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1/*
2 * Copyright (c) 2002 Apple Computer, Inc. All rights reserved.
3 *
4 * @APPLE_LICENSE_HEADER_START@
5 *
6 * The contents of this file constitute Original Code as defined in and
7 * are subject to the Apple Public Source License Version 1.1 (the
8 * "License"). You may not use this file except in compliance with the
9 * License. Please obtain a copy of the License at
10 * http://www.apple.com/publicsource and read it before using this file.
11 *
12 * This Original Code and all software distributed under the License are
13 * distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY KIND, EITHER
14 * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
15 * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
16 * FITNESS FOR A PARTICULAR PURPOSE OR NON-INFRINGEMENT. Please see the
17 * License for the specific language governing rights and limitations
18 * under the License.
19 *
20 * @APPLE_LICENSE_HEADER_END@
21 */
22
23/*******************************************************************************
24* *
25* File: math.h *
26* *
27* Contains: typedefs, prototypes, and macros germane to C99 floating point.*
28* *
29*******************************************************************************/
30#ifndef __MATH__
31#define __MATH__
32
33#include "sys/cdefs.h" /* For definition of __DARWIN_UNIX03 et al */
34
35#if (!defined(__WANT_LONG_DOUBLE_FORMAT__))
36#if defined(__APPLE_CC__) && defined(__LONG_DOUBLE_128__)
37#define __WANT_LONG_DOUBLE_FORMAT__ 128
38#else
39#define __WANT_LONG_DOUBLE_FORMAT__ 64
40#endif
41#endif
42
43#if ( __WANT_LONG_DOUBLE_FORMAT__ - 0L == 128L )
44#define __LIBMLDBL_COMPAT(sym) __asm("_" __STRING(sym) "$LDBL128")
45#elif ( __WANT_LONG_DOUBLE_FORMAT__ - 0L == 64L )
46#define __LIBMLDBL_COMPAT(sym) /* NOTHING */
47#else
48#define __LIBMLDBL_COMPAT(sym) /* NOTHING */
49#endif
50
51#ifdef __cplusplus
52extern "C" {
53#endif
54
55/******************************************************************************
56* Floating point data types *
57******************************************************************************/
58
59/* Define float_t and double_t per C standard, ISO/IEC 9899:1999 7.12 2,
60 taking advantage of GCC's __FLT_EVAL_METHOD__ (which a compiler may
61 define anytime and GCC does) that shadows FLT_EVAL_METHOD (which a compiler
62 must and may define only in float.h).
63*/
64#if __FLT_EVAL_METHOD__ == 0
65 typedef float float_t;
66 typedef double double_t;
67#elif __FLT_EVAL_METHOD__ == 1
68 typedef double float_t;
69 typedef double double_t;
70#elif __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ == -1
71 typedef long double float_t;
72 typedef long double double_t;
73#else /* __FLT_EVAL_METHOD__ */
74 #error "Unsupported value of __FLT_EVAL_METHOD__."
75#endif /* __FLT_EVAL_METHOD__ */
76
77
78#if defined(__GNUC__) && ! defined( __XLC__ )
79 #define HUGE_VAL __builtin_huge_val()
80 #define HUGE_VALF __builtin_huge_valf()
81 #define HUGE_VALL __builtin_huge_vall()
82 #define NAN __builtin_nanf("0x7fc00000") /* Constant expression, can be used as initializer. */
83 #define __MATH_H_ALWAYS_INLINE__ __attribute__ ((always_inline))
84#else
85 #define HUGE_VAL 1e500
86 #define HUGE_VALF 1e50f
87 #define HUGE_VALL 1e500L
88 #define NAN __nan( )
89 #define __MATH_H_ALWAYS_INLINE__
90#endif
91
92#define INFINITY HUGE_VALF
93
94/******************************************************************************
95* Taxonomy of floating point data types *
96******************************************************************************/
97
98#define FP_NAN 1
99#define FP_INFINITE 2
100#define FP_ZERO 3
101#define FP_NORMAL 4
102#define FP_SUBNORMAL 5
103#define FP_SUPERNORMAL 6
104
105/* fma() *function call* is more costly than equivalent (in-line) multiply and add operations */
106#undef FP_FAST_FMA
107#undef FP_FAST_FMAF
108#undef FP_FAST_FMAL
109
110/* The values returned by `ilogb' for 0 and NaN respectively. */
111#define FP_ILOGB0 (-2147483647)
112#define FP_ILOGBNAN (2147483647)
113
114/* Bitmasks for the math_errhandling macro. */
115#define MATH_ERRNO 1 /* errno set by math functions. */
116#define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
117
118#define math_errhandling (__math_errhandling())
119extern int __math_errhandling ( void );
120
121/********************************************************************************
122* *
123* Inquiry macros *
124* *
125* fpclassify Returns one of the FP_* values. *
126* isnormal Non-zero if and only if the argument x is normalized. *
127* isfinite Non-zero if and only if the argument x is finite. *
128* isnan Non-zero if and only if the argument x is a NaN. *
129* signbit Non-zero if and only if the sign of the argument x is *
130* negative. This includes, NaNs, infinities and zeros. *
131* *
132********************************************************************************/
133
134#if (__WANT_LONG_DOUBLE_FORMAT__ - 0L == 128L)
135 #define fpclassify(x) \
136 ( sizeof (x) == sizeof(float ) ? __fpclassifyf((float)x) \
137 : sizeof (x) == sizeof(double) ? __fpclassifyd((double)x) \
138 : __fpclassify ((long double)x))
139
140 extern int __fpclassifyf(float );
141 extern int __fpclassifyd(double );
142 extern int __fpclassify (long double);
143
144 #if defined( __GNUC__ ) && ! defined( __XLC__ ) && 0 == __FINITE_MATH_ONLY__
145 /* Yes, that's right. You only get the fast iswhatever() macros if you do NOT turn on -ffast-math. */
146 /* These inline functions require the compiler to be compiling to standard in order to work. */
147 /* -ffast-math, among other things, implies that NaNs don't happen. The compiler can in that case */
148 /* optimize x != x to be false always, wheras it would be true for NaNs. That breaks __inline_isnan() */
149 /* below. */
150
151 #define isnormal(x) \
152 ( sizeof (x) == sizeof(float ) ? __inline_isnormalf((float)(x)) \
153 : sizeof (x) == sizeof(double) ? __inline_isnormald((double)(x)) \
154 : __inline_isnormal ((long double)(x)))
155
156 #define isfinite(x) \
157 ( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x)) \
158 : sizeof (x) == sizeof(double) ? __inline_isfinited((double)(x)) \
159 : __inline_isfinite ((long double)(x)))
160
161 #define isinf(x) \
162 ( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) \
163 : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) \
164 : __inline_isinf ((long double)(x)))
165
166 #define isnan(x) \
167 ( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) \
168 : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) \
169 : __inline_isnan ((long double)(x)))
170
171 #define signbit(x) \
172 ( sizeof (x) == sizeof(float ) ? __inline_signbitf((float)(x)) \
173 : sizeof (x) == sizeof(double) ? __inline_signbitd((double)(x)) \
174 : __inline_signbit((long double)(x)))
175
176 /* Developers who are calling __isnan, __isnormal, __isinf, etc. and now encountering errors are calling private APIs */
177 /* that are deprecated. Please use the official C99 sanctioned macros listed above instead. */
178
179 static __inline__ int __inline_isfinitef (float ) __MATH_H_ALWAYS_INLINE__;
180 static __inline__ int __inline_isfinited (double ) __MATH_H_ALWAYS_INLINE__;
181 static __inline__ int __inline_isfinite (long double) __MATH_H_ALWAYS_INLINE__;
182 static __inline__ int __inline_isinff (float ) __MATH_H_ALWAYS_INLINE__;
183 static __inline__ int __inline_isinfd (double ) __MATH_H_ALWAYS_INLINE__;
184 static __inline__ int __inline_isinf (long double) __MATH_H_ALWAYS_INLINE__;
185 static __inline__ int __inline_isnanf (float ) __MATH_H_ALWAYS_INLINE__;
186 static __inline__ int __inline_isnand (double ) __MATH_H_ALWAYS_INLINE__;
187 static __inline__ int __inline_isnan (long double) __MATH_H_ALWAYS_INLINE__;
188 static __inline__ int __inline_isnormalf (float ) __MATH_H_ALWAYS_INLINE__;
189 static __inline__ int __inline_isnormald (double ) __MATH_H_ALWAYS_INLINE__;
190 static __inline__ int __inline_isnormal (long double) __MATH_H_ALWAYS_INLINE__;
191 static __inline__ int __inline_signbitf (float ) __MATH_H_ALWAYS_INLINE__;
192 static __inline__ int __inline_signbitd (double ) __MATH_H_ALWAYS_INLINE__;
193 static __inline__ int __inline_signbit (long double) __MATH_H_ALWAYS_INLINE__;
194
195 static __inline__ int __inline_isinff( float __x ) { return __builtin_fabsf(__x) == __builtin_inff(); }
196 static __inline__ int __inline_isinfd( double __x ) { return __builtin_fabs(__x) == __builtin_inf(); }
197 static __inline__ int __inline_isinf( long double __x ) { return __builtin_fabsl(__x) == __builtin_infl(); }
198 static __inline__ int __inline_isfinitef( float __x ) { return __x == __x && __builtin_fabsf(__x) != __builtin_inff(); }
199 static __inline__ int __inline_isfinited( double __x ) { return __x == __x && __builtin_fabs(__x) != __builtin_inf(); }
200 static __inline__ int __inline_isfinite( long double __x ) { return __x == __x && __builtin_fabsl(__x) != __builtin_infl(); }
201 static __inline__ int __inline_isnanf( float __x ) { return __x != __x; }
202 static __inline__ int __inline_isnand( double __x ) { return __x != __x; }
203 static __inline__ int __inline_isnan( long double __x ) { return __x != __x; }
204 static __inline__ int __inline_signbitf( float __x ) { union{ float __f; unsigned int __u; }__u; __u.__f = __x; return (int)(__u.__u >> 31); }
205 static __inline__ int __inline_signbitd( double __x ) { union{ double __f; unsigned long __u; }__u; __u.__f = __x; return (int)(__u.__u >> ( 8 * sizeof( __u.__u) - 1)); }
206 static __inline__ int __inline_signbit( long double __x ){ union{ long double __ld; unsigned long __p; }__u; __u.__ld = __x; return (int) (__u.__p >> ( 8 * sizeof( __u.__p) - 1)); }
207 static __inline__ int __inline_isnormalf( float __x ) { float fabsf = __builtin_fabsf(__x); if( __x != __x ) return 0; return fabsf < __builtin_inff() && fabsf >= __FLT_MIN__; }
208 static __inline__ int __inline_isnormald( double __x ) { double fabsf = __builtin_fabs(__x); if( __x != __x ) return 0; return fabsf < __builtin_inf() && fabsf >= __DBL_MIN__; }
209 static __inline__ int __inline_isnormal( long double __x ) { long double fabsf = __builtin_fabsl(__x); if( __x != __x ) return 0; return fabsf < __builtin_infl() && fabsf >= __LDBL_MIN__; }
210
211 #else
212
213 #define isnormal(x) \
214 ( sizeof (x) == sizeof(float ) ? __isnormalf((float)(x)) \
215 : sizeof (x) == sizeof(double) ? __isnormald((double)(x)) \
216 : __isnormal ((long double)(x)))
217
218 #define isfinite(x) \
219 ( sizeof (x) == sizeof(float ) ? __isfinitef((float)(x)) \
220 : sizeof (x) == sizeof(double) ? __isfinited((double)(x)) \
221 : __isfinite ((long double)(x)))
222
223 #define isinf(x) \
224 ( sizeof (x) == sizeof(float ) ? __isinff((float)(x)) \
225 : sizeof (x) == sizeof(double) ? __isinfd((double)(x)) \
226 : __isinf ((long double)(x)))
227
228 #define isnan(x) \
229 ( sizeof (x) == sizeof(float ) ? __isnanf((float)(x)) \
230 : sizeof (x) == sizeof(double) ? __isnand((double)(x)) \
231 : __isnan ((long double)(x)))
232
233 #define signbit(x) \
234 ( sizeof (x) == sizeof(float ) ? __signbitf((float)(x)) \
235 : sizeof (x) == sizeof(double) ? __signbitd((double)(x)) \
236 : __signbitl((long double)(x)))
237
238
239 extern int __isnormalf (float );
240 extern int __isnormald (double );
241 extern int __isnormal (long double);
242
243 extern int __isfinitef (float );
244 extern int __isfinited (double );
245 extern int __isfinite (long double);
246
247 extern int __isinff (float );
248 extern int __isinfd (double );
249 extern int __isinf (long double);
250
251 extern int __isnanf (float );
252 extern int __isnand (double );
253 extern int __isnan (long double);
254
255 extern int __signbitf (float );
256 extern int __signbitd (double );
257 extern int __signbitl (long double);
258
259 #endif
260
261#else
262 #define fpclassify(x) \
263 ( sizeof (x) == sizeof(float ) ? __fpclassifyf((float)(x)) : __fpclassifyd((double)(x)) )
264
265 extern int __fpclassifyf(float );
266 extern int __fpclassifyd(double );
267
268 #if defined( __GNUC__ ) && ! defined( __XLC__ ) && 0 == __FINITE_MATH_ONLY__
269 /* Yes, that's right. You only get the fast iswhatever() macros if you do NOT turn on -ffast-math. */
270 /* These inline functions require the compiler to be compiling to standard in order to work. */
271 /* -ffast-math, among other things, implies that NaNs don't happen. The compiler can in that case */
272 /* optimize x != x to be false always, wheras it would be true for NaNs. That breaks __inline_isnan() */
273 /* below. */
274 #define isnormal(x) \
275 ( sizeof (x) == sizeof(float ) ? __inline_isnormalf((float)(x)) : __inline_isnormald((double)(x)) )
276
277 #define isfinite(x) \
278 ( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x)) : __inline_isfinited((double)(x)) )
279
280 #define isinf(x) \
281 ( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : __inline_isinfd((double)(x)) )
282
283 #define isnan(x) \
284 ( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : __inline_isnand((double)(x)) )
285
286 #define signbit(x) \
287 ( sizeof (x) == sizeof(float ) ? __inline_signbitf((float)(x)) : __inline_signbitd((double)(x)) )
288
289 /* Developers who are calling __isnan, __isnormal, __isinf, etc. and now encountering errors are calling private APIs */
290 /* that are deprecated. Please use the official C99 sanctioned macros listed above instead. */
291
292 static __inline__ int __inline_isfinitef (float ) __MATH_H_ALWAYS_INLINE__;
293 static __inline__ int __inline_isfinited (double ) __MATH_H_ALWAYS_INLINE__;
294 static __inline__ int __inline_isfinite (long double) __MATH_H_ALWAYS_INLINE__;
295 static __inline__ int __inline_isinff (float ) __MATH_H_ALWAYS_INLINE__;
296 static __inline__ int __inline_isinfd (double ) __MATH_H_ALWAYS_INLINE__;
297 static __inline__ int __inline_isinf (long double) __MATH_H_ALWAYS_INLINE__;
298 static __inline__ int __inline_isnanf (float ) __MATH_H_ALWAYS_INLINE__;
299 static __inline__ int __inline_isnand (double ) __MATH_H_ALWAYS_INLINE__;
300 static __inline__ int __inline_isnan (long double) __MATH_H_ALWAYS_INLINE__;
301 static __inline__ int __inline_isnormalf (float ) __MATH_H_ALWAYS_INLINE__;
302 static __inline__ int __inline_isnormald (double ) __MATH_H_ALWAYS_INLINE__;
303 static __inline__ int __inline_isnormal (long double) __MATH_H_ALWAYS_INLINE__;
304 static __inline__ int __inline_signbitf (float ) __MATH_H_ALWAYS_INLINE__;
305 static __inline__ int __inline_signbitd (double ) __MATH_H_ALWAYS_INLINE__;
306 static __inline__ int __inline_signbit (long double) __MATH_H_ALWAYS_INLINE__;
307
308 static __inline__ int __inline_isinff( float __x ) { return __builtin_fabsf(__x) == __builtin_inff(); }
309 static __inline__ int __inline_isinfd( double __x ) { return __builtin_fabs(__x) == __builtin_inf(); }
310 static __inline__ int __inline_isinf( long double __x ) { return __builtin_fabsl(__x) == __builtin_infl(); }
311 static __inline__ int __inline_isfinitef( float __x ) { return __x == __x && __builtin_fabsf(__x) != __builtin_inff(); }
312 static __inline__ int __inline_isfinited( double __x ) { return __x == __x && __builtin_fabs(__x) != __builtin_inf(); }
313 static __inline__ int __inline_isfinite( long double __x ) { return __x == __x && __builtin_fabsl(__x) != __builtin_infl(); }
314 static __inline__ int __inline_isnanf( float __x ) { return __x != __x; }
315 static __inline__ int __inline_isnand( double __x ) { return __x != __x; }
316 static __inline__ int __inline_isnan( long double __x ) { return __x != __x; }
317 static __inline__ int __inline_signbitf( float __x ) { union{ float __f; unsigned int __u; }__u; __u.__f = __x; return (int)(__u.__u >> 31); }
318 static __inline__ int __inline_signbitd( double __x ) { union{ double __f; unsigned long __u; }__u; __u.__f = __x; return (int)(__u.__u >> ( 8 * sizeof( __u.__u) - 1)); }
319 static __inline__ int __inline_signbit( long double __x ){ union{ long double __ld; unsigned long __p; }__u; __u.__ld = __x; return (int) (__u.__p >> ( 8 * sizeof( __u.__p) - 1)); }
320 static __inline__ int __inline_isnormalf( float __x ) { float fabsf = __builtin_fabsf(__x); if( __x != __x ) return 0; return fabsf < __builtin_inff() && fabsf >= __FLT_MIN__; }
321 static __inline__ int __inline_isnormald( double __x ) { double fabsf = __builtin_fabs(__x); if( __x != __x ) return 0; return fabsf < __builtin_inf() && fabsf >= __DBL_MIN__; }
322 static __inline__ int __inline_isnormal( long double __x ) { long double fabsf = __builtin_fabsl(__x); if( __x != __x ) return 0; return fabsf < __builtin_infl() && fabsf >= __LDBL_MIN__; }
323
324 #else
325
326 #define isnormal(x) \
327 ( sizeof (x) == sizeof(float ) ? __isnormalf((float)(x)) : __isnormald((double)(x)) )
328
329 #define isfinite(x) \
330 ( sizeof (x) == sizeof(float ) ? __isfinitef((float)(x)) : __isfinited((double)(x)) )
331
332 #define isinf(x) \
333 ( sizeof (x) == sizeof(float ) ? __isinff((float)(x)) : __isinfd((double)(x)) )
334
335 #define isnan(x) \
336 ( sizeof (x) == sizeof(float ) ? __isnanf((float)(x)) : __isnand((double)(x)) )
337
338 #define signbit(x) \
339 ( sizeof (x) == sizeof(float ) ? __signbitf((float)(x)) : __signbitd((double)(x)) )
340
341
342 extern int __isnormalf (float );
343 extern int __isnormald (double );
344
345 extern int __isfinitef (float );
346 extern int __isfinited (double );
347
348 extern int __isinff (float );
349 extern int __isinfd (double );
350
351 extern int __isnanf (float );
352 extern int __isnand (double );
353
354 extern int __signbitf (float );
355 extern int __signbitd (double );
356
357 #endif
358
359#endif /* __WANT_LONG_DOUBLE_FORMAT__ */
360
361
362/********************************************************************************
363* *
364* Math Functions *
365* *
366********************************************************************************/
367
368extern double acos( double );
369extern float acosf( float );
370
371extern double asin( double );
372extern float asinf( float );
373
374extern double atan( double );
375extern float atanf( float );
376
377extern double atan2( double, double );
378extern float atan2f( float, float );
379
380extern double cos( double );
381extern float cosf( float );
382
383extern double sin( double );
384extern float sinf( float );
385
386extern double tan( double );
387extern float tanf( float );
388
389extern double acosh( double );
390extern float acoshf( float );
391
392extern double asinh( double );
393extern float asinhf( float );
394
395extern double atanh( double );
396extern float atanhf( float );
397
398extern double cosh( double );
399extern float coshf( float );
400
401extern double sinh( double );
402extern float sinhf( float );
403
404extern double tanh( double );
405extern float tanhf( float );
406
407extern double exp( double );
408extern float expf( float );
409
410extern double exp2( double );
411extern float exp2f( float );
412
413extern double expm1( double );
414extern float expm1f( float );
415
416extern double log( double );
417extern float logf( float );
418
419extern double log10( double );
420extern float log10f( float );
421
422extern double log2( double );
423extern float log2f( float );
424
425extern double log1p( double );
426extern float log1pf( float );
427
428extern double logb( double );
429extern float logbf( float );
430
431extern double modf( double, double * );
432extern float modff( float, float * );
433
434extern double ldexp( double, int );
435extern float ldexpf( float, int );
436
437extern double frexp( double, int * );
438extern float frexpf( float, int * );
439
440extern int ilogb( double );
441extern int ilogbf( float );
442
443extern double scalbn( double, int );
444extern float scalbnf( float, int );
445
446extern double scalbln( double, long int );
447extern float scalblnf( float, long int );
448
449extern double fabs( double );
450extern float fabsf( float );
451
452extern double cbrt( double );
453extern float cbrtf( float );
454
455extern double hypot( double, double );
456extern float hypotf( float, float );
457
458extern double pow( double, double );
459extern float powf( float, float );
460
461extern double sqrt( double );
462extern float sqrtf( float );
463
464extern double erf( double );
465extern float erff( float );
466
467extern double erfc( double );
468extern float erfcf( float );
469
470extern double lgamma( double );
471extern float lgammaf( float );
472
473extern double tgamma( double );
474extern float tgammaf( float );
475
476extern double ceil( double );
477extern float ceilf( float );
478
479extern double floor( double );
480extern float floorf( float );
481
482extern double nearbyint( double );
483extern float nearbyintf( float );
484
485extern double rint( double );
486extern float rintf( float );
487
488extern long int lrint( double );
489extern long int lrintf( float );
490
491extern double round( double );
492extern float roundf( float );
493
494extern long int lround( double );
495extern long int lroundf( float );
496
497#if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ )
498 /* C90 doesn't know about long long. Make sure you are passing -std=c99 or -std=gnu99 or better if you need this. */
499 extern long long int llrint( double );
500 extern long long int llrintf( float );
501
502 extern long long int llround( double );
503 extern long long int llroundf( float );
504#endif /*#if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) */
505
506extern double trunc( double );
507extern float truncf( float );
508
509extern double fmod( double, double );
510extern float fmodf( float, float );
511
512extern double remainder( double, double );
513extern float remainderf( float, float );
514
515extern double remquo( double, double, int * );
516extern float remquof( float, float, int * );
517
518extern double copysign( double, double );
519extern float copysignf( float, float );
520
521extern double nan( const char * );
522extern float nanf( const char * );
523
524extern double nextafter( double, double );
525extern float nextafterf( float, float );
526
527
528extern double fdim( double, double );
529extern float fdimf( float, float );
530
531extern double fmax( double, double );
532extern float fmaxf( float, float );
533
534extern double fmin( double, double );
535extern float fminf( float, float );
536
537extern double fma( double, double, double );
538extern float fmaf( float, float, float );
539
540#if ( __WANT_LONG_DOUBLE_FORMAT__ - 0L > 0L )
541extern long double acosl( long double ) __LIBMLDBL_COMPAT(acosl);
542extern long double asinl( long double ) __LIBMLDBL_COMPAT(asinl);
543extern long double atanl( long double ) __LIBMLDBL_COMPAT(atanl);
544extern long double atan2l( long double, long double ) __LIBMLDBL_COMPAT(atan2l);
545extern long double cosl( long double ) __LIBMLDBL_COMPAT(cosl);
546extern long double sinl( long double ) __LIBMLDBL_COMPAT(sinl);
547extern long double tanl( long double ) __LIBMLDBL_COMPAT(tanl);
548extern long double acoshl( long double ) __LIBMLDBL_COMPAT(acoshl);
549extern long double asinhl( long double ) __LIBMLDBL_COMPAT(asinhl);
550extern long double atanhl( long double ) __LIBMLDBL_COMPAT(atanhl);
551extern long double coshl( long double ) __LIBMLDBL_COMPAT(coshl);
552extern long double sinhl( long double ) __LIBMLDBL_COMPAT(sinhl);
553extern long double tanhl( long double ) __LIBMLDBL_COMPAT(tanhl);
554extern long double expl( long double ) __LIBMLDBL_COMPAT(expl);
555extern long double exp2l( long double ) __LIBMLDBL_COMPAT(exp2l);
556extern long double expm1l( long double ) __LIBMLDBL_COMPAT(expm1l);
557extern long double logl( long double ) __LIBMLDBL_COMPAT(logl);
558extern long double log10l( long double ) __LIBMLDBL_COMPAT(log10l);
559extern long double log2l( long double ) __LIBMLDBL_COMPAT(log2l);
560extern long double log1pl( long double ) __LIBMLDBL_COMPAT(log1pl);
561extern long double logbl( long double ) __LIBMLDBL_COMPAT(logbl);
562extern long double modfl( long double, long double * ) __LIBMLDBL_COMPAT(modfl);
563extern long double ldexpl( long double, int ) __LIBMLDBL_COMPAT(ldexpl);
564extern long double frexpl( long double, int * ) __LIBMLDBL_COMPAT(frexpl);
565extern int ilogbl( long double ) __LIBMLDBL_COMPAT(ilogbl);
566extern long double scalbnl( long double, int ) __LIBMLDBL_COMPAT(scalbnl);
567extern long double scalblnl( long double, long int ) __LIBMLDBL_COMPAT(scalblnl);
568extern long double fabsl( long double ) __LIBMLDBL_COMPAT(fabsl);
569extern long double cbrtl( long double ) __LIBMLDBL_COMPAT(cbrtl);
570extern long double hypotl( long double, long double ) __LIBMLDBL_COMPAT(hypotl);
571extern long double powl( long double, long double ) __LIBMLDBL_COMPAT(powl);
572extern long double sqrtl( long double ) __LIBMLDBL_COMPAT(sqrtl);
573extern long double erfl( long double ) __LIBMLDBL_COMPAT(erfl);
574extern long double erfcl( long double ) __LIBMLDBL_COMPAT(erfcl);
575extern long double lgammal( long double ) __LIBMLDBL_COMPAT(lgammal);
576extern long double tgammal( long double ) __LIBMLDBL_COMPAT(tgammal);
577extern long double ceill( long double ) __LIBMLDBL_COMPAT(ceill);
578extern long double floorl( long double ) __LIBMLDBL_COMPAT(floorl);
579extern long double nearbyintl( long double ) __LIBMLDBL_COMPAT(nearbyintl);
580extern long double rintl( long double ) __LIBMLDBL_COMPAT(rintl);
581extern long int lrintl( long double ) __LIBMLDBL_COMPAT(lrintl);
582extern long double roundl( long double ) __LIBMLDBL_COMPAT(roundl);
583extern long int lroundl( long double ) __LIBMLDBL_COMPAT(lroundl);
584
585#if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ )
586 /* C90 doesn't know about long long. Make sure you are passing -std=c99 or -std=gnu99 or better if you need this. */
587 extern long long int llrintl( long double ) __LIBMLDBL_COMPAT(llrintl);
588 extern long long int llroundl( long double ) __LIBMLDBL_COMPAT(llroundl);
589#endif /* #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) */
590
591extern long double truncl( long double ) __LIBMLDBL_COMPAT(truncl);
592extern long double fmodl( long double, long double) __LIBMLDBL_COMPAT(fmodl);
593extern long double remainderl( long double, long double ) __LIBMLDBL_COMPAT(remainderl);
594extern long double remquol( long double, long double, int * ) __LIBMLDBL_COMPAT(remquol);
595extern long double copysignl( long double, long double ) __LIBMLDBL_COMPAT(copysignl);
596extern long double nanl( const char * ) __LIBMLDBL_COMPAT(nanl);
597extern long double nextafterl( long double, long double ) __LIBMLDBL_COMPAT(nextafterl);
598extern double nexttoward( double, long double ) __LIBMLDBL_COMPAT(nexttoward);
599extern float nexttowardf( float, long double ) __LIBMLDBL_COMPAT(nexttowardf);
600extern long double nexttowardl( long double, long double ) __LIBMLDBL_COMPAT(nexttowardl);
601extern long double fdiml( long double, long double ) __LIBMLDBL_COMPAT(fdiml);
602extern long double fmaxl( long double, long double ) __LIBMLDBL_COMPAT(fmaxl);
603extern long double fminl( long double, long double ) __LIBMLDBL_COMPAT(fminl);
604extern long double fmal( long double, long double, long double ) __LIBMLDBL_COMPAT(fmal);
605#endif /* __WANT_LONG_DOUBLE_FORMAT__ */
606
607#define isgreater(x, y) __builtin_isgreater ((x),(y))
608#define isgreaterequal(x, y) __builtin_isgreaterequal ((x),(y))
609#define isless(x, y) __builtin_isless ((x),(y))
610#define islessequal(x, y) __builtin_islessequal ((x),(y))
611#define islessgreater(x, y) __builtin_islessgreater ((x),(y))
612#define isunordered(x, y) __builtin_isunordered ((x),(y))
613
614extern double __inf( void );
615extern float __inff( void );
616extern float __nan( void ); /* 10.3 (and later) must retain in ABI for backward compatability */
617
618#if !defined(_ANSI_SOURCE)
619extern double j0 ( double );
620extern double j1 ( double );
621extern double jn ( int, double );
622
623extern double y0 ( double );
624extern double y1 ( double );
625extern double yn ( int, double );
626
627/*
628 * Scalb Travellers' advisory:
629 * ---------------------------
630 *
631 * Reduction of Information advisory -- This advisory may constitute "too much information". Readers who are easily panicked
632 * or confused may be needlessly panicked or confused by this advisory.
633 *
634 * We are in the process of retiring the legacy scalb. IEEE-754 did not specify what the argument types should be
635 * for scalb. We guessed scalb(double, int) -- ints are faster to use here -- but our guess and what later standards
636 * standard eventually settled on did not agree. To be compliant with these standards, our scalb needs to be scalb(double, double).
637 * Unfortunately, we have a commitment to be binary compatible with old software compiled against scalb(double, int)
638 * for older operating systems, so the old symbol _scalb must live on in perpetuity in the __ppc__ binary interface to service
639 * this need. To deal with this problem, we have introduced a new binary symbol _scalb$UNIX2003 and did some magic below
640 * so that when you now compile against scalb() on a __ppc__ application, you get linked to _scalb$UNIX2003 instead. Thus,
641 * this constitutes a source level *** API CHANGE *** from scalb( double, int ) to scalb( double, double) on __ppc__ only
642 * that your source will need to contend with if you compile with this header. On __ppc__, all ints are exactly representable
643 * as doubles so from an arithmetic standpoint, this should cause no changes arithmetically from parameters of int type, but there
644 * remains the danger of triggering various compiler warnings that might balloon to more serious problems under -Werror.
645 *
646 * On __ppc64__, __i386__ and future archs, scalb has always been scalb( double, double) and will continue to be so. Thus, this change
647 * will make scalb on all platforms behave identically, with the same parameter types. The change will also eliminate GCC warnings about
648 * the math.h scalb declaration not matching the gcc4 builtin version.
649 *
650 * The intent is that you will "never know" that a change occurred, and your code should "just do the right thing" without modification.
651 * However, if you would like to sidestep any problems associated with this move, it is suggested that you use the C99 scalbn or scalbln
652 * or single/long double variants as appropriate instead. Their behavior and type is rigorously defined. There should be no hidden arithmetic
653 * "gotchas" if you simply replace all legacy calls to scalb with scalbn, since they essentially do the same thing. If you
654 * decide to take this step, you should exercise due diligence to make sure that scalbn is present in the oldest version of
655 * MacOS X that you support. Otherwise, your application may fail to load on older systems. C99 support was introduced in MacOS X.3.9.
656 *
657 * Use of the symbol _scalb$UNIX2003 should not in itself be construed to mean that scalb$UNIX2003 necessarily is UNIX 2003 compliant.
658 * UNIX is a registered trademark of The Open Group.
659 */
660
661/* maps to _scalb$UNIX2003 on __ppc__ and _scalb elsewhere */
662#if defined( __ppc__ )
663 #if defined( __GNUC__ ) && ! defined( __XLC__ ) && ( ! defined( __ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__) || __ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__-0 >= 1040 )
664 extern double scalb ( double, double ) __asm("_scalb$UNIX2003" );
665 #else
666 extern double scalb ( double , int );
667 #endif
668#else
669 extern double scalb ( double, double );
670#endif
671
672#define M_E 2.71828182845904523536028747135266250 /* e */
673#define M_LOG2E 1.44269504088896340735992468100189214 /* log_2(e) */
674#define M_LOG10E 0.434294481903251827651128918916605082 /* log_10(e) */
675#define M_LN2 0.693147180559945309417232121458176568 /* log_e(2) */
676#define M_LN10 2.30258509299404568401799145468436421 /* log_e(10) */
677#define M_PI 3.14159265358979323846264338327950288 /* pi */
678#define M_PI_2 1.57079632679489661923132169163975144 /* pi/2 */
679#define M_PI_4 0.785398163397448309615660845819875721 /* pi/4 */
680#define M_1_PI 0.318309886183790671537767526745028724 /* 1/pi */
681#define M_2_PI 0.636619772367581343075535053490057448 /* 2/pi */
682#define M_2_SQRTPI 1.12837916709551257389615890312154517 /* 2/sqrt(pi) */
683#define M_SQRT2 1.41421356237309504880168872420969808 /* sqrt(2) */
684#define M_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */
685
686#define MAXFLOAT ((float)3.40282346638528860e+38)
687extern int signgam;
688
689#endif /* !defined(_ANSI_SOURCE) */
690
691#if !defined(__NOEXTENSIONS__) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))
692#define __WANT_EXTENSIONS__
693#endif
694
695#ifdef __WANT_EXTENSIONS__
696
697#define FP_SNAN FP_NAN
698#define FP_QNAN FP_NAN
699
700extern long int rinttol ( double );
701
702extern long int roundtol ( double );
703
704typedef struct __complex_s {
705 double Real;
706 double Imag;
707} __complex_t;
708
709/*
710 * XOPEN/SVID
711 */
712#if !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))
713
714#if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))
715enum fdversion {_fdlibm_ieee = -1, _fdlibm_svid, _fdlibm_xopen, _fdlibm_posix}; /* Legacy fdlibm constructs */
716#define fdlibm_ieee _fdlibm_ieee
717#define fdlibm_svid _fdlibm_svid
718#define fdlibm_xopen _fdlibm_xopen
719#define fdlibm_posix _fdlibm_posix
720
721#define _LIB_VERSION_TYPE enum fdversion
722#define _LIB_VERSION _fdlib_version
723
724/* if global variable _LIB_VERSION is not desirable, one may
725 * change the following to be a constant by:
726 * #define _LIB_VERSION_TYPE const enum version
727 * In that case, after one initializes the value _LIB_VERSION (see
728 * s_lib_version.c) during compile time, it cannot be modified
729 * in the middle of a program
730 */
731extern _LIB_VERSION_TYPE _LIB_VERSION;
732
733#define _IEEE_ fdlibm_ieee
734#define _SVID_ fdlibm_svid
735#define _XOPEN_ fdlibm_xopen
736#define _POSIX_ fdlibm_posix
737
738#if !defined(__cplusplus)
739struct exception {
740 int type;
741 char *name;
742 double arg1;
743 double arg2;
744 double retval;
745};
746#endif
747
748#define HUGE MAXFLOAT
749
750/*
751 * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
752 * (one may replace the following line by "#include <values.h>")
753 */
754
755#define X_TLOSS 1.41484755040568800000e+16
756
757#define DOMAIN 1
758#define SING 2
759#define OVERFLOW 3
760#define UNDERFLOW 4
761#define TLOSS 5
762#define PLOSS 6
763
764#endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */
765#endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */
766
767#if !defined( __STRICT_ANSI__) && !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))
768
769extern int finite ( double );
770
771extern double gamma ( double );
772
773#if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))
774
775#if !defined(__cplusplus)
776extern int matherr ( struct exception * );
777#endif
778
779/*
780 * IEEE Test Vector
781 */
782extern double significand ( double );
783
784/*
785 * BSD math library entry points
786 */
787extern double drem ( double, double );
788
789/*
790 * Reentrant version of gamma & lgamma; passes signgam back by reference
791 * as the second argument; user must allocate space for signgam.
792 */
793#ifdef _REENTRANT
794extern double gamma_r ( double, int * );
795extern double lgamma_r ( double, int * );
796#endif /* _REENTRANT */
797#endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */
798#endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */
799
800#endif /* __WANT_EXTENSIONS__ */
801
802/*
803 * The following replacements for libm's floor, floorf, ceil, and ceilf are activated
804 * when the flag "-ffast-math" is passed to the gcc compiler. These functions do not
805 * distinguish between -0.0 and 0.0, so are not IEC6509 compliant for argument -0.0.
806 */
807#if defined(__FAST_MATH__) && !defined(__cplusplus)
808
809#define __FSELS(e,t,f) (((e) >= 0.0f) ? (t) : (f))
810#define __FSEL(e,t,f) (((e) >= 0.0) ? (t) : (f))
811
812static __inline__ float __fastmath_floorf( float f ) __attribute__((__always_inline__));
813static __inline__ float __fastmath_floorf( float f )
814{
815 float b, c, d, e, g, h, t;
816
817 c = __FSELS( f, -8388608.f, 8388608.f ); b = fabsf( f );
818 d = f - c; e = b - 8388608.f;
819 __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */
820 d = d + c;
821 g = f - d;
822 h = __FSELS( g, 0.0f, 1.0f );
823 t = d - h;
824 return __FSELS( e, f, t );
825}
826
827static __inline__ float __fastmath_ceilf( float f ) __attribute__((__always_inline__));
828static __inline__ float __fastmath_ceilf( float f )
829{
830 float b, c, d, e, g, h, t;
831
832 c = __FSELS( f, -8388608.f, 8388608.f ); b = fabsf( f );
833 d = f - c; e = b - 8388608.f;
834 __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */
835 d = d + c;
836 g = d - f;
837 h = __FSELS( g, 0.0f, 1.0f );
838 t = d + h;
839 return __FSELS( e, f, t );
840}
841
842static __inline__ double __fastmath_floor( double f ) __attribute__((__always_inline__));
843static __inline__ double __fastmath_floor( double f )
844{
845 double b, c, d, e, g, h, t;
846
847 c = __FSEL( f, -4503599627370496., 4503599627370496. ); b = fabs( f );
848 d = f - c; e = b - 4503599627370496.;
849 __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */
850 d = d + c;
851 g = f - d;
852 h = __FSEL( g, 0.0, 1.0 );
853 t = d - h;
854 return __FSEL( e, f, t );
855}
856
857static __inline__ double __fastmath_ceil( double f ) __attribute__((__always_inline__));
858static __inline__ double __fastmath_ceil( double f )
859{
860 double b, c, d, e, g, h, t;
861
862 c = __FSEL( f, -4503599627370496., 4503599627370496. ); b = fabs( f );
863 d = f - c; e = b - 4503599627370496.;
864 __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */
865 d = d + c;
866 g = d - f;
867 h = __FSEL( g, 0.0, 1.0 );
868 t = d + h;
869 return __FSEL( e, f, t );
870}
871
872#define floorf(x) __fastmath_floorf((x))
873#define ceilf(x) __fastmath_ceilf((x))
874#define floor(x) __fastmath_floor((x))
875#define ceil(x) __fastmath_ceil((x))
876
877#endif /* __FAST_MATH__ && !__cplusplus */
878
879#ifdef __cplusplus
880}
881#endif
882
883#endif /* __MATH__ */