Root/
| Source at commit 1672 created 12 years 8 months ago. By blackosx, Reset language translations for the Welcome/Description and Conclusion files to english to match latest style I have for English (Sorry everyone who had previously translated). Localizable strings remain as they were as ErmaC had previously amended those to include my recent additions. French translation up to date - thanks Tenval. This will ease merging to the Trunk. | |
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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␊ |
| 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 | |
