/* * 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__ */ #define HUGE_VAL 1e500 #define HUGE_VALF 1e50f #define HUGE_VALL 1e500L #define INFINITY HUGE_VALF #if defined(__GNUC__) #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 */ _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 */ #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(double) ) ? \ __fpclassifyd ( (double)(x) ) : \ ( sizeof ( (x) ) == sizeof( float) ) ? \ __fpclassifyf ( (float)(x) ) : \ __fpclassify ( ( long double )(x) ) ) #define isnormal( x ) ( ( sizeof ( (x) ) == sizeof(double) ) ? \ __isnormald ( (double)(x) ) : \ ( sizeof ( (x) ) == sizeof( float) ) ? \ __isnormalf ( (float)(x) ) : \ __isnormal ( ( long double )(x) ) ) #define isfinite( x ) ( ( sizeof ( (x) ) == sizeof(double) ) ? \ __isfinited ( (double)(x) ) : \ ( sizeof ( (x) ) == sizeof( float) ) ? \ __isfinitef ( (float)(x) ) : \ __isfinite ( ( long double )(x) ) ) #define isinf( x ) ( ( sizeof ( (x) ) == sizeof(double) ) ? \ __isinfd ( (double)(x) ) : \ ( sizeof ( (x) ) == sizeof( float) ) ? \ __isinff ( (float)(x) ) : \ __isinf ( ( long double )(x) ) ) #define isnan( x ) ( ( sizeof ( (x) ) == sizeof(double) ) ? \ __isnand ( (double)(x) ) : \ ( sizeof ( (x) ) == sizeof( float) ) ? \ __isnanf ( (float)(x) ) : \ __isnan ( ( long double )(x) ) ) #define signbit( x ) ( ( sizeof ( (x) ) == sizeof(double) ) ? \ __signbitd ( (double)(x) ) : \ ( sizeof ( (x) ) == sizeof( float) ) ? \ __signbitf ( (float)(x) ) : \ __signbitl ( ( long double )(x) ) ) extern int __fpclassify( long double ); extern int __isnormal( long double ); extern int __isfinite( long double ); extern int __isinf( long double ); extern int __isnan( long double ); extern int __signbitl( long double ); #else #define fpclassify( x ) ( ( sizeof ( (x) ) == sizeof( float) ) ? \ __fpclassifyf ( (float)(x) ) : __fpclassifyd ( (double)(x) ) ) #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) ) ) #endif /* __WANT_LONG_DOUBLE_FORMAT__ */ extern int __fpclassifyd( double ); extern int __fpclassifyf( float ); extern int __isnormald( double ); extern int __isnormalf( float ); extern int __isfinited( double ); extern int __isfinitef( float ); extern int __isinfd( double ); extern int __isinff( float ); extern int __isnand( double ); extern int __isnanf( float ); extern int __signbitd( double ); extern int __signbitf( float ); /******************************************************************************** * * * 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 ); #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 long int llrintl( long double ) __LIBMLDBL_COMPAT(llrintl); extern long double roundl( long double ) __LIBMLDBL_COMPAT(roundl); extern long int lroundl( long double ) __LIBMLDBL_COMPAT(lroundl); extern long long int llroundl( long double ) __LIBMLDBL_COMPAT(llroundl); 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 ); #if __DARWIN_UNIX03 extern double scalb ( double, double ) __DARWIN_ALIAS(scalb); /* UNIX03 legacy signature */ #else extern double scalb ( double, int ); /* Mac OS X legacy signature */ #endif /* __DARWIN_UNIX03 */ #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) #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) #if !defined(_XOPEN_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 */ #endif /* !_ANSI_SOURCE && !_POSIX_C_SOURCE */ #if !defined(_ANSI_SOURCE) && !defined(_POSIX_C_SOURCE) extern int finite ( double ); extern double gamma ( double ); #if !defined(_XOPEN_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 */ #endif /* !_ANSI_SOURCE && !_POSIX_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, -0x1.0p+23f, 0x1.0p+23f ); b = fabsf( f ); d = f - c; e = b - 0x1.0p+23f; __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, -0x1.0p+23f, 0x1.0p+23f ); b = fabsf( f ); d = f - c; e = b - 0x1.0p+23f; __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, -0x1.0p+52, 0x1.0p+52 ); b = fabs( f ); d = f - c; e = b - 0x1.0p+52; __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, -0x1.0p+52, 0x1.0p+52 ); b = fabs( f ); d = f - c; e = b - 0x1.0p+52; __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__ */