From 780944f375bb3e06d476ab79222f38ab4f6b58a9 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Sun, 1 Aug 2021 00:48:16 +0800
Subject: [PATCH 1/5] Add seq function.

---
 doc/specs/stdlib_math.md         | 58 ++++++++++++++++++++++++++++++++
 src/CMakeLists.txt               |  1 +
 src/Makefile.manual              |  4 +++
 src/stdlib_math.fypp             | 16 +++++++++
 src/stdlib_math_seq.fypp         | 58 ++++++++++++++++++++++++++++++++
 src/tests/math/CMakeLists.txt    |  3 +-
 src/tests/math/Makefile.manual   |  3 +-
 src/tests/math/test_math_seq.f90 | 53 +++++++++++++++++++++++++++++
 8 files changed, 194 insertions(+), 2 deletions(-)
 create mode 100644 src/stdlib_math_seq.fypp
 create mode 100644 src/tests/math/test_math_seq.f90

diff --git a/doc/specs/stdlib_math.md b/doc/specs/stdlib_math.md
index 2e09796de..ea2cdd0ed 100644
--- a/doc/specs/stdlib_math.md
+++ b/doc/specs/stdlib_math.md
@@ -275,3 +275,61 @@ program demo_logspace_rstart_cbase
 
 end program demo_logspace_rstart_cbase
 ```
+## `seq` - Creates an vector of `integer/real` type with evenly spaced values within a given interval.
+
+### Status
+
+Experimental
+
+### Class
+
+Pure function.
+
+### Description
+
+Creates an vector of `integer/real` type with evenly spaced values within a given interval.
+
+### Syntax
+
+`result = [[stdlib_math(module):seq(interface)]](start [, end, by])`
+
+### Arguments
+
+`start`: Shall be an `integer/real` scalar.
+This is an `intent(in)` argument.
+
+`end`: Shall be an `integer/real` scalar.
+This is an `intent(in)` and `optional` argument.
+
+`by`: Shall be an `integer/real` scalar and large than `0`.
+This is an `intent(in)` and `optional` argument.  
+
+Warning:  
+If `by = 0`, the `by` argument will be corrected to `1/1.0` by the internal process of the `seq` function.   
+If `by < 0`, the `by` argument will be corrected to `abs(by)` by the internal process of the `seq` function. 
+
+### Return value
+
+Vector of evenly spaced values.
+
+For floating point arguments, the length of the result is `floor((end - start)/by) + 1`.
+
+### Example
+
+```fortran
+program demo_math_seq
+    use stdlib_math, only: seq
+
+    print *, seq(3)                 !! [1,2,3]
+    print *, seq(3.0)               !! [1.0,2.0,3.0]
+    print *, seq(-1)                !! [1,0,-1]
+    print *, seq(0,2)               !! [0,1,2]
+    print *, seq(1,-1)              !! [1,0,-1]
+    print *, seq(0, 2, 2)           !! [0,2]
+    print *, (1.0,1.0)*seq(3)       !! [(1.0,1.0),(2.0,2.0),[3.0,3.0]]
+
+    print *, seq(0.0,2.0,-2.0)      !! [0.0,2.0]. Not recommended: `by` argument is negative!
+    print *, seq(0.0,2.0,0.0)       !! [0.0,1.0]. Not recommended: `by` argument is zero!
+
+end program demo_math_seq
+```
\ No newline at end of file
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index c4f6d76e7..69e73afd3 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -32,6 +32,7 @@ set(fppFiles
     stdlib_math.fypp
     stdlib_math_linspace.fypp
     stdlib_math_logspace.fypp
+    stdlib_math_seq.fypp
     stdlib_string_type.fypp
 )
 
diff --git a/src/Makefile.manual b/src/Makefile.manual
index a12f81255..89b84e6f8 100644
--- a/src/Makefile.manual
+++ b/src/Makefile.manual
@@ -7,6 +7,7 @@ SRCFYPP =\
         stdlib_linalg.fypp \
         stdlib_linalg_diag.fypp \
         stdlib_linalg_outer_product.fypp \
+        stdlib_math_seq.fypp \
         stdlib_optval.fypp \
         stdlib_quadrature.fypp \
         stdlib_quadrature_trapz.fypp \
@@ -154,4 +155,7 @@ stdlib_math_linspace.o: \
 	stdlib_math.o
 stdlib_math_logspace.o: \
 	stdlib_math_linspace.o
+stdlib_math_seq.o: \
+    stdlib_math.o \
+    stdlib_kinds.o
 stdlib_linalg_outer_product.o: stdlib_linalg.o
diff --git a/src/stdlib_math.fypp b/src/stdlib_math.fypp
index 7a3296158..1521c3f17 100644
--- a/src/stdlib_math.fypp
+++ b/src/stdlib_math.fypp
@@ -10,6 +10,7 @@ module stdlib_math
     public :: clip, linspace, logspace
     public :: EULERS_NUMBER_SP, EULERS_NUMBER_DP, EULERS_NUMBER_QP
     public :: DEFAULT_LINSPACE_LENGTH, DEFAULT_LOGSPACE_BASE, DEFAULT_LOGSPACE_LENGTH
+    public :: seq
 
     integer, parameter :: DEFAULT_LINSPACE_LENGTH = 100
     integer, parameter :: DEFAULT_LOGSPACE_LENGTH = 50
@@ -261,6 +262,21 @@ module stdlib_math
 
   end interface
 
+    !> Version: experimental
+    !>
+    !> `seq` creates an vector of `integer/real` type 
+    !>  with evenly spaced values within a given interval.
+    interface seq
+        #:set RI_KINDS_TYPES = REAL_KINDS_TYPES + INT_KINDS_TYPES
+        #:for k1, t1 in RI_KINDS_TYPES
+        pure module function seq_${t1[0]}$_${k1}$(start, end, by) result(result)
+            ${t1}$, intent(in) :: start
+            ${t1}$, intent(in), optional :: end, by
+            ${t1}$, allocatable :: result(:)
+        end function seq_${t1[0]}$_${k1}$
+        #:endfor
+    end interface seq
+
 contains
 
     #:for k1, t1 in IR_KINDS_TYPES
diff --git a/src/stdlib_math_seq.fypp b/src/stdlib_math_seq.fypp
new file mode 100644
index 000000000..cc5a3fd1a
--- /dev/null
+++ b/src/stdlib_math_seq.fypp
@@ -0,0 +1,58 @@
+#:include "common.fypp"
+submodule(stdlib_math) stdlib_math_seq
+
+    implicit none
+
+contains
+
+    #:for k1, t1 in REAL_KINDS_TYPES
+    !> `seq` creates an vector of `${t1}$` type 
+    !>  with evenly spaced values within a given interval.
+    pure module function seq_${t1[0]}$_${k1}$(start, end, by) result(result)
+
+        ${t1}$, intent(in) :: start
+        ${t1}$, intent(in), optional :: end, by
+        ${t1}$, allocatable :: result(:)
+        
+        ${t1}$ :: start_, end_, by_
+        integer :: i
+
+        start_ = merge(start, 1.0_${k1}$, present(end))
+        end_   = merge(end,   start,      present(end))
+        by_    = sign(merge(merge(by, 1.0_${k1}$, by /= 0.0_${k1}$), &
+                 1.0_${k1}$, present(by)), end_ - start_)
+
+        allocate(result(floor((end_ - start_)/by_) + 1))
+            #!TODO: ??
+            #! floor or ceiling, floor is better.
+
+        result = [(start_ + (i - 1)*by_, i=1, size(result), 1)]
+
+    end function seq_${t1[0]}$_${k1}$
+    #:endfor
+
+    #:for k1, t1 in INT_KINDS_TYPES
+    !> `seq` creates an vector of `${t1}$` type 
+    !>  with evenly spaced values within a given interval.
+    pure module function seq_${t1[0]}$_${k1}$(start, end, by) result(result)
+
+        ${t1}$, intent(in) :: start
+        ${t1}$, intent(in), optional :: end, by
+        ${t1}$, allocatable :: result(:)
+        
+        ${t1}$ :: start_, end_, by_
+        ${t1}$ :: i
+
+        start_ = merge(start, 1_${k1}$, present(end))
+        end_   = merge(end,   start,    present(end))
+        by_    = sign(merge(merge(by, 1_${k1}$, by /= 0_${k1}$), &
+                 1_${k1}$, present(by) ), end_ - start_)
+
+        allocate(result((end_ - start_)/by_ + 1))
+
+        result = [(i, i=start_, end_, by_)]
+
+    end function seq_${t1[0]}$_${k1}$
+    #:endfor
+
+end submodule stdlib_math_seq
diff --git a/src/tests/math/CMakeLists.txt b/src/tests/math/CMakeLists.txt
index c4335e9ce..6fedb0376 100644
--- a/src/tests/math/CMakeLists.txt
+++ b/src/tests/math/CMakeLists.txt
@@ -1,3 +1,4 @@
 ADDTEST(stdlib_math)
 ADDTEST(linspace)
-ADDTEST(logspace)
\ No newline at end of file
+ADDTEST(logspace)
+ADDTEST(math_seq)
\ No newline at end of file
diff --git a/src/tests/math/Makefile.manual b/src/tests/math/Makefile.manual
index 209990732..ae8acb6a2 100644
--- a/src/tests/math/Makefile.manual
+++ b/src/tests/math/Makefile.manual
@@ -1,4 +1,5 @@
-PROGS_SRC = test_stdlib_math.f90 test_linspace.f90 test_logspace.f90
+PROGS_SRC = test_stdlib_math.f90 test_linspace.f90 test_logspace.f90 \
+    test_math_seq.f90
 
 
 include ../Makefile.manual.test.mk
diff --git a/src/tests/math/test_math_seq.f90 b/src/tests/math/test_math_seq.f90
new file mode 100644
index 000000000..83361979c
--- /dev/null
+++ b/src/tests/math/test_math_seq.f90
@@ -0,0 +1,53 @@
+!> SPDX-Identifier: MIT
+module test_math_seq
+
+    use stdlib_error, only: check
+    use stdlib_math, only: seq
+    implicit none
+
+    logical, private :: warn = .false.
+
+contains
+
+    subroutine test_math_seq_real
+        !> Normal
+        call check(all(seq(3.0) == [1.0, 2.0, 3.0]),        msg="all(seq(3.0) == [1.0,2.0,3.0]) failed.",           warn=warn)
+        call check(all(seq(-1.0) == [1.0, 0.0, -1.0]),      msg="all(seq(-1.0) == [1.0,0.0,-1.0]) failed.",         warn=warn)
+        call check(all(seq(0.0, 2.0) == [0.0, 1.0, 2.0]),   msg="all(seq(0.0,2.0) == [0.0,1.0,2.0]) failed.",       warn=warn)
+        call check(all(seq(1.0, -1.0) == [1.0, 0.0, -1.0]), msg="all(seq(1.0,-1.0) == [1.0,0.0,-1.0]) failed.",     warn=warn)
+        call check(all(seq(1.0, 1.0) == [1.0]),             msg="all(seq(1.0,1.0) == [1.0]) failed.",               warn=warn)
+        call check(all(seq(0.0, 2.0, 2.0) == [0.0, 2.0]),   msg="all(seq(0.0,2.0,2.0) == [0.0,2.0]) failed.",       warn=warn)
+        call check(all(seq(1.0, -1.0, 2.0) == [1.0, -1.0]), msg="all(seq(1.0,-1.0,2.0) == [1.0,-1.0]) failed.",     warn=warn)
+        !> Not recommended
+        call check(all(seq(0.0, 2.0, -2.0) == [0.0, 2.0]),  msg="all(seq(0.0,2.0,-2.0) == [0.0,2.0]) failed.",      warn=warn)
+        call check(all(seq(1.0, -1.0, -2.0) == [1.0, -1.0]),msg="all(seq(1.0,-1.0,-2.0) == [1.0,-1.0]) failed.",    warn=warn)
+        call check(all(seq(0.0, 2.0, 0.0) == [0.0,1.0,2.0]),msg="all(seq(0.0, 2.0, 0.0) == [0.0,1.0,2.0]) failed.", warn=warn)
+    end subroutine test_math_seq_real
+
+    subroutine test_math_seq_integer
+        !> Normal
+        call check(all(seq(3) == [1, 2, 3]),        msg="all(seq(3) == [1,2,3]) failed.",       warn=warn)
+        call check(all(seq(-1) == [1, 0, -1]),      msg="all(seq(-1) == [1,0,-1]) failed.",     warn=warn)
+        call check(all(seq(0, 2) == [0, 1, 2]),     msg="all(seq(0,2) == [0,1,2]) failed.",     warn=warn)
+        call check(all(seq(1, -1) == [1, 0, -1]),   msg="all(seq(1,-1) == [1,0,-1]) failed.",   warn=warn)
+        call check(all(seq(1, 1) == [1]),           msg="all(seq(1,1) == [1]) failed.",         warn=warn)
+        call check(all(seq(0, 2, 2) == [0, 2]),     msg="all(seq(0,2,2) == [0,2]) failed.",     warn=warn)
+        call check(all(seq(1, -1, 2) == [1, -1]),   msg="all(seq(1,-1,2) == [1,-1]) failed.",   warn=warn)
+        !> Not recommended
+        call check(all(seq(0, 2, -2) == [0, 2]),    msg="all(seq(0,2,-2) == [0,2]) failed.",    warn=warn)
+        call check(all(seq(1, -1, -2) == [1, -1]),  msg="all(seq(1,-1,-2) == [1,-1]) failed.",  warn=warn)
+        call check(all(seq(0, 2, 0) == [0,1,2]),    msg="all(seq(0, 2, 0) == [0,1,2]) failed.", warn=warn)
+    end subroutine test_math_seq_integer
+
+end module test_math_seq
+
+program tester
+
+    use test_math_seq
+
+    call test_math_seq_real
+    call test_math_seq_integer
+    
+    print *, "All tests in `test_math_seq` passed."
+
+end program tester

From 0c9036c792c7aab1d348fb32047b0a284aed6634 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Tue, 3 Aug 2021 14:20:30 +0800
Subject: [PATCH 2/5] Rename function `seq` to `arange`. Update related docs.

---
 doc/specs/stdlib_math.md                      | 55 +++++++++++--------
 src/CMakeLists.txt                            |  2 +-
 src/Makefile.manual                           |  4 +-
 src/stdlib_math.fypp                          | 15 +++--
 ..._math_seq.fypp => stdlib_math_arange.fypp} | 18 +++---
 src/tests/math/CMakeLists.txt                 |  2 +-
 src/tests/math/Makefile.manual                |  2 +-
 src/tests/math/test_math_arange.f90           | 53 ++++++++++++++++++
 src/tests/math/test_math_seq.f90              | 53 ------------------
 9 files changed, 106 insertions(+), 98 deletions(-)
 rename src/{stdlib_math_seq.fypp => stdlib_math_arange.fypp} (74%)
 create mode 100644 src/tests/math/test_math_arange.f90
 delete mode 100644 src/tests/math/test_math_seq.f90

diff --git a/doc/specs/stdlib_math.md b/doc/specs/stdlib_math.md
index ea2cdd0ed..17a634e4e 100644
--- a/doc/specs/stdlib_math.md
+++ b/doc/specs/stdlib_math.md
@@ -275,7 +275,7 @@ program demo_logspace_rstart_cbase
 
 end program demo_logspace_rstart_cbase
 ```
-## `seq` - Creates an vector of `integer/real` type with evenly spaced values within a given interval.
+## `arange` - Create a vector of the `integer/real` type with evenly spaced values within a given interval.
 
 ### Status
 
@@ -287,49 +287,56 @@ Pure function.
 
 ### Description
 
-Creates an vector of `integer/real` type with evenly spaced values within a given interval.
+Create a vector of the `integer/real` type with evenly spaced values within a given interval.
 
 ### Syntax
 
-`result = [[stdlib_math(module):seq(interface)]](start [, end, by])`
+`result = [[stdlib_math(module):arange(interface)]](start [, end, by])`
 
 ### Arguments
 
 `start`: Shall be an `integer/real` scalar.
-This is an `intent(in)` argument.
+This is an `intent(in)` argument.  
+The default `start` value is `1`.
 
 `end`: Shall be an `integer/real` scalar.
-This is an `intent(in)` and `optional` argument.
-
-`by`: Shall be an `integer/real` scalar and large than `0`.
 This is an `intent(in)` and `optional` argument.  
+The default `end` value is the inputted `start` value.
+
+`by`: Shall be an `integer/real` scalar and large than `0`. 
+This is an `intent(in)` and `optional` argument.   
+The default `by` value is `1`.
 
-Warning:  
-If `by = 0`, the `by` argument will be corrected to `1/1.0` by the internal process of the `seq` function.   
-If `by < 0`, the `by` argument will be corrected to `abs(by)` by the internal process of the `seq` function. 
+#### Warning
+If `by = 0`, the `by` argument will be corrected to `1/1.0` by the internal process of the `arange` function.   
+If `by < 0`, the `by` argument will be corrected to `abs(by)` by the internal process of the `arange` function. 
 
 ### Return value
 
-Vector of evenly spaced values.
+Return a vector of evenly spaced values.
 
-For floating point arguments, the length of the result is `floor((end - start)/by) + 1`.
+For `real` type arguments, the length of the result vector is `floor((end - start)/by) + 1`.
 
 ### Example
 
 ```fortran
-program demo_math_seq
-    use stdlib_math, only: seq
+program demo_math_arange
+    use stdlib_math, only: arange
+
+    print *, arange(3)                 !! [1,2,3]
+    print *, arange(-1)                !! [1,0,-1]
+    print *, arange(0,2)               !! [0,1,2]
+    print *, arange(1,-1)              !! [1,0,-1]
+    print *, arange(0, 2, 2)           !! [0,2]
+
+    print *, arange(3.0)               !! [1.0,2.0,3.0]
+    print *, arange(0.0,5.0)           !! [0.0,1.0,2.0,3.0,4.0,5.0]
+    print *, arange(0.0,5.0,2.0)       !! [0.0,2.0,4.0]
 
-    print *, seq(3)                 !! [1,2,3]
-    print *, seq(3.0)               !! [1.0,2.0,3.0]
-    print *, seq(-1)                !! [1,0,-1]
-    print *, seq(0,2)               !! [0,1,2]
-    print *, seq(1,-1)              !! [1,0,-1]
-    print *, seq(0, 2, 2)           !! [0,2]
-    print *, (1.0,1.0)*seq(3)       !! [(1.0,1.0),(2.0,2.0),[3.0,3.0]]
+    print *, (1.0,1.0)*arange(3)       !! [(1.0,1.0),(2.0,2.0),[3.0,3.0]]
 
-    print *, seq(0.0,2.0,-2.0)      !! [0.0,2.0]. Not recommended: `by` argument is negative!
-    print *, seq(0.0,2.0,0.0)       !! [0.0,1.0]. Not recommended: `by` argument is zero!
+    print *, arange(0.0,2.0,-2.0)      !! [0.0,2.0].     Not recommended: `by` argument is negative!
+    print *, arange(0.0,2.0,0.0)       !! [0.0,1.0,2.0]. Not recommended: `by` argument is zero!
 
-end program demo_math_seq
+end program demo_math_arange
 ```
\ No newline at end of file
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 69e73afd3..c4c6cf858 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -32,7 +32,7 @@ set(fppFiles
     stdlib_math.fypp
     stdlib_math_linspace.fypp
     stdlib_math_logspace.fypp
-    stdlib_math_seq.fypp
+    stdlib_math_arange.fypp
     stdlib_string_type.fypp
 )
 
diff --git a/src/Makefile.manual b/src/Makefile.manual
index 89b84e6f8..1dad165c2 100644
--- a/src/Makefile.manual
+++ b/src/Makefile.manual
@@ -7,7 +7,7 @@ SRCFYPP =\
         stdlib_linalg.fypp \
         stdlib_linalg_diag.fypp \
         stdlib_linalg_outer_product.fypp \
-        stdlib_math_seq.fypp \
+        stdlib_math_arange.fypp \
         stdlib_optval.fypp \
         stdlib_quadrature.fypp \
         stdlib_quadrature_trapz.fypp \
@@ -155,7 +155,7 @@ stdlib_math_linspace.o: \
 	stdlib_math.o
 stdlib_math_logspace.o: \
 	stdlib_math_linspace.o
-stdlib_math_seq.o: \
+stdlib_math_arange.o: \
     stdlib_math.o \
     stdlib_kinds.o
 stdlib_linalg_outer_product.o: stdlib_linalg.o
diff --git a/src/stdlib_math.fypp b/src/stdlib_math.fypp
index 1521c3f17..2fcd5afde 100644
--- a/src/stdlib_math.fypp
+++ b/src/stdlib_math.fypp
@@ -10,7 +10,7 @@ module stdlib_math
     public :: clip, linspace, logspace
     public :: EULERS_NUMBER_SP, EULERS_NUMBER_DP, EULERS_NUMBER_QP
     public :: DEFAULT_LINSPACE_LENGTH, DEFAULT_LOGSPACE_BASE, DEFAULT_LOGSPACE_LENGTH
-    public :: seq
+    public :: arange
 
     integer, parameter :: DEFAULT_LINSPACE_LENGTH = 100
     integer, parameter :: DEFAULT_LOGSPACE_LENGTH = 50
@@ -264,18 +264,21 @@ module stdlib_math
 
     !> Version: experimental
     !>
-    !> `seq` creates an vector of `integer/real` type 
+    !> `arange` creates a vector of the `integer/real` type 
     !>  with evenly spaced values within a given interval.
-    interface seq
+    !> ([Specification](../page/specs/stdlib_math.html#
+    !>arange-create-a-vector-of-the-integerreal-type-
+    !>with-evenly-spaced-values-within-a-given-interval))
+    interface arange
         #:set RI_KINDS_TYPES = REAL_KINDS_TYPES + INT_KINDS_TYPES
         #:for k1, t1 in RI_KINDS_TYPES
-        pure module function seq_${t1[0]}$_${k1}$(start, end, by) result(result)
+        pure module function arange_${t1[0]}$_${k1}$(start, end, by) result(result)
             ${t1}$, intent(in) :: start
             ${t1}$, intent(in), optional :: end, by
             ${t1}$, allocatable :: result(:)
-        end function seq_${t1[0]}$_${k1}$
+        end function arange_${t1[0]}$_${k1}$
         #:endfor
-    end interface seq
+    end interface arange
 
 contains
 
diff --git a/src/stdlib_math_seq.fypp b/src/stdlib_math_arange.fypp
similarity index 74%
rename from src/stdlib_math_seq.fypp
rename to src/stdlib_math_arange.fypp
index cc5a3fd1a..0fddd503f 100644
--- a/src/stdlib_math_seq.fypp
+++ b/src/stdlib_math_arange.fypp
@@ -1,14 +1,14 @@
 #:include "common.fypp"
-submodule(stdlib_math) stdlib_math_seq
+submodule(stdlib_math) stdlib_math_arange
 
     implicit none
 
 contains
 
     #:for k1, t1 in REAL_KINDS_TYPES
-    !> `seq` creates an vector of `${t1}$` type 
+    !> `arange` creates a vector of the `${t1}$` type 
     !>  with evenly spaced values within a given interval.
-    pure module function seq_${t1[0]}$_${k1}$(start, end, by) result(result)
+    pure module function arange_${t1[0]}$_${k1}$(start, end, by) result(result)
 
         ${t1}$, intent(in) :: start
         ${t1}$, intent(in), optional :: end, by
@@ -23,18 +23,16 @@ contains
                  1.0_${k1}$, present(by)), end_ - start_)
 
         allocate(result(floor((end_ - start_)/by_) + 1))
-            #!TODO: ??
-            #! floor or ceiling, floor is better.
 
         result = [(start_ + (i - 1)*by_, i=1, size(result), 1)]
 
-    end function seq_${t1[0]}$_${k1}$
+    end function arange_${t1[0]}$_${k1}$
     #:endfor
 
     #:for k1, t1 in INT_KINDS_TYPES
-    !> `seq` creates an vector of `${t1}$` type 
+    !> `arange` creates a vector of the `${t1}$` type 
     !>  with evenly spaced values within a given interval.
-    pure module function seq_${t1[0]}$_${k1}$(start, end, by) result(result)
+    pure module function arange_${t1[0]}$_${k1}$(start, end, by) result(result)
 
         ${t1}$, intent(in) :: start
         ${t1}$, intent(in), optional :: end, by
@@ -52,7 +50,7 @@ contains
 
         result = [(i, i=start_, end_, by_)]
 
-    end function seq_${t1[0]}$_${k1}$
+    end function arange_${t1[0]}$_${k1}$
     #:endfor
 
-end submodule stdlib_math_seq
+end submodule stdlib_math_arange
diff --git a/src/tests/math/CMakeLists.txt b/src/tests/math/CMakeLists.txt
index 6fedb0376..0bcaf1e1a 100644
--- a/src/tests/math/CMakeLists.txt
+++ b/src/tests/math/CMakeLists.txt
@@ -1,4 +1,4 @@
 ADDTEST(stdlib_math)
 ADDTEST(linspace)
 ADDTEST(logspace)
-ADDTEST(math_seq)
\ No newline at end of file
+ADDTEST(math_arange)
\ No newline at end of file
diff --git a/src/tests/math/Makefile.manual b/src/tests/math/Makefile.manual
index ae8acb6a2..f11cbf7a4 100644
--- a/src/tests/math/Makefile.manual
+++ b/src/tests/math/Makefile.manual
@@ -1,5 +1,5 @@
 PROGS_SRC = test_stdlib_math.f90 test_linspace.f90 test_logspace.f90 \
-    test_math_seq.f90
+    test_math_arange.f90
 
 
 include ../Makefile.manual.test.mk
diff --git a/src/tests/math/test_math_arange.f90 b/src/tests/math/test_math_arange.f90
new file mode 100644
index 000000000..0da565afe
--- /dev/null
+++ b/src/tests/math/test_math_arange.f90
@@ -0,0 +1,53 @@
+!> SPDX-Identifier: MIT
+module test_math_arange
+
+    use stdlib_error, only: check
+    use stdlib_math, only: arange
+    implicit none
+
+    logical, private :: warn = .false.
+
+contains
+
+    subroutine test_math_arange_real
+        !> Normal
+        call check(all(arange(3.0) == [1.0, 2.0, 3.0]),        msg="all(arange(3.0) == [1.0,2.0,3.0]) failed.",           warn=warn)
+        call check(all(arange(-1.0) == [1.0, 0.0, -1.0]),      msg="all(arange(-1.0) == [1.0,0.0,-1.0]) failed.",         warn=warn)
+        call check(all(arange(0.0, 2.0) == [0.0, 1.0, 2.0]),   msg="all(arange(0.0,2.0) == [0.0,1.0,2.0]) failed.",       warn=warn)
+        call check(all(arange(1.0, -1.0) == [1.0, 0.0, -1.0]), msg="all(arange(1.0,-1.0) == [1.0,0.0,-1.0]) failed.",     warn=warn)
+        call check(all(arange(1.0, 1.0) == [1.0]),             msg="all(arange(1.0,1.0) == [1.0]) failed.",               warn=warn)
+        call check(all(arange(0.0, 2.0, 2.0) == [0.0, 2.0]),   msg="all(arange(0.0,2.0,2.0) == [0.0,2.0]) failed.",       warn=warn)
+        call check(all(arange(1.0, -1.0, 2.0) == [1.0, -1.0]), msg="all(arange(1.0,-1.0,2.0) == [1.0,-1.0]) failed.",     warn=warn)
+        !> Not recommended
+        call check(all(arange(0.0, 2.0, -2.0) == [0.0, 2.0]),  msg="all(arange(0.0,2.0,-2.0) == [0.0,2.0]) failed.",      warn=warn)
+        call check(all(arange(1.0, -1.0, -2.0) == [1.0, -1.0]),msg="all(arange(1.0,-1.0,-2.0) == [1.0,-1.0]) failed.",    warn=warn)
+        call check(all(arange(0.0, 2.0, 0.0) == [0.0,1.0,2.0]),msg="all(arange(0.0, 2.0, 0.0) == [0.0,1.0,2.0]) failed.", warn=warn)
+    end subroutine test_math_arange_real
+
+    subroutine test_math_arange_integer
+        !> Normal
+        call check(all(arange(3) == [1, 2, 3]),        msg="all(arange(3) == [1,2,3]) failed.",       warn=warn)
+        call check(all(arange(-1) == [1, 0, -1]),      msg="all(arange(-1) == [1,0,-1]) failed.",     warn=warn)
+        call check(all(arange(0, 2) == [0, 1, 2]),     msg="all(arange(0,2) == [0,1,2]) failed.",     warn=warn)
+        call check(all(arange(1, -1) == [1, 0, -1]),   msg="all(arange(1,-1) == [1,0,-1]) failed.",   warn=warn)
+        call check(all(arange(1, 1) == [1]),           msg="all(arange(1,1) == [1]) failed.",         warn=warn)
+        call check(all(arange(0, 2, 2) == [0, 2]),     msg="all(arange(0,2,2) == [0,2]) failed.",     warn=warn)
+        call check(all(arange(1, -1, 2) == [1, -1]),   msg="all(arange(1,-1,2) == [1,-1]) failed.",   warn=warn)
+        !> Not recommended
+        call check(all(arange(0, 2, -2) == [0, 2]),    msg="all(arange(0,2,-2) == [0,2]) failed.",    warn=warn)
+        call check(all(arange(1, -1, -2) == [1, -1]),  msg="all(arange(1,-1,-2) == [1,-1]) failed.",  warn=warn)
+        call check(all(arange(0, 2, 0) == [0,1,2]),    msg="all(arange(0, 2, 0) == [0,1,2]) failed.", warn=warn)
+    end subroutine test_math_arange_integer
+
+end module test_math_arange
+
+program tester
+
+    use test_math_arange
+
+    call test_math_arange_real
+    call test_math_arange_integer
+    
+    print *, "All tests in `test_math_arange` passed."
+
+end program tester
diff --git a/src/tests/math/test_math_seq.f90 b/src/tests/math/test_math_seq.f90
deleted file mode 100644
index 83361979c..000000000
--- a/src/tests/math/test_math_seq.f90
+++ /dev/null
@@ -1,53 +0,0 @@
-!> SPDX-Identifier: MIT
-module test_math_seq
-
-    use stdlib_error, only: check
-    use stdlib_math, only: seq
-    implicit none
-
-    logical, private :: warn = .false.
-
-contains
-
-    subroutine test_math_seq_real
-        !> Normal
-        call check(all(seq(3.0) == [1.0, 2.0, 3.0]),        msg="all(seq(3.0) == [1.0,2.0,3.0]) failed.",           warn=warn)
-        call check(all(seq(-1.0) == [1.0, 0.0, -1.0]),      msg="all(seq(-1.0) == [1.0,0.0,-1.0]) failed.",         warn=warn)
-        call check(all(seq(0.0, 2.0) == [0.0, 1.0, 2.0]),   msg="all(seq(0.0,2.0) == [0.0,1.0,2.0]) failed.",       warn=warn)
-        call check(all(seq(1.0, -1.0) == [1.0, 0.0, -1.0]), msg="all(seq(1.0,-1.0) == [1.0,0.0,-1.0]) failed.",     warn=warn)
-        call check(all(seq(1.0, 1.0) == [1.0]),             msg="all(seq(1.0,1.0) == [1.0]) failed.",               warn=warn)
-        call check(all(seq(0.0, 2.0, 2.0) == [0.0, 2.0]),   msg="all(seq(0.0,2.0,2.0) == [0.0,2.0]) failed.",       warn=warn)
-        call check(all(seq(1.0, -1.0, 2.0) == [1.0, -1.0]), msg="all(seq(1.0,-1.0,2.0) == [1.0,-1.0]) failed.",     warn=warn)
-        !> Not recommended
-        call check(all(seq(0.0, 2.0, -2.0) == [0.0, 2.0]),  msg="all(seq(0.0,2.0,-2.0) == [0.0,2.0]) failed.",      warn=warn)
-        call check(all(seq(1.0, -1.0, -2.0) == [1.0, -1.0]),msg="all(seq(1.0,-1.0,-2.0) == [1.0,-1.0]) failed.",    warn=warn)
-        call check(all(seq(0.0, 2.0, 0.0) == [0.0,1.0,2.0]),msg="all(seq(0.0, 2.0, 0.0) == [0.0,1.0,2.0]) failed.", warn=warn)
-    end subroutine test_math_seq_real
-
-    subroutine test_math_seq_integer
-        !> Normal
-        call check(all(seq(3) == [1, 2, 3]),        msg="all(seq(3) == [1,2,3]) failed.",       warn=warn)
-        call check(all(seq(-1) == [1, 0, -1]),      msg="all(seq(-1) == [1,0,-1]) failed.",     warn=warn)
-        call check(all(seq(0, 2) == [0, 1, 2]),     msg="all(seq(0,2) == [0,1,2]) failed.",     warn=warn)
-        call check(all(seq(1, -1) == [1, 0, -1]),   msg="all(seq(1,-1) == [1,0,-1]) failed.",   warn=warn)
-        call check(all(seq(1, 1) == [1]),           msg="all(seq(1,1) == [1]) failed.",         warn=warn)
-        call check(all(seq(0, 2, 2) == [0, 2]),     msg="all(seq(0,2,2) == [0,2]) failed.",     warn=warn)
-        call check(all(seq(1, -1, 2) == [1, -1]),   msg="all(seq(1,-1,2) == [1,-1]) failed.",   warn=warn)
-        !> Not recommended
-        call check(all(seq(0, 2, -2) == [0, 2]),    msg="all(seq(0,2,-2) == [0,2]) failed.",    warn=warn)
-        call check(all(seq(1, -1, -2) == [1, -1]),  msg="all(seq(1,-1,-2) == [1,-1]) failed.",  warn=warn)
-        call check(all(seq(0, 2, 0) == [0,1,2]),    msg="all(seq(0, 2, 0) == [0,1,2]) failed.", warn=warn)
-    end subroutine test_math_seq_integer
-
-end module test_math_seq
-
-program tester
-
-    use test_math_seq
-
-    call test_math_seq_real
-    call test_math_seq_integer
-    
-    print *, "All tests in `test_math_seq` passed."
-
-end program tester

From 3c7cf6546ba4f90f9b3b4d709e325a619cd23ee4 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Thu, 5 Aug 2021 00:20:37 +0800
Subject: [PATCH 3/5] Improve `arange` func and doc.

---
 doc/specs/stdlib_math.md    | 15 +++++++++++----
 src/stdlib_math.fypp        |  4 +---
 src/stdlib_math_arange.fypp |  2 --
 3 files changed, 12 insertions(+), 9 deletions(-)

diff --git a/doc/specs/stdlib_math.md b/doc/specs/stdlib_math.md
index 17a634e4e..2a70a08bb 100644
--- a/doc/specs/stdlib_math.md
+++ b/doc/specs/stdlib_math.md
@@ -275,7 +275,7 @@ program demo_logspace_rstart_cbase
 
 end program demo_logspace_rstart_cbase
 ```
-## `arange` - Create a vector of the `integer/real` type with evenly spaced values within a given interval.
+## `arange`
 
 ### Status
 
@@ -287,7 +287,11 @@ Pure function.
 
 ### Description
 
-Create a vector of the `integer/real` type with evenly spaced values within a given interval.
+Create a vector of the `integer/real` type with given fixed spaced values within a given interval.
+
+#### Note
+
+Because of the `i` (`huge(integer :: i) = 2147483647`) index inside the `arange` function , the dimensional maximum length of array created by the `arange` function is `2147483647`. 
 
 ### Syntax
 
@@ -295,6 +299,8 @@ Create a vector of the `integer/real` type with evenly spaced values within a gi
 
 ### Arguments
 
+All arguments should be the same type and kind.
+
 `start`: Shall be an `integer/real` scalar.
 This is an `intent(in)` argument.  
 The default `start` value is `1`.
@@ -313,8 +319,9 @@ If `by < 0`, the `by` argument will be corrected to `abs(by)` by the internal pr
 
 ### Return value
 
-Return a vector of evenly spaced values.
+Return a vector of fixed spaced spaced values.
 
+For `integer` type arguments, the length of the result vector is `(end - start)/by + 1`.  
 For `real` type arguments, the length of the result vector is `floor((end - start)/by) + 1`.
 
 ### Example
@@ -331,7 +338,7 @@ program demo_math_arange
 
     print *, arange(3.0)               !! [1.0,2.0,3.0]
     print *, arange(0.0,5.0)           !! [0.0,1.0,2.0,3.0,4.0,5.0]
-    print *, arange(0.0,5.0,2.0)       !! [0.0,2.0,4.0]
+    print *, arange(0.0,6.0,2.5)       !! [0.0,2.5,5.0]
 
     print *, (1.0,1.0)*arange(3)       !! [(1.0,1.0),(2.0,2.0),[3.0,3.0]]
 
diff --git a/src/stdlib_math.fypp b/src/stdlib_math.fypp
index 2fcd5afde..1ed901d22 100644
--- a/src/stdlib_math.fypp
+++ b/src/stdlib_math.fypp
@@ -266,9 +266,7 @@ module stdlib_math
     !>
     !> `arange` creates a vector of the `integer/real` type 
     !>  with evenly spaced values within a given interval.
-    !> ([Specification](../page/specs/stdlib_math.html#
-    !>arange-create-a-vector-of-the-integerreal-type-
-    !>with-evenly-spaced-values-within-a-given-interval))
+    !> ([Specification](../page/specs/stdlib_math.html#arange))
     interface arange
         #:set RI_KINDS_TYPES = REAL_KINDS_TYPES + INT_KINDS_TYPES
         #:for k1, t1 in RI_KINDS_TYPES
diff --git a/src/stdlib_math_arange.fypp b/src/stdlib_math_arange.fypp
index 0fddd503f..a63cd58c7 100644
--- a/src/stdlib_math_arange.fypp
+++ b/src/stdlib_math_arange.fypp
@@ -1,8 +1,6 @@
 #:include "common.fypp"
 submodule(stdlib_math) stdlib_math_arange
 
-    implicit none
-
 contains
 
     #:for k1, t1 in REAL_KINDS_TYPES

From bac5e860edab1c4b01f4f841029e08455717c924 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Thu, 5 Aug 2021 11:17:57 +0800
Subject: [PATCH 4/5] Update `arange` func and doc: 1. `merge` -> `optval`
 inside. 2. `by` -> `step` argument name.

---
 doc/specs/stdlib_math.md    | 18 +++++++++---------
 src/Makefile.manual         |  6 +++---
 src/stdlib_math.fypp        |  9 +++++----
 src/stdlib_math_arange.fypp | 32 ++++++++++++++++----------------
 4 files changed, 33 insertions(+), 32 deletions(-)

diff --git a/doc/specs/stdlib_math.md b/doc/specs/stdlib_math.md
index 2a70a08bb..646989d51 100644
--- a/doc/specs/stdlib_math.md
+++ b/doc/specs/stdlib_math.md
@@ -287,7 +287,7 @@ Pure function.
 
 ### Description
 
-Create a vector of the `integer/real` type with given fixed spaced values within a given interval.
+Create a one-dimensional `array` of the `integer/real` type with fixed-spaced values of given spacing, within a given interval.
 
 #### Note
 
@@ -295,7 +295,7 @@ Because of the `i` (`huge(integer :: i) = 2147483647`) index inside the `arange`
 
 ### Syntax
 
-`result = [[stdlib_math(module):arange(interface)]](start [, end, by])`
+`result = [[stdlib_math(module):arange(interface)]](start [, end, step])`
 
 ### Arguments
 
@@ -309,20 +309,20 @@ The default `start` value is `1`.
 This is an `intent(in)` and `optional` argument.  
 The default `end` value is the inputted `start` value.
 
-`by`: Shall be an `integer/real` scalar and large than `0`. 
+`step`: Shall be an `integer/real` scalar and large than `0`. 
 This is an `intent(in)` and `optional` argument.   
-The default `by` value is `1`.
+The default `step` value is `1`.
 
 #### Warning
-If `by = 0`, the `by` argument will be corrected to `1/1.0` by the internal process of the `arange` function.   
-If `by < 0`, the `by` argument will be corrected to `abs(by)` by the internal process of the `arange` function. 
+If `step = 0`, the `step` argument will be corrected to `1/1.0` by the internal process of the `arange` function.   
+If `step < 0`, the `step` argument will be corrected to `abs(by)` by the internal process of the `arange` function. 
 
 ### Return value
 
-Return a vector of fixed spaced spaced values.
+Return a one-dimensional `array` of fixed-spaced values.
 
-For `integer` type arguments, the length of the result vector is `(end - start)/by + 1`.  
-For `real` type arguments, the length of the result vector is `floor((end - start)/by) + 1`.
+For `integer` type arguments, the length of the result vector is `(end - start)/step + 1`.  
+For `real` type arguments, the length of the result vector is `floor((end - start)/step) + 1`.
 
 ### Example
 
diff --git a/src/Makefile.manual b/src/Makefile.manual
index 1dad165c2..9e78df5d8 100644
--- a/src/Makefile.manual
+++ b/src/Makefile.manual
@@ -150,12 +150,12 @@ stdlib_string_type.o: stdlib_ascii.o \
 stdlib_strings.o: stdlib_ascii.o \
     stdlib_string_type.o \
 	stdlib_optval.o
-stdlib_math.o: stdlib_kinds.o
+stdlib_math.o: stdlib_kinds.o \
+    stdlib_optval.o
 stdlib_math_linspace.o: \
 	stdlib_math.o
 stdlib_math_logspace.o: \
 	stdlib_math_linspace.o
 stdlib_math_arange.o: \
-    stdlib_math.o \
-    stdlib_kinds.o
+    stdlib_math.o
 stdlib_linalg_outer_product.o: stdlib_linalg.o
diff --git a/src/stdlib_math.fypp b/src/stdlib_math.fypp
index 1ed901d22..2ca0f543d 100644
--- a/src/stdlib_math.fypp
+++ b/src/stdlib_math.fypp
@@ -4,6 +4,7 @@
 
 module stdlib_math
     use stdlib_kinds, only: int8, int16, int32, int64, sp, dp, qp
+    use stdlib_optval, only: optval
 
     implicit none
     private
@@ -264,15 +265,15 @@ module stdlib_math
 
     !> Version: experimental
     !>
-    !> `arange` creates a vector of the `integer/real` type 
-    !>  with evenly spaced values within a given interval.
+    !> `arange` creates a one-dimensional `array` of the `integer/real` type 
+    !>  with fixed-spaced values of given spacing, within a given interval.
     !> ([Specification](../page/specs/stdlib_math.html#arange))
     interface arange
         #:set RI_KINDS_TYPES = REAL_KINDS_TYPES + INT_KINDS_TYPES
         #:for k1, t1 in RI_KINDS_TYPES
-        pure module function arange_${t1[0]}$_${k1}$(start, end, by) result(result)
+        pure module function arange_${t1[0]}$_${k1}$(start, end, step) result(result)
             ${t1}$, intent(in) :: start
-            ${t1}$, intent(in), optional :: end, by
+            ${t1}$, intent(in), optional :: end, step
             ${t1}$, allocatable :: result(:)
         end function arange_${t1[0]}$_${k1}$
         #:endfor
diff --git a/src/stdlib_math_arange.fypp b/src/stdlib_math_arange.fypp
index a63cd58c7..075d76f7a 100644
--- a/src/stdlib_math_arange.fypp
+++ b/src/stdlib_math_arange.fypp
@@ -6,23 +6,23 @@ contains
     #:for k1, t1 in REAL_KINDS_TYPES
     !> `arange` creates a vector of the `${t1}$` type 
     !>  with evenly spaced values within a given interval.
-    pure module function arange_${t1[0]}$_${k1}$(start, end, by) result(result)
+    pure module function arange_${t1[0]}$_${k1}$(start, end, step) result(result)
 
         ${t1}$, intent(in) :: start
-        ${t1}$, intent(in), optional :: end, by
+        ${t1}$, intent(in), optional :: end, step
         ${t1}$, allocatable :: result(:)
         
-        ${t1}$ :: start_, end_, by_
+        ${t1}$ :: start_, end_, step_
         integer :: i
 
         start_ = merge(start, 1.0_${k1}$, present(end))
-        end_   = merge(end,   start,      present(end))
-        by_    = sign(merge(merge(by, 1.0_${k1}$, by /= 0.0_${k1}$), &
-                 1.0_${k1}$, present(by)), end_ - start_)
+        end_   = optval(end, start)
+        step_  = optval(step, 1.0_${k1}$)
+        step_  = sign(merge(step_, 1.0_${k1}$, step_ /= 0.0_${k1}$), end_ - start_)
 
-        allocate(result(floor((end_ - start_)/by_) + 1))
+        allocate(result(floor((end_ - start_)/step_) + 1))
 
-        result = [(start_ + (i - 1)*by_, i=1, size(result), 1)]
+        result = [(start_ + (i - 1)*step_, i=1, size(result), 1)]
 
     end function arange_${t1[0]}$_${k1}$
     #:endfor
@@ -30,23 +30,23 @@ contains
     #:for k1, t1 in INT_KINDS_TYPES
     !> `arange` creates a vector of the `${t1}$` type 
     !>  with evenly spaced values within a given interval.
-    pure module function arange_${t1[0]}$_${k1}$(start, end, by) result(result)
+    pure module function arange_${t1[0]}$_${k1}$(start, end, step) result(result)
 
         ${t1}$, intent(in) :: start
-        ${t1}$, intent(in), optional :: end, by
+        ${t1}$, intent(in), optional :: end, step
         ${t1}$, allocatable :: result(:)
         
-        ${t1}$ :: start_, end_, by_
+        ${t1}$ :: start_, end_, step_
         ${t1}$ :: i
 
         start_ = merge(start, 1_${k1}$, present(end))
-        end_   = merge(end,   start,    present(end))
-        by_    = sign(merge(merge(by, 1_${k1}$, by /= 0_${k1}$), &
-                 1_${k1}$, present(by) ), end_ - start_)
+        end_   = optval(end, start)
+        step_  = optval(step, 1_${k1}$)
+        step_  = sign(merge(step_, 1_${k1}$, step_ /= 0_${k1}$), end_ - start_)
 
-        allocate(result((end_ - start_)/by_ + 1))
+        allocate(result((end_ - start_)/step_ + 1))
 
-        result = [(i, i=start_, end_, by_)]
+        result = [(i, i=start_, end_, step_)]
 
     end function arange_${t1[0]}$_${k1}$
     #:endfor

From 55da7c004b5bde1081ed1d76a648a76c7e34b5f9 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Fri, 6 Aug 2021 21:57:58 +0800
Subject: [PATCH 5/5] Update `arange` doc: Fix some typos.

---
 doc/specs/stdlib_math.md | 14 +++++---------
 1 file changed, 5 insertions(+), 9 deletions(-)

diff --git a/doc/specs/stdlib_math.md b/doc/specs/stdlib_math.md
index 646989d51..8d7fb516b 100644
--- a/doc/specs/stdlib_math.md
+++ b/doc/specs/stdlib_math.md
@@ -287,11 +287,7 @@ Pure function.
 
 ### Description
 
-Create a one-dimensional `array` of the `integer/real` type with fixed-spaced values of given spacing, within a given interval.
-
-#### Note
-
-Because of the `i` (`huge(integer :: i) = 2147483647`) index inside the `arange` function , the dimensional maximum length of array created by the `arange` function is `2147483647`. 
+Creates a one-dimensional `array` of the `integer/real` type with fixed-spaced values of given spacing, within a given interval.
 
 ### Syntax
 
@@ -315,11 +311,11 @@ The default `step` value is `1`.
 
 #### Warning
 If `step = 0`, the `step` argument will be corrected to `1/1.0` by the internal process of the `arange` function.   
-If `step < 0`, the `step` argument will be corrected to `abs(by)` by the internal process of the `arange` function. 
+If `step < 0`, the `step` argument will be corrected to `abs(step)` by the internal process of the `arange` function. 
 
 ### Return value
 
-Return a one-dimensional `array` of fixed-spaced values.
+Returns a one-dimensional `array` of fixed-spaced values.
 
 For `integer` type arguments, the length of the result vector is `(end - start)/step + 1`.  
 For `real` type arguments, the length of the result vector is `floor((end - start)/step) + 1`.
@@ -342,8 +338,8 @@ program demo_math_arange
 
     print *, (1.0,1.0)*arange(3)       !! [(1.0,1.0),(2.0,2.0),[3.0,3.0]]
 
-    print *, arange(0.0,2.0,-2.0)      !! [0.0,2.0].     Not recommended: `by` argument is negative!
-    print *, arange(0.0,2.0,0.0)       !! [0.0,1.0,2.0]. Not recommended: `by` argument is zero!
+    print *, arange(0.0,2.0,-2.0)      !! [0.0,2.0].     Not recommended: `step` argument is negative!
+    print *, arange(0.0,2.0,0.0)       !! [0.0,1.0,2.0]. Not recommended: `step` argument is zero!
 
 end program demo_math_arange
 ```
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