diff options
Diffstat (limited to 'gcc/fortran/intrinsic.texi')
| -rw-r--r-- | gcc/fortran/intrinsic.texi | 526 |
1 files changed, 458 insertions, 68 deletions
diff --git a/gcc/fortran/intrinsic.texi b/gcc/fortran/intrinsic.texi index 48c2d60..5831995 100644 --- a/gcc/fortran/intrinsic.texi +++ b/gcc/fortran/intrinsic.texi @@ -24,15 +24,22 @@ Some basic guidelines for editing this document: @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 @@ -49,6 +56,7 @@ Some basic guidelines for editing this document: * @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 @@ -62,12 +70,15 @@ Some basic guidelines for editing this document: * @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 @@ -116,6 +127,7 @@ Some basic guidelines for editing this document: * @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 @@ -296,6 +308,7 @@ Some basic guidelines for editing this document: * @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 @@ -312,6 +325,7 @@ Some basic guidelines for editing this document: * @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 @@ -754,6 +768,62 @@ Inverse 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 @@ -1469,6 +1539,62 @@ Inverse function: @* +@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 @@ -1608,68 +1734,6 @@ Degrees function: @* -@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 @@ -1798,6 +1862,117 @@ Radians function: @* @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 @@ -1851,6 +2026,70 @@ Inverse function: @* +@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 @@ -4391,6 +4630,57 @@ Inverse function: @* +@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 @@ -13677,6 +13967,57 @@ a GNU extension +@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 @@ -14574,6 +14915,55 @@ Fortran 2018 and later. +@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 |