| 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 | #ifdef __cplusplus␊ |
| 36 | extern "C" {␊ |
| 37 | #endif␊ |
| 38 | ␊ |
| 39 | /******************************************************************************␊ |
| 40 | * Floating point data types *␊ |
| 41 | ******************************************************************************/␊ |
| 42 | ␊ |
| 43 | /*␉Define float_t and double_t per C standard, ISO/IEC 9899:1999 7.12 2,␊ |
| 44 | ␉taking advantage of GCC's __FLT_EVAL_METHOD__ (which a compiler may␊ |
| 45 | ␉define anytime and GCC does) that shadows FLT_EVAL_METHOD (which a compiler␊ |
| 46 | ␉must and may define only in float.h).␊ |
| 47 | */␊ |
| 48 | #if __FLT_EVAL_METHOD__ == 0␊ |
| 49 | ␉typedef float float_t;␊ |
| 50 | ␉typedef double double_t;␊ |
| 51 | #elif __FLT_EVAL_METHOD__ == 1␊ |
| 52 | ␉typedef double float_t;␊ |
| 53 | ␉typedef double double_t;␊ |
| 54 | #elif __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ == -1␊ |
| 55 | ␉typedef long double float_t;␊ |
| 56 | ␉typedef long double double_t;␊ |
| 57 | #else /* __FLT_EVAL_METHOD__ */␊ |
| 58 | ␉#error "Unsupported value of __FLT_EVAL_METHOD__."␊ |
| 59 | #endif /* __FLT_EVAL_METHOD__ */␊ |
| 60 | ␊ |
| 61 | ␊ |
| 62 | #if defined(__GNUC__)␊ |
| 63 | ␉#define␉HUGE_VAL␉__builtin_huge_val()␊ |
| 64 | ␉#define␉HUGE_VALF␉__builtin_huge_valf()␊ |
| 65 | ␉#define␉HUGE_VALL␉__builtin_huge_vall()␊ |
| 66 | #define NAN __builtin_nanf("0x7fc00000") /* Constant expression, can be used as initializer. */␊ |
| 67 | #define __MATH_H_ALWAYS_INLINE__␉␉__attribute__ ((always_inline))␊ |
| 68 | #else␊ |
| 69 | #define␉HUGE_VAL␉1e500␊ |
| 70 | #define␉HUGE_VALF␉1e50f␊ |
| 71 | #define␉HUGE_VALL␉1e5000L␊ |
| 72 | #define NAN␉␉__nan( )␊ |
| 73 | #define __MATH_H_ALWAYS_INLINE__␊ |
| 74 | #endif␊ |
| 75 | ␊ |
| 76 | #define INFINITY␉HUGE_VALF␊ |
| 77 | ␊ |
| 78 | ␊ |
| 79 | /******************************************************************************␊ |
| 80 | * Taxonomy of floating point data types *␊ |
| 81 | ******************************************************************************/␊ |
| 82 | ␊ |
| 83 | #define FP_NAN 1␊ |
| 84 | #define FP_INFINITE 2␊ |
| 85 | #define FP_ZERO 3␊ |
| 86 | #define FP_NORMAL 4␊ |
| 87 | #define FP_SUBNORMAL 5␊ |
| 88 | #define FP_SUPERNORMAL 6 /* meaningful only on PowerPC */␊ |
| 89 | ␊ |
| 90 | /* fma() *function call* is more costly than equivalent (in-line) multiply and add operations */␊ |
| 91 | /* For single and double precision, the cost isn't too bad, because we can fall back on higher */␊ |
| 92 | /* precision hardware, with the necessary range to handle infinite precision products. However, */␊ |
| 93 | /* expect the long double fma to be at least an order of magnitude slower than a simple multiply */␊ |
| 94 | /* and an add. */␊ |
| 95 | #undef FP_FAST_FMA␊ |
| 96 | #undef FP_FAST_FMAF␊ |
| 97 | #undef FP_FAST_FMAL␊ |
| 98 | ␊ |
| 99 | /* The values returned by `ilogb' for 0 and NaN respectively. */␊ |
| 100 | #define FP_ILOGB0␉(-2147483647 - 1)␊ |
| 101 | #define FP_ILOGBNAN␉(-2147483647 - 1)␊ |
| 102 | ␊ |
| 103 | /* Bitmasks for the math_errhandling macro. */␊ |
| 104 | #define MATH_ERRNO␉1␉/* errno set by math functions. */␊ |
| 105 | #define MATH_ERREXCEPT␉2␉/* Exceptions raised by math functions. */␊ |
| 106 | ␊ |
| 107 | #define math_errhandling (__math_errhandling())␊ |
| 108 | extern unsigned int __math_errhandling ( void );␊ |
| 109 | ␊ |
| 110 | /********************************************************************************␊ |
| 111 | * *␊ |
| 112 | * Inquiry macros *␊ |
| 113 | * *␊ |
| 114 | |
| 115 | * isnormal Non-zero if and only if the argument x is normalized. *␊ |
| 116 | * isfinite Non-zero if and only if the argument x is finite. *␊ |
| 117 | * isnan Non-zero if and only if the argument x is a NaN. *␊ |
| 118 | * signbit Non-zero if and only if the sign of the argument x is *␊ |
| 119 | * negative. This includes, NaNs, infinities and zeros. *␊ |
| 120 | * *␊ |
| 121 | ********************************************************************************/␊ |
| 122 | ␊ |
| 123 | #define fpclassify(x)␉\␊ |
| 124 | ␉(␉sizeof (x) == sizeof(float )␉?␉__fpclassifyf((float)(x))␉\␊ |
| 125 | ␉:␉sizeof (x) == sizeof(double)␉?␉__fpclassifyd((double)(x))␉\␊ |
| 126 | ␉␉␉␉␉␉␉␉␉␉:␉__fpclassify ((long double)(x)))␊ |
| 127 | ␊ |
| 128 | extern int __fpclassifyf(float );␊ |
| 129 | extern int __fpclassifyd(double );␊ |
| 130 | extern int __fpclassify (long double);␊ |
| 131 | ␊ |
| 132 | #if defined( __GNUC__ ) && 0 == __FINITE_MATH_ONLY__ ␊ |
| 133 | /* Yes, that's right. You only get the fast iswhatever() macros if you do NOT turn on -ffast-math. */␊ |
| 134 | /* These inline functions require the compiler to be compiling to standard in order to work. */␊ |
| 135 | /* -ffast-math, among other things, implies that NaNs don't happen. The compiler can in that case */␊ |
| 136 | /* optimize x != x to be false always, wheras it would be true for NaNs. That breaks __inline_isnan() */␊ |
| 137 | /* below. */␊ |
| 138 | ␉#define isnormal(x)␉\␊ |
| 139 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__inline_isnormalf((float)(x))␉\␊ |
| 140 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__inline_isnormald((double)(x))␉\␊ |
| 141 | ␉␉␉␉␉␉␉␉␉␉␉:␉__inline_isnormal ((long double)(x)))␊ |
| 142 | ␊ |
| 143 | ␉#define isfinite(x)␉\␊ |
| 144 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__inline_isfinitef((float)(x))␉\␊ |
| 145 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__inline_isfinited((double)(x))␉\␊ |
| 146 | ␉␉␉␉␉␉␉␉␉␉␉:␉__inline_isfinite ((long double)(x)))␊ |
| 147 | ␊ |
| 148 | ␉#define isinf(x)␉\␊ |
| 149 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__inline_isinff((float)(x))␉\␊ |
| 150 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__inline_isinfd((double)(x))␉\␊ |
| 151 | ␉␉␉␉␉␉␉␉␉␉␉:␉__inline_isinf ((long double)(x)))␊ |
| 152 | ␊ |
| 153 | ␉#define isnan(x)␉\␊ |
| 154 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__inline_isnanf((float)(x))␉\␊ |
| 155 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__inline_isnand((double)(x))␉\␊ |
| 156 | ␉␉␉␉␉␉␉␉␉␉␉:␉__inline_isnan ((long double)(x)))␊ |
| 157 | ␊ |
| 158 | ␉#define signbit(x)␉\␊ |
| 159 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__inline_signbitf((float)(x))␉\␊ |
| 160 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__inline_signbitd((double)(x))␉\␊ |
| 161 | ␉␉␉␉␉␉␉␉␉␉␉:␉__inline_signbit((long double)(x)))␊ |
| 162 | ␊ |
| 163 | ␉static __inline__ int __inline_isfinitef␉(float ) __MATH_H_ALWAYS_INLINE__;␊ |
| 164 | ␉static __inline__ int __inline_isfinited␉(double ) __MATH_H_ALWAYS_INLINE__;␊ |
| 165 | ␉static __inline__ int __inline_isfinite␉(long double) __MATH_H_ALWAYS_INLINE__;␊ |
| 166 | ␉static __inline__ int __inline_isinff␉␉(float ) __MATH_H_ALWAYS_INLINE__;␊ |
| 167 | ␉static __inline__ int __inline_isinfd␉␉(double ) __MATH_H_ALWAYS_INLINE__;␊ |
| 168 | ␉static __inline__ int __inline_isinf␉␉(long double) __MATH_H_ALWAYS_INLINE__;␊ |
| 169 | ␉static __inline__ int __inline_isnanf␉␉(float ) __MATH_H_ALWAYS_INLINE__;␊ |
| 170 | ␉static __inline__ int __inline_isnand␉␉(double ) __MATH_H_ALWAYS_INLINE__;␊ |
| 171 | ␉static __inline__ int __inline_isnan␉␉(long double) __MATH_H_ALWAYS_INLINE__;␊ |
| 172 | ␉static __inline__ int __inline_isnormalf (float ) __MATH_H_ALWAYS_INLINE__;␊ |
| 173 | ␉static __inline__ int __inline_isnormald (double ) __MATH_H_ALWAYS_INLINE__;␊ |
| 174 | ␉static __inline__ int __inline_isnormal (long double) __MATH_H_ALWAYS_INLINE__;␊ |
| 175 | ␉static __inline__ int __inline_signbitf (float ) __MATH_H_ALWAYS_INLINE__;␊ |
| 176 | ␉static __inline__ int __inline_signbitd (double ) __MATH_H_ALWAYS_INLINE__;␊ |
| 177 | ␉static __inline__ int __inline_signbit (long double) __MATH_H_ALWAYS_INLINE__;␊ |
| 178 | ␉␊ |
| 179 | ␉static __inline__ int __inline_isinff( float __x ) { return __builtin_fabsf(__x) == __builtin_inff(); }␊ |
| 180 | ␉static __inline__ int __inline_isinfd( double __x ) { return __builtin_fabs(__x) == __builtin_inf(); }␊ |
| 181 | ␉static __inline__ int __inline_isinf( long double __x ) { return __builtin_fabsl(__x) == __builtin_infl(); }␊ |
| 182 | ␉static __inline__ int __inline_isfinitef( float __x ) { return __x == __x && __builtin_fabsf(__x) != __builtin_inff(); }␊ |
| 183 | ␉static __inline__ int __inline_isfinited( double __x ) { return __x == __x && __builtin_fabs(__x) != __builtin_inf(); }␊ |
| 184 | ␉static __inline__ int __inline_isfinite( long double __x ) { return __x == __x && __builtin_fabsl(__x) != __builtin_infl(); }␊ |
| 185 | ␉static __inline__ int __inline_isnanf( float __x ) { return __x != __x; }␊ |
| 186 | ␉static __inline__ int __inline_isnand( double __x ) { return __x != __x; }␊ |
| 187 | ␉static __inline__ int __inline_isnan( long double __x ) { return __x != __x; }␊ |
| 188 | ␉static __inline__ int __inline_signbitf( float __x ) { union{ float __f; unsigned int __u; }__u; __u.__f = __x; return (int)(__u.__u >> 31); }␊ |
| 189 | ␉static __inline__ int __inline_signbitd( double __x ) { union{ double __f; unsigned int __u[2]; }__u; __u.__f = __x; return (int)(__u.__u[1] >> 31); }␊ |
| 190 | ␉static __inline__ int __inline_signbit( long double __x ){ union{ long double __ld; struct{ unsigned int __m[2]; short __sexp; }__p; }__u; __u.__ld = __x; return (int) (((unsigned short) __u.__p.__sexp) >> 15); } ␊ |
| 191 | ␉static __inline__ int __inline_isnormalf( float __x ) { float fabsf = __builtin_fabsf(__x); if( __x != __x ) return 0; return fabsf < __builtin_inff() && fabsf >= __FLT_MIN__; } ␊ |
| 192 | ␉static __inline__ int __inline_isnormald( double __x ) { double fabsf = __builtin_fabs(__x); if( __x != __x ) return 0; return fabsf < __builtin_inf() && fabsf >= __DBL_MIN__; } ␊ |
| 193 | ␉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__; } ␊ |
| 194 | ␉␊ |
| 195 | #else␊ |
| 196 | ␊ |
| 197 | ␉#define isnormal(x)␉\␊ |
| 198 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__isnormalf((float)(x))␉\␊ |
| 199 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__isnormald((double)(x))␉\␊ |
| 200 | ␉␉␉␉␉␉␉␉␉␉␉:␉__isnormal ((long double)(x)))␊ |
| 201 | ␊ |
| 202 | ␉#define isfinite(x)␉\␊ |
| 203 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__isfinitef((float)(x))␉\␊ |
| 204 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__isfinited((double)(x))␉\␊ |
| 205 | ␉␉␉␉␉␉␉␉␉␉␉:␉__isfinite ((long double)(x)))␊ |
| 206 | ␊ |
| 207 | ␉#define isinf(x)␉\␊ |
| 208 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__isinff((float)(x))␉\␊ |
| 209 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__isinfd((double)(x))␉\␊ |
| 210 | ␉␉␉␉␉␉␉␉␉␉␉:␉__isinf ((long double)(x)))␊ |
| 211 | ␊ |
| 212 | ␉#define isnan(x)␉\␊ |
| 213 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__isnanf((float)(x))␉\␊ |
| 214 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__isnand((double)(x))␉\␊ |
| 215 | ␉␉␉␉␉␉␉␉␉␉␉:␉__isnan ((long double)(x)))␊ |
| 216 | ␊ |
| 217 | ␉#define signbit(x)␉\␊ |
| 218 | ␉␉(␉sizeof (x) == sizeof(float )␉?␉__signbitf((float)(x))␉\␊ |
| 219 | ␉␉:␉sizeof (x) == sizeof(double)␉?␉__signbitd((double)(x))␉\␊ |
| 220 | ␉␉␉␉␉␉␉␉␉␉␉:␉__signbitl((long double)(x)))␊ |
| 221 | ␊ |
| 222 | ␊ |
| 223 | ␉extern int __isnormalf (float );␊ |
| 224 | ␉extern int __isnormald (double );␊ |
| 225 | ␉extern int __isnormal (long double);␊ |
| 226 | ␊ |
| 227 | ␉extern int __isfinitef (float );␊ |
| 228 | ␉extern int __isfinited (double );␊ |
| 229 | ␉extern int __isfinite (long double);␊ |
| 230 | ␊ |
| 231 | ␉extern int __isinff (float );␊ |
| 232 | ␉extern int __isinfd (double );␊ |
| 233 | ␉extern int __isinf (long double);␊ |
| 234 | ␊ |
| 235 | ␉extern int __isnanf (float );␊ |
| 236 | ␉extern int __isnand (double );␊ |
| 237 | ␉extern int __isnan (long double);␊ |
| 238 | ␊ |
| 239 | ␉extern int __signbitf (float );␊ |
| 240 | ␉extern int __signbitd (double );␊ |
| 241 | ␉extern int __signbitl (long double);␊ |
| 242 | ␊ |
| 243 | #endif␊ |
| 244 | ␊ |
| 245 | ␊ |
| 246 | ␊ |
| 247 | /********************************************************************************␊ |
| 248 | * *␊ |
| 249 | * Math Functions *␊ |
| 250 | * *␊ |
| 251 | ********************************************************************************/␊ |
| 252 | ␊ |
| 253 | extern double acos( double );␊ |
| 254 | extern float acosf( float );␊ |
| 255 | ␊ |
| 256 | extern double asin( double );␊ |
| 257 | extern float asinf( float );␊ |
| 258 | ␊ |
| 259 | extern double atan( double );␊ |
| 260 | extern float atanf( float );␊ |
| 261 | ␊ |
| 262 | extern double atan2( double, double );␊ |
| 263 | extern float atan2f( float, float );␊ |
| 264 | ␊ |
| 265 | extern double cos( double );␊ |
| 266 | extern float cosf( float );␊ |
| 267 | ␊ |
| 268 | extern double sin( double );␊ |
| 269 | extern float sinf( float );␊ |
| 270 | ␊ |
| 271 | extern double tan( double );␊ |
| 272 | extern float tanf( float );␊ |
| 273 | ␊ |
| 274 | extern double acosh( double );␊ |
| 275 | extern float acoshf( float );␊ |
| 276 | ␊ |
| 277 | extern double asinh( double );␊ |
| 278 | extern float asinhf( float );␊ |
| 279 | ␊ |
| 280 | extern double atanh( double );␊ |
| 281 | extern float atanhf( float );␊ |
| 282 | ␊ |
| 283 | extern double cosh( double );␊ |
| 284 | extern float coshf( float );␊ |
| 285 | ␊ |
| 286 | extern double sinh( double );␊ |
| 287 | extern float sinhf( float );␊ |
| 288 | ␊ |
| 289 | extern double tanh( double );␊ |
| 290 | extern float tanhf( float );␊ |
| 291 | ␊ |
| 292 | extern double exp ( double );␊ |
| 293 | extern float expf ( float );␊ |
| 294 | ␊ |
| 295 | extern double exp2 ( double ); ␊ |
| 296 | extern float exp2f ( float );␊ |
| 297 | ␊ |
| 298 | extern double expm1 ( double ); ␊ |
| 299 | extern float expm1f ( float );␊ |
| 300 | ␊ |
| 301 | extern double log ( double );␊ |
| 302 | extern float logf ( float );␊ |
| 303 | ␊ |
| 304 | extern double log10 ( double );␊ |
| 305 | extern float log10f ( float );␊ |
| 306 | ␊ |
| 307 | extern double log2 ( double );␊ |
| 308 | extern float log2f ( float );␊ |
| 309 | ␊ |
| 310 | extern double log1p ( double );␊ |
| 311 | extern float log1pf ( float );␊ |
| 312 | ␊ |
| 313 | extern double logb ( double );␊ |
| 314 | extern float logbf ( float );␊ |
| 315 | ␊ |
| 316 | extern double modf ( double, double * );␊ |
| 317 | extern float modff ( float, float * );␊ |
| 318 | ␊ |
| 319 | extern double ldexp ( double, int );␊ |
| 320 | extern float ldexpf ( float, int );␊ |
| 321 | ␊ |
| 322 | extern double frexp ( double, int * );␊ |
| 323 | extern float frexpf ( float, int * );␊ |
| 324 | ␊ |
| 325 | extern int ilogb ( double );␊ |
| 326 | extern int ilogbf ( float );␊ |
| 327 | ␊ |
| 328 | extern double scalbn ( double, int );␊ |
| 329 | extern float scalbnf ( float, int );␊ |
| 330 | ␊ |
| 331 | extern double scalbln ( double, long int );␊ |
| 332 | extern float scalblnf ( float, long int );␊ |
| 333 | ␊ |
| 334 | extern double fabs( double );␊ |
| 335 | extern float fabsf( float );␊ |
| 336 | ␊ |
| 337 | extern double cbrt( double );␊ |
| 338 | extern float cbrtf( float );␊ |
| 339 | ␊ |
| 340 | extern double hypot ( double, double );␊ |
| 341 | extern float hypotf ( float, float );␊ |
| 342 | ␊ |
| 343 | extern double pow ( double, double );␊ |
| 344 | extern float powf ( float, float );␊ |
| 345 | ␊ |
| 346 | extern double sqrt( double );␊ |
| 347 | extern float sqrtf( float );␊ |
| 348 | ␊ |
| 349 | extern double erf( double );␊ |
| 350 | extern float erff( float );␊ |
| 351 | ␊ |
| 352 | extern double erfc( double );␊ |
| 353 | extern float erfcf( float );␊ |
| 354 | ␊ |
| 355 | /*␉lgamma and lgammaf are not thread-safe. The thread-safe variants␊ |
| 356 | *␉lgamma_r and lgammaf_r are available on OS X 10.6 and later.␊ |
| 357 | *␊ |
| 358 | *␉To use the thread-safe variants, you must define the _REENTRANT symbol.␊ |
| 359 | */␊ |
| 360 | extern double lgamma( double );␊ |
| 361 | extern float lgammaf( float );␊ |
| 362 | ␊ |
| 363 | extern double tgamma( double );␊ |
| 364 | extern float tgammaf( float );␊ |
| 365 | ␊ |
| 366 | extern double ceil ( double );␊ |
| 367 | extern float ceilf ( float );␊ |
| 368 | ␊ |
| 369 | extern double floor ( double );␊ |
| 370 | extern float floorf ( float );␊ |
| 371 | ␊ |
| 372 | extern double nearbyint ( double );␊ |
| 373 | extern float nearbyintf ( float );␊ |
| 374 | ␊ |
| 375 | extern double rint ( double );␊ |
| 376 | extern float rintf ( float );␊ |
| 377 | ␊ |
| 378 | extern long int lrint ( double );␊ |
| 379 | extern long int lrintf ( float );␊ |
| 380 | ␊ |
| 381 | extern double round ( double );␊ |
| 382 | extern float roundf ( float );␊ |
| 383 | ␊ |
| 384 | extern long int lround ( double );␊ |
| 385 | extern long int lroundf ( float );␊ |
| 386 | ␊ |
| 387 | #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ )␊ |
| 388 | ␊ |
| 389 | /* long long is not part of C90. Make sure you are passing -std=c99 or -std=gnu99 or better if you need this. */␊ |
| 390 | extern long long int llrint ( double );␊ |
| 391 | extern long long int llrintf ( float );␊ |
| 392 | ␊ |
| 393 | extern long long int llround ( double );␊ |
| 394 | extern long long int llroundf ( float );␊ |
| 395 | ␊ |
| 396 | #endif /* #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) */␊ |
| 397 | ␊ |
| 398 | extern double trunc ( double );␊ |
| 399 | extern float truncf ( float );␊ |
| 400 | ␊ |
| 401 | extern double fmod ( double, double );␊ |
| 402 | extern float fmodf ( float, float );␊ |
| 403 | ␊ |
| 404 | extern double remainder ( double, double );␊ |
| 405 | extern float remainderf ( float, float );␊ |
| 406 | ␊ |
| 407 | extern double remquo ( double, double, int * );␊ |
| 408 | extern float remquof ( float, float, int * );␊ |
| 409 | ␊ |
| 410 | extern double copysign ( double, double );␊ |
| 411 | extern float copysignf ( float, float );␊ |
| 412 | ␊ |
| 413 | extern double nan( const char * );␊ |
| 414 | extern float nanf( const char * );␊ |
| 415 | ␊ |
| 416 | extern double nextafter ( double, double );␊ |
| 417 | extern float nextafterf ( float, float );␊ |
| 418 | ␊ |
| 419 | extern double fdim ( double, double );␊ |
| 420 | extern float fdimf ( float, float );␊ |
| 421 | ␊ |
| 422 | extern double fmax ( double, double );␊ |
| 423 | extern float fmaxf ( float, float );␊ |
| 424 | ␊ |
| 425 | extern double fmin ( double, double );␊ |
| 426 | extern float fminf ( float, float );␊ |
| 427 | ␊ |
| 428 | extern double fma ( double, double, double );␊ |
| 429 | extern float fmaf ( float, float, float );␊ |
| 430 | ␊ |
| 431 | extern long double acosl(long double);␊ |
| 432 | extern long double asinl(long double);␊ |
| 433 | extern long double atanl(long double);␊ |
| 434 | extern long double atan2l(long double, long double);␊ |
| 435 | extern long double cosl(long double);␊ |
| 436 | extern long double sinl(long double);␊ |
| 437 | extern long double tanl(long double);␊ |
| 438 | extern long double acoshl(long double);␊ |
| 439 | extern long double asinhl(long double);␊ |
| 440 | extern long double atanhl(long double);␊ |
| 441 | extern long double coshl(long double);␊ |
| 442 | extern long double sinhl(long double);␊ |
| 443 | extern long double tanhl(long double);␊ |
| 444 | extern long double expl(long double);␊ |
| 445 | extern long double exp2l(long double);␊ |
| 446 | extern long double expm1l(long double);␊ |
| 447 | extern long double logl(long double);␊ |
| 448 | extern long double log10l(long double);␊ |
| 449 | extern long double log2l(long double);␊ |
| 450 | extern long double log1pl(long double);␊ |
| 451 | extern long double logbl(long double);␊ |
| 452 | extern long double modfl(long double, long double *);␊ |
| 453 | extern long double ldexpl(long double, int);␊ |
| 454 | extern long double frexpl(long double, int *);␊ |
| 455 | extern int ilogbl(long double);␊ |
| 456 | extern long double scalbnl(long double, int);␊ |
| 457 | extern long double scalblnl(long double, long int);␊ |
| 458 | extern long double fabsl(long double);␊ |
| 459 | extern long double cbrtl(long double);␊ |
| 460 | extern long double hypotl(long double, long double);␊ |
| 461 | extern long double powl(long double, long double);␊ |
| 462 | extern long double sqrtl(long double);␊ |
| 463 | extern long double erfl(long double);␊ |
| 464 | extern long double erfcl(long double);␊ |
| 465 | ␉␊ |
| 466 | /*␉lgammal is not thread-safe.␊ |
| 467 | *␉The thread-safe variant lgammal_r is available on OS X 10.6 and later.␊ |
| 468 | *␊ |
| 469 | *␉To use the thread-safe variant, you must define the _REENTRANT symbol.␊ |
| 470 | */␊ |
| 471 | extern long double lgammal(long double);␊ |
| 472 | ␉␊ |
| 473 | extern long double tgammal(long double);␊ |
| 474 | extern long double ceill(long double);␊ |
| 475 | extern long double floorl(long double);␊ |
| 476 | extern long double nearbyintl(long double);␊ |
| 477 | extern long double rintl(long double);␊ |
| 478 | extern long int lrintl(long double);␊ |
| 479 | extern long double roundl(long double);␊ |
| 480 | extern long int lroundl(long double);␊ |
| 481 | ␊ |
| 482 | #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ )␊ |
| 483 | /* long long is not part of C90. Make sure you are passing -std=c99 or -std=gnu99 or better if you need this. */␊ |
| 484 | extern long long int llrintl(long double);␊ |
| 485 | extern long long int llroundl(long double);␊ |
| 486 | #endif /* #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) */␊ |
| 487 | ␊ |
| 488 | extern long double truncl(long double);␊ |
| 489 | extern long double fmodl(long double, long double);␊ |
| 490 | extern long double remainderl(long double, long double);␊ |
| 491 | extern long double remquol(long double, long double, int *);␊ |
| 492 | extern long double copysignl(long double, long double);␊ |
| 493 | extern long double nanl(const char *);␊ |
| 494 | extern long double nextafterl(long double, long double);␊ |
| 495 | extern double nexttoward(double, long double);␊ |
| 496 | extern float nexttowardf(float, long double);␊ |
| 497 | extern long double nexttowardl(long double, long double);␊ |
| 498 | extern long double fdiml(long double, long double);␊ |
| 499 | extern long double fmaxl(long double, long double);␊ |
| 500 | extern long double fminl(long double, long double);␊ |
| 501 | extern long double fmal(long double, long double, long double);␊ |
| 502 | ␊ |
| 503 | #define isgreater(x, y) __builtin_isgreater ((x),(y))␊ |
| 504 | #define isgreaterequal(x, y) __builtin_isgreaterequal ((x),(y))␊ |
| 505 | #define isless(x, y) __builtin_isless ((x),(y))␊ |
| 506 | #define islessequal(x, y) __builtin_islessequal ((x),(y))␊ |
| 507 | #define islessgreater(x, y) __builtin_islessgreater ((x),(y))␊ |
| 508 | #define isunordered(x, y) __builtin_isunordered ((x),(y))␊ |
| 509 | ␊ |
| 510 | extern double ␉␉__inf( void );␊ |
| 511 | extern float ␉␉__inff( void );␊ |
| 512 | extern long double __infl( void );␊ |
| 513 | extern float ␉␉__nan( void ); /* 10.3 (and later) must retain in ABI for backward compatability */␊ |
| 514 | ␊ |
| 515 | #if !defined(_ANSI_SOURCE)␊ |
| 516 | extern double j0 ( double );␊ |
| 517 | ␊ |
| 518 | extern double j1 ( double );␊ |
| 519 | ␊ |
| 520 | extern double jn ( int, double );␊ |
| 521 | ␊ |
| 522 | extern double y0 ( double );␊ |
| 523 | ␊ |
| 524 | extern double y1 ( double );␊ |
| 525 | ␊ |
| 526 | extern double yn ( int, double );␊ |
| 527 | ␊ |
| 528 | extern double scalb ( double, double ); ␊ |
| 529 | ␊ |
| 530 | ␊ |
| 531 | #define M_E 2.71828182845904523536028747135266250 /* e */␊ |
| 532 | #define M_LOG2E 1.44269504088896340735992468100189214 /* log 2e */␊ |
| 533 | #define M_LOG10E 0.434294481903251827651128918916605082 /* log 10e */␊ |
| 534 | #define M_LN2 0.693147180559945309417232121458176568 /* log e2 */␊ |
| 535 | #define M_LN10 2.30258509299404568401799145468436421 /* log e10 */␊ |
| 536 | #define M_PI 3.14159265358979323846264338327950288 /* pi */␊ |
| 537 | #define M_PI_2 1.57079632679489661923132169163975144 /* pi/2 */␊ |
| 538 | #define M_PI_4 0.785398163397448309615660845819875721 /* pi/4 */␊ |
| 539 | #define M_1_PI 0.318309886183790671537767526745028724 /* 1/pi */␊ |
| 540 | #define M_2_PI 0.636619772367581343075535053490057448 /* 2/pi */␊ |
| 541 | #define M_2_SQRTPI 1.12837916709551257389615890312154517 /* 2/sqrt(pi) */␊ |
| 542 | #define M_SQRT2 1.41421356237309504880168872420969808 /* sqrt(2) */␊ |
| 543 | #define M_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */␊ |
| 544 | ␊ |
| 545 | #define␉MAXFLOAT␉((float)3.40282346638528860e+38)␊ |
| 546 | extern int signgam; /* required for unix 2003 */␊ |
| 547 | ␊ |
| 548 | ␊ |
| 549 | #endif /* !defined(_ANSI_SOURCE) */␊ |
| 550 | ␊ |
| 551 | #if !defined(__NOEXTENSIONS__) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))␊ |
| 552 | #define __WANT_EXTENSIONS__␊ |
| 553 | #endif␊ |
| 554 | ␊ |
| 555 | #ifdef __WANT_EXTENSIONS__␊ |
| 556 | ␊ |
| 557 | #define FP_SNAN␉␉FP_NAN␊ |
| 558 | #define FP_QNAN␉␉FP_NAN␊ |
| 559 | ␊ |
| 560 | extern long int rinttol ( double );␉␉/* Legacy API: please use C99 lrint() instead. */␊ |
| 561 | ␊ |
| 562 | extern long int roundtol ( double );␉/* Legacy API: please use C99 lround() instead. */␊ |
| 563 | ␊ |
| 564 | /*␊ |
| 565 | * XOPEN/SVID␊ |
| 566 | */␊ |
| 567 | #if !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))␊ |
| 568 | #if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))␊ |
| 569 | #if !defined(__cplusplus)␊ |
| 570 | /* used by matherr below */␊ |
| 571 | struct exception {␊ |
| 572 | ␉int type;␊ |
| 573 | ␉char *name;␊ |
| 574 | ␉double arg1;␊ |
| 575 | ␉double arg2;␊ |
| 576 | ␉double retval;␊ |
| 577 | };␊ |
| 578 | #endif␊ |
| 579 | ␊ |
| 580 | #define␉HUGE␉␉MAXFLOAT␊ |
| 581 | ␊ |
| 582 | /* ␊ |
| 583 | * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>␊ |
| 584 | * (one may replace the following line by "#include <values.h>")␊ |
| 585 | */␊ |
| 586 | ␊ |
| 587 | #define X_TLOSS␉␉1.41484755040568800000e+16 ␊ |
| 588 | ␊ |
| 589 | #define␉DOMAIN␉␉1␊ |
| 590 | #define␉SING␉␉2␊ |
| 591 | #define␉OVERFLOW␉3␊ |
| 592 | #define␉UNDERFLOW␉4␊ |
| 593 | #define␉TLOSS␉␉5␊ |
| 594 | #define␉PLOSS␉␉6␊ |
| 595 | ␊ |
| 596 | #endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */␊ |
| 597 | #endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */␊ |
| 598 | ␊ |
| 599 | #if !defined( __STRICT_ANSI__) && !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))␊ |
| 600 | extern int finite ( double );␉␉␉/* Legacy API: please use C99 isfinite() instead. */␊ |
| 601 | ␊ |
| 602 | extern double gamma ( double );␉␉␉/* Legacy API: please use C99 tgamma() instead. */␊ |
| 603 | ␊ |
| 604 | #if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))␊ |
| 605 | ␊ |
| 606 | #if !defined(__cplusplus)␊ |
| 607 | extern int matherr ( struct exception * );␊ |
| 608 | #endif␊ |
| 609 | ␊ |
| 610 | /*␊ |
| 611 | * IEEE Test Vector␊ |
| 612 | */␊ |
| 613 | extern double significand ( double );␊ |
| 614 | ␊ |
| 615 | /*␊ |
| 616 | * BSD math library entry points␊ |
| 617 | */␊ |
| 618 | extern double drem ( double, double );␉/* Legacy API: please use C99 remainder() instead. */␊ |
| 619 | ␉␊ |
| 620 | /*␊ |
| 621 | * Reentrant version of lgamma; passes signgam back by reference␊ |
| 622 | * as the second argument; user must allocate space for signgam.␊ |
| 623 | */␊ |
| 624 | ␉␊ |
| 625 | #ifdef _REENTRANT␊ |
| 626 | ␉#include <AvailabilityMacros.h>␊ |
| 627 | ␉// Available on OS X 10.6 and later.␊ |
| 628 | ␉extern float lgammaf_r ( float, int * ) AVAILABLE_MAC_OS_X_VERSION_10_6_AND_LATER;␊ |
| 629 | ␉extern double lgamma_r ( double, int * ) AVAILABLE_MAC_OS_X_VERSION_10_6_AND_LATER;␊ |
| 630 | ␉extern long double lgammal_r ( long double, int * ) AVAILABLE_MAC_OS_X_VERSION_10_6_AND_LATER;␊ |
| 631 | #endif /* _REENTRANT */␊ |
| 632 | ␉␊ |
| 633 | #endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */␊ |
| 634 | #endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */␊ |
| 635 | ␊ |
| 636 | #endif /* __WANT_EXTENSIONS__ */␊ |
| 637 | ␊ |
| 638 | #ifdef __cplusplus␊ |
| 639 | }␊ |
| 640 | #endif␊ |
| 641 | ␊ |
| 642 | #endif /* __MATH__ */␊ |
| 643 | |
