@tex
\gdef\acosd{\mathop{\rm acosd}\nolimits}
-\gdef\asind{\mathop{\rm asind}\nolimits}
-\gdef\atand{\mathop{\rm atand}\nolimits}
-\gdef\acos{\mathop{\rm acos}\nolimits}
-\gdef\asin{\mathop{\rm asin}\nolimits}
-\gdef\atan{\mathop{\rm atan}\nolimits}
\gdef\acosh{\mathop{\rm acosh}\nolimits}
+\gdef\acospi{\mathop{\rm acospi}\nolimits}
+\gdef\acos{\mathop{\rm acos}\nolimits}
+\gdef\asind{\mathop{\rm asind}\nolimits}
\gdef\asinh{\mathop{\rm asinh}\nolimits}
+\gdef\asinpi{\mathop{\rm asinpi}\nolimits}
+\gdef\asin{\mathop{\rm asin}\nolimits}
+\gdef\atan2pi{\mathop{\rm atan2pi}\nolimits}
+\gdef\atand{\mathop{\rm atand}\nolimits}
\gdef\atanh{\mathop{\rm atanh}\nolimits}
+\gdef\atanpi{\mathop{\rm atanpi}\nolimits}
+\gdef\atan{\mathop{\rm atan}\nolimits}
\gdef\cosd{\mathop{\rm cosd}\nolimits}
+\gdef\cospi{\mathop{\rm cospi}\nolimits}
+\gdef\sinpi{\mathop{\rm sinpi}\nolimits}
+\gdef\tanpi{\mathop{\rm tanpi}\nolimits}
@end tex
* @code{ACOS}: ACOS, Arccosine function
* @code{ACOSD}: ACOSD, Arccosine function, degrees
* @code{ACOSH}: ACOSH, Inverse hyperbolic cosine function
+* @code{ACOSPI}: ACOSPI, Circular arc cosine function
* @code{ADJUSTL}: ADJUSTL, Left adjust a string
* @code{ADJUSTR}: ADJUSTR, Right adjust a string
* @code{AIMAG}: AIMAG, Imaginary part of complex number
* @code{ASIN}: ASIN, Arcsine function
* @code{ASIND}: ASIND, Arcsine function, degrees
* @code{ASINH}: ASINH, Inverse hyperbolic sine function
+* @code{ASINPI}: ASINPI, Circular arc sine function
* @code{ASSOCIATED}: ASSOCIATED, Status of a pointer or pointer/target pair
* @code{ATAN}: ATAN, Arctangent function
-* @code{ATAND}: ATAND, Arctangent function, degrees
* @code{ATAN2}: ATAN2, Arctangent function
* @code{ATAN2D}: ATAN2D, Arctangent function, degrees
+* @code{ATAN2PI}: ATAN2PI, Circular arc tangent function
+* @code{ATAND}: ATAND, Arctangent function, degrees
* @code{ATANH}: ATANH, Inverse hyperbolic tangent function
+* @code{ATANPI}: ATANPI, Circular arc tangent function
* @code{ATOMIC_ADD}: ATOMIC_ADD, Atomic ADD operation
* @code{ATOMIC_AND}: ATOMIC_AND, Atomic bitwise AND operation
* @code{ATOMIC_CAS}: ATOMIC_CAS, Atomic compare and swap
* @code{COS}: COS, Cosine function
* @code{COSD}: COSD, Cosine function, degrees
* @code{COSH}: COSH, Hyperbolic cosine function
+* @code{COSPI}: COSPI, Circular cosine function
* @code{COTAN}: COTAN, Cotangent function
* @code{COTAND}: COTAND, Cotangent function, degrees
* @code{COUNT}: COUNT, Count occurrences of TRUE in an array
* @code{SIN}: SIN, Sine function
* @code{SIND}: SIND, Sine function, degrees
* @code{SINH}: SINH, Hyperbolic sine function
+* @code{SINPI}: SINPI, Circular sine function
* @code{SIZE}: SIZE, Function to determine the size of an array
* @code{SIZEOF}: SIZEOF, Determine the size in bytes of an expression
* @code{SLEEP}: SLEEP, Sleep for the specified number of seconds
* @code{TAN}: TAN, Tangent function
* @code{TAND}: TAND, Tangent function, degrees
* @code{TANH}: TANH, Hyperbolic tangent function
+* @code{TANPI}: TANPI, Circular tangent function
* @code{TEAM_NUMBER}: TEAM_NUMBER, Retrieve team id of given team
* @code{THIS_IMAGE}: THIS_IMAGE, Cosubscript index of this image
* @code{TIME}: TIME, Time function
+@node ACOSPI
+@section @code{ACOSPI} --- Circular arc cosine function
+@fnindex ACOSPI
+@cindex trigonometric function, cosine, inverse
+
+@table @asis
+@item @emph{Description}:
+@code{ACOSPI(X)} computes @math{ \acos(x) / \pi}, which is a measure
+of an angle in half-revolutions.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@code{RESULT = ACOSPI(X)}
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{X} @tab The type shall be @code{REAL} with @math{-1 \leq x \leq 1}.
+@end multitable
+
+@item @emph{Return value}:
+The return value has the same type and kind as @var{X}.
+It is expressed in half-revolutions and satisfies
+@math{ 0 \leq \acospi (x) \leq 1}.
+
+@item @emph{Example}:
+@smallexample
+program test_acospi
+ implicit none
+ real, parameter :: x = 0.123, y(3) = [0.123, 0.45, 0.8]
+ real, parameter :: a = acospi(x), b(3) = acospi(y)
+ call foo(x, y)
+contains
+ subroutine foo(u, v)
+ real, intent(in) :: u, v(:)
+ real :: f, g(size(v))
+ f = acospi(u)
+ g = acospi(v)
+ if (abs(a - f) > 8 * epsilon(f)) stop 1
+ if (any(abs(g - b) > 8 * epsilon(f))) stop 2
+ end subroutine foo
+end program test_acospi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ASINPI} @*
+@ref{ATAN2PI} @*
+@ref{ATANPI} @*
+@end table
+
+
+
@node ADJUSTL
@section @code{ADJUSTL} --- Left adjust a string
@fnindex ADJUSTL
+@node ASINPI
+@section @code{ASINPI} --- Circular arc sine function
+@fnindex ASINPI
+@cindex trigonometric function, sine, inverse
+
+@table @asis
+@item @emph{Description}:
+@code{ASINPI(X)} computes @math{ \asin(x) / \pi}, which is a measure
+of an angle in half-revolutions.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@code{RESULT = ASINPI(X)}
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{X} @tab The type shall be @code{REAL} with @math{-1 \leq x \leq 1}.
+@end multitable
+
+@item @emph{Return value}:
+The return value has the same type and kind as @var{X}.
+It is expressed in half-revolutions and satisfies
+@math{ -0.5 \leq \asinpi (x) \leq 0.5}.
+
+@item @emph{Example}:
+@smallexample
+program test_asinpi
+ implicit none
+ real, parameter :: x = 0.123, y(3) = [0.123, 0.45, 0.8]
+ real, parameter :: a = asinpi(x), b(3) = asinpi(y)
+ call foo(x, y)
+contains
+ subroutine foo(u, v)
+ real, intent(in) :: u, v(:)
+ real :: f, g(size(v))
+ f = asinpi(u)
+ g = asinpi(v)
+ if (abs(a - f) > 8 * epsilon(f)) stop 1
+ if (any(abs(g - b) > 8 * epsilon(f))) stop 2
+ end subroutine foo
+end program test_asinpi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ACOSPI} @*
+@ref{ATAN2PI} @*
+@ref{ATANPI} @*
+@end table
+
+
+
@node ASSOCIATED
@section @code{ASSOCIATED} --- Status of a pointer or pointer/target pair
@fnindex ASSOCIATED
-@node ATAND
-@section @code{ATAND} --- Arctangent function, degrees
-@fnindex ATAND
-@fnindex DATAND
-@cindex trigonometric function, tangent, inverse, degrees
-@cindex tangent, inverse, degrees
-
-@table @asis
-@item @emph{Synopsis}:
-@multitable @columnfractions .80
-@item @code{RESULT = ATAND(X)}
-@item @code{RESULT = ATAND(Y, X)}
-@end multitable
-
-@item @emph{Description}:
-@code{ATAND(X)} computes the arctangent of @var{X} in degrees (inverse of
-@ref{TAND}).
-
-@item @emph{Class}:
-Elemental function
-
-@item @emph{Arguments}:
-@multitable @columnfractions .15 .70
-@item @var{X} @tab The type shall be @code{REAL}.
-@item @var{Y} @tab The type and kind type parameter shall be the same as @var{X}.
-@end multitable
-
-@item @emph{Return value}:
-The return value is of the same type and kind as @var{X}.
-If @var{Y} is present, the result is identical to @code{ATAN2D(Y, X)}.
-Otherwise, the result is in degrees and lies in the range
-@math{-90 \leq \atand(x) \leq 90}.
-
-@item @emph{Example}:
-@smallexample
-program test_atand
- real(8) :: x = 2.866_8
- real(4) :: x1 = 1.e0_4, y1 = 0.5e0_4
- x = atand(x)
- x1 = atand(y1, x1)
-end program test_atand
-@end smallexample
-
-@item @emph{Specific names}:
-@multitable @columnfractions .23 .23 .20 .30
-@headitem Name @tab Argument @tab Return type @tab Standard
-@item @code{ATAND(X)} @tab @code{REAL(4) X} @tab @code{REAL(4)} @tab Fortran 2023
-@item @code{DATAND(X)} @tab @code{REAL(8) X} @tab @code{REAL(8)} @tab GNU extension
-@end multitable
-
-@item @emph{Standard}:
-Fortran 2023
-
-@item @emph{See also}:
-Inverse function: @*
-@ref{TAND} @*
-Radians function: @*
-@ref{ATAN}
-@end table
-
-
-
@node ATAN2
@section @code{ATAN2} --- Arctangent function
@fnindex ATAN2
@ref{ATAN2}
@end table
+
+
+@node ATAN2PI
+@section @code{ATAN2PI} --- Circular arc tangent function
+@fnindex ATAN2PI
+@cindex trigonometric function, tangent, inverse
+
+@table @asis
+@item @emph{Description}:
+@code{ATAN2PI(Y, X)} computes @math{ {\rm {atan2}}(y, x) / \pi},
+and provides a measure of an angle in half-revolutions within
+the proper quadrant.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@code{RESULT = ATAN2PI(Y, X)}
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{Y} @tab The type shall be @code{REAL}.
+@item @var{X} @tab The type and kind type parameter shall be the
+same as @var{Y}. If @var{Y} is zero, then @var{X} shall be nonzero.
+@end multitable
+
+@item @emph{Return value}:
+The return value has the same type and kind type parameter as @var{Y}
+and satisfies @math{-1 \leq {\rm {atan2}}(y, x) / \pi \leq 1}.
+
+@item @emph{Example}:
+@smallexample
+program test_atan2pi
+ real(kind=4) :: x = 1.e0_4, y = 0.5e0_4
+ x = atan2pi(y, x)
+end program test_atan2pi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ACOSPI} @*
+@ref{ASINPI} @*
+@ref{ATANPI} @*
+@end table
+
+
+
+@node ATAND
+@section @code{ATAND} --- Arctangent function, degrees
+@fnindex ATAND
+@fnindex DATAND
+@cindex trigonometric function, tangent, inverse, degrees
+@cindex tangent, inverse, degrees
+
+@table @asis
+@item @emph{Synopsis}:
+@multitable @columnfractions .80
+@item @code{RESULT = ATAND(X)}
+@item @code{RESULT = ATAND(Y, X)}
+@end multitable
+
+@item @emph{Description}:
+@code{ATAND(X)} computes the arctangent of @var{X} in degrees (inverse of
+@ref{TAND}).
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{X} @tab The type shall be @code{REAL}.
+@item @var{Y} @tab The type and kind type parameter shall be the same as @var{X}.
+@end multitable
+
+@item @emph{Return value}:
+The return value is of the same type and kind as @var{X}.
+If @var{Y} is present, the result is identical to @code{ATAN2D(Y, X)}.
+Otherwise, the result is in degrees and lies in the range
+@math{-90 \leq \atand(x) \leq 90}.
+
+@item @emph{Example}:
+@smallexample
+program test_atand
+ real(8) :: x = 2.866_8
+ real(4) :: x1 = 1.e0_4, y1 = 0.5e0_4
+ x = atand(x)
+ x1 = atand(y1, x1)
+end program test_atand
+@end smallexample
+
+@item @emph{Specific names}:
+@multitable @columnfractions .23 .23 .20 .30
+@headitem Name @tab Argument @tab Return type @tab Standard
+@item @code{ATAND(X)} @tab @code{REAL(4) X} @tab @code{REAL(4)} @tab Fortran 2023
+@item @code{DATAND(X)} @tab @code{REAL(8) X} @tab @code{REAL(8)} @tab GNU extension
+@end multitable
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{See also}:
+Inverse function: @*
+@ref{TAND} @*
+Radians function: @*
+@ref{ATAN}
+@end table
+
+
+
@node ATANH
@section @code{ATANH} --- Inverse hyperbolic tangent function
@fnindex ATANH
+@node ATANPI
+@section @code{ATANPI} --- Circular arc tangent function
+@fnindex ATANPI
+@cindex trigonometric function, tangent, inverse
+
+@table @asis
+@item @emph{Description}:
+@code{ATANPI(X)} computes @math{ \atan(x) / \pi}.
+@code{ATANPI(Y, X)} computes @math{ {\rm atan2}(y, x) / \pi}.
+These provide a measure of an angle in half-revolutions.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@multitable @columnfractions .80
+@item @code{RESULT = ATANPI(X)}
+@item @code{RESULT = ATANPI(Y, X)}
+@end multitable
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{Y} @tab The type shall be @code{REAL}.
+@item @var{X} @tab If @var{Y} appears, @var{X} shall have the same type
+and kind as @var{Y}. If @var{Y} is zero, then @var{X} shall not be zero.
+If @var{Y} does not appear in a function reference, then @var{X} shall be
+@code{REAL}.
+@end multitable
+
+@item @emph{Return value}:
+The return value has the same type and kind as @var{X}.
+It is expressed in half-revolutions and satisfies
+@math{ -0.5 \leq \atanpi (x) \leq 0.5}.
+
+@item @emph{Example}:
+@smallexample
+program test_atanpi
+ implicit none
+ real, parameter :: x = 0.123, y(3) = [0.123, 0.45, 0.8]
+ real, parameter :: a = atanpi(x), b(3) = atanpi(y)
+ call foo(x, y)
+contains
+ subroutine foo(u, v)
+ real, intent(in) :: u, v(:)
+ real :: f, g(size(v))
+ f = atanpi(u)
+ g = atanpi(v)
+ if (abs(a - f) > 8 * epsilon(f)) stop 1
+ if (any(abs(g - b) > 8 * epsilon(f))) stop 2
+ end subroutine foo
+end program test_atanpi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ACOSPI} @*
+@ref{ASINPI} @*
+@ref{ATAN2PI} @*
+@end table
+
+
+
@node ATOMIC_ADD
@section @code{ATOMIC_ADD} --- Atomic ADD operation
@fnindex ATOMIC_ADD
+@node COSPI
+@section @code{COSPI} --- Circular cosine function
+@fnindex COSPI
+@cindex trigonometric function, cosine
+@cindex cosine
+
+@table @asis
+@item @emph{Description}:
+@code{COSPI(X)} computes @math{\cos(\pi x)} without performing
+an explicit multiplication by @math{\pi}. This is achieved
+through argument reduction where @math{ x = n + r } with
+@math{n} an integer and @math{0 \leq r \le 1}.
+Due to the
+properties of floating-point arithmetic, the useful range
+for @var{X} is defined by
+@code{ABS(X) <= REAL(2,KIND(X))**DIGITS(X)}.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@code{RESULT = COSPI(X)}
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{X} @tab The type shall be @code{REAL}.
+@end multitable
+
+@item @emph{Return value}:
+The return value is of the same type and kind as @var{X}.
+The result is in half-revolutions and satisfies
+@math{ -1 \leq \cospi (x) \leq 1}.
+
+@item @emph{Example}:
+@smallexample
+program test_cospi
+ real :: x = 0.0
+ x = cospi(x)
+end program test_cospi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ACOSPI} @*
+@ref{COS} @*
+@end table
+
+
+
@node COTAN
@section @code{COTAN} --- Cotangent function
@fnindex COTAN
+@node SINPI
+@section @code{SINPI} --- Circular sine function
+@fnindex SINPI
+@cindex trigonometric function, sine
+@cindex sine
+
+@table @asis
+@item @emph{Description}:
+@code{SINPI(X)} computes @math{\sin(\pi x)} without performing
+an explicit multiplication by @math{\pi}. This is achieved
+through argument reduction where @math{ |x| = n + r } with
+@math{n} an integer and @math{0 \leq r \le 1}.
+Due to the
+properties of floating-point arithmetic, the useful range
+for @var{X} is defined by
+@code{ABS(X) <= REAL(2,KIND(X))**DIGITS(X)}.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@code{RESULT = SINPI(X)}
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{X} @tab The type shall be @code{REAL}.
+@end multitable
+
+@item @emph{Return value}:
+The return value is of the same type and kind as @var{X}.
+The result is in half-revolutions and satisfies
+@math{ -1 \leq \sinpi (x) \leq 1}.
+
+@item @emph{Example}:
+@smallexample
+program test_sinpi
+ real :: x = 0.0
+ x = sinpi(x)
+end program test_sinpi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ASINPI} @*
+@ref{SIN} @*
+@end table
+
+
+
@node SIZE
@section @code{SIZE} --- Determine the size of an array
@fnindex SIZE
+@node TANPI
+@section @code{TANPI} --- Circular tangent function
+@fnindex TANPI
+@cindex trigonometric function, tangent
+@cindex tangent
+
+@table @asis
+@item @emph{Description}:
+@code{TANPI(X)} computes @math{\tan(\pi x)} without performing
+an explicit multiplication by @math{\pi}. This is achieved
+through argument reduction where @math{ |x| = n + r } with
+@math{n} an integer and @math{0 \leq r \le 1}.
+Due to the
+properties of floating-point arithmetic, the useful range
+for @var{X} is defined by
+@code{ABS(X) <= REAL(2,KIND(X))**DIGITS(X)}.
+
+@item @emph{Standard}:
+Fortran 2023
+
+@item @emph{Class}:
+Elemental function
+
+@item @emph{Syntax}:
+@code{RESULT = TANPI(X)}
+
+@item @emph{Arguments}:
+@multitable @columnfractions .15 .70
+@item @var{X} @tab The type shall be @code{REAL}.
+@end multitable
+
+@item @emph{Return value}:
+The return value is of the same type and kind as @var{X}.
+
+@item @emph{Example}:
+@smallexample
+program test_tanpi
+ real :: x = 0.0
+ x = tanpi(x)
+end program test_tanpi
+@end smallexample
+
+@item @emph{See also}:
+@ref{ATANPI} @*
+@ref{TAN} @*
+@end table
+
+
+
@node THIS_IMAGE
@section @code{THIS_IMAGE} --- Function that returns the cosubscript index of this image
@fnindex THIS_IMAGE
projects / thirdparty / gcc.git / commitdiff
