/* * 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__ #ifdef __cplusplus extern "C" { #endif /****************************************************************************** * Floating point data types * ******************************************************************************/ typedef float float_t; typedef double double_t; #define HUGE_VAL 1e500 #define HUGE_VALF 1e50f #define INFINITY HUGE_VALF #if defined(__APPLE_CC__) && (__APPLE_CC__ >= 1345) #define NAN __builtin_nanf("0x7fc00000") /* Constant expression, can be used as initializer. */ #else #define NAN __nan( ) #endif /****************************************************************************** * 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 */ }; /* "Fused" multiply-add is well supported on PowerPC */ #define FP_FAST_FMA 1 #define FP_FAST_FMAF 1 /* 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. * * * ********************************************************************************/ #define fpclassify( x ) ( ( sizeof ( x ) == sizeof(double) ) ? \ __fpclassifyd ( x ) : \ ( sizeof ( x ) == sizeof( float) ) ? \ __fpclassifyf ( x ) : \ __fpclassify ( x ) ) #define isnormal( x ) ( ( sizeof ( x ) == sizeof(double) ) ? \ __isnormald ( x ) : \ ( sizeof ( x ) == sizeof( float) ) ? \ __isnormalf ( x ) : \ __isnormal ( x ) ) #define isfinite( x ) ( ( sizeof ( x ) == sizeof(double) ) ? \ __isfinited ( x ) : \ ( sizeof ( x ) == sizeof( float) ) ? \ __isfinitef ( x ) : \ __isfinite ( x ) ) #define isinf( x ) ( ( sizeof ( x ) == sizeof(double) ) ? \ __isinfd ( x ) : \ ( sizeof ( x ) == sizeof( float) ) ? \ __isinff ( x ) : \ __isinf ( x ) ) #define isnan( x ) ( ( sizeof ( x ) == sizeof(double) ) ? \ __isnand ( x ) : \ ( sizeof ( x ) == sizeof( float) ) ? \ __isnanf ( x ) : \ __isnan ( x ) ) #define signbit( x ) ( ( sizeof ( x ) == sizeof(double) ) ? \ __signbitd ( x ) : \ ( sizeof ( x ) == sizeof( float) ) ? \ __signbitf ( x ) : \ __signbitl ( x ) ) #define __TYPE_LONGDOUBLE_IS_DOUBLE 1 extern long __fpclassifyd( double ); extern long __fpclassifyf( float ); extern long __fpclassify( long double ); #if __TYPE_LONGDOUBLE_IS_DOUBLE #ifdef __cplusplus inline long __fpclassify( long double x ) { return __fpclassifyd((double)( x )); } #else #define __fpclassify( x ) (__fpclassifyd((double)( x ))) #endif #endif extern long __isnormald( double ); extern long __isnormalf( float ); extern long __isnormal( long double ); #if __TYPE_LONGDOUBLE_IS_DOUBLE #ifdef __cplusplus inline long __isnormal( long double x ) { return __isnormald((double)( x )); } #else #define __isnormal( x ) (__isnormald((double)( x ))) #endif #endif extern long __isfinited( double ); extern long __isfinitef( float ); extern long __isfinite( long double ); #if __TYPE_LONGDOUBLE_IS_DOUBLE #ifdef __cplusplus inline long __isfinite( long double x ) { return __isfinited((double)( x )); } #else #define __isfinite( x ) (__isfinited((double)( x ))) #endif #endif extern long __isinfd( double ); extern long __isinff( float ); extern long __isinf( long double ); #if __TYPE_LONGDOUBLE_IS_DOUBLE #ifdef __cplusplus inline long __isinf( long double x ) { return __isinfd((double)( x )); } #else #define __isinf( x ) (__isinfd((double)( x ))) #endif #endif extern long __isnand( double ); extern long __isnanf( float ); extern long __isnan( long double ); #if __TYPE_LONGDOUBLE_IS_DOUBLE #ifdef __cplusplus inline long __isnan( long double x ) { return __isnand((double)( x )); } #else #define __isnan( x ) (__isnand((double)( x ))) #endif #endif extern long __signbitd( double ); extern long __signbitf( float ); extern long __signbitl( long double ); #if __TYPE_LONGDOUBLE_IS_DOUBLE #ifdef __cplusplus inline long __signbitl( long double x ) { return __signbitd((double)( x )); } #else #define __signbitl( x ) (__signbitd((double)( x ))) #endif #endif /******************************************************************************** * * * Math Functions * * * ********************************************************************************/ /* * N.B. When using the C99 "float" entry points that follow, an additional flag must * be added to the link step that produces the executable binary -- specify "-lmx". */ 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 ); #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 */ #ifndef __NOEXTENSIONS__ #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_SOURCE) #define M_E 2.7182818284590452354 /* e */ #define M_LOG2E 1.4426950408889634074 /* log 2e */ #define M_LOG10E 0.43429448190325182765 /* log 10e */ #define M_LN2 0.69314718055994530942 /* log e2 */ #define M_LN10 2.30258509299404568402 /* log e10 */ #define M_PI 3.14159265358979323846 /* pi */ #define M_PI_2 1.57079632679489661923 /* pi/2 */ #define M_PI_4 0.78539816339744830962 /* pi/4 */ #define M_1_PI 0.31830988618379067154 /* 1/pi */ #define M_2_PI 0.63661977236758134308 /* 2/pi */ #define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ #define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ #define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ #define MAXFLOAT ((float)3.40282346638528860e+38) extern int signgam; #if !defined(_XOPEN_SOURCE) enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, 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 */ #endif /* !_ANSI_SOURCE && !_POSIX_SOURCE */ #if !defined(_ANSI_SOURCE) && !defined(_POSIX_SOURCE) extern int finite ( double ); extern double gamma ( double ); 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 ); #if !defined(_XOPEN_SOURCE) extern double scalb ( double, int ); #if !defined(__cplusplus) extern int matherr ( struct exception * ); #endif /* * IEEE Test Vector */ extern double significand ( double ); /* * BSD math library entry points */ #ifndef __COMPLEX__ #ifdef __APPLE_CC__ #define complex _Complex extern double cabs ( double complex ); #undef complex #else extern double cabs ( __complex_t ); #endif /* __APPLE_CC__ */ #endif /* __COMPLEX__ */ 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 */ #endif /* !_ANSI_SOURCE && !_POSIX_SOURCE */ #endif /* __NOEXTENSIONS__ */ #ifdef __cplusplus } #endif #endif /* __MATH__ */