arg**: aimag(log(..)) -> atan2(..),

update tests.

doc/specs/stdlib_math.md

@@ -389,7 +389,7 @@ program demo_math_arange
 end program demo_math_arange
 ```
 
-## `arg`
+## `arg` - Computes the phase angle in radian of a complex scalar
 
 ### Status
 
@@ -402,7 +402,7 @@ Elemental function.
 ### Description
 
 `arg` computes the phase angle (radian version) of `complex` scalar in the interval (-π,π]. 
-The angles in `theta` are such that `z = abs(z)*exp((0.0, theta))`.
+The angles in `θ` are such that `z = abs(z)*exp((0.0, θ))`.
 
 ### Syntax
 
@@ -417,9 +417,7 @@ This is an `intent(in)` argument.
 
 Returns the `real` type phase angle (radian version) of the `complex` argument `z`.
 
-#### Notes
-
-Although the angle of the complex number `0` is undefined, `arg((0,0))` returns the value `0`.
+Notes: Although the angle of the complex number `0` is undefined, `arg((0,0))` returns the value `0`.
 
 ### Example
 
@@ -432,7 +430,7 @@ program demo_math_arg
 end program demo_math_arg
 ```
 
-## `argd`
+## `argd` - Computes the phase angle in degree of a complex scalar
 
 ### Status
 
@@ -445,7 +443,7 @@ Elemental function.
 ### Description
 
 `argd` computes the phase angle (degree version) of `complex` scalar in the interval (-180.0,180.0]. 
-The angles in `theta` are such that `z = abs(z)*exp((0.0, theta*π/180.0))`.
+The angles in `θ` are such that `z = abs(z)*exp((0.0, θ*π/180.0))`.
 
 ### Syntax
 
@@ -460,9 +458,7 @@ This is an `intent(in)` argument.
 
 Returns the `real` type phase angle (degree version) of the `complex` argument `z`.
 
-#### Notes
-
-Although the angle of the complex number `0` is undefined, `argd((0,0))` returns the value `0`.
+Notes: Although the angle of the complex number `0` is undefined, `argd((0,0))` returns the value `0`.
 
 ### Example
 
@@ -475,7 +471,7 @@ program demo_math_argd
 end program demo_math_argd
 ```
 
-## `argpi`
+## `argpi` - Computes the phase angle in circular of a complex scalar
 
 ### Status
 
@@ -487,8 +483,8 @@ Elemental function.
 
 ### Description
 
-`argpi` computes the phase angle (circular version) of `complex` scalar in the interval (-1.0,1.0]. 
-The angles in `theta` are such that `z = abs(z)*exp((0.0, theta*π))`.
+`argpi` computes the phase angle (IEEE circular version) of `complex` scalar in the interval (-1.0,1.0]. 
+The angles in `θ` are such that `z = abs(z)*exp((0.0, θ*π))`.
 
 ### Syntax
 
@@ -503,9 +499,7 @@ This is an `intent(in)` argument.
 
 Returns the `real` type phase angle (circular version) of the `complex` argument `z`.
 
-#### Notes
-
-Although the angle of the complex number `0` is undefined, `argpi((0,0))` returns the value `0`.
+Notes: Although the angle of the complex number `0` is undefined, `argpi((0,0))` returns the value `0`.
 
 ### Example
 

src/stdlib_math.fypp

@@ -29,7 +29,7 @@ module stdlib_math
 
  !> Useful constants `PI` for `argd/argpi`
  #:for k1 in REAL_KINDS
- real(kind=${k1}$), parameter :: PI_${k1}$ = 4.0_${k1}$*atan(1.0_${k1}$)
+ real(kind=${k1}$), parameter :: PI_${k1}$ = acos(-1.0_${k1}$)
  #:endfor
 
  interface clip
@@ -321,7 +321,7 @@ module stdlib_math
 
  !> Version: experimental
  !>
- !> `argpi` computes the phase angle of IEEE circular version in the interval (-1.0,1.0].
+ !> `argpi` computes the phase angle of circular version in the interval (-1.0,1.0].
  !> ([Specification](../page/specs/stdlib_math.html#argpi))
  interface argpi
  #:for k1 in CMPLX_KINDS
@@ -348,23 +348,25 @@ contains
  ${t1}$, intent(in) :: z
  real(${k1}$) :: result
 
- result = aimag(log(z))
+ result = merge(0.0_${k1}$, atan2(z%im, z%re), z == (0.0_${k1}$, 0.0_${k1}$))
 
  end function arg_${k1}$
 
  elemental function argd_${k1}$(z) result(result) 
  ${t1}$, intent(in) :: z
  real(${k1}$) :: result
 
- result = aimag(log(z))*180.0_${k1}$/PI_${k1}$
+ result = merge(0.0_${k1}$, atan2(z%im, z%re), z == (0.0_${k1}$, 0.0_${k1}$)) &
+ *180.0_${k1}$/PI_${k1}$
 
  end function argd_${k1}$
 
  elemental function argpi_${k1}$(z) result(result) 
  ${t1}$, intent(in) :: z
  real(${k1}$) :: result
 
- result = aimag(log(z))/PI_${k1}$
+ result = merge(0.0_${k1}$, atan2(z%im, z%re), z == (0.0_${k1}$, 0.0_${k1}$)) &
+ /PI_${k1}$
 
  end function argpi_${k1}$
  #:endfor

src/tests/math/test_stdlib_math.fypp

@@ -4,11 +4,15 @@
 
 module test_stdlib_math
  use testdrive, only : new_unittest, unittest_type, error_type, check, skip_test
- use stdlib_math, only: clip, arg, argd, argpi
+ use stdlib_math, only: clip, arg, argd, argpi, arange
  use stdlib_kinds, only: int8, int16, int32, int64, sp, dp, xdp, qp
  implicit none
 
  public :: collect_stdlib_math
+
+ #:for k1 in REAL_KINDS
+ real(kind=${k1}$), parameter :: PI_${k1}$ = acos(-1.0_${k1}$)
+ #:endfor
 
 contains
 
@@ -214,7 +218,8 @@ contains
  #:for k1 in CMPLX_KINDS
  subroutine test_arg_${k1}$(error)
  type(error_type), allocatable, intent(out) :: error
- real(${k1}$), parameter :: tol = epsilon(1.0_${k1}$)
+ real(${k1}$), parameter :: tol = sqrt(epsilon(1.0_${k1}$))
+ real(${k1}$), allocatable :: theta(:)
 
  #! For scalar
  call check(error, abs(arg(2*exp((0.0_${k1}$, 0.5_${k1}$))) - 0.5_${k1}$) < tol, &
@@ -223,18 +228,17 @@ contains
  call check(error, abs(arg((0.0_${k1}$, 0.0_${k1}$)) - 0.0_${k1}$) < tol, &
  "test_zero_scalar")
 
- #! and for array
- call check(error, all(abs(arg([2*exp((0.0_${k1}$, 0.5_${k1}$))]) - [0.5_${k1}$]) < [tol]), &
- "test_nonzero_array")
- if (allocated(error)) return
- call check(error, all(abs(arg([(0.0_${k1}$, 0.0_${k1}$)]) - [0.0_${k1}$]) < [tol]), &
- "test_zero_array")
+ #! and for array (180.0° see scalar version)
+ theta = arange(-179.0_${k1}$, 179.0_${k1}$, 3.58_${k1}$)
+ call check(error, all(abs(arg(exp(cmplx(0.0_${k1}$, theta/180*PI_${k1}$, ${k1}$))) - theta/180*PI_${k1}$) < tol), &
+ "test_array")
 
  end subroutine test_arg_${k1}$
 
  subroutine test_argd_${k1}$(error)
  type(error_type), allocatable, intent(out) :: error
- real(${k1}$), parameter :: tol = epsilon(1.0_${k1}$)
+ real(${k1}$), parameter :: tol = sqrt(epsilon(1.0_${k1}$))
+ real(${k1}$), allocatable :: theta(:)
 
  #! For scalar
  call check(error, abs(argd((-1.0_${k1}$, 0.0_${k1}$)) - 180.0_${k1}$) < tol, &
@@ -243,18 +247,17 @@ contains
  call check(error, abs(argd((0.0_${k1}$, 0.0_${k1}$)) - 0.0_${k1}$) < tol, &
  "test_zero_scalar")
 
- #! and for array
- call check(error, all(abs(argd([(-1.0_${k1}$, 0.0_${k1}$)]) - [180.0_${k1}$]) < [tol]), &
- "test_nonzero_array")
- if (allocated(error)) return
- call check(error, all(abs(argd([(0.0_${k1}$, 0.0_${k1}$)]) - [0.0_${k1}$]) < [tol]), &
- "test_zero_array")
+ #! and for array (180.0° see scalar version)
+ theta = arange(-179.0_${k1}$, 179.0_${k1}$, 3.58_${k1}$)
+ call check(error, all(abs(argd(exp(cmplx(0.0_${k1}$, theta/180*PI_${k1}$, ${k1}$))) - theta) < tol), &
+ "test_array")
 
  end subroutine test_argd_${k1}$
 
  subroutine test_argpi_${k1}$(error)
  type(error_type), allocatable, intent(out) :: error
- real(${k1}$), parameter :: tol = epsilon(1.0_${k1}$)
+ real(${k1}$), parameter :: tol = sqrt(epsilon(1.0_${k1}$))
+ real(${k1}$), allocatable :: theta(:)
 
  #! For scalar
  call check(error, abs(argpi((-1.0_${k1}$, 0.0_${k1}$)) - 1.0_${k1}$) < tol, &
@@ -263,12 +266,10 @@ contains
  call check(error, abs(argpi((0.0_${k1}$, 0.0_${k1}$)) - 0.0_${k1}$) < tol, &
  "test_zero_scalar")
 
- #! and for array
- call check(error, all(abs(argpi([(-1.0_${k1}$, 0.0_${k1}$)]) - [1.0_${k1}$]) < [tol]), &
- "test_nonzero_array")
- if (allocated(error)) return
- call check(error, all(abs(argpi([(0.0_${k1}$, 0.0_${k1}$)]) - [0.0_${k1}$]) < [tol]), &
- "test_zero_array")
+ #! and for array (180.0° see scalar version)
+ theta = arange(-179.0_${k1}$, 179.0_${k1}$, 3.58_${k1}$)
+ call check(error, all(abs(argpi(exp(cmplx(0.0_${k1}$, theta/180*PI_${k1}$, ${k1}$))) - theta/180) < tol), &
+ "test_array")
 
  end subroutine test_argpi_${k1}$
  #:endfor