type=pathlib.Path, default=pathlib.Path("config/v100_scaling_suite.json"))
+    parser.add_argument("--hardware", type=pathlib.Path, default=pathlib.Path("configs/hardware/v100_sxm2_16gb.json"))
+    parser.add_argument("--ncu-attribution", type=pathlib.Path,
+                        default=pathlib.Path("results/ncu_scaling_crossovers/attribution.csv"))
+    parser.add_argument("--top-k", type=int, default=3)
+    parser.add_argument("--include-external", action="store_true")
+    parser.add_argument("--evaluate", action="store_true")
+    parser.add_argument("--evaluation-output", type=pathlib.Path)
+    parser.add_argument("--metrics-output", type=pathlib.Path)
+    parser.add_argument("--operator")
+    parser.add_argument("--precision")
+    parser.add_argument("--logN", type=int)
+    parser.add_argument("--batch", type=int)
+    args = parser.parse_args()
+    if args.top_k < 1:
+        raise ValueError("--top-k must be positive")
+    cases = load_cases(args.manifest)
+    rows = load_rows(args.summary, cases, not args.include_external)
+    hardware = json.loads(args.hardware.read_text())
+    if args.evaluate:
+        records, metrics = evaluate(rows, hardware, args.top_k)
+        if args.evaluation_output:
+            write_evaluation(args.evaluation_output, records)
+        rendered = json.dumps(metrics, indent=2) + "\n"
+        if args.metrics_output:
+            args.metrics_output.parent.mkdir(parents=True, exist_ok=True)
+            args.metrics_output.write_text(rendered)
+        print(rendered, end="")
+        return
+    required = (args.operator, args.precision, args.logN, args.batch)
+    if any(value is None for value in required):
+        raise ValueError("selection requires --operator, --precision, --logN, and --batch")
+    candidates = [row for row in rows if row["operator"] == args.operator
+                  and row["precision"] == args.precision and row["logN_int"] == args.logN
+                  and row["batch"] == args.batch]
+    if not candidates:
+        raise ValueError("workload is outside the calibrated manifest; measurement is required")
+    ncu_rows = []
+    if args.ncu_attribution.exists():
+        with args.ncu_attribution.open() as source:
+            ncu_rows = list(csv.DictReader(source))
+    ranked = rank_shape(candidates, rows, hardware, excluded_shape=shape_key(candidates[0]), ncu_rows=ncu_rows)
+    print(json.dumps({"hardware": hardware["name"], "candidates": ranked[:args.top_k]}, indent=2))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/summarize_comprehensive_suite.py b/scripts/summarize_comprehensive_suite.py
index 1ca58e4..23b8895 100644
--- a/scripts/summarize_comprehensive_suite.py
+++ b/scripts/summarize_comprehensive_suite.py
@@ -13,7 +13,7 @@
 )
 
 CONFIG_FIELDS = (
-    "backend", "compute_unit", "fft_core", "local_exchange", "cross_twiddle",
+    "backend", "compute_unit", "fft_core", "local_exchange", "shared_layout", "cross_twiddle",
 )
 
 
@@ -182,7 +182,7 @@ def write_markdown(path, rows, external_evidence):
                 f"{row['throughput_vs_basis']:.3f}x | {row['basis_implementation']} | "
                 f"{row['stability_class']} |")
         lines.append("")
-    lines += ["## External Coverage Gaps", ""]
+    lines += ["## External Evidence", ""]
     if external_evidence:
         for item in external_evidence:
             lines.append(
diff --git a/scripts/summarize_cubutterfly_designs.py b/scripts/summarize_cubutterfly_designs.py
index 29d4ceb..fbff475 100644
--- a/scripts/summarize_cubutterfly_designs.py
+++ b/scripts/summarize_cubutterfly_designs.py
@@ -5,7 +5,7 @@
 import statistics
 
 
-CONFIG_FIELDS = ("backend", "compute_unit", "complex_multiply", "cross_twiddle", "local_exchange", "fft_core", "stage_space", "tile_threads", "prefix_threads", "suffix_threads", "prefix_ept", "suffix_ept", "prefix_units_per_cta", "suffix_units_per_cta", "local_stages", "reorder_columns", "warp_stages", "pipeline_warps", "stage_handoff")
+CONFIG_FIELDS = ("backend", "compute_unit", "complex_multiply", "cross_twiddle", "local_exchange", "shared_layout", "fft_core", "stage_space", "tile_threads", "prefix_threads", "suffix_threads", "prefix_ept", "suffix_ept", "prefix_units_per_cta", "suffix_units_per_cta", "local_stages", "reorder_columns", "warp_stages", "pipeline_warps", "stage_handoff")
 GROUP_FIELDS = ("operator", "precision", "direction", "normalization", "placement", "logN", "N", "batch", "element_stride", "batch_stride")
 
 
@@ -24,7 +24,8 @@ def main():
 
     groups = {}
     for row in rows:
-        key = tuple(row.get(field, "0") for field in GROUP_FIELDS + CONFIG_FIELDS)
+        key = tuple((row.get(field) or "linear") if field == "shared_layout" else row.get(field, "0")
+                    for field in GROUP_FIELDS + CONFIG_FIELDS)
         groups.setdefault(key, []).append(row)
 
     summaries = []
diff --git a/scripts/summarize_external_baseline_suite.py b/scripts/summarize_external_baseline_suite.py
new file mode 100755
index 0000000..72c0561
--- /dev/null
+++ b/scripts/summarize_external_baseline_suite.py
@@ -0,0 +1,84 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+import statistics
+
+
+def summarize(rows, max_relative_range=0.03, timing_floor_ms=0.020):
+    groups = {}
+    for row in rows:
+        groups.setdefault((row["group"], row["implementation"]), []).append(row)
+    summaries = []
+    for (_, _), samples in sorted(groups.items()):
+        times = [float(row["kernel_ms"]) for row in samples]
+        ordered = sorted(times)
+        central = ordered[1:-1] if len(ordered) >= 5 else ordered
+        median = statistics.median(times)
+        relative_range = (max(times) - min(times)) / median
+        central_relative_range = (max(central) - min(central)) / median
+        if central_relative_range > max_relative_range:
+            stability = "unstable"
+        elif relative_range > max_relative_range:
+            stability = "stable-with-outlier"
+        else:
+            stability = "stable"
+        first = samples[0]
+        summaries.append({
+            **{field: first[field] for field in ("group", "implementation", "reference", "runner", "operator",
+                                                  "precision", "direction", "normalization", "placement", "output_order",
+                                                  "logN", "N", "batch", "modulus", "modulus_bits", "warmup", "repeat")},
+            "trials": len(samples),
+            "median_kernel_ms": median,
+            "min_kernel_ms": min(times),
+            "max_kernel_ms": max(times),
+            "relative_range": relative_range,
+            "central_relative_range": central_relative_range,
+            "stability_class": stability,
+            "timing_quality": "below-timing-floor" if median < timing_floor_ms else stability,
+            "correct": int(all(row["correct"] == "1" for row in samples)),
+        })
+    by_group = {}
+    for row in summaries:
+        by_group.setdefault(row["group"], []).append(row)
+    for rows_in_group in by_group.values():
+        reference = next(row for row in rows_in_group if row["reference"] == "1")
+        for row in rows_in_group:
+            row["throughput_vs_reference"] = reference["median_kernel_ms"] / row["median_kernel_ms"]
+    return summaries
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Summarize the matching-protocol external baseline suite.")
+    parser.add_argument("input", type=pathlib.Path)
+    parser.add_argument("--output", required=True, type=pathlib.Path)
+    parser.add_argument("--markdown", type=pathlib.Path)
+    args = parser.parse_args()
+    with args.input.open() as source:
+        rows = list(csv.DictReader(source))
+    summaries = summarize(rows)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    with args.output.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=summaries[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        for row in summaries:
+            formatted = dict(row)
+            for field in ("median_kernel_ms", "min_kernel_ms", "max_kernel_ms", "relative_range",
+                          "central_relative_range", "throughput_vs_reference"):
+                formatted[field] = f"{row[field]:.6f}"
+            writer.writerow(formatted)
+    if args.markdown:
+        lines = ["# V100 Matching-Protocol External Baselines", "",
+                 "All rows use 1000 warmups, 100 repetitions, five independent process trials, and correctness checks.", "",
+                 "Rows below 0.020 ms are retained but are not used for stable latency claims.", "",
+                 "| Operator | logN | Batch | Output | Implementation | Median ms | vs cuButterfly/cuNTT | Timing quality |",
+                 "|:--|--:|--:|:--|:--|--:|--:|:--|"]
+        for row in summaries:
+            lines.append(f"| {row['operator']} | {row['logN']} | {int(row['batch']):,} | {row['output_order']} | "
+                         f"{row['implementation']} | {row['median_kernel_ms']:.6f} | {row['throughput_vs_reference']:.3f}x | {row['timing_quality']} |")
+        args.markdown.parent.mkdir(parents=True, exist_ok=True)
+        args.markdown.write_text("\n".join(lines) + "\n")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/summarize_fft_pipeline.py b/scripts/summarize_fft_pipeline.py
new file mode 100755
index 0000000..65ae10e
--- /dev/null
+++ b/scripts/summarize_fft_pipeline.py
@@ -0,0 +1,102 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+import statistics
+
+
+CONFIG_FIELDS = ("candidate_id", "group", "implementation", "reference", "static_score", "mapping_id",
+                 "decomposition_count", "stages_per_decomposition", "segment_threads", "segment_ept",
+                 "boundary_twiddles", "boundary_layouts", "boundary_residencies", "execution_group_count",
+                 "execution_group_stages", "group_threads", "group_ept", "processing_unit",
+                 "prefix_log_n", "suffix_log_n",
+                 "prefix_threads", "suffix_threads",
+                 "prefix_ept", "suffix_ept", "cross_twiddle", "direct_boundary", "operator", "precision", "direction",
+                 "normalization", "placement", "backend", "fft_core", "logN", "N", "batch")
+
+
+def summarize(rows):
+    groups = {}
+    for row in rows:
+        groups.setdefault(row["candidate_id"], []).append(row)
+    candidates = []
+    for samples in groups.values():
+        times = [float(row["kernel_ms"]) for row in samples]
+        first = samples[0]
+        candidates.append({
+            **{field: first.get(field, "") for field in CONFIG_FIELDS},
+            "trials": len(samples), "median_kernel_ms": statistics.median(times),
+            "min_kernel_ms": min(times), "max_kernel_ms": max(times),
+            "correct": int(all(row["correct"] == "1" for row in samples)),
+        })
+    by_shape = {}
+    for row in candidates:
+        by_shape.setdefault(row["group"], []).append(row)
+    output = []
+    def shape_key(shape_rows):
+        first = shape_rows[0]
+        try:
+            return (int(first["logN"]), int(first["batch"]), first["group"])
+        except (KeyError, TypeError, ValueError):
+            return (0, 0, first["group"])
+
+    ordered_shapes = sorted(by_shape.values(), key=shape_key)
+    for shape_rows in ordered_shapes:
+        reference = next(row for row in shape_rows if row["reference"] == "1")
+        internal = sorted((row for row in shape_rows if row["reference"] != "1"),
+                          key=lambda row: row["median_kernel_ms"])
+        for rank, row in enumerate(internal, 1):
+            output.append({
+                **row, "rank": rank, "cufft_median_ms": reference["median_kernel_ms"],
+                "throughput_vs_cufft": reference["median_kernel_ms"] / row["median_kernel_ms"],
+                "slowdown_vs_internal_best": row["median_kernel_ms"] / internal[0]["median_kernel_ms"],
+            })
+    return output
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        for row in rows:
+            formatted = dict(row)
+            for field in ("median_kernel_ms", "min_kernel_ms", "max_kernel_ms", "cufft_median_ms",
+                          "throughput_vs_cufft", "slowdown_vs_internal_best"):
+                formatted[field] = f"{row[field]:.6f}"
+            writer.writerow(formatted)
+
+
+def write_markdown(path, rows):
+    winners = [row for row in rows if row["rank"] == 1]
+    lines = ["# Generated V100 FFT Pipeline Search", "",
+             "| logN | Batch | Logical stages | Physical groups | Threads/EPT | Residency | Median ms | cuFFT ms | Throughput ratio |",
+             "|--:|--:|:--|:--|:--|:--|--:|--:|--:|"]
+    for row in winners:
+        physical_groups = row["execution_group_stages"] or row["stages_per_decomposition"]
+        threads = row["group_threads"] or row["segment_threads"]
+        ept = row["group_ept"] or row["segment_ept"]
+        lines.append(f"| {row['logN']} | {row['batch']} | {row['stages_per_decomposition']} | "
+                     f"{physical_groups} | {threads} / {ept} | {row['boundary_residencies']} | "
+                     f"{row['median_kernel_ms']:.6f} | {row['cufft_median_ms']:.6f} | "
+                     f"{row['throughput_vs_cufft']:.3f}x |")
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines) + "\n")
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Rank generated FFT mapping candidates.")
+    parser.add_argument("input", type=pathlib.Path)
+    parser.add_argument("--output", required=True, type=pathlib.Path)
+    parser.add_argument("--markdown", type=pathlib.Path)
+    args = parser.parse_args()
+    with args.input.open() as source:
+        rows = list(csv.DictReader(source))
+    summary = summarize(rows)
+    write_csv(args.output, summary)
+    if args.markdown:
+        write_markdown(args.markdown, summary)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/summarize_ncu.py b/scripts/summarize_ncu.py
index 9dd705e..6e5b4d5 100755
--- a/scripts/summarize_ncu.py
+++ b/scripts/summarize_ncu.py
@@ -18,6 +18,7 @@
     "smsp__inst_executed.sum": ("warp_instructions", 1.0),
     "smsp__sass_thread_inst_executed_op_integer_pred_on.sum": ("integer_thread_instructions", 1.0),
     "smsp__sass_thread_inst_executed_op_fp32_pred_on.sum": ("fp32_thread_instructions", 1.0),
+    "smsp__sass_thread_inst_executed_op_fp64_pred_on.sum": ("fp64_thread_instructions", 1.0),
     "smsp__inst_executed_pipe_tensor.sum": ("tensor_warp_instructions", 1.0),
     "sm__pipe_tensor_cycles_active.avg.pct_of_peak_sustained_active": ("tensor_active_pct", 1.0),
     "sm__warps_active.avg.pct_of_peak_sustained_active": ("active_warps_pct", 1.0),
diff --git a/scripts/summarize_scaling_suite.py b/scripts/summarize_scaling_suite.py
new file mode 100755
index 0000000..d8f9ebc
--- /dev/null
+++ b/scripts/summarize_scaling_suite.py
@@ -0,0 +1,145 @@
+#!/usr/bin/env python3
+import argparse
+import csv
+import pathlib
+
+from summarize_comprehensive_suite import read_rows, summarize
+
+
+SERIES_FIELDS = (
+    "operator", "precision", "direction", "normalization", "placement", "logN",
+    "element_stride", "output_order", "implementation",
+)
+
+
+def analyze(rows, saturation_fraction=0.90, timing_floor_ms=0.020):
+    summary = summarize(rows)
+    series = {}
+    for row in summary:
+        key = tuple(row.get(field, "") for field in SERIES_FIELDS)
+        series.setdefault(key, []).append(row)
+    output = []
+    for series_rows in series.values():
+        ordered = sorted(series_rows, key=lambda row: int(row["performance_batch"]))
+        eligible = [row for row in ordered
+                    if row["median_kernel_ms"] >= timing_floor_ms and row["stability_class"] != "unstable"]
+        saturation_basis = eligible if eligible else ordered
+        peak = max(row["billion_points_s"] for row in saturation_basis)
+        peak_row = max(saturation_basis, key=lambda row: row["billion_points_s"])
+        saturated = [row for row in saturation_basis if row["billion_points_s"] >= saturation_fraction * peak]
+        saturation_batch = min(int(row["performance_batch"]) for row in saturated)
+        batch_one = next((row for row in ordered if int(row["performance_batch"]) == 1), None)
+        for row in ordered:
+            batch = int(row["performance_batch"])
+            fraction = row["billion_points_s"] / peak if peak else 0.0
+            if batch_one and batch_one["billion_points_s"]:
+                throughput_speedup = row["billion_points_s"] / batch_one["billion_points_s"]
+                batch_efficiency = throughput_speedup / batch
+            else:
+                throughput_speedup = 0.0
+                batch_efficiency = 0.0
+            region = "saturated" if fraction >= saturation_fraction else ("ramp" if fraction >= 0.5 else "launch-limited")
+            timing_quality = "below-timing-floor" if row["median_kernel_ms"] < timing_floor_ms else row["stability_class"]
+            eligible_for_saturation = row in saturation_basis
+            output.append({
+                **row,
+                "peak_billion_points_s": peak,
+                "peak_batch": int(peak_row["performance_batch"]),
+                "fraction_of_peak": fraction,
+                "saturation_fraction": saturation_fraction,
+                "saturation_batch": saturation_batch,
+                "throughput_speedup_vs_batch1": throughput_speedup,
+                "batch_efficiency_vs_batch1": batch_efficiency,
+                "scaling_region": region,
+                "timing_floor_ms": timing_floor_ms,
+                "timing_quality": timing_quality,
+                "eligible_for_saturation": int(eligible_for_saturation),
+            })
+    return sorted(output, key=lambda row: (
+        row["operator"], int(row["logN"]), row["implementation"], int(row["performance_batch"])))
+
+
+def write_csv(path, rows):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", newline="") as destination:
+        writer = csv.DictWriter(destination, fieldnames=rows[0].keys(), lineterminator="\n")
+        writer.writeheader()
+        for row in rows:
+            formatted = dict(row)
+            for field in (
+                "median_kernel_ms", "min_kernel_ms", "max_kernel_ms", "basis_kernel_ms",
+                "million_transforms_s", "billion_points_s", "peak_billion_points_s",
+            ):
+                formatted[field] = f"{row[field]:.9f}"
+            for field in (
+                "relative_range", "central_relative_range", "throughput_vs_basis",
+                "fraction_of_peak", "saturation_fraction", "throughput_speedup_vs_batch1",
+                "batch_efficiency_vs_batch1",
+                "timing_floor_ms",
+            ):
+                formatted[field] = f"{row[field]:.6f}"
+            writer.writerow(formatted)
+
+
+def write_markdown(path, rows):
+    series = {}
+    for row in rows:
+        key = (row["operator"], row["precision"], row["logN"], row["implementation"])
+        series.setdefault(key, []).append(row)
+    lines = [
+        "# V100 Orthogonal Length/Batch Scaling", "",
+        "`Batch@90%` is the smallest measured batch reaching 90% of that",
+        "implementation's peak measured `Gpoint/s` at fixed transform length.",
+        "Rows below the configured 0.020 ms timing floor are retained but are not",
+        "used as stable latency claims or peak/saturation references.", "",
+        "## Saturation Summary", "",
+        "| Operator | Numeric | logN | Implementation | Batch@90% | Peak batch | Peak Gpoint/s | Batch-1 ms |",
+        "|:--|:--|--:|:--|--:|--:|--:|--:|",
+    ]
+    for key, series_rows in sorted(series.items(), key=lambda item: (item[0][0], int(item[0][2]), item[0][3])):
+        first = series_rows[0]
+        batch_one = next((row for row in series_rows if int(row["performance_batch"]) == 1), None)
+        batch_one_text = f"{batch_one['median_kernel_ms']:.6f}" if batch_one else "-"
+        lines.append(
+            f"| {key[0]} | {key[1]} | {key[2]} | {key[3]} | {first['saturation_batch']} | "
+            f"{first['peak_batch']} | {first['peak_billion_points_s']:.3f} | {batch_one_text} |")
+    lines += ["", "## Detailed Scaling", "",
+              "| Operator | logN | Batch | Implementation | Median ms | Gpoint/s | Peak fraction | vs basis | Region | Timing quality |",
+              "|:--|--:|--:|:--|--:|--:|--:|--:|:--|:--|"]
+    for row in rows:
+        lines.append(
+            f"| {row['operator']} | {row['logN']} | {int(row['performance_batch']):,} | "
+            f"{row['implementation']} | {row['median_kernel_ms']:.6f} | "
+            f"{row['billion_points_s']:.3f} | {row['fraction_of_peak']:.3f} | "
+            f"{row['throughput_vs_basis']:.3f}x | {row['scaling_region']} | {row['timing_quality']} |")
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines) + "\n")
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Summarize orthogonal length/batch scaling.")
+    parser.add_argument("inputs", nargs="+", type=pathlib.Path)
+    parser.add_argument("--output", "-o", required=True, type=pathlib.Path)
+    parser.add_argument("--markdown", type=pathlib.Path)
+    parser.add_argument("--saturation-fraction", type=float, default=0.90)
+    parser.add_argument("--timing-floor-ms", type=float, default=0.020)
+    parser.add_argument("--require-stable", action="store_true")
+    args = parser.parse_args()
+    if not 0.0 < args.saturation_fraction <= 1.0:
+        raise ValueError("saturation fraction must be in (0, 1]")
+    raw = []
+    for path in args.inputs:
+        raw.extend(read_rows(path))
+    if args.timing_floor_ms < 0.0:
+        raise ValueError("timing floor must be non-negative")
+    rows = analyze(raw, args.saturation_fraction, args.timing_floor_ms)
+    write_csv(args.output, rows)
+    if args.markdown:
+        write_markdown(args.markdown, rows)
+    unstable = sorted({row["case_id"] for row in rows if row["timing_quality"] == "unstable"})
+    if args.require_stable and unstable:
+        raise ValueError(f"unstable scaling cases: {unstable}")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/sweep_cubutterfly_designs.py b/scripts/sweep_cubutterfly_designs.py
index c5e595e..e64a301 100644
--- a/scripts/sweep_cubutterfly_designs.py
+++ b/scripts/sweep_cubutterfly_designs.py
@@ -176,6 +176,42 @@ def configurations(operator, precision, log_n, tile_threads, hierarchical_local_
                 "fft_core": "turbofft-generated", "tile_threads": 32, "local_stages": 0, "reorder_columns": 0, "warp_stages": 0,
                 "pipeline_warps": 0, "stage_space": 0,
             }
+    if operator == "fft" and precision == "fp64":
+        if 3 <= log_n <= 10:
+            yield {
+                "backend": "temporal-tile", "compute_unit": "auto", "complex_multiply": "four-mul",
+                "local_exchange": "shared", "fft_core": "cufftdx-block", "tile_threads": 32,
+                "local_stages": 0, "reorder_columns": 0, "warp_stages": 0,
+                "pipeline_warps": 0, "stage_space": 0,
+            }
+        for local_stages in hierarchical_local_stages:
+            remaining_stages = log_n - local_stages
+            if not (7 <= local_stages <= 9 and 7 <= remaining_stages <= 9):
+                continue
+            prefix_n = 1 << local_stages
+            suffix_n = 1 << remaining_stages
+            for prefix_threads in prefix_thread_options:
+                for prefix_ept in prefix_ept_options:
+                    if prefix_threads not in (128, 256, 512) or prefix_ept not in (4, 8) or \
+                            prefix_threads * prefix_ept < prefix_n or (prefix_threads * prefix_ept) % prefix_n:
+                        continue
+                    for suffix_threads in suffix_thread_options:
+                        for suffix_ept in suffix_ept_options:
+                            if suffix_threads not in (128, 256, 512) or suffix_ept not in (4, 8) or \
+                                    suffix_threads * suffix_ept < suffix_n or (suffix_threads * suffix_ept) % suffix_n:
+                                continue
+                            for cross_twiddle in ("table", "recurrence"):
+                                for shared_layout in ("linear", "xor-swizzle"):
+                                    yield {
+                                        "backend": "online-reorder", "compute_unit": "auto",
+                                        "complex_multiply": "four-mul", "cross_twiddle": cross_twiddle,
+                                        "local_exchange": "shared", "shared_layout": shared_layout,
+                                        "fft_core": "cufftdx-block", "tile_threads": 32,
+                                        "prefix_threads": prefix_threads, "suffix_threads": suffix_threads,
+                                        "prefix_ept": prefix_ept, "suffix_ept": suffix_ept,
+                                        "local_stages": local_stages, "reorder_columns": 1, "warp_stages": 0,
+                                        "pipeline_warps": 0, "stage_space": 0,
+                                    }
 
 
 def run(binary, operator, precision, config, log_n, direction, normalization, placement, batch, element_stride, batch_stride, warmup, repeat):
@@ -185,6 +221,7 @@ def run(binary, operator, precision, config, log_n, direction, normalization, pl
         "--complex-multiply", config["complex_multiply"],
         "--cross-twiddle", config.get("cross_twiddle", "table"),
         "--local-exchange", config["local_exchange"],
+        "--shared-layout", config.get("shared_layout", "linear"),
         "--fft-core", config["fft_core"],
         "--normalization", normalization, "--placement", placement,
         "--batch", str(batch), "--warmup", str(warmup), "--repeat", str(repeat), "--csv",
@@ -234,6 +271,7 @@ def main():
     parser.add_argument("--complex-multiplies", nargs="+", choices=("four-mul", "gauss3"), default=("four-mul", "gauss3"))
     parser.add_argument("--cross-twiddles", nargs="+", choices=("table", "recurrence"), default=("table",))
     parser.add_argument("--local-exchanges", nargs="+", choices=("shared", "warp-register"), default=("shared", "warp-register"))
+    parser.add_argument("--shared-layouts", nargs="+", choices=("linear", "xor-swizzle"), default=("linear", "xor-swizzle"))
     parser.add_argument("--fft-cores", nargs="+",
                         choices=("scalar", "thread-dft8", "cta-dft8", "wmma-dft8", "cufftdx-block", "cufftdx-direct", "cufftdx-resident", "turbofft-generated"),
                         default=("scalar", "thread-dft8", "cta-dft8", "wmma-dft8"))
@@ -293,6 +331,8 @@ def main():
                                     continue
                                 if config["local_exchange"] not in args.local_exchanges:
                                     continue
+                                if config.get("shared_layout", "linear") not in args.shared_layouts:
+                                    continue
                                 if config["fft_core"] not in args.fft_cores:
                                     continue
                                 if config["fft_core"] == "cufftdx-block" and config["backend"] == "online-reorder":
diff --git a/src/butterfly.cu b/src/butterfly.cu
index c905caa..5679394 100644
--- a/src/butterfly.cu
+++ b/src/butterfly.cu
@@ -11,6 +11,7 @@
 
 #include "cuntt/butterfly.hpp"
 #include "external_fft_units.cuh"
+#include "generated_fft_dispatch.cuh"
 #include "generated_unit_api.cuh"
 #include "stage_pipeline.cuh"
 
@@ -464,6 +465,136 @@ class ButterflyPlan::Impl {
         if (config_.log_n == 0 || config_.log_n > 20) {
             throw std::invalid_argument("butterfly log_n must be in [1, 20]");
         }
+        const bool explicit_stage_partition = !config_.stage_partition.empty();
+        if (config_.auto_select && explicit_stage_partition) {
+            throw std::invalid_argument("auto-select owns the stage partition");
+        }
+        if (config_.auto_select) {
+            const std::size_t contiguous_stride = std::size_t{1} << config_.log_n;
+            if (config_.op != ButterflyOperator::Fft || config_.precision != ButterflyPrecision::Fp32 ||
+                config_.inverse || config_.placement != ButterflyPlacement::InPlace || config_.normalize_inverse ||
+                config_.element_stride != 1 || (config_.batch_stride != 0 && config_.batch_stride != contiguous_stride)) {
+                throw std::invalid_argument(
+                    "generated FFT selection requires FP32 forward, in-place, contiguous, no-normalization semantics");
+            }
+            int device = 0;
+            cudaDeviceProp properties{};
+            CUB_CUDA_CHECK(cudaGetDevice(&device));
+            CUB_CUDA_CHECK(cudaGetDeviceProperties(&properties, device));
+            if (properties.major != 7 || properties.minor != 0) {
+                throw std::invalid_argument("generated FFT selection is calibrated only for V100 sm_70");
+            }
+            detail::GeneratedFftMapping mapping{};
+            if (!detail::select_generated_fft_mapping(config_.log_n, config_.batch, mapping)) {
+                throw std::invalid_argument("no generated V100 FFT mapping exists for this length and batch");
+            }
+            config_.backend         = ButterflyBackend::OnlineReorder;
+            config_.fft_core        = FftCore::CufftDxBlock;
+            config_.local_exchange  = LocalExchange::SharedMemory;
+            config_.local_stages    = mapping.local_stages;
+            config_.reorder_columns = 1;
+            config_.prefix_threads  = mapping.prefix_threads;
+            config_.suffix_threads  = mapping.suffix_threads;
+            config_.prefix_ept      = mapping.prefix_ept;
+            config_.suffix_ept      = mapping.suffix_ept;
+            config_.cross_twiddle   = mapping.recurrence_twiddle ? CrossTwiddleMode::Recurrence : CrossTwiddleMode::Table;
+            config_.direct_boundary = mapping.prefix_tiled_transpose
+                                          ? DirectBoundary::PrefixTiledTranspose
+                                          : (mapping.suffix_tiled_transpose ? DirectBoundary::TiledTranspose
+                                                                            : DirectBoundary::Strided);
+            config_.stage_partition = {mapping.local_stages, config_.log_n - mapping.local_stages};
+        }
+        if (config_.backend == ButterflyBackend::OnlineReorder && config_.stage_partition.empty()) {
+            config_.stage_partition = {config_.local_stages, config_.log_n - config_.local_stages};
+        }
+        if (!config_.stage_partition.empty()) {
+            std::uint32_t stage_sum = 0;
+            for (const auto stages : config_.stage_partition) {
+                if (stages == 0 || stages > config_.log_n || stage_sum > config_.log_n - stages)
+                    throw std::invalid_argument("stage partition must contain positive values summing to log_n");
+                stage_sum += stages;
+            }
+            if (stage_sum != config_.log_n)
+                throw std::invalid_argument("stage partition must sum to log_n");
+            if (config_.backend != ButterflyBackend::OnlineReorder) {
+                if (explicit_stage_partition)
+                    throw std::invalid_argument("explicit stage partitions currently require online-reorder");
+            } else {
+                if (config_.stage_partition.size() < 2 || config_.stage_partition.size() > 8)
+                    throw std::invalid_argument("online-reorder requires decomposition_count in [2, 8]");
+                config_.local_stages = config_.stage_partition.front();
+                if (config_.segment_mappings.empty()) {
+                    config_.segment_mappings.reserve(config_.stage_partition.size());
+                    for (std::size_t segment = 0; segment < config_.stage_partition.size(); ++segment) {
+                        FftSegmentMapping mapping;
+                        if (config_.stage_partition.size() == 2) {
+                            mapping.threads = segment == 0 ? config_.prefix_threads : config_.suffix_threads;
+                            mapping.ept = segment == 0 ? config_.prefix_ept : config_.suffix_ept;
+                        } else {
+                            mapping.threads = 256;
+                            mapping.ept = std::max(8U, (1U << config_.stage_partition[segment]) / mapping.threads);
+                        }
+                        config_.segment_mappings.push_back(mapping);
+                    }
+                }
+                if (config_.segment_mappings.size() != config_.stage_partition.size())
+                    throw std::invalid_argument("segment_mappings count must equal decomposition_count");
+                if (config_.boundaries.empty()) {
+                    config_.boundaries.assign(config_.stage_partition.size() - 1,
+                                              FftBoundaryMapping{config_.cross_twiddle, config_.direct_boundary});
+                }
+                if (config_.boundaries.size() + 1 != config_.stage_partition.size())
+                    throw std::invalid_argument("boundary count must equal decomposition_count - 1");
+                execution_stage_partition_.clear();
+                execution_boundaries_.clear();
+                std::uint32_t group_stages = config_.stage_partition.front();
+                for (std::size_t boundary = 0; boundary < config_.boundaries.size(); ++boundary) {
+                    if (config_.boundaries[boundary].residency == FftBoundaryResidency::Fused) {
+                        group_stages += config_.stage_partition[boundary + 1];
+                    } else {
+                        execution_stage_partition_.push_back(group_stages);
+                        execution_boundaries_.push_back(config_.boundaries[boundary]);
+                        group_stages = config_.stage_partition[boundary + 1];
+                    }
+                }
+                execution_stage_partition_.push_back(group_stages);
+                if (execution_stage_partition_.size() < 2)
+                    throw std::invalid_argument("fully fused FFT requires a whole-transform processing unit");
+                if (config_.execution_group_mappings.empty()) {
+                    if (execution_stage_partition_.size() == config_.stage_partition.size()) {
+                        config_.execution_group_mappings = config_.segment_mappings;
+                    } else {
+                        for (const auto stages : execution_stage_partition_) {
+                            FftSegmentMapping mapping;
+                            if (stages >= 11) {
+                                mapping.threads = 256;
+                                mapping.ept = (1U << stages) / mapping.threads;
+                            } else if (stages == 10 && config_.batch <= 2) {
+                                mapping.threads = 512;
+                                mapping.ept = 8;
+                            } else if (stages == 10) {
+                                mapping.threads = 256;
+                                mapping.ept = 16;
+                            } else {
+                                mapping.threads = 128;
+                                mapping.ept = std::max(8U, (1U << stages) / mapping.threads);
+                            }
+                            config_.execution_group_mappings.push_back(mapping);
+                        }
+                    }
+                }
+                if (config_.execution_group_mappings.size() != execution_stage_partition_.size())
+                    throw std::invalid_argument("execution group mapping count does not match fused boundary lowering");
+                if (config_.stage_partition.size() == 2) {
+                    config_.prefix_threads = config_.segment_mappings[0].threads;
+                    config_.prefix_ept = config_.segment_mappings[0].ept;
+                    config_.suffix_threads = config_.segment_mappings[1].threads;
+                    config_.suffix_ept = config_.segment_mappings[1].ept;
+                    config_.cross_twiddle = config_.boundaries[0].cross_twiddle;
+                    config_.direct_boundary = config_.boundaries[0].layout;
+                }
+            }
+        }
         if (config_.backend == ButterflyBackend::TemporalTile && config_.local_exchange == LocalExchange::SharedMemory &&
             config_.log_n > 10 && config_.fft_core != FftCore::CufftDxDirect) {
             throw std::invalid_argument("temporal-tile requires log_n in [1, 10]");
@@ -479,23 +610,54 @@ class ButterflyPlan::Impl {
             (config_.local_stages < 5 || config_.local_stages > 10 || config_.local_stages >= config_.log_n)) {
             throw std::invalid_argument("hierarchical requires local_stages in [5, 10] and smaller than log_n");
         }
-        if (config_.backend == ButterflyBackend::OnlineReorder &&
-            (config_.local_stages < 5 || config_.local_stages > 10 || config_.local_stages >= config_.log_n ||
-             config_.log_n - config_.local_stages > 10)) {
-            throw std::invalid_argument("online-reorder requires local and remaining stages in [1, 10], with local_stages >= 5");
+        const std::uint32_t online_max_dimension = config_.fft_core == FftCore::CufftDxBlock ? 12U : 10U;
+        if (config_.backend == ButterflyBackend::OnlineReorder && config_.stage_partition.size() == 2 &&
+            (config_.local_stages < 5 || config_.local_stages > online_max_dimension ||
+             config_.local_stages >= config_.log_n || config_.log_n - config_.local_stages > online_max_dimension)) {
+            throw std::invalid_argument(
+                "online-reorder dimensions exceed the selected processing unit's supported range");
         }
         if (config_.backend == ButterflyBackend::OnlineReorder) {
-            const std::uint32_t local_n     = 1U << config_.local_stages;
-            const std::uint32_t remaining_n = 1U << (config_.log_n - config_.local_stages);
-            if (config_.reorder_columns == 0) {
-                config_.reorder_columns = std::min(local_n, 1024U / remaining_n);
+            if (config_.fft_core == FftCore::CufftDxBlock) {
+                config_.reorder_columns = 1;
+            } else {
+                const std::uint32_t local_n     = 1U << config_.local_stages;
+                const std::uint32_t remaining_n = 1U << (config_.log_n - config_.local_stages);
+                if (config_.reorder_columns == 0) {
+                    config_.reorder_columns = std::min(local_n, 1024U / remaining_n);
+                }
+                if (config_.reorder_columns == 0 || config_.reorder_columns > local_n ||
+                    config_.reorder_columns * remaining_n > 1024 ||
+                    (config_.reorder_columns & (config_.reorder_columns - 1)) != 0) {
+                    throw std::invalid_argument(
+                        "online-reorder columns must be a power of two and retain at most 1024 values per CTA");
+                }
+            }
+        }
+        if (config_.backend == ButterflyBackend::OnlineReorder && config_.stage_partition.size() > 2) {
+            if (config_.precision == ButterflyPrecision::Fp64)
+                throw std::invalid_argument("FP64 cuFFTDx currently supports a two-segment online decomposition");
+            const auto valid_threads = [](std::uint32_t threads) {
+                return threads == 128 || threads == 256 || threads == 512 || threads == 1024;
+            };
+            for (std::size_t segment = 0; segment < config_.stage_partition.size(); ++segment) {
+                const std::uint32_t segment_log_n = config_.stage_partition[segment];
+                auto& mapping = config_.segment_mappings[segment];
+                if (mapping.core != FftCore::CufftDxBlock || mapping.exchange != LocalExchange::SharedMemory)
+                    throw std::invalid_argument("multi-segment runtime currently requires cuFFTDx-block with shared exchange");
+                if (!valid_threads(mapping.threads) || segment_log_n < 3 || segment_log_n > 12 ||
+                    mapping.threads * mapping.ept < (1U << segment_log_n) ||
+                    (mapping.threads * mapping.ept) % (1U << segment_log_n) != 0 ||
+                    !detail::cufftdx_online_available(segment_log_n, mapping.threads, mapping.ept))
+                    throw std::invalid_argument("multi-segment processing-unit mapping is not compiled or cannot cover its segment");
             }
-            if (config_.reorder_columns == 0 || config_.reorder_columns > local_n || config_.reorder_columns * remaining_n > 1024 ||
-                (config_.reorder_columns & (config_.reorder_columns - 1)) != 0) {
-                throw std::invalid_argument("online-reorder columns must be a power of two and retain at most 1024 values per CTA");
+            for (const auto& boundary : config_.boundaries) {
+                if (boundary.layout != DirectBoundary::Strided)
+                    throw std::invalid_argument("multi-segment runtime currently requires direct-strided boundaries");
             }
         }
-        if (config_.fft_core == FftCore::CufftDxBlock && config_.backend == ButterflyBackend::OnlineReorder) {
+        if (config_.fft_core == FftCore::CufftDxBlock && config_.backend == ButterflyBackend::OnlineReorder &&
+            config_.stage_partition.size() == 2) {
             if (config_.prefix_threads == 0)
                 config_.prefix_threads = 512;
             if (config_.suffix_threads == 0)
@@ -513,14 +675,62 @@ class ButterflyPlan::Impl {
                 throw std::invalid_argument(
                     "online cuFFTDx thread/EPT products must cover an integer number of local FFTs");
             }
-            if (!detail::cufftdx_online_available(config_.local_stages, config_.prefix_threads, config_.prefix_ept) ||
-                !detail::cufftdx_online_available(config_.log_n - config_.local_stages,
-                                                  config_.suffix_threads, config_.suffix_ept)) {
+            const auto online_available = config_.precision == ButterflyPrecision::Fp64
+                                              ? detail::cufftdx_fp64_online_available
+                                              : detail::cufftdx_online_available;
+            if (!online_available(config_.local_stages, config_.prefix_threads, config_.prefix_ept) ||
+                !online_available(config_.log_n - config_.local_stages,
+                                  config_.suffix_threads, config_.suffix_ept)) {
                 throw std::invalid_argument(
                     "requested online cuFFTDx thread/EPT point is hardware-feasible but was not selected for this build");
             }
             config_.prefix_units_per_cta = config_.prefix_threads * config_.prefix_ept / prefix_n;
             config_.suffix_units_per_cta = config_.suffix_threads * config_.suffix_ept / suffix_n;
+            if (config_.execution_group_mappings[0].threads == 0) {
+                config_.execution_group_mappings[0].threads = config_.prefix_threads;
+                config_.execution_group_mappings[0].ept = config_.prefix_ept;
+            }
+            if (config_.execution_group_mappings[1].threads == 0) {
+                config_.execution_group_mappings[1].threads = config_.suffix_threads;
+                config_.execution_group_mappings[1].ept = config_.suffix_ept;
+            }
+        }
+        if (config_.backend == ButterflyBackend::OnlineReorder && config_.fft_core == FftCore::CufftDxBlock) {
+            const auto valid_threads = [](std::uint32_t threads) {
+                return threads == 128 || threads == 256 || threads == 512 || threads == 1024;
+            };
+            if (config_.execution_group_mappings.size() != execution_stage_partition_.size())
+                throw std::invalid_argument("execution group mapping count must equal physical execution group count");
+            for (std::size_t group = 0; group < execution_stage_partition_.size(); ++group) {
+                const std::uint32_t stages = execution_stage_partition_[group];
+                const auto& mapping = config_.execution_group_mappings[group];
+                if (mapping.core != FftCore::CufftDxBlock || mapping.exchange != LocalExchange::SharedMemory ||
+                    !valid_threads(mapping.threads) || stages < 3 || stages > 12 ||
+                    mapping.threads * mapping.ept < (1U << stages) ||
+                    (mapping.threads * mapping.ept) % (1U << stages) != 0 ||
+                    !(config_.precision == ButterflyPrecision::Fp64
+                          ? detail::cufftdx_fp64_online_available(stages, mapping.threads, mapping.ept)
+                          : detail::cufftdx_online_available(stages, mapping.threads, mapping.ept)))
+                    throw std::invalid_argument(
+                        "execution-group processing-unit mapping is not compiled or cannot cover its stages");
+            }
+        }
+        if (config_.direct_boundary == DirectBoundary::TiledTranspose) {
+            const std::uint32_t suffix_log_n = config_.log_n - config_.local_stages;
+            if (config_.op != ButterflyOperator::Fft || config_.backend != ButterflyBackend::OnlineReorder ||
+                config_.fft_core != FftCore::CufftDxBlock ||
+                (suffix_log_n != 11 && suffix_log_n != 12)) {
+                throw std::invalid_argument(
+                    "tiled-transpose direct boundary currently requires an online cuFFTDx FFT with suffix logN=11 or 12");
+            }
+        }
+        if (config_.direct_boundary == DirectBoundary::PrefixTiledTranspose) {
+            if (config_.op != ButterflyOperator::Fft || config_.backend != ButterflyBackend::OnlineReorder ||
+                config_.fft_core != FftCore::CufftDxBlock ||
+                (config_.local_stages != 11 && config_.local_stages != 12)) {
+                throw std::invalid_argument(
+                    "prefix-tiled-transpose direct boundary currently requires an online cuFFTDx FFT with prefix logN=11 or 12");
+            }
         }
         if (config_.batch == 0) {
             throw std::invalid_argument("butterfly batch must be positive");
@@ -586,14 +796,19 @@ class ButterflyPlan::Impl {
                 }
                 config_.tile_threads = 256;
             } else if (config_.fft_core == FftCore::CufftDxBlock) {
+                const bool fp64 = config_.precision == ButterflyPrecision::Fp64;
+                const auto online_available = fp64 ? detail::cufftdx_fp64_online_available
+                                                   : detail::cufftdx_online_available;
                 const bool supported = config_.backend == ButterflyBackend::TemporalTile
-                                           ? detail::cufftdx_block_available(config_.log_n)
-                                           : detail::cufftdx_block_available(config_.local_stages) &&
-                                                 detail::cufftdx_block_available(config_.log_n - config_.local_stages);
-                if (config_.precision != ButterflyPrecision::Fp32 || !supported) {
-                    throw std::invalid_argument(
-                        "cufftdx-block requires FP32 and local FFT dimensions in logN=3..10");
-                }
+                                           ? (fp64 ? detail::cufftdx_fp64_block_available(config_.log_n)
+                                                   : detail::cufftdx_block_available(config_.log_n))
+                                           : (!fp64 && config_.stage_partition.size() > 2) ||
+                                                 (online_available(config_.local_stages, config_.prefix_threads,
+                                                                   config_.prefix_ept) &&
+                                                  online_available(config_.log_n - config_.local_stages,
+                                                                   config_.suffix_threads, config_.suffix_ept));
+                if ((config_.precision != ButterflyPrecision::Fp32 && !fp64) || !supported)
+                    throw std::invalid_argument("cufftdx-block precision or compiled local FFT mapping is unsupported");
             } else if (config_.fft_core == FftCore::CufftDxDirect) {
                 if (config_.precision != ButterflyPrecision::Fp32 || !detail::cufftdx_direct_available(config_.log_n) ||
                     !resident_tile_threads || (config_.log_n == 14 && config_.tile_threads == 256)) {
@@ -649,6 +864,14 @@ class ButterflyPlan::Impl {
             (config_.op != ButterflyOperator::Fft || config_.backend == ButterflyBackend::CuFft)) {
             throw std::invalid_argument("Gauss complex multiplication requires a self-kernel FFT backend");
         }
+        if (config_.shared_layout == SharedLayout::XorSwizzle &&
+            (config_.op != ButterflyOperator::Fft || config_.precision != ButterflyPrecision::Fp64 ||
+             config_.backend != ButterflyBackend::OnlineReorder || config_.fft_core != FftCore::CufftDxBlock ||
+             config_.stage_partition.size() != 2 || config_.local_stages < 7 || config_.local_stages > 9 ||
+             config_.log_n - config_.local_stages < 7 || config_.log_n - config_.local_stages > 9)) {
+            throw std::invalid_argument(
+                "xor-swizzle shared layout requires FP64 online cuFFTDx with two logN=7..9 segments");
+        }
         if (config_.cross_twiddle == CrossTwiddleMode::Recurrence &&
             (config_.op != ButterflyOperator::Fft || config_.backend != ButterflyBackend::OnlineReorder ||
              (config_.fft_core != FftCore::CufftDxBlock && config_.fft_core != FftCore::CufftDxResident))) {
@@ -672,6 +895,12 @@ class ButterflyPlan::Impl {
         if (config_.backend != ButterflyBackend::WarpHybrid) {
             config_.warp_stages = 0;
         }
+        if (config_.stage_partition.empty()) {
+            config_.stage_partition = config_.backend == ButterflyBackend::OnlineReorder
+                                          ? std::vector<std::uint32_t>{config_.local_stages,
+                                                                       config_.log_n - config_.local_stages}
+                                          : std::vector<std::uint32_t>{config_.log_n};
+        }
 
         points_ = std::size_t{1} << config_.log_n;
         if (config_.element_stride == 0) {
@@ -713,6 +942,10 @@ class ButterflyPlan::Impl {
         if (config_.backend == ButterflyBackend::Hierarchical || config_.backend == ButterflyBackend::OnlineReorder) {
             device_scratch_.allocate(data_bytes_);
         }
+        if (config_.direct_boundary == DirectBoundary::PrefixTiledTranspose ||
+            (config_.backend == ButterflyBackend::OnlineReorder && execution_stage_partition_.size() > 2)) {
+            device_workspace_.allocate(data_bytes_);
+        }
 
         if (config_.op == ButterflyOperator::Fft && config_.backend != ButterflyBackend::CuFft) {
             constexpr double kPi = 3.141592653589793238462643383279502884;
@@ -888,13 +1121,50 @@ class ButterflyPlan::Impl {
                 return;
             }
             if (config_.fft_core == FftCore::CufftDxBlock) {
+                if (config_.precision == ButterflyPrecision::Fp64) {
+                    if (config_.backend == ButterflyBackend::OnlineReorder) {
+                        const auto& prefix = config_.execution_group_mappings[0];
+                        const auto& suffix = config_.execution_group_mappings[1];
+                        const auto& boundary = execution_boundaries_[0];
+                        detail::launch_cufftdx_fp64_online_reorder(
+                            config_.log_n, execution_stage_partition_[0], device_input_.as<Complex64>(),
+                            result_buffer<Complex64>(), device_scratch_.as<Complex64>(),
+                            device_twiddles_.as<Complex64>(), config_.batch, config_.batch_stride,
+                            config_.element_stride, config_.inverse,
+                            config_.inverse && config_.normalize_inverse, boundary.cross_twiddle,
+                            config_.shared_layout, prefix.threads, suffix.threads,
+                            prefix.ept, suffix.ept);
+                    } else {
+                        detail::launch_cufftdx_fp64_block(
+                            config_.log_n, device_input_.as<Complex64>(), result_buffer<Complex64>(),
+                            config_.batch, config_.batch_stride, config_.element_stride, config_.inverse,
+                            config_.inverse && config_.normalize_inverse);
+                    }
+                    CUB_CUDA_CHECK(cudaGetLastError());
+                    return;
+                }
                 if (config_.backend == ButterflyBackend::OnlineReorder) {
-                    detail::launch_cufftdx_online_reorder(
-                        config_.log_n, config_.local_stages, device_input_.as<Complex32>(), result_buffer<Complex32>(),
-                        device_scratch_.as<Complex32>(), device_twiddles_.as<Complex32>(), config_.batch,
-                        config_.batch_stride, config_.element_stride, config_.inverse,
-                        config_.inverse && config_.normalize_inverse, config_.cross_twiddle,
-                        config_.prefix_threads, config_.suffix_threads, config_.prefix_ept, config_.suffix_ept);
+                    if (execution_stage_partition_.size() > 2) {
+                        detail::launch_cufftdx_multisegment(
+                            config_.log_n, execution_stage_partition_, config_.execution_group_mappings,
+                            execution_boundaries_,
+                            device_input_.as<Complex32>(), result_buffer<Complex32>(),
+                            device_scratch_.as<Complex32>(), device_workspace_.as<Complex32>(),
+                            device_twiddles_.as<Complex32>(), config_.batch, config_.batch_stride,
+                            config_.element_stride, config_.inverse,
+                            config_.inverse && config_.normalize_inverse);
+                    } else {
+                        const auto& prefix = config_.execution_group_mappings[0];
+                        const auto& suffix = config_.execution_group_mappings[1];
+                        const auto& boundary = execution_boundaries_[0];
+                        detail::launch_cufftdx_online_reorder(
+                            config_.log_n, execution_stage_partition_[0], device_input_.as<Complex32>(), result_buffer<Complex32>(),
+                            device_scratch_.as<Complex32>(), device_workspace_.as<Complex32>(),
+                            device_twiddles_.as<Complex32>(), config_.batch,
+                            config_.batch_stride, config_.element_stride, config_.inverse,
+                            config_.inverse && config_.normalize_inverse, boundary.cross_twiddle,
+                            prefix.threads, suffix.threads, prefix.ept, suffix.ept, boundary.layout);
+                    }
                 } else {
                     detail::launch_cufftdx_block(config_.log_n, device_input_.as<Complex32>(), result_buffer<Complex32>(), config_.batch,
                                                  config_.batch_stride, config_.element_stride, config_.inverse,
@@ -983,12 +1253,15 @@ class ButterflyPlan::Impl {
     }
 
     ButterflyConfig config_;
+    std::vector<std::uint32_t> execution_stage_partition_;
+    std::vector<FftBoundaryMapping> execution_boundaries_;
     std::size_t     data_bytes_    = 0;
     std::size_t     data_elements_ = 0;
     std::size_t     points_        = 0;
     DeviceBuffer    device_input_;
     DeviceBuffer    device_output_;
     DeviceBuffer    device_scratch_;
+    DeviceBuffer    device_workspace_;
     DeviceBuffer    device_twiddles_;
     cufftHandle     cufft_plan_ = 0;
 };
diff --git a/src/butterfly_reference.cpp b/src/butterfly_reference.cpp
index b97483f..ce48fb1 100644
--- a/src/butterfly_reference.cpp
+++ b/src/butterfly_reference.cpp
@@ -51,7 +51,7 @@ std::vector<ButterflyCapability> butterfly_capabilities() {
         {ButterflyBackend::Hierarchical, 6, 20, true, true, true, false, false, false, false, true, true, true, true, false, true, true, true,
          "local_stages=5..10 and local_stages<logN"},
         {ButterflyBackend::OnlineReorder, 6, 20, true, true, true, false, false, false, false, true, true, true, true, false, true, true, true,
-         "local_stages and remaining stages are each <=10"},
+         "scalar dimensions are <=10; cuFFTDx mixed block/direct dimensions are <=12"},
         {ButterflyBackend::WarpHybrid, 8, 8, true, false, false, false, false, false, false, true, true, true, true, false, true, true, true, "N=256"},
         {ButterflyBackend::StagePipeline, 8, 8, true, false, false, false, false, false, false, true, true, true, true, false, true, true, true,
          "FP64 complex exceeds V100 CTA shared memory"},
@@ -96,6 +96,46 @@ CrossTwiddleMode parse_cross_twiddle_mode(const std::string& name) {
     throw std::invalid_argument("unknown cross twiddle mode: " + name);
 }
 
+const char* direct_boundary_name(DirectBoundary boundary) noexcept {
+    switch (boundary) {
+        case DirectBoundary::Strided:
+            return "direct-strided";
+        case DirectBoundary::TiledTranspose:
+            return "tiled-transpose";
+        case DirectBoundary::PrefixTiledTranspose:
+            return "prefix-tiled-transpose";
+    }
+    return "unknown";
+}
+
+DirectBoundary parse_direct_boundary(const std::string& name) {
+    if (name == "direct-strided")
+        return DirectBoundary::Strided;
+    if (name == "tiled-transpose")
+        return DirectBoundary::TiledTranspose;
+    if (name == "prefix-tiled-transpose")
+        return DirectBoundary::PrefixTiledTranspose;
+    throw std::invalid_argument("unknown direct boundary: " + name);
+}
+
+const char* fft_boundary_residency_name(FftBoundaryResidency residency) noexcept {
+    switch (residency) {
+        case FftBoundaryResidency::GlobalScratch:
+            return "global-scratch";
+        case FftBoundaryResidency::Fused:
+            return "fused";
+    }
+    return "unknown";
+}
+
+FftBoundaryResidency parse_fft_boundary_residency(const std::string& name) {
+    if (name == "global-scratch")
+        return FftBoundaryResidency::GlobalScratch;
+    if (name == "fused")
+        return FftBoundaryResidency::Fused;
+    throw std::invalid_argument("unknown FFT boundary residency: " + name);
+}
+
 const char* local_exchange_name(LocalExchange exchange) noexcept {
     switch (exchange) {
         case LocalExchange::SharedMemory:
@@ -114,6 +154,24 @@ LocalExchange parse_local_exchange(const std::string& name) {
     throw std::invalid_argument("unknown local exchange: " + name);
 }
 
+const char* shared_layout_name(SharedLayout layout) noexcept {
+    switch (layout) {
+        case SharedLayout::Linear:
+            return "linear";
+        case SharedLayout::XorSwizzle:
+            return "xor-swizzle";
+    }
+    return "unknown";
+}
+
+SharedLayout parse_shared_layout(const std::string& name) {
+    if (name == "linear")
+        return SharedLayout::Linear;
+    if (name == "xor-swizzle")
+        return SharedLayout::XorSwizzle;
+    throw std::invalid_argument("unknown shared layout: " + name);
+}
+
 const char* fft_core_name(FftCore core) noexcept {
     switch (core) {
         case FftCore::Scalar:
diff --git a/src/cufftdx_fft.cu b/src/cufftdx_fft.cu
index 2ac34e2..27b669a 100644
--- a/src/cufftdx_fft.cu
+++ b/src/cufftdx_fft.cu
@@ -121,19 +121,64 @@ __launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_online_fir
     const std::uint32_t flat_thread = threadIdx.y * blockDim.x + threadIdx.x;
     const std::uint32_t flat_threads = blockDim.x * blockDim.y;
     constexpr std::uint32_t tile_values = FFT::input_length * FFT::ffts_per_block;
-    for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
-        const std::uint32_t element = work / FFT::ffts_per_block;
-        const std::uint32_t slot    = work - element * FFT::ffts_per_block;
-        const std::uint64_t staged_transform = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
-        const bool staged_active = staged_transform < total_local;
-        if (staged_active) {
-            const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
-            const std::uint32_t staged_n2 = static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
-            const std::uint64_t logical = static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
-            const Complex32 value = input[staged_batch * batch_distance + logical * element_stride];
-            tile[work] = Value{value.real, value.imag};
+    // Pair adjacent transforms when the boundary layout permits aligned 128-bit transactions.
+    if constexpr (FFT::ffts_per_block >= 2 && (FFT::ffts_per_block & 1) == 0) {
+        if (remaining_n >= 2 && element_stride == 1 && (batch_distance & 1) == 0) {
+            constexpr std::uint32_t tile_pairs = tile_values / 2;
+            for (std::uint32_t pair = flat_thread; pair < tile_pairs; pair += flat_threads) {
+                const std::uint32_t work    = pair * 2;
+                const std::uint32_t element = work / FFT::ffts_per_block;
+                const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+                const std::uint64_t staged_transform =
+                    static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+                if (staged_transform + 1 < total_local) {
+                    const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
+                    const std::uint32_t staged_n2 =
+                        static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+                    const std::uint64_t logical = static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
+                    reinterpret_cast<float4*>(tile)[pair] =
+                        *reinterpret_cast<const float4*>(input + staged_batch * batch_distance + logical);
+                } else {
+                    tile[work] = Value{0.0F, 0.0F};
+                    tile[work + 1] = Value{0.0F, 0.0F};
+                }
+            }
         } else {
-            tile[work] = Value{0.0F, 0.0F};
+            for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+                const std::uint32_t element = work / FFT::ffts_per_block;
+                const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+                const std::uint64_t staged_transform =
+                    static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+                const bool staged_active = staged_transform < total_local;
+                if (staged_active) {
+                    const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
+                    const std::uint32_t staged_n2 =
+                        static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+                    const std::uint64_t logical = static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
+                    const Complex32 value = input[staged_batch * batch_distance + logical * element_stride];
+                    tile[work] = Value{value.real, value.imag};
+                } else {
+                    tile[work] = Value{0.0F, 0.0F};
+                }
+            }
+        }
+    } else {
+        for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+            const std::uint32_t element = work / FFT::ffts_per_block;
+            const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+            const std::uint64_t staged_transform =
+                static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+            const bool staged_active = staged_transform < total_local;
+            if (staged_active) {
+                const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
+                const std::uint32_t staged_n2 =
+                    static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+                const std::uint64_t logical = static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
+                const Complex32 value = input[staged_batch * batch_distance + logical * element_stride];
+                tile[work] = Value{value.real, value.imag};
+            } else {
+                tile[work] = Value{0.0F, 0.0F};
+            }
         }
     }
     __syncthreads();
@@ -178,16 +223,56 @@ __launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_online_fir
         k1 += FFT::stride;
     }
     __syncthreads();
-    for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
-        const std::uint32_t element = work / FFT::ffts_per_block;
-        const std::uint32_t slot    = work - element * FFT::ffts_per_block;
-        const std::uint64_t staged_transform = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
-        if (staged_transform < total_local) {
-            const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
-            const std::uint32_t staged_n2 = static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
-            const std::uint64_t reordered = static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
-            const Value value = tile[work];
-            scratch[staged_batch * batch_distance + reordered * element_stride] = {value.x, value.y};
+    if constexpr (FFT::ffts_per_block >= 2 && (FFT::ffts_per_block & 1) == 0) {
+        if (remaining_n >= 2 && element_stride == 1 && (batch_distance & 1) == 0) {
+            constexpr std::uint32_t tile_pairs = tile_values / 2;
+            for (std::uint32_t pair = flat_thread; pair < tile_pairs; pair += flat_threads) {
+                const std::uint32_t work    = pair * 2;
+                const std::uint32_t element = work / FFT::ffts_per_block;
+                const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+                const std::uint64_t staged_transform =
+                    static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+                if (staged_transform + 1 < total_local) {
+                    const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
+                    const std::uint32_t staged_n2 =
+                        static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+                    const std::uint64_t reordered =
+                        static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
+                    *reinterpret_cast<float4*>(scratch + staged_batch * batch_distance + reordered) =
+                        reinterpret_cast<const float4*>(tile)[pair];
+                }
+            }
+        } else {
+            for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+                const std::uint32_t element = work / FFT::ffts_per_block;
+                const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+                const std::uint64_t staged_transform =
+                    static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+                if (staged_transform < total_local) {
+                    const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
+                    const std::uint32_t staged_n2 =
+                        static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+                    const std::uint64_t reordered =
+                        static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
+                    const Value value = tile[work];
+                    scratch[staged_batch * batch_distance + reordered * element_stride] = {value.x, value.y};
+                }
+            }
+        }
+    } else {
+        for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+            const std::uint32_t element = work / FFT::ffts_per_block;
+            const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+            const std::uint64_t staged_transform =
+                static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+            if (staged_transform < total_local) {
+                const std::uint64_t staged_batch = staged_transform >> remaining_log_n;
+                const std::uint32_t staged_n2 =
+                    static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+                const std::uint64_t reordered = static_cast<std::uint64_t>(element) * remaining_n + staged_n2;
+                const Value value = tile[work];
+                scratch[staged_batch * batch_distance + reordered * element_stride] = {value.x, value.y};
+            }
         }
     }
 }
@@ -242,20 +327,329 @@ __launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_online_sec
     const std::uint32_t flat_thread = threadIdx.y * blockDim.x + threadIdx.x;
     const std::uint32_t flat_threads = blockDim.x * blockDim.y;
     constexpr std::uint32_t tile_values = FFT::output_length * FFT::ffts_per_block;
+    if constexpr (FFT::ffts_per_block >= 2 && (FFT::ffts_per_block & 1) == 0) {
+        if (element_stride == 1 && (batch_distance & 1) == 0) {
+            constexpr std::uint32_t tile_pairs = tile_values / 2;
+            for (std::uint32_t pair = flat_thread; pair < tile_pairs; pair += flat_threads) {
+                const std::uint32_t work    = pair * 2;
+                const std::uint32_t element = work / FFT::ffts_per_block;
+                const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+                const std::uint64_t staged_transform =
+                    static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+                if (staged_transform + 1 < total_local) {
+                    const std::uint64_t staged_batch = staged_transform >> local_log_n;
+                    const std::uint32_t staged_k1 =
+                        static_cast<std::uint32_t>(staged_transform) & (local_n - 1);
+                    const std::uint64_t logical = static_cast<std::uint64_t>(element) * local_n + staged_k1;
+                    *reinterpret_cast<float4*>(output + staged_batch * batch_distance + logical) =
+                        reinterpret_cast<const float4*>(tile)[pair];
+                }
+            }
+        } else {
+            for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+                const std::uint32_t element = work / FFT::ffts_per_block;
+                const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+                const std::uint64_t staged_transform =
+                    static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+                if (staged_transform < total_local) {
+                    const std::uint64_t staged_batch = staged_transform >> local_log_n;
+                    const std::uint32_t staged_k1 =
+                        static_cast<std::uint32_t>(staged_transform) & (local_n - 1);
+                    const std::uint64_t logical = static_cast<std::uint64_t>(element) * local_n + staged_k1;
+                    const Value value = tile[work];
+                    output[staged_batch * batch_distance + logical * element_stride] = {value.x, value.y};
+                }
+            }
+        }
+    } else {
+        for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+            const std::uint32_t element = work / FFT::ffts_per_block;
+            const std::uint32_t slot    = work - element * FFT::ffts_per_block;
+            const std::uint64_t staged_transform =
+                static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+            if (staged_transform < total_local) {
+                const std::uint64_t staged_batch = staged_transform >> local_log_n;
+                const std::uint32_t staged_k1 =
+                    static_cast<std::uint32_t>(staged_transform) & (local_n - 1);
+                const std::uint64_t logical = static_cast<std::uint64_t>(element) * local_n + staged_k1;
+                const Value value = tile[work];
+                output[staged_batch * batch_distance + logical * element_stride] = {value.x, value.y};
+            }
+        }
+    }
+}
+
+struct StagePartitionDescriptor {
+    std::uint32_t count;
+    std::uint32_t input_shift[8];
+    std::uint32_t output_shift[8];
+    std::uint32_t mask[8];
+};
+
+__device__ __forceinline__ std::uint32_t reverse_stage_groups(
+    std::uint32_t logical, const StagePartitionDescriptor& partition) {
+    std::uint32_t reordered = 0;
+#pragma unroll
+    for (std::uint32_t segment = 0; segment < 8; ++segment) {
+        if (segment < partition.count) {
+            const std::uint32_t digit = (logical >> partition.input_shift[segment]) & partition.mask[segment];
+            reordered |= digit << partition.output_shift[segment];
+        }
+    }
+    return reordered;
+}
+
+template <class FFT, bool FinalSegment>
+__launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_multisegment_kernel(
+    const Complex32* input, Complex32* output, const Complex32* twiddles,
+    std::uint64_t transforms, std::uint32_t log_n, std::uint32_t prefix_log_n,
+    std::uint32_t segment_log_n, std::uint32_t remaining_log_n,
+    std::uint64_t batch_distance, std::uint64_t element_stride,
+    bool recurrence_twiddle, bool normalize, StagePartitionDescriptor partition) {
+    using Value = typename FFT::value_type;
+    // Intermediate layouts keep completed frequency digits before the remaining time digits.
+    // The final pass reverses those radix groups into natural FFT output order.
+    const std::uint32_t prefix_n = 1U << prefix_log_n;
+    const std::uint32_t remaining_n = 1U << remaining_log_n;
+    const std::uint64_t local_per_batch = static_cast<std::uint64_t>(prefix_n) * remaining_n;
+    const std::uint64_t local_transform = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + threadIdx.y;
+    const std::uint64_t total_local = transforms * local_per_batch;
+    const bool active = local_transform < total_local;
+    const std::uint64_t within = active ? local_transform % local_per_batch : 0;
+    const std::uint32_t remainder = static_cast<std::uint32_t>(within) & (remaining_n - 1);
+
+    extern __shared__ __align__(16) unsigned char storage[];
+    Value* tile = reinterpret_cast<Value*>(storage);
+    const std::uint32_t flat_thread = threadIdx.y * blockDim.x + threadIdx.x;
+    const std::uint32_t flat_threads = blockDim.x * blockDim.y;
+    constexpr std::uint32_t tile_values = FFT::input_length * FFT::ffts_per_block;
     for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
         const std::uint32_t element = work / FFT::ffts_per_block;
-        const std::uint32_t slot    = work - element * FFT::ffts_per_block;
-        const std::uint64_t staged_transform = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
-        if (staged_transform < total_local) {
-            const std::uint64_t staged_batch = staged_transform >> local_log_n;
-            const std::uint32_t staged_k1 = static_cast<std::uint32_t>(staged_transform) & (local_n - 1);
-            const std::uint64_t logical = static_cast<std::uint64_t>(element) * local_n + staged_k1;
+        const std::uint32_t slot = work - element * FFT::ffts_per_block;
+        const std::uint64_t staged_local = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+        if (staged_local < total_local) {
+            const std::uint64_t staged_transform = staged_local / local_per_batch;
+            const std::uint64_t staged_within = staged_local - staged_transform * local_per_batch;
+            const std::uint32_t staged_prefix = static_cast<std::uint32_t>(staged_within >> remaining_log_n);
+            const std::uint32_t staged_remainder = static_cast<std::uint32_t>(staged_within) & (remaining_n - 1);
+            const std::uint64_t logical =
+                (static_cast<std::uint64_t>(staged_prefix) * FFT::input_length + element) * remaining_n + staged_remainder;
+            const Complex32 value = input[staged_transform * batch_distance + logical * element_stride];
+            tile[work] = Value{value.real, value.imag};
+        } else {
+            tile[work] = Value{0.0F, 0.0F};
+        }
+    }
+    __syncthreads();
+
+    Value thread_data[FFT::storage_size];
+    std::uint32_t element = threadIdx.x;
+#pragma unroll
+    for (unsigned int item = 0; item < FFT::storage_size; ++item) {
+        thread_data[item] = active && element < FFT::input_length
+                                ? tile[element * FFT::ffts_per_block + threadIdx.y]
+                                : Value{0.0F, 0.0F};
+        element += FFT::stride;
+    }
+    __syncthreads();
+    FFT().execute(thread_data, storage);
+    __syncthreads();
+
+    Complex32 running_root = {1.0F, 0.0F};
+    Complex32 root_step = {1.0F, 0.0F};
+    if constexpr (!FinalSegment) {
+        if (active && recurrence_twiddle) {
+            const std::uint64_t exponent_scale = static_cast<std::uint64_t>(prefix_n) * remainder;
+            running_root = cross_root(twiddles, log_n, exponent_scale * threadIdx.x);
+            root_step = cross_root(twiddles, log_n, exponent_scale * FFT::stride);
+        }
+    }
+    std::uint32_t frequency = threadIdx.x;
+#pragma unroll
+    for (unsigned int item = 0; item < FFT::storage_size; ++item) {
+        if (active && frequency < FFT::output_length) {
+            Value value = thread_data[item];
+            if constexpr (!FinalSegment) {
+                const std::uint64_t exponent = static_cast<std::uint64_t>(prefix_n) * frequency * remainder;
+                const Complex32 root = recurrence_twiddle ? running_root : cross_root(twiddles, log_n, exponent);
+                value = Value{value.x * root.real - value.y * root.imag,
+                              value.x * root.imag + value.y * root.real};
+            } else if (normalize) {
+                const float scale = 1.0F / static_cast<float>(1U << log_n);
+                value = Value{value.x * scale, value.y * scale};
+            }
+            tile[frequency * FFT::ffts_per_block + threadIdx.y] = value;
+        }
+        if constexpr (!FinalSegment) {
+            if (recurrence_twiddle) {
+                running_root = {running_root.real * root_step.real - running_root.imag * root_step.imag,
+                                running_root.real * root_step.imag + running_root.imag * root_step.real};
+            }
+        }
+        frequency += FFT::stride;
+    }
+    __syncthreads();
+
+    for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+        const std::uint32_t staged_frequency = work / FFT::ffts_per_block;
+        const std::uint32_t slot = work - staged_frequency * FFT::ffts_per_block;
+        const std::uint64_t staged_local = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+        if (staged_local < total_local) {
+            const std::uint64_t staged_transform = staged_local / local_per_batch;
+            const std::uint64_t staged_within = staged_local - staged_transform * local_per_batch;
+            const std::uint32_t staged_prefix = static_cast<std::uint32_t>(staged_within >> remaining_log_n);
+            const std::uint32_t staged_remainder = static_cast<std::uint32_t>(staged_within) & (remaining_n - 1);
+            std::uint32_t logical = static_cast<std::uint32_t>(
+                (static_cast<std::uint64_t>(staged_prefix) * FFT::output_length + staged_frequency) * remaining_n +
+                staged_remainder);
+            if constexpr (FinalSegment)
+                logical = reverse_stage_groups(logical, partition);
             const Value value = tile[work];
-            output[staged_batch * batch_distance + logical * element_stride] = {value.x, value.y};
+            output[staged_transform * batch_distance + static_cast<std::uint64_t>(logical) * element_stride] =
+                {value.x, value.y};
         }
     }
 }
 
+template <class FFT, bool ContiguousInput>
+__launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_online_direct_first_kernel(
+    const Complex32* input, Complex32* scratch, const Complex32* twiddles, std::uint32_t log_n,
+    std::uint32_t local_log_n, std::uint64_t batch_distance,
+    std::uint64_t element_stride, bool recurrence_twiddle) {
+    using Value = typename FFT::value_type;
+    const std::uint32_t remaining_log_n = log_n - local_log_n;
+    const std::uint32_t remaining_n     = 1U << remaining_log_n;
+    const std::uint64_t local_transform = blockIdx.x;
+    const std::uint64_t transform       = local_transform >> remaining_log_n;
+    const std::uint32_t n2              = static_cast<std::uint32_t>(local_transform) & (remaining_n - 1);
+    const std::uint64_t base            = transform * batch_distance;
+
+    Value thread_data[FFT::storage_size];
+    std::uint32_t n1 = threadIdx.x;
+#pragma unroll
+    for (unsigned int item = 0; item < FFT::storage_size; ++item) {
+        const std::uint64_t logical = ContiguousInput
+                                          ? static_cast<std::uint64_t>(n2) * FFT::input_length + n1
+                                          : static_cast<std::uint64_t>(n1) * remaining_n + n2;
+        const Complex32 value = input[base + logical * element_stride];
+        thread_data[item] = Value{value.real, value.imag};
+        n1 += FFT::stride;
+    }
+
+    extern __shared__ __align__(16) unsigned char storage[];
+    FFT().execute(thread_data, storage);
+
+    Complex32 running_root = {1.0F, 0.0F};
+    Complex32 root_step    = {1.0F, 0.0F};
+    if (recurrence_twiddle) {
+        running_root = cross_root(twiddles, log_n, static_cast<std::uint64_t>(threadIdx.x) * n2);
+        root_step    = cross_root(twiddles, log_n, static_cast<std::uint64_t>(FFT::stride) * n2);
+    }
+    std::uint32_t k1 = threadIdx.x;
+#pragma unroll
+    for (unsigned int item = 0; item < FFT::storage_size; ++item) {
+        const Value value = thread_data[item];
+        const Complex32 root = recurrence_twiddle
+                                   ? running_root
+                                   : cross_root(twiddles, log_n, static_cast<std::uint64_t>(k1) * n2);
+        const Complex32 crossed = {value.x * root.real - value.y * root.imag,
+                                   value.x * root.imag + value.y * root.real};
+        const std::uint64_t reordered = static_cast<std::uint64_t>(k1) * remaining_n + n2;
+        scratch[base + reordered * element_stride] = crossed;
+        if (recurrence_twiddle) {
+            running_root = {running_root.real * root_step.real - running_root.imag * root_step.imag,
+                            running_root.real * root_step.imag + running_root.imag * root_step.real};
+        }
+        k1 += FFT::stride;
+    }
+}
+
+template <class FFT, bool ContiguousOutput>
+__launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_online_direct_second_kernel(
+    const Complex32* scratch, Complex32* output, std::uint32_t log_n, std::uint32_t local_log_n,
+    std::uint64_t batch_distance, std::uint64_t element_stride,
+    bool normalize) {
+    using Value = typename FFT::value_type;
+    const std::uint32_t local_n         = 1U << local_log_n;
+    const std::uint32_t remaining_log_n = log_n - local_log_n;
+    const std::uint32_t remaining_n     = 1U << remaining_log_n;
+    const std::uint64_t local_transform = blockIdx.x;
+    const std::uint64_t transform       = local_transform >> local_log_n;
+    const std::uint32_t k1              = static_cast<std::uint32_t>(local_transform) & (local_n - 1);
+    const std::uint64_t base            = transform * batch_distance;
+
+    Value thread_data[FFT::storage_size];
+    std::uint32_t n2 = threadIdx.x;
+#pragma unroll
+    for (unsigned int item = 0; item < FFT::storage_size; ++item) {
+        const std::uint64_t reordered = static_cast<std::uint64_t>(k1) * remaining_n + n2;
+        const Complex32 value = scratch[base + reordered * element_stride];
+        thread_data[item] = Value{value.real, value.imag};
+        n2 += FFT::stride;
+    }
+
+    extern __shared__ __align__(16) unsigned char storage[];
+    FFT().execute(thread_data, storage);
+    const float scale = normalize ? 1.0F / static_cast<float>(1U << log_n) : 1.0F;
+    std::uint32_t k2 = threadIdx.x;
+#pragma unroll
+    for (unsigned int item = 0; item < FFT::storage_size; ++item) {
+        const Value value = thread_data[item];
+        const std::uint64_t logical = ContiguousOutput
+                                          ? static_cast<std::uint64_t>(k1) * remaining_n + k2
+                                          : static_cast<std::uint64_t>(k2) * local_n + k1;
+        output[base + logical * element_stride] = {value.x * scale, value.y * scale};
+        k2 += FFT::stride;
+    }
+}
+
+__global__ void transpose_complex32_kernel(const Complex32* input, Complex32* output,
+                                           std::uint32_t rows, std::uint32_t columns,
+                                           std::uint64_t tiles_per_transform,
+                                           std::uint64_t batch_distance,
+                                           std::uint64_t element_stride) {
+    __shared__ Complex32 tile[32][33];
+    const std::uint64_t flat_block = blockIdx.x;
+    const std::uint64_t transform = flat_block / tiles_per_transform;
+    const std::uint64_t tile_index = flat_block - transform * tiles_per_transform;
+    const std::uint32_t tiles_x = (columns + 31U) / 32U;
+    const std::uint32_t tile_y = static_cast<std::uint32_t>(tile_index / tiles_x);
+    const std::uint32_t tile_x = static_cast<std::uint32_t>(tile_index - static_cast<std::uint64_t>(tile_y) * tiles_x);
+    const std::uint64_t base = transform * batch_distance;
+
+#pragma unroll
+    for (std::uint32_t offset = 0; offset < 32; offset += 8) {
+        const std::uint32_t row = tile_y * 32U + threadIdx.y + offset;
+        const std::uint32_t column = tile_x * 32U + threadIdx.x;
+        if (row < rows && column < columns)
+            tile[threadIdx.y + offset][threadIdx.x] =
+                input[base + (static_cast<std::uint64_t>(row) * columns + column) * element_stride];
+    }
+    __syncthreads();
+
+#pragma unroll
+    for (std::uint32_t offset = 0; offset < 32; offset += 8) {
+        const std::uint32_t output_row = tile_x * 32U + threadIdx.y + offset;
+        const std::uint32_t output_column = tile_y * 32U + threadIdx.x;
+        if (output_row < columns && output_column < rows)
+            output[base + (static_cast<std::uint64_t>(output_row) * rows + output_column) * element_stride] =
+                tile[threadIdx.x][threadIdx.y + offset];
+    }
+}
+
+void launch_transpose_complex32(const Complex32* input, Complex32* output, std::uint32_t rows,
+                                std::uint32_t columns, std::uint64_t transforms,
+                                std::uint64_t batch_distance, std::uint64_t element_stride) {
+    const std::uint64_t tiles_x = (columns + 31U) / 32U;
+    const std::uint64_t tiles_y = (rows + 31U) / 32U;
+    const std::uint64_t tiles_per_transform = tiles_x * tiles_y;
+    const std::uint64_t blocks = transforms * tiles_per_transform;
+    if (blocks > 0x7fffffffULL)
+        throw std::invalid_argument("tiled transpose grid exceeds the CUDA grid.x limit");
+    transpose_complex32_kernel<<<static_cast<unsigned int>(blocks), dim3(32, 8)>>>(
+        input, output, rows, columns, tiles_per_transform, batch_distance, element_stride);
+}
+
 template <class FFT>
 __launch_bounds__(FFT::max_threads_per_block) __global__ void cufftdx_resident_4096_kernel(
     const Complex32* input, Complex32* output, const Complex32* twiddles, std::uint64_t transforms,
@@ -540,6 +934,171 @@ void launch_online_second(std::uint32_t log_n, std::uint32_t local_log_n, const
     }
 }
 
+template <class FFT, bool FinalSegment>
+void launch_multisegment_kernel(const Complex32* input, Complex32* output, const Complex32* twiddles,
+                                std::uint64_t transforms, std::uint32_t log_n,
+                                std::uint32_t prefix_log_n, std::uint32_t segment_log_n,
+                                std::uint32_t remaining_log_n, std::uint64_t batch_distance,
+                                std::uint64_t element_stride, bool recurrence_twiddle, bool normalize,
+                                StagePartitionDescriptor partition) {
+    const std::uint64_t local_transforms = transforms << (log_n - segment_log_n);
+    const std::uint64_t block_count = (local_transforms + FFT::ffts_per_block - 1) / FFT::ffts_per_block;
+    if (block_count > 0x7fffffffULL)
+        throw std::invalid_argument("multi-segment cuFFTDx grid exceeds the CUDA grid.x limit");
+    constexpr std::size_t tile_bytes = FFT::input_length * FFT::ffts_per_block * sizeof(typename FFT::value_type);
+    constexpr std::size_t shared_bytes = FFT::shared_memory_size > tile_bytes ? FFT::shared_memory_size : tile_bytes;
+    if constexpr (shared_bytes > 48U * 1024U)
+        cudaFuncSetAttribute(cufftdx_multisegment_kernel<FFT, FinalSegment>,
+                             cudaFuncAttributeMaxDynamicSharedMemorySize, shared_bytes);
+    cufftdx_multisegment_kernel<FFT, FinalSegment>
+        <<<static_cast<unsigned int>(block_count), FFT::block_dim, shared_bytes>>>(
+            input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n,
+            remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition);
+}
+
+template <unsigned int Size, unsigned int Threads, unsigned int Ept,
+          cufftdx::fft_direction Direction, bool FinalSegment>
+void launch_multisegment_online(const Complex32* input, Complex32* output, const Complex32* twiddles,
+                                std::uint64_t transforms, std::uint32_t log_n,
+                                std::uint32_t prefix_log_n, std::uint32_t segment_log_n,
+                                std::uint32_t remaining_log_n, std::uint64_t batch_distance,
+                                std::uint64_t element_stride, bool recurrence_twiddle, bool normalize,
+                                StagePartitionDescriptor partition) {
+    if constexpr (Ept <= Size && Threads * Ept >= Size && (Threads * Ept) % Size == 0) {
+        using FFT = OnlineBlockFft<Size, Threads, Ept, Direction>;
+        launch_multisegment_kernel<FFT, FinalSegment>(
+            input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n,
+            remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition);
+    } else {
+        throw std::invalid_argument("multi-segment cuFFTDx thread/EPT point cannot cover an integer number of FFTs");
+    }
+}
+
+template <unsigned int Size, unsigned int Threads, unsigned int Ept,
+          cufftdx::fft_direction Direction, bool FinalSegment>
+void launch_multisegment_direct(const Complex32* input, Complex32* output, const Complex32* twiddles,
+                                std::uint64_t transforms, std::uint32_t log_n,
+                                std::uint32_t prefix_log_n, std::uint32_t segment_log_n,
+                                std::uint32_t remaining_log_n, std::uint64_t batch_distance,
+                                std::uint64_t element_stride, bool recurrence_twiddle, bool normalize,
+                                StagePartitionDescriptor partition) {
+    if constexpr (Threads * Ept == Size) {
+        using FFT = DirectFft<Size, Ept, Direction>;
+        static_assert(FFT::block_dim.x == Threads);
+        launch_multisegment_kernel<FFT, FinalSegment>(
+            input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n,
+            remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition);
+    } else {
+        throw std::invalid_argument("multi-segment direct cuFFTDx requires exactly one FFT per CTA");
+    }
+}
+
+template <unsigned int Size, unsigned int Threads, unsigned int Ept, cufftdx::fft_direction Direction,
+          bool ContiguousInput>
+void launch_online_direct_first(std::uint32_t log_n, std::uint32_t local_log_n, const Complex32* input,
+                                Complex32* scratch, const Complex32* twiddles, std::uint64_t transforms,
+                                std::uint64_t batch_distance, std::uint64_t element_stride,
+                                bool recurrence_twiddle) {
+    if constexpr (Threads * Ept == Size) {
+        using FFT = DirectFft<Size, Ept, Direction>;
+        static_assert(FFT::block_dim.x == Threads);
+        if constexpr (FFT::shared_memory_size > 48U * 1024U)
+            cudaFuncSetAttribute(cufftdx_online_direct_first_kernel<FFT, ContiguousInput>, cudaFuncAttributeMaxDynamicSharedMemorySize,
+                                 FFT::shared_memory_size);
+        const auto blocks = static_cast<unsigned int>(transforms << (log_n - local_log_n));
+        cufftdx_online_direct_first_kernel<FFT, ContiguousInput><<<blocks, FFT::block_dim, FFT::shared_memory_size>>>(
+            input, scratch, twiddles, log_n, local_log_n, batch_distance, element_stride, recurrence_twiddle);
+    } else {
+        throw std::invalid_argument("cuFFTDx direct prefix requires exactly one FFT per CTA");
+    }
+}
+
+template <unsigned int Size, unsigned int Threads, unsigned int Ept, cufftdx::fft_direction Direction,
+          bool ContiguousOutput>
+void launch_online_direct_second(std::uint32_t log_n, std::uint32_t local_log_n, Complex32* scratch,
+                                 Complex32* output, std::uint64_t transforms, std::uint64_t batch_distance,
+                                 std::uint64_t element_stride, bool normalize) {
+    if constexpr (Threads * Ept == Size) {
+        using FFT = DirectFft<Size, Ept, Direction>;
+        static_assert(FFT::block_dim.x == Threads);
+        if constexpr (FFT::shared_memory_size > 48U * 1024U)
+            cudaFuncSetAttribute(cufftdx_online_direct_second_kernel<FFT, ContiguousOutput>, cudaFuncAttributeMaxDynamicSharedMemorySize,
+                                 FFT::shared_memory_size);
+        const auto blocks = static_cast<unsigned int>(transforms << local_log_n);
+        cufftdx_online_direct_second_kernel<FFT, ContiguousOutput><<<blocks, FFT::block_dim, FFT::shared_memory_size>>>(
+            scratch, ContiguousOutput ? scratch : output, log_n, local_log_n,
+            batch_distance, element_stride, normalize);
+    } else {
+        throw std::invalid_argument("cuFFTDx direct suffix requires exactly one FFT per CTA");
+    }
+}
+
+template <unsigned int Size, cufftdx::fft_direction Direction, bool ContiguousInput>
+void dispatch_online_direct_first_threads_impl(std::uint32_t threads, std::uint32_t ept, std::uint32_t log_n,
+                                               std::uint32_t local_log_n, const Complex32* input, Complex32* scratch,
+                                               const Complex32* twiddles, std::uint64_t transforms,
+                                               std::uint64_t batch_distance, std::uint64_t element_stride,
+                                               bool recurrence_twiddle) {
+    switch ((ept << 16) | threads) {
+        case (2U << 16) | 1024U: launch_online_direct_first<Size, 1024, 2, Direction, ContiguousInput>(log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case (4U << 16) | 512U: launch_online_direct_first<Size, 512, 4, Direction, ContiguousInput>(log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case (4U << 16) | 1024U: launch_online_direct_first<Size, 1024, 4, Direction, ContiguousInput>(log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case (8U << 16) | 256U: launch_online_direct_first<Size, 256, 8, Direction, ContiguousInput>(log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case (8U << 16) | 512U: launch_online_direct_first<Size, 512, 8, Direction, ContiguousInput>(log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case (16U << 16) | 256U: launch_online_direct_first<Size, 256, 16, Direction, ContiguousInput>(log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        default: throw std::invalid_argument("unsupported cuFFTDx direct prefix thread/EPT point");
+    }
+}
+
+template <unsigned int Size, cufftdx::fft_direction Direction>
+void dispatch_online_direct_first_threads(std::uint32_t threads, std::uint32_t ept, std::uint32_t log_n,
+                                          std::uint32_t local_log_n, const Complex32* input, Complex32* scratch,
+                                          const Complex32* twiddles, std::uint64_t transforms,
+                                          std::uint64_t batch_distance, std::uint64_t element_stride,
+                                          bool recurrence_twiddle, bool contiguous_input) {
+    if (contiguous_input)
+        dispatch_online_direct_first_threads_impl<Size, Direction, true>(threads, ept, log_n, local_log_n,
+                                                                         input, scratch, twiddles, transforms,
+                                                                         batch_distance, element_stride,
+                                                                         recurrence_twiddle);
+    else
+        dispatch_online_direct_first_threads_impl<Size, Direction, false>(threads, ept, log_n, local_log_n,
+                                                                          input, scratch, twiddles, transforms,
+                                                                          batch_distance, element_stride,
+                                                                          recurrence_twiddle);
+}
+
+template <unsigned int Size, cufftdx::fft_direction Direction, bool ContiguousOutput>
+void dispatch_online_direct_second_threads_impl(std::uint32_t threads, std::uint32_t ept, std::uint32_t log_n,
+                                                std::uint32_t local_log_n, Complex32* scratch, Complex32* output,
+                                                std::uint64_t transforms, std::uint64_t batch_distance,
+                                                std::uint64_t element_stride, bool normalize) {
+    switch ((ept << 16) | threads) {
+        case (2U << 16) | 1024U: launch_online_direct_second<Size, 1024, 2, Direction, ContiguousOutput>(log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case (4U << 16) | 512U: launch_online_direct_second<Size, 512, 4, Direction, ContiguousOutput>(log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case (4U << 16) | 1024U: launch_online_direct_second<Size, 1024, 4, Direction, ContiguousOutput>(log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case (8U << 16) | 256U: launch_online_direct_second<Size, 256, 8, Direction, ContiguousOutput>(log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case (8U << 16) | 512U: launch_online_direct_second<Size, 512, 8, Direction, ContiguousOutput>(log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case (16U << 16) | 256U: launch_online_direct_second<Size, 256, 16, Direction, ContiguousOutput>(log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        default: throw std::invalid_argument("unsupported cuFFTDx direct suffix thread/EPT point");
+    }
+}
+
+template <unsigned int Size, cufftdx::fft_direction Direction>
+void dispatch_online_direct_second_threads(std::uint32_t threads, std::uint32_t ept, std::uint32_t log_n,
+                                           std::uint32_t local_log_n, Complex32* scratch, Complex32* output,
+                                           std::uint64_t transforms, std::uint64_t batch_distance,
+                                           std::uint64_t element_stride, bool normalize, bool tiled_transpose) {
+    if (tiled_transpose)
+        dispatch_online_direct_second_threads_impl<Size, Direction, true>(threads, ept, log_n, local_log_n,
+                                                                          scratch, output, transforms, batch_distance,
+                                                                          element_stride, normalize);
+    else
+        dispatch_online_direct_second_threads_impl<Size, Direction, false>(threads, ept, log_n, local_log_n,
+                                                                           scratch, output, transforms, batch_distance,
+                                                                           element_stride, normalize);
+}
+
 template <unsigned int Size, cufftdx::fft_direction Direction>
 void dispatch_online_first_threads(std::uint32_t threads, std::uint32_t ept, std::uint32_t log_n, std::uint32_t local_log_n,
                                    const Complex32* input, Complex32* scratch, const Complex32* twiddles,
@@ -567,39 +1126,134 @@ void dispatch_online_second_threads(std::uint32_t threads, std::uint32_t ept, st
     }
 }
 
+template <unsigned int Size, cufftdx::fft_direction Direction, bool FinalSegment>
+void dispatch_multisegment_online_threads(
+    std::uint32_t threads, std::uint32_t ept, const Complex32* input, Complex32* output,
+    const Complex32* twiddles, std::uint64_t transforms, std::uint32_t log_n,
+    std::uint32_t prefix_log_n, std::uint32_t segment_log_n, std::uint32_t remaining_log_n,
+    std::uint64_t batch_distance, std::uint64_t element_stride, bool recurrence_twiddle,
+    bool normalize, StagePartitionDescriptor partition) {
+    switch ((ept << 16) | threads) {
+#define CUNTT_CUFFTDX_ONLINE_LAUNCH(Threads, Ept)                                                    \
+        launch_multisegment_online<Size, Threads, Ept, Direction, FinalSegment>(                    \
+            input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n,                \
+            remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition)
+#include "generated_cufftdx_online_dispatch.inc"
+#undef CUNTT_CUFFTDX_ONLINE_LAUNCH
+        default: throw std::invalid_argument("requested multi-segment cuFFTDx thread/EPT point was not generated");
+    }
+}
+
+template <unsigned int Size, cufftdx::fft_direction Direction, bool FinalSegment>
+void dispatch_multisegment_direct_threads(
+    std::uint32_t threads, std::uint32_t ept, const Complex32* input, Complex32* output,
+    const Complex32* twiddles, std::uint64_t transforms, std::uint32_t log_n,
+    std::uint32_t prefix_log_n, std::uint32_t segment_log_n, std::uint32_t remaining_log_n,
+    std::uint64_t batch_distance, std::uint64_t element_stride, bool recurrence_twiddle,
+    bool normalize, StagePartitionDescriptor partition) {
+    switch ((ept << 16) | threads) {
+        case (2U << 16) | 1024U:
+            launch_multisegment_direct<Size, 1024, 2, Direction, FinalSegment>(input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        case (4U << 16) | 512U:
+            launch_multisegment_direct<Size, 512, 4, Direction, FinalSegment>(input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        case (4U << 16) | 1024U:
+            launch_multisegment_direct<Size, 1024, 4, Direction, FinalSegment>(input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        case (8U << 16) | 256U:
+            launch_multisegment_direct<Size, 256, 8, Direction, FinalSegment>(input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        case (8U << 16) | 512U:
+            launch_multisegment_direct<Size, 512, 8, Direction, FinalSegment>(input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        case (16U << 16) | 256U:
+            launch_multisegment_direct<Size, 256, 16, Direction, FinalSegment>(input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        default: throw std::invalid_argument("unsupported multi-segment direct cuFFTDx thread/EPT point");
+    }
+}
+
+template <cufftdx::fft_direction Direction, bool FinalSegment>
+void dispatch_multisegment(
+    std::uint32_t segment_log_n, std::uint32_t threads, std::uint32_t ept,
+    const Complex32* input, Complex32* output, const Complex32* twiddles,
+    std::uint64_t transforms, std::uint32_t log_n, std::uint32_t prefix_log_n,
+    std::uint32_t remaining_log_n, std::uint64_t batch_distance,
+    std::uint64_t element_stride, bool recurrence_twiddle, bool normalize,
+    StagePartitionDescriptor partition) {
+#define CUNTT_DISPATCH_SEGMENT(Size)                                                                  \
+    dispatch_multisegment_online_threads<Size, Direction, FinalSegment>(                              \
+        threads, ept, input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n,       \
+        remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition)
+    switch (segment_log_n) {
+        case 3: CUNTT_DISPATCH_SEGMENT(8); return;
+        case 4: CUNTT_DISPATCH_SEGMENT(16); return;
+        case 5: CUNTT_DISPATCH_SEGMENT(32); return;
+        case 6: CUNTT_DISPATCH_SEGMENT(64); return;
+        case 7: CUNTT_DISPATCH_SEGMENT(128); return;
+        case 8: CUNTT_DISPATCH_SEGMENT(256); return;
+        case 9: CUNTT_DISPATCH_SEGMENT(512); return;
+        case 10: CUNTT_DISPATCH_SEGMENT(1024); return;
+        case 11:
+            dispatch_multisegment_direct_threads<2048, Direction, FinalSegment>(threads, ept, input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        case 12:
+            dispatch_multisegment_direct_threads<4096, Direction, FinalSegment>(threads, ept, input, output, twiddles, transforms, log_n, prefix_log_n, segment_log_n, remaining_log_n, batch_distance, element_stride, recurrence_twiddle, normalize, partition); return;
+        default: throw std::invalid_argument("multi-segment cuFFTDx supports segment logN=3..12");
+    }
+#undef CUNTT_DISPATCH_SEGMENT
+}
+
 template <cufftdx::fft_direction Direction>
 void dispatch_online_first(std::uint32_t log_n, std::uint32_t local_log_n, const Complex32* input,
                            Complex32* scratch, const Complex32* twiddles, std::uint64_t transforms,
                            std::uint64_t batch_distance, std::uint64_t element_stride, bool recurrence_twiddle,
-                           std::uint32_t threads, std::uint32_t ept) {
+                           std::uint32_t threads, std::uint32_t ept, bool contiguous_input) {
     switch (local_log_n) {
-        case 3: dispatch_online_first_threads<8, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 4: dispatch_online_first_threads<16, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 5: dispatch_online_first_threads<32, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 6: dispatch_online_first_threads<64, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 7: dispatch_online_first_threads<128, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 8: dispatch_online_first_threads<256, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 9: dispatch_online_first_threads<512, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        case 10: dispatch_online_first_threads<1024, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
-        default: throw std::invalid_argument("cufftdx online first pass supports logN=3..10");
+        case 3: if (contiguous_input) break; dispatch_online_first_threads<8, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 4: if (contiguous_input) break; dispatch_online_first_threads<16, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 5: if (contiguous_input) break; dispatch_online_first_threads<32, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 6: if (contiguous_input) break; dispatch_online_first_threads<64, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 7: if (contiguous_input) break; dispatch_online_first_threads<128, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 8: if (contiguous_input) break; dispatch_online_first_threads<256, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 9: if (contiguous_input) break; dispatch_online_first_threads<512, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 10: if (contiguous_input) break; dispatch_online_first_threads<1024, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle); return;
+        case 11: dispatch_online_direct_first_threads<2048, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle, contiguous_input); return;
+        case 12: dispatch_online_direct_first_threads<4096, Direction>(threads, ept, log_n, local_log_n, input, scratch, twiddles, transforms, batch_distance, element_stride, recurrence_twiddle, contiguous_input); return;
+        default: throw std::invalid_argument("cufftdx online first pass supports logN=3..12");
     }
+    throw std::invalid_argument("prefix tiled transpose requires a direct prefix in logN=11..12");
 }
 
 template <cufftdx::fft_direction Direction>
-void dispatch_online_second(std::uint32_t log_n, std::uint32_t local_log_n, const Complex32* scratch,
+void dispatch_online_second(std::uint32_t log_n, std::uint32_t local_log_n, Complex32* scratch,
                             Complex32* output, std::uint64_t transforms, std::uint64_t batch_distance,
-                            std::uint64_t element_stride, bool normalize, std::uint32_t threads, std::uint32_t ept) {
+                            std::uint64_t element_stride, bool normalize, std::uint32_t threads, std::uint32_t ept,
+                            bool tiled_transpose) {
     switch (log_n - local_log_n) {
-        case 3: dispatch_online_second_threads<8, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 4: dispatch_online_second_threads<16, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 5: dispatch_online_second_threads<32, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 6: dispatch_online_second_threads<64, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 7: dispatch_online_second_threads<128, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 8: dispatch_online_second_threads<256, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 9: dispatch_online_second_threads<512, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        case 10: dispatch_online_second_threads<1024, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
-        default: throw std::invalid_argument("cufftdx online second pass supports logN=3..10");
+        case 3: if (tiled_transpose) break; dispatch_online_second_threads<8, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 4: if (tiled_transpose) break; dispatch_online_second_threads<16, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 5: if (tiled_transpose) break; dispatch_online_second_threads<32, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 6: if (tiled_transpose) break; dispatch_online_second_threads<64, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 7: if (tiled_transpose) break; dispatch_online_second_threads<128, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 8: if (tiled_transpose) break; dispatch_online_second_threads<256, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 9: if (tiled_transpose) break; dispatch_online_second_threads<512, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 10: if (tiled_transpose) break; dispatch_online_second_threads<1024, Direction>(threads, ept, log_n, local_log_n, scratch, output, transforms, batch_distance, element_stride, normalize); return;
+        case 11:
+            dispatch_online_direct_second_threads<2048, Direction>(threads, ept, log_n, local_log_n, scratch, output,
+                                                                   transforms, batch_distance, element_stride, normalize,
+                                                                   tiled_transpose);
+            if (tiled_transpose)
+                launch_transpose_complex32(scratch, output, 1U << local_log_n,
+                                           1U << (log_n - local_log_n), transforms,
+                                           batch_distance, element_stride);
+            return;
+        case 12:
+            dispatch_online_direct_second_threads<4096, Direction>(threads, ept, log_n, local_log_n, scratch, output,
+                                                                   transforms, batch_distance, element_stride, normalize,
+                                                                   tiled_transpose);
+            if (tiled_transpose)
+                launch_transpose_complex32(scratch, output, 1U << local_log_n,
+                                           1U << (log_n - local_log_n), transforms,
+                                           batch_distance, element_stride);
+            return;
+        default: throw std::invalid_argument("cufftdx online second pass supports logN=3..12");
     }
+    throw std::invalid_argument("tiled transpose requires a direct suffix in logN=11..12");
 }
 
 template <unsigned int Elements, cufftdx::fft_direction Direction>
@@ -719,6 +1373,10 @@ void launch_persistent_16384(const Complex32* input, Complex32* output, Complex3
 bool cufftdx_block_available(std::uint32_t log_n) noexcept { return log_n >= 3 && log_n <= 10; }
 
 bool cufftdx_online_available(std::uint32_t log_n, std::uint32_t threads, std::uint32_t ept) noexcept {
+    if (log_n == 11 || log_n == 12) {
+        return (threads == 256 || threads == 512 || threads == 1024) &&
+               static_cast<std::uint64_t>(threads) * ept == (1ULL << log_n);
+    }
     return generated_cufftdx_online_available(log_n, threads, ept);
 }
 
@@ -752,25 +1410,103 @@ void launch_cufftdx_direct(std::uint32_t log_n, const Complex32* input, Complex3
 }
 
 void launch_cufftdx_online_reorder(std::uint32_t log_n, std::uint32_t local_log_n, const Complex32* input,
-                                   Complex32* output, Complex32* scratch, const Complex32* twiddles,
+                                   Complex32* output, Complex32* scratch, Complex32* workspace,
+                                   const Complex32* twiddles,
                                    std::uint64_t transforms, std::uint64_t batch_distance,
                                    std::uint64_t element_stride, bool inverse, bool normalize,
                                    CrossTwiddleMode cross_twiddle, std::uint32_t prefix_threads,
                                    std::uint32_t suffix_threads, std::uint32_t prefix_ept,
-                                   std::uint32_t suffix_ept) {
+                                   std::uint32_t suffix_ept, DirectBoundary direct_boundary) {
     const bool recurrence_twiddle = cross_twiddle == CrossTwiddleMode::Recurrence;
+    const bool suffix_tiled_transpose = direct_boundary == DirectBoundary::TiledTranspose;
+    const bool prefix_tiled_transpose = direct_boundary == DirectBoundary::PrefixTiledTranspose;
+    const Complex32* prefix_input = input;
+    if (prefix_tiled_transpose) {
+        if (workspace == nullptr)
+            throw std::invalid_argument("prefix tiled transpose requires a workspace buffer");
+        launch_transpose_complex32(input, workspace, 1U << local_log_n,
+                                   1U << (log_n - local_log_n), transforms,
+                                   batch_distance, element_stride);
+        prefix_input = workspace;
+    }
     if (inverse) {
-        dispatch_online_first<cufftdx::fft_direction::inverse>(log_n, local_log_n, input, scratch, twiddles,
+        dispatch_online_first<cufftdx::fft_direction::inverse>(log_n, local_log_n, prefix_input, scratch, twiddles,
                                                                transforms, batch_distance, element_stride, recurrence_twiddle,
-                                                               prefix_threads, prefix_ept);
+                                                               prefix_threads, prefix_ept, prefix_tiled_transpose);
         dispatch_online_second<cufftdx::fft_direction::inverse>(log_n, local_log_n, scratch, output, transforms,
-                                                                batch_distance, element_stride, normalize, suffix_threads, suffix_ept);
+                                                                batch_distance, element_stride, normalize, suffix_threads, suffix_ept,
+                                                                suffix_tiled_transpose);
     } else {
-        dispatch_online_first<cufftdx::fft_direction::forward>(log_n, local_log_n, input, scratch, twiddles,
+        dispatch_online_first<cufftdx::fft_direction::forward>(log_n, local_log_n, prefix_input, scratch, twiddles,
                                                                transforms, batch_distance, element_stride, recurrence_twiddle,
-                                                               prefix_threads, prefix_ept);
+                                                               prefix_threads, prefix_ept, prefix_tiled_transpose);
         dispatch_online_second<cufftdx::fft_direction::forward>(log_n, local_log_n, scratch, output, transforms,
-                                                                batch_distance, element_stride, false, suffix_threads, suffix_ept);
+                                                                batch_distance, element_stride, false, suffix_threads, suffix_ept,
+                                                                suffix_tiled_transpose);
+    }
+}
+
+void launch_cufftdx_multisegment(std::uint32_t log_n, const std::vector<std::uint32_t>& stage_partition,
+                                 const std::vector<FftSegmentMapping>& segment_mappings,
+                                 const std::vector<FftBoundaryMapping>& boundaries,
+                                 const Complex32* input, Complex32* output, Complex32* scratch,
+                                 Complex32* workspace, const Complex32* twiddles,
+                                 std::uint64_t transforms, std::uint64_t batch_distance,
+                                 std::uint64_t element_stride, bool inverse, bool normalize) {
+    if (stage_partition.size() < 3 || stage_partition.size() > 8 ||
+        segment_mappings.size() != stage_partition.size() ||
+        boundaries.size() + 1 != stage_partition.size())
+        throw std::invalid_argument("invalid multi-segment FFT runtime descriptors");
+    if (scratch == nullptr || workspace == nullptr)
+        throw std::invalid_argument("multi-segment FFT requires two scratch buffers");
+
+    StagePartitionDescriptor descriptor{};
+    descriptor.count = static_cast<std::uint32_t>(stage_partition.size());
+    std::uint32_t input_shift = log_n;
+    std::uint32_t output_shift = 0;
+    for (std::size_t segment = 0; segment < stage_partition.size(); ++segment) {
+        input_shift -= stage_partition[segment];
+        descriptor.input_shift[segment] = input_shift;
+        descriptor.output_shift[segment] = output_shift;
+        descriptor.mask[segment] = (1U << stage_partition[segment]) - 1U;
+        output_shift += stage_partition[segment];
+    }
+
+    const Complex32* source = input;
+    std::uint32_t prefix_log_n = 0;
+    for (std::size_t segment = 0; segment < stage_partition.size(); ++segment) {
+        const bool final_segment = segment + 1 == stage_partition.size();
+        const std::uint32_t segment_log_n = stage_partition[segment];
+        const std::uint32_t remaining_log_n = log_n - prefix_log_n - segment_log_n;
+        Complex32* destination = final_segment ? output : (segment % 2 == 0 ? scratch : workspace);
+        const bool recurrence = !final_segment &&
+                                boundaries[segment].cross_twiddle == CrossTwiddleMode::Recurrence;
+        const auto& mapping = segment_mappings[segment];
+        if (inverse) {
+            if (final_segment)
+                dispatch_multisegment<cufftdx::fft_direction::inverse, true>(
+                    segment_log_n, mapping.threads, mapping.ept, source, destination, twiddles,
+                    transforms, log_n, prefix_log_n, remaining_log_n, batch_distance,
+                    element_stride, false, normalize, descriptor);
+            else
+                dispatch_multisegment<cufftdx::fft_direction::inverse, false>(
+                    segment_log_n, mapping.threads, mapping.ept, source, destination, twiddles,
+                    transforms, log_n, prefix_log_n, remaining_log_n, batch_distance,
+                    element_stride, recurrence, false, descriptor);
+        } else {
+            if (final_segment)
+                dispatch_multisegment<cufftdx::fft_direction::forward, true>(
+                    segment_log_n, mapping.threads, mapping.ept, source, destination, twiddles,
+                    transforms, log_n, prefix_log_n, remaining_log_n, batch_distance,
+                    element_stride, false, false, descriptor);
+            else
+                dispatch_multisegment<cufftdx::fft_direction::forward, false>(
+                    segment_log_n, mapping.threads, mapping.ept, source, destination, twiddles,
+                    transforms, log_n, prefix_log_n, remaining_log_n, batch_distance,
+                    element_stride, recurrence, false, descriptor);
+        }
+        source = destination;
+        prefix_log_n += segment_log_n;
     }
 }
 
diff --git a/src/cufftdx_fft_fp64.cu b/src/cufftdx_fft_fp64.cu
new file mode 100644
index 0000000..ce24e3b
--- /dev/null
+++ b/src/cufftdx_fft_fp64.cu
@@ -0,0 +1,437 @@
+#include <cuda_runtime.h>
+#include <cufftdx.hpp>
+
+#include <stdexcept>
+
+#include "external_fft_units.cuh"
+
+namespace cuntt::detail {
+namespace {
+
+template <unsigned Size, cufftdx::fft_direction Direction>
+using Fp64BlockFft = decltype(cufftdx::Block() + cufftdx::Size<Size>() +
+                              cufftdx::Type<cufftdx::fft_type::c2c>() + cufftdx::Direction<Direction>() +
+                              cufftdx::Precision<double>() + cufftdx::ElementsPerThread<8>() +
+                              cufftdx::FFTsPerBlock<1024 / Size>() + cufftdx::SM<700>());
+
+template <unsigned Size, unsigned Threads, unsigned Ept, cufftdx::fft_direction Direction>
+using Fp64OnlineFft = decltype(cufftdx::Block() + cufftdx::Size<Size>() +
+                               cufftdx::Type<cufftdx::fft_type::c2c>() + cufftdx::Direction<Direction>() +
+                               cufftdx::Precision<double>() + cufftdx::ElementsPerThread<Ept>() +
+                               cufftdx::FFTsPerBlock<(Threads * Ept) / Size>() + cufftdx::SM<700>());
+
+template <class FFT>
+__launch_bounds__(FFT::max_threads_per_block) __global__ void fp64_block_kernel(
+    const Complex64* input, Complex64* output, std::uint64_t transforms,
+    std::uint64_t batch_distance, std::uint64_t element_stride, bool normalize) {
+    using Value = typename FFT::value_type;
+    const std::uint64_t transform = static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + threadIdx.y;
+    const bool active = transform < transforms;
+    const std::uint64_t base = transform * batch_distance;
+    Value thread_data[FFT::storage_size];
+    unsigned index = threadIdx.x;
+#pragma unroll
+    for (unsigned item = 0; item < FFT::storage_size; ++item) {
+        if (active && index < FFT::input_length) {
+            const Complex64 value = input[base + static_cast<std::uint64_t>(index) * element_stride];
+            thread_data[item] = Value{value.real, value.imag};
+        } else {
+            thread_data[item] = Value{0.0, 0.0};
+        }
+        index += FFT::stride;
+    }
+    extern __shared__ __align__(16) unsigned char storage[];
+    FFT().execute(thread_data, storage);
+    const double scale = normalize ? 1.0 / static_cast<double>(FFT::input_length) : 1.0;
+    index = threadIdx.x;
+#pragma unroll
+    for (unsigned item = 0; item < FFT::storage_size; ++item) {
+        if (active && index < FFT::output_length) {
+            const Value value = thread_data[item];
+            output[base + static_cast<std::uint64_t>(index) * element_stride] =
+                {value.x * scale, value.y * scale};
+        }
+        index += FFT::stride;
+    }
+}
+
+__device__ __forceinline__ Complex64 fp64_cross_root(const Complex64* twiddles, std::uint32_t log_n,
+                                                      std::uint64_t exponent) {
+    const std::uint32_t n = 1U << log_n;
+    const std::uint32_t half = n >> 1;
+    const std::uint32_t power = static_cast<std::uint32_t>(exponent) & (n - 1);
+    const bool negate = power >= half;
+    const Complex64 root = twiddles[half - 1 + (negate ? power - half : power)];
+    return negate ? Complex64{-root.real, -root.imag} : root;
+}
+
+template <class FFT, bool XorSwizzle>
+__device__ __forceinline__ std::uint32_t fp64_tile_index(std::uint32_t element, std::uint32_t slot) {
+    static_assert((FFT::ffts_per_block & (FFT::ffts_per_block - 1)) == 0);
+    if constexpr (XorSwizzle)
+        slot ^= (element >> 1) & (FFT::ffts_per_block - 1);
+    return element * FFT::ffts_per_block + slot;
+}
+
+template <class FFT, bool XorSwizzle>
+__launch_bounds__(FFT::max_threads_per_block) __global__ void fp64_online_first_kernel(
+    const Complex64* input, Complex64* scratch, const Complex64* twiddles,
+    std::uint64_t transforms, std::uint32_t log_n, std::uint32_t local_log_n,
+    std::uint64_t batch_distance, std::uint64_t element_stride, bool recurrence_twiddle) {
+    using Value = typename FFT::value_type;
+    const std::uint32_t remaining_log_n = log_n - local_log_n;
+    const std::uint32_t remaining_n = 1U << remaining_log_n;
+    const std::uint64_t local_transform =
+        static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + threadIdx.y;
+    const std::uint64_t total_local = transforms * remaining_n;
+    const bool active = local_transform < total_local;
+    const std::uint32_t n2 = static_cast<std::uint32_t>(local_transform) & (remaining_n - 1);
+    const std::uint32_t flat_thread = threadIdx.y * blockDim.x + threadIdx.x;
+    constexpr std::uint32_t flat_threads = FFT::max_threads_per_block;
+    constexpr std::uint32_t elements_per_block_step = flat_threads / FFT::ffts_per_block;
+    constexpr std::uint32_t tile_item_step = FFT::stride * FFT::ffts_per_block;
+    constexpr std::uint32_t tile_values = FFT::input_length * FFT::ffts_per_block;
+    constexpr bool stable_block_swizzle =
+        !XorSwizzle || elements_per_block_step % (2 * FFT::ffts_per_block) == 0;
+    constexpr bool stable_item_swizzle =
+        !XorSwizzle || FFT::stride % (2 * FFT::ffts_per_block) == 0;
+    static_assert(flat_threads % FFT::ffts_per_block == 0);
+    extern __shared__ __align__(16) unsigned char storage[];
+    Value* tile = reinterpret_cast<Value*>(storage);
+
+    const std::uint32_t first_element = flat_thread / FFT::ffts_per_block;
+    const std::uint32_t slot = flat_thread - first_element * FFT::ffts_per_block;
+    const std::uint64_t staged_transform =
+        static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+    std::uint32_t stage_element = first_element;
+    std::uint32_t stage_index = fp64_tile_index<FFT, XorSwizzle>(first_element, slot);
+    if (staged_transform < total_local) {
+        const std::uint64_t batch = staged_transform >> remaining_log_n;
+        const std::uint32_t staged_n2 = static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+        std::uint64_t global_index = batch * batch_distance +
+                                     (static_cast<std::uint64_t>(first_element) * remaining_n + staged_n2) * element_stride;
+        const std::uint64_t global_step =
+            static_cast<std::uint64_t>(elements_per_block_step) * remaining_n * element_stride;
+        for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+            const Complex64 value = input[global_index];
+            tile[stage_index] = Value{value.real, value.imag};
+            stage_element += elements_per_block_step;
+            if constexpr (stable_block_swizzle)
+                stage_index += flat_threads;
+            else
+                stage_index = fp64_tile_index<FFT, XorSwizzle>(stage_element, slot);
+            global_index += global_step;
+        }
+    } else {
+        for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+            tile[stage_index] = Value{0.0, 0.0};
+            stage_element += elements_per_block_step;
+            if constexpr (stable_block_swizzle)
+                stage_index += flat_threads;
+            else
+                stage_index = fp64_tile_index<FFT, XorSwizzle>(stage_element, slot);
+        }
+    }
+    __syncthreads();
+
+    Value thread_data[FFT::storage_size];
+    unsigned n1 = threadIdx.x;
+    std::uint32_t load_index = fp64_tile_index<FFT, XorSwizzle>(n1, threadIdx.y);
+#pragma unroll
+    for (unsigned item = 0; item < FFT::storage_size; ++item) {
+        thread_data[item] = active && n1 < FFT::input_length ? tile[load_index] : Value{0.0, 0.0};
+        n1 += FFT::stride;
+        if constexpr (stable_item_swizzle)
+            load_index += tile_item_step;
+        else
+            load_index = fp64_tile_index<FFT, XorSwizzle>(n1, threadIdx.y);
+    }
+    __syncthreads();
+    FFT().execute(thread_data, storage);
+    __syncthreads();
+
+    Complex64 running_root{1.0, 0.0};
+    Complex64 root_step{1.0, 0.0};
+    if (active && recurrence_twiddle) {
+        running_root = fp64_cross_root(twiddles, log_n, static_cast<std::uint64_t>(threadIdx.x) * n2);
+        root_step = fp64_cross_root(twiddles, log_n, static_cast<std::uint64_t>(FFT::stride) * n2);
+    }
+    unsigned k1 = threadIdx.x;
+    std::uint32_t store_index = fp64_tile_index<FFT, XorSwizzle>(k1, threadIdx.y);
+#pragma unroll
+    for (unsigned item = 0; item < FFT::storage_size; ++item) {
+        if (active && k1 < FFT::output_length) {
+            const Value value = thread_data[item];
+            const Complex64 root = recurrence_twiddle
+                                       ? running_root
+                                       : fp64_cross_root(twiddles, log_n, static_cast<std::uint64_t>(k1) * n2);
+            tile[store_index] =
+                Value{value.x * root.real - value.y * root.imag,
+                      value.x * root.imag + value.y * root.real};
+        }
+        if (recurrence_twiddle) {
+            running_root = {running_root.real * root_step.real - running_root.imag * root_step.imag,
+                            running_root.real * root_step.imag + running_root.imag * root_step.real};
+        }
+        k1 += FFT::stride;
+        if constexpr (stable_item_swizzle)
+            store_index += tile_item_step;
+        else
+            store_index = fp64_tile_index<FFT, XorSwizzle>(k1, threadIdx.y);
+    }
+    __syncthreads();
+
+    if (staged_transform < total_local) {
+        const std::uint64_t batch = staged_transform >> remaining_log_n;
+        const std::uint32_t staged_n2 = static_cast<std::uint32_t>(staged_transform) & (remaining_n - 1);
+        std::uint64_t global_index = batch * batch_distance +
+                                     (static_cast<std::uint64_t>(first_element) * remaining_n + staged_n2) * element_stride;
+        const std::uint64_t global_step =
+            static_cast<std::uint64_t>(elements_per_block_step) * remaining_n * element_stride;
+        std::uint32_t export_element = first_element;
+        std::uint32_t export_index = fp64_tile_index<FFT, XorSwizzle>(first_element, slot);
+        for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+            const Value value = tile[export_index];
+            scratch[global_index] = {value.x, value.y};
+            export_element += elements_per_block_step;
+            if constexpr (stable_block_swizzle)
+                export_index += flat_threads;
+            else
+                export_index = fp64_tile_index<FFT, XorSwizzle>(export_element, slot);
+            global_index += global_step;
+        }
+    }
+}
+
+template <class FFT>
+__launch_bounds__(FFT::max_threads_per_block) __global__ void fp64_online_second_kernel(
+    const Complex64* scratch, Complex64* output, std::uint64_t transforms,
+    std::uint32_t log_n, std::uint32_t local_log_n, std::uint64_t batch_distance,
+    std::uint64_t element_stride, bool normalize) {
+    using Value = typename FFT::value_type;
+    const std::uint32_t local_n = 1U << local_log_n;
+    const std::uint32_t remaining_log_n = log_n - local_log_n;
+    const std::uint32_t remaining_n = 1U << remaining_log_n;
+    const std::uint64_t local_transform =
+        static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + threadIdx.y;
+    const std::uint64_t total_local = transforms * local_n;
+    const bool active = local_transform < total_local;
+    const std::uint64_t batch = local_transform >> local_log_n;
+    const std::uint32_t k1 = static_cast<std::uint32_t>(local_transform) & (local_n - 1);
+
+    Value thread_data[FFT::storage_size];
+    unsigned n2 = threadIdx.x;
+#pragma unroll
+    for (unsigned item = 0; item < FFT::storage_size; ++item) {
+        if (active && n2 < FFT::input_length) {
+            const std::uint64_t logical = static_cast<std::uint64_t>(k1) * remaining_n + n2;
+            const Complex64 value = scratch[batch * batch_distance + logical * element_stride];
+            thread_data[item] = Value{value.real, value.imag};
+        } else {
+            thread_data[item] = Value{0.0, 0.0};
+        }
+        n2 += FFT::stride;
+    }
+    extern __shared__ __align__(16) unsigned char storage[];
+    FFT().execute(thread_data, storage);
+    __syncthreads();
+    Value* tile = reinterpret_cast<Value*>(storage);
+    const double scale = normalize ? 1.0 / static_cast<double>(1U << log_n) : 1.0;
+    unsigned k2 = threadIdx.x;
+#pragma unroll
+    for (unsigned item = 0; item < FFT::storage_size; ++item) {
+        if (active && k2 < FFT::output_length) {
+            const Value value = thread_data[item];
+            tile[k2 * FFT::ffts_per_block + threadIdx.y] = Value{value.x * scale, value.y * scale};
+        }
+        k2 += FFT::stride;
+    }
+    __syncthreads();
+
+    const std::uint32_t flat_thread = threadIdx.y * blockDim.x + threadIdx.x;
+    const std::uint32_t flat_threads = blockDim.x * blockDim.y;
+    constexpr std::uint32_t tile_values = FFT::output_length * FFT::ffts_per_block;
+    for (std::uint32_t work = flat_thread; work < tile_values; work += flat_threads) {
+        const std::uint32_t element = work / FFT::ffts_per_block;
+        const std::uint32_t slot = work - element * FFT::ffts_per_block;
+        const std::uint64_t staged_transform =
+            static_cast<std::uint64_t>(blockIdx.x) * FFT::ffts_per_block + slot;
+        if (staged_transform < total_local) {
+            const std::uint64_t staged_batch = staged_transform >> local_log_n;
+            const std::uint32_t staged_k1 = static_cast<std::uint32_t>(staged_transform) & (local_n - 1);
+            const std::uint64_t logical = static_cast<std::uint64_t>(element) * local_n + staged_k1;
+            const Value value = tile[work];
+            output[staged_batch * batch_distance + logical * element_stride] = {value.x, value.y};
+        }
+    }
+}
+
+template <unsigned Size, cufftdx::fft_direction Direction>
+void launch_fp64_block_impl(const Complex64* input, Complex64* output, std::uint64_t transforms,
+                            std::uint64_t batch_distance, std::uint64_t element_stride, bool normalize) {
+    using FFT = Fp64BlockFft<Size, Direction>;
+    if constexpr (FFT::shared_memory_size > 48U * 1024U)
+        cudaFuncSetAttribute(fp64_block_kernel<FFT>, cudaFuncAttributeMaxDynamicSharedMemorySize,
+                             FFT::shared_memory_size);
+    const auto blocks = static_cast<unsigned>((transforms + FFT::ffts_per_block - 1) / FFT::ffts_per_block);
+    fp64_block_kernel<FFT><<<blocks, FFT::block_dim, FFT::shared_memory_size>>>(
+        input, output, transforms, batch_distance, element_stride, normalize);
+}
+
+template <cufftdx::fft_direction Direction>
+void dispatch_fp64_block(std::uint32_t log_n, const Complex64* input, Complex64* output,
+                         std::uint64_t transforms, std::uint64_t batch_distance,
+                         std::uint64_t element_stride, bool normalize) {
+    switch (log_n) {
+        case 3: launch_fp64_block_impl<8, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 4: launch_fp64_block_impl<16, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 5: launch_fp64_block_impl<32, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 6: launch_fp64_block_impl<64, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 7: launch_fp64_block_impl<128, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 8: launch_fp64_block_impl<256, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 9: launch_fp64_block_impl<512, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        case 10: launch_fp64_block_impl<1024, Direction>(input, output, transforms, batch_distance, element_stride, normalize); return;
+        default: throw std::invalid_argument("FP64 cufftdx-block supports logN=3..10");
+    }
+}
+
+template <unsigned Size, unsigned Threads, unsigned Ept, cufftdx::fft_direction Direction>
+void launch_fp64_online_first(std::uint32_t log_n, std::uint32_t local_log_n,
+                              const Complex64* input, Complex64* scratch, const Complex64* twiddles,
+                              std::uint64_t transforms, std::uint64_t batch_distance,
+                              std::uint64_t element_stride, bool recurrence_twiddle, bool xor_swizzle) {
+    using FFT = Fp64OnlineFft<Size, Threads, Ept, Direction>;
+    constexpr std::size_t tile_bytes = Size * FFT::ffts_per_block * sizeof(typename FFT::value_type);
+    constexpr std::size_t shared_bytes = FFT::shared_memory_size > tile_bytes ? FFT::shared_memory_size : tile_bytes;
+    if constexpr (shared_bytes > 48U * 1024U)
+        if (xor_swizzle)
+            cudaFuncSetAttribute(fp64_online_first_kernel<FFT, true>, cudaFuncAttributeMaxDynamicSharedMemorySize, shared_bytes);
+        else
+            cudaFuncSetAttribute(fp64_online_first_kernel<FFT, false>, cudaFuncAttributeMaxDynamicSharedMemorySize, shared_bytes);
+    const auto local_transforms = transforms << (log_n - local_log_n);
+    const auto blocks = static_cast<unsigned>((local_transforms + FFT::ffts_per_block - 1) / FFT::ffts_per_block);
+    if (xor_swizzle)
+        fp64_online_first_kernel<FFT, true><<<blocks, FFT::block_dim, shared_bytes>>>(
+            input, scratch, twiddles, transforms, log_n, local_log_n,
+            batch_distance, element_stride, recurrence_twiddle);
+    else
+        fp64_online_first_kernel<FFT, false><<<blocks, FFT::block_dim, shared_bytes>>>(
+            input, scratch, twiddles, transforms, log_n, local_log_n,
+            batch_distance, element_stride, recurrence_twiddle);
+}
+
+template <unsigned Size, unsigned Threads, unsigned Ept, cufftdx::fft_direction Direction>
+void launch_fp64_online_second(std::uint32_t log_n, std::uint32_t local_log_n,
+                               const Complex64* scratch, Complex64* output, std::uint64_t transforms,
+                               std::uint64_t batch_distance, std::uint64_t element_stride, bool normalize) {
+    using FFT = Fp64OnlineFft<Size, Threads, Ept, Direction>;
+    constexpr std::size_t tile_bytes = Size * FFT::ffts_per_block * sizeof(typename FFT::value_type);
+    constexpr std::size_t shared_bytes = FFT::shared_memory_size > tile_bytes ? FFT::shared_memory_size : tile_bytes;
+    if constexpr (shared_bytes > 48U * 1024U)
+        cudaFuncSetAttribute(fp64_online_second_kernel<FFT>, cudaFuncAttributeMaxDynamicSharedMemorySize, shared_bytes);
+    const auto local_transforms = transforms << local_log_n;
+    const auto blocks = static_cast<unsigned>((local_transforms + FFT::ffts_per_block - 1) / FFT::ffts_per_block);
+    fp64_online_second_kernel<FFT><<<blocks, FFT::block_dim, shared_bytes>>>(
+        scratch, output, transforms, log_n, local_log_n, batch_distance, element_stride, normalize);
+}
+
+template <unsigned Size, cufftdx::fft_direction Direction, bool First>
+void dispatch_fp64_online_point(std::uint32_t log_n, std::uint32_t local_log_n,
+                                std::uint32_t threads, std::uint32_t ept,
+                                const Complex64* input, Complex64* output, const Complex64* twiddles,
+                                std::uint64_t transforms, std::uint64_t batch_distance,
+                                std::uint64_t element_stride, bool option, bool xor_swizzle) {
+#define CUNTT_FP64_POINT(T, E) \
+    case ((E) << 16) | (T): \
+        if constexpr (First) launch_fp64_online_first<Size, T, E, Direction>(log_n, local_log_n, input, output, twiddles, transforms, batch_distance, element_stride, option, xor_swizzle); \
+        else launch_fp64_online_second<Size, T, E, Direction>(log_n, local_log_n, input, output, transforms, batch_distance, element_stride, option); \
+        return
+    switch ((ept << 16) | threads) {
+        CUNTT_FP64_POINT(128, 4);
+        CUNTT_FP64_POINT(256, 4);
+        CUNTT_FP64_POINT(512, 4);
+        CUNTT_FP64_POINT(128, 8);
+        CUNTT_FP64_POINT(256, 8);
+        CUNTT_FP64_POINT(512, 8);
+        default: throw std::invalid_argument("unsupported FP64 cuFFTDx thread/EPT point");
+    }
+#undef CUNTT_FP64_POINT
+}
+
+template <cufftdx::fft_direction Direction, bool First>
+void dispatch_fp64_online_size(std::uint32_t segment_log_n, std::uint32_t log_n,
+                               std::uint32_t local_log_n, std::uint32_t threads, std::uint32_t ept,
+                               const Complex64* input, Complex64* output, const Complex64* twiddles,
+                               std::uint64_t transforms, std::uint64_t batch_distance,
+                               std::uint64_t element_stride, bool option, bool xor_swizzle) {
+#define CUNTT_FP64_SIZE(LOG_N, SIZE) \
+    case (LOG_N): \
+        dispatch_fp64_online_point<SIZE, Direction, First>(log_n, local_log_n, threads, ept, input, output, twiddles, transforms, batch_distance, element_stride, option, xor_swizzle); \
+        return
+    switch (segment_log_n) {
+        CUNTT_FP64_SIZE(7, 128);
+        CUNTT_FP64_SIZE(8, 256);
+        CUNTT_FP64_SIZE(9, 512);
+        default: throw std::invalid_argument("FP64 online cuFFTDx supports segment logN=7..9");
+    }
+#undef CUNTT_FP64_SIZE
+}
+
+} // namespace
+
+bool cufftdx_fp64_block_available(std::uint32_t log_n) noexcept { return log_n >= 3 && log_n <= 10; }
+
+bool cufftdx_fp64_online_available(std::uint32_t log_n, std::uint32_t threads, std::uint32_t ept) noexcept {
+    if (log_n < 7 || log_n > 9 ||
+        (threads != 128 && threads != 256 && threads != 512) || (ept != 4 && ept != 8))
+        return false;
+    const std::uint32_t size = 1U << log_n;
+    return threads * ept >= size && (threads * ept) % size == 0;
+}
+
+void launch_cufftdx_fp64_block(std::uint32_t log_n, const Complex64* input, Complex64* output,
+                               std::uint64_t transforms, std::uint64_t batch_distance,
+                               std::uint64_t element_stride, bool inverse, bool normalize) {
+    if (inverse)
+        dispatch_fp64_block<cufftdx::fft_direction::inverse>(log_n, input, output, transforms,
+                                                             batch_distance, element_stride, normalize);
+    else
+        dispatch_fp64_block<cufftdx::fft_direction::forward>(log_n, input, output, transforms,
+                                                             batch_distance, element_stride, false);
+}
+
+void launch_cufftdx_fp64_online_reorder(std::uint32_t log_n, std::uint32_t local_log_n,
+                                        const Complex64* input, Complex64* output, Complex64* scratch,
+                                        const Complex64* twiddles, std::uint64_t transforms,
+                                        std::uint64_t batch_distance, std::uint64_t element_stride,
+                                        bool inverse, bool normalize, CrossTwiddleMode cross_twiddle,
+                                        SharedLayout shared_layout, std::uint32_t prefix_threads,
+                                        std::uint32_t suffix_threads, std::uint32_t prefix_ept,
+                                        std::uint32_t suffix_ept) {
+    const std::uint32_t remaining_log_n = log_n - local_log_n;
+    if (local_log_n < 7 || local_log_n > 9 || remaining_log_n < 7 || remaining_log_n > 9)
+        throw std::invalid_argument("FP64 online cuFFTDx requires two logN=7..9 segments");
+    const bool recurrence_twiddle = cross_twiddle == CrossTwiddleMode::Recurrence;
+    const bool xor_swizzle = shared_layout == SharedLayout::XorSwizzle;
+    if (inverse) {
+        dispatch_fp64_online_size<cufftdx::fft_direction::inverse, true>(
+            local_log_n, log_n, local_log_n, prefix_threads, prefix_ept,
+            input, scratch, twiddles, transforms,
+            batch_distance, element_stride, recurrence_twiddle, xor_swizzle);
+        dispatch_fp64_online_size<cufftdx::fft_direction::inverse, false>(
+            remaining_log_n, log_n, local_log_n, suffix_threads, suffix_ept,
+            scratch, output, nullptr, transforms,
+            batch_distance, element_stride, normalize, false);
+    } else {
+        dispatch_fp64_online_size<cufftdx::fft_direction::forward, true>(
+            local_log_n, log_n, local_log_n, prefix_threads, prefix_ept,
+            input, scratch, twiddles, transforms,
+            batch_distance, element_stride, recurrence_twiddle, xor_swizzle);
+        dispatch_fp64_online_size<cufftdx::fft_direction::forward, false>(
+            remaining_log_n, log_n, local_log_n, suffix_threads, suffix_ept,
+            scratch, output, nullptr, transforms,
+            batch_distance, element_stride, false, false);
+    }
+}
+
+} // namespace cuntt::detail
diff --git a/src/cufftdx_fft_stub.cpp b/src/cufftdx_fft_stub.cpp
index c8dd11d..470f23d 100644
--- a/src/cufftdx_fft_stub.cpp
+++ b/src/cufftdx_fft_stub.cpp
@@ -11,6 +11,21 @@ void launch_cufftdx_block(std::uint32_t, const Complex32*, Complex32*, std::uint
     throw std::runtime_error("cufftdx-block was not enabled at build time");
 }
 
+bool cufftdx_fp64_block_available(std::uint32_t) noexcept { return false; }
+bool cufftdx_fp64_online_available(std::uint32_t, std::uint32_t, std::uint32_t) noexcept { return false; }
+
+void launch_cufftdx_fp64_block(std::uint32_t, const Complex64*, Complex64*, std::uint64_t, std::uint64_t,
+                               std::uint64_t, bool, bool) {
+    throw std::runtime_error("FP64 cufftdx-block was not enabled at build time");
+}
+
+void launch_cufftdx_fp64_online_reorder(std::uint32_t, std::uint32_t, const Complex64*, Complex64*, Complex64*,
+                                        const Complex64*, std::uint64_t, std::uint64_t, std::uint64_t, bool, bool,
+                                        CrossTwiddleMode, SharedLayout, std::uint32_t, std::uint32_t,
+                                        std::uint32_t, std::uint32_t) {
+    throw std::runtime_error("FP64 online cufftdx-block was not enabled at build time");
+}
+
 bool cufftdx_direct_available(std::uint32_t) noexcept { return false; }
 
 void launch_cufftdx_direct(std::uint32_t, const Complex32*, Complex32*, std::uint64_t, std::uint64_t,
@@ -18,9 +33,10 @@ void launch_cufftdx_direct(std::uint32_t, const Complex32*, Complex32*, std::uin
     throw std::runtime_error("cufftdx-direct was not enabled at build time");
 }
 
-void launch_cufftdx_online_reorder(std::uint32_t, std::uint32_t, const Complex32*, Complex32*, Complex32*,
+void launch_cufftdx_online_reorder(std::uint32_t, std::uint32_t, const Complex32*, Complex32*, Complex32*, Complex32*,
                                    const Complex32*, std::uint64_t, std::uint64_t, std::uint64_t, bool, bool,
-                                   CrossTwiddleMode, std::uint32_t, std::uint32_t, std::uint32_t, std::uint32_t) {
+                                   CrossTwiddleMode, std::uint32_t, std::uint32_t, std::uint32_t, std::uint32_t,
+                                   DirectBoundary) {
     throw std::runtime_error("cufftdx-block was not enabled at build time");
 }
 
diff --git a/src/external_fft_units.cuh b/src/external_fft_units.cuh
index e4977e2..ff5395b 100644
--- a/src/external_fft_units.cuh
+++ b/src/external_fft_units.cuh
@@ -11,17 +11,38 @@ bool cufftdx_block_available(std::uint32_t log_n) noexcept;
 bool cufftdx_online_available(std::uint32_t log_n, std::uint32_t threads, std::uint32_t ept) noexcept;
 void launch_cufftdx_block(std::uint32_t log_n, const Complex32* input, Complex32* output, std::uint64_t transforms,
                           std::uint64_t batch_distance, std::uint64_t element_stride, bool inverse, bool normalize);
+bool cufftdx_fp64_block_available(std::uint32_t log_n) noexcept;
+bool cufftdx_fp64_online_available(std::uint32_t log_n, std::uint32_t threads, std::uint32_t ept) noexcept;
+void launch_cufftdx_fp64_block(std::uint32_t log_n, const Complex64* input, Complex64* output,
+                               std::uint64_t transforms, std::uint64_t batch_distance,
+                               std::uint64_t element_stride, bool inverse, bool normalize);
+void launch_cufftdx_fp64_online_reorder(std::uint32_t log_n, std::uint32_t local_log_n,
+                                        const Complex64* input, Complex64* output, Complex64* scratch,
+                                        const Complex64* twiddles, std::uint64_t transforms,
+                                        std::uint64_t batch_distance, std::uint64_t element_stride,
+                                        bool inverse, bool normalize, CrossTwiddleMode cross_twiddle,
+                                        SharedLayout shared_layout, std::uint32_t prefix_threads,
+                                        std::uint32_t suffix_threads, std::uint32_t prefix_ept,
+                                        std::uint32_t suffix_ept);
 bool cufftdx_direct_available(std::uint32_t log_n) noexcept;
 void launch_cufftdx_direct(std::uint32_t log_n, const Complex32* input, Complex32* output,
                            std::uint64_t transforms, std::uint64_t batch_distance, std::uint64_t element_stride,
                            bool inverse, bool normalize, std::uint32_t tile_threads);
 void launch_cufftdx_online_reorder(std::uint32_t log_n, std::uint32_t local_log_n, const Complex32* input,
-                                   Complex32* output, Complex32* scratch, const Complex32* twiddles,
+                                   Complex32* output, Complex32* scratch, Complex32* workspace,
+                                   const Complex32* twiddles,
                                    std::uint64_t transforms, std::uint64_t batch_distance,
                                    std::uint64_t element_stride, bool inverse, bool normalize,
                                    CrossTwiddleMode cross_twiddle, std::uint32_t prefix_threads,
                                    std::uint32_t suffix_threads, std::uint32_t prefix_ept,
-                                   std::uint32_t suffix_ept);
+                                   std::uint32_t suffix_ept, DirectBoundary direct_boundary);
+void launch_cufftdx_multisegment(std::uint32_t log_n, const std::vector<std::uint32_t>& stage_partition,
+                                 const std::vector<FftSegmentMapping>& segment_mappings,
+                                 const std::vector<FftBoundaryMapping>& boundaries,
+                                 const Complex32* input, Complex32* output, Complex32* scratch,
+                                 Complex32* workspace, const Complex32* twiddles,
+                                 std::uint64_t transforms, std::uint64_t batch_distance,
+                                 std::uint64_t element_stride, bool inverse, bool normalize);
 bool cufftdx_resident_available(std::uint32_t log_n, std::uint32_t local_log_n) noexcept;
 void launch_cufftdx_resident(std::uint32_t log_n, std::uint32_t local_log_n, const Complex32* input,
                              Complex32* output, Complex32* scratch, const Complex32* twiddles, std::uint64_t transforms,
diff --git a/tests/test_comprehensive_suite.py b/tests/test_comprehensive_suite.py
index dce227c..d07cb58 100644
--- a/tests/test_comprehensive_suite.py
+++ b/tests/test_comprehensive_suite.py
@@ -75,6 +75,11 @@ def test_csv_parser_ignores_non_csv_output(self):
         output = "notice\ndevice,kernel_ms,correct\n\"V100\",0.125,1\n"
         self.assertEqual(parse_csv_record(output)["kernel_ms"], "0.125")
 
+    def test_exact_case_filter_does_not_match_batch_prefix(self):
+        scaling = load_manifest(ROOT / "config" / "v100_scaling_suite.json")
+        cases = selected_cases(scaling, "full", ["fft8_cufft_b1"], exact=True)
+        self.assertEqual([case["id"] for case in cases], ["fft8_cufft_b1"])
+
     def test_summary_uses_declared_reference_and_group_fastest(self):
         base = {
             "suite_tier": "quick", "suite_runner": "butterfly", "trial": "1",
diff --git a/tests/test_external_baseline_suite.py b/tests/test_external_baseline_suite.py
new file mode 100644
index 0000000..9a7ad05
--- /dev/null
+++ b/tests/test_external_baseline_suite.py
@@ -0,0 +1,49 @@
+#!/usr/bin/env python3
+import csv
+import importlib.util
+import io
+import json
+import pathlib
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+
+
+def load(name):
+    spec = importlib.util.spec_from_file_location(name, ROOT / "scripts" / f"{name}.py")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+RUNNER = load("run_external_baseline_suite")
+SUMMARY = load("summarize_external_baseline_suite")
+
+
+class ExternalBaselineSuiteTest(unittest.TestCase):
+    def test_manifest_expands_matching_pairs(self):
+        document = json.loads((ROOT / "config" / "v100_external_baseline_suite.json").read_text())
+        cases = RUNNER.expand(document)
+        self.assertEqual(len(cases), 24)
+        groups = {}
+        for case in cases:
+            groups.setdefault(case["group"], []).append(case)
+        self.assertTrue(all(len(cases_in_group) == 2 for cases_in_group in groups.values()))
+
+    def test_parser_skips_non_csv_notices(self):
+        output = "notice\nimplementation,logN,kernel_ms\nGPU-NTT,16,0.25\n"
+        self.assertEqual(RUNNER.read_one_csv(output)["kernel_ms"], "0.25")
+
+    def test_summary_uses_declared_local_reference(self):
+        text = "group,implementation,reference,runner,operator,precision,direction,normalization,placement,output_order,logN,N,batch,modulus,modulus_bits,warmup,repeat,kernel_ms,correct\n"
+        text += "g,local,1,ntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,q,60,1,1,2.0,1\n"
+        text += "g,external,0,gpuntt,ntt,uint64,forward,none,out-of-place,natural,16,65536,4,q,60,1,1,1.0,1\n"
+        rows = list(csv.DictReader(io.StringIO(text)))
+        summary = SUMMARY.summarize(rows)
+        external = next(row for row in summary if row["implementation"] == "external")
+        self.assertEqual(external["throughput_vs_reference"], 2.0)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_fft_design_space.py b/tests/test_fft_design_space.py
index b737247..1ae244f 100644
--- a/tests/test_fft_design_space.py
+++ b/tests/test_fft_design_space.py
@@ -45,20 +45,37 @@ def test_selected_ept_is_compiled(self):
         status, reason = classify_online_point(point, self.hardware, self.compiled)
         self.assertEqual((status, reason), ("compiled", ""))
 
-    def test_large_dimension_requires_layout_kernel(self):
+    def test_direct_codegen_points_are_explicit(self):
+        self.assertIn((11, 256, 8), self.compiled)
+        self.assertIn((12, 512, 8), self.compiled)
+        self.assertNotIn((11, 256, 16), self.compiled)
+
+    def test_direct_online_dimension_is_compiled(self):
         point = self.point(prefix_log_n=4, suffix_log_n=12, prefix_threads=128,
                            suffix_threads=512, suffix_ept=8)
         status, reason = classify_online_point(point, self.hardware, self.compiled)
+        self.assertEqual((status, reason), ("compiled", ""))
+
+    def test_dimension_beyond_direct_online_requires_layout_kernel(self):
+        point = self.point(prefix_log_n=4, suffix_log_n=13, prefix_threads=128,
+                           suffix_threads=512, suffix_ept=16)
+        status, reason = classify_online_point(point, self.hardware, self.compiled)
         self.assertEqual(status, "requires-new-kernel")
         self.assertEqual(reason, "large-dimension-layout")
 
+    def test_direct_online_rejects_multiple_units_per_cta(self):
+        point = self.point(prefix_log_n=4, suffix_log_n=11, prefix_threads=128,
+                           suffix_threads=256, suffix_ept=16)
+        status, reason = classify_online_point(point, self.hardware, self.compiled)
+        self.assertEqual((status, reason), ("requires-new-kernel", "suffix-direct-single-unit"))
+
     def test_invalid_coverage_is_hardware_infeasible(self):
         point = self.point(prefix_threads=32, prefix_ept=4)
         status, _ = classify_online_point(point, self.hardware, self.compiled)
         self.assertEqual(status, "hardware-infeasible")
 
     def test_enumerator_contains_compiled_and_future_points(self):
-        rows = list(enumerate_online(self.space, "v100-sm70", [18], [256], [2, 4, 8], ["recurrence"], self.compiled))
+        rows = list(enumerate_online(self.space, "v100-sm70", [18], [256], [2, 4, 8, 32], ["recurrence"], self.compiled))
         statuses = {row["status"] for row in rows}
         self.assertIn("compiled", statuses)
         self.assertIn("awaiting-codegen", statuses)
diff --git a/tests/test_fft_dispatch_generator.py b/tests/test_fft_dispatch_generator.py
new file mode 100644
index 0000000..2d00adc
--- /dev/null
+++ b/tests/test_fft_dispatch_generator.py
@@ -0,0 +1,71 @@
+#!/usr/bin/env python3
+import importlib.util
+import pathlib
+import tempfile
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+SPEC = importlib.util.spec_from_file_location("generate_fft_dispatch", ROOT / "scripts" / "generate_fft_dispatch.py")
+MODULE = importlib.util.module_from_spec(SPEC)
+SPEC.loader.exec_module(MODULE)
+
+
+class FftDispatchGeneratorTest(unittest.TestCase):
+    def rows(self):
+        return [
+            {"rank": "1", "logN": "18", "batch": "2", "candidate_id": "low", "prefix_log_n": "8",
+             "suffix_log_n": "10", "prefix_threads": "256", "suffix_threads": "128", "prefix_ept": "8",
+             "suffix_ept": "16", "cross_twiddle": "recurrence", "median_kernel_ms": "1",
+             "direct_boundary": "tiled-transpose",
+             "cufft_median_ms": "1", "throughput_vs_cufft": "1"},
+            {"rank": "1", "logN": "18", "batch": "16", "candidate_id": "mid", "prefix_log_n": "9",
+             "suffix_log_n": "9", "prefix_threads": "128", "suffix_threads": "128", "prefix_ept": "16",
+             "suffix_ept": "16", "cross_twiddle": "table", "median_kernel_ms": "1",
+             "direct_boundary": "prefix-tiled-transpose",
+             "cufft_median_ms": "1", "throughput_vs_cufft": "1"},
+            {"rank": "2", "logN": "18", "batch": "16", "candidate_id": "loser", "prefix_log_n": "9",
+             "suffix_log_n": "9", "prefix_threads": "256", "suffix_threads": "256", "prefix_ept": "8",
+             "suffix_ept": "8", "cross_twiddle": "table", "median_kernel_ms": "2",
+             "cufft_median_ms": "1", "throughput_vs_cufft": "0.5"},
+        ]
+
+    def test_threshold_uses_log_batch_midpoint(self):
+        entries = MODULE.select_dispatch(self.rows())
+        self.assertEqual(entries[0]["max_batch"], 4)
+        self.assertIsNone(entries[1]["max_batch"])
+
+    def test_header_contains_selected_dimensions(self):
+        document = {"schema_version": 1, "target": "v100-sm70", "entries": MODULE.select_dispatch(self.rows())}
+        with tempfile.TemporaryDirectory() as directory:
+            path = pathlib.Path(directory) / "dispatch.cuh"
+            MODULE.generate_header(path, document)
+            text = path.read_text()
+            self.assertIn("log_n == 18U && batch <= 4ULL", text)
+            self.assertIn("mapping = {8U, 256U, 128U, 8U, 16U, true, true, false}", text)
+            self.assertIn("mapping = {9U, 128U, 128U, 16U, 16U, false, false, true}", text)
+
+    def test_fused_logical_segments_dispatch_as_physical_groups(self):
+        row = self.rows()[0] | {
+            "execution_group_stages": "9x9",
+            "group_threads": "512x256",
+            "group_ept": "8x16",
+        }
+        entry = MODULE.select_dispatch([row])[0]
+        self.assertEqual(entry["prefix_log_n"], 9)
+        self.assertEqual(entry["suffix_log_n"], 9)
+        self.assertEqual(entry["prefix_threads"], 512)
+        self.assertEqual(entry["suffix_threads"], 256)
+
+    def test_dispatch_rejects_more_than_two_physical_groups(self):
+        row = self.rows()[0] | {
+            "execution_group_stages": "6x6x6",
+            "group_threads": "256x256x256",
+            "group_ept": "8x8x8",
+        }
+        with self.assertRaisesRegex(ValueError, "exactly two physical groups"):
+            MODULE.select_dispatch([row])
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_fft_pipeline_generator.py b/tests/test_fft_pipeline_generator.py
new file mode 100644
index 0000000..db01928
--- /dev/null
+++ b/tests/test_fft_pipeline_generator.py
@@ -0,0 +1,156 @@
+#!/usr/bin/env python3
+import pathlib
+import sys
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+sys.path.insert(0, str(ROOT / "scripts"))
+
+from fft_design_space import load_codegen_points, load_space
+from generate_fft_pipeline import (enumerate_decomposition_topologies, enumerate_pipeline,
+                                   load_pipeline, stage_partitions)
+
+
+class FftPipelineGeneratorTest(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.pipeline = load_pipeline(ROOT / "config" / "v100_fft_pipeline.json")
+        cls.architecture = load_space(ROOT / "config" / "fft_architecture_space.json")
+        cls.codegen = load_codegen_points(ROOT / "config" / "v100_fft_codegen.json")
+        cls.runnable, cls.backlog = enumerate_pipeline(cls.pipeline, cls.architecture, cls.codegen)
+        cls.topologies = enumerate_decomposition_topologies(cls.pipeline)
+
+    def test_runnable_points_are_bounded_per_shape(self):
+        counts = {}
+        for point in self.runnable:
+            counts.setdefault((point["mapping_id"], point["batch"]), 0)
+            counts[(point["mapping_id"], point["batch"])] += 1
+        self.assertEqual(len(counts), 6)
+        limits = {mapping["id"]: mapping["max_runnable_candidates_per_shape"]
+                  for mapping in self.pipeline["mapping_spaces"]}
+        self.assertTrue(all(value <= limits[mapping] for (mapping, _), value in counts.items()))
+        self.assertTrue(all(point["selection_pool_size"] >= point["selection_limit"] for point in self.runnable))
+
+    def test_fft18_contains_asymmetric_compiled_factorizations(self):
+        splits = {(point["prefix_log_n"], point["suffix_log_n"]) for point in self.runnable
+                  if point["mapping_id"] == "fft18-fp32" and point["decomposition_count"] == 2}
+        self.assertEqual(splits, {(6, 12), (7, 11), (8, 10), (9, 9), (10, 8), (11, 7), (12, 6)})
+
+    def test_stage_partition_is_an_ordered_composition(self):
+        partitions = list(stage_partitions(18, 3, 3, 12))
+        self.assertIn((6, 6, 6), partitions)
+        self.assertIn((3, 7, 8), partitions)
+        self.assertTrue(all(len(item) == 3 and sum(item) == 18 for item in partitions))
+
+    def test_multisegment_topologies_are_compiled_runtime_points(self):
+        counts = {(item["logN"], item["decomposition_count"], item["status"])
+                  for item in self.topologies}
+        self.assertIn((18, 2, "compiled-runtime"), counts)
+        self.assertIn((18, 3, "compiled-runtime"), counts)
+        self.assertIn((20, 4, "compiled-runtime"), counts)
+        self.assertTrue(all(sum(item["stages_per_decomposition"]) == item["logN"]
+                            for item in self.topologies))
+
+    def test_fft20_large_dimensions_are_compiled_mixed_unit_points(self):
+        points = [point for point in self.runnable
+                  if point["mapping_id"] == "fft20-fp32" and point["decomposition_count"] == 2]
+        splits = {(point["prefix_log_n"], point["suffix_log_n"]) for point in points}
+        self.assertTrue({(8, 12), (9, 11), (11, 9), (12, 8)} <= splits)
+        mixed = [point for point in points if point["prefix_processing_unit"] != point["suffix_processing_unit"]]
+        self.assertTrue(mixed)
+        self.assertFalse(self.backlog)
+
+    def test_multisegment_candidates_have_per_segment_and_boundary_parameters(self):
+        point = next(point for point in self.runnable if point["decomposition_count"] > 2)
+        self.assertEqual(len(point["segment_mappings"]), point["decomposition_count"])
+        self.assertEqual(len(point["boundaries"]), point["decomposition_count"] - 1)
+        self.assertIn("--segment-threads", point["args"])
+        self.assertIn("--segment-ept", point["args"])
+        self.assertIn("--boundary-twiddle", point["args"])
+
+    def test_fused_logical_boundaries_lower_to_two_execution_groups(self):
+        point = next(point for point in self.runnable
+                     if point["decomposition_count"] > 2 and
+                     any(boundary.get("residency") == "fused" for boundary in point["boundaries"]))
+        self.assertEqual(point["execution_group_count"], 2)
+        self.assertEqual(sum(point["execution_group_stages"]), point["logN"])
+        self.assertEqual(len(point["execution_group_mappings"]), 2)
+        self.assertIn("--boundary-residency", point["args"])
+        self.assertIn("--group-threads", point["args"])
+
+    def test_each_multisegment_decomposition_retains_global_and_fused_lowerings(self):
+        for mapping_id in {point["mapping_id"] for point in self.runnable}:
+            for batch in {point["batch"] for point in self.runnable
+                          if point["mapping_id"] == mapping_id}:
+                points = [point for point in self.runnable
+                          if point["mapping_id"] == mapping_id and point["batch"] == batch]
+                for decomposition_count in (3, 4):
+                    lowerings = [point for point in points
+                                 if point["decomposition_count"] == decomposition_count]
+                    self.assertTrue(any(all(boundary.get("residency") == "global-scratch"
+                                            for boundary in point["boundaries"])
+                                        for point in lowerings))
+                    self.assertTrue(any(any(boundary.get("residency") == "fused"
+                                            for boundary in point["boundaries"])
+                                        for point in lowerings))
+
+    def test_fused_lowerings_reuse_measured_d2_processing_unit_mappings(self):
+        expected = {"fft18-fp32": ((9, 9), ((256, 8), (256, 8))),
+                    "fft20-fp32": ((10, 10), ((512, 8), (512, 8)))}
+        for mapping_id, (stages, mappings) in expected.items():
+            points = [point for point in self.runnable
+                      if point["mapping_id"] == mapping_id and point["decomposition_count"] > 2 and
+                      tuple(point.get("execution_group_stages", [])) == stages and
+                      next(boundary["cross_twiddle"] for boundary in point["boundaries"]
+                           if boundary.get("residency", "global-scratch") == "global-scratch") == "recurrence" and
+                      tuple((item["threads"], item["ept"])
+                            for item in point.get("execution_group_mappings", [])) == mappings]
+            self.assertTrue(points)
+
+    def test_suffix_direct_points_include_both_boundary_realizations(self):
+        points = [point for point in self.runnable
+                  if point["mapping_id"] == "fft20-fp32" and point["decomposition_count"] == 2
+                  and point["suffix_log_n"] >= 11]
+        self.assertEqual({point["direct_boundary"] for point in points},
+                         {"direct-strided", "tiled-transpose"})
+        self.assertTrue(all(point["id"].endswith("_tx")
+                            for point in points if point["direct_boundary"] == "tiled-transpose"))
+
+    def test_prefix_direct_points_include_both_boundary_realizations(self):
+        points = [point for point in self.runnable
+                  if point["mapping_id"] == "fft20-fp32" and point["decomposition_count"] == 2
+                  and point["prefix_log_n"] >= 11]
+        self.assertEqual({point["direct_boundary"] for point in points},
+                         {"direct-strided", "prefix-tiled-transpose"})
+        self.assertTrue(all(point["id"].endswith("_ptx")
+                            for point in points if point["direct_boundary"] == "prefix-tiled-transpose"))
+
+    def test_generated_runtime_arguments_keep_dimensions_independent(self):
+        point = next(point for point in self.runnable
+                     if point["decomposition_count"] == 2 and point["prefix_log_n"] != point["suffix_log_n"])
+        self.assertEqual(point["decomposition_count"], 2)
+        self.assertEqual(sum(point["stages_per_decomposition"]), point["logN"])
+        args = point["args"]
+        self.assertIn("--prefix-threads", args)
+        self.assertIn("--suffix-threads", args)
+        self.assertIn("--prefix-ept", args)
+        self.assertIn("--suffix-ept", args)
+        self.assertIn("--direct-boundary", args)
+
+    def test_each_shape_retains_measured_incumbent(self):
+        expected_by_log_n = {18: [(9, 256, 256, 8, 8)],
+                             20: [(10, 512, 512, 8, 8), (10, 256, 128, 16, 16)]}
+        for log_n, expected_points in expected_by_log_n.items():
+            batches = {point["batch"] for point in self.runnable if point["logN"] == log_n}
+            for batch in batches:
+                candidates = [point for point in self.runnable
+                              if point["logN"] == log_n and point["batch"] == batch]
+                actual = {(point["prefix_log_n"], point["prefix_threads"], point["suffix_threads"],
+                           point["prefix_ept"], point["suffix_ept"]) for point in candidates}
+                for expected in expected_points:
+                    self.assertIn(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_fft_pipeline_model.py b/tests/test_fft_pipeline_model.py
new file mode 100755
index 0000000..cefa928
--- /dev/null
+++ b/tests/test_fft_pipeline_model.py
@@ -0,0 +1,50 @@
+#!/usr/bin/env python3
+import importlib.util
+import pathlib
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+SPEC = importlib.util.spec_from_file_location(
+    "analyze_fft_pipeline_model", ROOT / "scripts" / "analyze_fft_pipeline_model.py")
+MODULE = importlib.util.module_from_spec(SPEC)
+SPEC.loader.exec_module(MODULE)
+
+
+class FftPipelineModelTest(unittest.TestCase):
+    def test_reports_recall_and_regret(self):
+        rows = [
+            {"group": "g", "candidate_id": "a", "static_score": "1", "median_kernel_ms": "2",
+             "logN": "10", "batch": "4"},
+            {"group": "g", "candidate_id": "b", "static_score": "2", "median_kernel_ms": "1",
+             "logN": "10", "batch": "4"},
+            {"group": "g", "candidate_id": "c", "static_score": "3", "median_kernel_ms": "3",
+             "logN": "10", "batch": "4"},
+        ]
+        evaluations, metrics = MODULE.evaluate(rows)
+        self.assertEqual(evaluations[0]["winner_static_rank"], 2)
+        self.assertEqual(evaluations[0]["top1_regret"], 2.0)
+        self.assertEqual(evaluations[0]["top3_regret"], 1.0)
+        self.assertEqual(metrics["top1_exact_recall"], 0.0)
+        self.assertEqual(metrics["top3_exact_recall"], 1.0)
+
+    def test_rank_values_average_ties(self):
+        self.assertEqual(MODULE.rank_values([2, 1, 1]), [3.0, 1.5, 1.5])
+
+    def test_calibrated_selector_holds_out_target_batch(self):
+        rows = []
+        for batch, a_time, b_time in ((2, 1.0, 2.0), (4, 2.0, 3.0), (8, 4.0, 5.0)):
+            for candidate, score, latency in (("a", 1, a_time), ("b", 2, b_time)):
+                rows.append({
+                    "group": f"g{batch}", "candidate_id": f"{candidate}{batch}",
+                    "mapping_id": candidate, "static_score": str(score),
+                    "median_kernel_ms": str(latency), "logN": "10", "batch": str(batch),
+                })
+        evaluations, metrics = MODULE.evaluate_calibrated(rows)
+        self.assertEqual(len(evaluations), 3)
+        self.assertTrue(all(row["top1_regret"] == 1.0 for row in evaluations))
+        self.assertEqual(metrics["top1_exact_recall"], 1.0)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_fft_pipeline_runner.py b/tests/test_fft_pipeline_runner.py
new file mode 100644
index 0000000..59d232d
--- /dev/null
+++ b/tests/test_fft_pipeline_runner.py
@@ -0,0 +1,62 @@
+#!/usr/bin/env python3
+import csv
+import importlib.util
+import io
+import json
+import pathlib
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+
+
+def load(name):
+    spec = importlib.util.spec_from_file_location(name, ROOT / "scripts" / f"{name}.py")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+RUNNER = load("run_fft_pipeline")
+SUMMARY = load("summarize_fft_pipeline")
+
+
+class FftPipelineRunnerTest(unittest.TestCase):
+    def test_expansion_adds_one_cufft_per_shape(self):
+        document = json.loads((ROOT / "config" / "v100_fft_pipeline_candidates.json").read_text())
+        cases = RUNNER.expand(document)
+        self.assertEqual(sum(case["reference"] for case in cases), 6)
+        self.assertEqual(len(cases), len(document["runnable_candidates"]) + 6)
+
+    def test_parser_skips_notices(self):
+        text = "notice\ndevice,operator,kernel_ms,correct\nV100,fft,0.2,1\n"
+        self.assertEqual(RUNNER.parse_record(text)["kernel_ms"], "0.2")
+
+    def test_current_manifest_ids_can_filter_stale_resume_rows(self):
+        document = json.loads((ROOT / "config" / "v100_fft_pipeline_candidates.json").read_text())
+        cases = RUNNER.expand(document)
+        rows = [{"candidate_id": "fft20-fp32_b8_cufft"}, {"candidate_id": "removed-candidate"}]
+        self.assertEqual(RUNNER.filter_existing(rows, cases), rows[:1])
+
+    def test_case_metadata_refreshes_generated_fields(self):
+        document = json.loads((ROOT / "config" / "v100_fft_pipeline_candidates.json").read_text())
+        case = RUNNER.expand(document)[0]
+        metadata = RUNNER.case_metadata(case, 3)
+        self.assertEqual(metadata["candidate_id"], case["id"])
+        self.assertEqual(metadata["static_score"], case["static_score"])
+        self.assertEqual(metadata["trial"], 3)
+        self.assertEqual(metadata["direct_boundary"], case["direct_boundary"])
+        self.assertIn("boundary_residencies", metadata)
+        self.assertIn("execution_group_count", metadata)
+
+    def test_summary_ranks_internal_and_compares_reference(self):
+        header = "candidate_id,group,implementation,reference,kernel_ms,correct\n"
+        text = header + "a,g,a,0,2.0,1\nb,g,b,0,1.0,1\nr,g,cuFFT,1,1.5,1\n"
+        rows = list(csv.DictReader(io.StringIO(text)))
+        summary = SUMMARY.summarize(rows)
+        self.assertEqual(summary[0]["candidate_id"], "b")
+        self.assertEqual(summary[0]["throughput_vs_cufft"], 1.5)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_fft_vectorized_ncu.py b/tests/test_fft_vectorized_ncu.py
new file mode 100755
index 0000000..a341bb5
--- /dev/null
+++ b/tests/test_fft_vectorized_ncu.py
@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+import importlib.util
+import pathlib
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+SPEC = importlib.util.spec_from_file_location(
+    "analyze_fft_vectorized_ncu", ROOT / "scripts" / "analyze_fft_vectorized_ncu.py")
+MODULE = importlib.util.module_from_spec(SPEC)
+SPEC.loader.exec_module(MODULE)
+
+
+class FftVectorizedNcuTest(unittest.TestCase):
+    def test_aggregate_sums_counters_and_weights_percentages(self):
+        rows = [
+            {"time_us": "1", "warp_instructions": "10", "dram_peak_pct": "20",
+             "shared_load_bank_conflicts": "2", "shared_store_bank_conflicts": "3"},
+            {"time_us": "3", "warp_instructions": "20", "dram_peak_pct": "40",
+             "shared_load_bank_conflicts": "5", "shared_store_bank_conflicts": "7"},
+        ]
+        result = MODULE.aggregate(rows)
+        self.assertEqual(result["time_us"], 4.0)
+        self.assertEqual(result["warp_instructions"], 30.0)
+        self.assertEqual(result["shared_bank_conflicts"], 17.0)
+        self.assertEqual(result["dram_peak_pct"], 35.0)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_fp64_fft_ncu.py b/tests/test_fp64_fft_ncu.py
new file mode 100644
index 0000000..27382f5
--- /dev/null
+++ b/tests/test_fp64_fft_ncu.py
@@ -0,0 +1,56 @@
+#!/usr/bin/env python3
+import pathlib
+import sys
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+sys.path.insert(0, str(ROOT / "scripts"))
+
+from analyze_fp64_fft_ncu import aggregate, analyze  # noqa: E402
+
+
+def kernel(label, time_us, warp_instructions, fp64_instructions, conflicts):
+    return {
+        "label": label,
+        "time_us": str(time_us),
+        "dram_read_mib": "64",
+        "dram_write_mib": "64",
+        "shared_load_bank_conflicts": str(conflicts),
+        "shared_store_bank_conflicts": "0",
+        "warp_instructions": str(warp_instructions),
+        "integer_thread_instructions": str(warp_instructions * 10),
+        "fp64_thread_instructions": str(fp64_instructions),
+        "dram_peak_pct": "50",
+        "l2_hit_pct": "40",
+        "l1_hit_pct": "30",
+        "active_warps_pct": "20",
+        "barrier_stall_pct": "10",
+        "long_scoreboard_stall_pct": "5",
+    }
+
+
+def main():
+    batch = 7
+    rows = [
+        kernel("fp64_scalar_b7", 30, 300, 600, 30),
+        kernel("fp64_cufftdx_b7", 20, 200, 400, 20),
+        kernel("fp64_recurrence_b7", 15, 180, 450, 18),
+        kernel("fp64_xor_swizzle_b7", 14, 170, 450, 9),
+        kernel("fp64_cufft_b7", 10, 100, 500, 2),
+    ]
+    totals = aggregate(rows[:2])
+    assert totals["time_us"] == 50
+    assert totals["dram_total_mib"] == 256
+    output = analyze(rows, {"scalar": 3.0, "cufftdx": 2.0, "recurrence": 1.5,
+                            "xor_swizzle": 1.4, "cufft": 1.0}, batch)
+    by_name = {row["implementation"]: row for row in output}
+    assert by_name["cufftdx"]["warp_instructions_vs_cufft"] == 2.0
+    assert by_name["xor_swizzle"]["integer_thread_instructions_vs_cufft"] == 1.7
+    assert by_name["cufftdx"]["fp64_thread_instructions_vs_cufft"] == 0.8
+    assert by_name["scalar"]["cuda_event_ms_vs_cufft"] == 3.0
+    assert by_name["recurrence"]["time_us_vs_cufft"] == 1.5
+    assert by_name["xor_swizzle"]["shared_bank_conflicts_vs_cufft"] == 4.5
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tests/test_fp64_fft_robustness.py b/tests/test_fp64_fft_robustness.py
new file mode 100644
index 0000000..58e07bf
--- /dev/null
+++ b/tests/test_fp64_fft_robustness.py
@@ -0,0 +1,34 @@
+#!/usr/bin/env python3
+import pathlib
+import sys
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+sys.path.insert(0, str(ROOT / "scripts"))
+
+from analyze_fp64_fft_robustness import analyze  # noqa: E402
+
+
+def row(log_n, batch, backend, time):
+    return {
+        "logN": str(log_n), "batch": str(batch), "backend": backend,
+        "kernel_ms": str(time), "local_stages": "7", "prefix_threads": "128",
+        "prefix_ept": "4", "suffix_threads": "128", "suffix_ept": "8",
+    }
+
+
+def main():
+    rows = [
+        row(15, 4, "online-reorder", 2.0), row(15, 4, "cufft", 3.0),
+        row(15, 4, "online-reorder", 2.2), row(15, 4, "cufft", 3.2),
+    ]
+    result = analyze(rows)[0]
+    assert result["total_points"] == 131072
+    assert result["cuntt_median_ms"] == 2.1
+    assert result["cufft_median_ms"] == 3.1
+    assert result["timing_quality"] == "stable"
+    assert result["range_separation"] == "faster"
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tests/test_mapping_selector.py b/tests/test_mapping_selector.py
new file mode 100644
index 0000000..7c7cd0b
--- /dev/null
+++ b/tests/test_mapping_selector.py
@@ -0,0 +1,53 @@
+#!/usr/bin/env python3
+import importlib.util
+import pathlib
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+SPEC = importlib.util.spec_from_file_location("select_mapping", ROOT / "scripts" / "select_mapping.py")
+MODULE = importlib.util.module_from_spec(SPEC)
+SPEC.loader.exec_module(MODULE)
+
+
+class MappingSelectorTest(unittest.TestCase):
+    def test_argument_parser_separates_mapping_and_processing_unit(self):
+        parsed = MODULE.parse_args_list(["--backend", "online-reorder", "--compute-unit", "radix4"])
+        self.assertEqual(parsed["backend"], "online-reorder")
+        self.assertEqual(parsed["compute_unit"], "radix4")
+
+    def test_interpolation_uses_log_batch_and_latency(self):
+        samples = [{"batch": 1, "kernel_ms": 1.0}, {"batch": 4, "kernel_ms": 4.0}]
+        predicted, confidence = MODULE.interpolate_log_latency(samples, 2)
+        self.assertAlmostEqual(predicted, 2.0)
+        self.assertEqual(confidence, "interpolated")
+
+    def test_extrapolation_clamps_nonphysical_negative_slope(self):
+        samples = [{"batch": 1, "kernel_ms": 2.0}, {"batch": 2, "kernel_ms": 1.0}]
+        predicted, confidence = MODULE.interpolate_log_latency(samples, 4)
+        self.assertAlmostEqual(predicted, 1.0)
+        self.assertEqual(confidence, "extrapolated-high")
+
+    def test_counter_evidence_reports_grid_underfill(self):
+        row = {"operator": "fwht", "logN_int": 15, "batch": 4,
+               "processing_unit": "warp-register", "parameters": {}}
+        counters = [{"operator": "fwht", "logN": "15", "batch": "4", "implementation": "warp",
+                     "total_waves_per_sm": "0.05", "registers_per_thread": "255",
+                     "barrier_stall_pct": "1", "long_scoreboard_stall_pct": "6"}]
+        evidence = MODULE.counter_evidence(row, counters)
+        self.assertIn("grid underfills", evidence)
+        self.assertIn("register-limited", evidence)
+
+    def test_v100_evaluation_covers_multiple_operators(self):
+        cases = MODULE.load_cases(ROOT / "config" / "v100_scaling_suite.json")
+        rows = MODULE.load_rows(ROOT / "results" / "v100_scaling_full_summary.csv", cases)
+        import json
+        hardware = json.loads((ROOT / "configs" / "hardware" / "v100_sxm2_16gb.json").read_text())
+        records, metrics = MODULE.evaluate(rows, hardware)
+        self.assertGreater(len(records), 20)
+        self.assertGreaterEqual(len({row["operator"] for row in records}), 3)
+        self.assertGreaterEqual(metrics["top3_recall"], 0.9)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_scaling_ncu_analysis.py b/tests/test_scaling_ncu_analysis.py
new file mode 100644
index 0000000..c406c30
--- /dev/null
+++ b/tests/test_scaling_ncu_analysis.py
@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+import importlib.util
+import pathlib
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+SPEC = importlib.util.spec_from_file_location("analyze_scaling_ncu", ROOT / "scripts" / "analyze_scaling_ncu.py")
+MODULE = importlib.util.module_from_spec(SPEC)
+SPEC.loader.exec_module(MODULE)
+
+
+class ScalingNcuAnalysisTest(unittest.TestCase):
+    def test_aggregate_sums_kernels_and_weights_percentages(self):
+        rows = [
+            {"label": "fft18_online_b2", "time_us": "1", "dram_read_mib": "1", "dram_write_mib": "1",
+             "dram_peak_pct": "20", "active_warps_pct": "30", "registers_per_thread": "40", "waves_per_sm": "1"},
+            {"label": "fft18_online_b2", "time_us": "3", "dram_read_mib": "2", "dram_write_mib": "2",
+             "dram_peak_pct": "40", "active_warps_pct": "50", "registers_per_thread": "48", "waves_per_sm": "2"},
+        ]
+        record = MODULE.aggregate(rows)[0]
+        self.assertEqual(record["kernels"], 2)
+        self.assertEqual(record["time_us"], 4)
+        self.assertEqual(record["dram_peak_pct"], 35)
+        self.assertEqual(record["registers_per_thread"], 48)
+        self.assertEqual(record["total_waves_per_sm"], 3)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_scaling_suite.py b/tests/test_scaling_suite.py
new file mode 100644
index 0000000..4f200a8
--- /dev/null
+++ b/tests/test_scaling_suite.py
@@ -0,0 +1,70 @@
+#!/usr/bin/env python3
+import json
+import pathlib
+import sys
+import unittest
+
+
+ROOT = pathlib.Path(__file__).resolve().parents[1]
+sys.path.insert(0, str(ROOT / "scripts"))
+
+from generate_scaling_suite import expand
+from run_comprehensive_suite import load_manifest, selected_cases
+from summarize_scaling_suite import analyze
+
+
+class ScalingSuiteTest(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.space = json.loads((ROOT / "config" / "v100_scaling_space.json").read_text())
+        cls.suite = expand(cls.space)
+
+    def test_generated_space_has_orthogonal_coverage(self):
+        self.assertEqual(len(self.space["workloads"]), 12)
+        self.assertGreaterEqual(len(self.suite["cases"]), 180)
+        self.assertEqual({case["operator"] for case in self.suite["cases"]}, {"fft", "ntt", "fwht", "xor-zeta"})
+        for case in self.suite["cases"]:
+            self.assertLessEqual(case["batch"] * (1 << case["logN"]), self.space["max_points"])
+
+    def test_generated_suite_passes_comprehensive_validation(self):
+        path = ROOT / "config" / "v100_scaling_suite.json"
+        self.assertEqual(self.suite, json.loads(path.read_text()))
+        document = load_manifest(path)
+        self.assertGreater(len(selected_cases(document, "full", None)), len(selected_cases(document, "quick", None)))
+
+    def test_scaling_metrics_find_saturation(self):
+        raw = []
+        for batch, kernel_ms in ((1, 1.0), (2, 1.0), (4, 1.1), (8, 2.0)):
+            raw.append({
+                "suite_case_id": f"case-{batch}", "suite_group": f"group-{batch}",
+                "suite_tier": "quick", "suite_runner": "butterfly", "implementation": "unit",
+                "reference": "0", "trial": "1", "performance_batch": str(batch),
+                "preflight_correct": "1", "operator": "fwht", "precision": "fp32",
+                "direction": "forward", "normalization": "none", "placement": "out-of-place",
+                "logN": "8", "N": "256", "element_stride": "1", "batch_stride": "256",
+                "kernel_ms": str(kernel_ms),
+            })
+        rows = analyze(raw, 0.90, timing_floor_ms=0.0)
+        self.assertEqual(rows[0]["saturation_batch"], 4)
+        self.assertEqual(rows[2]["scaling_region"], "saturated")
+        self.assertAlmostEqual(rows[2]["batch_efficiency_vs_batch1"], 1.0 / 1.1)
+
+    def test_sub_floor_point_cannot_define_peak(self):
+        raw = []
+        for batch, kernel_ms in ((1, 0.001), (64, 0.100), (128, 0.210)):
+            raw.append({
+                "suite_case_id": f"floor-{batch}", "suite_group": f"floor-group-{batch}",
+                "suite_tier": "full", "suite_runner": "butterfly", "implementation": "unit",
+                "reference": "0", "trial": "1", "performance_batch": str(batch),
+                "preflight_correct": "1", "operator": "fwht", "precision": "fp32",
+                "direction": "forward", "normalization": "none", "placement": "out-of-place",
+                "logN": "8", "N": "256", "element_stride": "1", "batch_stride": "256",
+                "kernel_ms": str(kernel_ms),
+            })
+        rows = analyze(raw, timing_floor_ms=0.020)
+        self.assertEqual(rows[0]["eligible_for_saturation"], 0)
+        self.assertEqual(rows[0]["peak_batch"], 64)
+
+
+if __name__ == "__main__":
+    unittest.main()