sysdeps/i386/fpu/bits/mathinline.h

   1 /* Inline math functions for i387.
   2    Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2003, 2004
   3    Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5    Contributed by John C. Bowman <bowman@math.ualberta.ca>, 1995.
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    The GNU C Library is distributed in the hope that it will be useful,
  13    but WITHOUT ANY WARRANTY; without even the implied warranty of
  14    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15    Lesser General Public License for more details.
  16
  17    You should have received a copy of the GNU Lesser General Public
  18    License along with the GNU C Library; if not, write to the Free
  19    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  20    02111-1307 USA.  */
  21
  22 #ifndef _MATH_H
  23 # error "Never use <bits/mathinline.h> directly; include <math.h> instead."
  24 #endif
  25
  26 #ifdef __cplusplus
  27 # define __MATH_INLINE __inline
  28 #else
  29 # define __MATH_INLINE extern __inline
  30 #endif
  31
  32
  33 #if defined __USE_ISOC99 && defined __GNUC__ && __GNUC__ >= 2
  34 /* GCC 2.97 and up have builtins that actually can be used.  */
  35 # if !__GNUC_PREREQ (2,97)
  36 /* ISO C99 defines some macros to perform unordered comparisons.  The
  37    ix87 FPU supports this with special opcodes and we should use them.
  38    These must not be inline functions since we have to be able to handle
  39    all floating-point types.  */
  40 #  undef isgreater
  41 #  undef isgreaterequal
  42 #  undef isless
  43 #  undef islessequal
  44 #  undef islessgreater
  45 #  undef isunordered
  46 #  ifdef __i686__
  47 /* For the PentiumPro and more recent processors we can provide
  48    better code.  */
  49 #   define isgreater(x, y) \
  50      ({ register char __result;                                               \
  51         __asm__ ("fucomip %%st(1), %%st; seta %%al"                           \
  52                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");          \
  53         __result; })
  54 #   define isgreaterequal(x, y) \
  55      ({ register char __result;                                               \
  56         __asm__ ("fucomip %%st(1), %%st; setae %%al"                          \
  57                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");          \
  58         __result; })
  59
  60 #   define isless(x, y) \
  61      ({ register char __result;                                               \
  62         __asm__ ("fucomip %%st(1), %%st; seta %%al"                           \
  63                  : "=a" (__result) : "u" (x), "t" (y) : "cc", "st");          \
  64         __result; })
  65
  66 #   define islessequal(x, y) \
  67      ({ register char __result;                                               \
  68         __asm__ ("fucomip %%st(1), %%st; setae %%al"                          \
  69                  : "=a" (__result) : "u" (x), "t" (y) : "cc", "st");          \
  70         __result; })
  71
  72 #   define islessgreater(x, y) \
  73      ({ register char __result;                                               \
  74         __asm__ ("fucomip %%st(1), %%st; setne %%al"                          \
  75                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");          \
  76         __result; })
  77
  78 #   define isunordered(x, y) \
  79      ({ register char __result;                                               \
  80         __asm__ ("fucomip %%st(1), %%st; setp %%al"                           \
  81                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");          \
  82         __result; })
  83 #  else
  84 /* This is the dumb, portable code for i386 and above.  */
  85 #   define isgreater(x, y) \
  86      ({ register char __result;                                               \
  87         __asm__ ("fucompp; fnstsw; testb $0x45, %%ah; setz %%al"              \
  88                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
  89         __result; })
  90
  91 #   define isgreaterequal(x, y) \
  92      ({ register char __result;                                               \
  93         __asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al"              \
  94                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
  95         __result; })
  96
  97 #   define isless(x, y) \
  98      ({ register char __result;                                               \
  99         __asm__ ("fucompp; fnstsw; testb $0x45, %%ah; setz %%al"              \
 100                  : "=a" (__result) : "u" (x), "t" (y) : "cc", "st", "st(1)"); \
 101         __result; })
 102
 103 #   define islessequal(x, y) \
 104      ({ register char __result;                                               \
 105         __asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al"              \
 106                  : "=a" (__result) : "u" (x), "t" (y) : "cc", "st", "st(1)"); \
 107         __result; })
 108
 109 #   define islessgreater(x, y) \
 110      ({ register char __result;                                               \
 111         __asm__ ("fucompp; fnstsw; testb $0x44, %%ah; setz %%al"              \
 112                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
 113         __result; })
 114
 115 #   define isunordered(x, y) \
 116      ({ register char __result;                                               \
 117         __asm__ ("fucompp; fnstsw; sahf; setp %%al"                           \
 118                  : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
 119         __result; })
 120 #  endif /* __i686__ */
 121 # endif /* GCC 2.97 */
 122
 123 /* The gcc, version 2.7 or below, has problems with all this inlining
 124    code.  So disable it for this version of the compiler.  */
 125 # if __GNUC_PREREQ (2, 8)
 126 /* Test for negative number.  Used in the signbit() macro.  */
 127 __MATH_INLINE int
 128 __NTH (__signbitf (float __x))
 129 {
 130   __extension__ union { float __f; int __i; } __u = { __f: __x };
 131   return __u.__i < 0;
 132 }
 133 __MATH_INLINE int
 134 __NTH (__signbit (double __x))
 135 {
 136   __extension__ union { double __d; int __i[2]; } __u = { __d: __x };
 137   return __u.__i[1] < 0;
 138 }
 139 __MATH_INLINE int
 140 __NTH (__signbitl (long double __x))
 141 {
 142   __extension__ union { long double __l; int __i[3]; } __u = { __l: __x };
 143   return (__u.__i[2] & 0x8000) != 0;
 144 }
 145 # endif
 146 #endif
 147
 148
 149 /* The gcc, version 2.7 or below, has problems with all this inlining
 150    code.  So disable it for this version of the compiler.  */
 151 #if __GNUC_PREREQ (2, 8)
 152
 153 #if ((!defined __NO_MATH_INLINES || defined __LIBC_INTERNAL_MATH_INLINES) \
 154      && defined __OPTIMIZE__)
 155
 156 /* A macro to define float, double, and long double versions of various
 157    math functions for the ix87 FPU.  FUNC is the function name (which will
 158    be suffixed with f and l for the float and long double version,
 159    respectively).  OP is the name of the FPU operation.
 160    We define two sets of macros.  The set with the additional NP
 161    doesn't add a prototype declaration.  */
 162
 163 #if defined __USE_MISC || defined __USE_ISOC99
 164 # define __inline_mathop(func, op) \
 165   __inline_mathop_ (double, func, op)                                         \
 166   __inline_mathop_ (float, __CONCAT(func,f), op)                              \
 167   __inline_mathop_ (long double, __CONCAT(func,l), op)
 168 # define __inline_mathopNP(func, op) \
 169   __inline_mathopNP_ (double, func, op)                                       \
 170   __inline_mathopNP_ (float, __CONCAT(func,f), op)                            \
 171   __inline_mathopNP_ (long double, __CONCAT(func,l), op)
 172 #else
 173 # define __inline_mathop(func, op) \
 174   __inline_mathop_ (double, func, op)
 175 # define __inline_mathopNP(func, op) \
 176   __inline_mathopNP_ (double, func, op)
 177 #endif
 178
 179 #define __inline_mathop_(float_type, func, op) \
 180   __inline_mathop_decl_ (float_type, func, op, "0" (__x))
 181 #define __inline_mathopNP_(float_type, func, op) \
 182   __inline_mathop_declNP_ (float_type, func, op, "0" (__x))
 183
 184
 185 #if defined __USE_MISC || defined __USE_ISOC99
 186 # define __inline_mathop_decl(func, op, params...) \
 187   __inline_mathop_decl_ (double, func, op, params)                            \
 188   __inline_mathop_decl_ (float, __CONCAT(func,f), op, params)                 \
 189   __inline_mathop_decl_ (long double, __CONCAT(func,l), op, params)
 190 # define __inline_mathop_declNP(func, op, params...) \
 191   __inline_mathop_declNP_ (double, func, op, params)                          \
 192   __inline_mathop_declNP_ (float, __CONCAT(func,f), op, params)               \
 193   __inline_mathop_declNP_ (long double, __CONCAT(func,l), op, params)
 194 #else
 195 # define __inline_mathop_decl(func, op, params...) \
 196   __inline_mathop_decl_ (double, func, op, params)
 197 # define __inline_mathop_declNP(func, op, params...) \
 198   __inline_mathop_declNP_ (double, func, op, params)
 199 #endif
 200
 201 #define __inline_mathop_decl_(float_type, func, op, params...) \
 202   __MATH_INLINE float_type func (float_type) __THROW;                         \
 203   __inline_mathop_declNP_ (float_type, func, op, params)
 204
 205 #define __inline_mathop_declNP_(float_type, func, op, params...) \
 206   __MATH_INLINE float_type __NTH (func (float_type __x))                      \
 207   {                                                                           \
 208     register float_type __result;                                             \
 209     __asm __volatile__ (op : "=t" (__result) : params);                       \
 210     return __result;                                                          \
 211   }
 212
 213
 214 #if defined __USE_MISC || defined __USE_ISOC99
 215 # define __inline_mathcode(func, arg, code) \
 216   __inline_mathcode_ (double, func, arg, code)                                \
 217   __inline_mathcode_ (float, __CONCAT(func,f), arg, code)                     \
 218   __inline_mathcode_ (long double, __CONCAT(func,l), arg, code)
 219 # define __inline_mathcodeNP(func, arg, code) \
 220   __inline_mathcodeNP_ (double, func, arg, code)                              \
 221   __inline_mathcodeNP_ (float, __CONCAT(func,f), arg, code)                   \
 222   __inline_mathcodeNP_ (long double, __CONCAT(func,l), arg, code)
 223 # define __inline_mathcode2(func, arg1, arg2, code) \
 224   __inline_mathcode2_ (double, func, arg1, arg2, code)                        \
 225   __inline_mathcode2_ (float, __CONCAT(func,f), arg1, arg2, code)             \
 226   __inline_mathcode2_ (long double, __CONCAT(func,l), arg1, arg2, code)
 227 # define __inline_mathcodeNP2(func, arg1, arg2, code) \
 228   __inline_mathcodeNP2_ (double, func, arg1, arg2, code)                      \
 229   __inline_mathcodeNP2_ (float, __CONCAT(func,f), arg1, arg2, code)           \
 230   __inline_mathcodeNP2_ (long double, __CONCAT(func,l), arg1, arg2, code)
 231 # define __inline_mathcode3(func, arg1, arg2, arg3, code) \
 232   __inline_mathcode3_ (double, func, arg1, arg2, arg3, code)                  \
 233   __inline_mathcode3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code)       \
 234   __inline_mathcode3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
 235 # define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
 236   __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)                \
 237   __inline_mathcodeNP3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code)     \
 238   __inline_mathcodeNP3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
 239 #else
 240 # define __inline_mathcode(func, arg, code) \
 241   __inline_mathcode_ (double, func, (arg), code)
 242 # define __inline_mathcodeNP(func, arg, code) \
 243   __inline_mathcodeNP_ (double, func, (arg), code)
 244 # define __inline_mathcode2(func, arg1, arg2, code) \
 245   __inline_mathcode2_ (double, func, arg1, arg2, code)
 246 # define __inline_mathcodeNP2(func, arg1, arg2, code) \
 247   __inline_mathcodeNP2_ (double, func, arg1, arg2, code)
 248 # define __inline_mathcode3(func, arg1, arg2, arg3, code) \
 249   __inline_mathcode3_ (double, func, arg1, arg2, arg3, code)
 250 # define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
 251   __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)
 252 #endif
 253
 254 #define __inline_mathcode_(float_type, func, arg, code) \
 255   __MATH_INLINE float_type func (float_type) __THROW;                         \
 256   __inline_mathcodeNP_(float_type, func, arg, code)
 257
 258 #define __inline_mathcodeNP_(float_type, func, arg, code) \
 259   __MATH_INLINE float_type __NTH (func (float_type arg))                      \
 260   {                                                                           \
 261     code;                                                                     \
 262   }
 263
 264
 265 #define __inline_mathcode2_(float_type, func, arg1, arg2, code) \
 266   __MATH_INLINE float_type func (float_type, float_type) __THROW;             \
 267   __inline_mathcodeNP2_ (float_type, func, arg1, arg2, code)
 268
 269 #define __inline_mathcodeNP2_(float_type, func, arg1, arg2, code) \
 270   __MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2))    \
 271   {                                                                           \
 272     code;                                                                     \
 273   }
 274
 275 #define __inline_mathcode3_(float_type, func, arg1, arg2, arg3, code) \
 276   __MATH_INLINE float_type func (float_type, float_type, float_type) __THROW; \
 277   __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code)
 278
 279 #define __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) \
 280   __MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2,     \
 281                                         float_type arg3))                     \
 282   {                                                                           \
 283     code;                                                                     \
 284   }
 285 #endif
 286
 287
 288 #if !defined __NO_MATH_INLINES && defined __OPTIMIZE__
 289 /* Miscellaneous functions */
 290
 291 __inline_mathcode (__sgn, __x, \
 292   return __x == 0.0 ? 0.0 : (__x > 0.0 ? 1.0 : -1.0))
 293
 294 /* __FAST_MATH__ is defined by gcc -ffast-math.  */
 295 #ifdef __FAST_MATH__
 296 __inline_mathcode (__pow2, __x, \
 297   register long double __value;                                               \
 298   register long double __exponent;                                            \
 299   __extension__ long long int __p = (long long int) __x;                      \
 300   if (__x == (long double) __p)                                               \
 301     {                                                                         \
 302       __asm __volatile__                                                      \
 303         ("fscale"                                                             \
 304          : "=t" (__value) : "0" (1.0), "u" (__x));                            \
 305       return __value;                                                         \
 306     }                                                                         \
 307   __asm __volatile__                                                          \
 308     ("fld       %%st(0)\n\t"                                                  \
 309      "frndint                   # int(x)\n\t"                                 \
 310      "fxch\n\t"                                                               \
 311      "fsub      %%st(1)         # fract(x)\n\t"                               \
 312      "f2xm1                     # 2^(fract(x)) - 1\n\t"                       \
 313      : "=t" (__value), "=u" (__exponent) : "0" (__x));                        \
 314   __value += 1.0;                                                             \
 315   __asm __volatile__                                                          \
 316     ("fscale"                                                                 \
 317      : "=t" (__value) : "0" (__value), "u" (__exponent));                     \
 318   return __value)
 319
 320 # ifdef __USE_GNU
 321 #  define __sincos_code \
 322   register long double __cosr;                                                \
 323   register long double __sinr;                                                \
 324   __asm __volatile__                                                          \
 325     ("fsincos\n\t"                                                            \
 326      "fnstsw    %%ax\n\t"                                                     \
 327      "testl     $0x400, %%eax\n\t"                                            \
 328      "jz        1f\n\t"                                                       \
 329      "fldpi\n\t"                                                              \
 330      "fadd      %%st(0)\n\t"                                                  \
 331      "fxch      %%st(1)\n\t"                                                  \
 332      "2: fprem1\n\t"                                                          \
 333      "fnstsw    %%ax\n\t"                                                     \
 334      "testl     $0x400, %%eax\n\t"                                            \
 335      "jnz       2b\n\t"                                                       \
 336      "fstp      %%st(1)\n\t"                                                  \
 337      "fsincos\n\t"                                                            \
 338      "1:"                                                                     \
 339      : "=t" (__cosr), "=u" (__sinr) : "0" (__x));                             \
 340   *__sinx = __sinr;                                                           \
 341   *__cosx = __cosr
 342
 343 __MATH_INLINE void
 344 __NTH (__sincos (double __x, double *__sinx, double *__cosx))
 345 {
 346   __sincos_code;
 347 }
 348
 349 __MATH_INLINE void
 350 __NTH (__sincosf (float __x, float *__sinx, float *__cosx))
 351 {
 352   __sincos_code;
 353 }
 354
 355 __MATH_INLINE void
 356 __NTH (__sincosl (long double __x, long double *__sinx, long double *__cosx))
 357 {
 358   __sincos_code;
 359 }
 360 # endif
 361
 362
 363 /* Optimized inline implementation, sometimes with reduced precision
 364    and/or argument range.  */
 365
 366 # if __GNUC_PREREQ (3, 5)
 367 #  define __expm1_code \
 368   register long double __temp;                                                \
 369   __temp = __builtin_expm1l (__x);                                            \
 370   return __temp ? __temp : __x
 371 # else
 372 #  define __expm1_code \
 373   register long double __value;                                               \
 374   register long double __exponent;                                            \
 375   register long double __temp;                                                \
 376   __asm __volatile__                                                          \
 377     ("fldl2e                    # e^x - 1 = 2^(x * log2(e)) - 1\n\t"          \
 378      "fmul      %%st(1)         # x * log2(e)\n\t"                            \
 379      "fst       %%st(1)\n\t"                                                  \
 380      "frndint                   # int(x * log2(e))\n\t"                       \
 381      "fxch\n\t"                                                               \
 382      "fsub      %%st(1)         # fract(x * log2(e))\n\t"                     \
 383      "f2xm1                     # 2^(fract(x * log2(e))) - 1\n\t"             \
 384      "fscale                    # 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t" \
 385      : "=t" (__value), "=u" (__exponent) : "0" (__x));                        \
 386   __asm __volatile__                                                          \
 387     ("fscale                    # 2^int(x * log2(e))\n\t"                     \
 388      : "=t" (__temp) : "0" (1.0), "u" (__exponent));                          \
 389   __temp -= 1.0;                                                              \
 390   __temp += __value;                                                          \
 391   return __temp ? __temp : __x
 392 # endif
 393 __inline_mathcodeNP_ (long double, __expm1l, __x, __expm1_code)
 394
 395 # if __GNUC_PREREQ (3, 4)
 396 __inline_mathcodeNP_ (long double, __expl, __x, return __builtin_expl (__x))
 397 # else
 398 #  define __exp_code \
 399   register long double __value;                                               \
 400   register long double __exponent;                                            \
 401   __asm __volatile__                                                          \
 402     ("fldl2e                    # e^x = 2^(x * log2(e))\n\t"                  \
 403      "fmul      %%st(1)         # x * log2(e)\n\t"                            \
 404      "fst       %%st(1)\n\t"                                                  \
 405      "frndint                   # int(x * log2(e))\n\t"                       \
 406      "fxch\n\t"                                                               \
 407      "fsub      %%st(1)         # fract(x * log2(e))\n\t"                     \
 408      "f2xm1                     # 2^(fract(x * log2(e))) - 1\n\t"             \
 409      : "=t" (__value), "=u" (__exponent) : "0" (__x));                        \
 410   __value += 1.0;                                                             \
 411   __asm __volatile__                                                          \
 412     ("fscale"                                                                 \
 413      : "=t" (__value) : "0" (__value), "u" (__exponent));                     \
 414   return __value
 415 __inline_mathcodeNP (exp, __x, __exp_code)
 416 __inline_mathcodeNP_ (long double, __expl, __x, __exp_code)
 417 # endif
 418
 419
 420 # if !__GNUC_PREREQ (3, 5)
 421 __inline_mathcodeNP (tan, __x, \
 422   register long double __value;                                               \
 423   register long double __value2 __attribute__ ((__unused__));                 \
 424   __asm __volatile__                                                          \
 425     ("fptan"                                                                  \
 426      : "=t" (__value2), "=u" (__value) : "0" (__x));                          \
 427   return __value)
 428 # endif
 429 #endif /* __FAST_MATH__ */
 430
 431
 432 #if __GNUC_PREREQ (3, 4)
 433 __inline_mathcodeNP2_ (long double, __atan2l, __y, __x,
 434                        return __builtin_atan2l (__y, __x))
 435 #else
 436 # define __atan2_code \
 437   register long double __value;                                               \
 438   __asm __volatile__                                                          \
 439     ("fpatan"                                                                 \
 440      : "=t" (__value) : "0" (__x), "u" (__y) : "st(1)");                      \
 441   return __value
 442 # ifdef __FAST_MATH__
 443 __inline_mathcodeNP2 (atan2, __y, __x, __atan2_code)
 444 # endif
 445 __inline_mathcodeNP2_ (long double, __atan2l, __y, __x, __atan2_code)
 446 #endif
 447
 448
 449 #if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
 450 __inline_mathcodeNP2 (fmod, __x, __y, \
 451   register long double __value;                                               \
 452   __asm __volatile__                                                          \
 453     ("1:        fprem\n\t"                                                    \
 454      "fnstsw    %%ax\n\t"                                                     \
 455      "sahf\n\t"                                                               \
 456      "jp        1b"                                                           \
 457      : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");                   \
 458   return __value)
 459 #endif
 460
 461
 462 #ifdef __FAST_MATH__
 463 # if !__GNUC_PREREQ (3,3)
 464 __inline_mathopNP (sqrt, "fsqrt")
 465 __inline_mathopNP_ (long double, __sqrtl, "fsqrt")
 466 #  define __libc_sqrtl(n) __sqrtl (n)
 467 # else
 468 #  define __libc_sqrtl(n) __builtin_sqrtl (n)
 469 # endif
 470 #endif
 471
 472 #if __GNUC_PREREQ (2, 8)
 473 __inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x))
 474 # if defined __USE_MISC || defined __USE_ISOC99
 475 __inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x))
 476 __inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x))
 477 # endif
 478 __inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x))
 479 #else
 480 __inline_mathop (fabs, "fabs")
 481 __inline_mathop_ (long double, __fabsl, "fabs")
 482 #endif
 483
 484 #ifdef __FAST_MATH__
 485 # if !__GNUC_PREREQ (3, 4)
 486 /* The argument range of this inline version is reduced.  */
 487 __inline_mathopNP (sin, "fsin")
 488 /* The argument range of this inline version is reduced.  */
 489 __inline_mathopNP (cos, "fcos")
 490
 491 __inline_mathop_declNP (log, "fldln2; fxch; fyl2x", "0" (__x) : "st(1)")
 492 # endif
 493
 494 # if !__GNUC_PREREQ (3, 5)
 495 __inline_mathop_declNP (log10, "fldlg2; fxch; fyl2x", "0" (__x) : "st(1)")
 496
 497 __inline_mathcodeNP (asin, __x, return __atan2l (__x, __libc_sqrtl (1.0 - __x * __x)))
 498 __inline_mathcodeNP (acos, __x, return __atan2l (__libc_sqrtl (1.0 - __x * __x), __x))
 499 # endif
 500
 501 # if !__GNUC_PREREQ (3, 4)
 502 __inline_mathop_declNP (atan, "fld1; fpatan", "0" (__x) : "st(1)")
 503 # endif
 504 #endif /* __FAST_MATH__ */
 505
 506 __inline_mathcode_ (long double, __sgn1l, __x, \
 507   __extension__ union { long double __xld; unsigned int __xi[3]; } __n =      \
 508     { __xld: __x };                                                           \
 509   __n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff;                              \
 510   __n.__xi[1] = 0x80000000;                                                   \
 511   __n.__xi[0] = 0;                                                            \
 512   return __n.__xld)
 513
 514
 515 #ifdef __FAST_MATH__
 516 /* The argument range of the inline version of sinhl is slightly reduced.  */
 517 __inline_mathcodeNP (sinh, __x, \
 518   register long double __exm1 = __expm1l (__fabsl (__x));                     \
 519   return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x))
 520
 521 __inline_mathcodeNP (cosh, __x, \
 522   register long double __ex = __expl (__x);                                   \
 523   return 0.5 * (__ex + 1.0 / __ex))
 524
 525 __inline_mathcodeNP (tanh, __x, \
 526   register long double __exm1 = __expm1l (-__fabsl (__x + __x));              \
 527   return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x))
 528 #endif
 529
 530 __inline_mathcodeNP (floor, __x, \
 531   register long double __value;                                               \
 532   __volatile unsigned short int __cw;                                         \
 533   __volatile unsigned short int __cwtmp;                                      \
 534   __asm __volatile ("fnstcw %0" : "=m" (__cw));                               \
 535   __cwtmp = (__cw & 0xf3ff) | 0x0400; /* rounding down */                     \
 536   __asm __volatile ("fldcw %0" : : "m" (__cwtmp));                            \
 537   __asm __volatile ("frndint" : "=t" (__value) : "0" (__x));                  \
 538   __asm __volatile ("fldcw %0" : : "m" (__cw));                               \
 539   return __value)
 540
 541 __inline_mathcodeNP (ceil, __x, \
 542   register long double __value;                                               \
 543   __volatile unsigned short int __cw;                                         \
 544   __volatile unsigned short int __cwtmp;                                      \
 545   __asm __volatile ("fnstcw %0" : "=m" (__cw));                               \
 546   __cwtmp = (__cw & 0xf3ff) | 0x0800; /* rounding up */                       \
 547   __asm __volatile ("fldcw %0" : : "m" (__cwtmp));                            \
 548   __asm __volatile ("frndint" : "=t" (__value) : "0" (__x));                  \
 549   __asm __volatile ("fldcw %0" : : "m" (__cw));                               \
 550   return __value)
 551
 552 #ifdef __FAST_MATH__
 553 # define __ldexp_code \
 554   register long double __value;                                               \
 555   __asm __volatile__                                                          \
 556     ("fscale"                                                                 \
 557      : "=t" (__value) : "0" (__x), "u" ((long double) __y));                  \
 558   return __value
 559
 560 __MATH_INLINE double
 561 __NTH (ldexp (double __x, int __y))
 562 {
 563   __ldexp_code;
 564 }
 565 #endif
 566
 567
 568 /* Optimized versions for some non-standardized functions.  */
 569 #if defined __USE_ISOC99 || defined __USE_MISC
 570
 571 # ifdef __FAST_MATH__
 572 __inline_mathcodeNP (expm1, __x, __expm1_code)
 573
 574 /* We cannot rely on M_SQRT being defined.  So we do it for ourself
 575    here.  */
 576 #  define __M_SQRT2     1.41421356237309504880L /* sqrt(2) */
 577
 578 #  if !__GNUC_PREREQ (3, 5)
 579 __inline_mathcodeNP (log1p, __x, \
 580   register long double __value;                                               \
 581   if (__fabsl (__x) >= 1.0 - 0.5 * __M_SQRT2)                                 \
 582     __value = logl (1.0 + __x);                                               \
 583   else                                                                        \
 584     __asm __volatile__                                                        \
 585       ("fldln2\n\t"                                                           \
 586        "fxch\n\t"                                                             \
 587        "fyl2xp1"                                                              \
 588        : "=t" (__value) : "0" (__x) : "st(1)");                               \
 589   return __value)
 590 #  endif
 591
 592
 593 /* The argument range of the inline version of asinhl is slightly reduced.  */
 594 __inline_mathcodeNP (asinh, __x, \
 595   register long double  __y = __fabsl (__x);                                  \
 596   return (log1pl (__y * __y / (__libc_sqrtl (__y * __y + 1.0) + 1.0) + __y)   \
 597           * __sgn1l (__x)))
 598
 599 __inline_mathcodeNP (acosh, __x, \
 600   return logl (__x + __libc_sqrtl (__x - 1.0) * __libc_sqrtl (__x + 1.0)))
 601
 602 __inline_mathcodeNP (atanh, __x, \
 603   register long double __y = __fabsl (__x);                                   \
 604   return -0.5 * log1pl (-(__y + __y) / (1.0 + __y)) * __sgn1l (__x))
 605
 606 /* The argument range of the inline version of hypotl is slightly reduced.  */
 607 __inline_mathcodeNP2 (hypot, __x, __y,
 608                       return __libc_sqrtl (__x * __x + __y * __y))
 609
 610 #  if !__GNUC_PREREQ (3, 5)
 611 __inline_mathcodeNP(logb, __x, \
 612   register long double __value;                                               \
 613   register long double __junk;                                                \
 614   __asm __volatile__                                                          \
 615     ("fxtract\n\t"                                                            \
 616      : "=t" (__junk), "=u" (__value) : "0" (__x));                            \
 617   return __value)
 618 #  endif
 619
 620 # endif
 621 #endif
 622
 623 #ifdef __USE_ISOC99
 624 # ifdef __FAST_MATH__
 625
 626 #  if !__GNUC_PREREQ (3, 5)
 627 __inline_mathop_declNP (log2, "fld1; fxch; fyl2x", "0" (__x) : "st(1)")
 628 #  endif
 629
 630 __MATH_INLINE float
 631 __NTH (ldexpf (float __x, int __y))
 632 {
 633   __ldexp_code;
 634 }
 635
 636 __MATH_INLINE long double
 637 __NTH (ldexpl (long double __x, int __y))
 638 {
 639   __ldexp_code;
 640 }
 641
 642 __inline_mathcodeNP3 (fma, __x, __y, __z, return (__x * __y) + __z)
 643
 644 __inline_mathopNP (rint, "frndint")
 645 # endif /* __FAST_MATH__ */
 646
 647 # define __lrint_code \
 648   long int __lrintres;                                                        \
 649   __asm__ __volatile__                                                        \
 650     ("fistpl %0"                                                              \
 651      : "=m" (__lrintres) : "t" (__x) : "st");                                 \
 652   return __lrintres
 653 __MATH_INLINE long int
 654 __NTH (lrintf (float __x))
 655 {
 656   __lrint_code;
 657 }
 658 __MATH_INLINE long int
 659 __NTH (lrint (double __x))
 660 {
 661   __lrint_code;
 662 }
 663 __MATH_INLINE long int
 664 __NTH (lrintl (long double __x))
 665 {
 666   __lrint_code;
 667 }
 668 # undef __lrint_code
 669
 670 # define __llrint_code \
 671   long long int __llrintres;                                                  \
 672   __asm__ __volatile__                                                        \
 673     ("fistpll %0"                                                             \
 674      : "=m" (__llrintres) : "t" (__x) : "st");                                \
 675   return __llrintres
 676 __MATH_INLINE long long int
 677 __NTH (llrintf (float __x))
 678 {
 679   __llrint_code;
 680 }
 681 __MATH_INLINE long long int
 682 __NTH (llrint (double __x))
 683 {
 684   __llrint_code;
 685 }
 686 __MATH_INLINE long long int
 687 __NTH (llrintl (long double __x))
 688 {
 689   __llrint_code;
 690 }
 691 # undef __llrint_code
 692
 693 #endif
 694
 695
 696 #ifdef __USE_MISC
 697
 698 # if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
 699 __inline_mathcodeNP2 (drem, __x, __y, \
 700   register double __value;                                                    \
 701   register int __clobbered;                                                   \
 702   __asm __volatile__                                                          \
 703     ("1:        fprem1\n\t"                                                   \
 704      "fstsw     %%ax\n\t"                                                     \
 705      "sahf\n\t"                                                               \
 706      "jp        1b"                                                           \
 707      : "=t" (__value), "=&a" (__clobbered) : "0" (__x), "u" (__y) : "cc");    \
 708   return __value)
 709 # endif
 710
 711
 712 /* This function is used in the `isfinite' macro.  */
 713 __MATH_INLINE int
 714 __NTH (__finite (double __x))
 715 {
 716   return (__extension__
 717           (((((union { double __d; int __i[2]; }) {__d: __x}).__i[1]
 718              | 0x800fffffu) + 1) >> 31));
 719 }
 720
 721 /* Miscellaneous functions */
 722 # ifdef __FAST_MATH__
 723 __inline_mathcode (__coshm1, __x, \
 724   register long double __exm1 = __expm1l (__fabsl (__x));                     \
 725   return 0.5 * (__exm1 / (__exm1 + 1.0)) * __exm1)
 726
 727 __inline_mathcode (__acosh1p, __x, \
 728   return log1pl (__x + __libc_sqrtl (__x) * __libc_sqrtl (__x + 2.0)))
 729
 730 # endif /* __FAST_MATH__ */
 731 #endif /* __USE_MISC  */
 732
 733 /* Undefine some of the large macros which are not used anymore.  */
 734 #undef __atan2_code
 735 #ifdef __FAST_MATH__
 736 # undef __expm1_code
 737 # undef __exp_code
 738 # undef __sincos_code
 739 #endif /* __FAST_MATH__ */
 740
 741 #endif /* __NO_MATH_INLINES  */
 742
 743
 744 /* This code is used internally in the GNU libc.  */
 745 #ifdef __LIBC_INTERNAL_MATH_INLINES
 746 __inline_mathop (__ieee754_sqrt, "fsqrt")
 747 __inline_mathcode2 (__ieee754_atan2, __y, __x,
 748                     register long double __value;
 749                     __asm __volatile__ ("fpatan\n\t"
 750                                         : "=t" (__value)
 751                                         : "0" (__x), "u" (__y) : "st(1)");
 752                     return __value;)
 753 #endif
 754
 755 #endif /* __GNUC__  */