#ifndef _MATH_H_ #define _MATH_H_ #include #include #include #include "_ansi.h" _BEGIN_STD_C /* __dmath, __fmath, and __ldmath are only here for backwards compatibility * in case any code used them. They are no longer used by Newlib, itself, * other than legacy. */ union __dmath { double d; __ULong i[2]; }; union __fmath { float f; __ULong i[1]; }; #if defined(_HAVE_LONG_DOUBLE) union __ldmath { long double ld; __ULong i[4]; }; #endif /* Natural log of 2 */ #define _M_LN2 0.693147180559945309417 #if __GNUC_PREREQ (3, 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 fixed defines instead. (All 3 HUGE plus the INFINITY * and NAN macros are required to be constant expressions. Using a variable-- * even a static const--does not meet this requirement, as it cannot be * evaluated at translation time.) * The infinities are done using numbers that are far in excess of * something that would be expected to be encountered in a floating-point * implementation. (A more certain way uses values from float.h, but that is * avoided because system includes are not supposed to include each other.) * This method might produce warnings from some compilers. (It does in * newer GCCs, but not for ones that would hit this #else.) If this happens, * please report details to the Newlib mailing list. */ #ifndef HUGE_VAL #define HUGE_VAL (1.0e999999999) #endif #ifndef HUGE_VALF #define HUGE_VALF (1.0e999999999F) #endif #if !defined(HUGE_VALL) && defined(_HAVE_LONG_DOUBLE) #define HUGE_VALL (1.0e999999999L) #endif #if !defined(INFINITY) #define INFINITY (HUGE_VALF) #endif #if !defined(NAN) #if defined(__GNUC__) && defined(__cplusplus) /* Exception: older g++ versions warn about the divide by 0 used in the * normal case (even though older gccs do not). This trick suppresses the * warning, but causes errors for plain gcc, so is only used in the one * special case. */ static const union { __ULong __i[1]; float __d; } __Nanf = {0x7FC00000}; #define NAN (__Nanf.__d) #else #define NAN (0.0F/0.0F) #endif #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_68881 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 __ISO_C_VISIBLE >= 1999 /* ISO C99 types and macros. */ /* FIXME: FLT_EVAL_METHOD should somehow be gotten from float.h (which is hard, * considering that the standard says the includes it defines should not * include other includes that it defines) and that value used. (This can be * solved, but autoconf has a bug which makes the solution more difficult, so * it has been skipped for now.) */ #if !defined(FLT_EVAL_METHOD) && defined(__FLT_EVAL_METHOD__) #define FLT_EVAL_METHOD __FLT_EVAL_METHOD__ #define __TMP_FLT_EVAL_METHOD #endif /* FLT_EVAL_METHOD */ #if defined FLT_EVAL_METHOD #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 typedef long double float_t; typedef long double double_t; #else /* Implementation-defined. Assume float_t and double_t have been * defined previously for this configuration (e.g. config.h). */ #endif #else /* Assume basic definitions. */ typedef float float_t; typedef double double_t; #endif #if defined(__TMP_FLT_EVAL_METHOD) #undef FLT_EVAL_METHOD #endif #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) \ ((sizeof(__x) == sizeof(float)) ? __fpclassifyf(__x) : \ __fpclassifyd(__x)) #ifndef isfinite #define isfinite(__y) \ (__extension__ ({int __cy = fpclassify(__y); \ __cy != FP_INFINITE && __cy != 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 * (prototypes for them are in ). */ #ifndef isinf #define isinf(y) (fpclassify(y) == FP_INFINITE) #endif #ifndef isnan #define isnan(y) (fpclassify(y) == FP_NAN) #endif #define isnormal(y) (fpclassify(y) == FP_NORMAL) #define signbit(__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 long double precision functions. */ extern int finitel _PARAMS((long double)); /* 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 double logb _PARAMS((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 long long int llrint _PARAMS((double)); extern double round _PARAMS((double)); extern long int lround _PARAMS((double)); extern long long int llround _PARAMS((double)); extern double trunc _PARAMS((double)); extern double remquo _PARAMS((double, double, int *)); 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)); extern double log2 _PARAMS((double)); #if !defined(__cplusplus) #define log2(x) (log (x) / _M_LN2) #endif #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 long long int llrintf _PARAMS((float)); extern float roundf _PARAMS((float)); extern long int lroundf _PARAMS((float)); extern long long int llroundf _PARAMS((float)); extern float truncf _PARAMS((float)); extern float remquof _PARAMS((float, float, int *)); 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 finitef _PARAMS((float)); extern float copysignf _PARAMS((float, float)); extern float logbf _PARAMS((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)); extern float log2f _PARAMS((float)); extern float hypotf _PARAMS((float, float)); #endif /* ! defined (_REENT_ONLY) */ /* On platforms where long double equals double. */ #ifdef _LDBL_EQ_DBL /* Reentrant ANSI C functions. */ #ifndef __math_68881 extern long double atanl _PARAMS((long double)); extern long double cosl _PARAMS((long double)); extern long double sinl _PARAMS((long double)); extern long double tanl _PARAMS((long double)); extern long double tanhl _PARAMS((long double)); extern long double frexpl _PARAMS((long double, int *)); extern long double modfl _PARAMS((long double, long double *)); extern long double ceill _PARAMS((long double)); extern long double fabsl _PARAMS((long double)); extern long double floorl _PARAMS((long double)); extern long double log1pl _PARAMS((long double)); extern long double expm1l _PARAMS((long double)); #endif /* ! defined (__math_68881) */ /* Non reentrant ANSI C functions. */ #ifndef _REENT_ONLY #ifndef __math_68881 extern long double acosl _PARAMS((long double)); extern long double asinl _PARAMS((long double)); extern long double atan2l _PARAMS((long double, long double)); extern long double coshl _PARAMS((long double)); extern long double sinhl _PARAMS((long double)); extern long double expl _PARAMS((long double)); extern long double ldexpl _PARAMS((long double, int)); extern long double logl _PARAMS((long double)); extern long double log10l _PARAMS((long double)); extern long double powl _PARAMS((long double, long double)); extern long double sqrtl _PARAMS((long double)); extern long double fmodl _PARAMS((long double, long double)); extern long double hypotl _PARAMS((long double, long double)); #endif /* ! defined (__math_68881) */ #endif /* ! defined (_REENT_ONLY) */ extern long double copysignl _PARAMS((long double, long double)); extern long double nanl _PARAMS((const char *)); extern int ilogbl _PARAMS((long double)); extern long double asinhl _PARAMS((long double)); extern long double cbrtl _PARAMS((long double)); extern long double nextafterl _PARAMS((long double, long double)); extern float nexttowardf _PARAMS((float, long double)); extern double nexttoward _PARAMS((double, long double)); extern long double nexttowardl _PARAMS((long double, long double)); extern long double logbl _PARAMS((long double)); extern long double log2l _PARAMS((long double)); extern long double rintl _PARAMS((long double)); extern long double scalbnl _PARAMS((long double, int)); extern long double exp2l _PARAMS((long double)); extern long double scalblnl _PARAMS((long double, long)); extern long double tgammal _PARAMS((long double)); extern long double nearbyintl _PARAMS((long double)); extern long int lrintl _PARAMS((long double)); extern long long int llrintl _PARAMS((long double)); extern long double roundl _PARAMS((long double)); extern long lroundl _PARAMS((long double)); extern long long int llroundl _PARAMS((long double)); extern long double truncl _PARAMS((long double)); extern long double remquol _PARAMS((long double, long double, int *)); extern long double fdiml _PARAMS((long double, long double)); extern long double fmaxl _PARAMS((long double, long double)); extern long double fminl _PARAMS((long double, long double)); extern long double fmal _PARAMS((long double, long double, long double)); #ifndef _REENT_ONLY extern long double acoshl _PARAMS((long double)); extern long double atanhl _PARAMS((long double)); extern long double remainderl _PARAMS((long double, long double)); extern long double lgammal _PARAMS((long double)); extern long double erfl _PARAMS((long double)); extern long double erfcl _PARAMS((long double)); #endif /* ! defined (_REENT_ONLY) */ #else /* !_LDBL_EQ_DBL */ extern long double hypotl _PARAMS((long double, long double)); extern long double sqrtl _PARAMS((long double)); #ifdef __i386__ /* Other long double precision functions. */ extern _LONG_DOUBLE rintl _PARAMS((_LONG_DOUBLE)); extern long int lrintl _PARAMS((_LONG_DOUBLE)); extern long long int llrintl _PARAMS((_LONG_DOUBLE)); #endif /* __i386__ */ #endif /* !_LDBL_EQ_DBL */ #endif /* __ISO_C_VISIBLE >= 1999 */ #if __MISC_VISIBLE extern double drem _PARAMS((double, double)); extern float dremf _PARAMS((float, float)); extern double gamma_r _PARAMS((double, int *)); extern double lgamma_r _PARAMS((double, int *)); extern float gammaf_r _PARAMS((float, int *)); extern float lgammaf_r _PARAMS((float, int *)); #endif #if __MISC_VISIBLE || __XSI_VISIBLE 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)); #endif #if __MISC_VISIBLE || __XSI_VISIBLE >= 600 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)); #endif /* GNU extensions */ #if __GNU_VISIBLE extern void sincos _PARAMS((double, double *, double *)); extern void sincosf _PARAMS((float, float *, float *)); # 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 /* __GNU_VISIBLE */ #if __MISC_VISIBLE || __XSI_VISIBLE /* 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) #endif /* __MISC_VISIBLE || __XSI_VISIBLE */ #if __SVID_VISIBLE /* 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 #endif /* __SVID_VISIBLE */ /* Useful constants. */ #if __BSD_VISIBLE || __XSI_VISIBLE >= 500 #define MAXFLOAT 3.40282347e+38F #define M_E 2.7182818284590452354 #define M_LOG2E 1.4426950408889634074 #define M_LOG10E 0.43429448190325182765 #define M_LN2 _M_LN2 #define M_LN10 2.30258509299404568402 #define M_PI 3.14159265358979323846 #define M_PI_2 1.57079632679489661923 #define M_PI_4 0.78539816339744830962 #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 #endif #if __BSD_VISIBLE #define M_TWOPI (M_PI * 2.0) #define M_3PI_4 2.3561944901923448370E0 #define M_SQRTPI 1.77245385090551602792981 #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 _M_LN2 #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 /* __BSD_VISIBLE */ _END_STD_C #ifdef __FAST_MATH__ #include #endif #endif /* _MATH_H_ */