Implement torch.igamma (pytorch#46183)

Summary:
Fixes pytorch#41637
This is regularized lower incomplete gamma function, equivalent to scipy's `gammainc` and tensorflow `igamma`.

cc fritzo mruberry

Pull Request resolved: pytorch#46183

Reviewed By: gchanan

Differential Revision: D24479126

Pulled By: mruberry

fbshipit-source-id: fdf8ea289fe4ca1b408810732192411e948fcdfe

Author: mfkasim1

NOTICE

@@ -284,6 +284,112 @@ Apache License Version 2.0:
       incurred by, or claims asserted against, such Contributor by reason
       of your accepting any such warranty or additional liability.
 
+=======================================================================
+Cephes's 3-Clause BSD License
+=======================================================================
+
+Code derived from implementations in the Cephes Math Library should mention
+its derivation and reference the following license:
+
+   3-Clause BSD License for the Cephes Math Library
+   Copyright (c) 2018, Steven Moshier
+   All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions are met:
+
+   * Redistributions of source code must retain the above copyright
+   notice, this list of conditions and the following disclaimer.
+
+   * Redistributions in binary form must reproduce the above copyright
+   notice, this list of conditions and the following disclaimer in the
+   documentation and/or other materials provided with the distribution.
+
+   * Neither the name of the nor the
+   names of its contributors may be used to endorse or promote products
+   derived from this software without specific prior written permission.
+
+   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+   ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+   WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+   DISCLAIMED. IN NO EVENT SHALL Steven Moshier BE LIABLE FOR ANY
+   DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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+   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+=======================================================================
+SciPy's 3-Clause BSD License
+=======================================================================
+
+Code derived from implementations in SciPy should mention its derivation
+and reference the following license:
+
+   Copyright (c) 2001-2002 Enthought, Inc.  2003-2019, SciPy Developers.
+   All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
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+   1. Redistributions of source code must retain the above copyright
+     notice, this list of conditions and the following disclaimer.
+
+   2. Redistributions in binary form must reproduce the above
+     copyright notice, this list of conditions and the following
+     disclaimer in the documentation and/or other materials provided
+     with the distribution.
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+   3. Neither the name of the copyright holder nor the names of its
+     contributors may be used to endorse or promote products derived
+     from this software without specific prior written permission.
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+   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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+   LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+   DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+   THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+   OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+=======================================================================
+Boost's 1.0 Software License
+=======================================================================
+
+Code derived from implementations in Boost 1.0 should mention its
+derivation and reference the following license:
+
+   Boost Software License - Version 1.0 - August 17th, 2003
+
+   Permission is hereby granted, free of charge, to any person or organization
+   obtaining a copy of the software and accompanying documentation covered by
+   this license (the "Software") to use, reproduce, display, distribute,
+   execute, and transmit the Software, and to prepare derivative works of the
+   Software, and to permit third-parties to whom the Software is furnished to
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+   ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+   DEALINGS IN THE SOFTWARE.
+
    END OF TERMS AND CONDITIONS
 
    APPENDIX: How to apply the Apache License to your work.

aten/src/ATen/core/NamedRegistrations.cpp

@@ -210,6 +210,9 @@ TORCH_LIBRARY_IMPL(aten, Named, m) {
   m.impl("i0", CppFunction::makeFallthrough());
   m.impl("i0.out", CppFunction::makeFallthrough());
   m.impl("i0_", CppFunction::makeFallthrough());
+  m.impl("igamma", CppFunction::makeFallthrough());
+  m.impl("igamma.out", CppFunction::makeFallthrough());
+  m.impl("igamma_", CppFunction::makeFallthrough());
   m.impl("imag", CppFunction::makeFallthrough());
   m.impl("index_fill.Dimname_Scalar", CppFunction::makeFallthrough());
   m.impl("index_fill.Dimname_Tensor", CppFunction::makeFallthrough());

aten/src/ATen/core/aten_interned_strings.h

@@ -371,6 +371,8 @@ _(aten, hstack) \
 _(aten, hypot) \
 _(aten, i0) \
 _(aten, i0_) \
+_(aten, igamma) \
+_(aten, igamma_) \
 _(aten, ifft) \
 _(aten, index) \
 _(aten, index_add) \

aten/src/ATen/cpu/vec256/vec256_base.h

@@ -394,6 +394,13 @@ struct Vec256 {
   Vec256<T> i0() const {
     return map(calc_i0);
   }
+  Vec256<T> igamma(const Vec256<T> &x) const {
+    Vec256<T> ret;
+    for (int64_t i = 0; i < size(); i++) {
+      ret[i] = calc_igamma(values[i], x[i]);
+    }
+    return ret;
+  }
   Vec256<T> neg() const {
     // NB: the trailing return type is needed because we need to coerce the
     // return value back to T in the case of unary operator- incuring a

aten/src/ATen/cpu/vec256/vec256_bfloat16.h

@@ -290,6 +290,25 @@ template <> class Vec256<BFloat16> {
     auto o2 = _mm256_loadu_ps(tmp2);
     return cvtfp32_bf16(o1, o2);
   }
+  Vec256<BFloat16> igamma(const Vec256<BFloat16> &x) const {
+    __m256 lo, hi;
+    __m256 xlo, xhi;
+    cvtbf16_fp32(values, lo, hi);
+    cvtbf16_fp32(x.values, xlo, xhi);
+    __at_align32__ float tmp1[size() / 2], tmp2[size() / 2];
+    _mm256_storeu_ps(reinterpret_cast<float*>(tmp1), lo);
+    _mm256_storeu_ps(reinterpret_cast<float*>(tmp2), hi);
+    __at_align32__ float tmpx1[size() / 2], tmpx2[size() / 2];
+    _mm256_storeu_ps(reinterpret_cast<float*>(tmpx1), xlo);
+    _mm256_storeu_ps(reinterpret_cast<float*>(tmpx2), xhi);
+    for (int64_t i = 0; i < size() / 2; ++i) {
+      tmp1[i] = calc_igamma(tmp1[i], tmpx1[i]);
+      tmp2[i] = calc_igamma(tmp2[i], tmpx2[i]);
+    }
+    auto o1 = _mm256_loadu_ps(tmp1);
+    auto o2 = _mm256_loadu_ps(tmp2);
+    return cvtfp32_bf16(o1, o2);
+  }
   Vec256<BFloat16> log() const {
     return map(Sleef_logf8_u10);
   }

aten/src/ATen/cpu/vec256/vec256_complex_double.h

@@ -252,6 +252,9 @@ template <> class Vec256<c10::complex<double>> {
   Vec256<c10::complex<double>> hypot(const Vec256<c10::complex<double>> &b) const {
     AT_ERROR("not supported for complex numbers");
   }
+  Vec256<c10::complex<double>> igamma(const Vec256<c10::complex<double>> &x) const {
+    AT_ERROR("not supported for complex numbers");
+  }
   Vec256<c10::complex<double>> neg() const {
     auto zero = _mm256_setzero_pd();
     return _mm256_sub_pd(zero, values);

aten/src/ATen/cpu/vec256/vec256_complex_float.h

@@ -290,6 +290,9 @@ template <> class Vec256<c10::complex<float>> {
   Vec256<c10::complex<float>> hypot(const Vec256<c10::complex<float>> &b) const {
     AT_ERROR("not supported for complex numbers");
   }
+  Vec256<c10::complex<float>> igamma(const Vec256<c10::complex<float>> &x) const {
+    AT_ERROR("not supported for complex numbers");
+  }
   Vec256<c10::complex<float>> neg() const {
     auto zero = _mm256_setzero_ps();
     return _mm256_sub_ps(zero, values);

aten/src/ATen/cpu/vec256/vec256_double.h

@@ -155,6 +155,16 @@ template <> class Vec256<double> {
   Vec256<double> i0() const {
     return map(calc_i0);
   }
+  Vec256<double> igamma(const Vec256<double> &x) const {
+    __at_align32__ double tmp[size()];
+    __at_align32__ double tmp_x[size()];
+    store(tmp);
+    x.store(tmp_x);
+    for (int64_t i = 0; i < size(); i++) {
+      tmp[i] = calc_igamma(tmp[i], tmp_x[i]);
+    }
+    return loadu(tmp);
+  }
   Vec256<double> log() const {
     return Vec256<double>(Sleef_logd4_u10(values));
   }

aten/src/ATen/cpu/vec256/vec256_float.h

@@ -193,6 +193,16 @@ template <> class Vec256<float> {
   Vec256<float> i0() const {
     return map(calc_i0);
   }
+  Vec256<float> igamma(const Vec256<float> &x) const {
+    __at_align32__ float tmp[size()];
+    __at_align32__ float tmp_x[size()];
+    store(tmp);
+    x.store(tmp_x);
+    for (int64_t i = 0; i < size(); i++) {
+      tmp[i] = calc_igamma(tmp[i], tmp_x[i]);
+    }
+    return loadu(tmp);
+  }
   Vec256<float> neg() const {
     return _mm256_xor_ps(_mm256_set1_ps(-0.f), values);
   }

aten/src/ATen/cpu/vec256/vec256_float_neon.h

@@ -362,6 +362,16 @@ template <> class Vec256<float> {
   Vec256<float> i0() const {
     return map(calc_i0);
   }
+  Vec256<float> igamma(const Vec256<float> &x) const {
+    __at_align32__ float tmp[size()];
+    __at_align32__ float tmp_x[size()];
+    store(tmp);
+    x.store(tmp_x);
+    for (int64_t i = 0; i < size(); i++) {
+      tmp[i] = calc_igamma(tmp[i], tmp_x[i]);
+    }
+    return loadu(tmp);
+  }
   Vec256<float> log() const {
     return map(std::log);
   }

aten/src/ATen/native/BinaryOps.cpp

@@ -46,6 +46,7 @@ DEFINE_DISPATCH(logaddexp2_stub);
 DEFINE_DISPATCH(gcd_stub);
 DEFINE_DISPATCH(lcm_stub);
 DEFINE_DISPATCH(hypot_stub);
+DEFINE_DISPATCH(igamma_stub);
 DEFINE_DISPATCH(nextafter_stub);
 DEFINE_DISPATCH(heaviside_stub);
 
@@ -968,6 +969,23 @@ Tensor& hypot_(Tensor& self, const Tensor& other) {
   return at::hypot_out(self, self, other);
 }
 
+Tensor& igamma_out(Tensor& result, const Tensor& self, const Tensor& other) {
+  auto iter = TensorIterator::binary_op(result, self, other);
+  igamma_stub(iter.device_type(), iter);
+  return result;
+}
+
+Tensor igamma(const Tensor& self, const Tensor& other) {
+  Tensor result;
+  auto iter = TensorIterator::binary_op(result, self, other);
+  igamma_stub(iter.device_type(), iter);
+  return iter.output();
+}
+
+Tensor& igamma_(Tensor& self, const Tensor& other) {
+  return at::igamma_out(self, self, other);
+}
+
 Tensor& nextafter_out(Tensor& result, const Tensor& self, const Tensor& other) {
   auto iter = TensorIterator::binary_op(result, self, other);
   nextafter_stub(iter.device_type(), iter);

aten/src/ATen/native/BinaryOps.h

@@ -10,7 +10,7 @@ namespace at { namespace native {
 inline void alpha_check(const ScalarType dtype, Scalar alpha) {
   TORCH_CHECK(! alpha.isBoolean() || dtype == ScalarType::Bool,
               "Boolean alpha only supported for Boolean results.");
-  TORCH_CHECK(isFloatingType(dtype) || isComplexType(dtype) 
+  TORCH_CHECK(isFloatingType(dtype) || isComplexType(dtype)
               || alpha.isIntegral(true),
               "For integral input tensors, argument alpha must not be a floating point number.");
 }
@@ -68,6 +68,7 @@ DECLARE_DISPATCH(binary_fn, logaddexp2_stub);
 DECLARE_DISPATCH(binary_fn, gcd_stub);
 DECLARE_DISPATCH(binary_fn, lcm_stub);
 DECLARE_DISPATCH(binary_fn, hypot_stub);
+DECLARE_DISPATCH(binary_fn, igamma_stub);
 DECLARE_DISPATCH(binary_fn, nextafter_stub);
 DECLARE_DISPATCH(binary_fn, heaviside_stub);