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#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 __cplusplusextern "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 int __math_errhandling ( void );
/********************************************************************************* ** Inquiry macros ** ** fpclassify Returns one of the FP_* 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 <values.h> * (one may replace the following line by "#include <values.h>") */
#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 _REENTRANTextern 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__ */