/* * 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 */ #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__) #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 1e5000L #define NAN __nan( ) #define __MATH_H_ALWAYS_INLINE__ #endif #define INFINITY HUGE_VALF /****************************************************************************** * Taxonomy of floating point data types * ******************************************************************************/ enum { _FP_NAN = 1, /* NaN */ _FP_INFINITE = 2, /* + or - infinity */ _FP_ZERO = 3, /* + or - zero */ _FP_NORMAL = 4, /* all normal numbers */ _FP_SUBNORMAL = 5, /* denormal numbers */ _FP_SUPERNORMAL = 6 /* long double delivering > LDBL_DIG, e.g. 1. + 2^-1000 */ }; #define FP_NAN _FP_NAN #define FP_INFINITE _FP_INFINITE #define FP_ZERO _FP_ZERO #define FP_NORMAL _FP_NORMAL #define FP_SUBNORMAL _FP_SUBNORMAL #define FP_SUPERNORMAL _FP_SUPERNORMAL /* fma() *function call* is more costly than equivalent (in-line) multiply and add operations */ /* For single and double precision, the cost isn't too bad, because we can fall back on higher */ /* precision hardware, with the necessary range to handle infinite precision products. However, */ /* expect the long double fma to be at least an order of magnitude slower than a simple multiply */ /* and an add. */ #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 - 1) #define FP_ILOGBNAN (-2147483647 - 1) /* 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. * * * ********************************************************************************/ #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__ ) #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))) 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 = {__x}; return (int)(__u.__u >> 31); } static __inline__ int __inline_signbitd( double __x ) { union{ double __f; unsigned long long __u; }__u = {__x}; return (int)(__u.__u >> 63); } static __inline__ int __inline_signbit( long double __x ){ union{ long double __ld; struct{ unsigned long long __m; short __sexp; }__p; }__u = {__x}; return (int) ((unsigned int) __u.__p.__sexp >> 15); } 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 /******************************************************************************** * * * 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 long long int llrint ( double ); extern long long int llrintf ( float ); extern double round ( double ); extern float roundf ( float ); extern long int lround ( double ); extern long int lroundf ( float ); extern long long int llround ( double ); extern long long int llroundf ( float ); 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 ); extern long double acosl(long double); extern long double asinl(long double); extern long double atanl(long double); extern long double atan2l(long double, long double); extern long double cosl(long double); extern long double sinl(long double); extern long double tanl(long double); extern long double acoshl(long double); extern long double asinhl(long double); extern long double atanhl(long double); extern long double coshl(long double); extern long double sinhl(long double); extern long double tanhl(long double); extern long double expl(long double); extern long double exp2l(long double); extern long double expm1l(long double); extern long double logl(long double); extern long double log10l(long double); extern long double log2l(long double); extern long double log1pl(long double); extern long double logbl(long double); extern long double modfl(long double, long double *); extern long double ldexpl(long double, int); extern long double frexpl(long double, int *); extern int ilogbl(long double); extern long double scalbnl(long double, int); extern long double scalblnl(long double, long int); extern long double fabsl(long double); extern long double cbrtl(long double); extern long double hypotl(long double, long double); extern long double powl(long double, long double); extern long double sqrtl(long double); extern long double erfl(long double); extern long double erfcl(long double); extern long double lgammal(long double); extern long double tgammal(long double); extern long double ceill(long double); extern long double floorl(long double); extern long double nearbyintl(long double); extern long double rintl(long double); extern long int lrintl(long double); extern long long int llrintl(long double); extern long double roundl(long double); extern long int lroundl(long double); extern long long int llroundl(long double); extern long double truncl(long double); extern long double fmodl(long double, long double); extern long double remainderl(long double, long double); extern long double remquol(long double, long double, int *); extern long double copysignl(long double, long double); extern long double nanl(const char *); extern long double nextafterl(long double, long double); extern double nexttoward(double, long double); extern float nexttowardf(float, long double); extern long double nexttowardl(long double, long double); extern long double fdiml(long double, long double); extern long double fmaxl(long double, long double); extern long double fminl(long double, long double); extern long double fmal(long double, long double, long double); #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 long double __infl( 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 ); extern double scalb ( double, double ); #define M_E 2.71828182845904523536028747135266250 /* e */ #define M_LOG2E 1.44269504088896340735992468100189214 /* log 2e */ #define M_LOG10E 0.434294481903251827651128918916605082 /* log 10e */ #define M_LN2 0.693147180559945309417232121458176568 /* log e2 */ #define M_LN10 2.30258509299404568401799145468436421 /* log e10 */ #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; /* required for unix 2003 */ #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 ); /* Legacy API: please use C99 lrint() instead. */ extern long int roundtol ( double ); /* Legacy API: please use C99 lround() instead. */ /* * XOPEN/SVID */ #if !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE)) #if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE)) #if !defined(__cplusplus) /* used by matherr below */ 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(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE)) extern int finite ( double ); /* Legacy API: please use C99 isfinite() instead. */ extern double gamma ( double ); /* Legacy API: please use C99 tgamma() instead. */ #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 ); /* Legacy API: please use C99 remainder() instead. */ #endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */ #endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */ #endif /* __WANT_EXTENSIONS__ */ #ifdef __cplusplus } #endif #endif /* __MATH__ */