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glibc/math/tgmath.h
Joseph Myers 06caf53adf Implement C23 rootn. 
C23 adds various <math.h> function families originally defined in TS
18661-4.  Add the rootn functions, which compute the Yth root of X for
integer Y (with a domain error if Y is 0, even if X is a NaN).  The
integer exponent has type long long int in C23; it was intmax_t in TS
18661-4, and as with other interfaces changed after their initial
appearance in the TS, I don't think we need to support the original
version of the interface.

As with pown and compoundn, I strongly encourage searching for worst
cases for ulps error for these implementations (necessarily
non-exhaustively, given the size of the input space).  I also expect a
custom implementation for a given format could be much faster as well
as more accurate, although the implementation is simpler than those
for pown and compoundn.

This completes adding to glibc those TS 18661-4 functions (ignoring
DFP) that are included in C23.  See
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=118592 regarding the C23
mathematical functions (not just the TS 18661-4 ones) missing built-in
functions in GCC, where such functions might usefully be added.

Tested for x86_64 and x86, and with build-many-glibcs.py.
2025-05-14 10:51:46 +00:00

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/* Copyright (C) 1997-2025 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
/*
* ISO C99 Standard: 7.22 Type-generic math <tgmath.h>
*/
#ifndef _TGMATH_H
#define _TGMATH_H 1
#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
#include <bits/libc-header-start.h>
/* Include the needed headers. */
#include <bits/floatn.h>
#include <math.h>
#include <complex.h>
/* There are two variant implementations of type-generic macros in
this file: one for GCC 8 and later, using __builtin_tgmath and
where each macro expands each of its arguments only once, and one
for older GCC, using other compiler extensions but with macros
expanding their arguments many times (so resulting in exponential
blowup of the size of expansions when calls to such macros are
nested inside arguments to such macros). Because of a long series
of defect fixes made after the initial release of TS 18661-1, GCC
versions before GCC 13 have __builtin_tgmath semantics that, when
integer arguments are passed to narrowing macros returning
_Float32x, or non-narrowing macros with at least two generic
arguments, do not always correspond to the C23 semantics, so more
complicated macro definitions are also used in some cases for
versions from GCC 8 to GCC 12. */
#define __HAVE_BUILTIN_TGMATH __GNUC_PREREQ (8, 0)
#define __HAVE_BUILTIN_TGMATH_C23 __GNUC_PREREQ (13, 0)
#if __GNUC_PREREQ (2, 7)
/* Certain cases of narrowing macros only need to call a single
function so cannot use __builtin_tgmath and do not need any
complicated logic. */
# if __HAVE_FLOAT128X
# error "Unsupported _Float128x type for <tgmath.h>."
# endif
# if ((__HAVE_FLOAT64X && !__HAVE_FLOAT128) \
|| (__HAVE_FLOAT128 && !__HAVE_FLOAT64X))
# error "Unsupported combination of types for <tgmath.h>."
# endif
# define __TGMATH_1_NARROW_D(F, X) \
(F ## l (X))
# define __TGMATH_2_NARROW_D(F, X, Y) \
(F ## l (X, Y))
# define __TGMATH_3_NARROW_D(F, X, Y, Z) \
(F ## l (X, Y, Z))
# define __TGMATH_1_NARROW_F64X(F, X) \
(F ## f128 (X))
# define __TGMATH_2_NARROW_F64X(F, X, Y) \
(F ## f128 (X, Y))
# define __TGMATH_3_NARROW_F64X(F, X, Y, Z) \
(F ## f128 (X, Y, Z))
# if !__HAVE_FLOAT128
# define __TGMATH_1_NARROW_F32X(F, X) \
(F ## f64 (X))
# define __TGMATH_2_NARROW_F32X(F, X, Y) \
(F ## f64 (X, Y))
# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
(F ## f64 (X, Y, Z))
# endif
# if __HAVE_BUILTIN_TGMATH
# if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F16_ARG(X) X ## f16,
# else
# define __TG_F16_ARG(X)
# endif
# if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F32_ARG(X) X ## f32,
# else
# define __TG_F32_ARG(X)
# endif
# if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F64_ARG(X) X ## f64,
# else
# define __TG_F64_ARG(X)
# endif
# if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F128_ARG(X) X ## f128,
# else
# define __TG_F128_ARG(X)
# endif
# if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F32X_ARG(X) X ## f32x,
# else
# define __TG_F32X_ARG(X)
# endif
# if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F64X_ARG(X) X ## f64x,
# else
# define __TG_F64X_ARG(X)
# endif
# if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define __TG_F128X_ARG(X) X ## f128x,
# else
# define __TG_F128X_ARG(X)
# endif
# define __TGMATH_FUNCS(X) X ## f, X, X ## l, \
__TG_F16_ARG (X) __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
__TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
# define __TGMATH_RCFUNCS(F, C) __TGMATH_FUNCS (F) __TGMATH_FUNCS (C)
# define __TGMATH_1(F, X) __builtin_tgmath (__TGMATH_FUNCS (F) (X))
# define __TGMATH_2(F, X, Y) __builtin_tgmath (__TGMATH_FUNCS (F) (X), (Y))
# define __TGMATH_2STD(F, X, Y) __builtin_tgmath (F ## f, F, F ## l, (X), (Y))
# define __TGMATH_3(F, X, Y, Z) __builtin_tgmath (__TGMATH_FUNCS (F) \
(X), (Y), (Z))
# define __TGMATH_1C(F, C, X) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) (X))
# define __TGMATH_2C(F, C, X, Y) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) \
(X), (Y))
# define __TGMATH_NARROW_FUNCS_F(X) X, X ## l,
# define __TGMATH_NARROW_FUNCS_F16(X) \
__TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
__TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
# define __TGMATH_NARROW_FUNCS_F32(X) \
__TG_F64_ARG (X) __TG_F128_ARG (X) \
__TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
# define __TGMATH_NARROW_FUNCS_F64(X) \
__TG_F128_ARG (X) \
__TG_F64X_ARG (X) __TG_F128X_ARG (X)
# define __TGMATH_NARROW_FUNCS_F32X(X) \
__TG_F64X_ARG (X) __TG_F128X_ARG (X) \
__TG_F64_ARG (X) __TG_F128_ARG (X)
# define __TGMATH_1_NARROW_F(F, X) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X))
# define __TGMATH_2_NARROW_F(F, X, Y) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X), (Y))
# define __TGMATH_3_NARROW_F(F, X, Y, Z) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X), (Y), (Z))
# define __TGMATH_1_NARROW_F16(F, X) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X))
# define __TGMATH_2_NARROW_F16(F, X, Y) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X), (Y))
# define __TGMATH_3_NARROW_F16(F, X, Y, Z) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X), (Y), (Z))
# define __TGMATH_1_NARROW_F32(F, X) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X))
# define __TGMATH_2_NARROW_F32(F, X, Y) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X), (Y))
# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X), (Y), (Z))
# define __TGMATH_1_NARROW_F64(F, X) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X))
# define __TGMATH_2_NARROW_F64(F, X, Y) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X), (Y))
# define __TGMATH_3_NARROW_F64(F, X, Y, Z) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X), (Y), (Z))
# if __HAVE_FLOAT128 && __HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_1_NARROW_F32X(F, X) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X))
# define __TGMATH_2_NARROW_F32X(F, X, Y) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X), (Y))
# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
__builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X), (Y), (Z))
# endif
# endif
# if !__HAVE_BUILTIN_TGMATH_C23
# ifdef __NO_LONG_DOUBLE_MATH
# define __tgml(fct) fct
# else
# define __tgml(fct) fct ## l
# endif
/* __floating_type expands to 1 if TYPE is a floating type (including
complex floating types), 0 if TYPE is an integer type (including
complex integer types). __real_integer_type expands to 1 if TYPE
is a real integer type. __complex_integer_type expands to 1 if
TYPE is a complex integer type. All these macros expand to integer
constant expressions. All these macros can assume their argument
has an arithmetic type (not vector, decimal floating-point or
fixed-point), valid to pass to tgmath.h macros. */
# if __GNUC_PREREQ (3, 1)
/* __builtin_classify_type expands to an integer constant expression
in GCC 3.1 and later. Default conversions applied to the argument
of __builtin_classify_type mean it always returns 1 for real
integer types rather than ever returning different values for
character, boolean or enumerated types. */
# define __floating_type(type) \
(__builtin_classify_type (__real__ ((type) 0)) == 8)
# define __real_integer_type(type) \
(__builtin_classify_type ((type) 0) == 1)
# define __complex_integer_type(type) \
(__builtin_classify_type ((type) 0) == 9 \
&& __builtin_classify_type (__real__ ((type) 0)) == 1)
# else
/* GCC versions predating __builtin_classify_type are also looser on
what counts as an integer constant expression. */
# define __floating_type(type) (((type) 1.25) != 1)
# define __real_integer_type(type) (((type) (1.25 + _Complex_I)) == 1)
# define __complex_integer_type(type) \
(((type) (1.25 + _Complex_I)) == (1 + _Complex_I))
# endif
/* Whether an expression (of arithmetic type) has a real type. */
# define __expr_is_real(E) (__builtin_classify_type (E) != 9)
/* Type T1 if E is 1, type T2 is E is 0. */
# define __tgmath_type_if(T1, T2, E) \
__typeof__ (*(0 ? (__typeof__ (0 ? (T2 *) 0 : (void *) (E))) 0 \
: (__typeof__ (0 ? (T1 *) 0 : (void *) (!(E)))) 0))
/* The tgmath real type for T, where E is 0 if T is an integer type
and 1 for a floating type. If T has a complex type, it is
unspecified whether the return type is real or complex (but it has
the correct corresponding real type). */
# define __tgmath_real_type_sub(T, E) \
__tgmath_type_if (T, double, E)
/* The tgmath real type of EXPR. */
# define __tgmath_real_type(expr) \
__tgmath_real_type_sub (__typeof__ ((__typeof__ (+(expr))) 0), \
__floating_type (__typeof__ (+(expr))))
/* The tgmath complex type for T, where E1 is 1 if T has a floating
type and 0 otherwise, E2 is 1 if T has a real integer type and 0
otherwise, and E3 is 1 if T has a complex type and 0 otherwise. */
# define __tgmath_complex_type_sub(T, E1, E2, E3) \
__typeof__ (*(0 \
? (__typeof__ (0 ? (T *) 0 : (void *) (!(E1)))) 0 \
: (__typeof__ (0 \
? (__typeof__ (0 \
? (double *) 0 \
: (void *) (!(E2)))) 0 \
: (__typeof__ (0 \
? (_Complex double *) 0 \
: (void *) (!(E3)))) 0)) 0))
/* The tgmath complex type of EXPR. */
# define __tgmath_complex_type(expr) \
__tgmath_complex_type_sub (__typeof__ ((__typeof__ (+(expr))) 0), \
__floating_type (__typeof__ (+(expr))), \
__real_integer_type (__typeof__ (+(expr))), \
__complex_integer_type (__typeof__ (+(expr))))
/* The tgmath real type of EXPR1 combined with EXPR2, without handling
the C23 rule of interpreting integer arguments as _Float32x if any
argument is _FloatNx. */
# define __tgmath_real_type2_base(expr1, expr2) \
__typeof ((__tgmath_real_type (expr1)) 0 + (__tgmath_real_type (expr2)) 0)
/* The tgmath complex type of EXPR1 combined with EXPR2, without
handling the C23 rule of interpreting integer arguments as
_Float32x if any argument is _FloatNx. */
# define __tgmath_complex_type2_base(expr1, expr2) \
__typeof ((__tgmath_complex_type (expr1)) 0 \
+ (__tgmath_complex_type (expr2)) 0)
/* The tgmath real type of EXPR1 combined with EXPR2 and EXPR3,
without handling the C23 rule of interpreting integer arguments as
_Float32x if any argument is _FloatNx. */
# define __tgmath_real_type3_base(expr1, expr2, expr3) \
__typeof ((__tgmath_real_type (expr1)) 0 \
+ (__tgmath_real_type (expr2)) 0 \
+ (__tgmath_real_type (expr3)) 0)
/* The tgmath real or complex type of EXPR1 combined with EXPR2 (and
EXPR3 if applicable). */
# if __HAVE_FLOATN_NOT_TYPEDEF
# define __tgmath_real_type2(expr1, expr2) \
__tgmath_type_if (_Float32x, __tgmath_real_type2_base (expr1, expr2), \
_Generic ((expr1) + (expr2), _Float32x: 1, default: 0))
# define __tgmath_complex_type2(expr1, expr2) \
__tgmath_type_if (_Float32x, \
__tgmath_type_if (_Complex _Float32x, \
__tgmath_complex_type2_base (expr1, \
expr2), \
_Generic ((expr1) + (expr2), \
_Complex _Float32x: 1, \
default: 0)), \
_Generic ((expr1) + (expr2), _Float32x: 1, default: 0))
# define __tgmath_real_type3(expr1, expr2, expr3) \
__tgmath_type_if (_Float32x, \
__tgmath_real_type3_base (expr1, expr2, expr3), \
_Generic ((expr1) + (expr2) + (expr3), \
_Float32x: 1, default: 0))
# else
# define __tgmath_real_type2(expr1, expr2) \
__tgmath_real_type2_base (expr1, expr2)
# define __tgmath_complex_type2(expr1, expr2) \
__tgmath_complex_type2_base (expr1, expr2)
# define __tgmath_real_type3(expr1, expr2, expr3) \
__tgmath_real_type3_base (expr1, expr2, expr3)
# endif
# if (__HAVE_DISTINCT_FLOAT16 \
|| __HAVE_DISTINCT_FLOAT32 \
|| __HAVE_DISTINCT_FLOAT64 \
|| __HAVE_DISTINCT_FLOAT32X \
|| __HAVE_DISTINCT_FLOAT64X \
|| __HAVE_DISTINCT_FLOAT128X)
# error "Unsupported _FloatN or _FloatNx types for <tgmath.h>."
# endif
/* Expand to text that checks if ARG_COMB has type _Float128, and if
so calls the appropriately suffixed FCT (which may include a cast),
or FCT and CFCT for complex functions, with arguments ARG_CALL.
__TGMATH_F128LD (only used in the __HAVE_FLOAT64X_LONG_DOUBLE case,
for narrowing macros) handles long double the same as
_Float128. */
# if __HAVE_DISTINCT_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# if (!__HAVE_FLOAT64X \
|| __HAVE_FLOAT64X_LONG_DOUBLE \
|| !__HAVE_FLOATN_NOT_TYPEDEF)
# define __TGMATH_F128(arg_comb, fct, arg_call) \
__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
? fct ## f128 arg_call :
# define __TGMATH_F128LD(arg_comb, fct, arg_call) \
(__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
|| __builtin_types_compatible_p (__typeof (+(arg_comb)), long double)) \
? fct ## f128 arg_call :
# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) \
__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
? (__expr_is_real (arg_comb) \
? fct ## f128 arg_call \
: cfct ## f128 arg_call) :
# else
/* _Float64x is a distinct type at the C language level, which must be
handled like _Float128. */
# define __TGMATH_F128(arg_comb, fct, arg_call) \
(__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
|| __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float64x)) \
? fct ## f128 arg_call :
# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) \
(__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
|| __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), \
_Float64x)) \
? (__expr_is_real (arg_comb) \
? fct ## f128 arg_call \
: cfct ## f128 arg_call) :
# endif
# else
# define __TGMATH_F128(arg_comb, fct, arg_call) /* Nothing. */
# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) /* Nothing. */
# endif
# endif /* !__HAVE_BUILTIN_TGMATH_C23. */
/* We have two kinds of generic macros: to support functions which are
only defined on real valued parameters and those which are defined
for complex functions as well. */
# if __HAVE_BUILTIN_TGMATH
# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
# define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
__TGMATH_2 (Fct, (Val1), (Val2))
# define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
__TGMATH_2STD (Fct, (Val1), (Val2))
# if __HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
__TGMATH_2 (Fct, (Val1), (Val2))
# endif
# define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
__TGMATH_2STD (Fct, (Val1), (Val2))
# if __HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
__TGMATH_3 (Fct, (Val1), (Val2), (Val3))
# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
__TGMATH_3 (Fct, (Val1), (Val2), (Val3))
# endif
# define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
__TGMATH_3 (Fct, (Val1), (Val2), (Val3))
# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
__TGMATH_1C (Fct, Cfct, (Val))
# define __TGMATH_UNARY_IMAG(Val, Cfct) __TGMATH_1 (Cfct, (Val))
# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
__TGMATH_1C (Fct, Cfct, (Val))
# define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct) \
__TGMATH_1 (Cfct, (Val))
# if __HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
__TGMATH_2C (Fct, Cfct, (Val1), (Val2))
# endif
# endif
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) \
(__extension__ ((sizeof (+(Val)) == sizeof (double) \
|| __builtin_classify_type (Val) != 8) \
? (__tgmath_real_type (Val)) Fct (Val) \
: (sizeof (+(Val)) == sizeof (float)) \
? (__tgmath_real_type (Val)) Fct##f (Val) \
: __TGMATH_F128 ((Val), (__tgmath_real_type (Val)) Fct, \
(Val)) \
(__tgmath_real_type (Val)) __tgml(Fct) (Val)))
# define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) \
(__extension__ ((sizeof (+(Val)) == sizeof (double) \
|| __builtin_classify_type (Val) != 8) \
? Fct (Val) \
: (sizeof (+(Val)) == sizeof (float)) \
? Fct##f (Val) \
: __TGMATH_F128 ((Val), Fct, (Val)) \
__tgml(Fct) (Val)))
# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
(__extension__ ((sizeof (+(Val1)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8) \
? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
: (sizeof (+(Val1)) == sizeof (float)) \
? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
: __TGMATH_F128 ((Val1), (__tgmath_real_type (Val1)) Fct, \
(Val1, Val2)) \
(__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
# define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
(__extension__ ((sizeof (+(Val1)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8) \
? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
: (sizeof (+(Val1)) == sizeof (float)) \
? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
: (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
# endif
# if !__HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
(__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
&& __builtin_classify_type ((Val1) + (Val2)) == 8) \
? __TGMATH_F128 ((Val1) + (Val2), \
(__tgmath_real_type2 (Val1, Val2)) Fct, \
(Val1, Val2)) \
(__tgmath_real_type2 (Val1, Val2)) \
__tgml(Fct) (Val1, Val2) \
: (sizeof (+(Val1)) == sizeof (double) \
|| sizeof (+(Val2)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8) \
? (__tgmath_real_type2 (Val1, Val2)) \
Fct (Val1, Val2) \
: (__tgmath_real_type2 (Val1, Val2)) \
Fct##f (Val1, Val2)))
# endif
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
(__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
&& __builtin_classify_type ((Val1) + (Val2)) == 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
__tgml(Fct) (Val1, Val2) \
: (sizeof (+(Val1)) == sizeof (double) \
|| sizeof (+(Val2)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct (Val1, Val2) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct##f (Val1, Val2)))
# endif
# if !__HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
(__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
&& __builtin_classify_type ((Val1) + (Val2)) == 8) \
? __TGMATH_F128 ((Val1) + (Val2), \
(__tgmath_real_type2 (Val1, Val2)) Fct, \
(Val1, Val2, Val3)) \
(__tgmath_real_type2 (Val1, Val2)) \
__tgml(Fct) (Val1, Val2, Val3) \
: (sizeof (+(Val1)) == sizeof (double) \
|| sizeof (+(Val2)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8) \
? (__tgmath_real_type2 (Val1, Val2)) \
Fct (Val1, Val2, Val3) \
: (__tgmath_real_type2 (Val1, Val2)) \
Fct##f (Val1, Val2, Val3)))
# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
(__extension__ ((sizeof ((Val1) + (Val2) + (Val3)) > sizeof (double) \
&& __builtin_classify_type ((Val1) + (Val2) + (Val3)) \
== 8) \
? __TGMATH_F128 ((Val1) + (Val2) + (Val3), \
(__tgmath_real_type3 (Val1, Val2, \
Val3)) Fct, \
(Val1, Val2, Val3)) \
(__tgmath_real_type3 (Val1, Val2, Val3)) \
__tgml(Fct) (Val1, Val2, Val3) \
: (sizeof (+(Val1)) == sizeof (double) \
|| sizeof (+(Val2)) == sizeof (double) \
|| sizeof (+(Val3)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8 \
|| __builtin_classify_type (Val3) != 8) \
? (__tgmath_real_type3 (Val1, Val2, Val3)) \
Fct (Val1, Val2, Val3) \
: (__tgmath_real_type3 (Val1, Val2, Val3)) \
Fct##f (Val1, Val2, Val3)))
# endif
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
(__extension__ ((sizeof (+(Val1)) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8) \
? Fct (Val1, Val2, Val3) \
: (sizeof (+(Val1)) == sizeof (float)) \
? Fct##f (Val1, Val2, Val3) \
: __TGMATH_F128 ((Val1), Fct, (Val1, Val2, Val3)) \
__tgml(Fct) (Val1, Val2, Val3)))
/* XXX This definition has to be changed as soon as the compiler understands
the imaginary keyword. */
# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
(__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val)) != 8) \
? (__expr_is_real (Val) \
? (__tgmath_complex_type (Val)) Fct (Val) \
: (__tgmath_complex_type (Val)) Cfct (Val)) \
: (sizeof (+__real__ (Val)) == sizeof (float)) \
? (__expr_is_real (Val) \
? (__tgmath_complex_type (Val)) Fct##f (Val) \
: (__tgmath_complex_type (Val)) Cfct##f (Val)) \
: __TGMATH_CF128 ((Val), \
(__tgmath_complex_type (Val)) Fct, \
(__tgmath_complex_type (Val)) Cfct, \
(Val)) \
(__expr_is_real (Val) \
? (__tgmath_complex_type (Val)) __tgml(Fct) (Val) \
: (__tgmath_complex_type (Val)) __tgml(Cfct) (Val))))
# define __TGMATH_UNARY_IMAG(Val, Cfct) \
(__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val)) != 8) \
? (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) Cfct (Val) \
: (sizeof (+__real__ (Val)) == sizeof (float)) \
? (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) Cfct##f (Val) \
: __TGMATH_F128 (__real__ (Val), \
(__typeof__ \
((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) Cfct, (Val)) \
(__typeof__ ((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) __tgml(Cfct) (Val)))
/* XXX This definition has to be changed as soon as the compiler understands
the imaginary keyword. */
# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
(__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val)) != 8) \
? (__expr_is_real (Val) \
? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Fct (Val) \
: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Cfct (Val)) \
: (sizeof (+__real__ (Val)) == sizeof (float)) \
? (__expr_is_real (Val) \
? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Fct##f (Val) \
: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Cfct##f (Val)) \
: __TGMATH_CF128 ((Val), \
(__typeof__ \
(__real__ \
(__tgmath_real_type (Val)) 0)) Fct, \
(__typeof__ \
(__real__ \
(__tgmath_real_type (Val)) 0)) Cfct, \
(Val)) \
(__expr_is_real (Val) \
? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0)) \
__tgml(Fct) (Val) \
: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0)) \
__tgml(Cfct) (Val))))
# define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct) \
__TGMATH_UNARY_REAL_IMAG_RET_REAL ((Val), Cfct, Cfct)
# endif
# if !__HAVE_BUILTIN_TGMATH_C23
/* XXX This definition has to be changed as soon as the compiler understands
the imaginary keyword. */
# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
(__extension__ ((sizeof (__real__ (Val1) \
+ __real__ (Val2)) > sizeof (double) \
&& __builtin_classify_type (__real__ (Val1) \
+ __real__ (Val2)) == 8) \
? __TGMATH_CF128 ((Val1) + (Val2), \
(__tgmath_complex_type2 (Val1, Val2)) \
Fct, \
(__tgmath_complex_type2 (Val1, Val2)) \
Cfct, \
(Val1, Val2)) \
(__expr_is_real ((Val1) + (Val2)) \
? (__tgmath_complex_type2 (Val1, Val2)) \
__tgml(Fct) (Val1, Val2) \
: (__tgmath_complex_type2 (Val1, Val2)) \
__tgml(Cfct) (Val1, Val2)) \
: (sizeof (+__real__ (Val1)) == sizeof (double) \
|| sizeof (+__real__ (Val2)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val1)) != 8 \
|| __builtin_classify_type (__real__ (Val2)) != 8) \
? (__expr_is_real ((Val1) + (Val2)) \
? (__tgmath_complex_type2 (Val1, Val2)) \
Fct (Val1, Val2) \
: (__tgmath_complex_type2 (Val1, Val2)) \
Cfct (Val1, Val2)) \
: (__expr_is_real ((Val1) + (Val2)) \
? (__tgmath_complex_type2 (Val1, Val2)) \
Fct##f (Val1, Val2) \
: (__tgmath_complex_type2 (Val1, Val2)) \
Cfct##f (Val1, Val2))))
# endif
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_1_NARROW_F(F, X) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (double) \
? F ## l (X) \
: F (X)))
# define __TGMATH_2_NARROW_F(F, X, Y) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0) > sizeof (double) \
? F ## l (X, Y) \
: F (X, Y)))
# define __TGMATH_3_NARROW_F(F, X, Y, Z) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0 \
+ (__tgmath_real_type (Z)) 0) > sizeof (double) \
? F ## l (X, Y, Z) \
: F (X, Y, Z)))
# endif
/* In most cases, these narrowing macro definitions based on sizeof
ensure that the function called has the right argument format, as
for other <tgmath.h> macros for compilers before GCC 8, but may not
have exactly the argument type (among the types with that format)
specified in the standard logic.
In the case of macros for _Float32x return type, when _Float64x
exists, _Float64 arguments should result in the *f64 function being
called while _Float32x, float and double arguments should result in
the *f64x function being called (and integer arguments are
considered to have type _Float32x if any argument has type
_FloatNx, or double otherwise). These cases cannot be
distinguished using sizeof (or at all if the types are typedefs
rather than different types, in which case we err on the side of
using the wider type if unsure). */
# if !__HAVE_BUILTIN_TGMATH_C23
# if __HAVE_FLOATN_NOT_TYPEDEF
# define __TGMATH_NARROW_F32X_USE_F64X(X) \
!__builtin_types_compatible_p (__typeof (+(X)), _Float64)
# else
# define __TGMATH_NARROW_F32X_USE_F64X(X) \
(__builtin_types_compatible_p (__typeof (+(X)), double) \
|| __builtin_types_compatible_p (__typeof (+(X)), float) \
|| !__floating_type (__typeof (+(X))))
# endif
# endif
# if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_1_NARROW_F32(F, X) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
? __TGMATH_F128LD ((X), F, (X)) \
F ## f64x (X) \
: F ## f64 (X)))
# define __TGMATH_2_NARROW_F32(F, X, Y) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
? __TGMATH_F128LD ((X) + (Y), F, (X, Y)) \
F ## f64x (X, Y) \
: F ## f64 (X, Y)))
# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0 \
+ (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
? __TGMATH_F128LD ((X) + (Y) + (Z), F, (X, Y, Z)) \
F ## f64x (X, Y, Z) \
: F ## f64 (X, Y, Z)))
# define __TGMATH_1_NARROW_F64(F, X) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
? __TGMATH_F128LD ((X), F, (X)) \
F ## f64x (X) \
: F ## f128 (X)))
# define __TGMATH_2_NARROW_F64(F, X, Y) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
? __TGMATH_F128LD ((X) + (Y), F, (X, Y)) \
F ## f64x (X, Y) \
: F ## f128 (X, Y)))
# define __TGMATH_3_NARROW_F64(F, X, Y, Z) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0 \
+ (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
? __TGMATH_F128LD ((X) + (Y) + (Z), F, (X, Y, Z)) \
F ## f64x (X, Y, Z) \
: F ## f128 (X, Y, Z)))
# endif
# if !__HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_1_NARROW_F32X(F, X) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
|| __TGMATH_NARROW_F32X_USE_F64X (X) \
? __TGMATH_F128 ((X), F, (X)) \
F ## f64x (X) \
: F ## f64 (X)))
# define __TGMATH_2_NARROW_F32X(F, X, Y) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
|| __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y)) \
? __TGMATH_F128 ((X) + (Y), F, (X, Y)) \
F ## f64x (X, Y) \
: F ## f64 (X, Y)))
# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0 \
+ (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
|| __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y) + (Z)) \
? __TGMATH_F128 ((X) + (Y) + (Z), F, (X, Y, Z)) \
F ## f64x (X, Y, Z) \
: F ## f64 (X, Y, Z)))
# endif
# elif __HAVE_FLOAT128
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_1_NARROW_F32(F, X) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
? F ## f128 (X) \
: F ## f64 (X)))
# define __TGMATH_2_NARROW_F32(F, X, Y) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
? F ## f128 (X, Y) \
: F ## f64 (X, Y)))
# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0 \
+ (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
? F ## f128 (X, Y, Z) \
: F ## f64 (X, Y, Z)))
# define __TGMATH_1_NARROW_F64(F, X) \
(F ## f128 (X))
# define __TGMATH_2_NARROW_F64(F, X, Y) \
(F ## f128 (X, Y))
# define __TGMATH_3_NARROW_F64(F, X, Y, Z) \
(F ## f128 (X, Y, Z))
# endif
# if !__HAVE_BUILTIN_TGMATH_C23
# define __TGMATH_1_NARROW_F32X(F, X) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float32x) \
|| __TGMATH_NARROW_F32X_USE_F64X (X) \
? F ## f64x (X) \
: F ## f64 (X)))
# define __TGMATH_2_NARROW_F32X(F, X, Y) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0) > sizeof (_Float32x) \
|| __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y)) \
? F ## f64x (X, Y) \
: F ## f64 (X, Y)))
# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
(__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
+ (__tgmath_real_type (Y)) 0 \
+ (__tgmath_real_type (Z)) 0) > sizeof (_Float32x) \
|| __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y) + (Z)) \
? F ## f64x (X, Y, Z) \
: F ## f64 (X, Y, Z)))
# endif
# else
# if !__HAVE_BUILTIN_TGMATH
# define __TGMATH_1_NARROW_F32(F, X) \
(F ## f64 (X))
# define __TGMATH_2_NARROW_F32(F, X, Y) \
(F ## f64 (X, Y))
# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
(F ## f64 (X, Y, Z))
# endif
# endif
#else
# error "Unsupported compiler; you cannot use <tgmath.h>"
#endif
/* Unary functions defined for real and complex values. */
/* Trigonometric functions. */
/* Arc cosine of X. */
#define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
/* Arc sine of X. */
#define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
/* Arc tangent of X. */
#define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
/* Arc tangent of Y/X. */
#define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
/* Cosine of X. */
#define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
/* Sine of X. */
#define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
/* Tangent of X. */
#define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
/* Arc cosine of X, divided by pi.. */
# define acospi(Val) __TGMATH_UNARY_REAL_ONLY (Val, acospi)
/* Arc sine of X, divided by pi.. */
# define asinpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, asinpi)
/* Arc tangent of X, divided by pi. */
# define atanpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, atanpi)
/* Arc tangent of Y/X, divided by pi. */
#define atan2pi(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2pi)
/* Cosine of pi * X. */
# define cospi(Val) __TGMATH_UNARY_REAL_ONLY (Val, cospi)
/* Sine of pi * X. */
# define sinpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, sinpi)
/* Tangent of pi * X. */
# define tanpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, tanpi)
#endif
/* Hyperbolic functions. */
/* Hyperbolic arc cosine of X. */
#define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
/* Hyperbolic arc sine of X. */
#define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
/* Hyperbolic arc tangent of X. */
#define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
/* Hyperbolic cosine of X. */
#define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
/* Hyperbolic sine of X. */
#define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
/* Hyperbolic tangent of X. */
#define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
/* Exponential and logarithmic functions. */
/* Exponential function of X. */
#define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
/* Break VALUE into a normalized fraction and an integral power of 2. */
#define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
/* X times (two to the EXP power). */
#define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
/* Natural logarithm of X. */
#define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
/* Base-ten logarithm of X. */
#ifdef __USE_GNU
# define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
#else
# define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
#endif
/* Return exp(X) - 1. */
#define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
/* Return log(1 + X). */
#define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
/* Return the base 2 signed integral exponent of X. */
#define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
/* Compute base-2 exponential of X. */
#define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
/* Compute base-2 logarithm of X. */
#define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
/* Compute exponent to base ten. */
#define exp10(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp10)
/* Return exp2(X) - 1. */
#define exp2m1(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2m1)
/* Return exp10(X) - 1. */
#define exp10m1(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp10m1)
/* Return log2(1 + X). */
#define log2p1(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2p1)
/* Return log10(1 + X). */
#define log10p1(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10p1)
/* Return log(1 + X). */
#define logp1(Val) __TGMATH_UNARY_REAL_ONLY (Val, logp1)
#endif
/* Power functions. */
/* Return X to the Y power. */
#define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
/* Return the square root of X. */
#define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
/* Return `sqrt(X*X + Y*Y)'. */
#define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
/* Return the cube root of X. */
#define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
/* Return 1+X to the Y power. */
# define compoundn(Val1, Val2) \
__TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, compoundn)
/* Return X to the Y power. */
# define pown(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, pown)
/* Return X to the Y power. */
# define powr(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, powr)
/* Return the Yth root of X. */
# define rootn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, rootn)
/* Return 1/sqrt(X). */
# define rsqrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, rsqrt)
#endif
/* Nearest integer, absolute value, and remainder functions. */
/* Smallest integral value not less than X. */
#define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
/* Absolute value of X. */
#define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
/* Largest integer not greater than X. */
#define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
/* Floating-point modulo remainder of X/Y. */
#define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
/* Round X to integral valuein floating-point format using current
rounding direction, but do not raise inexact exception. */
#define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
/* Round X to nearest integral value, rounding halfway cases away from
zero. */
#define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
/* Round X to the integral value in floating-point format nearest but
not larger in magnitude. */
#define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
/* Compute remainder of X and Y and put in *QUO a value with sign of x/y
and magnitude congruent `mod 2^n' to the magnitude of the integral
quotient x/y, with n >= 3. */
#define remquo(Val1, Val2, Val3) \
__TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
/* Round X to nearest integral value according to current rounding
direction. */
#define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
#define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)
/* Round X to nearest integral value, rounding halfway cases away from
zero. */
#define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
#define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)
/* Return X with its signed changed to Y's. */
#define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
/* Error and gamma functions. */
#define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
#define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
#define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
#define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
/* Return the integer nearest X in the direction of the
prevailing rounding mode. */
#define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
#if __GLIBC_USE (IEC_60559_BFP_EXT_C23)
/* Return X - epsilon. */
# define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
/* Return X + epsilon. */
# define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
#endif
/* Return X + epsilon if X < Y, X - epsilon if X > Y. */
#define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
#define nexttoward(Val1, Val2) \
__TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)
/* Return the remainder of integer division X / Y with infinite precision. */
#define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
/* Return X times (2 to the Nth power). */
#ifdef __USE_MISC
# define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
#endif
/* Return X times (2 to the Nth power). */
#define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
/* Return X times (2 to the Nth power). */
#define scalbln(Val1, Val2) \
__TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
/* Return the binary exponent of X, which must be nonzero. */
#define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)
/* Return positive difference between X and Y. */
#define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
#if __GLIBC_USE (ISOC23) && !defined __USE_GNU
/* Return maximum numeric value from X and Y. */
# define fmax(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmax)
/* Return minimum numeric value from X and Y. */
# define fmin(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmin)
#else
/* Return maximum numeric value from X and Y. */
# define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
/* Return minimum numeric value from X and Y. */
# define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
#endif
/* Multiply-add function computed as a ternary operation. */
#define fma(Val1, Val2, Val3) \
__TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
#if __GLIBC_USE (IEC_60559_BFP_EXT_C23)
/* Round X to nearest integer value, rounding halfway cases to even. */
# define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)
# define fromfp(Val1, Val2, Val3) \
__TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)
# define ufromfp(Val1, Val2, Val3) \
__TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)
# define fromfpx(Val1, Val2, Val3) \
__TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)
# define ufromfpx(Val1, Val2, Val3) \
__TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)
/* Like ilogb, but returning long int. */
# define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)
#endif
#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Return value with maximum magnitude. */
# define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
/* Return value with minimum magnitude. */
# define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
#endif
#if __GLIBC_USE (ISOC23)
/* Return maximum value from X and Y. */
# define fmaximum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum)
/* Return minimum value from X and Y. */
# define fminimum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum)
/* Return maximum numeric value from X and Y. */
# define fmaximum_num(Val1, Val2) \
__TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_num)
/* Return minimum numeric value from X and Y. */
# define fminimum_num(Val1, Val2) \
__TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_num)
/* Return value with maximum magnitude. */
# define fmaximum_mag(Val1, Val2) \
__TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag)
/* Return value with minimum magnitude. */
# define fminimum_mag(Val1, Val2) \
__TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag)
/* Return numeric value with maximum magnitude. */
# define fmaximum_mag_num(Val1, Val2) \
__TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag_num)
/* Return numeric value with minimum magnitude. */
# define fminimum_mag_num(Val1, Val2) \
__TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag_num)
#endif
/* Absolute value, conjugates, and projection. */
/* Argument value of Z. */
#define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)
/* Complex conjugate of Z. */
#define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
/* Projection of Z onto the Riemann sphere. */
#define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
/* Decomposing complex values. */
/* Imaginary part of Z. */
#define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)
/* Real part of Z. */
#define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)
/* Narrowing functions. */
#if __GLIBC_USE (IEC_60559_BFP_EXT_C23)
/* Add. */
# define fadd(Val1, Val2) __TGMATH_2_NARROW_F (fadd, Val1, Val2)
# define dadd(Val1, Val2) __TGMATH_2_NARROW_D (dadd, Val1, Val2)
/* Divide. */
# define fdiv(Val1, Val2) __TGMATH_2_NARROW_F (fdiv, Val1, Val2)
# define ddiv(Val1, Val2) __TGMATH_2_NARROW_D (ddiv, Val1, Val2)
/* Multiply. */
# define fmul(Val1, Val2) __TGMATH_2_NARROW_F (fmul, Val1, Val2)
# define dmul(Val1, Val2) __TGMATH_2_NARROW_D (dmul, Val1, Val2)
/* Subtract. */
# define fsub(Val1, Val2) __TGMATH_2_NARROW_F (fsub, Val1, Val2)
# define dsub(Val1, Val2) __TGMATH_2_NARROW_D (dsub, Val1, Val2)
/* Square root. */
# define fsqrt(Val) __TGMATH_1_NARROW_F (fsqrt, Val)
# define dsqrt(Val) __TGMATH_1_NARROW_D (dsqrt, Val)
/* Fused multiply-add. */
# define ffma(Val1, Val2, Val3) __TGMATH_3_NARROW_F (ffma, Val1, Val2, Val3)
# define dfma(Val1, Val2, Val3) __TGMATH_3_NARROW_D (dfma, Val1, Val2, Val3)
#endif
#if __GLIBC_USE (IEC_60559_TYPES_EXT)
# if __HAVE_FLOAT16
# define f16add(Val1, Val2) __TGMATH_2_NARROW_F16 (f16add, Val1, Val2)
# define f16div(Val1, Val2) __TGMATH_2_NARROW_F16 (f16div, Val1, Val2)
# define f16mul(Val1, Val2) __TGMATH_2_NARROW_F16 (f16mul, Val1, Val2)
# define f16sub(Val1, Val2) __TGMATH_2_NARROW_F16 (f16sub, Val1, Val2)
# define f16sqrt(Val) __TGMATH_1_NARROW_F16 (f16sqrt, Val)
# define f16fma(Val1, Val2, Val3) \
__TGMATH_3_NARROW_F16 (f16fma, Val1, Val2, Val3)
# endif
# if __HAVE_FLOAT32
# define f32add(Val1, Val2) __TGMATH_2_NARROW_F32 (f32add, Val1, Val2)
# define f32div(Val1, Val2) __TGMATH_2_NARROW_F32 (f32div, Val1, Val2)
# define f32mul(Val1, Val2) __TGMATH_2_NARROW_F32 (f32mul, Val1, Val2)
# define f32sub(Val1, Val2) __TGMATH_2_NARROW_F32 (f32sub, Val1, Val2)
# define f32sqrt(Val) __TGMATH_1_NARROW_F32 (f32sqrt, Val)
# define f32fma(Val1, Val2, Val3) \
__TGMATH_3_NARROW_F32 (f32fma, Val1, Val2, Val3)
# endif
# if __HAVE_FLOAT64 && (__HAVE_FLOAT64X || __HAVE_FLOAT128)
# define f64add(Val1, Val2) __TGMATH_2_NARROW_F64 (f64add, Val1, Val2)
# define f64div(Val1, Val2) __TGMATH_2_NARROW_F64 (f64div, Val1, Val2)
# define f64mul(Val1, Val2) __TGMATH_2_NARROW_F64 (f64mul, Val1, Val2)
# define f64sub(Val1, Val2) __TGMATH_2_NARROW_F64 (f64sub, Val1, Val2)
# define f64sqrt(Val) __TGMATH_1_NARROW_F64 (f64sqrt, Val)
# define f64fma(Val1, Val2, Val3) \
__TGMATH_3_NARROW_F64 (f64fma, Val1, Val2, Val3)
# endif
# if __HAVE_FLOAT32X
# define f32xadd(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xadd, Val1, Val2)
# define f32xdiv(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xdiv, Val1, Val2)
# define f32xmul(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xmul, Val1, Val2)
# define f32xsub(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xsub, Val1, Val2)
# define f32xsqrt(Val) __TGMATH_1_NARROW_F32X (f32xsqrt, Val)
# define f32xfma(Val1, Val2, Val3) \
__TGMATH_3_NARROW_F32X (f32xfma, Val1, Val2, Val3)
# endif
# if __HAVE_FLOAT64X && (__HAVE_FLOAT128X || __HAVE_FLOAT128)
# define f64xadd(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xadd, Val1, Val2)
# define f64xdiv(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xdiv, Val1, Val2)
# define f64xmul(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xmul, Val1, Val2)
# define f64xsub(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xsub, Val1, Val2)
# define f64xsqrt(Val) __TGMATH_1_NARROW_F64X (f64xsqrt, Val)
# define f64xfma(Val1, Val2, Val3) \
__TGMATH_3_NARROW_F64X (f64xfma, Val1, Val2, Val3)
# endif
#endif
#endif /* tgmath.h */
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