/*** *math.h - definitions and declarations for math library * * Copyright (c) Microsoft Corporation. All rights reserved. * *Purpose: * This file contains constant definitions and external subroutine * declarations for the math subroutine library. * [ANSI/System V] * * [Public] * ****/ #ifndef _INC_MATH #define _INC_MATH #include #ifdef _MSC_VER /* * Currently, all MS C compilers for Win32 platforms default to 8 byte * alignment. */ #pragma pack(push,_CRT_PACKING) #endif /* _MSC_VER */ #ifdef __cplusplus extern "C" { #endif #ifndef __assembler /* Protect from assembler */ /* Definition of _exception struct - this struct is passed to the matherr * routine when a floating point exception is detected */ #ifndef _EXCEPTION_DEFINED struct _exception { int type; /* exception type - see below */ char *name; /* name of function where error occured */ double arg1; /* first argument to function */ double arg2; /* second argument (if any) to function */ double retval; /* value to be returned by function */ } ; #define _EXCEPTION_DEFINED #endif /* Definition of a _complex struct to be used by those who use cabs and * want type checking on their argument */ #ifndef _COMPLEX_DEFINED struct _complex { double x,y; /* real and imaginary parts */ } ; #if !__STDC__ && !defined (__cplusplus) /* Non-ANSI name for compatibility */ #define complex _complex #endif #define _COMPLEX_DEFINED #endif #endif /* __assembler */ /* Constant definitions for the exception type passed in the _exception struct */ #define _DOMAIN 1 /* argument domain error */ #define _SING 2 /* argument singularity */ #define _OVERFLOW 3 /* overflow range error */ #define _UNDERFLOW 4 /* underflow range error */ #define _TLOSS 5 /* total loss of precision */ #define _PLOSS 6 /* partial loss of precision */ #define EDOM 33 #define ERANGE 34 /* Definitions of _HUGE and HUGE_VAL - respectively the XENIX and ANSI names * for a value returned in case of error by a number of the floating point * math routines */ #ifndef __assembler /* Protect from assembler */ #if !defined(_M_CEE_PURE) _CRTIMP extern double _HUGE; #else const double _HUGE = System::Double::PositiveInfinity; #endif /* !defined(_M_CEE_PURE) */ #endif /* __assembler */ #define HUGE_VAL _HUGE /* Function prototypes */ #if !defined(__assembler) /* Protect from assembler */ #ifndef _CRT_ABS_DEFINED #define _CRT_ABS_DEFINED int __cdecl abs(__in int _X); long __cdecl labs(__in long _X); #endif double __cdecl acos(__in double _X); double __cdecl asin(__in double _X); double __cdecl atan(__in double _X); double __cdecl atan2(__in double _Y, __in double _X); #ifndef _SIGN_DEFINED _CRTIMP __checkReturn double __cdecl _copysign (__in double _Number, __in double _Sign); _CRTIMP __checkReturn double __cdecl _chgsign (__in double _X); #define _SIGN_DEFINED #endif double __cdecl cos(__in double _X); double __cdecl cosh(__in double _X); double __cdecl exp(__in double _X); _CRT_JIT_INTRINSIC double __cdecl fabs(__in double _X); double __cdecl fmod(__in double _X, __in double _Y); double __cdecl log(__in double _X); double __cdecl log10(__in double _X); double __cdecl pow(__in double _X, __in double _Y); double __cdecl sin(__in double _X); double __cdecl sinh(__in double _X); double __cdecl tan(__in double _X); double __cdecl tanh(__in double _X); double __cdecl sqrt(__in double _X); #ifndef _CRT_ATOF_DEFINED #define _CRT_ATOF_DEFINED _CRTIMP double __cdecl atof(__in_z const char *_String); _CRTIMP double __cdecl _atof_l(__in_z const char *_String, __in_opt _locale_t _Locale); #endif _CRTIMP double __cdecl _cabs(__in struct _complex _Complex); _CRTIMP double __cdecl ceil(__in double _X); _CRTIMP double __cdecl floor(__in double _X); _CRTIMP double __cdecl frexp(__in double _X, __out int * _Y); _CRTIMP double __cdecl _hypot(__in double _X, __in double _Y); _CRTIMP double __cdecl _j0(__in double _X ); _CRTIMP double __cdecl _j1(__in double _X ); _CRTIMP double __cdecl _jn(int _X, __in double _Y); _CRTIMP double __cdecl ldexp(__in double _X, __in int _Y); #ifndef _CRT_MATHERR_DEFINED #define _CRT_MATHERR_DEFINED #if defined(MRTDLL) || defined(_M_CEE_PURE) int __CRTDECL _matherr(__inout struct _exception * _Except); #else int __cdecl _matherr(__inout struct _exception * _Except); #endif #endif _CRTIMP double __cdecl modf(__in double _X, __out double * _Y); _CRTIMP double __cdecl _y0(__in double _X); _CRTIMP double __cdecl _y1(__in double _X); _CRTIMP double __cdecl _yn(__in int _X, __in double _Y); #if defined(_M_IX86) _CRTIMP int __cdecl _set_SSE2_enable(__in int _Flag); _CRTIMP float __cdecl _hypotf(__in float _X, __in float _Y); #endif #if defined(_M_IA64) /* ANSI C, 4.5 Mathematics */ /* 4.5.2 Trigonometric functions */ _CRTIMP float __cdecl acosf( __in float _X); _CRTIMP float __cdecl asinf( __in float _X); _CRTIMP float __cdecl atanf( __in float _X); _CRTIMP float __cdecl atan2f( __in float _Y, float _X); _CRTIMP float __cdecl cosf( __in float _X); _CRTIMP float __cdecl sinf( __in float _X); _CRTIMP float __cdecl tanf( __in float _X); /* 4.5.3 Hyperbolic functions */ _CRTIMP float __cdecl coshf( __in float _X); _CRTIMP float __cdecl sinhf( __in float _X); _CRTIMP float __cdecl tanhf( __in float _X); /* 4.5.4 Exponential and logarithmic functions */ _CRTIMP float __cdecl expf( __in float _X); _CRTIMP float __cdecl logf( __in float _X); _CRTIMP float __cdecl log10f( __in float _X); _CRTIMP float __cdecl modff( float _X, __out float* _Y); /* 4.5.5 Power functions */ _CRTIMP float __cdecl powf( __in float _Base, __in float _Exp); _CRTIMP float __cdecl sqrtf( __in float _X); /* 4.5.6 Nearest integer, absolute value, and remainder functions */ _CRTIMP float __cdecl ceilf( __in float _X); _CRT_JIT_INTRINSIC _CRTIMP float __cdecl fabsf( __in float _X); _CRTIMP float __cdecl floorf( __in float _X); _CRTIMP float __cdecl fmodf( __in float _X, __in float _Y); _CRTIMP float __cdecl _hypotf(__in float _X, __in float _Y); _CRTIMP float __cdecl ldexpf(__in float _X, __in int _Y); #endif /* _M_IA64 */ #if defined(_M_AMD64) /* ANSI C, 4.5 Mathematics */ /* 4.5.2 Trigonometric functions */ _CRTIMP float __cdecl acosf( __in float _X); _CRTIMP float __cdecl asinf( __in float _X); _CRTIMP float __cdecl atanf( __in float _X); _CRTIMP float __cdecl atan2f( __in float _X, __in float _Y); _CRTIMP float __cdecl cosf( __in float _X); _CRTIMP float __cdecl sinf( __in float _X); _CRTIMP float __cdecl tanf( __in float _X); /* 4.5.3 Hyperbolic functions */ _CRTIMP float __cdecl coshf( __in float _X); _CRTIMP float __cdecl sinhf( __in float _X); _CRTIMP float __cdecl tanhf( __in float _X); /* 4.5.4 Exponential and logarithmic functions */ _CRTIMP float __cdecl expf( __in float _X); _CRTIMP float __cdecl logf( __in float _X); _CRTIMP float __cdecl log10f( __in float _X); _CRTIMP float __cdecl modff( __in float _X, __out float* _Y); /* 4.5.5 Power functions */ _CRTIMP float __cdecl powf( __in float _X, __in float _Y); _CRTIMP float __cdecl sqrtf( __in float _X); /* 4.5.6 Nearest integer, absolute value, and remainder functions */ _CRTIMP float __cdecl ceilf( __in float _X); _CRTIMP float __cdecl floorf( __in float _X); _CRTIMP float __cdecl fmodf( __in float _X, __in float _Y); _CRTIMP float __cdecl _hypotf(__in float _X, __in float _Y); _CRTIMP float __cdecl _copysignf (__in float _Number, __in float _Sign); _CRTIMP float __cdecl _chgsignf (__in float _X); _CRTIMP float __cdecl _logbf(__in float _X); _CRTIMP float __cdecl _nextafterf(__in float _X, __in float _Y); _CRTIMP int __cdecl _finitef(__in float _X); _CRTIMP int __cdecl _isnanf(__in float _X); _CRTIMP int __cdecl _fpclassf(__in float _X); #endif /* _M_AMD64 */ /* Macros defining long double functions to be their double counterparts * (long double is synonymous with double in this implementation). */ #ifndef __cplusplus #define acosl(x) ((long double)acos((double)(x))) #define asinl(x) ((long double)asin((double)(x))) #define atanl(x) ((long double)atan((double)(x))) #define atan2l(x,y) ((long double)atan2((double)(x), (double)(y))) #define ceill(x) ((long double)ceil((double)(x))) #define cosl(x) ((long double)cos((double)(x))) #define coshl(x) ((long double)cosh((double)(x))) #define expl(x) ((long double)exp((double)(x))) #define fabsl(x) ((long double)fabs((double)(x))) #define floorl(x) ((long double)floor((double)(x))) #define fmodl(x,y) ((long double)fmod((double)(x), (double)(y))) #define frexpl(x,y) ((long double)frexp((double)(x), (y))) #define _hypotl(x,y) ((long double)_hypot((double)(x), (double)(y))) #define ldexpl(x,y) ((long double)ldexp((double)(x), (y))) #define logl(x) ((long double)log((double)(x))) #define log10l(x) ((long double)log10((double)(x))) #define _matherrl _matherr #define modfl(x,y) ((long double)modf((double)(x), (double *)(y))) #define powl(x,y) ((long double)pow((double)(x), (double)(y))) #define sinl(x) ((long double)sin((double)(x))) #define sinhl(x) ((long double)sinh((double)(x))) #define sqrtl(x) ((long double)sqrt((double)(x))) #define tanl(x) ((long double)tan((double)(x))) #define tanhl(x) ((long double)tanh((double)(x))) #define _chgsignl(x) ((long double)_chgsign((double)(x))) #define _copysignl(x,y) ((long double)_copysign((double)(x), (double)(y))) #define frexpf(x,y) ((float)frexp((double)(x),(y))) #if !defined (_M_IA64) #define fabsf(x) ((float)fabs((double)(x))) #define ldexpf(x,y) ((float)ldexp((double)(x),(y))) #if !defined (_M_AMD64) #define acosf(x) ((float)acos((double)(x))) #define asinf(x) ((float)asin((double)(x))) #define atanf(x) ((float)atan((double)(x))) #define atan2f(x,y) ((float)atan2((double)(x), (double)(y))) #define ceilf(x) ((float)ceil((double)(x))) #define cosf(x) ((float)cos((double)(x))) #define coshf(x) ((float)cosh((double)(x))) #define expf(x) ((float)exp((double)(x))) #define floorf(x) ((float)floor((double)(x))) #define fmodf(x,y) ((float)fmod((double)(x), (double)(y))) #define logf(x) ((float)log((double)(x))); #define log10f(x) ((float)log10((double)(x))) #define modff(x,y) ((float)modf((double)(x), (double *)(y))) #define powf(x,y) ((float)pow((double)(x), (double)(y))) #define sinf(x) ((float)sin((double)(x))) #define sinhf(x) ((float)sinh((double)(x))) #define sqrtf(x) ((float)sqrt((double)(x))) #define tanf(x) ((float)tan((double)(x))) #define tanhf(x) ((float)tanh((double)(x))) #endif /* !defined (_M_AMD64) */ #endif /* !defined (_M_IA64) */ #else /* __cplusplus */ inline long double acosl(__in long double _X) {return (acos((double)_X)); } inline long double asinl(__in long double _X) {return (asin((double)_X)); } inline long double atanl(__in long double _X) {return (atan((double)_X)); } inline long double atan2l(__in long double _X, __in long double _Y) {return (atan2((double)_X, (double)_Y)); } inline long double ceill(__in long double _X) {return (ceil((double)_X)); } inline long double cosl(__in long double _X) {return (cos((double)_X)); } inline long double coshl(__in long double _X) {return (cosh((double)_X)); } inline long double expl(__in long double _X) {return (exp((double)_X)); } inline long double fabsl(__in long double _X) {return (fabs((double)_X)); } inline long double floorl(__in long double _X) {return (floor((double)_X)); } inline long double fmodl(__in long double _X, __in long double _Y) {return (fmod((double)_X, (double)_Y)); } inline long double frexpl(__in long double _X, __out int *_Y) {return (frexp((double)_X, _Y)); } inline long double ldexpl(__in long double _X, __in int _Y) {return (ldexp((double)_X, _Y)); } inline long double logl(__in long double _X) {return (log((double)_X)); } inline long double log10l(__in long double _X) {return (log10((double)_X)); } inline long double modfl(__in long double _X, __out long double *_Y) {double _Di, _Df = modf((double)_X, &_Di); *_Y = (long double)_Di; return (_Df); } inline long double powl(__in long double _X, __in long double _Y) {return (pow((double)_X, (double)_Y)); } inline long double sinl(__in long double _X) {return (sin((double)_X)); } inline long double sinhl(__in long double _X) {return (sinh((double)_X)); } inline long double sqrtl(__in long double _X) {return (sqrt((double)_X)); } #ifndef _M_IA64 inline long double tanl(__in long double _X) {return (tan((double)_X)); } #else _CRTIMP long double __cdecl tanl(__in long double _X); #endif inline long double tanhl(__in long double _X) {return (tanh((double)_X)); } inline long double _chgsignl(__in long double _Number) { return _chgsign(static_cast(_Number)); } inline long double _copysignl(__in long double _Number, __in long double _Sign) { return _copysign(static_cast(_Number), static_cast(_Sign)); } inline float frexpf(__in float _X, __out int *_Y) {return ((float)frexp((double)_X, _Y)); } #if !defined(_M_IA64) inline float fabsf(__in float _X) {return ((float)fabs((double)_X)); } inline float ldexpf(__in float _X, __in int _Y) {return ((float)ldexp((double)_X, _Y)); } #if !defined(_M_AMD64) inline float acosf(__in float _X) {return ((float)acos((double)_X)); } inline float asinf(__in float _X) {return ((float)asin((double)_X)); } inline float atanf(__in float _X) {return ((float)atan((double)_X)); } inline float atan2f(__in float _X, __in float _Y) {return ((float)atan2((double)_X, (double)_Y)); } inline float ceilf(__in float _X) {return ((float)ceil((double)_X)); } inline float cosf(__in float _X) {return ((float)cos((double)_X)); } inline float coshf(__in float _X) {return ((float)cosh((double)_X)); } inline float expf(__in float _X) {return ((float)exp((double)_X)); } inline float floorf(__in float _X) {return ((float)floor((double)_X)); } inline float fmodf(__in float _X, __in float _Y) {return ((float)fmod((double)_X, (double)_Y)); } inline float logf(__in float _X) {return ((float)log((double)_X)); } inline float log10f(__in float _X) {return ((float)log10((double)_X)); } inline float modff(__in float _X, __out float *_Y) { double _Di, _Df = modf((double)_X, &_Di); *_Y = (float)_Di; return ((float)_Df); } inline float powf(__in float _X, __in float _Y) {return ((float)pow((double)_X, (double)_Y)); } inline float sinf(__in float _X) {return ((float)sin((double)_X)); } inline float sinhf(__in float _X) {return ((float)sinh((double)_X)); } inline float sqrtf(__in float _X) {return ((float)sqrt((double)_X)); } inline float tanf(__in float _X) {return ((float)tan((double)_X)); } inline float tanhf(__in float _X) {return ((float)tanh((double)_X)); } #endif /* !defined(_M_AMD64) */ #endif /* !defined(_M_IA64) */ #endif /* __cplusplus */ #endif /* __assembler */ #if !__STDC__ /* Non-ANSI names for compatibility */ #define DOMAIN _DOMAIN #define SING _SING #define OVERFLOW _OVERFLOW #define UNDERFLOW _UNDERFLOW #define TLOSS _TLOSS #define PLOSS _PLOSS #define matherr _matherr #ifndef __assembler /* Protect from assembler */ #if !defined(_M_CEE_PURE) _CRTIMP extern double HUGE; #else const double HUGE = _HUGE; #endif /* !defined(_M_CEE_PURE) */ _CRT_NONSTDC_DEPRECATE(_cabs) _CRTIMP double __cdecl cabs(__in struct _complex _X); _CRT_NONSTDC_DEPRECATE(_hypot) _CRTIMP double __cdecl hypot(__in double _X, __in double _Y); _CRT_NONSTDC_DEPRECATE(_j0) _CRTIMP double __cdecl j0(__in double _X); _CRT_NONSTDC_DEPRECATE(_j1) _CRTIMP double __cdecl j1(__in double _X); _CRT_NONSTDC_DEPRECATE(_jn) _CRTIMP double __cdecl jn(__in int _X, __in double _Y); _CRT_NONSTDC_DEPRECATE(_y0) _CRTIMP double __cdecl y0(__in double _X); _CRT_NONSTDC_DEPRECATE(_y1) _CRTIMP double __cdecl y1(__in double _X); _CRT_NONSTDC_DEPRECATE(_yn) _CRTIMP double __cdecl yn(__in int _X, __in double _Y); #endif /* __assembler */ #endif /* __STDC__ */ #ifdef __cplusplus } extern "C++" { template inline _Ty _Pow_int(_Ty _X, int _Y) {unsigned int _N; if (_Y >= 0) _N = (unsigned int)_Y; else _N = (unsigned int)(-_Y); for (_Ty _Z = _Ty(1); ; _X *= _X) {if ((_N & 1) != 0) _Z *= _X; if ((_N >>= 1) == 0) return (_Y < 0 ? _Ty(1) / _Z : _Z); }} inline long __CRTDECL abs(__in long _X) {return (labs(_X)); } inline double __CRTDECL abs(__in double _X) {return (fabs(_X)); } inline double __CRTDECL pow(__in double _X, __in int _Y) {return (_Pow_int(_X, _Y)); } inline float __CRTDECL abs(__in float _X) {return (fabsf(_X)); } inline float __CRTDECL acos(__in float _X) {return (acosf(_X)); } inline float __CRTDECL asin(__in float _X) {return (asinf(_X)); } inline float __CRTDECL atan(__in float _X) {return (atanf(_X)); } inline float __CRTDECL atan2(__in float _Y, __in float _X) {return (atan2f(_Y, _X)); } inline float __CRTDECL ceil(__in float _X) {return (ceilf(_X)); } inline float __CRTDECL cos(__in float _X) {return (cosf(_X)); } inline float __CRTDECL cosh(__in float _X) {return (coshf(_X)); } inline float __CRTDECL exp(__in float _X) {return (expf(_X)); } inline float __CRTDECL fabs(__in float _X) {return (fabsf(_X)); } inline float __CRTDECL floor(__in float _X) {return (floorf(_X)); } inline float __CRTDECL fmod(__in float _X, __in float _Y) {return (fmodf(_X, _Y)); } inline float __CRTDECL frexp(__in float _X, __out int * _Y) {return (frexpf(_X, _Y)); } inline float __CRTDECL ldexp(__in float _X, __in int _Y) {return (ldexpf(_X, _Y)); } inline float __CRTDECL log(__in float _X) {return (logf(_X)); } inline float __CRTDECL log10(__in float _X) {return (log10f(_X)); } inline float __CRTDECL modf(__in float _X, __out float * _Y) {return (modff(_X, _Y)); } inline float __CRTDECL pow(__in float _X, __in float _Y) {return (powf(_X, _Y)); } inline float __CRTDECL pow(__in float _X, __in int _Y) {return (_Pow_int(_X, _Y)); } inline float __CRTDECL sin(__in float _X) {return (sinf(_X)); } inline float __CRTDECL sinh(__in float _X) {return (sinhf(_X)); } inline float __CRTDECL sqrt(__in float _X) {return (sqrtf(_X)); } inline float __CRTDECL tan(__in float _X) {return (tanf(_X)); } inline float __CRTDECL tanh(__in float _X) {return (tanhf(_X)); } inline long double __CRTDECL abs(__in long double _X) {return (fabsl(_X)); } inline long double __CRTDECL acos(__in long double _X) {return (acosl(_X)); } inline long double __CRTDECL asin(__in long double _X) {return (asinl(_X)); } inline long double __CRTDECL atan(__in long double _X) {return (atanl(_X)); } inline long double __CRTDECL atan2(__in long double _Y, __in long double _X) {return (atan2l(_Y, _X)); } inline long double __CRTDECL ceil(__in long double _X) {return (ceill(_X)); } inline long double __CRTDECL cos(__in long double _X) {return (cosl(_X)); } inline long double __CRTDECL cosh(__in long double _X) {return (coshl(_X)); } inline long double __CRTDECL exp(__in long double _X) {return (expl(_X)); } inline long double __CRTDECL fabs(__in long double _X) {return (fabsl(_X)); } inline long double __CRTDECL floor(__in long double _X) {return (floorl(_X)); } inline long double __CRTDECL fmod(__in long double _X, __in long double _Y) {return (fmodl(_X, _Y)); } inline long double __CRTDECL frexp(__in long double _X, __out int * _Y) {return (frexpl(_X, _Y)); } inline long double __CRTDECL ldexp(__in long double _X, __in int _Y) {return (ldexpl(_X, _Y)); } inline long double __CRTDECL log(__in long double _X) {return (logl(_X)); } inline long double __CRTDECL log10(__in long double _X) {return (log10l(_X)); } inline long double __CRTDECL modf(__in long double _X, __out long double * _Y) {return (modfl(_X, _Y)); } inline long double __CRTDECL pow(__in long double _X, __in long double _Y) {return (powl(_X, _Y)); } inline long double __CRTDECL pow(__in long double _X, __in int _Y) {return (_Pow_int(_X, _Y)); } inline long double __CRTDECL sin(__in long double _X) {return (sinl(_X)); } inline long double __CRTDECL sinh(__in long double _X) {return (sinhl(_X)); } inline long double __CRTDECL sqrt(__in long double _X) {return (sqrtl(_X)); } inline long double __CRTDECL tan(__in long double _X) {return (tanl(_X)); } inline long double __CRTDECL tanh(__in long double _X) {return (tanhl(_X)); } } #endif /* __cplusplus */ #ifdef _MSC_VER #pragma pack(pop) #endif /* _MSC_VER */ #endif /* _INC_MATH */ #if defined(_USE_MATH_DEFINES) && !defined(_MATH_DEFINES_DEFINED) #define _MATH_DEFINES_DEFINED /* Define _USE_MATH_DEFINES before including math.h to expose these macro * definitions for common math constants. These are placed under an #ifdef * since these commonly-defined names are not part of the C/C++ standards. */ /* Definitions of useful mathematical constants * M_E - e * M_LOG2E - log2(e) * M_LOG10E - log10(e) * M_LN2 - ln(2) * M_LN10 - ln(10) * M_PI - pi * M_PI_2 - pi/2 * M_PI_4 - pi/4 * M_1_PI - 1/pi * M_2_PI - 2/pi * M_2_SQRTPI - 2/sqrt(pi) * M_SQRT2 - sqrt(2) * M_SQRT1_2 - 1/sqrt(2) */ #define M_E 2.71828182845904523536 #define M_LOG2E 1.44269504088896340736 #define M_LOG10E 0.434294481903251827651 #define M_LN2 0.693147180559945309417 #define M_LN10 2.30258509299404568402 #define M_PI 3.14159265358979323846 #define M_PI_2 1.57079632679489661923 #define M_PI_4 0.785398163397448309616 #define M_1_PI 0.318309886183790671538 #define M_2_PI 0.636619772367581343076 #define M_2_SQRTPI 1.12837916709551257390 #define M_SQRT2 1.41421356237309504880 #define M_SQRT1_2 0.707106781186547524401 #endif /* _USE_MATH_DEFINES */