master
   1/* Copyright (C) 1997-2025 Free Software Foundation, Inc.
   2   This file is part of the GNU C Library.
   3
   4   The GNU C Library is free software; you can redistribute it and/or
   5   modify it under the terms of the GNU Lesser General Public
   6   License as published by the Free Software Foundation; either
   7   version 2.1 of the License, or (at your option) any later version.
   8
   9   The GNU C Library is distributed in the hope that it will be useful,
  10   but WITHOUT ANY WARRANTY; without even the implied warranty of
  11   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12   Lesser General Public License for more details.
  13
  14   You should have received a copy of the GNU Lesser General Public
  15   License along with the GNU C Library; if not, see
  16   <https://www.gnu.org/licenses/>.  */
  17
  18/*
  19 *	ISO C99 Standard: 7.22 Type-generic math	<tgmath.h>
  20 */
  21
  22#ifndef _TGMATH_H
  23#define _TGMATH_H	1
  24
  25#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
  26#include <bits/libc-header-start.h>
  27
  28/* Include the needed headers.  */
  29#include <bits/floatn.h>
  30#include <math.h>
  31#include <complex.h>
  32
  33
  34/* There are two variant implementations of type-generic macros in
  35   this file: one for GCC 8 and later, using __builtin_tgmath and
  36   where each macro expands each of its arguments only once, and one
  37   for older GCC, using other compiler extensions but with macros
  38   expanding their arguments many times (so resulting in exponential
  39   blowup of the size of expansions when calls to such macros are
  40   nested inside arguments to such macros).  Because of a long series
  41   of defect fixes made after the initial release of TS 18661-1, GCC
  42   versions before GCC 13 have __builtin_tgmath semantics that, when
  43   integer arguments are passed to narrowing macros returning
  44   _Float32x, or non-narrowing macros with at least two generic
  45   arguments, do not always correspond to the C23 semantics, so more
  46   complicated macro definitions are also used in some cases for
  47   versions from GCC 8 to GCC 12.  */
  48
  49#define __HAVE_BUILTIN_TGMATH __GNUC_PREREQ (8, 0)
  50#define __HAVE_BUILTIN_TGMATH_C23 __GNUC_PREREQ (13, 0)
  51
  52#if __GNUC_PREREQ (2, 7)
  53
  54/* Certain cases of narrowing macros only need to call a single
  55   function so cannot use __builtin_tgmath and do not need any
  56   complicated logic.  */
  57# if __HAVE_FLOAT128X
  58#  error "Unsupported _Float128x type for <tgmath.h>."
  59# endif
  60# if ((__HAVE_FLOAT64X && !__HAVE_FLOAT128)		\
  61      || (__HAVE_FLOAT128 && !__HAVE_FLOAT64X))
  62#  error "Unsupported combination of types for <tgmath.h>."
  63# endif
  64# define __TGMATH_1_NARROW_D(F, X)		\
  65  (F ## l (X))
  66# define __TGMATH_2_NARROW_D(F, X, Y)		\
  67  (F ## l (X, Y))
  68# define __TGMATH_3_NARROW_D(F, X, Y, Z)	\
  69  (F ## l (X, Y, Z))
  70# define __TGMATH_1_NARROW_F64X(F, X)		\
  71  (F ## f128 (X))
  72# define __TGMATH_2_NARROW_F64X(F, X, Y)	\
  73  (F ## f128 (X, Y))
  74# define __TGMATH_3_NARROW_F64X(F, X, Y, Z)	\
  75  (F ## f128 (X, Y, Z))
  76# if !__HAVE_FLOAT128
  77#  define __TGMATH_1_NARROW_F32X(F, X)		\
  78  (F ## f64 (X))
  79#  define __TGMATH_2_NARROW_F32X(F, X, Y)	\
  80  (F ## f64 (X, Y))
  81#  define __TGMATH_3_NARROW_F32X(F, X, Y, Z)	\
  82  (F ## f64 (X, Y, Z))
  83# endif
  84
  85# if __HAVE_BUILTIN_TGMATH
  86
  87#  if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  88#   define __TG_F16_ARG(X) X ## f16,
  89#  else
  90#   define __TG_F16_ARG(X)
  91#  endif
  92#  if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  93#   define __TG_F32_ARG(X) X ## f32,
  94#  else
  95#   define __TG_F32_ARG(X)
  96#  endif
  97#  if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  98#   define __TG_F64_ARG(X) X ## f64,
  99#  else
 100#   define __TG_F64_ARG(X)
 101#  endif
 102#  if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
 103#   define __TG_F128_ARG(X) X ## f128,
 104#  else
 105#   define __TG_F128_ARG(X)
 106#  endif
 107#  if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
 108#   define __TG_F32X_ARG(X) X ## f32x,
 109#  else
 110#   define __TG_F32X_ARG(X)
 111#  endif
 112#  if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
 113#   define __TG_F64X_ARG(X) X ## f64x,
 114#  else
 115#   define __TG_F64X_ARG(X)
 116#  endif
 117#  if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
 118#   define __TG_F128X_ARG(X) X ## f128x,
 119#  else
 120#   define __TG_F128X_ARG(X)
 121#  endif
 122
 123#  define __TGMATH_FUNCS(X) X ## f, X, X ## l,				\
 124    __TG_F16_ARG (X) __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
 125    __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
 126#  define __TGMATH_RCFUNCS(F, C) __TGMATH_FUNCS (F) __TGMATH_FUNCS (C)
 127#  define __TGMATH_1(F, X) __builtin_tgmath (__TGMATH_FUNCS (F) (X))
 128#  define __TGMATH_2(F, X, Y) __builtin_tgmath (__TGMATH_FUNCS (F) (X), (Y))
 129#  define __TGMATH_2STD(F, X, Y) __builtin_tgmath (F ## f, F, F ## l, (X), (Y))
 130#  define __TGMATH_3(F, X, Y, Z) __builtin_tgmath (__TGMATH_FUNCS (F)	\
 131						   (X), (Y), (Z))
 132#  define __TGMATH_1C(F, C, X) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) (X))
 133#  define __TGMATH_2C(F, C, X, Y) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) \
 134						    (X), (Y))
 135
 136#  define __TGMATH_NARROW_FUNCS_F(X) X, X ## l,
 137#  define __TGMATH_NARROW_FUNCS_F16(X)				\
 138    __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X)		\
 139    __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
 140#  define __TGMATH_NARROW_FUNCS_F32(X)				\
 141    __TG_F64_ARG (X) __TG_F128_ARG (X)				\
 142    __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
 143#  define __TGMATH_NARROW_FUNCS_F64(X)		\
 144    __TG_F128_ARG (X)				\
 145    __TG_F64X_ARG (X) __TG_F128X_ARG (X)
 146#  define __TGMATH_NARROW_FUNCS_F32X(X)		\
 147    __TG_F64X_ARG (X) __TG_F128X_ARG (X)	\
 148    __TG_F64_ARG (X) __TG_F128_ARG (X)
 149
 150#  define __TGMATH_1_NARROW_F(F, X)				\
 151  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X))
 152#  define __TGMATH_2_NARROW_F(F, X, Y)				\
 153  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X), (Y))
 154#  define __TGMATH_3_NARROW_F(F, X, Y, Z)			\
 155  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X), (Y), (Z))
 156#  define __TGMATH_1_NARROW_F16(F, X)				\
 157  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X))
 158#  define __TGMATH_2_NARROW_F16(F, X, Y)			\
 159  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X), (Y))
 160#  define __TGMATH_3_NARROW_F16(F, X, Y, Z)				\
 161  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X), (Y), (Z))
 162#  define __TGMATH_1_NARROW_F32(F, X)				\
 163  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X))
 164#  define __TGMATH_2_NARROW_F32(F, X, Y)			\
 165  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X), (Y))
 166#  define __TGMATH_3_NARROW_F32(F, X, Y, Z)				\
 167  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X), (Y), (Z))
 168#  define __TGMATH_1_NARROW_F64(F, X)				\
 169  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X))
 170#  define __TGMATH_2_NARROW_F64(F, X, Y)			\
 171  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X), (Y))
 172#  define __TGMATH_3_NARROW_F64(F, X, Y, Z)				\
 173  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X), (Y), (Z))
 174#  if __HAVE_FLOAT128 && __HAVE_BUILTIN_TGMATH_C23
 175#   define __TGMATH_1_NARROW_F32X(F, X)				\
 176  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X))
 177#   define __TGMATH_2_NARROW_F32X(F, X, Y)			\
 178  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X), (Y))
 179#   define __TGMATH_3_NARROW_F32X(F, X, Y, Z)				\
 180  __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X), (Y), (Z))
 181#  endif
 182
 183# endif
 184
 185# if !__HAVE_BUILTIN_TGMATH_C23
 186#  ifdef __NO_LONG_DOUBLE_MATH
 187#   define __tgml(fct) fct
 188#  else
 189#   define __tgml(fct) fct ## l
 190#  endif
 191
 192/* __floating_type expands to 1 if TYPE is a floating type (including
 193   complex floating types), 0 if TYPE is an integer type (including
 194   complex integer types).  __real_integer_type expands to 1 if TYPE
 195   is a real integer type.  __complex_integer_type expands to 1 if
 196   TYPE is a complex integer type.  All these macros expand to integer
 197   constant expressions.  All these macros can assume their argument
 198   has an arithmetic type (not vector, decimal floating-point or
 199   fixed-point), valid to pass to tgmath.h macros.  */
 200#  if __GNUC_PREREQ (3, 1)
 201/* __builtin_classify_type expands to an integer constant expression
 202   in GCC 3.1 and later.  Default conversions applied to the argument
 203   of __builtin_classify_type mean it always returns 1 for real
 204   integer types rather than ever returning different values for
 205   character, boolean or enumerated types.  */
 206#   define __floating_type(type)				\
 207  (__builtin_classify_type (__real__ ((type) 0)) == 8)
 208#   define __real_integer_type(type)		\
 209  (__builtin_classify_type ((type) 0) == 1)
 210#   define __complex_integer_type(type)				\
 211  (__builtin_classify_type ((type) 0) == 9			\
 212   && __builtin_classify_type (__real__ ((type) 0)) == 1)
 213#  else
 214/* GCC versions predating __builtin_classify_type are also looser on
 215   what counts as an integer constant expression.  */
 216#   define __floating_type(type) (((type) 1.25) != 1)
 217#   define __real_integer_type(type) (((type) (1.25 + _Complex_I)) == 1)
 218#   define __complex_integer_type(type)			\
 219  (((type) (1.25 + _Complex_I)) == (1 + _Complex_I))
 220#  endif
 221
 222/* Whether an expression (of arithmetic type) has a real type.  */
 223#  define __expr_is_real(E) (__builtin_classify_type (E) != 9)
 224
 225/* Type T1 if E is 1, type T2 is E is 0.  */
 226#  define __tgmath_type_if(T1, T2, E)					\
 227  __typeof__ (*(0 ? (__typeof__ (0 ? (T2 *) 0 : (void *) (E))) 0	\
 228		: (__typeof__ (0 ? (T1 *) 0 : (void *) (!(E)))) 0))
 229
 230/* The tgmath real type for T, where E is 0 if T is an integer type
 231   and 1 for a floating type.  If T has a complex type, it is
 232   unspecified whether the return type is real or complex (but it has
 233   the correct corresponding real type).  */
 234#  define __tgmath_real_type_sub(T, E) \
 235  __tgmath_type_if (T, double, E)
 236
 237/* The tgmath real type of EXPR.  */
 238#  define __tgmath_real_type(expr) \
 239  __tgmath_real_type_sub (__typeof__ ((__typeof__ (+(expr))) 0),	      \
 240			  __floating_type (__typeof__ (+(expr))))
 241
 242/* The tgmath complex type for T, where E1 is 1 if T has a floating
 243   type and 0 otherwise, E2 is 1 if T has a real integer type and 0
 244   otherwise, and E3 is 1 if T has a complex type and 0 otherwise.  */
 245#  define __tgmath_complex_type_sub(T, E1, E2, E3)			\
 246  __typeof__ (*(0							\
 247		? (__typeof__ (0 ? (T *) 0 : (void *) (!(E1)))) 0	\
 248		: (__typeof__ (0					\
 249			       ? (__typeof__ (0				\
 250					      ? (double *) 0		\
 251					      : (void *) (!(E2)))) 0	\
 252			       : (__typeof__ (0				\
 253					      ? (_Complex double *) 0	\
 254					      : (void *) (!(E3)))) 0)) 0))
 255
 256/* The tgmath complex type of EXPR.  */
 257#  define __tgmath_complex_type(expr)					\
 258  __tgmath_complex_type_sub (__typeof__ ((__typeof__ (+(expr))) 0),	\
 259			     __floating_type (__typeof__ (+(expr))),	\
 260			     __real_integer_type (__typeof__ (+(expr))), \
 261			     __complex_integer_type (__typeof__ (+(expr))))
 262
 263/* The tgmath real type of EXPR1 combined with EXPR2, without handling
 264   the C23 rule of interpreting integer arguments as _Float32x if any
 265   argument is _FloatNx.  */
 266#  define __tgmath_real_type2_base(expr1, expr2)			\
 267  __typeof ((__tgmath_real_type (expr1)) 0 + (__tgmath_real_type (expr2)) 0)
 268
 269/* The tgmath complex type of EXPR1 combined with EXPR2, without
 270   handling the C23 rule of interpreting integer arguments as
 271   _Float32x if any argument is _FloatNx.  */
 272#  define __tgmath_complex_type2_base(expr1, expr2)	\
 273  __typeof ((__tgmath_complex_type (expr1)) 0		\
 274	    + (__tgmath_complex_type (expr2)) 0)
 275
 276/* The tgmath real type of EXPR1 combined with EXPR2 and EXPR3,
 277   without handling the C23 rule of interpreting integer arguments as
 278   _Float32x if any argument is _FloatNx.  */
 279#  define __tgmath_real_type3_base(expr1, expr2, expr3)	\
 280  __typeof ((__tgmath_real_type (expr1)) 0		\
 281	    + (__tgmath_real_type (expr2)) 0		\
 282	    + (__tgmath_real_type (expr3)) 0)
 283
 284/* The tgmath real or complex type of EXPR1 combined with EXPR2 (and
 285   EXPR3 if applicable).  */
 286#  if __HAVE_FLOATN_NOT_TYPEDEF
 287#   define __tgmath_real_type2(expr1, expr2)				\
 288  __tgmath_type_if (_Float32x, __tgmath_real_type2_base (expr1, expr2), \
 289		    _Generic ((expr1) + (expr2), _Float32x: 1, default: 0))
 290#   define __tgmath_complex_type2(expr1, expr2)				\
 291  __tgmath_type_if (_Float32x,						\
 292		    __tgmath_type_if (_Complex _Float32x,		\
 293				      __tgmath_complex_type2_base (expr1, \
 294								   expr2), \
 295				      _Generic ((expr1) + (expr2),	\
 296						_Complex _Float32x: 1,	\
 297						default: 0)),		\
 298		    _Generic ((expr1) + (expr2), _Float32x: 1, default: 0))
 299#   define __tgmath_real_type3(expr1, expr2, expr3)			\
 300  __tgmath_type_if (_Float32x,						\
 301		    __tgmath_real_type3_base (expr1, expr2, expr3),	\
 302		    _Generic ((expr1) + (expr2) + (expr3),		\
 303			      _Float32x: 1, default: 0))
 304#  else
 305#   define __tgmath_real_type2(expr1, expr2)	\
 306  __tgmath_real_type2_base (expr1, expr2)
 307#   define __tgmath_complex_type2(expr1, expr2)	\
 308  __tgmath_complex_type2_base (expr1, expr2)
 309#   define __tgmath_real_type3(expr1, expr2, expr3)	\
 310  __tgmath_real_type3_base (expr1, expr2, expr3)
 311#  endif
 312
 313#  if (__HAVE_DISTINCT_FLOAT16			\
 314      || __HAVE_DISTINCT_FLOAT32		\
 315      || __HAVE_DISTINCT_FLOAT64		\
 316      || __HAVE_DISTINCT_FLOAT32X		\
 317      || __HAVE_DISTINCT_FLOAT64X		\
 318      || __HAVE_DISTINCT_FLOAT128X)
 319#   error "Unsupported _FloatN or _FloatNx types for <tgmath.h>."
 320#  endif
 321
 322/* Expand to text that checks if ARG_COMB has type _Float128, and if
 323   so calls the appropriately suffixed FCT (which may include a cast),
 324   or FCT and CFCT for complex functions, with arguments ARG_CALL.
 325   __TGMATH_F128LD (only used in the __HAVE_FLOAT64X_LONG_DOUBLE case,
 326   for narrowing macros) handles long double the same as
 327   _Float128.  */
 328#  if __HAVE_DISTINCT_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
 329#   if (!__HAVE_FLOAT64X			\
 330       || __HAVE_FLOAT64X_LONG_DOUBLE		\
 331       || !__HAVE_FLOATN_NOT_TYPEDEF)
 332#    define __TGMATH_F128(arg_comb, fct, arg_call)			\
 333  __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)	\
 334  ? fct ## f128 arg_call :
 335#    define __TGMATH_F128LD(arg_comb, fct, arg_call)			\
 336  (__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)	\
 337   || __builtin_types_compatible_p (__typeof (+(arg_comb)), long double)) \
 338  ? fct ## f128 arg_call :
 339#    define __TGMATH_CF128(arg_comb, fct, cfct, arg_call)		\
 340  __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
 341  ? (__expr_is_real (arg_comb)						\
 342     ? fct ## f128 arg_call						\
 343     : cfct ## f128 arg_call) :
 344#   else
 345/* _Float64x is a distinct type at the C language level, which must be
 346   handled like _Float128.  */
 347#    define __TGMATH_F128(arg_comb, fct, arg_call)			\
 348  (__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)	\
 349   || __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float64x)) \
 350  ? fct ## f128 arg_call :
 351#    define __TGMATH_CF128(arg_comb, fct, cfct, arg_call)		\
 352  (__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
 353   || __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)),	\
 354				    _Float64x))				\
 355  ? (__expr_is_real (arg_comb)						\
 356     ? fct ## f128 arg_call						\
 357     : cfct ## f128 arg_call) :
 358#   endif
 359#  else
 360#   define __TGMATH_F128(arg_comb, fct, arg_call) /* Nothing.  */
 361#   define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) /* Nothing.  */
 362#  endif
 363
 364# endif /* !__HAVE_BUILTIN_TGMATH_C23.  */
 365
 366/* We have two kinds of generic macros: to support functions which are
 367   only defined on real valued parameters and those which are defined
 368   for complex functions as well.  */
 369# if __HAVE_BUILTIN_TGMATH
 370
 371#  define __TGMATH_UNARY_REAL_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
 372#  define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
 373#  define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct)	\
 374  __TGMATH_2 (Fct, (Val1), (Val2))
 375#  define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct)	\
 376  __TGMATH_2STD (Fct, (Val1), (Val2))
 377#  if __HAVE_BUILTIN_TGMATH_C23
 378#   define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct)	\
 379  __TGMATH_2 (Fct, (Val1), (Val2))
 380#  endif
 381#  define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct)	\
 382  __TGMATH_2STD (Fct, (Val1), (Val2))
 383#  if __HAVE_BUILTIN_TGMATH_C23
 384#   define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
 385  __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
 386#   define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct)	\
 387  __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
 388#  endif
 389#  define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct)	\
 390  __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
 391#  define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct)	\
 392  __TGMATH_1C (Fct, Cfct, (Val))
 393#  define __TGMATH_UNARY_IMAG(Val, Cfct) __TGMATH_1 (Cfct, (Val))
 394#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct)	\
 395  __TGMATH_1C (Fct, Cfct, (Val))
 396#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct)	\
 397  __TGMATH_1 (Cfct, (Val))
 398#  if __HAVE_BUILTIN_TGMATH_C23
 399#   define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct)	\
 400  __TGMATH_2C (Fct, Cfct, (Val1), (Val2))
 401#  endif
 402
 403# endif
 404
 405# if !__HAVE_BUILTIN_TGMATH
 406#  define __TGMATH_UNARY_REAL_ONLY(Val, Fct)				\
 407  (__extension__ ((sizeof (+(Val)) == sizeof (double)			      \
 408		      || __builtin_classify_type (Val) != 8)		      \
 409		     ? (__tgmath_real_type (Val)) Fct (Val)		      \
 410		     : (sizeof (+(Val)) == sizeof (float))		      \
 411		     ? (__tgmath_real_type (Val)) Fct##f (Val)		      \
 412		     : __TGMATH_F128 ((Val), (__tgmath_real_type (Val)) Fct,  \
 413				      (Val))				      \
 414		     (__tgmath_real_type (Val)) __tgml(Fct) (Val)))
 415
 416#  define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) \
 417     (__extension__ ((sizeof (+(Val)) == sizeof (double)		      \
 418		      || __builtin_classify_type (Val) != 8)		      \
 419		     ? Fct (Val)					      \
 420		     : (sizeof (+(Val)) == sizeof (float))		      \
 421		     ? Fct##f (Val)					      \
 422		     : __TGMATH_F128 ((Val), Fct, (Val))		      \
 423		     __tgml(Fct) (Val)))
 424
 425#  define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
 426     (__extension__ ((sizeof (+(Val1)) == sizeof (double)		      \
 427		      || __builtin_classify_type (Val1) != 8)		      \
 428		     ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)	      \
 429		     : (sizeof (+(Val1)) == sizeof (float))		      \
 430		     ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)	      \
 431		     : __TGMATH_F128 ((Val1), (__tgmath_real_type (Val1)) Fct, \
 432				    (Val1, Val2))			      \
 433		     (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
 434
 435#  define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
 436     (__extension__ ((sizeof (+(Val1)) == sizeof (double)		      \
 437		      || __builtin_classify_type (Val1) != 8)		      \
 438		     ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)	      \
 439		     : (sizeof (+(Val1)) == sizeof (float))		      \
 440		     ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)	      \
 441		     : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
 442# endif
 443
 444# if !__HAVE_BUILTIN_TGMATH_C23
 445#  define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
 446     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
 447		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 448		     ? __TGMATH_F128 ((Val1) + (Val2),			      \
 449				      (__tgmath_real_type2 (Val1, Val2)) Fct, \
 450				      (Val1, Val2))			      \
 451		     (__tgmath_real_type2 (Val1, Val2))			      \
 452		     __tgml(Fct) (Val1, Val2)				      \
 453		     : (sizeof (+(Val1)) == sizeof (double)		      \
 454			|| sizeof (+(Val2)) == sizeof (double)		      \
 455			|| __builtin_classify_type (Val1) != 8		      \
 456			|| __builtin_classify_type (Val2) != 8)		      \
 457		     ? (__tgmath_real_type2 (Val1, Val2))		      \
 458		       Fct (Val1, Val2)					      \
 459		     : (__tgmath_real_type2 (Val1, Val2))		      \
 460		       Fct##f (Val1, Val2)))
 461# endif
 462
 463# if !__HAVE_BUILTIN_TGMATH
 464#  define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
 465     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
 466		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 467		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
 468				  + (__tgmath_real_type (Val2)) 0))	      \
 469		       __tgml(Fct) (Val1, Val2)				      \
 470		     : (sizeof (+(Val1)) == sizeof (double)		      \
 471			|| sizeof (+(Val2)) == sizeof (double)		      \
 472			|| __builtin_classify_type (Val1) != 8		      \
 473			|| __builtin_classify_type (Val2) != 8)		      \
 474		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
 475				   + (__tgmath_real_type (Val2)) 0))	      \
 476		       Fct (Val1, Val2)					      \
 477		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
 478				   + (__tgmath_real_type (Val2)) 0))	      \
 479		       Fct##f (Val1, Val2)))
 480# endif
 481
 482# if !__HAVE_BUILTIN_TGMATH_C23
 483#  define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
 484     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
 485		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 486		     ? __TGMATH_F128 ((Val1) + (Val2),			      \
 487				      (__tgmath_real_type2 (Val1, Val2)) Fct, \
 488				      (Val1, Val2, Val3))		      \
 489		     (__tgmath_real_type2 (Val1, Val2))			      \
 490		     __tgml(Fct) (Val1, Val2, Val3)			      \
 491		     : (sizeof (+(Val1)) == sizeof (double)		      \
 492			|| sizeof (+(Val2)) == sizeof (double)		      \
 493			|| __builtin_classify_type (Val1) != 8		      \
 494			|| __builtin_classify_type (Val2) != 8)		      \
 495		     ? (__tgmath_real_type2 (Val1, Val2))		      \
 496		       Fct (Val1, Val2, Val3)				      \
 497		     : (__tgmath_real_type2 (Val1, Val2))		      \
 498		       Fct##f (Val1, Val2, Val3)))
 499
 500#  define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
 501     (__extension__ ((sizeof ((Val1) + (Val2) + (Val3)) > sizeof (double)     \
 502		      && __builtin_classify_type ((Val1) + (Val2) + (Val3))   \
 503			 == 8)						      \
 504		     ? __TGMATH_F128 ((Val1) + (Val2) + (Val3),		      \
 505				      (__tgmath_real_type3 (Val1, Val2,	      \
 506							    Val3)) Fct,	      \
 507				      (Val1, Val2, Val3))		      \
 508		     (__tgmath_real_type3 (Val1, Val2, Val3))		      \
 509		       __tgml(Fct) (Val1, Val2, Val3)			      \
 510		     : (sizeof (+(Val1)) == sizeof (double)		      \
 511			|| sizeof (+(Val2)) == sizeof (double)		      \
 512			|| sizeof (+(Val3)) == sizeof (double)		      \
 513			|| __builtin_classify_type (Val1) != 8		      \
 514			|| __builtin_classify_type (Val2) != 8		      \
 515			|| __builtin_classify_type (Val3) != 8)		      \
 516		     ? (__tgmath_real_type3 (Val1, Val2, Val3))		      \
 517		       Fct (Val1, Val2, Val3)				      \
 518		     : (__tgmath_real_type3 (Val1, Val2, Val3))		      \
 519		       Fct##f (Val1, Val2, Val3)))
 520# endif
 521
 522# if !__HAVE_BUILTIN_TGMATH
 523#  define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
 524     (__extension__ ((sizeof (+(Val1)) == sizeof (double)		\
 525		      || __builtin_classify_type (Val1) != 8)		\
 526		     ? Fct (Val1, Val2, Val3)				\
 527		     : (sizeof (+(Val1)) == sizeof (float))		\
 528		     ? Fct##f (Val1, Val2, Val3)			\
 529		     : __TGMATH_F128 ((Val1), Fct, (Val1, Val2, Val3))	\
 530		     __tgml(Fct) (Val1, Val2, Val3)))
 531
 532/* XXX This definition has to be changed as soon as the compiler understands
 533   the imaginary keyword.  */
 534#  define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
 535     (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)	      \
 536		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
 537		     ? (__expr_is_real (Val)				      \
 538			? (__tgmath_complex_type (Val)) Fct (Val)	      \
 539			: (__tgmath_complex_type (Val)) Cfct (Val))	      \
 540		     : (sizeof (+__real__ (Val)) == sizeof (float))	      \
 541		     ? (__expr_is_real (Val)				      \
 542			? (__tgmath_complex_type (Val)) Fct##f (Val)	      \
 543			: (__tgmath_complex_type (Val)) Cfct##f (Val))	      \
 544		     : __TGMATH_CF128 ((Val),				      \
 545				       (__tgmath_complex_type (Val)) Fct,     \
 546				       (__tgmath_complex_type (Val)) Cfct,    \
 547				       (Val))				      \
 548		     (__expr_is_real (Val)				      \
 549		      ? (__tgmath_complex_type (Val)) __tgml(Fct) (Val)	      \
 550		      : (__tgmath_complex_type (Val)) __tgml(Cfct) (Val))))
 551
 552#  define __TGMATH_UNARY_IMAG(Val, Cfct) \
 553     (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)	      \
 554		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
 555		     ? (__typeof__ ((__tgmath_real_type (Val)) 0	      \
 556				    + _Complex_I)) Cfct (Val)		      \
 557		     : (sizeof (+__real__ (Val)) == sizeof (float))	      \
 558		     ? (__typeof__ ((__tgmath_real_type (Val)) 0	      \
 559				    + _Complex_I)) Cfct##f (Val)	      \
 560		     : __TGMATH_F128 (__real__ (Val),			      \
 561				      (__typeof__			      \
 562				       ((__tgmath_real_type (Val)) 0	      \
 563					+ _Complex_I)) Cfct, (Val))	      \
 564		     (__typeof__ ((__tgmath_real_type (Val)) 0		      \
 565				  + _Complex_I)) __tgml(Cfct) (Val)))
 566
 567/* XXX This definition has to be changed as soon as the compiler understands
 568   the imaginary keyword.  */
 569#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
 570     (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)	      \
 571		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
 572		     ? (__expr_is_real (Val)				      \
 573			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 574			  Fct (Val)					      \
 575			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 576			  Cfct (Val))					      \
 577		     : (sizeof (+__real__ (Val)) == sizeof (float))	      \
 578		     ? (__expr_is_real (Val)				      \
 579			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 580			  Fct##f (Val)					      \
 581			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 582			  Cfct##f (Val))				      \
 583		     : __TGMATH_CF128 ((Val), \
 584				       (__typeof__			      \
 585					(__real__			      \
 586					 (__tgmath_real_type (Val)) 0)) Fct,  \
 587				       (__typeof__			      \
 588					(__real__			      \
 589					 (__tgmath_real_type (Val)) 0)) Cfct, \
 590				       (Val))				      \
 591		     (__expr_is_real (Val)				      \
 592		      ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))  \
 593		      __tgml(Fct) (Val)					      \
 594		      : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))  \
 595		      __tgml(Cfct) (Val))))
 596#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct)	\
 597  __TGMATH_UNARY_REAL_IMAG_RET_REAL ((Val), Cfct, Cfct)
 598# endif
 599
 600# if !__HAVE_BUILTIN_TGMATH_C23
 601/* XXX This definition has to be changed as soon as the compiler understands
 602   the imaginary keyword.  */
 603#  define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
 604     (__extension__ ((sizeof (__real__ (Val1)				      \
 605			      + __real__ (Val2)) > sizeof (double)	      \
 606		      && __builtin_classify_type (__real__ (Val1)	      \
 607						  + __real__ (Val2)) == 8)    \
 608		     ? __TGMATH_CF128 ((Val1) + (Val2),			      \
 609				       (__tgmath_complex_type2 (Val1, Val2))  \
 610				       Fct,				      \
 611				       (__tgmath_complex_type2 (Val1, Val2))  \
 612				       Cfct,				      \
 613				       (Val1, Val2))			      \
 614		     (__expr_is_real ((Val1) + (Val2))			      \
 615		      ? (__tgmath_complex_type2 (Val1, Val2))		      \
 616		      __tgml(Fct) (Val1, Val2)				      \
 617		      : (__tgmath_complex_type2 (Val1, Val2))		      \
 618		      __tgml(Cfct) (Val1, Val2))			      \
 619		     : (sizeof (+__real__ (Val1)) == sizeof (double)	      \
 620			|| sizeof (+__real__ (Val2)) == sizeof (double)	      \
 621			|| __builtin_classify_type (__real__ (Val1)) != 8     \
 622			|| __builtin_classify_type (__real__ (Val2)) != 8)    \
 623		     ? (__expr_is_real ((Val1) + (Val2))		      \
 624			? (__tgmath_complex_type2 (Val1, Val2))		      \
 625			  Fct (Val1, Val2)				      \
 626			: (__tgmath_complex_type2 (Val1, Val2))		      \
 627			  Cfct (Val1, Val2))				      \
 628		     : (__expr_is_real ((Val1) + (Val2))		      \
 629			? (__tgmath_complex_type2 (Val1, Val2))		      \
 630			  Fct##f (Val1, Val2)				      \
 631			: (__tgmath_complex_type2 (Val1, Val2))		      \
 632			  Cfct##f (Val1, Val2))))
 633# endif
 634
 635# if !__HAVE_BUILTIN_TGMATH
 636#  define __TGMATH_1_NARROW_F(F, X)					\
 637  (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (double) \
 638		  ? F ## l (X)						\
 639		  : F (X)))
 640#  define __TGMATH_2_NARROW_F(F, X, Y)					\
 641  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 642			  + (__tgmath_real_type (Y)) 0) > sizeof (double) \
 643		  ? F ## l (X, Y)					\
 644		  : F (X, Y)))
 645#  define __TGMATH_3_NARROW_F(F, X, Y, Z)				\
 646  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 647			  + (__tgmath_real_type (Y)) 0			\
 648			  + (__tgmath_real_type (Z)) 0) > sizeof (double) \
 649		  ? F ## l (X, Y, Z)					\
 650		  : F (X, Y, Z)))
 651# endif
 652/* In most cases, these narrowing macro definitions based on sizeof
 653   ensure that the function called has the right argument format, as
 654   for other <tgmath.h> macros for compilers before GCC 8, but may not
 655   have exactly the argument type (among the types with that format)
 656   specified in the standard logic.
 657
 658   In the case of macros for _Float32x return type, when _Float64x
 659   exists, _Float64 arguments should result in the *f64 function being
 660   called while _Float32x, float and double arguments should result in
 661   the *f64x function being called (and integer arguments are
 662   considered to have type _Float32x if any argument has type
 663   _FloatNx, or double otherwise).  These cases cannot be
 664   distinguished using sizeof (or at all if the types are typedefs
 665   rather than different types, in which case we err on the side of
 666   using the wider type if unsure).  */
 667# if !__HAVE_BUILTIN_TGMATH_C23
 668#  if __HAVE_FLOATN_NOT_TYPEDEF
 669#   define __TGMATH_NARROW_F32X_USE_F64X(X)			\
 670  !__builtin_types_compatible_p (__typeof (+(X)), _Float64)
 671#  else
 672#   define __TGMATH_NARROW_F32X_USE_F64X(X)			\
 673  (__builtin_types_compatible_p (__typeof (+(X)), double)	\
 674   || __builtin_types_compatible_p (__typeof (+(X)), float)	\
 675   || !__floating_type (__typeof (+(X))))
 676#  endif
 677# endif
 678# if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128
 679#  if !__HAVE_BUILTIN_TGMATH
 680#   define __TGMATH_1_NARROW_F32(F, X)					\
 681  (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
 682		  ? __TGMATH_F128LD ((X), F, (X))			\
 683		  F ## f64x (X)						\
 684		  : F ## f64 (X)))
 685#   define __TGMATH_2_NARROW_F32(F, X, Y)				\
 686  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 687			  + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
 688		  ? __TGMATH_F128LD ((X) + (Y), F, (X, Y))		\
 689		  F ## f64x (X, Y)					\
 690		  : F ## f64 (X, Y)))
 691#   define __TGMATH_3_NARROW_F32(F, X, Y, Z)				\
 692  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 693			  + (__tgmath_real_type (Y)) 0			\
 694			  + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
 695		  ? __TGMATH_F128LD ((X) + (Y) + (Z), F, (X, Y, Z))	\
 696		  F ## f64x (X, Y, Z)					\
 697		  : F ## f64 (X, Y, Z)))
 698#   define __TGMATH_1_NARROW_F64(F, X)					\
 699  (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
 700		  ? __TGMATH_F128LD ((X), F, (X))			\
 701		  F ## f64x (X)						\
 702		  : F ## f128 (X)))
 703#   define __TGMATH_2_NARROW_F64(F, X, Y)				\
 704  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 705			  + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
 706		  ? __TGMATH_F128LD ((X) + (Y), F, (X, Y))		\
 707		  F ## f64x (X, Y)					\
 708		  : F ## f128 (X, Y)))
 709#   define __TGMATH_3_NARROW_F64(F, X, Y, Z)				\
 710  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 711			  + (__tgmath_real_type (Y)) 0			\
 712			  + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
 713		  ? __TGMATH_F128LD ((X) + (Y) + (Z), F, (X, Y, Z))	\
 714		  F ## f64x (X, Y, Z)					\
 715		  : F ## f128 (X, Y, Z)))
 716#  endif
 717#  if !__HAVE_BUILTIN_TGMATH_C23
 718#   define __TGMATH_1_NARROW_F32X(F, X)					\
 719  (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
 720		  || __TGMATH_NARROW_F32X_USE_F64X (X)			\
 721		  ? __TGMATH_F128 ((X), F, (X))				\
 722		  F ## f64x (X)						\
 723		  : F ## f64 (X)))
 724#   define __TGMATH_2_NARROW_F32X(F, X, Y)				\
 725  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 726			  + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
 727		  || __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y))		\
 728		  ? __TGMATH_F128 ((X) + (Y), F, (X, Y))		\
 729		  F ## f64x (X, Y)					\
 730		  : F ## f64 (X, Y)))
 731#   define __TGMATH_3_NARROW_F32X(F, X, Y, Z)				\
 732  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 733			  + (__tgmath_real_type (Y)) 0			\
 734			  + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
 735		  || __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y) + (Z))	\
 736		  ? __TGMATH_F128 ((X) + (Y) + (Z), F, (X, Y, Z))	\
 737		  F ## f64x (X, Y, Z)					\
 738		  : F ## f64 (X, Y, Z)))
 739#  endif
 740# elif __HAVE_FLOAT128
 741#  if !__HAVE_BUILTIN_TGMATH
 742#   define __TGMATH_1_NARROW_F32(F, X)					\
 743  (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
 744		  ? F ## f128 (X)					\
 745		  : F ## f64 (X)))
 746#   define __TGMATH_2_NARROW_F32(F, X, Y)				\
 747  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 748			  + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
 749		  ? F ## f128 (X, Y)					\
 750		  : F ## f64 (X, Y)))
 751#   define __TGMATH_3_NARROW_F32(F, X, Y, Z)				\
 752  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 753			  + (__tgmath_real_type (Y)) 0			\
 754			  + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
 755		  ? F ## f128 (X, Y, Z)					\
 756		  : F ## f64 (X, Y, Z)))
 757#   define __TGMATH_1_NARROW_F64(F, X)		\
 758  (F ## f128 (X))
 759#   define __TGMATH_2_NARROW_F64(F, X, Y)	\
 760  (F ## f128 (X, Y))
 761#   define __TGMATH_3_NARROW_F64(F, X, Y, Z)	\
 762  (F ## f128 (X, Y, Z))
 763#  endif
 764#  if !__HAVE_BUILTIN_TGMATH_C23
 765#   define __TGMATH_1_NARROW_F32X(F, X)					\
 766  (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float32x) \
 767		  || __TGMATH_NARROW_F32X_USE_F64X (X)			\
 768		  ? F ## f64x (X)					\
 769		  : F ## f64 (X)))
 770#   define __TGMATH_2_NARROW_F32X(F, X, Y)				\
 771  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 772			  + (__tgmath_real_type (Y)) 0) > sizeof (_Float32x) \
 773		  || __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y))		\
 774		  ? F ## f64x (X, Y)					\
 775		  : F ## f64 (X, Y)))
 776#   define __TGMATH_3_NARROW_F32X(F, X, Y, Z)				\
 777  (__extension__ (sizeof ((__tgmath_real_type (X)) 0			\
 778			  + (__tgmath_real_type (Y)) 0			\
 779			  + (__tgmath_real_type (Z)) 0) > sizeof (_Float32x) \
 780		  || __TGMATH_NARROW_F32X_USE_F64X ((X) + (Y) + (Z))	\
 781		  ? F ## f64x (X, Y, Z)					\
 782		  : F ## f64 (X, Y, Z)))
 783#  endif
 784# else
 785#  if !__HAVE_BUILTIN_TGMATH
 786#   define __TGMATH_1_NARROW_F32(F, X)		\
 787  (F ## f64 (X))
 788#   define __TGMATH_2_NARROW_F32(F, X, Y)	\
 789  (F ## f64 (X, Y))
 790#   define __TGMATH_3_NARROW_F32(F, X, Y, Z)	\
 791  (F ## f64 (X, Y, Z))
 792#  endif
 793# endif
 794#else
 795# error "Unsupported compiler; you cannot use <tgmath.h>"
 796#endif
 797
 798
 799/* Unary functions defined for real and complex values.  */
 800
 801
 802/* Trigonometric functions.  */
 803
 804/* Arc cosine of X.  */
 805#define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
 806/* Arc sine of X.  */
 807#define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
 808/* Arc tangent of X.  */
 809#define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
 810/* Arc tangent of Y/X.  */
 811#define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
 812
 813/* Cosine of X.  */
 814#define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
 815/* Sine of X.  */
 816#define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
 817/* Tangent of X.  */
 818#define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
 819
 820#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
 821/* Arc cosine of X, divided by pi..  */
 822# define acospi(Val) __TGMATH_UNARY_REAL_ONLY (Val, acospi)
 823/* Arc sine of X, divided by pi..  */
 824# define asinpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, asinpi)
 825/* Arc tangent of X, divided by pi.  */
 826# define atanpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, atanpi)
 827/* Arc tangent of Y/X, divided by pi.  */
 828#define atan2pi(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2pi)
 829
 830/* Cosine of pi * X.  */
 831# define cospi(Val) __TGMATH_UNARY_REAL_ONLY (Val, cospi)
 832/* Sine of pi * X.  */
 833# define sinpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, sinpi)
 834/* Tangent of pi * X.  */
 835# define tanpi(Val) __TGMATH_UNARY_REAL_ONLY (Val, tanpi)
 836#endif
 837
 838/* Hyperbolic functions.  */
 839
 840/* Hyperbolic arc cosine of X.  */
 841#define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
 842/* Hyperbolic arc sine of X.  */
 843#define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
 844/* Hyperbolic arc tangent of X.  */
 845#define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
 846
 847/* Hyperbolic cosine of X.  */
 848#define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
 849/* Hyperbolic sine of X.  */
 850#define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
 851/* Hyperbolic tangent of X.  */
 852#define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
 853
 854
 855/* Exponential and logarithmic functions.  */
 856
 857/* Exponential function of X.  */
 858#define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
 859
 860/* Break VALUE into a normalized fraction and an integral power of 2.  */
 861#define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
 862
 863/* X times (two to the EXP power).  */
 864#define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
 865
 866/* Natural logarithm of X.  */
 867#define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
 868
 869/* Base-ten logarithm of X.  */
 870#ifdef __USE_GNU
 871# define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
 872#else
 873# define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
 874#endif
 875
 876/* Return exp(X) - 1.  */
 877#define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
 878
 879/* Return log(1 + X).  */
 880#define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
 881
 882/* Return the base 2 signed integral exponent of X.  */
 883#define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
 884
 885/* Compute base-2 exponential of X.  */
 886#define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
 887
 888/* Compute base-2 logarithm of X.  */
 889#define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
 890
 891#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
 892/* Compute exponent to base ten.  */
 893#define exp10(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp10)
 894
 895/* Return exp2(X) - 1.  */
 896#define exp2m1(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2m1)
 897
 898/* Return exp10(X) - 1.  */
 899#define exp10m1(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp10m1)
 900
 901/* Return log2(1 + X).  */
 902#define log2p1(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2p1)
 903
 904/* Return log10(1 + X).  */
 905#define log10p1(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10p1)
 906
 907/* Return log(1 + X).  */
 908#define logp1(Val) __TGMATH_UNARY_REAL_ONLY (Val, logp1)
 909#endif
 910
 911
 912/* Power functions.  */
 913
 914/* Return X to the Y power.  */
 915#define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
 916
 917/* Return the square root of X.  */
 918#define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
 919
 920/* Return `sqrt(X*X + Y*Y)'.  */
 921#define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
 922
 923/* Return the cube root of X.  */
 924#define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
 925
 926#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
 927/* Return 1+X to the Y power.  */
 928# define compoundn(Val1, Val2)					\
 929  __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, compoundn)
 930
 931/* Return X to the Y power.  */
 932# define pown(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, pown)
 933
 934/* Return X to the Y power.  */
 935# define powr(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, powr)
 936
 937/* Return the Yth root of X.  */
 938# define rootn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, rootn)
 939
 940/* Return 1/sqrt(X).  */
 941# define rsqrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, rsqrt)
 942#endif
 943
 944
 945/* Nearest integer, absolute value, and remainder functions.  */
 946
 947/* Smallest integral value not less than X.  */
 948#define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
 949
 950/* Absolute value of X.  */
 951#define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
 952
 953/* Largest integer not greater than X.  */
 954#define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
 955
 956/* Floating-point modulo remainder of X/Y.  */
 957#define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
 958
 959/* Round X to integral valuein floating-point format using current
 960   rounding direction, but do not raise inexact exception.  */
 961#define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
 962
 963/* Round X to nearest integral value, rounding halfway cases away from
 964   zero.  */
 965#define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
 966
 967/* Round X to the integral value in floating-point format nearest but
 968   not larger in magnitude.  */
 969#define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
 970
 971/* Compute remainder of X and Y and put in *QUO a value with sign of x/y
 972   and magnitude congruent `mod 2^n' to the magnitude of the integral
 973   quotient x/y, with n >= 3.  */
 974#define remquo(Val1, Val2, Val3) \
 975     __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
 976
 977/* Round X to nearest integral value according to current rounding
 978   direction.  */
 979#define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
 980#define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)
 981
 982/* Round X to nearest integral value, rounding halfway cases away from
 983   zero.  */
 984#define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
 985#define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)
 986
 987
 988/* Return X with its signed changed to Y's.  */
 989#define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
 990
 991/* Error and gamma functions.  */
 992#define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
 993#define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
 994#define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
 995#define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
 996
 997
 998/* Return the integer nearest X in the direction of the
 999   prevailing rounding mode.  */
1000#define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
1001
1002#if __GLIBC_USE (IEC_60559_BFP_EXT_C23)
1003/* Return X - epsilon.  */
1004# define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
1005/* Return X + epsilon.  */
1006# define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
1007#endif
1008
1009/* Return X + epsilon if X < Y, X - epsilon if X > Y.  */
1010#define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
1011#define nexttoward(Val1, Val2) \
1012     __TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)
1013
1014/* Return the remainder of integer division X / Y with infinite precision.  */
1015#define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
1016
1017/* Return X times (2 to the Nth power).  */
1018#ifdef __USE_MISC
1019# define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
1020#endif
1021
1022/* Return X times (2 to the Nth power).  */
1023#define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
1024
1025/* Return X times (2 to the Nth power).  */
1026#define scalbln(Val1, Val2) \
1027     __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
1028
1029/* Return the binary exponent of X, which must be nonzero.  */
1030#define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)
1031
1032
1033/* Return positive difference between X and Y.  */
1034#define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
1035
1036#if __GLIBC_USE (ISOC23) && !defined __USE_GNU
1037/* Return maximum numeric value from X and Y.  */
1038# define fmax(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmax)
1039
1040/* Return minimum numeric value from X and Y.  */
1041# define fmin(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmin)
1042#else
1043/* Return maximum numeric value from X and Y.  */
1044# define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
1045
1046/* Return minimum numeric value from X and Y.  */
1047# define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
1048#endif
1049
1050
1051/* Multiply-add function computed as a ternary operation.  */
1052#define fma(Val1, Val2, Val3) \
1053     __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
1054
1055#if __GLIBC_USE (IEC_60559_BFP_EXT_C23)
1056/* Round X to nearest integer value, rounding halfway cases to even.  */
1057# define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)
1058
1059# define fromfp(Val1, Val2, Val3)					\
1060  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)
1061
1062# define ufromfp(Val1, Val2, Val3)					\
1063  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)
1064
1065# define fromfpx(Val1, Val2, Val3)					\
1066  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)
1067
1068# define ufromfpx(Val1, Val2, Val3)					\
1069  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)
1070
1071/* Like ilogb, but returning long int.  */
1072# define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)
1073#endif
1074
1075#if __GLIBC_USE (IEC_60559_BFP_EXT)
1076/* Return value with maximum magnitude.  */
1077# define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
1078
1079/* Return value with minimum magnitude.  */
1080# define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
1081#endif
1082
1083#if __GLIBC_USE (ISOC23)
1084/* Return maximum value from X and Y.  */
1085# define fmaximum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum)
1086
1087/* Return minimum value from X and Y.  */
1088# define fminimum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum)
1089
1090/* Return maximum numeric value from X and Y.  */
1091# define fmaximum_num(Val1, Val2)			\
1092  __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_num)
1093
1094/* Return minimum numeric value from X and Y.  */
1095# define fminimum_num(Val1, Val2)			\
1096  __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_num)
1097
1098/* Return value with maximum magnitude.  */
1099# define fmaximum_mag(Val1, Val2)			\
1100  __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag)
1101
1102/* Return value with minimum magnitude.  */
1103# define fminimum_mag(Val1, Val2)			\
1104  __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag)
1105
1106/* Return numeric value with maximum magnitude.  */
1107# define fmaximum_mag_num(Val1, Val2)				\
1108  __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag_num)
1109
1110/* Return numeric value with minimum magnitude.  */
1111# define fminimum_mag_num(Val1, Val2)				\
1112  __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag_num)
1113#endif
1114
1115
1116/* Absolute value, conjugates, and projection.  */
1117
1118/* Argument value of Z.  */
1119#define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)
1120
1121/* Complex conjugate of Z.  */
1122#define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
1123
1124/* Projection of Z onto the Riemann sphere.  */
1125#define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
1126
1127
1128/* Decomposing complex values.  */
1129
1130/* Imaginary part of Z.  */
1131#define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)
1132
1133/* Real part of Z.  */
1134#define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)
1135
1136
1137/* Narrowing functions.  */
1138
1139#if __GLIBC_USE (IEC_60559_BFP_EXT_C23)
1140
1141/* Add.  */
1142# define fadd(Val1, Val2) __TGMATH_2_NARROW_F (fadd, Val1, Val2)
1143# define dadd(Val1, Val2) __TGMATH_2_NARROW_D (dadd, Val1, Val2)
1144
1145/* Divide.  */
1146# define fdiv(Val1, Val2) __TGMATH_2_NARROW_F (fdiv, Val1, Val2)
1147# define ddiv(Val1, Val2) __TGMATH_2_NARROW_D (ddiv, Val1, Val2)
1148
1149/* Multiply.  */
1150# define fmul(Val1, Val2) __TGMATH_2_NARROW_F (fmul, Val1, Val2)
1151# define dmul(Val1, Val2) __TGMATH_2_NARROW_D (dmul, Val1, Val2)
1152
1153/* Subtract.  */
1154# define fsub(Val1, Val2) __TGMATH_2_NARROW_F (fsub, Val1, Val2)
1155# define dsub(Val1, Val2) __TGMATH_2_NARROW_D (dsub, Val1, Val2)
1156
1157/* Square root.  */
1158# define fsqrt(Val) __TGMATH_1_NARROW_F (fsqrt, Val)
1159# define dsqrt(Val) __TGMATH_1_NARROW_D (dsqrt, Val)
1160
1161/* Fused multiply-add.  */
1162# define ffma(Val1, Val2, Val3) __TGMATH_3_NARROW_F (ffma, Val1, Val2, Val3)
1163# define dfma(Val1, Val2, Val3) __TGMATH_3_NARROW_D (dfma, Val1, Val2, Val3)
1164
1165#endif
1166
1167#if __GLIBC_USE (IEC_60559_TYPES_EXT)
1168
1169# if __HAVE_FLOAT16
1170#  define f16add(Val1, Val2) __TGMATH_2_NARROW_F16 (f16add, Val1, Val2)
1171#  define f16div(Val1, Val2) __TGMATH_2_NARROW_F16 (f16div, Val1, Val2)
1172#  define f16mul(Val1, Val2) __TGMATH_2_NARROW_F16 (f16mul, Val1, Val2)
1173#  define f16sub(Val1, Val2) __TGMATH_2_NARROW_F16 (f16sub, Val1, Val2)
1174#  define f16sqrt(Val) __TGMATH_1_NARROW_F16 (f16sqrt, Val)
1175#  define f16fma(Val1, Val2, Val3)			\
1176  __TGMATH_3_NARROW_F16 (f16fma, Val1, Val2, Val3)
1177# endif
1178
1179# if __HAVE_FLOAT32
1180#  define f32add(Val1, Val2) __TGMATH_2_NARROW_F32 (f32add, Val1, Val2)
1181#  define f32div(Val1, Val2) __TGMATH_2_NARROW_F32 (f32div, Val1, Val2)
1182#  define f32mul(Val1, Val2) __TGMATH_2_NARROW_F32 (f32mul, Val1, Val2)
1183#  define f32sub(Val1, Val2) __TGMATH_2_NARROW_F32 (f32sub, Val1, Val2)
1184#  define f32sqrt(Val) __TGMATH_1_NARROW_F32 (f32sqrt, Val)
1185#  define f32fma(Val1, Val2, Val3)			\
1186  __TGMATH_3_NARROW_F32 (f32fma, Val1, Val2, Val3)
1187# endif
1188
1189# if __HAVE_FLOAT64 && (__HAVE_FLOAT64X || __HAVE_FLOAT128)
1190#  define f64add(Val1, Val2) __TGMATH_2_NARROW_F64 (f64add, Val1, Val2)
1191#  define f64div(Val1, Val2) __TGMATH_2_NARROW_F64 (f64div, Val1, Val2)
1192#  define f64mul(Val1, Val2) __TGMATH_2_NARROW_F64 (f64mul, Val1, Val2)
1193#  define f64sub(Val1, Val2) __TGMATH_2_NARROW_F64 (f64sub, Val1, Val2)
1194#  define f64sqrt(Val) __TGMATH_1_NARROW_F64 (f64sqrt, Val)
1195#  define f64fma(Val1, Val2, Val3)			\
1196  __TGMATH_3_NARROW_F64 (f64fma, Val1, Val2, Val3)
1197# endif
1198
1199# if __HAVE_FLOAT32X
1200#  define f32xadd(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xadd, Val1, Val2)
1201#  define f32xdiv(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xdiv, Val1, Val2)
1202#  define f32xmul(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xmul, Val1, Val2)
1203#  define f32xsub(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xsub, Val1, Val2)
1204#  define f32xsqrt(Val) __TGMATH_1_NARROW_F32X (f32xsqrt, Val)
1205#  define f32xfma(Val1, Val2, Val3)			\
1206  __TGMATH_3_NARROW_F32X (f32xfma, Val1, Val2, Val3)
1207# endif
1208
1209# if __HAVE_FLOAT64X && (__HAVE_FLOAT128X || __HAVE_FLOAT128)
1210#  define f64xadd(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xadd, Val1, Val2)
1211#  define f64xdiv(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xdiv, Val1, Val2)
1212#  define f64xmul(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xmul, Val1, Val2)
1213#  define f64xsub(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xsub, Val1, Val2)
1214#  define f64xsqrt(Val) __TGMATH_1_NARROW_F64X (f64xsqrt, Val)
1215#  define f64xfma(Val1, Val2, Val3)			\
1216  __TGMATH_3_NARROW_F64X (f64xfma, Val1, Val2, Val3)
1217# endif
1218
1219#endif
1220
1221#endif /* tgmath.h */