| 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␊ |
| 52 | extern "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())␊ |
| 119 | extern unsigned int __math_errhandling ( void );␊ |
| 120 | ␊ |
| 121 | /********************************************************************************␊ |
| 122 | * *␊ |
| 123 | * Inquiry macros *␊ |
| 124 | * *␊ |
| 125 | |
| 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 | ␊ |
| 368 | extern double acos( double );␊ |
| 369 | extern float acosf( float );␊ |
| 370 | ␊ |
| 371 | extern double asin( double );␊ |
| 372 | extern float asinf( float );␊ |
| 373 | ␊ |
| 374 | extern double atan( double );␊ |
| 375 | extern float atanf( float );␊ |
| 376 | ␊ |
| 377 | extern double atan2( double, double );␊ |
| 378 | extern float atan2f( float, float );␊ |
| 379 | ␊ |
| 380 | extern double cos( double );␊ |
| 381 | extern float cosf( float );␊ |
| 382 | ␊ |
| 383 | extern double sin( double );␊ |
| 384 | extern float sinf( float );␊ |
| 385 | ␊ |
| 386 | extern double tan( double );␊ |
| 387 | extern float tanf( float );␊ |
| 388 | ␊ |
| 389 | extern double acosh( double );␊ |
| 390 | extern float acoshf( float );␊ |
| 391 | ␊ |
| 392 | extern double asinh( double );␊ |
| 393 | extern float asinhf( float );␊ |
| 394 | ␊ |
| 395 | extern double atanh( double );␊ |
| 396 | extern float atanhf( float );␊ |
| 397 | ␊ |
| 398 | extern double cosh( double );␊ |
| 399 | extern float coshf( float );␊ |
| 400 | ␊ |
| 401 | extern double sinh( double );␊ |
| 402 | extern float sinhf( float );␊ |
| 403 | ␊ |
| 404 | extern double tanh( double );␊ |
| 405 | extern float tanhf( float );␊ |
| 406 | ␊ |
| 407 | extern double exp( double );␊ |
| 408 | extern float expf( float );␊ |
| 409 | ␊ |
| 410 | extern double exp2( double );␊ |
| 411 | extern float exp2f( float );␊ |
| 412 | ␊ |
| 413 | extern double expm1( double );␊ |
| 414 | extern float expm1f( float );␊ |
| 415 | ␊ |
| 416 | extern double log( double );␊ |
| 417 | extern float logf( float );␊ |
| 418 | ␊ |
| 419 | extern double log10( double );␊ |
| 420 | extern float log10f( float );␊ |
| 421 | ␊ |
| 422 | extern double log2( double );␊ |
| 423 | extern float log2f( float );␊ |
| 424 | ␊ |
| 425 | extern double log1p( double );␊ |
| 426 | extern float log1pf( float );␊ |
| 427 | ␊ |
| 428 | extern double logb( double );␊ |
| 429 | extern float logbf( float );␊ |
| 430 | ␊ |
| 431 | extern double modf( double, double * );␊ |
| 432 | extern float modff( float, float * );␊ |
| 433 | ␊ |
| 434 | extern double ldexp( double, int );␊ |
| 435 | extern float ldexpf( float, int );␊ |
| 436 | ␊ |
| 437 | extern double frexp( double, int * );␊ |
| 438 | extern float frexpf( float, int * );␊ |
| 439 | ␊ |
| 440 | extern int ilogb( double );␊ |
| 441 | extern int ilogbf( float );␊ |
| 442 | ␊ |
| 443 | extern double scalbn( double, int );␊ |
| 444 | extern float scalbnf( float, int );␊ |
| 445 | ␊ |
| 446 | extern double scalbln( double, long int );␊ |
| 447 | extern float scalblnf( float, long int );␊ |
| 448 | ␊ |
| 449 | extern double fabs( double );␊ |
| 450 | extern float fabsf( float );␊ |
| 451 | ␊ |
| 452 | extern double cbrt( double );␊ |
| 453 | extern float cbrtf( float );␊ |
| 454 | ␊ |
| 455 | extern double hypot( double, double );␊ |
| 456 | extern float hypotf( float, float );␊ |
| 457 | ␊ |
| 458 | extern double pow( double, double );␊ |
| 459 | extern float powf( float, float );␊ |
| 460 | ␊ |
| 461 | extern double sqrt( double );␊ |
| 462 | extern float sqrtf( float );␊ |
| 463 | ␊ |
| 464 | extern double erf( double );␊ |
| 465 | extern float erff( float );␊ |
| 466 | ␊ |
| 467 | extern double erfc( double );␊ |
| 468 | extern float erfcf( float );␊ |
| 469 | ␊ |
| 470 | extern double lgamma( double );␊ |
| 471 | extern float lgammaf( float );␊ |
| 472 | ␊ |
| 473 | extern double tgamma( double );␊ |
| 474 | extern float tgammaf( float );␊ |
| 475 | ␊ |
| 476 | extern double ceil( double );␊ |
| 477 | extern float ceilf( float );␊ |
| 478 | ␊ |
| 479 | extern double floor( double );␊ |
| 480 | extern float floorf( float );␊ |
| 481 | ␊ |
| 482 | extern double nearbyint( double );␊ |
| 483 | extern float nearbyintf( float );␊ |
| 484 | ␊ |
| 485 | extern double rint( double );␊ |
| 486 | extern float rintf( float );␊ |
| 487 | ␊ |
| 488 | extern long int lrint( double );␊ |
| 489 | extern long int lrintf( float );␊ |
| 490 | ␊ |
| 491 | extern double round( double );␊ |
| 492 | extern float roundf( float );␊ |
| 493 | ␊ |
| 494 | extern long int lround( double );␊ |
| 495 | extern 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 | ␊ |
| 506 | extern double trunc( double );␊ |
| 507 | extern float truncf( float );␊ |
| 508 | ␊ |
| 509 | extern double fmod( double, double );␊ |
| 510 | extern float fmodf( float, float );␊ |
| 511 | ␊ |
| 512 | extern double remainder( double, double );␊ |
| 513 | extern float remainderf( float, float );␊ |
| 514 | ␊ |
| 515 | extern double remquo( double, double, int * );␊ |
| 516 | extern float remquof( float, float, int * );␊ |
| 517 | ␊ |
| 518 | extern double copysign( double, double );␊ |
| 519 | extern float copysignf( float, float );␊ |
| 520 | ␊ |
| 521 | extern double nan( const char * );␊ |
| 522 | extern float nanf( const char * );␊ |
| 523 | ␊ |
| 524 | extern double nextafter( double, double );␊ |
| 525 | extern float nextafterf( float, float );␊ |
| 526 | ␊ |
| 527 | ␊ |
| 528 | extern double fdim( double, double );␊ |
| 529 | extern float fdimf( float, float );␊ |
| 530 | ␊ |
| 531 | extern double fmax( double, double );␊ |
| 532 | extern float fmaxf( float, float );␊ |
| 533 | ␊ |
| 534 | extern double fmin( double, double );␊ |
| 535 | extern float fminf( float, float );␊ |
| 536 | ␊ |
| 537 | extern double fma( double, double, double );␊ |
| 538 | extern float fmaf( float, float, float );␊ |
| 539 | ␊ |
| 540 | #if ( __WANT_LONG_DOUBLE_FORMAT__ - 0L > 0L ) ␊ |
| 541 | extern long double acosl( long double ) __LIBMLDBL_COMPAT(acosl);␊ |
| 542 | extern long double asinl( long double ) __LIBMLDBL_COMPAT(asinl);␊ |
| 543 | extern long double atanl( long double ) __LIBMLDBL_COMPAT(atanl);␊ |
| 544 | extern long double atan2l( long double, long double ) __LIBMLDBL_COMPAT(atan2l);␊ |
| 545 | extern long double cosl( long double ) __LIBMLDBL_COMPAT(cosl);␊ |
| 546 | extern long double sinl( long double ) __LIBMLDBL_COMPAT(sinl);␊ |
| 547 | extern long double tanl( long double ) __LIBMLDBL_COMPAT(tanl);␊ |
| 548 | extern long double acoshl( long double ) __LIBMLDBL_COMPAT(acoshl);␊ |
| 549 | extern long double asinhl( long double ) __LIBMLDBL_COMPAT(asinhl);␊ |
| 550 | extern long double atanhl( long double ) __LIBMLDBL_COMPAT(atanhl);␊ |
| 551 | extern long double coshl( long double ) __LIBMLDBL_COMPAT(coshl);␊ |
| 552 | extern long double sinhl( long double ) __LIBMLDBL_COMPAT(sinhl);␊ |
| 553 | extern long double tanhl( long double ) __LIBMLDBL_COMPAT(tanhl);␊ |
| 554 | extern long double expl( long double ) __LIBMLDBL_COMPAT(expl);␊ |
| 555 | extern long double exp2l( long double ) __LIBMLDBL_COMPAT(exp2l);␊ |
| 556 | extern long double expm1l( long double ) __LIBMLDBL_COMPAT(expm1l);␊ |
| 557 | extern long double logl( long double ) __LIBMLDBL_COMPAT(logl);␊ |
| 558 | extern long double log10l( long double ) __LIBMLDBL_COMPAT(log10l);␊ |
| 559 | extern long double log2l( long double ) __LIBMLDBL_COMPAT(log2l);␊ |
| 560 | extern long double log1pl( long double ) __LIBMLDBL_COMPAT(log1pl);␊ |
| 561 | extern long double logbl( long double ) __LIBMLDBL_COMPAT(logbl);␊ |
| 562 | extern long double modfl( long double, long double * ) __LIBMLDBL_COMPAT(modfl);␊ |
| 563 | extern long double ldexpl( long double, int ) __LIBMLDBL_COMPAT(ldexpl);␊ |
| 564 | extern long double frexpl( long double, int * ) __LIBMLDBL_COMPAT(frexpl);␊ |
| 565 | extern int ilogbl( long double ) __LIBMLDBL_COMPAT(ilogbl);␊ |
| 566 | extern long double scalbnl( long double, int ) __LIBMLDBL_COMPAT(scalbnl);␊ |
| 567 | extern long double scalblnl( long double, long int ) __LIBMLDBL_COMPAT(scalblnl);␊ |
| 568 | extern long double fabsl( long double ) __LIBMLDBL_COMPAT(fabsl);␊ |
| 569 | extern long double cbrtl( long double ) __LIBMLDBL_COMPAT(cbrtl);␊ |
| 570 | extern long double hypotl( long double, long double ) __LIBMLDBL_COMPAT(hypotl);␊ |
| 571 | extern long double powl( long double, long double ) __LIBMLDBL_COMPAT(powl);␊ |
| 572 | extern long double sqrtl( long double ) __LIBMLDBL_COMPAT(sqrtl);␊ |
| 573 | extern long double erfl( long double ) __LIBMLDBL_COMPAT(erfl);␊ |
| 574 | extern long double erfcl( long double ) __LIBMLDBL_COMPAT(erfcl);␊ |
| 575 | extern long double lgammal( long double ) __LIBMLDBL_COMPAT(lgammal);␊ |
| 576 | extern long double tgammal( long double ) __LIBMLDBL_COMPAT(tgammal);␊ |
| 577 | extern long double ceill( long double ) __LIBMLDBL_COMPAT(ceill);␊ |
| 578 | extern long double floorl( long double ) __LIBMLDBL_COMPAT(floorl);␊ |
| 579 | extern long double nearbyintl( long double ) __LIBMLDBL_COMPAT(nearbyintl);␊ |
| 580 | extern long double rintl( long double ) __LIBMLDBL_COMPAT(rintl);␊ |
| 581 | extern long int lrintl( long double ) __LIBMLDBL_COMPAT(lrintl);␊ |
| 582 | extern long double roundl( long double ) __LIBMLDBL_COMPAT(roundl);␊ |
| 583 | extern 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 | ␊ |
| 591 | extern long double truncl( long double ) __LIBMLDBL_COMPAT(truncl);␊ |
| 592 | extern long double fmodl( long double, long double) __LIBMLDBL_COMPAT(fmodl);␊ |
| 593 | extern long double remainderl( long double, long double ) __LIBMLDBL_COMPAT(remainderl);␊ |
| 594 | extern long double remquol( long double, long double, int * ) __LIBMLDBL_COMPAT(remquol);␊ |
| 595 | extern long double copysignl( long double, long double ) __LIBMLDBL_COMPAT(copysignl);␊ |
| 596 | extern long double nanl( const char * ) __LIBMLDBL_COMPAT(nanl);␊ |
| 597 | extern long double nextafterl( long double, long double ) __LIBMLDBL_COMPAT(nextafterl);␊ |
| 598 | extern double nexttoward( double, long double ) __LIBMLDBL_COMPAT(nexttoward);␊ |
| 599 | extern float nexttowardf( float, long double ) __LIBMLDBL_COMPAT(nexttowardf);␊ |
| 600 | extern long double nexttowardl( long double, long double ) __LIBMLDBL_COMPAT(nexttowardl);␊ |
| 601 | extern long double fdiml( long double, long double ) __LIBMLDBL_COMPAT(fdiml);␊ |
| 602 | extern long double fmaxl( long double, long double ) __LIBMLDBL_COMPAT(fmaxl);␊ |
| 603 | extern long double fminl( long double, long double ) __LIBMLDBL_COMPAT(fminl);␊ |
| 604 | extern 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 | ␊ |
| 614 | extern double __inf( void );␊ |
| 615 | extern float __inff( void );␊ |
| 616 | extern float __nan( void ); /* 10.3 (and later) must retain in ABI for backward compatability */␊ |
| 617 | ␊ |
| 618 | #if !defined(_ANSI_SOURCE)␊ |
| 619 | extern double j0 ( double );␊ |
| 620 | extern double j1 ( double );␊ |
| 621 | extern double jn ( int, double );␊ |
| 622 | ␊ |
| 623 | extern double y0 ( double );␊ |
| 624 | extern double y1 ( double );␊ |
| 625 | extern 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)␊ |
| 687 | extern 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 | ␊ |
| 700 | extern long int rinttol ( double );␊ |
| 701 | ␊ |
| 702 | extern long int roundtol ( double );␊ |
| 703 | ␊ |
| 704 | typedef 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))␊ |
| 715 | enum 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 | */ ␊ |
| 731 | extern _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)␊ |
| 739 | struct 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 | ␊ |
| 769 | extern int finite ( double );␊ |
| 770 | ␊ |
| 771 | extern double gamma ( double );␊ |
| 772 | ␊ |
| 773 | #if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))␊ |
| 774 | ␊ |
| 775 | #if !defined(__cplusplus)␊ |
| 776 | extern int matherr ( struct exception * );␊ |
| 777 | #endif␊ |
| 778 | ␊ |
| 779 | /*␊ |
| 780 | * IEEE Test Vector␊ |
| 781 | */␊ |
| 782 | extern double significand ( double );␊ |
| 783 | ␊ |
| 784 | /*␊ |
| 785 | * BSD math library entry points␊ |
| 786 | */␊ |
| 787 | extern 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␊ |
| 794 | extern double gamma_r ( double, int * );␊ |
| 795 | extern 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 | ␊ |
| 812 | static __inline__ float __fastmath_floorf( float f ) __attribute__((__always_inline__));␊ |
| 813 | static __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 | ␊ |
| 827 | static __inline__ float __fastmath_ceilf( float f ) __attribute__((__always_inline__));␊ |
| 828 | static __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 | ␊ |
| 842 | static __inline__ double __fastmath_floor( double f ) __attribute__((__always_inline__));␊ |
| 843 | static __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 | ␊ |
| 857 | static __inline__ double __fastmath_ceil( double f ) __attribute__((__always_inline__));␊ |
| 858 | static __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__ */␊ |
| 884 | |
