math/tgmath.h

   1 /* Copyright (C) 1997-2017 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    <http://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).  */
  41
  42 #define __HAVE_BUILTIN_TGMATH __GNUC_PREREQ (8, 0)
  43
  44 #if __GNUC_PREREQ (2, 7)
  45
  46 # if __HAVE_BUILTIN_TGMATH
  47
  48 #  if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  49 #   define __TG_F16_ARG(X) X ## f16,
  50 #  else
  51 #   define __TG_F16_ARG(X)
  52 #  endif
  53 #  if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  54 #   define __TG_F32_ARG(X) X ## f32,
  55 #  else
  56 #   define __TG_F32_ARG(X)
  57 #  endif
  58 #  if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  59 #   define __TG_F64_ARG(X) X ## f64,
  60 #  else
  61 #   define __TG_F64_ARG(X)
  62 #  endif
  63 #  if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
  64 #   define __TG_F128_ARG(X) X ## f128,
  65 #  else
  66 #   define __TG_F128_ARG(X)
  67 #  endif
  68 #  if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
  69 #   define __TG_F32X_ARG(X) X ## f32x,
  70 #  else
  71 #   define __TG_F32X_ARG(X)
  72 #  endif
  73 #  if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
  74 #   define __TG_F64X_ARG(X) X ## f64x,
  75 #  else
  76 #   define __TG_F64X_ARG(X)
  77 #  endif
  78 #  if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
  79 #   define __TG_F128X_ARG(X) X ## f128x,
  80 #  else
  81 #   define __TG_F128X_ARG(X)
  82 #  endif
  83
  84 #  define __TGMATH_FUNCS(X) X ## f, X, X ## l,                          \
  85     __TG_F16_ARG (X) __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
  86     __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
  87 #  define __TGMATH_RCFUNCS(F, C) __TGMATH_FUNCS (F) __TGMATH_FUNCS (C)
  88 #  define __TGMATH_1(F, X) __builtin_tgmath (__TGMATH_FUNCS (F) (X))
  89 #  define __TGMATH_2(F, X, Y) __builtin_tgmath (__TGMATH_FUNCS (F) (X), (Y))
  90 #  define __TGMATH_2STD(F, X, Y) __builtin_tgmath (F ## f, F, F ## l, (X), (Y))
  91 #  define __TGMATH_3(F, X, Y, Z) __builtin_tgmath (__TGMATH_FUNCS (F)   \
  92                                                    (X), (Y), (Z))
  93 #  define __TGMATH_1C(F, C, X) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) (X))
  94 #  define __TGMATH_2C(F, C, X, Y) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) \
  95                                                     (X), (Y))
  96
  97 # else /* !__HAVE_BUILTIN_TGMATH.  */
  98
  99 #  ifdef __NO_LONG_DOUBLE_MATH
 100 #   define __tgml(fct) fct
 101 #  else
 102 #   define __tgml(fct) fct ## l
 103 #  endif
 104
 105 /* __floating_type expands to 1 if TYPE is a floating type (including
 106    complex floating types), 0 if TYPE is an integer type (including
 107    complex integer types).  __real_integer_type expands to 1 if TYPE
 108    is a real integer type.  __complex_integer_type expands to 1 if
 109    TYPE is a complex integer type.  All these macros expand to integer
 110    constant expressions.  All these macros can assume their argument
 111    has an arithmetic type (not vector, decimal floating-point or
 112    fixed-point), valid to pass to tgmath.h macros.  */
 113 #  if __GNUC_PREREQ (3, 1)
 114 /* __builtin_classify_type expands to an integer constant expression
 115    in GCC 3.1 and later.  Default conversions applied to the argument
 116    of __builtin_classify_type mean it always returns 1 for real
 117    integer types rather than ever returning different values for
 118    character, boolean or enumerated types.  */
 119 #   define __floating_type(type)                                \
 120   (__builtin_classify_type (__real__ ((type) 0)) == 8)
 121 #   define __real_integer_type(type)            \
 122   (__builtin_classify_type ((type) 0) == 1)
 123 #   define __complex_integer_type(type)                         \
 124   (__builtin_classify_type ((type) 0) == 9                      \
 125    && __builtin_classify_type (__real__ ((type) 0)) == 1)
 126 #  else
 127 /* GCC versions predating __builtin_classify_type are also looser on
 128    what counts as an integer constant expression.  */
 129 #   define __floating_type(type) (((type) 1.25) != 1)
 130 #   define __real_integer_type(type) (((type) (1.25 + _Complex_I)) == 1)
 131 #   define __complex_integer_type(type)                 \
 132   (((type) (1.25 + _Complex_I)) == (1 + _Complex_I))
 133 #  endif
 134
 135 /* Whether an expression (of arithmetic type) has a real type.  */
 136 #  define __expr_is_real(E) (__builtin_classify_type (E) != 9)
 137
 138 /* The tgmath real type for T, where E is 0 if T is an integer type
 139    and 1 for a floating type.  If T has a complex type, it is
 140    unspecified whether the return type is real or complex (but it has
 141    the correct corresponding real type).  */
 142 #  define __tgmath_real_type_sub(T, E) \
 143   __typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0          \
 144                   : (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0))
 145
 146 /* The tgmath real type of EXPR.  */
 147 #  define __tgmath_real_type(expr) \
 148   __tgmath_real_type_sub (__typeof__ ((__typeof__ (+(expr))) 0),              \
 149                           __floating_type (__typeof__ (+(expr))))
 150
 151 /* The tgmath complex type for T, where E1 is 1 if T has a floating
 152    type and 0 otherwise, E2 is 1 if T has a real integer type and 0
 153    otherwise, and E3 is 1 if T has a complex type and 0 otherwise.  */
 154 #  define __tgmath_complex_type_sub(T, E1, E2, E3)                      \
 155   __typeof__ (*(0                                                       \
 156                 ? (__typeof__ (0 ? (T *) 0 : (void *) (!(E1)))) 0       \
 157                 : (__typeof__ (0                                        \
 158                                ? (__typeof__ (0                         \
 159                                               ? (double *) 0            \
 160                                               : (void *) (!(E2)))) 0    \
 161                                : (__typeof__ (0                         \
 162                                               ? (_Complex double *) 0   \
 163                                               : (void *) (!(E3)))) 0)) 0))
 164
 165 /* The tgmath complex type of EXPR.  */
 166 #  define __tgmath_complex_type(expr)                                   \
 167   __tgmath_complex_type_sub (__typeof__ ((__typeof__ (+(expr))) 0),     \
 168                              __floating_type (__typeof__ (+(expr))),    \
 169                              __real_integer_type (__typeof__ (+(expr))), \
 170                              __complex_integer_type (__typeof__ (+(expr))))
 171
 172 #  if (__HAVE_DISTINCT_FLOAT16                  \
 173       || __HAVE_DISTINCT_FLOAT32                \
 174       || __HAVE_DISTINCT_FLOAT64                \
 175       || __HAVE_DISTINCT_FLOAT32X               \
 176       || __HAVE_DISTINCT_FLOAT64X               \
 177       || __HAVE_DISTINCT_FLOAT128X)
 178 #   error "Unsupported _FloatN or _FloatNx types for <tgmath.h>."
 179 #  endif
 180
 181 /* Expand to text that checks if ARG_COMB has type _Float128, and if
 182    so calls the appropriately suffixed FCT (which may include a cast),
 183    or FCT and CFCT for complex functions, with arguments ARG_CALL.  */
 184 #  if __HAVE_DISTINCT_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
 185 #   if (!__HAVE_FLOAT64X                        \
 186        || __HAVE_FLOAT64X_LONG_DOUBLE           \
 187        || !__HAVE_FLOATN_NOT_TYPEDEF)
 188 #    define __TGMATH_F128(arg_comb, fct, arg_call)                      \
 189   __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)      \
 190   ? fct ## f128 arg_call :
 191 #    define __TGMATH_CF128(arg_comb, fct, cfct, arg_call)               \
 192   __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
 193   ? (__expr_is_real (arg_comb)                                          \
 194      ? fct ## f128 arg_call                                             \
 195      : cfct ## f128 arg_call) :
 196 #   else
 197 /* _Float64x is a distinct type at the C language level, which must be
 198    handled like _Float128.  */
 199 #    define __TGMATH_F128(arg_comb, fct, arg_call)                      \
 200   (__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)     \
 201    || __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float64x)) \
 202   ? fct ## f128 arg_call :
 203 #    define __TGMATH_CF128(arg_comb, fct, cfct, arg_call)               \
 204   (__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
 205    || __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)),    \
 206                                     _Float64x))                         \
 207   ? (__expr_is_real (arg_comb)                                          \
 208      ? fct ## f128 arg_call                                             \
 209      : cfct ## f128 arg_call) :
 210 #   endif
 211 #  else
 212 #   define __TGMATH_F128(arg_comb, fct, arg_call) /* Nothing.  */
 213 #   define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) /* Nothing.  */
 214 #  endif
 215
 216 # endif /* !__HAVE_BUILTIN_TGMATH.  */
 217
 218 /* We have two kinds of generic macros: to support functions which are
 219    only defined on real valued parameters and those which are defined
 220    for complex functions as well.  */
 221 # if __HAVE_BUILTIN_TGMATH
 222
 223 #  define __TGMATH_UNARY_REAL_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
 224 #  define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
 225 #  define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct)      \
 226   __TGMATH_2 (Fct, (Val1), (Val2))
 227 #  define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct)  \
 228   __TGMATH_2STD (Fct, (Val1), (Val2))
 229 #  define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct)    \
 230   __TGMATH_2 (Fct, (Val1), (Val2))
 231 #  define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct)        \
 232   __TGMATH_2STD (Fct, (Val1), (Val2))
 233 #  define __TGMATH_BINARY_REAL_RET_ONLY(Val1, Val2, Fct)        \
 234   __TGMATH_2 (Fct, (Val1), (Val2))
 235 #  define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
 236   __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
 237 #  define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct)     \
 238   __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
 239 #  define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct)   \
 240   __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
 241 #  define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct)      \
 242   __TGMATH_1C (Fct, Cfct, (Val))
 243 #  define __TGMATH_UNARY_IMAG(Val, Cfct) __TGMATH_1 (Cfct, (Val))
 244 #  define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct)     \
 245   __TGMATH_1C (Fct, Cfct, (Val))
 246 #  define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct)     \
 247   __TGMATH_1 (Cfct, (Val))
 248 #  define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct)      \
 249   __TGMATH_2C (Fct, Cfct, (Val1), (Val2))
 250
 251 # else /* !__HAVE_BUILTIN_TGMATH.  */
 252
 253 #  define __TGMATH_UNARY_REAL_ONLY(Val, Fct)                            \
 254   (__extension__ ((sizeof (+(Val)) == sizeof (double)                         \
 255                       || __builtin_classify_type (Val) != 8)                  \
 256                      ? (__tgmath_real_type (Val)) Fct (Val)                   \
 257                      : (sizeof (+(Val)) == sizeof (float))                    \
 258                      ? (__tgmath_real_type (Val)) Fct##f (Val)                \
 259                      : __TGMATH_F128 ((Val), (__tgmath_real_type (Val)) Fct,  \
 260                                       (Val))                                  \
 261                      (__tgmath_real_type (Val)) __tgml(Fct) (Val)))
 262
 263 #  define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) \
 264      (__extension__ ((sizeof (+(Val)) == sizeof (double)                      \
 265                       || __builtin_classify_type (Val) != 8)                  \
 266                      ? Fct (Val)                                              \
 267                      : (sizeof (+(Val)) == sizeof (float))                    \
 268                      ? Fct##f (Val)                                           \
 269                      : __TGMATH_F128 ((Val), Fct, (Val))                      \
 270                      __tgml(Fct) (Val)))
 271
 272 #  define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
 273      (__extension__ ((sizeof (+(Val1)) == sizeof (double)                     \
 274                       || __builtin_classify_type (Val1) != 8)                 \
 275                      ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)           \
 276                      : (sizeof (+(Val1)) == sizeof (float))                   \
 277                      ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)        \
 278                      : __TGMATH_F128 ((Val1), (__tgmath_real_type (Val1)) Fct, \
 279                                     (Val1, Val2))                             \
 280                      (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
 281
 282 #  define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
 283      (__extension__ ((sizeof (+(Val1)) == sizeof (double)                     \
 284                       || __builtin_classify_type (Val1) != 8)                 \
 285                      ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)           \
 286                      : (sizeof (+(Val1)) == sizeof (float))                   \
 287                      ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)        \
 288                      : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
 289
 290 #  define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
 291      (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)              \
 292                       && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 293                      ? __TGMATH_F128 ((Val1) + (Val2),                        \
 294                                       (__typeof                               \
 295                                        ((__tgmath_real_type (Val1)) 0         \
 296                                         + (__tgmath_real_type (Val2)) 0)) Fct, \
 297                                       (Val1, Val2))                           \
 298                      (__typeof ((__tgmath_real_type (Val1)) 0                 \
 299                                 + (__tgmath_real_type (Val2)) 0))             \
 300                      __tgml(Fct) (Val1, Val2)                                 \
 301                      : (sizeof (+(Val1)) == sizeof (double)                   \
 302                         || sizeof (+(Val2)) == sizeof (double)                \
 303                         || __builtin_classify_type (Val1) != 8                \
 304                         || __builtin_classify_type (Val2) != 8)               \
 305                      ? (__typeof ((__tgmath_real_type (Val1)) 0               \
 306                                    + (__tgmath_real_type (Val2)) 0))          \
 307                        Fct (Val1, Val2)                                       \
 308                      : (__typeof ((__tgmath_real_type (Val1)) 0               \
 309                                    + (__tgmath_real_type (Val2)) 0))          \
 310                        Fct##f (Val1, Val2)))
 311
 312 #  define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
 313      (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)              \
 314                       && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 315                      ? (__typeof ((__tgmath_real_type (Val1)) 0               \
 316                                   + (__tgmath_real_type (Val2)) 0))           \
 317                        __tgml(Fct) (Val1, Val2)                               \
 318                      : (sizeof (+(Val1)) == sizeof (double)                   \
 319                         || sizeof (+(Val2)) == sizeof (double)                \
 320                         || __builtin_classify_type (Val1) != 8                \
 321                         || __builtin_classify_type (Val2) != 8)               \
 322                      ? (__typeof ((__tgmath_real_type (Val1)) 0               \
 323                                    + (__tgmath_real_type (Val2)) 0))          \
 324                        Fct (Val1, Val2)                                       \
 325                      : (__typeof ((__tgmath_real_type (Val1)) 0               \
 326                                    + (__tgmath_real_type (Val2)) 0))          \
 327                        Fct##f (Val1, Val2)))
 328
 329 #  define __TGMATH_BINARY_REAL_RET_ONLY(Val1, Val2, Fct) \
 330      (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)              \
 331                       && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 332                      ? __TGMATH_F128 ((Val1) + (Val2), Fct, (Val1, Val2))     \
 333                      __tgml(Fct) (Val1, Val2)                                 \
 334                      : (sizeof (+(Val1)) == sizeof (double)                   \
 335                         || sizeof (+(Val2)) == sizeof (double)                \
 336                         || __builtin_classify_type (Val1) != 8                \
 337                         || __builtin_classify_type (Val2) != 8)               \
 338                      ? Fct (Val1, Val2)                                       \
 339                      : Fct##f (Val1, Val2)))
 340
 341 #  define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
 342      (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)              \
 343                       && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
 344                      ? __TGMATH_F128 ((Val1) + (Val2),                        \
 345                                       (__typeof                               \
 346                                        ((__tgmath_real_type (Val1)) 0         \
 347                                         + (__tgmath_real_type (Val2)) 0)) Fct, \
 348                                       (Val1, Val2, Val3))                     \
 349                      (__typeof ((__tgmath_real_type (Val1)) 0                 \
 350                                 + (__tgmath_real_type (Val2)) 0))             \
 351                      __tgml(Fct) (Val1, Val2, Val3)                           \
 352                      : (sizeof (+(Val1)) == sizeof (double)                   \
 353                         || sizeof (+(Val2)) == sizeof (double)                \
 354                         || __builtin_classify_type (Val1) != 8                \
 355                         || __builtin_classify_type (Val2) != 8)               \
 356                      ? (__typeof ((__tgmath_real_type (Val1)) 0               \
 357                                    + (__tgmath_real_type (Val2)) 0))          \
 358                        Fct (Val1, Val2, Val3)                                 \
 359                      : (__typeof ((__tgmath_real_type (Val1)) 0               \
 360                                    + (__tgmath_real_type (Val2)) 0))          \
 361                        Fct##f (Val1, Val2, Val3)))
 362
 363 #  define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
 364      (__extension__ ((sizeof ((Val1) + (Val2) + (Val3)) > sizeof (double)     \
 365                       && __builtin_classify_type ((Val1) + (Val2) + (Val3))   \
 366                          == 8)                                                \
 367                      ? __TGMATH_F128 ((Val1) + (Val2) + (Val3),               \
 368                                       (__typeof                               \
 369                                        ((__tgmath_real_type (Val1)) 0         \
 370                                         + (__tgmath_real_type (Val2)) 0       \
 371                                         + (__tgmath_real_type (Val3)) 0)) Fct, \
 372                                       (Val1, Val2, Val3))                     \
 373                      (__typeof ((__tgmath_real_type (Val1)) 0                 \
 374                                 + (__tgmath_real_type (Val2)) 0               \
 375                                 + (__tgmath_real_type (Val3)) 0))             \
 376                        __tgml(Fct) (Val1, Val2, Val3)                         \
 377                      : (sizeof (+(Val1)) == sizeof (double)                   \
 378                         || sizeof (+(Val2)) == sizeof (double)                \
 379                         || sizeof (+(Val3)) == sizeof (double)                \
 380                         || __builtin_classify_type (Val1) != 8                \
 381                         || __builtin_classify_type (Val2) != 8                \
 382                         || __builtin_classify_type (Val3) != 8)               \
 383                      ? (__typeof ((__tgmath_real_type (Val1)) 0               \
 384                                    + (__tgmath_real_type (Val2)) 0            \
 385                                    + (__tgmath_real_type (Val3)) 0))          \
 386                        Fct (Val1, Val2, Val3)                                 \
 387                      : (__typeof ((__tgmath_real_type (Val1)) 0               \
 388                                    + (__tgmath_real_type (Val2)) 0            \
 389                                    + (__tgmath_real_type (Val3)) 0))          \
 390                        Fct##f (Val1, Val2, Val3)))
 391
 392 #  define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
 393      (__extension__ ((sizeof (+(Val1)) == sizeof (double)               \
 394                       || __builtin_classify_type (Val1) != 8)           \
 395                      ? Fct (Val1, Val2, Val3)                           \
 396                      : (sizeof (+(Val1)) == sizeof (float))             \
 397                      ? Fct##f (Val1, Val2, Val3)                        \
 398                      : __TGMATH_F128 ((Val1), Fct, (Val1, Val2, Val3))  \
 399                      __tgml(Fct) (Val1, Val2, Val3)))
 400
 401 /* XXX This definition has to be changed as soon as the compiler understands
 402    the imaginary keyword.  */
 403 #  define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
 404      (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)             \
 405                       || __builtin_classify_type (__real__ (Val)) != 8)       \
 406                      ? (__expr_is_real (Val)                                  \
 407                         ? (__tgmath_complex_type (Val)) Fct (Val)             \
 408                         : (__tgmath_complex_type (Val)) Cfct (Val))           \
 409                      : (sizeof (+__real__ (Val)) == sizeof (float))           \
 410                      ? (__expr_is_real (Val)                                  \
 411                         ? (__tgmath_complex_type (Val)) Fct##f (Val)          \
 412                         : (__tgmath_complex_type (Val)) Cfct##f (Val))        \
 413                      : __TGMATH_CF128 ((Val),                                 \
 414                                        (__tgmath_complex_type (Val)) Fct,     \
 415                                        (__tgmath_complex_type (Val)) Cfct,    \
 416                                        (Val))                                 \
 417                      (__expr_is_real (Val)                                    \
 418                       ? (__tgmath_complex_type (Val)) __tgml(Fct) (Val)       \
 419                       : (__tgmath_complex_type (Val)) __tgml(Cfct) (Val))))
 420
 421 #  define __TGMATH_UNARY_IMAG(Val, Cfct) \
 422      (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)             \
 423                       || __builtin_classify_type (__real__ (Val)) != 8)       \
 424                      ? (__typeof__ ((__tgmath_real_type (Val)) 0              \
 425                                     + _Complex_I)) Cfct (Val)                 \
 426                      : (sizeof (+__real__ (Val)) == sizeof (float))           \
 427                      ? (__typeof__ ((__tgmath_real_type (Val)) 0              \
 428                                     + _Complex_I)) Cfct##f (Val)              \
 429                      : __TGMATH_F128 (__real__ (Val),                         \
 430                                       (__typeof__                             \
 431                                        ((__tgmath_real_type (Val)) 0          \
 432                                         + _Complex_I)) Cfct, (Val))           \
 433                      (__typeof__ ((__tgmath_real_type (Val)) 0                \
 434                                   + _Complex_I)) __tgml(Cfct) (Val)))
 435
 436 /* XXX This definition has to be changed as soon as the compiler understands
 437    the imaginary keyword.  */
 438 #  define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
 439      (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)             \
 440                       || __builtin_classify_type (__real__ (Val)) != 8)       \
 441                      ? (__expr_is_real (Val)                                  \
 442                         ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 443                           Fct (Val)                                           \
 444                         : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 445                           Cfct (Val))                                         \
 446                      : (sizeof (+__real__ (Val)) == sizeof (float))           \
 447                      ? (__expr_is_real (Val)                                  \
 448                         ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 449                           Fct##f (Val)                                        \
 450                         : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
 451                           Cfct##f (Val))                                      \
 452                      : __TGMATH_CF128 ((Val), \
 453                                        (__typeof__                            \
 454                                         (__real__                             \
 455                                          (__tgmath_real_type (Val)) 0)) Fct,  \
 456                                        (__typeof__                            \
 457                                         (__real__                             \
 458                                          (__tgmath_real_type (Val)) 0)) Cfct, \
 459                                        (Val))                                 \
 460                      (__expr_is_real (Val)                                    \
 461                       ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))  \
 462                       __tgml(Fct) (Val)                                       \
 463                       : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))  \
 464                       __tgml(Cfct) (Val))))
 465 #  define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct)     \
 466   __TGMATH_UNARY_REAL_IMAG_RET_REAL ((Val), Cfct, Cfct)
 467
 468 /* XXX This definition has to be changed as soon as the compiler understands
 469    the imaginary keyword.  */
 470 #  define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
 471      (__extension__ ((sizeof (__real__ (Val1)                                 \
 472                               + __real__ (Val2)) > sizeof (double)            \
 473                       && __builtin_classify_type (__real__ (Val1)             \
 474                                                   + __real__ (Val2)) == 8)    \
 475                      ? __TGMATH_CF128 ((Val1) + (Val2),                       \
 476                                        (__typeof                              \
 477                                         ((__tgmath_complex_type (Val1)) 0     \
 478                                          + (__tgmath_complex_type (Val2)) 0)) \
 479                                        Fct,                                   \
 480                                        (__typeof                              \
 481                                         ((__tgmath_complex_type (Val1)) 0     \
 482                                          + (__tgmath_complex_type (Val2)) 0)) \
 483                                        Cfct,                                  \
 484                                        (Val1, Val2))                          \
 485                      (__expr_is_real ((Val1) + (Val2))                        \
 486                       ? (__typeof ((__tgmath_complex_type (Val1)) 0           \
 487                                    + (__tgmath_complex_type (Val2)) 0))       \
 488                       __tgml(Fct) (Val1, Val2)                                \
 489                       : (__typeof ((__tgmath_complex_type (Val1)) 0           \
 490                                    + (__tgmath_complex_type (Val2)) 0))       \
 491                       __tgml(Cfct) (Val1, Val2))                              \
 492                      : (sizeof (+__real__ (Val1)) == sizeof (double)          \
 493                         || sizeof (+__real__ (Val2)) == sizeof (double)       \
 494                         || __builtin_classify_type (__real__ (Val1)) != 8     \
 495                         || __builtin_classify_type (__real__ (Val2)) != 8)    \
 496                      ? (__expr_is_real ((Val1) + (Val2))                      \
 497                         ? (__typeof ((__tgmath_complex_type (Val1)) 0         \
 498                                    + (__tgmath_complex_type (Val2)) 0))       \
 499                           Fct (Val1, Val2)                                    \
 500                         : (__typeof ((__tgmath_complex_type (Val1)) 0         \
 501                                    + (__tgmath_complex_type (Val2)) 0))       \
 502                           Cfct (Val1, Val2))                                  \
 503                      : (__expr_is_real ((Val1) + (Val2))                      \
 504                         ? (__typeof ((__tgmath_complex_type (Val1)) 0         \
 505                                    + (__tgmath_complex_type (Val2)) 0))       \
 506                           Fct##f (Val1, Val2)                                 \
 507                         : (__typeof ((__tgmath_complex_type (Val1)) 0         \
 508                                    + (__tgmath_complex_type (Val2)) 0))       \
 509                           Cfct##f (Val1, Val2))))
 510 # endif /* !__HAVE_BUILTIN_TGMATH.  */
 511 #else
 512 # error "Unsupported compiler; you cannot use <tgmath.h>"
 513 #endif
 514
 515
 516 /* Unary functions defined for real and complex values.  */
 517
 518
 519 /* Trigonometric functions.  */
 520
 521 /* Arc cosine of X.  */
 522 #define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
 523 /* Arc sine of X.  */
 524 #define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
 525 /* Arc tangent of X.  */
 526 #define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
 527 /* Arc tangent of Y/X.  */
 528 #define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
 529
 530 /* Cosine of X.  */
 531 #define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
 532 /* Sine of X.  */
 533 #define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
 534 /* Tangent of X.  */
 535 #define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
 536
 537
 538 /* Hyperbolic functions.  */
 539
 540 /* Hyperbolic arc cosine of X.  */
 541 #define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
 542 /* Hyperbolic arc sine of X.  */
 543 #define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
 544 /* Hyperbolic arc tangent of X.  */
 545 #define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
 546
 547 /* Hyperbolic cosine of X.  */
 548 #define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
 549 /* Hyperbolic sine of X.  */
 550 #define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
 551 /* Hyperbolic tangent of X.  */
 552 #define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
 553
 554
 555 /* Exponential and logarithmic functions.  */
 556
 557 /* Exponential function of X.  */
 558 #define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
 559
 560 /* Break VALUE into a normalized fraction and an integral power of 2.  */
 561 #define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
 562
 563 /* X times (two to the EXP power).  */
 564 #define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
 565
 566 /* Natural logarithm of X.  */
 567 #define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
 568
 569 /* Base-ten logarithm of X.  */
 570 #ifdef __USE_GNU
 571 # define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
 572 #else
 573 # define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
 574 #endif
 575
 576 /* Return exp(X) - 1.  */
 577 #define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
 578
 579 /* Return log(1 + X).  */
 580 #define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
 581
 582 /* Return the base 2 signed integral exponent of X.  */
 583 #define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
 584
 585 /* Compute base-2 exponential of X.  */
 586 #define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
 587
 588 /* Compute base-2 logarithm of X.  */
 589 #define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
 590
 591
 592 /* Power functions.  */
 593
 594 /* Return X to the Y power.  */
 595 #define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
 596
 597 /* Return the square root of X.  */
 598 #define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
 599
 600 /* Return `sqrt(X*X + Y*Y)'.  */
 601 #define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
 602
 603 /* Return the cube root of X.  */
 604 #define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
 605
 606
 607 /* Nearest integer, absolute value, and remainder functions.  */
 608
 609 /* Smallest integral value not less than X.  */
 610 #define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
 611
 612 /* Absolute value of X.  */
 613 #define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
 614
 615 /* Largest integer not greater than X.  */
 616 #define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
 617
 618 /* Floating-point modulo remainder of X/Y.  */
 619 #define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
 620
 621 /* Round X to integral valuein floating-point format using current
 622    rounding direction, but do not raise inexact exception.  */
 623 #define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
 624
 625 /* Round X to nearest integral value, rounding halfway cases away from
 626    zero.  */
 627 #define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
 628
 629 /* Round X to the integral value in floating-point format nearest but
 630    not larger in magnitude.  */
 631 #define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
 632
 633 /* Compute remainder of X and Y and put in *QUO a value with sign of x/y
 634    and magnitude congruent `mod 2^n' to the magnitude of the integral
 635    quotient x/y, with n >= 3.  */
 636 #define remquo(Val1, Val2, Val3) \
 637      __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
 638
 639 /* Round X to nearest integral value according to current rounding
 640    direction.  */
 641 #define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
 642 #define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)
 643
 644 /* Round X to nearest integral value, rounding halfway cases away from
 645    zero.  */
 646 #define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
 647 #define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)
 648
 649
 650 /* Return X with its signed changed to Y's.  */
 651 #define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
 652
 653 /* Error and gamma functions.  */
 654 #define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
 655 #define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
 656 #define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
 657 #define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
 658
 659
 660 /* Return the integer nearest X in the direction of the
 661    prevailing rounding mode.  */
 662 #define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
 663
 664 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 665 /* Return X - epsilon.  */
 666 # define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
 667 /* Return X + epsilon.  */
 668 # define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
 669 #endif
 670
 671 /* Return X + epsilon if X < Y, X - epsilon if X > Y.  */
 672 #define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
 673 #define nexttoward(Val1, Val2) \
 674      __TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)
 675
 676 /* Return the remainder of integer divison X / Y with infinite precision.  */
 677 #define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
 678
 679 /* Return X times (2 to the Nth power).  */
 680 #ifdef __USE_MISC
 681 # define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
 682 #endif
 683
 684 /* Return X times (2 to the Nth power).  */
 685 #define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
 686
 687 /* Return X times (2 to the Nth power).  */
 688 #define scalbln(Val1, Val2) \
 689      __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
 690
 691 /* Return the binary exponent of X, which must be nonzero.  */
 692 #define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)
 693
 694
 695 /* Return positive difference between X and Y.  */
 696 #define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
 697
 698 /* Return maximum numeric value from X and Y.  */
 699 #define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
 700
 701 /* Return minimum numeric value from X and Y.  */
 702 #define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
 703
 704
 705 /* Multiply-add function computed as a ternary operation.  */
 706 #define fma(Val1, Val2, Val3) \
 707      __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
 708
 709 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 710 /* Round X to nearest integer value, rounding halfway cases to even.  */
 711 # define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)
 712
 713 # define fromfp(Val1, Val2, Val3)                                       \
 714   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)
 715
 716 # define ufromfp(Val1, Val2, Val3)                                      \
 717   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)
 718
 719 # define fromfpx(Val1, Val2, Val3)                                      \
 720   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)
 721
 722 # define ufromfpx(Val1, Val2, Val3)                                     \
 723   __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)
 724
 725 /* Like ilogb, but returning long int.  */
 726 # define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)
 727
 728 /* Return value with maximum magnitude.  */
 729 # define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
 730
 731 /* Return value with minimum magnitude.  */
 732 # define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
 733
 734 /* Total order operation.  */
 735 # define totalorder(Val1, Val2)                                 \
 736   __TGMATH_BINARY_REAL_RET_ONLY (Val1, Val2, totalorder)
 737
 738 /* Total order operation on absolute values.  */
 739 # define totalordermag(Val1, Val2)                              \
 740   __TGMATH_BINARY_REAL_RET_ONLY (Val1, Val2, totalordermag)
 741 #endif
 742
 743
 744 /* Absolute value, conjugates, and projection.  */
 745
 746 /* Argument value of Z.  */
 747 #define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)
 748
 749 /* Complex conjugate of Z.  */
 750 #define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
 751
 752 /* Projection of Z onto the Riemann sphere.  */
 753 #define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
 754
 755
 756 /* Decomposing complex values.  */
 757
 758 /* Imaginary part of Z.  */
 759 #define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)
 760
 761 /* Real part of Z.  */
 762 #define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)
 763
 764 #endif /* tgmath.h */