math/tgmath.h

   1 /* Copyright (C) 1997-2024 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 C2X 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_C2X __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_C2X
 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_C2X
 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 C2X 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 C2X 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 C2X 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_C2X.  */
 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_C2X
 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_C2X
 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_C2X
 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_C2X
 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_C2X
 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_C2X
 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_C2X
 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_C2X
 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_C2X
 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
 821 /* Hyperbolic functions.  */
 822
 823 /* Hyperbolic arc cosine of X.  */
 824 #define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
 825 /* Hyperbolic arc sine of X.  */
 826 #define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
 827 /* Hyperbolic arc tangent of X.  */
 828 #define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
 829
 830 /* Hyperbolic cosine of X.  */
 831 #define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
 832 /* Hyperbolic sine of X.  */
 833 #define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
 834 /* Hyperbolic tangent of X.  */
 835 #define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
 836
 837
 838 /* Exponential and logarithmic functions.  */
 839
 840 /* Exponential function of X.  */
 841 #define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
 842
 843 /* Break VALUE into a normalized fraction and an integral power of 2.  */
 844 #define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
 845
 846 /* X times (two to the EXP power).  */
 847 #define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
 848
 849 /* Natural logarithm of X.  */
 850 #define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
 851
 852 /* Base-ten logarithm of X.  */
 853 #ifdef __USE_GNU
 854 # define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
 855 #else
 856 # define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
 857 #endif
 858
 859 /* Return exp(X) - 1.  */
 860 #define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
 861
 862 /* Return log(1 + X).  */
 863 #define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
 864
 865 /* Return the base 2 signed integral exponent of X.  */
 866 #define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
 867
 868 /* Compute base-2 exponential of X.  */
 869 #define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
 870
 871 /* Compute base-2 logarithm of X.  */
 872 #define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
 873
 874 #if __GLIBC_USE (IEC_60559_FUNCS_EXT_C2X)
 875 /* Compute exponent to base ten.  */
 876 #define exp10(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp10)
 877 #endif
 878
 879
 880 /* Power functions.  */
 881
 882 /* Return X to the Y power.  */
 883 #define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
 884
 885 /* Return the square root of X.  */
 886 #define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
 887
 888 /* Return `sqrt(X*X + Y*Y)'.  */
 889 #define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
 890
 891 /* Return the cube root of X.  */
 892 #define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
 893
 894
 895 /* Nearest integer, absolute value, and remainder functions.  */
 896
 897 /* Smallest integral value not less than X.  */
 898 #define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
 899
 900 /* Absolute value of X.  */
 901 #define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
 902
 903 /* Largest integer not greater than X.  */
 904 #define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
 905
 906 /* Floating-point modulo remainder of X/Y.  */
 907 #define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
 908
 909 /* Round X to integral valuein floating-point format using current
 910    rounding direction, but do not raise inexact exception.  */
 911 #define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
 912
 913 /* Round X to nearest integral value, rounding halfway cases away from
 914    zero.  */
 915 #define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
 916
 917 /* Round X to the integral value in floating-point format nearest but
 918    not larger in magnitude.  */
 919 #define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
 920
 921 /* Compute remainder of X and Y and put in *QUO a value with sign of x/y
 922    and magnitude congruent `mod 2^n' to the magnitude of the integral
 923    quotient x/y, with n >= 3.  */
 924 #define remquo(Val1, Val2, Val3) \
 925      __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
 926
 927 /* Round X to nearest integral value according to current rounding
 928    direction.  */
 929 #define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
 930 #define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)
 931
 932 /* Round X to nearest integral value, rounding halfway cases away from
 933    zero.  */
 934 #define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
 935 #define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)
 936
 937
 938 /* Return X with its signed changed to Y's.  */
 939 #define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
 940
 941 /* Error and gamma functions.  */
 942 #define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
 943 #define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
 944 #define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
 945 #define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
 946
 947
 948 /* Return the integer nearest X in the direction of the
 949    prevailing rounding mode.  */
 950 #define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
 951
 952 #if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
 953 /* Return X - epsilon.  */
 954 # define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
 955 /* Return X + epsilon.  */
 956 # define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
 957 #endif
 958
 959 /* Return X + epsilon if X < Y, X - epsilon if X > Y.  */
 960 #define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
 961 #define nexttoward(Val1, Val2) \
 962      __TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)
 963
 964 /* Return the remainder of integer division X / Y with infinite precision.  */
 965 #define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
 966
 967 /* Return X times (2 to the Nth power).  */
 968 #ifdef __USE_MISC
 969 # define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
 970 #endif
 971
 972 /* Return X times (2 to the Nth power).  */
 973 #define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
 974
 975 /* Return X times (2 to the Nth power).  */
 976 #define scalbln(Val1, Val2) \
 977      __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
 978
 979 /* Return the binary exponent of X, which must be nonzero.  */
 980 #define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)
 981
 982
 983 /* Return positive difference between X and Y.  */
 984 #define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
 985
 986 #if __GLIBC_USE (ISOC2X) && !defined __USE_GNU
 987 /* Return maximum numeric value from X and Y.  */
 988 # define fmax(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmax)
 989
 990 /* Return minimum numeric value from X and Y.  */
 991 # define fmin(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmin)
 992 #else
 993 /* Return maximum numeric value from X and Y.  */
 994 # define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
 995
 996 /* Return minimum numeric value from X and Y.  */
 997 # define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
 998 #endif
 999
1000
1001 /* Multiply-add function computed as a ternary operation.  */
1002 #define fma(Val1, Val2, Val3) \
1003      __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
1004
1005 #if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
1006 /* Round X to nearest integer value, rounding halfway cases to even.  */
1007 # define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)
1008
1009 # define fromfp(Val1, Val2, Val3)                                       \
1010   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)
1011
1012 # define ufromfp(Val1, Val2, Val3)                                      \
1013   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)
1014
1015 # define fromfpx(Val1, Val2, Val3)                                      \
1016   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)
1017
1018 # define ufromfpx(Val1, Val2, Val3)                                     \
1019   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)
1020
1021 /* Like ilogb, but returning long int.  */
1022 # define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)
1023 #endif
1024
1025 #if __GLIBC_USE (IEC_60559_BFP_EXT)
1026 /* Return value with maximum magnitude.  */
1027 # define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
1028
1029 /* Return value with minimum magnitude.  */
1030 # define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
1031 #endif
1032
1033 #if __GLIBC_USE (ISOC2X)
1034 /* Return maximum value from X and Y.  */
1035 # define fmaximum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum)
1036
1037 /* Return minimum value from X and Y.  */
1038 # define fminimum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum)
1039
1040 /* Return maximum numeric value from X and Y.  */
1041 # define fmaximum_num(Val1, Val2)                       \
1042   __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_num)
1043
1044 /* Return minimum numeric value from X and Y.  */
1045 # define fminimum_num(Val1, Val2)                       \
1046   __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_num)
1047
1048 /* Return value with maximum magnitude.  */
1049 # define fmaximum_mag(Val1, Val2)                       \
1050   __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag)
1051
1052 /* Return value with minimum magnitude.  */
1053 # define fminimum_mag(Val1, Val2)                       \
1054   __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag)
1055
1056 /* Return numeric value with maximum magnitude.  */
1057 # define fmaximum_mag_num(Val1, Val2)                           \
1058   __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag_num)
1059
1060 /* Return numeric value with minimum magnitude.  */
1061 # define fminimum_mag_num(Val1, Val2)                           \
1062   __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag_num)
1063 #endif
1064
1065
1066 /* Absolute value, conjugates, and projection.  */
1067
1068 /* Argument value of Z.  */
1069 #define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)
1070
1071 /* Complex conjugate of Z.  */
1072 #define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
1073
1074 /* Projection of Z onto the Riemann sphere.  */
1075 #define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
1076
1077
1078 /* Decomposing complex values.  */
1079
1080 /* Imaginary part of Z.  */
1081 #define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)
1082
1083 /* Real part of Z.  */
1084 #define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)
1085
1086
1087 /* Narrowing functions.  */
1088
1089 #if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
1090
1091 /* Add.  */
1092 # define fadd(Val1, Val2) __TGMATH_2_NARROW_F (fadd, Val1, Val2)
1093 # define dadd(Val1, Val2) __TGMATH_2_NARROW_D (dadd, Val1, Val2)
1094
1095 /* Divide.  */
1096 # define fdiv(Val1, Val2) __TGMATH_2_NARROW_F (fdiv, Val1, Val2)
1097 # define ddiv(Val1, Val2) __TGMATH_2_NARROW_D (ddiv, Val1, Val2)
1098
1099 /* Multiply.  */
1100 # define fmul(Val1, Val2) __TGMATH_2_NARROW_F (fmul, Val1, Val2)
1101 # define dmul(Val1, Val2) __TGMATH_2_NARROW_D (dmul, Val1, Val2)
1102
1103 /* Subtract.  */
1104 # define fsub(Val1, Val2) __TGMATH_2_NARROW_F (fsub, Val1, Val2)
1105 # define dsub(Val1, Val2) __TGMATH_2_NARROW_D (dsub, Val1, Val2)
1106
1107 /* Square root.  */
1108 # define fsqrt(Val) __TGMATH_1_NARROW_F (fsqrt, Val)
1109 # define dsqrt(Val) __TGMATH_1_NARROW_D (dsqrt, Val)
1110
1111 /* Fused multiply-add.  */
1112 # define ffma(Val1, Val2, Val3) __TGMATH_3_NARROW_F (ffma, Val1, Val2, Val3)
1113 # define dfma(Val1, Val2, Val3) __TGMATH_3_NARROW_D (dfma, Val1, Val2, Val3)
1114
1115 #endif
1116
1117 #if __GLIBC_USE (IEC_60559_TYPES_EXT)
1118
1119 # if __HAVE_FLOAT16
1120 #  define f16add(Val1, Val2) __TGMATH_2_NARROW_F16 (f16add, Val1, Val2)
1121 #  define f16div(Val1, Val2) __TGMATH_2_NARROW_F16 (f16div, Val1, Val2)
1122 #  define f16mul(Val1, Val2) __TGMATH_2_NARROW_F16 (f16mul, Val1, Val2)
1123 #  define f16sub(Val1, Val2) __TGMATH_2_NARROW_F16 (f16sub, Val1, Val2)
1124 #  define f16sqrt(Val) __TGMATH_1_NARROW_F16 (f16sqrt, Val)
1125 #  define f16fma(Val1, Val2, Val3)                      \
1126   __TGMATH_3_NARROW_F16 (f16fma, Val1, Val2, Val3)
1127 # endif
1128
1129 # if __HAVE_FLOAT32
1130 #  define f32add(Val1, Val2) __TGMATH_2_NARROW_F32 (f32add, Val1, Val2)
1131 #  define f32div(Val1, Val2) __TGMATH_2_NARROW_F32 (f32div, Val1, Val2)
1132 #  define f32mul(Val1, Val2) __TGMATH_2_NARROW_F32 (f32mul, Val1, Val2)
1133 #  define f32sub(Val1, Val2) __TGMATH_2_NARROW_F32 (f32sub, Val1, Val2)
1134 #  define f32sqrt(Val) __TGMATH_1_NARROW_F32 (f32sqrt, Val)
1135 #  define f32fma(Val1, Val2, Val3)                      \
1136   __TGMATH_3_NARROW_F32 (f32fma, Val1, Val2, Val3)
1137 # endif
1138
1139 # if __HAVE_FLOAT64 && (__HAVE_FLOAT64X || __HAVE_FLOAT128)
1140 #  define f64add(Val1, Val2) __TGMATH_2_NARROW_F64 (f64add, Val1, Val2)
1141 #  define f64div(Val1, Val2) __TGMATH_2_NARROW_F64 (f64div, Val1, Val2)
1142 #  define f64mul(Val1, Val2) __TGMATH_2_NARROW_F64 (f64mul, Val1, Val2)
1143 #  define f64sub(Val1, Val2) __TGMATH_2_NARROW_F64 (f64sub, Val1, Val2)
1144 #  define f64sqrt(Val) __TGMATH_1_NARROW_F64 (f64sqrt, Val)
1145 #  define f64fma(Val1, Val2, Val3)                      \
1146   __TGMATH_3_NARROW_F64 (f64fma, Val1, Val2, Val3)
1147 # endif
1148
1149 # if __HAVE_FLOAT32X
1150 #  define f32xadd(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xadd, Val1, Val2)
1151 #  define f32xdiv(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xdiv, Val1, Val2)
1152 #  define f32xmul(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xmul, Val1, Val2)
1153 #  define f32xsub(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xsub, Val1, Val2)
1154 #  define f32xsqrt(Val) __TGMATH_1_NARROW_F32X (f32xsqrt, Val)
1155 #  define f32xfma(Val1, Val2, Val3)                     \
1156   __TGMATH_3_NARROW_F32X (f32xfma, Val1, Val2, Val3)
1157 # endif
1158
1159 # if __HAVE_FLOAT64X && (__HAVE_FLOAT128X || __HAVE_FLOAT128)
1160 #  define f64xadd(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xadd, Val1, Val2)
1161 #  define f64xdiv(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xdiv, Val1, Val2)
1162 #  define f64xmul(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xmul, Val1, Val2)
1163 #  define f64xsub(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xsub, Val1, Val2)
1164 #  define f64xsqrt(Val) __TGMATH_1_NARROW_F64X (f64xsqrt, Val)
1165 #  define f64xfma(Val1, Val2, Val3)                     \
1166   __TGMATH_3_NARROW_F64X (f64xfma, Val1, Val2, Val3)
1167 # endif
1168
1169 #endif
1170
1171 #endif /* tgmath.h */