#ifndef _MATH_H_ #define _MATH_H_ #include #include #include "_ansi.h" _BEGIN_STD_C union __dmath { __ULong i[2]; double d; }; union __fmath { __ULong i[1]; float f; }; union __ldmath { __ULong i[4]; _LONG_DOUBLE ld; }; /* Log2 of e */ #define _M_LOG2E 1.4426950408889634074 #if defined(__GNUC__) && \ ( (__GNUC__ >= 4) || \ ( (__GNUC__ >= 3) && defined(__GNUC_MINOR__) && (__GNUC_MINOR__ >= 3) ) ) /* gcc >= 3.3 implicitly defines builtins for HUGE_VALx values. */ # ifndef HUGE_VAL # define HUGE_VAL (__builtin_huge_val()) # endif # ifndef HUGE_VALF # define HUGE_VALF (__builtin_huge_valf()) # endif # ifndef HUGE_VALL # define HUGE_VALL (__builtin_huge_vall()) # endif # ifndef INFINITY # define INFINITY (__builtin_inff()) # endif # ifndef NAN # define NAN (__builtin_nanf("")) # endif #else /* !gcc >= 3.3 */ /* No builtins. Use floating-point unions instead. Declare as an array without bounds so no matter what small data support a port and/or library has, the reference will be via the general method for accessing globals. */ #ifndef HUGE_VAL extern __IMPORT const union __dmath __infinity[]; #define HUGE_VAL (__infinity[0].d) #endif #ifndef HUGE_VALF extern __IMPORT const union __fmath __infinityf[]; #define HUGE_VALF (__infinityf[0].f) #endif #ifndef HUGE_VALL extern __IMPORT const union __ldmath __infinityld[]; #define HUGE_VALL (__infinityld[0].ld) #endif #endif /* !gcc >= 3.3 */ /* Reentrant ANSI C functions. */ #ifndef __math_68881 extern double atan _PARAMS((double)); extern double cos _PARAMS((double)); extern double sin _PARAMS((double)); extern double tan _PARAMS((double)); extern double tanh _PARAMS((double)); extern double frexp _PARAMS((double, int *)); extern double modf _PARAMS((double, double *)); extern double ceil _PARAMS((double)); extern double fabs _PARAMS((double)); extern double floor _PARAMS((double)); #endif /* ! defined (__math_68881) */ /* Non reentrant ANSI C functions. */ #ifndef _REENT_ONLY #ifndef __math_6881 extern double acos _PARAMS((double)); extern double asin _PARAMS((double)); extern double atan2 _PARAMS((double, double)); extern double cosh _PARAMS((double)); extern double sinh _PARAMS((double)); extern double exp _PARAMS((double)); extern double ldexp _PARAMS((double, int)); extern double log _PARAMS((double)); extern double log10 _PARAMS((double)); extern double pow _PARAMS((double, double)); extern double sqrt _PARAMS((double)); extern double fmod _PARAMS((double, double)); #endif /* ! defined (__math_68881) */ #endif /* ! defined (_REENT_ONLY) */ #if !defined(__STRICT_ANSI__) || defined(__cplusplus) || __STDC_VERSION__ >= 199901L /* ISO C99 types and macros. */ #ifndef FLT_EVAL_METHOD #define FLT_EVAL_METHOD 0 typedef float float_t; typedef double double_t; #endif /* FLT_EVAL_METHOD */ #define FP_NAN 0 #define FP_INFINITE 1 #define FP_ZERO 2 #define FP_SUBNORMAL 3 #define FP_NORMAL 4 #ifndef FP_ILOGB0 # define FP_ILOGB0 (-INT_MAX) #endif #ifndef FP_ILOGBNAN # define FP_ILOGBNAN INT_MAX #endif #ifndef MATH_ERRNO # define MATH_ERRNO 1 #endif #ifndef MATH_ERREXCEPT # define MATH_ERREXCEPT 2 #endif #ifndef math_errhandling # define math_errhandling MATH_ERRNO #endif extern int __isinff (float x); extern int __isinfd (double x); extern int __isnanf (float x); extern int __isnand (double x); extern int __fpclassifyf (float x); extern int __fpclassifyd (double x); extern int __signbitf (float x); extern int __signbitd (double x); #define fpclassify(x) \ (__extension__ ({__typeof__(x) __x = (x); \ (sizeof (__x) == sizeof (float)) ? __fpclassifyf(__x) : __fpclassifyd(__x);})) #ifndef isfinite #define isfinite(y) \ (__extension__ ({__typeof__(y) __y = (y); \ fpclassify(__y) != FP_INFINITE && fpclassify(__y) != FP_NAN;})) #endif /* Note: isinf and isnan were once functions in newlib that took double * arguments. C99 specifies that these names are reserved for macros * supporting multiple floating point types. Thus, they are * now defined as macros. Implementations of the old functions * taking double arguments still exist for compatibility purposes. */ #ifndef isinf #define isinf(x) \ (__extension__ ({__typeof__(x) __x = (x); \ (sizeof (__x) == sizeof (float)) ? __isinff(__x) : __isinfd(__x);})) #endif #ifndef isnan #define isnan(x) \ (__extension__ ({__typeof__(x) __x = (x); \ (sizeof (__x) == sizeof (float)) ? __isnanf(__x) : __isnand(__x);})) #endif #define isnormal(y) (fpclassify(y) == FP_NORMAL) #define signbit(x) \ (__extension__ ({__typeof__(x) __x = (x); \ (sizeof(__x) == sizeof(float)) ? __signbitf(__x) : __signbitd(__x);})) #define isgreater(x,y) \ (__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered(__x,__y) && (__x > __y);})) #define isgreaterequal(x,y) \ (__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered(__x,__y) && (__x >= __y);})) #define isless(x,y) \ (__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered(__x,__y) && (__x < __y);})) #define islessequal(x,y) \ (__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered(__x,__y) && (__x <= __y);})) #define islessgreater(x,y) \ (__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered(__x,__y) && (__x < __y || __x > __y);})) #define isunordered(a,b) \ (__extension__ ({__typeof__(a) __a = (a); __typeof__(b) __b = (b); \ fpclassify(__a) == FP_NAN || fpclassify(__b) == FP_NAN;})) /* Non ANSI double precision functions. */ extern double infinity _PARAMS((void)); extern double nan _PARAMS((const char *)); extern int finite _PARAMS((double)); extern double copysign _PARAMS((double, double)); extern int ilogb _PARAMS((double)); extern double asinh _PARAMS((double)); extern double cbrt _PARAMS((double)); extern double nextafter _PARAMS((double, double)); extern double rint _PARAMS((double)); extern double scalbn _PARAMS((double, int)); extern double exp2 _PARAMS((double)); extern double scalbln _PARAMS((double, long int)); extern double tgamma _PARAMS((double)); extern double nearbyint _PARAMS((double)); extern long int lrint _PARAMS((double)); extern double round _PARAMS((double)); extern long int lround _PARAMS((double)); extern double trunc _PARAMS((double)); extern double remquo _PARAMS((double, double, int *)); extern double copysign _PARAMS((double, double)); extern double fdim _PARAMS((double, double)); extern double fmax _PARAMS((double, double)); extern double fmin _PARAMS((double, double)); extern double fma _PARAMS((double, double, double)); #ifndef __math_68881 extern double log1p _PARAMS((double)); extern double expm1 _PARAMS((double)); #endif /* ! defined (__math_68881) */ #ifndef _REENT_ONLY extern double acosh _PARAMS((double)); extern double atanh _PARAMS((double)); extern double remainder _PARAMS((double, double)); extern double gamma _PARAMS((double)); extern double lgamma _PARAMS((double)); extern double erf _PARAMS((double)); extern double erfc _PARAMS((double)); #define log2(x) (log (x) / _M_LOG2_E) #ifndef __math_68881 extern double hypot _PARAMS((double, double)); #endif #endif /* ! defined (_REENT_ONLY) */ /* Single precision versions of ANSI functions. */ extern float atanf _PARAMS((float)); extern float cosf _PARAMS((float)); extern float sinf _PARAMS((float)); extern float tanf _PARAMS((float)); extern float tanhf _PARAMS((float)); extern float frexpf _PARAMS((float, int *)); extern float modff _PARAMS((float, float *)); extern float ceilf _PARAMS((float)); extern float fabsf _PARAMS((float)); extern float floorf _PARAMS((float)); #ifndef _REENT_ONLY extern float acosf _PARAMS((float)); extern float asinf _PARAMS((float)); extern float atan2f _PARAMS((float, float)); extern float coshf _PARAMS((float)); extern float sinhf _PARAMS((float)); extern float expf _PARAMS((float)); extern float ldexpf _PARAMS((float, int)); extern float logf _PARAMS((float)); extern float log10f _PARAMS((float)); extern float powf _PARAMS((float, float)); extern float sqrtf _PARAMS((float)); extern float fmodf _PARAMS((float, float)); #endif /* ! defined (_REENT_ONLY) */ /* Other single precision functions. */ extern float exp2f _PARAMS((float)); extern float scalblnf _PARAMS((float, long int)); extern float tgammaf _PARAMS((float)); extern float nearbyintf _PARAMS((float)); extern long int lrintf _PARAMS((float)); extern float roundf _PARAMS((float)); extern long int lroundf _PARAMS((float)); extern float truncf _PARAMS((float)); extern float remquof _PARAMS((float, float, int *)); extern float copysignf _PARAMS((float, float)); extern float fdimf _PARAMS((float, float)); extern float fmaxf _PARAMS((float, float)); extern float fminf _PARAMS((float, float)); extern float fmaf _PARAMS((float, float, float)); extern float infinityf _PARAMS((void)); extern float nanf _PARAMS((const char *)); extern int isnanf _PARAMS((float)); extern int isinff _PARAMS((float)); extern int finitef _PARAMS((float)); extern float copysignf _PARAMS((float, float)); extern int ilogbf _PARAMS((float)); extern float asinhf _PARAMS((float)); extern float cbrtf _PARAMS((float)); extern float nextafterf _PARAMS((float, float)); extern float rintf _PARAMS((float)); extern float scalbnf _PARAMS((float, int)); extern float log1pf _PARAMS((float)); extern float expm1f _PARAMS((float)); #ifndef _REENT_ONLY extern float acoshf _PARAMS((float)); extern float atanhf _PARAMS((float)); extern float remainderf _PARAMS((float, float)); extern float gammaf _PARAMS((float)); extern float lgammaf _PARAMS((float)); extern float erff _PARAMS((float)); extern float erfcf _PARAMS((float)); #define log2f(x) (logf (x) / (float) _M_LOG2_E) extern float hypotf _PARAMS((float, float)); #endif /* ! defined (_REENT_ONLY) */ #endif /* !defined (__STRICT_ANSI__) || defined(__cplusplus) || __STDC_VERSION__ >= 199901L */ #if !defined (__STRICT_ANSI__) || defined(__cplusplus) extern double cabs(); extern double drem _PARAMS((double, double)); extern void sincos _PARAMS((double, double *, double *)); extern double gamma_r _PARAMS((double, int *)); extern double lgamma_r _PARAMS((double, int *)); extern double y0 _PARAMS((double)); extern double y1 _PARAMS((double)); extern double yn _PARAMS((int, double)); extern double j0 _PARAMS((double)); extern double j1 _PARAMS((double)); extern double jn _PARAMS((int, double)); extern float cabsf(); extern float dremf _PARAMS((float, float)); extern void sincosf _PARAMS((float, float *, float *)); extern float gammaf_r _PARAMS((float, int *)); extern float lgammaf_r _PARAMS((float, int *)); extern float y0f _PARAMS((float)); extern float y1f _PARAMS((float)); extern float ynf _PARAMS((int, float)); extern float j0f _PARAMS((float)); extern float j1f _PARAMS((float)); extern float jnf _PARAMS((int, float)); /* GNU extensions */ # ifndef exp10 extern double exp10 _PARAMS((double)); # endif # ifndef pow10 extern double pow10 _PARAMS((double)); # endif # ifndef exp10f extern float exp10f _PARAMS((float)); # endif # ifndef pow10f extern float pow10f _PARAMS((float)); # endif #endif /* !defined (__STRICT_ANSI__) || defined(__cplusplus) */ #ifndef __STRICT_ANSI__ /* The gamma functions use a global variable, signgam. */ #ifndef _REENT_ONLY #define signgam (*__signgam()) extern int *__signgam _PARAMS((void)); #endif /* ! defined (_REENT_ONLY) */ #define __signgam_r(ptr) _REENT_SIGNGAM(ptr) /* The exception structure passed to the matherr routine. */ /* We have a problem when using C++ since `exception' is a reserved name in C++. */ #ifdef __cplusplus struct __exception #else struct exception #endif { int type; char *name; double arg1; double arg2; double retval; int err; }; #ifdef __cplusplus extern int matherr _PARAMS((struct __exception *e)); #else extern int matherr _PARAMS((struct exception *e)); #endif /* Values for the type field of struct exception. */ #define DOMAIN 1 #define SING 2 #define OVERFLOW 3 #define UNDERFLOW 4 #define TLOSS 5 #define PLOSS 6 /* Useful constants. */ #define MAXFLOAT 3.40282347e+38F #define M_E 2.7182818284590452354 #define M_LOG2E _M_LOG2E #define M_LOG10E 0.43429448190325182765 #define M_LN2 0.69314718055994530942 #define M_LN10 2.30258509299404568402 #define M_PI 3.14159265358979323846 #define M_TWOPI (M_PI * 2.0) #define M_PI_2 1.57079632679489661923 #define M_PI_4 0.78539816339744830962 #define M_3PI_4 2.3561944901923448370E0 #define M_SQRTPI 1.77245385090551602792981 #define M_1_PI 0.31830988618379067154 #define M_2_PI 0.63661977236758134308 #define M_2_SQRTPI 1.12837916709551257390 #define M_SQRT2 1.41421356237309504880 #define M_SQRT1_2 0.70710678118654752440 #define M_LN2LO 1.9082149292705877000E-10 #define M_LN2HI 6.9314718036912381649E-1 #define M_SQRT3 1.73205080756887719000 #define M_IVLN10 0.43429448190325182765 /* 1 / log(10) */ #define M_LOG2_E 0.693147180559945309417 #define M_INVLN2 1.4426950408889633870E0 /* 1 / log(2) */ /* Global control over fdlibm error handling. */ enum __fdlibm_version { __fdlibm_ieee = -1, __fdlibm_svid, __fdlibm_xopen, __fdlibm_posix }; #define _LIB_VERSION_TYPE enum __fdlibm_version #define _LIB_VERSION __fdlib_version extern __IMPORT _LIB_VERSION_TYPE _LIB_VERSION; #define _IEEE_ __fdlibm_ieee #define _SVID_ __fdlibm_svid #define _XOPEN_ __fdlibm_xopen #define _POSIX_ __fdlibm_posix #endif /* ! defined (__STRICT_ANSI__) */ _END_STD_C #ifdef __FAST_MATH__ #include #endif #endif /* _MATH_H_ */