source: Daodan/MinGW/include/math.h@ 1122

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1/*
2 * math.h
3 *
4 * ANSI/POSIX + Microsoft compatible mathematical function prototypes,
5 * associated macros, and manifest constant definitions.
6 *
7 * $Id: math.h,v c96797f9657b 2016/04/12 14:36:20 keithmarshall $
8 *
9 * Written by Colin Peters <colin@bird.fu.is.saga-u.ac.jp>
10 * Copyright (C) 1997-2009, 2014-2016, MinGW.org Project.
11 *
12 *
13 * Permission is hereby granted, free of charge, to any person obtaining a
14 * copy of this software and associated documentation files (the "Software"),
15 * to deal in the Software without restriction, including without limitation
16 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
17 * and/or sell copies of the Software, and to permit persons to whom the
18 * Software is furnished to do so, subject to the following conditions:
19 *
20 * The above copyright notice, this permission notice, and the following
21 * disclaimer shall be included in all copies or substantial portions of
22 * the Software.
23 *
24 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
25 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
26 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
27 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
28 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
29 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OF OR OTHER
30 * DEALINGS IN THE SOFTWARE.
31 *
32 */
33#ifndef _MATH_H
34#define _MATH_H
35#pragma GCC system_header
36
37/* All the headers include this file.
38 */
39#include <_mingw.h>
40
41/* Types for the _exception structure.
42 */
43#define _DOMAIN 1 /* domain error in argument */
44#define _SING 2 /* singularity */
45#define _OVERFLOW 3 /* range overflow */
46#define _UNDERFLOW 4 /* range underflow */
47#define _TLOSS 5 /* total loss of precision */
48#define _PLOSS 6 /* partial loss of precision */
49
50#if ! defined __STRICT_ANSI__ && ! defined _NO_OLDNAMES
51/*
52 * Exception types with non-ANSI names for compatibility.
53 */
54#define DOMAIN _DOMAIN
55#define SING _SING
56#define OVERFLOW _OVERFLOW
57#define UNDERFLOW _UNDERFLOW
58#define TLOSS _TLOSS
59#define PLOSS _PLOSS
60
61#endif /* !__STRICT_ANSI__ && !_NO_OLDNAMES */
62
63
64#if _POSIX_C_SOURCE || defined _USE_MATH_DEFINES
65/* Traditional/XOPEN math constants (double precison). MSVC makes these
66 * available, only if _USE_MATH_DEFINES is specified; POSIX does so also,
67 * when _POSIX_C_SOURCE is defined and non-zero, (as will be the case by
68 * default in MinGW, unless __STRICT_ANSI__ checking is in effect).
69 */
70#define M_E 2.7182818284590452354
71#define M_LOG2E 1.4426950408889634074
72#define M_LOG10E 0.43429448190325182765
73#define M_LN2 0.69314718055994530942
74#define M_LN10 2.30258509299404568402
75#define M_PI 3.14159265358979323846
76#define M_PI_2 1.57079632679489661923
77#define M_PI_4 0.78539816339744830962
78#define M_1_PI 0.31830988618379067154
79#define M_2_PI 0.63661977236758134308
80#define M_2_SQRTPI 1.12837916709551257390
81#define M_SQRT2 1.41421356237309504880
82#define M_SQRT1_2 0.70710678118654752440
83#endif
84
85/* These are also defined in MinGW float.h; needed here as well,
86 * to work around GCC build issues.
87 *
88 * FIXME: Since they're needed both in MinGW float.h and here,
89 * they should be moved to a common "parts" header.
90 */
91#if ! defined __STRICT_ANSI__ && ! defined __MINGW_FPCLASS_DEFINED
92#define __MINGW_FPCLASS_DEFINED 1
93
94/* IEEE 754 classication
95 */
96#define _FPCLASS_SNAN 0x0001 /* Signaling "Not a Number" */
97#define _FPCLASS_QNAN 0x0002 /* Quiet "Not a Number" */
98#define _FPCLASS_NINF 0x0004 /* Negative Infinity */
99#define _FPCLASS_NN 0x0008 /* Negative Normal */
100#define _FPCLASS_ND 0x0010 /* Negative Denormal */
101#define _FPCLASS_NZ 0x0020 /* Negative Zero */
102#define _FPCLASS_PZ 0x0040 /* Positive Zero */
103#define _FPCLASS_PD 0x0080 /* Positive Denormal */
104#define _FPCLASS_PN 0x0100 /* Positive Normal */
105#define _FPCLASS_PINF 0x0200 /* Positive Infinity */
106
107#endif /* !__STRICT_ANSI__ && !__MINGW_FPCLASS_DEFINED */
108
109#ifndef RC_INVOKED
110
111_BEGIN_C_DECLS
112
113/* HUGE_VAL is returned by strtod when the value would overflow the
114 * representation of 'double'. There are other uses as well.
115 *
116 * __imp__HUGE is a pointer to the actual variable _HUGE in
117 * MSVCRT.DLL. If we used _HUGE directly we would get a pointer
118 * to a thunk function.
119 *
120 * NOTE: The CRTDLL version uses _HUGE_dll instead.
121 */
122#if __MINGW_GNUC_PREREQ(3, 3)
123#define HUGE_VAL __builtin_huge_val()
124
125#else
126#ifndef __DECLSPEC_SUPPORTED
127
128#ifdef __MSVCRT__
129extern double *_imp___HUGE;
130#define HUGE_VAL (*_imp___HUGE)
131
132#else /* CRTDLL */
133extern double *_imp___HUGE_dll;
134#define HUGE_VAL (*_imp___HUGE_dll)
135#endif
136
137#else /* __DECLSPEC_SUPPORTED */
138
139#ifdef __MSVCRT__
140__MINGW_IMPORT double _HUGE;
141#define HUGE_VAL _HUGE
142
143#else /* CRTDLL */
144__MINGW_IMPORT double _HUGE_dll;
145#define HUGE_VAL _HUGE_dll
146#endif
147
148#endif /* __DECLSPEC_SUPPORTED */
149#endif /* __MINGW_GNUC_PREREQ(3, 3) */
150
151struct _exception
152{
153 int type;
154 char *name;
155 double arg1;
156 double arg2;
157 double retval;
158};
159
160_CRTIMP double __cdecl sin (double);
161_CRTIMP double __cdecl cos (double);
162_CRTIMP double __cdecl tan (double);
163_CRTIMP double __cdecl sinh (double);
164_CRTIMP double __cdecl cosh (double);
165_CRTIMP double __cdecl tanh (double);
166_CRTIMP double __cdecl asin (double);
167_CRTIMP double __cdecl acos (double);
168_CRTIMP double __cdecl atan (double);
169_CRTIMP double __cdecl atan2 (double, double);
170_CRTIMP double __cdecl exp (double);
171_CRTIMP double __cdecl log (double);
172_CRTIMP double __cdecl log10 (double);
173_CRTIMP double __cdecl pow (double, double);
174_CRTIMP double __cdecl sqrt (double);
175_CRTIMP double __cdecl ceil (double);
176_CRTIMP double __cdecl floor (double);
177_CRTIMP double __cdecl fabs (double);
178_CRTIMP double __cdecl ldexp (double, int);
179_CRTIMP double __cdecl frexp (double, int*);
180_CRTIMP double __cdecl modf (double, double*);
181_CRTIMP double __cdecl fmod (double, double);
182
183#if 0
184/* Excess precision when using a 64-bit mantissa for FPU math ops can
185 * cause unexpected results with some of the MSVCRT math functions. For
186 * example, unless the function return value is stored (truncating to
187 * 53-bit mantissa), calls to pow with both x and y as integral values
188 * sometimes produce a non-integral result.
189 *
190 * One workaround is to reset the FPU env to 53-bit mantissa
191 * by a call to fesetenv (FE_PC53_ENV). Amother is to force storage
192 * of the return value of individual math functions using wrappers.
193 * NB, using these wrappers will disable builtin math functions and
194 * hence disable the folding of function results at compile time when
195 * arguments are constant.
196 */
197#define __DEFINE_FLOAT_STORE_MATHFN_D1(fn1) \
198static __inline__ double \
199__float_store_ ## fn1 (double x) \
200{ \
201 __volatile__ double res = (fn1) (x); \
202 return res; \
203}
204
205#define __DEFINE_FLOAT_STORE_MATHFN_D2(fn2) \
206static __inline__ double \
207__float_store_ ## fn2 (double x, double y) \
208{ \
209 __volatile__ double res = (fn2) (x, y); \
210 return res; \
211}
212
213/* For example, here is how to force the result of the pow function
214 * to be stored:
215 */
216#undef pow
217/* Define the ___float_store_pow function and use it instead of pow().
218 */
219__DEFINE_FLOAT_STORE_MATHFN_D2 (pow)
220#define pow __float_store_pow
221#endif
222
223#ifndef __STRICT_ANSI__
224
225struct _complex
226{ /* Complex number (for _cabs). This is the MS version; the
227 * ISO-C99 counterpart, _Complex, is an intrinsic type in GCC,
228 * and 'complex' is defined as a macro. See <complex.h>
229 */
230 double x; /* Real part */
231 double y; /* Imaginary part */
232};
233
234_CRTIMP double __cdecl _cabs (struct _complex);
235
236_CRTIMP double __cdecl _hypot (double, double);
237_CRTIMP double __cdecl _j0 (double);
238_CRTIMP double __cdecl _j1 (double);
239_CRTIMP double __cdecl _jn (int, double);
240_CRTIMP double __cdecl _y0 (double);
241_CRTIMP double __cdecl _y1 (double);
242_CRTIMP double __cdecl _yn (int, double);
243_CRTIMP int __cdecl _matherr (struct _exception *);
244
245/* These are also declared in MinGW's <float.h>; we need them
246 * here as well to work around GCC build issues.
247 */
248/* BEGIN FLOAT.H COPY */
249/*
250 * IEEE recommended functions
251 */
252_CRTIMP double __cdecl _chgsign (double);
253_CRTIMP double __cdecl _copysign (double, double);
254_CRTIMP double __cdecl _logb (double);
255_CRTIMP double __cdecl _nextafter (double, double);
256_CRTIMP double __cdecl _scalb (double, long);
257
258_CRTIMP int __cdecl _finite (double);
259_CRTIMP int __cdecl _fpclass (double);
260_CRTIMP int __cdecl _isnan (double);
261
262/* END FLOAT.H COPY */
263
264
265#ifndef _NO_OLDNAMES
266/* Non-underscored versions of non-ANSI functions.
267 * These reside in liboldnames.a.
268 */
269_CRTIMP double __cdecl j0 (double);
270_CRTIMP double __cdecl j1 (double);
271_CRTIMP double __cdecl jn (int, double);
272_CRTIMP double __cdecl y0 (double);
273_CRTIMP double __cdecl y1 (double);
274_CRTIMP double __cdecl yn (int, double);
275
276_CRTIMP double __cdecl chgsign (double);
277/*
278 * scalb() is a GCC built-in.
279 * Exclude this _scalb() stub; the semantics are incompatible
280 * with the built-in implementation.
281 *
282_CRTIMP double __cdecl scalb (double, long);
283 *
284 */
285_CRTIMP int __cdecl finite (double);
286_CRTIMP int __cdecl fpclass (double);
287
288#define FP_SNAN _FPCLASS_SNAN
289#define FP_QNAN _FPCLASS_QNAN
290#define FP_NINF _FPCLASS_NINF
291#define FP_PINF _FPCLASS_PINF
292#define FP_NDENORM _FPCLASS_ND
293#define FP_PDENORM _FPCLASS_PD
294#define FP_NZERO _FPCLASS_NZ
295#define FP_PZERO _FPCLASS_PZ
296#define FP_NNORM _FPCLASS_NN
297#define FP_PNORM _FPCLASS_PN
298
299#endif /* !_NO_OLDNAMES */
300
301#if _WIN32_WINNT >= _WIN32_WINNT_WINXP || __MSVCRT_VERSION__ >= __MSVCR70_DLL
302/*
303 * This requires WinXP, or MSVCR70.DLL, or later.
304 */
305_CRTIMP int __cdecl _set_SSE2_enable (int);
306
307#endif /* >= WINXP || >= __MSVCR70_DLL */
308#endif /* !__STRICT_ANSI__ */
309
310#if defined __cplusplus || defined _ISOC99_SOURCE
311
312# if __MINGW_GNUC_PREREQ(3, 3)
313# define HUGE_VALF __builtin_huge_valf()
314# define HUGE_VALL __builtin_huge_vall()
315# define INFINITY __builtin_inf()
316# define NAN __builtin_nan("")
317# else
318 extern const float __INFF;
319 extern const long double __INFL;
320 extern const double __QNAN;
321
322# define HUGE_VALF __INFF
323# define HUGE_VALL __INFL
324# define INFINITY HUGE_VALF
325# define NAN __QNAN
326
327# endif /* __MINGW_GNUC_PREREQ(3, 3) */
328
329#ifdef __FLT_EVAL_METHOD__
330/* Use the compiler's builtin definition for FLT_EVAL_METHOD
331 * to establish appropriate float_t and double_t typedefs.
332 */
333# if __FLT_EVAL_METHOD__ == 0
334 typedef float float_t;
335 typedef double double_t;
336
337# elif __FLT_EVAL_METHOD__ == 1
338 typedef double float_t;
339 typedef double double_t;
340
341# elif __FLT_EVAL_METHOD__ == 2
342 typedef long double float_t;
343 typedef long double double_t;
344
345# endif
346#else
347 /* ix87 FPU default
348 */
349 typedef long double float_t;
350 typedef long double double_t;
351#endif
352
353/* 7.12.3.1
354 * Return values for fpclassify.
355 * These are based on Intel x87 fpu condition codes
356 * in the high byte of status word and differ from
357 * the return values for MS IEEE 754 extension _fpclass()
358 */
359#define FP_NAN 0x0100
360#define FP_NORMAL 0x0400
361#define FP_INFINITE (FP_NAN | FP_NORMAL)
362#define FP_ZERO 0x4000
363#define FP_SUBNORMAL (FP_NORMAL | FP_ZERO)
364/* 0x0200 is signbit mask */
365
366/* We can't inline float or double, because we want to ensure
367 * truncation to semantic type before classification; (a normal
368 * long double value might become subnormal when converted to
369 * double, and zero when converted to float.)
370 */
371extern int __cdecl __fpclassifyf (float);
372extern int __cdecl __fpclassify (double);
373extern int __cdecl __fpclassifyl (long double);
374
375#ifndef __NO_INLINE__
376__CRT_INLINE int __cdecl __fpclassifyl (long double x){
377 unsigned short sw;
378 __asm__ ("fxam; fstsw %%ax;" : "=a" (sw): "t" (x));
379 return sw & (FP_NAN | FP_NORMAL | FP_ZERO );
380}
381#endif
382
383#define fpclassify(x) (sizeof (x) == sizeof (float) ? __fpclassifyf (x) \
384 : sizeof (x) == sizeof (double) ? __fpclassify (x) \
385 : __fpclassifyl (x))
386
387/* 7.12.3.2 */
388#define isfinite(x) ((fpclassify(x) & FP_NAN) == 0)
389
390/* 7.12.3.3 */
391#define isinf(x) (fpclassify(x) == FP_INFINITE)
392
393/* 7.12.3.4 */
394/* We don't need to worry about truncation here:
395 * a NaN stays a NaN.
396 */
397extern int __cdecl __isnan (double);
398extern int __cdecl __isnanf (float);
399extern int __cdecl __isnanl (long double);
400#ifndef __NO_INLINE__
401__CRT_INLINE int __cdecl __isnan (double _x)
402{
403 unsigned short sw;
404 __asm__ ("fxam;"
405 "fstsw %%ax": "=a" (sw) : "t" (_x));
406 return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
407 == FP_NAN;
408}
409
410__CRT_INLINE int __cdecl __isnanf (float _x)
411{
412 unsigned short sw;
413 __asm__ ("fxam;"
414 "fstsw %%ax": "=a" (sw) : "t" (_x));
415 return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
416 == FP_NAN;
417}
418
419__CRT_INLINE int __cdecl __isnanl (long double _x)
420{
421 unsigned short sw;
422 __asm__ ("fxam;"
423 "fstsw %%ax": "=a" (sw) : "t" (_x));
424 return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
425 == FP_NAN;
426}
427#endif
428
429#define isnan(x) (sizeof (x) == sizeof (float) ? __isnanf (x) \
430 : sizeof (x) == sizeof (double) ? __isnan (x) \
431 : __isnanl (x))
432
433/* 7.12.3.5 */
434#define isnormal(x) (fpclassify(x) == FP_NORMAL)
435
436/* 7.12.3.6 The signbit macro */
437extern int __cdecl __signbit (double);
438extern int __cdecl __signbitf (float);
439extern int __cdecl __signbitl (long double);
440#ifndef __NO_INLINE__
441__CRT_INLINE int __cdecl __signbit (double x) {
442 unsigned short stw;
443 __asm__ ( "fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
444 return (stw & 0x0200) != 0;
445}
446
447__CRT_INLINE int __cdecl __signbitf (float x) {
448 unsigned short stw;
449 __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
450 return (stw & 0x0200) != 0;
451}
452
453__CRT_INLINE int __cdecl __signbitl (long double x) {
454 unsigned short stw;
455 __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
456 return (stw & 0x0200) != 0;
457}
458#endif
459
460#define signbit(x) (sizeof (x) == sizeof (float) ? __signbitf (x) \
461 : sizeof (x) == sizeof (double) ? __signbit (x) \
462 : __signbitl (x))
463
464/* 7.12.4 Trigonometric functions: double in C89
465 */
466extern float __cdecl sinf (float);
467extern long double __cdecl sinl (long double);
468
469extern float __cdecl cosf (float);
470extern long double __cdecl cosl (long double);
471
472extern float __cdecl tanf (float);
473extern long double __cdecl tanl (long double);
474
475extern float __cdecl asinf (float);
476extern long double __cdecl asinl (long double);
477
478extern float __cdecl acosf (float);
479extern long double __cdecl acosl (long double);
480
481extern float __cdecl atanf (float);
482extern long double __cdecl atanl (long double);
483
484extern float __cdecl atan2f (float, float);
485extern long double __cdecl atan2l (long double, long double);
486
487/* 7.12.5 Hyperbolic functions: double in C89
488 */
489extern float __cdecl sinhf (float);
490#ifndef __NO_INLINE__
491__CRT_INLINE float __cdecl sinhf (float x)
492 {return (float) sinh (x);}
493#endif
494extern long double __cdecl sinhl (long double);
495
496extern float __cdecl coshf (float);
497#ifndef __NO_INLINE__
498__CRT_INLINE float __cdecl coshf (float x)
499 {return (float) cosh (x);}
500#endif
501extern long double __cdecl coshl (long double);
502
503extern float __cdecl tanhf (float);
504#ifndef __NO_INLINE__
505__CRT_INLINE float __cdecl tanhf (float x)
506 {return (float) tanh (x);}
507#endif
508extern long double __cdecl tanhl (long double);
509
510/* Inverse hyperbolic trig functions */
511/* 7.12.5.1 */
512extern double __cdecl acosh (double);
513extern float __cdecl acoshf (float);
514extern long double __cdecl acoshl (long double);
515
516/* 7.12.5.2 */
517extern double __cdecl asinh (double);
518extern float __cdecl asinhf (float);
519extern long double __cdecl asinhl (long double);
520
521/* 7.12.5.3 */
522extern double __cdecl atanh (double);
523extern float __cdecl atanhf (float);
524extern long double __cdecl atanhl (long double);
525
526/* Exponentials and logarithms */
527/* 7.12.6.1 Double in C89 */
528extern float __cdecl expf (float);
529#ifndef __NO_INLINE__
530__CRT_INLINE float __cdecl expf (float x)
531 {return (float) exp (x);}
532#endif
533extern long double __cdecl expl (long double);
534
535/* 7.12.6.2 */
536extern double __cdecl exp2(double);
537extern float __cdecl exp2f(float);
538extern long double __cdecl exp2l(long double);
539
540/* 7.12.6.3 The expm1 functions */
541/* TODO: These could be inlined */
542extern double __cdecl expm1(double);
543extern float __cdecl expm1f(float);
544extern long double __cdecl expm1l(long double);
545
546/* 7.12.6.4 Double in C89 */
547extern float __cdecl frexpf (float, int*);
548#ifndef __NO_INLINE__
549__CRT_INLINE float __cdecl frexpf (float x, int* expn)
550 {return (float) frexp (x, expn);}
551#endif
552extern long double __cdecl frexpl (long double, int*);
553
554/* 7.12.6.5 */
555#define FP_ILOGB0 ((int)0x80000000)
556#define FP_ILOGBNAN ((int)0x80000000)
557extern int __cdecl ilogb (double);
558extern int __cdecl ilogbf (float);
559extern int __cdecl ilogbl (long double);
560
561/* 7.12.6.6 Double in C89 */
562extern float __cdecl ldexpf (float, int);
563#ifndef __NO_INLINE__
564__CRT_INLINE float __cdecl ldexpf (float x, int expn)
565 {return (float) ldexp (x, expn);}
566#endif
567extern long double __cdecl ldexpl (long double, int);
568
569/* 7.12.6.7 Double in C89 */
570extern float __cdecl logf (float);
571extern long double __cdecl logl (long double);
572
573/* 7.12.6.8 Double in C89 */
574extern float __cdecl log10f (float);
575extern long double __cdecl log10l (long double);
576
577/* 7.12.6.9 */
578extern double __cdecl log1p(double);
579extern float __cdecl log1pf(float);
580extern long double __cdecl log1pl(long double);
581
582/* 7.12.6.10 */
583extern double __cdecl log2 (double);
584extern float __cdecl log2f (float);
585extern long double __cdecl log2l (long double);
586
587/* 7.12.6.11 */
588extern double __cdecl logb (double);
589extern float __cdecl logbf (float);
590extern long double __cdecl logbl (long double);
591
592/* Inline versions. GCC-4.0+ can do a better fast-math optimization
593 * with __builtins.
594 */
595#ifndef __NO_INLINE__
596#if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
597__CRT_INLINE double __cdecl logb (double x)
598{
599 double res;
600 __asm__ ("fxtract\n\t"
601 "fstp %%st" : "=t" (res) : "0" (x));
602 return res;
603}
604
605__CRT_INLINE float __cdecl logbf (float x)
606{
607 float res;
608 __asm__ ("fxtract\n\t"
609 "fstp %%st" : "=t" (res) : "0" (x));
610 return res;
611}
612
613__CRT_INLINE long double __cdecl logbl (long double x)
614{
615 long double res;
616 __asm__ ("fxtract\n\t"
617 "fstp %%st" : "=t" (res) : "0" (x));
618 return res;
619}
620#endif /* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4, 0) */
621#endif /* !__NO_INLINE__ */
622
623/* 7.12.6.12 Double in C89 */
624extern float __cdecl modff (float, float*);
625extern long double __cdecl modfl (long double, long double*);
626
627/* 7.12.6.13 */
628extern double __cdecl scalbn (double, int);
629extern float __cdecl scalbnf (float, int);
630extern long double __cdecl scalbnl (long double, int);
631
632extern double __cdecl scalbln (double, long);
633extern float __cdecl scalblnf (float, long);
634extern long double __cdecl scalblnl (long double, long);
635
636/* 7.12.7.1 */
637/* Implementations adapted from Cephes versions */
638extern double __cdecl cbrt (double);
639extern float __cdecl cbrtf (float);
640extern long double __cdecl cbrtl (long double);
641
642/* 7.12.7.2 The fabs functions: Double in C89 */
643extern float __cdecl fabsf (float x);
644extern long double __cdecl fabsl (long double x);
645
646/* 7.12.7.3 */
647extern double __cdecl hypot (double, double); /* in libmoldname.a */
648extern float __cdecl hypotf (float, float);
649extern long double __cdecl hypotl (long double, long double);
650
651/* 7.12.7.4 The pow functions. Double in C89 */
652extern float __cdecl powf (float, float);
653#ifndef __NO_INLINE__
654__CRT_INLINE float __cdecl powf (float x, float y)
655 {return (float) pow (x, y);}
656#endif
657extern long double __cdecl powl (long double, long double);
658
659/* 7.12.7.5 The sqrt functions. Double in C89. */
660extern float __cdecl sqrtf (float);
661extern long double __cdecl sqrtl (long double);
662
663/* 7.12.8.1 The erf functions */
664extern double __cdecl erf (double);
665extern float __cdecl erff (float);
666extern long double __cdecl erfl (long double);
667
668/* 7.12.8.2 The erfc functions */
669extern double __cdecl erfc (double);
670extern float __cdecl erfcf (float);
671extern long double __cdecl erfcl (long double);
672
673/* 7.12.8.3 The lgamma functions */
674extern double __cdecl lgamma (double);
675extern float __cdecl lgammaf (float);
676extern long double __cdecl lgammal (long double);
677
678/* 7.12.8.4 The tgamma functions */
679extern double __cdecl tgamma (double);
680extern float __cdecl tgammaf (float);
681extern long double __cdecl tgammal (long double);
682
683/* 7.12.9.1 Double in C89 */
684extern float __cdecl ceilf (float);
685extern long double __cdecl ceill (long double);
686
687/* 7.12.9.2 Double in C89 */
688extern float __cdecl floorf (float);
689extern long double __cdecl floorl (long double);
690
691/* 7.12.9.3 */
692extern double __cdecl nearbyint ( double);
693extern float __cdecl nearbyintf (float);
694extern long double __cdecl nearbyintl (long double);
695
696/* 7.12.9.4 */
697/* round, using fpu control word settings */
698extern double __cdecl rint (double);
699extern float __cdecl rintf (float);
700extern long double __cdecl rintl (long double);
701
702/* 7.12.9.5 */
703extern long __cdecl lrint (double);
704extern long __cdecl lrintf (float);
705extern long __cdecl lrintl (long double);
706
707extern long long __cdecl llrint (double);
708extern long long __cdecl llrintf (float);
709extern long long __cdecl llrintl (long double);
710
711/* Inline versions of above.
712 * GCC 4.0+ can do a better fast-math job with __builtins.
713 */
714#ifndef __NO_INLINE__
715#if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
716__CRT_INLINE double __cdecl rint (double x)
717{
718 double retval;
719 __asm__ ("frndint;": "=t" (retval) : "0" (x));
720 return retval;
721}
722
723__CRT_INLINE float __cdecl rintf (float x)
724{
725 float retval;
726 __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
727 return retval;
728}
729
730__CRT_INLINE long double __cdecl rintl (long double x)
731{
732 long double retval;
733 __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
734 return retval;
735}
736
737__CRT_INLINE long __cdecl lrint (double x)
738{
739 long retval;
740 __asm__ __volatile__
741 ("fistpl %0" : "=m" (retval) : "t" (x) : "st");
742 return retval;
743}
744
745__CRT_INLINE long __cdecl lrintf (float x)
746{
747 long retval;
748 __asm__ __volatile__
749 ("fistpl %0" : "=m" (retval) : "t" (x) : "st");
750 return retval;
751}
752
753__CRT_INLINE long __cdecl lrintl (long double x)
754{
755 long retval;
756 __asm__ __volatile__
757 ("fistpl %0" : "=m" (retval) : "t" (x) : "st");
758 return retval;
759}
760
761__CRT_INLINE long long __cdecl llrint (double x)
762{
763 long long retval;
764 __asm__ __volatile__
765 ("fistpll %0" : "=m" (retval) : "t" (x) : "st");
766 return retval;
767}
768
769__CRT_INLINE long long __cdecl llrintf (float x)
770{
771 long long retval;
772 __asm__ __volatile__
773 ("fistpll %0" : "=m" (retval) : "t" (x) : "st");
774 return retval;
775}
776
777__CRT_INLINE long long __cdecl llrintl (long double x)
778{
779 long long retval;
780 __asm__ __volatile__
781 ("fistpll %0" : "=m" (retval) : "t" (x) : "st");
782 return retval;
783}
784#endif /* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4,0) */
785#endif /* !__NO_INLINE__ */
786
787/* 7.12.9.6 */
788/* round away from zero, regardless of fpu control word settings */
789extern double __cdecl round (double);
790extern float __cdecl roundf (float);
791extern long double __cdecl roundl (long double);
792
793/* 7.12.9.7 */
794extern long __cdecl lround (double);
795extern long __cdecl lroundf (float);
796extern long __cdecl lroundl (long double);
797
798extern long long __cdecl llround (double);
799extern long long __cdecl llroundf (float);
800extern long long __cdecl llroundl (long double);
801
802/* 7.12.9.8 */
803/* round towards zero, regardless of fpu control word settings */
804extern double __cdecl trunc (double);
805extern float __cdecl truncf (float);
806extern long double __cdecl truncl (long double);
807
808/* 7.12.10.1 Double in C89 */
809extern float __cdecl fmodf (float, float);
810extern long double __cdecl fmodl (long double, long double);
811
812/* 7.12.10.2 */
813extern double __cdecl remainder (double, double);
814extern float __cdecl remainderf (float, float);
815extern long double __cdecl remainderl (long double, long double);
816
817/* 7.12.10.3 */
818extern double __cdecl remquo(double, double, int *);
819extern float __cdecl remquof(float, float, int *);
820extern long double __cdecl remquol(long double, long double, int *);
821
822/* 7.12.11.1 */
823extern double __cdecl copysign (double, double); /* in libmoldname.a */
824extern float __cdecl copysignf (float, float);
825extern long double __cdecl copysignl (long double, long double);
826
827/* 7.12.11.2 Return a NaN */
828extern double __cdecl nan(const char *tagp);
829extern float __cdecl nanf(const char *tagp);
830extern long double __cdecl nanl(const char *tagp);
831
832#ifndef __STRICT_ANSI__
833#define _nan() nan("")
834#define _nanf() nanf("")
835#define _nanl() nanl("")
836#endif
837
838/* 7.12.11.3 */
839extern double __cdecl nextafter (double, double); /* in libmoldname.a */
840extern float __cdecl nextafterf (float, float);
841extern long double __cdecl nextafterl (long double, long double);
842
843/* 7.12.11.4 The nexttoward functions */
844extern double __cdecl nexttoward (double, long double);
845extern float __cdecl nexttowardf (float, long double);
846extern long double __cdecl nexttowardl (long double, long double);
847
848/* 7.12.12.1 */
849/* x > y ? (x - y) : 0.0 */
850extern double __cdecl fdim (double x, double y);
851extern float __cdecl fdimf (float x, float y);
852extern long double __cdecl fdiml (long double x, long double y);
853
854/* fmax and fmin.
855 NaN arguments are treated as missing data: if one argument is a NaN
856 and the other numeric, then these functions choose the numeric
857 value. */
858
859/* 7.12.12.2 */
860extern double __cdecl fmax (double, double);
861extern float __cdecl fmaxf (float, float);
862extern long double __cdecl fmaxl (long double, long double);
863
864/* 7.12.12.3 */
865extern double __cdecl fmin (double, double);
866extern float __cdecl fminf (float, float);
867extern long double __cdecl fminl (long double, long double);
868
869/* 7.12.13.1 */
870/* return x * y + z as a ternary op */
871extern double __cdecl fma (double, double, double);
872extern float __cdecl fmaf (float, float, float);
873extern long double __cdecl fmal (long double, long double, long double);
874
875
876/* 7.12.14
877 * With these functions, comparisons involving quiet NaNs set the FP
878 * condition code to "unordered". The IEEE floating-point spec
879 * dictates that the result of floating-point comparisons should be
880 * false whenever a NaN is involved, with the exception of the != op,
881 * which always returns true: yes, (NaN != NaN) is true).
882 */
883#if __GNUC__ >= 3
884
885#define isgreater(x, y) __builtin_isgreater(x, y)
886#define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
887#define isless(x, y) __builtin_isless(x, y)
888#define islessequal(x, y) __builtin_islessequal(x, y)
889#define islessgreater(x, y) __builtin_islessgreater(x, y)
890#define isunordered(x, y) __builtin_isunordered(x, y)
891
892#else /* __GNUC__ < 3 */
893/* helper */
894extern int __cdecl __fp_unordered_compare (long double, long double);
895#ifndef __NO_INLINE__
896__CRT_INLINE int __cdecl
897__fp_unordered_compare (long double x, long double y){
898 unsigned short retval;
899 __asm__ ("fucom %%st(1);"
900 "fnstsw;": "=a" (retval) : "t" (x), "u" (y));
901 return retval;
902}
903#endif /* !__NO_INLINE__ */
904
905#define isgreater(x, y) ((__fp_unordered_compare(x, y) & 0x4500) == 0)
906#define isless(x, y) ((__fp_unordered_compare(y, x) & 0x4500) == 0)
907#define isgreaterequal(x, y) ((__fp_unordered_compare(x, y) & FP_INFINITE) == 0)
908#define islessequal(x, y) ((__fp_unordered_compare(y, x) & FP_INFINITE) == 0)
909#define islessgreater(x, y) ((__fp_unordered_compare(x, y) & FP_SUBNORMAL) == 0)
910#define isunordered(x, y) ((__fp_unordered_compare(x, y) & 0x4500) == 0x4500)
911
912#endif /* __GNUC__ < 3 */
913#endif /* __cplusplus || _ISOC99_SOURCE */
914
915_END_C_DECLS
916
917#endif /* ! RC_INVOKED */
918#endif /* !_MATH_H: $RCSfile: math.h,v $: end of file */
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