include/crt/math.h

   1 /*
   2  * math.h
   3  * This file has no copyright assigned and is placed in the Public Domain.
   4  * This file is a part of the mingw-runtime package.
   5  * No warranty is given; refer to the file DISCLAIMER within the package.
   6  *
   7  * Mathematical functions.
   8  *
   9  */
  10
  11
  12 #ifndef _MATH_H_
  13 #define _MATH_H_
  14
  15 #if __GNUC__ >= 3
  16 #pragma GCC system_header
  17 #endif
  18
  19 /* All the headers include this file. */
  20 #include <_mingw.h>
  21
  22 /*
  23  * Types for the _exception structure.
  24  */
  25
  26 #define _DOMAIN         1       /* domain error in argument */
  27 #define _SING           2       /* singularity */
  28 #define _OVERFLOW       3       /* range overflow */
  29 #define _UNDERFLOW      4       /* range underflow */
  30 #define _TLOSS          5       /* total loss of precision */
  31 #define _PLOSS          6       /* partial loss of precision */
  32
  33 /*
  34  * Exception types with non-ANSI names for compatibility.
  35  */
  36
  37 #ifndef __STRICT_ANSI__
  38 #ifndef _NO_OLDNAMES
  39
  40 #define DOMAIN          _DOMAIN
  41 #define SING            _SING
  42 #define OVERFLOW        _OVERFLOW
  43 #define UNDERFLOW       _UNDERFLOW
  44 #define TLOSS           _TLOSS
  45 #define PLOSS           _PLOSS
  46
  47 #endif  /* Not _NO_OLDNAMES */
  48 #endif  /* Not __STRICT_ANSI__ */
  49
  50
  51 /* Traditional/XOPEN math constants (double precison) */
  52 #ifndef __STRICT_ANSI__
  53 #define M_E             2.7182818284590452354
  54 #define M_LOG2E         1.4426950408889634074
  55 #define M_LOG10E        0.43429448190325182765
  56 #define M_LN2           0.69314718055994530942
  57 #define M_LN10          2.30258509299404568402
  58 #define M_PI            3.14159265358979323846
  59 #define M_PI_2          1.57079632679489661923
  60 #define M_PI_4          0.78539816339744830962
  61 #define M_1_PI          0.31830988618379067154
  62 #define M_2_PI          0.63661977236758134308
  63 #define M_2_SQRTPI      1.12837916709551257390
  64 #define M_SQRT2         1.41421356237309504880
  65 #define M_SQRT1_2       0.70710678118654752440
  66 #endif
  67
  68 /* These are also defined in Mingw float.h; needed here as well to work
  69    around GCC build issues.  */
  70 #ifndef __STRICT_ANSI__
  71 #ifndef __MINGW_FPCLASS_DEFINED
  72 #define __MINGW_FPCLASS_DEFINED 1
  73 /* IEEE 754 classication */
  74 #define _FPCLASS_SNAN   0x0001  /* Signaling "Not a Number" */
  75 #define _FPCLASS_QNAN   0x0002  /* Quiet "Not a Number" */
  76 #define _FPCLASS_NINF   0x0004  /* Negative Infinity */
  77 #define _FPCLASS_NN     0x0008  /* Negative Normal */
  78 #define _FPCLASS_ND     0x0010  /* Negative Denormal */
  79 #define _FPCLASS_NZ     0x0020  /* Negative Zero */
  80 #define _FPCLASS_PZ     0x0040  /* Positive Zero */
  81 #define _FPCLASS_PD     0x0080  /* Positive Denormal */
  82 #define _FPCLASS_PN     0x0100  /* Positive Normal */
  83 #define _FPCLASS_PINF   0x0200  /* Positive Infinity */
  84 #endif /* __MINGW_FPCLASS_DEFINED */
  85 #endif  /* Not __STRICT_ANSI__ */
  86
  87 #ifndef RC_INVOKED
  88
  89 #ifdef __cplusplus
  90 extern "C" {
  91 #endif
  92
  93 /*
  94  * HUGE_VAL is returned by strtod when the value would overflow the
  95  * representation of 'double'. There are other uses as well.
  96  *
  97  * __imp__HUGE is a pointer to the actual variable _HUGE in
  98  * MSVCRT.DLL. If we used _HUGE directly we would get a pointer
  99  * to a thunk function.
 100  *
 101  * NOTE: The CRTDLL version uses _HUGE_dll instead.
 102  */
 103
 104 #if __MINGW_GNUC_PREREQ(3, 3)
 105 #define HUGE_VAL __builtin_huge_val()
 106 #else
 107
 108 #ifndef __DECLSPEC_SUPPORTED
 109
 110 #ifdef __MSVCRT__
 111 extern double*  _imp___HUGE;
 112 #define HUGE_VAL        (*_imp___HUGE)
 113 #else
 114 /* CRTDLL */
 115 extern double*  _imp___HUGE_dll;
 116 #define HUGE_VAL        (*_imp___HUGE_dll)
 117 #endif
 118
 119 #else /* __DECLSPEC_SUPPORTED */
 120
 121 #ifdef __MSVCRT__
 122 __MINGW_IMPORT double   _HUGE;
 123 #define HUGE_VAL        _HUGE
 124 #else
 125 /* CRTDLL */
 126 __MINGW_IMPORT double   _HUGE_dll;
 127 #define HUGE_VAL        _HUGE_dll
 128 #endif
 129
 130 #endif /* __DECLSPEC_SUPPORTED */
 131 #endif /* __MINGW_GNUC_PREREQ(3, 3) */
 132
 133
 134 struct _exception
 135 {
 136         int     type;
 137         char    *name;
 138         double  arg1;
 139         double  arg2;
 140         double  retval;
 141 };
 142
 143 _CRTIMP double __cdecl sin (double);
 144 _CRTIMP double __cdecl cos (double);
 145 _CRTIMP double __cdecl tan (double);
 146 _CRTIMP double __cdecl sinh (double);
 147 _CRTIMP double __cdecl cosh (double);
 148 _CRTIMP double __cdecl tanh (double);
 149 _CRTIMP double __cdecl asin (double);
 150 _CRTIMP double __cdecl acos (double);
 151 _CRTIMP double __cdecl atan (double);
 152 _CRTIMP double __cdecl atan2 (double, double);
 153 _CRTIMP double __cdecl exp (double);
 154 _CRTIMP double __cdecl log (double);
 155 _CRTIMP double __cdecl log10 (double);
 156 _CRTIMP double __cdecl pow (double, double);
 157 _CRTIMP double __cdecl sqrt (double);
 158 _CRTIMP double __cdecl ceil (double);
 159 _CRTIMP double __cdecl floor (double);
 160 _CRTIMP double __cdecl fabs (double);
 161 _CRTIMP double __cdecl ldexp (double, int);
 162 _CRTIMP double __cdecl frexp (double, int*);
 163 _CRTIMP double __cdecl modf (double, double*);
 164 _CRTIMP double __cdecl fmod (double, double);
 165
 166 /* Excess precision when using a 64-bit mantissa for FPU math ops can
 167    cause unexpected results with some of the MSVCRT math functions.  For
 168    example, unless the function return value is stored (truncating to
 169    53-bit mantissa), calls to pow with both x and y as integral values
 170    sometimes produce a non-integral result.
 171    One workaround is to reset the FPU env to 53-bit mantissa
 172    by a call to fesetenv (FE_PC53_ENV).  Amother is to force storage
 173    of the return value of individual math functions using wrappers.
 174    NB, using these wrappers will disable builtin math functions and
 175    hence disable the folding of function results at compile time when
 176    arguments are constant.  */
 177
 178 #if 0
 179 #define __DEFINE_FLOAT_STORE_MATHFN_D1(fn1)     \
 180 static __inline__ double                        \
 181 __float_store_ ## fn1 (double x)                \
 182 {                                               \
 183    __volatile__ double res = (fn1) (x);         \
 184   return res;                                   \
 185 }
 186
 187 #define __DEFINE_FLOAT_STORE_MATHFN_D2(fn2)     \
 188 static __inline__ double                        \
 189 __float_store_ ## fn2 (double x, double y)      \
 190 {                                               \
 191   __volatile__ double res = (fn2) (x, y);       \
 192   return res;                                   \
 193 }
 194 #endif
 195
 196 /* For example, here is how to force the result of the pow function
 197    to be stored:   */
 198 #if 0
 199 #undef pow
 200 /* Define the ___float_store_pow function and use it instead of pow().  */
 201 __DEFINE_FLOAT_STORE_MATHFN_D2 (pow)
 202 #define pow __float_store_pow
 203 #endif
 204
 205 #ifndef __STRICT_ANSI__
 206
 207 /* Complex number (for _cabs). This is the MS version. The ISO
 208    C99 counterpart _Complex is an intrinsic type in GCC and
 209    'complex' is defined as a macro.  See complex.h  */
 210 struct _complex
 211 {
 212         double  x;      /* Real part */
 213         double  y;      /* Imaginary part */
 214 };
 215
 216 _CRTIMP double __cdecl _cabs (struct _complex);
 217
 218 _CRTIMP double __cdecl _hypot (double, double);
 219 _CRTIMP double __cdecl _j0 (double);
 220 _CRTIMP double __cdecl _j1 (double);
 221 _CRTIMP double __cdecl _jn (int, double);
 222 _CRTIMP double __cdecl _y0 (double);
 223 _CRTIMP double __cdecl _y1 (double);
 224 _CRTIMP double __cdecl _yn (int, double);
 225 _CRTIMP int __cdecl _matherr (struct _exception *);
 226
 227 /* These are also declared in Mingw float.h; needed here as well to work
 228    around GCC build issues.  */
 229 /* BEGIN FLOAT.H COPY */
 230 /*
 231  * IEEE recommended functions
 232  */
 233
 234 _CRTIMP double __cdecl _chgsign (double);
 235 _CRTIMP double __cdecl _copysign (double, double);
 236 _CRTIMP double __cdecl _logb (double);
 237 _CRTIMP double __cdecl _nextafter (double, double);
 238 _CRTIMP double __cdecl _scalb (double, long);
 239
 240 _CRTIMP int __cdecl _finite (double);
 241 _CRTIMP int __cdecl _fpclass (double);
 242 _CRTIMP int __cdecl _isnan (double);
 243
 244 /* END FLOAT.H COPY */
 245
 246
 247 /*
 248  * Non-underscored versions of non-ANSI functions.
 249  * These reside in liboldnames.a.
 250  */
 251
 252 #if !defined (_NO_OLDNAMES)
 253
 254 _CRTIMP double __cdecl j0 (double);
 255 _CRTIMP double __cdecl j1 (double);
 256 _CRTIMP double __cdecl jn (int, double);
 257 _CRTIMP double __cdecl y0 (double);
 258 _CRTIMP double __cdecl y1 (double);
 259 _CRTIMP double __cdecl yn (int, double);
 260
 261 _CRTIMP double __cdecl chgsign (double);
 262 _CRTIMP double __cdecl scalb (double, long);
 263 _CRTIMP int __cdecl finite (double);
 264 _CRTIMP int __cdecl fpclass (double);
 265
 266 #define FP_SNAN    _FPCLASS_SNAN
 267 #define FP_QNAN    _FPCLASS_QNAN
 268 #define FP_NINF    _FPCLASS_NINF
 269 #define FP_PINF    _FPCLASS_PINF
 270 #define FP_NDENORM _FPCLASS_ND
 271 #define FP_PDENORM _FPCLASS_PD
 272 #define FP_NZERO   _FPCLASS_NZ
 273 #define FP_PZERO   _FPCLASS_PZ
 274 #define FP_NNORM   _FPCLASS_NN
 275 #define FP_PNORM   _FPCLASS_PN
 276
 277 #endif /* Not _NO_OLDNAMES */
 278
 279 /* This require msvcr70.dll or higher. */
 280 #if __MSVCRT_VERSION__ >= 0x0700
 281 _CRTIMP int __cdecl _set_SSE2_enable (int);
 282 #endif /* __MSVCRT_VERSION__ >= 0x0700 */
 283
 284
 285 #endif /* __STRICT_ANSI__ */
 286
 287
 288 #ifndef __NO_ISOCEXT
 289 #if (defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L) \
 290         || !defined __STRICT_ANSI__ || defined __cplusplus
 291
 292 #if __MINGW_GNUC_PREREQ(3, 3)
 293 #define HUGE_VALF       __builtin_huge_valf()
 294 #define HUGE_VALL       __builtin_huge_vall()
 295 #define INFINITY        __builtin_inf()
 296 #define NAN             __builtin_nan("")
 297 #else
 298 extern const float __INFF;
 299 #define HUGE_VALF __INFF
 300 extern const long double  __INFL;
 301 #define HUGE_VALL __INFL
 302 #define INFINITY HUGE_VALF
 303 extern const double __QNAN;
 304 #define NAN __QNAN
 305 #endif /* __MINGW_GNUC_PREREQ(3, 3) */
 306
 307 /* 7.12.3.1 */
 308 /*
 309    Return values for fpclassify.
 310    These are based on Intel x87 fpu condition codes
 311    in the high byte of status word and differ from
 312    the return values for MS IEEE 754 extension _fpclass()
 313 */
 314 #define FP_NAN          0x0100
 315 #define FP_NORMAL       0x0400
 316 #define FP_INFINITE     (FP_NAN | FP_NORMAL)
 317 #define FP_ZERO         0x4000
 318 #define FP_SUBNORMAL    (FP_NORMAL | FP_ZERO)
 319 /* 0x0200 is signbit mask */
 320
 321
 322 /*
 323   We can't inline float or double, because we want to ensure truncation
 324   to semantic type before classification.
 325   (A normal long double value might become subnormal when
 326   converted to double, and zero when converted to float.)
 327 */
 328
 329 extern int __cdecl __fpclassifyf (float);
 330 extern int __cdecl __fpclassify (double);
 331
 332 __CRT_INLINE int __cdecl __fpclassifyl (long double x){
 333   unsigned short sw;
 334   __asm__ ("fxam; fstsw %%ax;" : "=a" (sw): "t" (x));
 335   return sw & (FP_NAN | FP_NORMAL | FP_ZERO );
 336 }
 337
 338 #define fpclassify(x) (sizeof (x) == sizeof (float) ? __fpclassifyf (x)   \
 339                        : sizeof (x) == sizeof (double) ? __fpclassify (x) \
 340                        : __fpclassifyl (x))
 341
 342 /* 7.12.3.2 */
 343 #define isfinite(x) ((fpclassify(x) & FP_NAN) == 0)
 344
 345 /* 7.12.3.3 */
 346 #define isinf(x) (fpclassify(x) == FP_INFINITE)
 347
 348 /* 7.12.3.4 */
 349 /* We don't need to worry about trucation here:
 350    A NaN stays a NaN. */
 351
 352 __CRT_INLINE int __cdecl __isnan (double _x)
 353 {
 354   unsigned short sw;
 355   __asm__ ("fxam;"
 356            "fstsw %%ax": "=a" (sw) : "t" (_x));
 357   return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
 358     == FP_NAN;
 359 }
 360
 361 __CRT_INLINE int __cdecl __isnanf (float _x)
 362 {
 363   unsigned short sw;
 364   __asm__ ("fxam;"
 365             "fstsw %%ax": "=a" (sw) : "t" (_x));
 366   return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
 367     == FP_NAN;
 368 }
 369
 370 __CRT_INLINE int __cdecl __isnanl (long double _x)
 371 {
 372   unsigned short sw;
 373   __asm__ ("fxam;"
 374             "fstsw %%ax": "=a" (sw) : "t" (_x));
 375   return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
 376     == FP_NAN;
 377 }
 378
 379
 380 #define isnan(x) (sizeof (x) == sizeof (float) ? __isnanf (x)   \
 381                   : sizeof (x) == sizeof (double) ? __isnan (x) \
 382                   : __isnanl (x))
 383
 384 /* 7.12.3.5 */
 385 #define isnormal(x) (fpclassify(x) == FP_NORMAL)
 386
 387 /* 7.12.3.6 The signbit macro */
 388 __CRT_INLINE int __cdecl __signbit (double x) {
 389   unsigned short stw;
 390   __asm__ ( "fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
 391   return (stw & 0x0200) != 0;
 392 }
 393
 394 __CRT_INLINE int __cdecl __signbitf (float x) {
 395   unsigned short stw;
 396   __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
 397   return (stw & 0x0200) != 0;
 398 }
 399
 400 __CRT_INLINE int __cdecl __signbitl (long double x) {
 401   unsigned short stw;
 402   __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
 403   return (stw & 0x0200) != 0;
 404 }
 405
 406 #define signbit(x) (sizeof (x) == sizeof (float) ? __signbitf (x)       \
 407                     : sizeof (x) == sizeof (double) ? __signbit (x)     \
 408                     : __signbitl (x))
 409
 410 /* 7.12.4 Trigonometric functions: Double in C89 */
 411 extern float __cdecl sinf (float);
 412 extern long double __cdecl sinl (long double);
 413
 414 extern float __cdecl cosf (float);
 415 extern long double __cdecl cosl (long double);
 416
 417 extern float __cdecl tanf (float);
 418 extern long double __cdecl tanl (long double);
 419
 420 extern float __cdecl asinf (float);
 421 extern long double __cdecl asinl (long double);
 422
 423 extern float __cdecl acosf (float);
 424 extern long double __cdecl acosl (long double);
 425
 426 extern float __cdecl atanf (float);
 427 extern long double __cdecl atanl (long double);
 428
 429 extern float __cdecl atan2f (float, float);
 430 extern long double __cdecl atan2l (long double, long double);
 431
 432 /* 7.12.5 Hyperbolic functions: Double in C89  */
 433 __CRT_INLINE float __cdecl sinhf (float x)
 434   {return (float) sinh (x);}
 435 extern long double __cdecl sinhl (long double);
 436
 437 __CRT_INLINE float __cdecl coshf (float x)
 438   {return (float) cosh (x);}
 439 extern long double __cdecl coshl (long double);
 440
 441 __CRT_INLINE float __cdecl tanhf (float x)
 442   {return (float) tanh (x);}
 443 extern long double __cdecl tanhl (long double);
 444
 445 /* Inverse hyperbolic trig functions  */
 446 /* 7.12.5.1 */
 447 extern double __cdecl acosh (double);
 448 extern float __cdecl acoshf (float);
 449 extern long double __cdecl acoshl (long double);
 450
 451 /* 7.12.5.2 */
 452 extern double __cdecl asinh (double);
 453 extern float __cdecl asinhf (float);
 454 extern long double __cdecl asinhl (long double);
 455
 456 /* 7.12.5.3 */
 457 extern double __cdecl atanh (double);
 458 extern float __cdecl atanf  (float);
 459 extern long double __cdecl atanhl (long double);
 460
 461 /* Exponentials and logarithms  */
 462 /* 7.12.6.1 Double in C89 */
 463 __CRT_INLINE float __cdecl expf (float x)
 464   {return (float) exp (x);}
 465 extern long double __cdecl expl (long double);
 466
 467 /* 7.12.6.2 */
 468 extern double __cdecl exp2(double);
 469 extern float __cdecl exp2f(float);
 470 extern long double __cdecl exp2l(long double);
 471
 472 /* 7.12.6.3 The expm1 functions */
 473 /* TODO: These could be inlined */
 474 extern double __cdecl expm1(double);
 475 extern float __cdecl expm1f(float);
 476 extern long double __cdecl expm1l(long double);
 477
 478 /* 7.12.6.4 Double in C89 */
 479 __CRT_INLINE float __cdecl frexpf (float x, int* expn)
 480   {return (float) frexp (x, expn);}
 481 extern long double __cdecl frexpl (long double, int*);
 482
 483 /* 7.12.6.5 */
 484 #define FP_ILOGB0 ((int)0x80000000)
 485 #define FP_ILOGBNAN ((int)0x80000000)
 486 extern int __cdecl ilogb (double);
 487 extern int __cdecl ilogbf (float);
 488 extern int __cdecl ilogbl (long double);
 489
 490 /* 7.12.6.6  Double in C89 */
 491 __CRT_INLINE float __cdecl ldexpf (float x, int expn)
 492   {return (float) ldexp (x, expn);}
 493 extern long double __cdecl ldexpl (long double, int);
 494
 495 /* 7.12.6.7 Double in C89 */
 496 extern float __cdecl logf (float);
 497 extern long double __cdecl logl (long double);
 498
 499 /* 7.12.6.8 Double in C89 */
 500 extern float __cdecl log10f (float);
 501 extern long double __cdecl log10l (long double);
 502
 503 /* 7.12.6.9 */
 504 extern double __cdecl log1p(double);
 505 extern float __cdecl log1pf(float);
 506 extern long double __cdecl log1pl(long double);
 507
 508 /* 7.12.6.10 */
 509 extern double __cdecl log2 (double);
 510 extern float __cdecl log2f (float);
 511 extern long double __cdecl log2l (long double);
 512
 513 /* 7.12.6.11 */
 514 extern double __cdecl logb (double);
 515 extern float __cdecl logbf (float);
 516 extern long double __cdecl logbl (long double);
 517
 518 /* Inline versions.  GCC-4.0+ can do a better fast-math optimization
 519    with __builtins. */
 520 #if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
 521 __CRT_INLINE double __cdecl logb (double x)
 522 {
 523   double res;
 524   __asm__ ("fxtract\n\t"
 525        "fstp    %%st" : "=t" (res) : "0" (x));
 526   return res;
 527 }
 528
 529 __CRT_INLINE float __cdecl logbf (float x)
 530 {
 531   float res;
 532   __asm__ ("fxtract\n\t"
 533        "fstp    %%st" : "=t" (res) : "0" (x));
 534   return res;
 535 }
 536
 537 __CRT_INLINE long double __cdecl logbl (long double x)
 538 {
 539   long double res;
 540   __asm__ ("fxtract\n\t"
 541        "fstp    %%st" : "=t" (res) : "0" (x));
 542   return res;
 543 }
 544 #endif /* !defined __FAST_MATH__ || !__MINGW_GNUC_PREREQ (4, 0) */
 545
 546 /* 7.12.6.12  Double in C89 */
 547 extern float __cdecl modff (float, float*);
 548 extern long double __cdecl modfl (long double, long double*);
 549
 550 /* 7.12.6.13 */
 551 extern double __cdecl scalbn (double, int);
 552 extern float __cdecl scalbnf (float, int);
 553 extern long double __cdecl scalbnl (long double, int);
 554
 555 extern double __cdecl scalbln (double, long);
 556 extern float __cdecl scalblnf (float, long);
 557 extern long double __cdecl scalblnl (long double, long);
 558
 559 /* 7.12.7.1 */
 560 /* Implementations adapted from Cephes versions */
 561 extern double __cdecl cbrt (double);
 562 extern float __cdecl cbrtf (float);
 563 extern long double __cdecl cbrtl (long double);
 564
 565 /* 7.12.7.2 The fabs functions: Double in C89 */
 566 extern  float __cdecl fabsf (float x);
 567 extern long double __cdecl fabsl (long double x);
 568
 569 /* 7.12.7.3  */
 570 extern double __cdecl hypot (double, double); /* in libmoldname.a */
 571 __CRT_INLINE float __cdecl hypotf (float x, float y)
 572   { return (float) hypot (x, y);}
 573 extern long double __cdecl hypotl (long double, long double);
 574
 575 /* 7.12.7.4 The pow functions. Double in C89 */
 576 __CRT_INLINE float __cdecl powf (float x, float y)
 577   {return (float) pow (x, y);}
 578 extern long double __cdecl powl (long double, long double);
 579
 580 /* 7.12.7.5 The sqrt functions. Double in C89. */
 581 extern float __cdecl sqrtf (float);
 582 extern long double __cdecl sqrtl (long double);
 583
 584 /* 7.12.8.1 The erf functions  */
 585 extern double __cdecl erf (double);
 586 extern float __cdecl erff (float);
 587 extern long double __cdecl erfl (long double);
 588
 589 /* 7.12.8.2 The erfc functions  */
 590 extern double __cdecl erfc (double);
 591 extern float __cdecl erfcf (float);
 592 extern long double __cdecl erfcl (long double);
 593
 594 /* 7.12.8.3 The lgamma functions */
 595 extern double __cdecl lgamma (double);
 596 extern float __cdecl lgammaf (float);
 597 extern long double __cdecl lgammal (long double);
 598
 599 /* 7.12.8.4 The tgamma functions */
 600 extern double __cdecl tgamma (double);
 601 extern float __cdecl tgammaf (float);
 602 extern long double __cdecl tgammal (long double);
 603
 604 /* 7.12.9.1 Double in C89 */
 605 extern float __cdecl ceilf (float);
 606 extern long double __cdecl ceill (long double);
 607
 608 /* 7.12.9.2 Double in C89 */
 609 extern float __cdecl floorf (float);
 610 extern long double __cdecl floorl (long double);
 611
 612 /* 7.12.9.3 */
 613 extern double __cdecl nearbyint ( double);
 614 extern float __cdecl nearbyintf (float);
 615 extern long double __cdecl nearbyintl (long double);
 616
 617 /* 7.12.9.4 */
 618 /* round, using fpu control word settings */
 619 extern double __cdecl rint (double);
 620 extern float __cdecl rintf (float);
 621 extern long double __cdecl rintl (long double);
 622
 623 /* 7.12.9.5 */
 624 extern long __cdecl lrint (double);
 625 extern long __cdecl lrintf (float);
 626 extern long __cdecl lrintl (long double);
 627
 628 extern long long __cdecl llrint (double);
 629 extern long long __cdecl llrintf (float);
 630 extern long long __cdecl llrintl (long double);
 631
 632 /* Inline versions of above.
 633    GCC 4.0+ can do a better fast-math job with __builtins. */
 634 #if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
 635 __CRT_INLINE double __cdecl rint (double x)
 636 {
 637   double retval;
 638   __asm__ ("frndint;": "=t" (retval) : "0" (x));
 639   return retval;
 640 }
 641
 642 __CRT_INLINE float __cdecl rintf (float x)
 643 {
 644   float retval;
 645   __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
 646   return retval;
 647 }
 648
 649 __CRT_INLINE long double __cdecl rintl (long double x)
 650 {
 651   long double retval;
 652   __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
 653   return retval;
 654 }
 655
 656 __CRT_INLINE long __cdecl lrint (double x)
 657 {
 658   long retval;
 659   __asm__ __volatile__
 660     ("fistpl %0"  : "=m" (retval) : "t" (x) : "st");
 661   return retval;
 662 }
 663
 664 __CRT_INLINE long __cdecl lrintf (float x)
 665 {
 666   long retval;
 667   __asm__ __volatile__
 668     ("fistpl %0"  : "=m" (retval) : "t" (x) : "st");
 669   return retval;
 670 }
 671
 672 __CRT_INLINE long __cdecl lrintl (long double x)
 673 {
 674   long retval;
 675   __asm__ __volatile__
 676     ("fistpl %0"  : "=m" (retval) : "t" (x) : "st");
 677   return retval;
 678 }
 679
 680 __CRT_INLINE long long __cdecl llrint (double x)
 681 {
 682   long long retval;
 683   __asm__ __volatile__
 684     ("fistpll %0"  : "=m" (retval) : "t" (x) : "st");
 685   return retval;
 686 }
 687
 688 __CRT_INLINE long long __cdecl llrintf (float x)
 689 {
 690   long long retval;
 691   __asm__ __volatile__
 692     ("fistpll %0"  : "=m" (retval) : "t" (x) : "st");
 693   return retval;
 694 }
 695
 696 __CRT_INLINE long long __cdecl llrintl (long double x)
 697 {
 698   long long retval;
 699   __asm__ __volatile__
 700     ("fistpll %0"  : "=m" (retval) : "t" (x) : "st");
 701   return retval;
 702 }
 703 #endif /* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4,0)  */
 704
 705 /* 7.12.9.6 */
 706 /* round away from zero, regardless of fpu control word settings */
 707 extern double __cdecl round (double);
 708 extern float __cdecl roundf (float);
 709 extern long double __cdecl roundl (long double);
 710
 711 /* 7.12.9.7  */
 712 extern long __cdecl lround (double);
 713 extern long __cdecl lroundf (float);
 714 extern long __cdecl lroundl (long double);
 715
 716 extern long long __cdecl llround (double);
 717 extern long long __cdecl llroundf (float);
 718 extern long long __cdecl llroundl (long double);
 719
 720 /* 7.12.9.8 */
 721 /* round towards zero, regardless of fpu control word settings */
 722 extern double __cdecl trunc (double);
 723 extern float __cdecl truncf (float);
 724 extern long double __cdecl truncl (long double);
 725
 726 /* 7.12.10.1 Double in C89 */
 727 extern float __cdecl fmodf (float, float);
 728 extern long double __cdecl fmodl (long double, long double);
 729
 730 /* 7.12.10.2 */
 731 extern double __cdecl remainder (double, double);
 732 extern float __cdecl remainderf (float, float);
 733 extern long double __cdecl remainderl (long double, long double);
 734
 735 /* 7.12.10.3 */
 736 extern double __cdecl remquo(double, double, int *);
 737 extern float __cdecl remquof(float, float, int *);
 738 extern long double __cdecl remquol(long double, long double, int *);
 739
 740 /* 7.12.11.1 */
 741 extern double __cdecl copysign (double, double); /* in libmoldname.a */
 742 extern float __cdecl copysignf (float, float);
 743 extern long double __cdecl copysignl (long double, long double);
 744
 745 /* 7.12.11.2 Return a NaN */
 746 extern double __cdecl nan(const char *tagp);
 747 extern float __cdecl nanf(const char *tagp);
 748 extern long double __cdecl nanl(const char *tagp);
 749
 750 #ifndef __STRICT_ANSI__
 751 #define _nan() nan("")
 752 #define _nanf() nanf("")
 753 #define _nanl() nanl("")
 754 #endif
 755
 756 /* 7.12.11.3 */
 757 extern double __cdecl nextafter (double, double); /* in libmoldname.a */
 758 extern float __cdecl nextafterf (float, float);
 759 extern long double __cdecl nextafterl (long double, long double);
 760
 761 /* 7.12.11.4 The nexttoward functions */
 762 extern double __cdecl nexttoward (double,  long double);
 763 extern float __cdecl nexttowardf (float,  long double);
 764 extern long double __cdecl nexttowardl (long double, long double);
 765
 766 /* 7.12.12.1 */
 767 /*  x > y ? (x - y) : 0.0  */
 768 extern double __cdecl fdim (double x, double y);
 769 extern float __cdecl fdimf (float x, float y);
 770 extern long double __cdecl fdiml (long double x, long double y);
 771
 772 /* fmax and fmin.
 773    NaN arguments are treated as missing data: if one argument is a NaN
 774    and the other numeric, then these functions choose the numeric
 775    value. */
 776
 777 /* 7.12.12.2 */
 778 extern double __cdecl fmax  (double, double);
 779 extern float __cdecl fmaxf (float, float);
 780 extern long double __cdecl fmaxl (long double, long double);
 781
 782 /* 7.12.12.3 */
 783 extern double __cdecl fmin (double, double);
 784 extern float __cdecl fminf (float, float);
 785 extern long double __cdecl fminl (long double, long double);
 786
 787 /* 7.12.13.1 */
 788 /* return x * y + z as a ternary op */
 789 extern double __cdecl fma (double, double, double);
 790 extern float __cdecl fmaf (float, float, float);
 791 extern long double __cdecl fmal (long double, long double, long double);
 792
 793
 794 /* 7.12.14 */
 795 /*
 796  *  With these functions, comparisons involving quiet NaNs set the FP
 797  *  condition code to "unordered".  The IEEE floating-point spec
 798  *  dictates that the result of floating-point comparisons should be
 799  *  false whenever a NaN is involved, with the exception of the != op,
 800  *  which always returns true: yes, (NaN != NaN) is true).
 801  */
 802
 803 #if __GNUC__ >= 3
 804
 805 #define isgreater(x, y) __builtin_isgreater(x, y)
 806 #define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
 807 #define isless(x, y) __builtin_isless(x, y)
 808 #define islessequal(x, y) __builtin_islessequal(x, y)
 809 #define islessgreater(x, y) __builtin_islessgreater(x, y)
 810 #define isunordered(x, y) __builtin_isunordered(x, y)
 811
 812 #else
 813 /*  helper  */
 814 __CRT_INLINE int  __cdecl
 815 __fp_unordered_compare (long double x, long double y){
 816   unsigned short retval;
 817   __asm__ ("fucom %%st(1);"
 818            "fnstsw;": "=a" (retval) : "t" (x), "u" (y));
 819   return retval;
 820 }
 821
 822 #define isgreater(x, y) ((__fp_unordered_compare(x, y) \
 823                            & 0x4500) == 0)
 824 #define isless(x, y) ((__fp_unordered_compare (y, x) \
 825                        & 0x4500) == 0)
 826 #define isgreaterequal(x, y) ((__fp_unordered_compare (x, y) \
 827                                & FP_INFINITE) == 0)
 828 #define islessequal(x, y) ((__fp_unordered_compare(y, x) \
 829                             & FP_INFINITE) == 0)
 830 #define islessgreater(x, y) ((__fp_unordered_compare(x, y) \
 831                               & FP_SUBNORMAL) == 0)
 832 #define isunordered(x, y) ((__fp_unordered_compare(x, y) \
 833                             & 0x4500) == 0x4500)
 834
 835 #endif
 836
 837
 838 #endif /* __STDC_VERSION__ >= 199901L */
 839 #endif /* __NO_ISOCEXT */
 840
 841
 842 #ifdef __cplusplus
 843 }
 844 #endif
 845 #endif  /* Not RC_INVOKED */
 846
 847
 848 #endif  /* Not _MATH_H_ */