/* * Copyright (c) 2002 Apple Computer, Inc. All rights reserved. * * @APPLE_LICENSE_HEADER_START@ * * The contents of this file constitute Original Code as defined in and * are subject to the Apple Public Source License Version 1.1 (the * "License"). You may not use this file except in compliance with the * License. Please obtain a copy of the License at * http://www.apple.com/publicsource and read it before using this file. * * This Original Code and all software distributed under the License are * distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY KIND, EITHER * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE OR NON-INFRINGEMENT. Please see the * License for the specific language governing rights and limitations * under the License. * * @APPLE_LICENSE_HEADER_END@ */ /******************************************************************************* * * * File: math.h * * * * Contains: typedefs, prototypes, and macros germane to C99 floating point.* * * *******************************************************************************/ #ifndef __MATH__ #define __MATH__ #include "sys/cdefs.h" /* For definition of __DARWIN_UNIX03 et al */ #if (!defined(__WANT_LONG_DOUBLE_FORMAT__)) #if defined(__APPLE_CC__) && defined(__LONG_DOUBLE_128__) #define __WANT_LONG_DOUBLE_FORMAT__ 128 #else #define __WANT_LONG_DOUBLE_FORMAT__ 64 #endif #endif #if ( __WANT_LONG_DOUBLE_FORMAT__ - 0L == 128L ) #define __LIBMLDBL_COMPAT(sym) __asm("_" __STRING(sym) "$LDBL128") #elif ( __WANT_LONG_DOUBLE_FORMAT__ - 0L == 64L ) #define __LIBMLDBL_COMPAT(sym) /* NOTHING */ #else #define __LIBMLDBL_COMPAT(sym) /* NOTHING */ #endif #ifdef __cplusplus extern "C" { #endif /****************************************************************************** * Floating point data types * ******************************************************************************/ /* Define float_t and double_t per C standard, ISO/IEC 9899:1999 7.12 2, taking advantage of GCC's __FLT_EVAL_METHOD__ (which a compiler may define anytime and GCC does) that shadows FLT_EVAL_METHOD (which a compiler must and may define only in float.h). */ #if __FLT_EVAL_METHOD__ == 0 typedef float float_t; typedef double double_t; #elif __FLT_EVAL_METHOD__ == 1 typedef double float_t; typedef double double_t; #elif __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ == -1 typedef long double float_t; typedef long double double_t; #else /* __FLT_EVAL_METHOD__ */ #error "Unsupported value of __FLT_EVAL_METHOD__." #endif /* __FLT_EVAL_METHOD__ */ #if defined(__GNUC__) && ! defined( __XLC__ ) #define HUGE_VAL __builtin_huge_val() #define HUGE_VALF __builtin_huge_valf() #define HUGE_VALL __builtin_huge_vall() #define NAN __builtin_nanf("0x7fc00000") /* Constant expression, can be used as initializer. */ #define __MATH_H_ALWAYS_INLINE__ __attribute__ ((always_inline)) #else #define HUGE_VAL 1e500 #define HUGE_VALF 1e50f #define HUGE_VALL 1e500L #define NAN __nan( ) #define __MATH_H_ALWAYS_INLINE__ #endif #define INFINITY HUGE_VALF /****************************************************************************** * Taxonomy of floating point data types * ******************************************************************************/ #define FP_NAN 1 #define FP_INFINITE 2 #define FP_ZERO 3 #define FP_NORMAL 4 #define FP_SUBNORMAL 5 #define FP_SUPERNORMAL 6 /* fma() *function call* is more costly than equivalent (in-line) multiply and add operations */ #undef FP_FAST_FMA #undef FP_FAST_FMAF #undef FP_FAST_FMAL /* The values returned by `ilogb' for 0 and NaN respectively. */ #define FP_ILOGB0 (-2147483647) #define FP_ILOGBNAN (2147483647) /* Bitmasks for the math_errhandling macro. */ #define MATH_ERRNO 1 /* errno set by math functions. */ #define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ #define math_errhandling (__math_errhandling()) extern unsigned int __math_errhandling ( void ); /******************************************************************************** * * * Inquiry macros * * * * fpclassify Returns one of the FP_Å values. * * isnormal Non-zero if and only if the argument x is normalized. * * isfinite Non-zero if and only if the argument x is finite. * * isnan Non-zero if and only if the argument x is a NaN. * * signbit Non-zero if and only if the sign of the argument x is * * negative. This includes, NaNs, infinities and zeros. * * * ********************************************************************************/ #if (__WANT_LONG_DOUBLE_FORMAT__ - 0L == 128L) #define fpclassify(x) \ ( sizeof (x) == sizeof(float ) ? __fpclassifyf((float)x) \ : sizeof (x) == sizeof(double) ? __fpclassifyd((double)x) \ : __fpclassify ((long double)x)) extern int __fpclassifyf(float ); extern int __fpclassifyd(double ); extern int __fpclassify (long double); #if defined( __GNUC__ ) && ! defined( __XLC__ ) && 0 == __FINITE_MATH_ONLY__ /* Yes, that's right. You only get the fast iswhatever() macros if you do NOT turn on -ffast-math. */ /* These inline functions require the compiler to be compiling to standard in order to work. */ /* -ffast-math, among other things, implies that NaNs don't happen. The compiler can in that case */ /* optimize x != x to be false always, wheras it would be true for NaNs. That breaks __inline_isnan() */ /* below. */ #define isnormal(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isnormalf((float)(x)) \ : sizeof (x) == sizeof(double) ? __inline_isnormald((double)(x)) \ : __inline_isnormal ((long double)(x))) #define isfinite(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x)) \ : sizeof (x) == sizeof(double) ? __inline_isfinited((double)(x)) \ : __inline_isfinite ((long double)(x))) #define isinf(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) \ : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) \ : __inline_isinf ((long double)(x))) #define isnan(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) \ : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) \ : __inline_isnan ((long double)(x))) #define signbit(x) \ ( sizeof (x) == sizeof(float ) ? __inline_signbitf((float)(x)) \ : sizeof (x) == sizeof(double) ? __inline_signbitd((double)(x)) \ : __inline_signbit((long double)(x))) /* Developers who are calling __isnan, __isnormal, __isinf, etc. and now encountering errors are calling private APIs */ /* that are deprecated. Please use the official C99 sanctioned macros listed above instead. */ static __inline__ int __inline_isfinitef (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isfinited (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isfinite (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinff (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinfd (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinf (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnanf (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnand (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnan (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnormalf (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnormald (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnormal (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_signbitf (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_signbitd (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_signbit (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinff( float __x ) { return __builtin_fabsf(__x) == __builtin_inff(); } static __inline__ int __inline_isinfd( double __x ) { return __builtin_fabs(__x) == __builtin_inf(); } static __inline__ int __inline_isinf( long double __x ) { return __builtin_fabsl(__x) == __builtin_infl(); } static __inline__ int __inline_isfinitef( float __x ) { return __x == __x && __builtin_fabsf(__x) != __builtin_inff(); } static __inline__ int __inline_isfinited( double __x ) { return __x == __x && __builtin_fabs(__x) != __builtin_inf(); } static __inline__ int __inline_isfinite( long double __x ) { return __x == __x && __builtin_fabsl(__x) != __builtin_infl(); } static __inline__ int __inline_isnanf( float __x ) { return __x != __x; } static __inline__ int __inline_isnand( double __x ) { return __x != __x; } static __inline__ int __inline_isnan( long double __x ) { return __x != __x; } static __inline__ int __inline_signbitf( float __x ) { union{ float __f; unsigned int __u; }__u; __u.__f = __x; return (int)(__u.__u >> 31); } 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)); } 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)); } static __inline__ int __inline_isnormalf( float __x ) { float fabsf = __builtin_fabsf(__x); if( __x != __x ) return 0; return fabsf < __builtin_inff() && fabsf >= __FLT_MIN__; } static __inline__ int __inline_isnormald( double __x ) { double fabsf = __builtin_fabs(__x); if( __x != __x ) return 0; return fabsf < __builtin_inf() && fabsf >= __DBL_MIN__; } 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__; } #else #define isnormal(x) \ ( sizeof (x) == sizeof(float ) ? __isnormalf((float)(x)) \ : sizeof (x) == sizeof(double) ? __isnormald((double)(x)) \ : __isnormal ((long double)(x))) #define isfinite(x) \ ( sizeof (x) == sizeof(float ) ? __isfinitef((float)(x)) \ : sizeof (x) == sizeof(double) ? __isfinited((double)(x)) \ : __isfinite ((long double)(x))) #define isinf(x) \ ( sizeof (x) == sizeof(float ) ? __isinff((float)(x)) \ : sizeof (x) == sizeof(double) ? __isinfd((double)(x)) \ : __isinf ((long double)(x))) #define isnan(x) \ ( sizeof (x) == sizeof(float ) ? __isnanf((float)(x)) \ : sizeof (x) == sizeof(double) ? __isnand((double)(x)) \ : __isnan ((long double)(x))) #define signbit(x) \ ( sizeof (x) == sizeof(float ) ? __signbitf((float)(x)) \ : sizeof (x) == sizeof(double) ? __signbitd((double)(x)) \ : __signbitl((long double)(x))) extern int __isnormalf (float ); extern int __isnormald (double ); extern int __isnormal (long double); extern int __isfinitef (float ); extern int __isfinited (double ); extern int __isfinite (long double); extern int __isinff (float ); extern int __isinfd (double ); extern int __isinf (long double); extern int __isnanf (float ); extern int __isnand (double ); extern int __isnan (long double); extern int __signbitf (float ); extern int __signbitd (double ); extern int __signbitl (long double); #endif #else #define fpclassify(x) \ ( sizeof (x) == sizeof(float ) ? __fpclassifyf((float)(x)) : __fpclassifyd((double)(x)) ) extern int __fpclassifyf(float ); extern int __fpclassifyd(double ); #if defined( __GNUC__ ) && ! defined( __XLC__ ) && 0 == __FINITE_MATH_ONLY__ /* Yes, that's right. You only get the fast iswhatever() macros if you do NOT turn on -ffast-math. */ /* These inline functions require the compiler to be compiling to standard in order to work. */ /* -ffast-math, among other things, implies that NaNs don't happen. The compiler can in that case */ /* optimize x != x to be false always, wheras it would be true for NaNs. That breaks __inline_isnan() */ /* below. */ #define isnormal(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isnormalf((float)(x)) : __inline_isnormald((double)(x)) ) #define isfinite(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x)) : __inline_isfinited((double)(x)) ) #define isinf(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : __inline_isinfd((double)(x)) ) #define isnan(x) \ ( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : __inline_isnand((double)(x)) ) #define signbit(x) \ ( sizeof (x) == sizeof(float ) ? __inline_signbitf((float)(x)) : __inline_signbitd((double)(x)) ) /* Developers who are calling __isnan, __isnormal, __isinf, etc. and now encountering errors are calling private APIs */ /* that are deprecated. Please use the official C99 sanctioned macros listed above instead. */ static __inline__ int __inline_isfinitef (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isfinited (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isfinite (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinff (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinfd (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinf (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnanf (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnand (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnan (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnormalf (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnormald (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isnormal (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_signbitf (float ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_signbitd (double ) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_signbit (long double) __MATH_H_ALWAYS_INLINE__; static __inline__ int __inline_isinff( float __x ) { return __builtin_fabsf(__x) == __builtin_inff(); } static __inline__ int __inline_isinfd( double __x ) { return __builtin_fabs(__x) == __builtin_inf(); } static __inline__ int __inline_isinf( long double __x ) { return __builtin_fabsl(__x) == __builtin_infl(); } static __inline__ int __inline_isfinitef( float __x ) { return __x == __x && __builtin_fabsf(__x) != __builtin_inff(); } static __inline__ int __inline_isfinited( double __x ) { return __x == __x && __builtin_fabs(__x) != __builtin_inf(); } static __inline__ int __inline_isfinite( long double __x ) { return __x == __x && __builtin_fabsl(__x) != __builtin_infl(); } static __inline__ int __inline_isnanf( float __x ) { return __x != __x; } static __inline__ int __inline_isnand( double __x ) { return __x != __x; } static __inline__ int __inline_isnan( long double __x ) { return __x != __x; } static __inline__ int __inline_signbitf( float __x ) { union{ float __f; unsigned int __u; }__u; __u.__f = __x; return (int)(__u.__u >> 31); } 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)); } 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)); } static __inline__ int __inline_isnormalf( float __x ) { float fabsf = __builtin_fabsf(__x); if( __x != __x ) return 0; return fabsf < __builtin_inff() && fabsf >= __FLT_MIN__; } static __inline__ int __inline_isnormald( double __x ) { double fabsf = __builtin_fabs(__x); if( __x != __x ) return 0; return fabsf < __builtin_inf() && fabsf >= __DBL_MIN__; } 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__; } #else #define isnormal(x) \ ( sizeof (x) == sizeof(float ) ? __isnormalf((float)(x)) : __isnormald((double)(x)) ) #define isfinite(x) \ ( sizeof (x) == sizeof(float ) ? __isfinitef((float)(x)) : __isfinited((double)(x)) ) #define isinf(x) \ ( sizeof (x) == sizeof(float ) ? __isinff((float)(x)) : __isinfd((double)(x)) ) #define isnan(x) \ ( sizeof (x) == sizeof(float ) ? __isnanf((float)(x)) : __isnand((double)(x)) ) #define signbit(x) \ ( sizeof (x) == sizeof(float ) ? __signbitf((float)(x)) : __signbitd((double)(x)) ) extern int __isnormalf (float ); extern int __isnormald (double ); extern int __isfinitef (float ); extern int __isfinited (double ); extern int __isinff (float ); extern int __isinfd (double ); extern int __isnanf (float ); extern int __isnand (double ); extern int __signbitf (float ); extern int __signbitd (double ); #endif #endif /* __WANT_LONG_DOUBLE_FORMAT__ */ /******************************************************************************** * * * Math Functions * * * ********************************************************************************/ extern double acos( double ); extern float acosf( float ); extern double asin( double ); extern float asinf( float ); extern double atan( double ); extern float atanf( float ); extern double atan2( double, double ); extern float atan2f( float, float ); extern double cos( double ); extern float cosf( float ); extern double sin( double ); extern float sinf( float ); extern double tan( double ); extern float tanf( float ); extern double acosh( double ); extern float acoshf( float ); extern double asinh( double ); extern float asinhf( float ); extern double atanh( double ); extern float atanhf( float ); extern double cosh( double ); extern float coshf( float ); extern double sinh( double ); extern float sinhf( float ); extern double tanh( double ); extern float tanhf( float ); extern double exp( double ); extern float expf( float ); extern double exp2( double ); extern float exp2f( float ); extern double expm1( double ); extern float expm1f( float ); extern double log( double ); extern float logf( float ); extern double log10( double ); extern float log10f( float ); extern double log2( double ); extern float log2f( float ); extern double log1p( double ); extern float log1pf( float ); extern double logb( double ); extern float logbf( float ); extern double modf( double, double * ); extern float modff( float, float * ); extern double ldexp( double, int ); extern float ldexpf( float, int ); extern double frexp( double, int * ); extern float frexpf( float, int * ); extern int ilogb( double ); extern int ilogbf( float ); extern double scalbn( double, int ); extern float scalbnf( float, int ); extern double scalbln( double, long int ); extern float scalblnf( float, long int ); extern double fabs( double ); extern float fabsf( float ); extern double cbrt( double ); extern float cbrtf( float ); extern double hypot( double, double ); extern float hypotf( float, float ); extern double pow( double, double ); extern float powf( float, float ); extern double sqrt( double ); extern float sqrtf( float ); extern double erf( double ); extern float erff( float ); extern double erfc( double ); extern float erfcf( float ); extern double lgamma( double ); extern float lgammaf( float ); extern double tgamma( double ); extern float tgammaf( float ); extern double ceil( double ); extern float ceilf( float ); extern double floor( double ); extern float floorf( float ); extern double nearbyint( double ); extern float nearbyintf( float ); extern double rint( double ); extern float rintf( float ); extern long int lrint( double ); extern long int lrintf( float ); extern double round( double ); extern float roundf( float ); extern long int lround( double ); extern long int lroundf( float ); #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) /* C90 doesn't know about long long. Make sure you are passing -std=c99 or -std=gnu99 or better if you need this. */ extern long long int llrint( double ); extern long long int llrintf( float ); extern long long int llround( double ); extern long long int llroundf( float ); #endif /*#if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) */ extern double trunc( double ); extern float truncf( float ); extern double fmod( double, double ); extern float fmodf( float, float ); extern double remainder( double, double ); extern float remainderf( float, float ); extern double remquo( double, double, int * ); extern float remquof( float, float, int * ); extern double copysign( double, double ); extern float copysignf( float, float ); extern double nan( const char * ); extern float nanf( const char * ); extern double nextafter( double, double ); extern float nextafterf( float, float ); extern double fdim( double, double ); extern float fdimf( float, float ); extern double fmax( double, double ); extern float fmaxf( float, float ); extern double fmin( double, double ); extern float fminf( float, float ); extern double fma( double, double, double ); extern float fmaf( float, float, float ); #if ( __WANT_LONG_DOUBLE_FORMAT__ - 0L > 0L ) extern long double acosl( long double ) __LIBMLDBL_COMPAT(acosl); extern long double asinl( long double ) __LIBMLDBL_COMPAT(asinl); extern long double atanl( long double ) __LIBMLDBL_COMPAT(atanl); extern long double atan2l( long double, long double ) __LIBMLDBL_COMPAT(atan2l); extern long double cosl( long double ) __LIBMLDBL_COMPAT(cosl); extern long double sinl( long double ) __LIBMLDBL_COMPAT(sinl); extern long double tanl( long double ) __LIBMLDBL_COMPAT(tanl); extern long double acoshl( long double ) __LIBMLDBL_COMPAT(acoshl); extern long double asinhl( long double ) __LIBMLDBL_COMPAT(asinhl); extern long double atanhl( long double ) __LIBMLDBL_COMPAT(atanhl); extern long double coshl( long double ) __LIBMLDBL_COMPAT(coshl); extern long double sinhl( long double ) __LIBMLDBL_COMPAT(sinhl); extern long double tanhl( long double ) __LIBMLDBL_COMPAT(tanhl); extern long double expl( long double ) __LIBMLDBL_COMPAT(expl); extern long double exp2l( long double ) __LIBMLDBL_COMPAT(exp2l); extern long double expm1l( long double ) __LIBMLDBL_COMPAT(expm1l); extern long double logl( long double ) __LIBMLDBL_COMPAT(logl); extern long double log10l( long double ) __LIBMLDBL_COMPAT(log10l); extern long double log2l( long double ) __LIBMLDBL_COMPAT(log2l); extern long double log1pl( long double ) __LIBMLDBL_COMPAT(log1pl); extern long double logbl( long double ) __LIBMLDBL_COMPAT(logbl); extern long double modfl( long double, long double * ) __LIBMLDBL_COMPAT(modfl); extern long double ldexpl( long double, int ) __LIBMLDBL_COMPAT(ldexpl); extern long double frexpl( long double, int * ) __LIBMLDBL_COMPAT(frexpl); extern int ilogbl( long double ) __LIBMLDBL_COMPAT(ilogbl); extern long double scalbnl( long double, int ) __LIBMLDBL_COMPAT(scalbnl); extern long double scalblnl( long double, long int ) __LIBMLDBL_COMPAT(scalblnl); extern long double fabsl( long double ) __LIBMLDBL_COMPAT(fabsl); extern long double cbrtl( long double ) __LIBMLDBL_COMPAT(cbrtl); extern long double hypotl( long double, long double ) __LIBMLDBL_COMPAT(hypotl); extern long double powl( long double, long double ) __LIBMLDBL_COMPAT(powl); extern long double sqrtl( long double ) __LIBMLDBL_COMPAT(sqrtl); extern long double erfl( long double ) __LIBMLDBL_COMPAT(erfl); extern long double erfcl( long double ) __LIBMLDBL_COMPAT(erfcl); extern long double lgammal( long double ) __LIBMLDBL_COMPAT(lgammal); extern long double tgammal( long double ) __LIBMLDBL_COMPAT(tgammal); extern long double ceill( long double ) __LIBMLDBL_COMPAT(ceill); extern long double floorl( long double ) __LIBMLDBL_COMPAT(floorl); extern long double nearbyintl( long double ) __LIBMLDBL_COMPAT(nearbyintl); extern long double rintl( long double ) __LIBMLDBL_COMPAT(rintl); extern long int lrintl( long double ) __LIBMLDBL_COMPAT(lrintl); extern long double roundl( long double ) __LIBMLDBL_COMPAT(roundl); extern long int lroundl( long double ) __LIBMLDBL_COMPAT(lroundl); #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) /* C90 doesn't know about long long. Make sure you are passing -std=c99 or -std=gnu99 or better if you need this. */ extern long long int llrintl( long double ) __LIBMLDBL_COMPAT(llrintl); extern long long int llroundl( long double ) __LIBMLDBL_COMPAT(llroundl); #endif /* #if ( defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L ) || ! defined( __STRICT_ANSI__ ) || ! defined( __GNUC__ ) */ extern long double truncl( long double ) __LIBMLDBL_COMPAT(truncl); extern long double fmodl( long double, long double) __LIBMLDBL_COMPAT(fmodl); extern long double remainderl( long double, long double ) __LIBMLDBL_COMPAT(remainderl); extern long double remquol( long double, long double, int * ) __LIBMLDBL_COMPAT(remquol); extern long double copysignl( long double, long double ) __LIBMLDBL_COMPAT(copysignl); extern long double nanl( const char * ) __LIBMLDBL_COMPAT(nanl); extern long double nextafterl( long double, long double ) __LIBMLDBL_COMPAT(nextafterl); extern double nexttoward( double, long double ) __LIBMLDBL_COMPAT(nexttoward); extern float nexttowardf( float, long double ) __LIBMLDBL_COMPAT(nexttowardf); extern long double nexttowardl( long double, long double ) __LIBMLDBL_COMPAT(nexttowardl); extern long double fdiml( long double, long double ) __LIBMLDBL_COMPAT(fdiml); extern long double fmaxl( long double, long double ) __LIBMLDBL_COMPAT(fmaxl); extern long double fminl( long double, long double ) __LIBMLDBL_COMPAT(fminl); extern long double fmal( long double, long double, long double ) __LIBMLDBL_COMPAT(fmal); #endif /* __WANT_LONG_DOUBLE_FORMAT__ */ #define isgreater(x, y) __builtin_isgreater ((x),(y)) #define isgreaterequal(x, y) __builtin_isgreaterequal ((x),(y)) #define isless(x, y) __builtin_isless ((x),(y)) #define islessequal(x, y) __builtin_islessequal ((x),(y)) #define islessgreater(x, y) __builtin_islessgreater ((x),(y)) #define isunordered(x, y) __builtin_isunordered ((x),(y)) extern double __inf( void ); extern float __inff( void ); extern float __nan( void ); /* 10.3 (and later) must retain in ABI for backward compatability */ #if !defined(_ANSI_SOURCE) extern double j0 ( double ); extern double j1 ( double ); extern double jn ( int, double ); extern double y0 ( double ); extern double y1 ( double ); extern double yn ( int, double ); /* * Scalb Travellers' advisory: * --------------------------- * * Reduction of Information advisory -- This advisory may constitute "too much information". Readers who are easily panicked * or confused may be needlessly panicked or confused by this advisory. * * We are in the process of retiring the legacy scalb. IEEE-754 did not specify what the argument types should be * for scalb. We guessed scalb(double, int) -- ints are faster to use here -- but our guess and what later standards * standard eventually settled on did not agree. To be compliant with these standards, our scalb needs to be scalb(double, double). * Unfortunately, we have a commitment to be binary compatible with old software compiled against scalb(double, int) * for older operating systems, so the old symbol _scalb must live on in perpetuity in the __ppc__ binary interface to service * this need. To deal with this problem, we have introduced a new binary symbol _scalb$UNIX2003 and did some magic below * so that when you now compile against scalb() on a __ppc__ application, you get linked to _scalb$UNIX2003 instead. Thus, * this constitutes a source level *** API CHANGE *** from scalb( double, int ) to scalb( double, double) on __ppc__ only * that your source will need to contend with if you compile with this header. On __ppc__, all ints are exactly representable * as doubles so from an arithmetic standpoint, this should cause no changes arithmetically from parameters of int type, but there * remains the danger of triggering various compiler warnings that might balloon to more serious problems under -Werror. * * On __ppc64__, __i386__ and future archs, scalb has always been scalb( double, double) and will continue to be so. Thus, this change * will make scalb on all platforms behave identically, with the same parameter types. The change will also eliminate GCC warnings about * the math.h scalb declaration not matching the gcc4 builtin version. * * The intent is that you will "never know" that a change occurred, and your code should "just do the right thing" without modification. * However, if you would like to sidestep any problems associated with this move, it is suggested that you use the C99 scalbn or scalbln * or single/long double variants as appropriate instead. Their behavior and type is rigorously defined. There should be no hidden arithmetic * "gotchas" if you simply replace all legacy calls to scalb with scalbn, since they essentially do the same thing. If you * decide to take this step, you should exercise due diligence to make sure that scalbn is present in the oldest version of * MacOS X that you support. Otherwise, your application may fail to load on older systems. C99 support was introduced in MacOS X.3.9. * * Use of the symbol _scalb$UNIX2003 should not in itself be construed to mean that scalb$UNIX2003 necessarily is UNIX 2003 compliant. * UNIX is a registered trademark of The Open Group. */ /* maps to _scalb$UNIX2003 on __ppc__ and _scalb elsewhere */ #if defined( __ppc__ ) #if defined( __GNUC__ ) && ! defined( __XLC__ ) && ( ! defined( __ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__) || __ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__-0 >= 1040 ) extern double scalb ( double, double ) __asm("_scalb$UNIX2003" ); #else extern double scalb ( double , int ); #endif #else extern double scalb ( double, double ); #endif #define M_E 2.71828182845904523536028747135266250 /* e */ #define M_LOG2E 1.44269504088896340735992468100189214 /* log_2(e) */ #define M_LOG10E 0.434294481903251827651128918916605082 /* log_10(e) */ #define M_LN2 0.693147180559945309417232121458176568 /* log_e(2) */ #define M_LN10 2.30258509299404568401799145468436421 /* log_e(10) */ #define M_PI 3.14159265358979323846264338327950288 /* pi */ #define M_PI_2 1.57079632679489661923132169163975144 /* pi/2 */ #define M_PI_4 0.785398163397448309615660845819875721 /* pi/4 */ #define M_1_PI 0.318309886183790671537767526745028724 /* 1/pi */ #define M_2_PI 0.636619772367581343075535053490057448 /* 2/pi */ #define M_2_SQRTPI 1.12837916709551257389615890312154517 /* 2/sqrt(pi) */ #define M_SQRT2 1.41421356237309504880168872420969808 /* sqrt(2) */ #define M_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */ #define MAXFLOAT ((float)3.40282346638528860e+38) extern int signgam; #endif /* !defined(_ANSI_SOURCE) */ #if !defined(__NOEXTENSIONS__) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE)) #define __WANT_EXTENSIONS__ #endif #ifdef __WANT_EXTENSIONS__ #define FP_SNAN FP_NAN #define FP_QNAN FP_NAN extern long int rinttol ( double ); extern long int roundtol ( double ); typedef struct __complex_s { double Real; double Imag; } __complex_t; /* * XOPEN/SVID */ #if !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE)) #if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE)) enum fdversion {_fdlibm_ieee = -1, _fdlibm_svid, _fdlibm_xopen, _fdlibm_posix}; /* Legacy fdlibm constructs */ #define fdlibm_ieee _fdlibm_ieee #define fdlibm_svid _fdlibm_svid #define fdlibm_xopen _fdlibm_xopen #define fdlibm_posix _fdlibm_posix #define _LIB_VERSION_TYPE enum fdversion #define _LIB_VERSION _fdlib_version /* if global variable _LIB_VERSION is not desirable, one may * change the following to be a constant by: * #define _LIB_VERSION_TYPE const enum version * In that case, after one initializes the value _LIB_VERSION (see * s_lib_version.c) during compile time, it cannot be modified * in the middle of a program */ extern _LIB_VERSION_TYPE _LIB_VERSION; #define _IEEE_ fdlibm_ieee #define _SVID_ fdlibm_svid #define _XOPEN_ fdlibm_xopen #define _POSIX_ fdlibm_posix #if !defined(__cplusplus) struct exception { int type; char *name; double arg1; double arg2; double retval; }; #endif #define HUGE MAXFLOAT /* * set X_TLOSS = pi*2**52, which is possibly defined in * (one may replace the following line by "#include ") */ #define X_TLOSS 1.41484755040568800000e+16 #define DOMAIN 1 #define SING 2 #define OVERFLOW 3 #define UNDERFLOW 4 #define TLOSS 5 #define PLOSS 6 #endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */ #endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */ #if !defined( __STRICT_ANSI__) && !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE)) extern int finite ( double ); extern double gamma ( double ); #if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE)) #if !defined(__cplusplus) extern int matherr ( struct exception * ); #endif /* * IEEE Test Vector */ extern double significand ( double ); /* * BSD math library entry points */ extern double drem ( double, double ); /* * Reentrant version of gamma & lgamma; passes signgam back by reference * as the second argument; user must allocate space for signgam. */ #ifdef _REENTRANT extern double gamma_r ( double, int * ); extern double lgamma_r ( double, int * ); #endif /* _REENTRANT */ #endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */ #endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */ #endif /* __WANT_EXTENSIONS__ */ /* * The following replacements for libm's floor, floorf, ceil, and ceilf are activated * when the flag "-ffast-math" is passed to the gcc compiler. These functions do not * distinguish between -0.0 and 0.0, so are not IEC6509 compliant for argument -0.0. */ #if defined(__FAST_MATH__) && !defined(__cplusplus) #define __FSELS(e,t,f) (((e) >= 0.0f) ? (t) : (f)) #define __FSEL(e,t,f) (((e) >= 0.0) ? (t) : (f)) static __inline__ float __fastmath_floorf( float f ) __attribute__((__always_inline__)); static __inline__ float __fastmath_floorf( float f ) { float b, c, d, e, g, h, t; c = __FSELS( f, -8388608.f, 8388608.f ); b = fabsf( f ); d = f - c; e = b - 8388608.f; __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */ d = d + c; g = f - d; h = __FSELS( g, 0.0f, 1.0f ); t = d - h; return __FSELS( e, f, t ); } static __inline__ float __fastmath_ceilf( float f ) __attribute__((__always_inline__)); static __inline__ float __fastmath_ceilf( float f ) { float b, c, d, e, g, h, t; c = __FSELS( f, -8388608.f, 8388608.f ); b = fabsf( f ); d = f - c; e = b - 8388608.f; __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */ d = d + c; g = d - f; h = __FSELS( g, 0.0f, 1.0f ); t = d + h; return __FSELS( e, f, t ); } static __inline__ double __fastmath_floor( double f ) __attribute__((__always_inline__)); static __inline__ double __fastmath_floor( double f ) { double b, c, d, e, g, h, t; c = __FSEL( f, -4503599627370496., 4503599627370496. ); b = fabs( f ); d = f - c; e = b - 4503599627370496.; __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */ d = d + c; g = f - d; h = __FSEL( g, 0.0, 1.0 ); t = d - h; return __FSEL( e, f, t ); } static __inline__ double __fastmath_ceil( double f ) __attribute__((__always_inline__)); static __inline__ double __fastmath_ceil( double f ) { double b, c, d, e, g, h, t; c = __FSEL( f, -4503599627370496., 4503599627370496. ); b = fabs( f ); d = f - c; e = b - 4503599627370496.; __asm__("" : "+f" (d)); /* Tell compiler value of d cannot be optimized away. */ d = d + c; g = d - f; h = __FSEL( g, 0.0, 1.0 ); t = d + h; return __FSEL( e, f, t ); } #define floorf(x) __fastmath_floorf((x)) #define ceilf(x) __fastmath_ceilf((x)) #define floor(x) __fastmath_floor((x)) #define ceil(x) __fastmath_ceil((x)) #endif /* __FAST_MATH__ && !__cplusplus */ #ifdef __cplusplus } #endif #endif /* __MATH__ */