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-/*
- * math.h
- *
- * Mathematical functions.
- *
- * This file is part of the Mingw32 package.
- *
- * Contributors:
- * Created by Colin Peters <colin@bird.fu.is.saga-u.ac.jp>
- *
- * THIS SOFTWARE IS NOT COPYRIGHTED
- *
- * This source code is offered for use in the public domain. You may
- * use, modify or distribute it freely.
- *
- * This code is distributed in the hope that it will be useful but
- * WITHOUT ANY WARRANTY. ALL WARRANTIES, EXPRESS OR IMPLIED ARE HEREBY
- * DISCLAIMED. This includes but is not limited to warranties of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
- *
- * $Revision$
- * $Author$
- * $Date$
- *
- */
-
-#ifndef _MATH_H_
-#define _MATH_H_
-
-/* All the headers include this file. */
-#include <_mingw.h>
-
-/*
- * Types for the _exception structure.
- */
-
-#define _DOMAIN 1 /* domain error in argument */
-#define _SING 2 /* singularity */
-#define _OVERFLOW 3 /* range overflow */
-#define _UNDERFLOW 4 /* range underflow */
-#define _TLOSS 5 /* total loss of precision */
-#define _PLOSS 6 /* partial loss of precision */
-
-/*
- * Exception types with non-ANSI names for compatibility.
- */
-
-#ifndef __STRICT_ANSI__
-#ifndef _NO_OLDNAMES
-
-#define DOMAIN _DOMAIN
-#define SING _SING
-#define OVERFLOW _OVERFLOW
-#define UNDERFLOW _UNDERFLOW
-#define TLOSS _TLOSS
-#define PLOSS _PLOSS
-
-#endif /* Not _NO_OLDNAMES */
-#endif /* Not __STRICT_ANSI__ */
-
-
-/* Traditional/XOPEN math constants (double precison) */
-#ifndef __STRICT_ANSI__
-#define M_E 2.7182818284590452354
-#define M_LOG2E 1.4426950408889634074
-#define M_LOG10E 0.43429448190325182765
-#define M_LN2 0.69314718055994530942
-#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
-
-/* These are also defined in Mingw float.h; needed here as well to work
- around GCC build issues. */
-#ifndef __STRICT_ANSI__
-#ifndef __MINGW_FPCLASS_DEFINED
-#define __MINGW_FPCLASS_DEFINED 1
-/* IEEE 754 classication */
-#define _FPCLASS_SNAN 0x0001 /* Signaling "Not a Number" */
-#define _FPCLASS_QNAN 0x0002 /* Quiet "Not a Number" */
-#define _FPCLASS_NINF 0x0004 /* Negative Infinity */
-#define _FPCLASS_NN 0x0008 /* Negative Normal */
-#define _FPCLASS_ND 0x0010 /* Negative Denormal */
-#define _FPCLASS_NZ 0x0020 /* Negative Zero */
-#define _FPCLASS_PZ 0x0040 /* Positive Zero */
-#define _FPCLASS_PD 0x0080 /* Positive Denormal */
-#define _FPCLASS_PN 0x0100 /* Positive Normal */
-#define _FPCLASS_PINF 0x0200 /* Positive Infinity */
-#endif /* __MINGW_FPCLASS_DEFINED */
-#endif /* Not __STRICT_ANSI__ */
-
-#ifndef RC_INVOKED
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/*
- * HUGE_VAL is returned by strtod when the value would overflow the
- * representation of 'double'. There are other uses as well.
- *
- * __imp__HUGE is a pointer to the actual variable _HUGE in
- * MSVCRT.DLL. If we used _HUGE directly we would get a pointer
- * to a thunk function.
- *
- * NOTE: The CRTDLL version uses _HUGE_dll instead.
- */
-
-#ifndef __DECLSPEC_SUPPORTED
-
-#ifdef __MSVCRT__
-extern double* _imp___HUGE;
-#define HUGE_VAL (*_imp___HUGE)
-#else
-/* CRTDLL */
-extern double* _imp___HUGE_dll;
-#define HUGE_VAL (*_imp___HUGE_dll)
-#endif
-
-#else /* __DECLSPEC_SUPPORTED */
-
-#ifdef __MSVCRT__
-__MINGW_IMPORT double _HUGE;
-#define HUGE_VAL _HUGE
-#else
-/* CRTDLL */
-__MINGW_IMPORT double _HUGE_dll;
-#define HUGE_VAL _HUGE_dll
-#endif
-
-#endif /* __DECLSPEC_SUPPORTED */
-
-struct _exception
-{
- int type;
- char *name;
- double arg1;
- double arg2;
- double retval;
-};
-
-
-double sin (double);
-double cos (double);
-double tan (double);
-double sinh (double);
-double cosh (double);
-double tanh (double);
-double asin (double);
-double acos (double);
-double atan (double);
-double atan2 (double, double);
-double exp (double);
-double log (double);
-double log10 (double);
-double pow (double, double);
-double sqrt (double);
-double ceil (double);
-double floor (double);
-double fabs (double);
-extern __inline__ double fabs (double x)
-{
- double res;
- __asm__ ("fabs;" : "=t" (res) : "0" (x));
- return res;
-}
-double ldexp (double, int);
-double frexp (double, int*);
-double modf (double, double*);
-double fmod (double, double);
-
-
-#ifndef __STRICT_ANSI__
-
-/* Complex number (for cabs). This really belongs in complex.h */
-struct _complex
-{
- double x; /* Real part */
- double y; /* Imaginary part */
-};
-
-double _cabs (struct _complex);
-
-double _hypot (double, double);
-double _j0 (double);
-double _j1 (double);
-double _jn (int, double);
-double _y0 (double);
-double _y1 (double);
-double _yn (int, double);
-int _matherr (struct _exception *);
-
-/* These are also declared in Mingw float.h; needed here as well to work
- around GCC build issues. */
-/* BEGIN FLOAT.H COPY */
-/*
- * IEEE recommended functions
- */
-
-double _chgsign (double);
-double _copysign (double, double);
-double _logb (double);
-double _nextafter (double, double);
-double _scalb (double, long);
-
-int _finite (double);
-int _fpclass (double);
-int _isnan (double);
-
-/* END FLOAT.H COPY */
-
-
-/*
- * Non-underscored versions of non-ANSI functions.
- * These reside in liboldnames.a.
- */
-
-#if !defined (_NO_OLDNAMES)
-
-double cabs (struct _complex);
-double j0 (double);
-double j1 (double);
-double jn (int, double);
-double y0 (double);
-double y1 (double);
-double yn (int, double);
-
-double chgsign (double);
-double scalb (double, long);
-int finite (double);
-int fpclass (double);
-
-#endif /* Not _NO_OLDNAMES */
-
-#endif /* __STRICT_ANSI__ */
-
-
-#ifndef __NO_ISOCEXT
-#if (defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L) \
- || !defined __STRICT_ANSI__ || defined __GLIBCPP__
-
-#define NAN (0.0F/0.0F)
-#define HUGE_VALF (1.0F/0.0F)
-#define HUGE_VALL (1.0L/0.0L)
-#define INFINITY (1.0F/0.0F)
-
-
-/* 7.12.3.1 */
-/*
- Return values for fpclassify.
- These are based on Intel x87 fpu condition codes
- in the high byte of status word and differ from
- the return values for MS IEEE 754 extension _fpclass()
-*/
-#define FP_NAN 0x0100
-#define FP_NORMAL 0x0400
-#define FP_INFINITE (FP_NAN | FP_NORMAL)
-#define FP_ZERO 0x4000
-#define FP_SUBNORMAL (FP_NORMAL | FP_ZERO)
-/* 0x0200 is signbit mask */
-
-
-/*
- We can't inline float or double, because we want to ensure truncation
- to semantic type before classification.
- (A normal long double value might become subnormal when
- converted to double, and zero when converted to float.)
-*/
-
-extern int __fpclassifyf (float);
-extern int __fpclassify (double);
-
-extern __inline__ int __fpclassifyl (long double x){
- unsigned short sw;
- __asm__ ("fxam; fstsw %%ax;" : "=a" (sw): "t" (x));
- return sw & (FP_NAN | FP_NORMAL | FP_ZERO );
-}
-
-#define fpclassify(x) (sizeof (x) == sizeof (float) ? __fpclassifyf (x) \
- : sizeof (x) == sizeof (double) ? __fpclassify (x) \
- : __fpclassifyl (x))
-
-/* 7.12.3.2 */
-#define isfinite(x) ((fpclassify(x) & FP_NAN) == 0)
-
-/* 7.12.3.3 */
-#define isinf(x) (fpclassify(x) == FP_INFINITE)
-
-/* 7.12.3.4 */
-/* We don't need to worry about trucation here:
- A NaN stays a NaN. */
-
-extern __inline__ int __isnan (double _x)
-{
- unsigned short sw;
- __asm__ ("fxam;"
- "fstsw %%ax": "=a" (sw) : "t" (_x));
- return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
- == FP_NAN;
-}
-
-extern __inline__ int __isnanf (float _x)
-{
- unsigned short sw;
- __asm__ ("fxam;"
- "fstsw %%ax": "=a" (sw) : "t" (_x));
- return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
- == FP_NAN;
-}
-
-extern __inline__ int __isnanl (long double _x)
-{
- unsigned short sw;
- __asm__ ("fxam;"
- "fstsw %%ax": "=a" (sw) : "t" (_x));
- return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
- == FP_NAN;
-}
-
-
-#define isnan(x) (sizeof (x) == sizeof (float) ? __isnanf (x) \
- : sizeof (x) == sizeof (double) ? __isnan (x) \
- : __isnanl (x))
-
-/* 7.12.3.5 */
-#define isnormal(x) (fpclassify(x) == FP_NORMAL)
-
-/* 7.12.3.6 The signbit macro */
-extern __inline__ int __signbit (double x) {
- unsigned short stw;
- __asm__ ( "fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
- return stw & 0x0200;
-}
-
-extern __inline__ int __signbitf (float x) {
- unsigned short stw;
- __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
- return stw & 0x0200;
-}
-extern __inline__ int __signbitl (long double x) {
- unsigned short stw;
- __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
- return stw & 0x0200;
-}
-
-
-#define signbit(x) (sizeof (x) == sizeof (float) ? __signbitf (x) \
- : sizeof (x) == sizeof (double) ? __signbit (x) \
- : __signbitl (x))
-
-/* 7.12.4 Trigonometric functions: Double in C89 */
-extern float sinf (float);
-extern long double sinl (long double);
-
-extern float cosf (float);
-extern long double cosl (long double);
-
-extern float tanf (float);
-extern long double tanl (long double);
-
-extern float asinf (float);
-extern long double asinl (long double);
-
-extern float acosf (float);
-extern long double acosl (long double);
-
-extern float atanf (float);
-extern long double atanl (long double);
-
-extern float atan2f (float, float);
-extern long double atan2l (long double, long double);
-
-/* 7.12.5 Hyperbolic functions: Double in C89 */
-extern __inline__ float sinhf (float x)
- {return (float) sinh (x);}
-extern long double sinhl (long double);
-
-extern __inline__ float coshf (float x)
- {return (float) cosh (x);}
-extern long double coshl (long double);
-
-extern __inline__ float tanhf (float x)
- {return (float) tanh (x);}
-extern long double tanhl (long double);
-
-/*
- * TODO: asinh, acosh, atanh
- */
-
-/* 7.12.6.1 Double in C89 */
-extern __inline__ float expf (float x)
- {return (float) exp (x);}
-extern long double expl (long double);
-
-/* 7.12.6.2 */
-extern double exp2(double);
-extern float exp2f(float);
-extern long double exp2l(long double);
-
-/* 7.12.6.3 The expm1 functions: TODO */
-
-/* 7.12.6.4 Double in C89 */
-extern __inline__ float frexpf (float x, int* expn)
- {return (float) frexp (x, expn);}
-extern long double frexpl (long double, int*);
-
-/* 7.12.6.5 */
-#define FP_ILOGB0 ((int)0x80000000)
-#define FP_ILOGBNAN ((int)0x80000000)
-extern int ilogb (double);
-extern int ilogbf (float);
-extern int ilogbl (long double);
-
-/* 7.12.6.6 Double in C89 */
-extern __inline__ float ldexpf (float x, int expn)
- {return (float) ldexp (x, expn);}
-extern long double ldexpl (long double, int);
-
-/* 7.12.6.7 Double in C89 */
-extern float logf (float);
-extern long double logl (long double);
-
-/* 7.12.6.8 Double in C89 */
-extern float log10f (float);
-extern long double log10l (long double);
-
-/* 7.12.6.9 */
-extern double log1p(double);
-extern float log1pf(float);
-extern long double log1pl(long double);
-
-/* 7.12.6.10 */
-extern double log2 (double);
-extern float log2f (float);
-extern long double log2l (long double);
-
-/* 7.12.6.11 */
-extern double logb (double);
-extern float logbf (float);
-extern long double logbl (long double);
-
-extern __inline__ double logb (double x)
-{
- double res;
- __asm__ ("fxtract\n\t"
- "fstp %%st" : "=t" (res) : "0" (x));
- return res;
-}
-
-extern __inline__ float logbf (float x)
-{
- float res;
- __asm__ ("fxtract\n\t"
- "fstp %%st" : "=t" (res) : "0" (x));
- return res;
-}
-
-extern __inline__ long double logbl (long double x)
-{
- long double res;
- __asm__ ("fxtract\n\t"
- "fstp %%st" : "=t" (res) : "0" (x));
- return res;
-}
-
-/* 7.12.6.12 Double in C89 */
-extern float modff (float, float*);
-extern long double modfl (long double, long double*);
-
-/* 7.12.6.13 */
-extern double scalbn (double, int);
-extern float scalbnf (float, int);
-extern long double scalbnl (long double, int);
-
-extern double scalbln (double, long);
-extern float scalblnf (float, long);
-extern long double scalblnl (long double, long);
-
-/* 7.12.7.1 */
-/* Implementations adapted from Cephes versions */
-extern double cbrt (double);
-extern float cbrtf (float);
-extern long double cbrtl (long double);
-
-/* 7.12.7.2 The fabs functions: Double in C89 */
-extern __inline__ float fabsf (float x)
-{
- float res;
- __asm__ ("fabs;" : "=t" (res) : "0" (x));
- return res;
-}
-
-extern __inline__ long double fabsl (long double x)
-{
- long double res;
- __asm__ ("fabs;" : "=t" (res) : "0" (x));
- return res;
-}
-
-/* 7.12.7.3 */
-extern double hypot (double, double); /* in libmoldname.a */
-extern __inline__ float hypotf (float x, float y)
- { return (float) hypot (x, y);}
-extern long double hypotl (long double, long double);
-
-/* 7.12.7.4 The pow functions. Double in C89 */
-extern __inline__ float powf (float x, float y)
- {return (float) pow (x, y);}
-extern long double powl (long double, long double);
-
-/* 7.12.7.5 The sqrt functions. Double in C89. */
-extern float sqrtf (float);
-extern long double sqrtl (long double);
-
-/* 7.12.8.1 The erf functions */
-extern double erf (double);
-extern float erff (float);
-/* TODO
-extern long double erfl (long double);
-*/
-
-/* 7.12.8.2 The erfc functions */
-extern double erfc (double);
-extern float erfcf (float);
-/* TODO
-extern long double erfcl (long double);
-*/
-
-/* 7.12.8.3 The lgamma functions */
-
-extern double lgamma (double);
-extern float lgammaf (float);
-extern long double lgammal (long double);
-
-/* 77.12.8.4 The tgamma functions */
-
-extern double tgamma (double);
-extern float tgammaf (float);
-extern long double tgammal (long double);
-
-/* 7.12.9.1 Double in C89 */
-extern float ceilf (float);
-extern long double ceill (long double);
-
-/* 7.12.9.2 Double in C89 */
-extern float floorf (float);
-extern long double floorl (long double);
-
-/* 7.12.9.3 */
-extern double nearbyint ( double);
-extern float nearbyintf (float);
-extern long double nearbyintl (long double);
-
-/* 7.12.9.4 */
-/* round, using fpu control word settings */
-extern __inline__ double rint (double x)
-{
- double retval;
- __asm__ ("frndint;": "=t" (retval) : "0" (x));
- return retval;
-}
-
-extern __inline__ float rintf (float x)
-{
- float retval;
- __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
- return retval;
-}
-
-extern __inline__ long double rintl (long double x)
-{
- long double retval;
- __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
- return retval;
-}
-
-/* 7.12.9.5 */
-extern __inline__ long lrint (double x)
-{
- long retval;
- __asm__ __volatile__ \
- ("fistpl %0" : "=m" (retval) : "t" (x) : "st"); \
- return retval;
-}
-
-extern __inline__ long lrintf (float x)
-{
- long retval;
- __asm__ __volatile__ \
- ("fistpl %0" : "=m" (retval) : "t" (x) : "st"); \
- return retval;
-}
-
-extern __inline__ long lrintl (long double x)
-{
- long retval;
- __asm__ __volatile__ \
- ("fistpl %0" : "=m" (retval) : "t" (x) : "st"); \
- return retval;
-}
-
-extern __inline__ long long llrint (double x)
-{
- long long retval;
- __asm__ __volatile__ \
- ("fistpll %0" : "=m" (retval) : "t" (x) : "st"); \
- return retval;
-}
-
-extern __inline__ long long llrintf (float x)
-{
- long long retval;
- __asm__ __volatile__ \
- ("fistpll %0" : "=m" (retval) : "t" (x) : "st"); \
- return retval;
-}
-
-extern __inline__ long long llrintl (long double x)
-{
- long long retval;
- __asm__ __volatile__ \
- ("fistpll %0" : "=m" (retval) : "t" (x) : "st"); \
- return retval;
-}
-
-/* 7.12.9.6 */
-/* round away from zero, regardless of fpu control word settings */
-extern double round (double);
-extern float roundf (float);
-extern long double roundl (long double);
-
-/* 7.12.9.7 */
-extern long lround (double);
-extern long lroundf (float);
-extern long lroundl (long double);
-
-extern long long llround (double);
-extern long long llroundf (float);
-extern long long llroundl (long double);
-
-/* 7.12.9.8 */
-/* round towards zero, regardless of fpu control word settings */
-extern double trunc (double);
-extern float truncf (float);
-extern long double truncl (long double);
-
-/* 7.12.10.1 Double in C89 */
-extern float fmodf (float, float);
-extern long double fmodl (long double, long double);
-
-/* 7.12.10.2 */
-extern double remainder (double, double);
-extern float remainderf (float, float);
-extern long double remainderl (long double, long double);
-
-/* 7.12.10.3 */
-extern double remquo(double, double, int *);
-extern float remquof(float, float, int *);
-extern long double remquol(long double, long double, int *);
-
-/* 7.12.11.1 */
-extern double copysign (double, double); /* in libmoldname.a */
-extern float copysignf (float, float);
-extern long double copysignl (long double, long double);
-
-/* 7.12.11.2 Return a NaN */
-extern double nan(const char *tagp);
-extern float nanf(const char *tagp);
-extern long double nanl(const char *tagp);
-
-#ifndef __STRICT_ANSI__
-#define _nan() nan("")
-#define _nanf() nanf("")
-#define _nanl() nanl("")
-#endif
-
-/* 7.12.11.3 */
-extern double nextafter (double, double); /* in libmoldname.a */
-extern float nextafterf (float, float);
-/* TODO: Not yet implemented */
-/* extern long double nextafterl (long double, long double); */
-
-/* 7.12.11.4 The nexttoward functions: TODO */
-
-/* 7.12.12.1 */
-/* x > y ? (x - y) : 0.0 */
-extern double fdim (double x, double y);
-extern float fdimf (float x, float y);
-extern long double fdiml (long double x, long double y);
-
-/* fmax and fmin.
- NaN arguments are treated as missing data: if one argument is a NaN
- and the other numeric, then these functions choose the numeric
- value. */
-
-/* 7.12.12.2 */
-extern double fmax (double, double);
-extern float fmaxf (float, float);
-extern long double fmaxl (long double, long double);
-
-/* 7.12.12.3 */
-extern double fmin (double, double);
-extern float fminf (float, float);
-extern long double fminl (long double, long double);
-
-/* 7.12.13.1 */
-/* return x * y + z as a ternary op */
-extern double fma (double, double, double);
-extern float fmaf (float, float, float);
-extern long double fmal (long double, long double, long double);
-
-
-/* 7.12.14 */
-/*
- * With these functions, comparisons involving quiet NaNs set the FP
- * condition code to "unordered". The IEEE floating-point spec
- * dictates that the result of floating-point comparisons should be
- * false whenever a NaN is involved, with the exception of the != op,
- * which always returns true: yes, (NaN != NaN) is true).
- */
-
-#if __GNUC__ >= 3
-
-#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)
-
-#else
-/* helper */
-extern __inline__ int
-__fp_unordered_compare (long double x, long double y){
- unsigned short retval;
- __asm__ ("fucom %%st(1);"
- "fnstsw;": "=a" (retval) : "t" (x), "u" (y));
- return retval;
-}
-
-#define isgreater(x, y) ((__fp_unordered_compare(x, y) \
- & 0x4500) == 0)
-#define isless(x, y) ((__fp_unordered_compare (y, x) \
- & 0x4500) == 0)
-#define isgreaterequal(x, y) ((__fp_unordered_compare (x, y) \
- & FP_INFINITE) == 0)
-#define islessequal(x, y) ((__fp_unordered_compare(y, x) \
- & FP_INFINITE) == 0)
-#define islessgreater(x, y) ((__fp_unordered_compare(x, y) \
- & FP_SUBNORMAL) == 0)
-#define isunordered(x, y) ((__fp_unordered_compare(x, y) \
- & 0x4500) == 0x4500)
-
-#endif
-
-
-#endif /* __STDC_VERSION__ >= 199901L */
-#endif /* __NO_ISOCEXT */
-
-
-#ifdef __cplusplus
-}
-#endif
-#endif /* Not RC_INVOKED */
-
-
-#endif /* Not _MATH_H_ */
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