/*
 * math.h
 *
 * ANSI/POSIX + Microsoft compatible mathematical function prototypes,
 * associated macros, and manifest constant definitions.
 *
 * $Id: math.h,v 27e354f59821 2017/11/28 17:33:30 keith $
 *
 * Written by Colin Peters <colin@bird.fu.is.saga-u.ac.jp>
 * Copyright (C) 1997-2009, 2014-2016, MinGW.org Project.
 *
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice, this permission notice, and the following
 * disclaimer shall be included in all copies or substantial portions of
 * the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OF OR OTHER
 * DEALINGS IN THE SOFTWARE.
 *
 */
#ifndef _MATH_H
#define _MATH_H
#pragma GCC system_header

/* 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 */

#if ! defined __STRICT_ANSI__ && ! defined _NO_OLDNAMES
/*
 * Exception types with non-ANSI names for compatibility.
 */
#define DOMAIN		_DOMAIN
#define SING		_SING
#define OVERFLOW	_OVERFLOW
#define UNDERFLOW	_UNDERFLOW
#define TLOSS		_TLOSS
#define PLOSS		_PLOSS

#endif	/* !__STRICT_ANSI__ && !_NO_OLDNAMES */


#if _POSIX_C_SOURCE || defined _USE_MATH_DEFINES
/* Traditional/XOPEN math constants (double precison).  MSVC makes these
 * available, only if _USE_MATH_DEFINES is specified; POSIX does so also,
 * when _POSIX_C_SOURCE is defined and non-zero, (as will be the case by
 * default in MinGW, unless __STRICT_ANSI__ checking is in effect).
 */
#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.
 *
 * FIXME: Since they're needed both in MinGW float.h and here,
 * they should be moved to a common "parts" header.
 */
#if ! defined __STRICT_ANSI__ && ! defined __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	/* !__STRICT_ANSI__ && !__MINGW_FPCLASS_DEFINED */

#ifndef RC_INVOKED

_BEGIN_C_DECLS

/* 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.
 */
#if __MINGW_GNUC_PREREQ(3, 3)
#define HUGE_VAL __builtin_huge_val()

#else
#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 */
#endif /* __MINGW_GNUC_PREREQ(3, 3) */

struct _exception
{
  int     type;
  char   *name;
  double  arg1;
  double  arg2;
  double  retval;
};

_CRTIMP double __cdecl sin (double);
_CRTIMP double __cdecl cos (double);
_CRTIMP double __cdecl tan (double);
_CRTIMP double __cdecl sinh (double);
_CRTIMP double __cdecl cosh (double);
_CRTIMP double __cdecl tanh (double);
_CRTIMP double __cdecl asin (double);
_CRTIMP double __cdecl acos (double);
_CRTIMP double __cdecl atan (double);
_CRTIMP double __cdecl atan2 (double, double);
_CRTIMP double __cdecl exp (double);
_CRTIMP double __cdecl log (double);
_CRTIMP double __cdecl log10 (double);
_CRTIMP	double __cdecl pow (double, double);
_CRTIMP double __cdecl sqrt (double);
_CRTIMP double __cdecl ceil (double);
_CRTIMP double __cdecl floor (double);
_CRTIMP double __cdecl fabs (double);
_CRTIMP double __cdecl ldexp (double, int);
_CRTIMP double __cdecl frexp (double, int*);
_CRTIMP double __cdecl modf (double, double*);
_CRTIMP double __cdecl fmod (double, double);

#if 0
/* Excess precision when using a 64-bit mantissa for FPU math ops can
 * cause unexpected results with some of the MSVCRT math functions.  For
 * example, unless the function return value is stored (truncating to
 * 53-bit mantissa), calls to pow with both x and y as integral values
 * sometimes produce a non-integral result.
 *
 * One workaround is to reset the FPU env to 53-bit mantissa
 * by a call to fesetenv (FE_PC53_ENV).  Amother is to force storage
 * of the return value of individual math functions using wrappers.
 * NB, using these wrappers will disable builtin math functions and
 * hence disable the folding of function results at compile time when
 * arguments are constant.
 */
#define __DEFINE_FLOAT_STORE_MATHFN_D1(fn1)	\
static __inline__ double			\
__float_store_ ## fn1 (double x)		\
{						\
   __volatile__ double res = (fn1) (x); 	\
  return res;					\
}

#define __DEFINE_FLOAT_STORE_MATHFN_D2(fn2)	\
static __inline__ double			\
__float_store_ ## fn2 (double x, double y)	\
{						\
  __volatile__ double res = (fn2) (x, y);	\
  return res;					\
}

/* For example, here is how to force the result of the pow function
 * to be stored:
 */
#undef pow
/* Define the ___float_store_pow function and use it instead of pow().
 */
__DEFINE_FLOAT_STORE_MATHFN_D2 (pow)
#define pow __float_store_pow
#endif

#ifndef __STRICT_ANSI__

struct _complex
{ /* Complex number (for _cabs).  This is the MS version; the
   * ISO-C99 counterpart, _Complex, is an intrinsic type in GCC,
   * and 'complex' is defined as a macro.  See <complex.h>
   */
  double  x;	/* Real part */
  double  y;	/* Imaginary part */
};

_CRTIMP double __cdecl _cabs (struct _complex);

_CRTIMP double __cdecl _hypot (double, double);
_CRTIMP double __cdecl _j0 (double);
_CRTIMP double __cdecl _j1 (double);
_CRTIMP double __cdecl _jn (int, double);
_CRTIMP double __cdecl _y0 (double);
_CRTIMP double __cdecl _y1 (double);
_CRTIMP double __cdecl _yn (int, double);
_CRTIMP int __cdecl _matherr (struct _exception *);

/* These are also declared in MinGW's <float.h>; we need them
 * here as well to work around GCC build issues.
 */
/* BEGIN FLOAT.H COPY */
/*
 * IEEE recommended functions
 */
_CRTIMP double __cdecl _chgsign (double);
_CRTIMP double __cdecl _copysign (double, double);
_CRTIMP double __cdecl _logb (double);
_CRTIMP double __cdecl _nextafter (double, double);
_CRTIMP double __cdecl _scalb (double, long);

_CRTIMP int __cdecl _finite (double);
_CRTIMP int __cdecl _fpclass (double);
_CRTIMP int __cdecl _isnan (double);

/* END FLOAT.H COPY */


#ifndef _NO_OLDNAMES
/* Non-underscored versions of non-ANSI functions.
 * These reside in liboldnames.a.
 */
_CRTIMP double __cdecl j0 (double);
_CRTIMP double __cdecl j1 (double);
_CRTIMP double __cdecl jn (int, double);
_CRTIMP double __cdecl y0 (double);
_CRTIMP double __cdecl y1 (double);
_CRTIMP double __cdecl yn (int, double);

_CRTIMP double __cdecl chgsign (double);
/*
 * scalb() is a GCC built-in.
 * Exclude this _scalb() stub; the semantics are incompatible
 * with the built-in implementation.
 *
_CRTIMP double __cdecl scalb (double, long);
 *
 */
_CRTIMP int __cdecl finite (double);
_CRTIMP int __cdecl fpclass (double);

#define FP_SNAN    _FPCLASS_SNAN
#define FP_QNAN    _FPCLASS_QNAN
#define FP_NINF    _FPCLASS_NINF
#define FP_PINF    _FPCLASS_PINF
#define FP_NDENORM _FPCLASS_ND
#define FP_PDENORM _FPCLASS_PD
#define FP_NZERO   _FPCLASS_NZ
#define FP_PZERO   _FPCLASS_PZ
#define FP_NNORM   _FPCLASS_NN
#define FP_PNORM   _FPCLASS_PN

#endif	/* !_NO_OLDNAMES */

#if _WIN32_WINNT >= _WIN32_WINNT_WINXP || __MSVCRT_VERSION__ >= __MSVCR70_DLL
/*
 * This requires WinXP, or MSVCR70.DLL, or later.
 */
_CRTIMP int __cdecl _set_SSE2_enable (int);

#endif	/* >= WINXP || >= __MSVCR70_DLL */
#endif	/* !__STRICT_ANSI__ */

#if defined __cplusplus || defined _ISOC99_SOURCE

# if __MINGW_GNUC_PREREQ(3, 3)
#  define HUGE_VALF		__builtin_huge_valf()
#  define HUGE_VALL		__builtin_huge_vall()
#  define INFINITY		__builtin_inf()
#  define NAN			__builtin_nan("")
# else
   extern const float		__INFF;
   extern const long double	__INFL;
   extern const double		__QNAN;

#  define HUGE_VALF		__INFF
#  define HUGE_VALL		__INFL
#  define INFINITY		  HUGE_VALF
#  define NAN			__QNAN

# endif /* __MINGW_GNUC_PREREQ(3, 3) */

/* Use the compiler's internal definition for FLT_EVAL_METHOD, if one
 * is available, to establish appropriate float_t and double_t typedefs;
 * in the case of GCC, this is specified as __FLT_EVAL_METHOD__, which
 * is expected to be assigned standardized values of 0, 1, or 2, (or
 * exceptionally, a value of -1, representing indeterminacy).
 */
#if ! defined __FLT_EVAL_METHOD__ || __valueless(__FLT_EVAL_METHOD__) \
 || (__FLT_EVAL_METHOD__ - 0) < 0 || (__FLT_EVAL_METHOD__ - 0) > 1
 /* __FLT_EVAL_METHOD__ has not been defined, or it is defined with no
  * value, or with a value of -1 (or less), or a value of 2 or more; in
  * the specific case of a value of 2, this represents an explicit choice
  * of the IX387 FPU configuration, while in each of the other cases, we
  * implicitly fall back to this same default configuration.
  *
  * NOTE: this configuration is correct for X87 FPU computations, (for
  * which __FLT_EVAL_METHOD__ is correctly specified as 2); however...
  */
# if defined __FLT_EVAL_METHOD__ && (__FLT_EVAL_METHOD__ - 0) != 2
  /* ...due to a GCC bug, introduced in GCC-6 and persisting into later
   * versions, it may be selected via __FLT_EVAL_METHOD__ == -1, for the
   * case of the "-msse -mfpmath=sse" option combination.  In this case,
   * it is (at best) an unsatisfactory compromise; to avoid it, you may
   * prefer to adopt "-mfpmath=387", or "-msse2 -mfpmath=sse" instead.
   */
#  warning "Default FLT_EVAL_METHOD is inderminate; assuming X87 semantics."
# endif
  typedef long double float_t;
  typedef long double double_t;

#else
 /* __FLT_EVAL_METHOD__ must have been defined with an explicit value
  * of either 0 or 1; select the corresponding SSE configuration which
  * is applicable in each case.
  */
# if __FLT_EVAL_METHOD__ == 0
   typedef float float_t;
   typedef double double_t;

# else /*  __FLT_EVAL_METHOD__ == 1 */
   typedef double float_t;
   typedef double double_t;
# endif
#endif

/* 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 __cdecl __fpclassifyf (float);
extern int __cdecl __fpclassify (double);
extern int __cdecl __fpclassifyl (long double);

#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl __fpclassifyl (long double x){
  unsigned short sw;
  __asm__ ("fxam; fstsw %%ax;" : "=a" (sw): "t" (x));
  return sw & (FP_NAN | FP_NORMAL | FP_ZERO );
}
#endif

#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 truncation here:
 * a NaN stays a NaN.
 */
extern int __cdecl __isnan (double);
extern int __cdecl __isnanf (float);
extern int __cdecl __isnanl (long double);
#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl __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;
}

__CRT_INLINE int __cdecl __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;
}

__CRT_INLINE int __cdecl __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;
}
#endif

#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 int __cdecl __signbit (double);
extern int __cdecl __signbitf (float);
extern int __cdecl __signbitl (long double);
#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl __signbit (double x) {
  unsigned short stw;
  __asm__ ( "fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
  return (stw & 0x0200) != 0;
}

__CRT_INLINE int __cdecl __signbitf (float x) {
  unsigned short stw;
  __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
  return (stw & 0x0200) != 0;
}

__CRT_INLINE int __cdecl __signbitl (long double x) {
  unsigned short stw;
  __asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
  return (stw & 0x0200) != 0;
}
#endif

#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 __cdecl sinf (float);
extern long double __cdecl sinl (long double);

extern float __cdecl cosf (float);
extern long double __cdecl cosl (long double);

extern float __cdecl tanf (float);
extern long double __cdecl tanl (long double);

extern float __cdecl asinf (float);
extern long double __cdecl asinl (long double);

extern float __cdecl acosf (float);
extern long double __cdecl acosl (long double);

extern float __cdecl atanf (float);
extern long double __cdecl atanl (long double);

extern float __cdecl atan2f (float, float);
extern long double __cdecl atan2l (long double, long double);

/* 7.12.5 Hyperbolic functions: double in C89
 */
extern float __cdecl sinhf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl sinhf (float x)
  {return (float) sinh (x);}
#endif
extern long double __cdecl sinhl (long double);

extern float __cdecl coshf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl coshf (float x)
  {return (float) cosh (x);}
#endif
extern long double __cdecl coshl (long double);

extern float __cdecl tanhf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl tanhf (float x)
  {return (float) tanh (x);}
#endif
extern long double __cdecl tanhl (long double);

/* Inverse hyperbolic trig functions  */
/* 7.12.5.1 */
extern double __cdecl acosh (double);
extern float __cdecl acoshf (float);
extern long double __cdecl acoshl (long double);

/* 7.12.5.2 */
extern double __cdecl asinh (double);
extern float __cdecl asinhf (float);
extern long double __cdecl asinhl (long double);

/* 7.12.5.3 */
extern double __cdecl atanh (double);
extern float __cdecl atanhf  (float);
extern long double __cdecl atanhl (long double);

/* Exponentials and logarithms  */
/* 7.12.6.1 Double in C89 */
extern float __cdecl expf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl expf (float x)
  {return (float) exp (x);}
#endif
extern long double __cdecl expl (long double);

/* 7.12.6.2 */
extern double __cdecl exp2(double);
extern float __cdecl exp2f(float);
extern long double __cdecl exp2l(long double);

/* 7.12.6.3 The expm1 functions */
/* TODO: These could be inlined */
extern double __cdecl expm1(double);
extern float __cdecl expm1f(float);
extern long double __cdecl expm1l(long double);

/* 7.12.6.4 Double in C89 */
extern float __cdecl frexpf (float, int*);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl frexpf (float x, int* expn)
  {return (float) frexp (x, expn);}
#endif
extern long double __cdecl frexpl (long double, int*);

/* 7.12.6.5 */
#define FP_ILOGB0 ((int)0x80000000)
#define FP_ILOGBNAN ((int)0x80000000)
extern int __cdecl ilogb (double);
extern int __cdecl ilogbf (float);
extern int __cdecl ilogbl (long double);

/* 7.12.6.6  Double in C89 */
extern float __cdecl ldexpf (float, int);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl ldexpf (float x, int expn)
  {return (float) ldexp (x, expn);}
#endif
extern long double __cdecl ldexpl (long double, int);

/* 7.12.6.7 Double in C89 */
extern float __cdecl logf (float);
extern long double __cdecl logl (long double);

/* 7.12.6.8 Double in C89 */
extern float __cdecl log10f (float);
extern long double __cdecl log10l (long double);

/* 7.12.6.9 */
extern double __cdecl log1p(double);
extern float __cdecl log1pf(float);
extern long double __cdecl log1pl(long double);

/* 7.12.6.10 */
extern double __cdecl log2 (double);
extern float __cdecl log2f (float);
extern long double __cdecl log2l (long double);

/* 7.12.6.11 */
extern double __cdecl logb (double);
extern float __cdecl logbf (float);
extern long double __cdecl logbl (long double);

/* Inline versions.  GCC-4.0+ can do a better fast-math optimization
 * with __builtins.
 */
#ifndef __NO_INLINE__
#if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
__CRT_INLINE double __cdecl logb (double x)
{
  double res;
  __asm__ ("fxtract\n\t"
       "fstp	%%st" : "=t" (res) : "0" (x));
  return res;
}

__CRT_INLINE float __cdecl logbf (float x)
{
  float res;
  __asm__ ("fxtract\n\t"
       "fstp	%%st" : "=t" (res) : "0" (x));
  return res;
}

__CRT_INLINE long double __cdecl logbl (long double x)
{
  long double res;
  __asm__ ("fxtract\n\t"
       "fstp	%%st" : "=t" (res) : "0" (x));
  return res;
}
#endif /* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4, 0) */
#endif /* !__NO_INLINE__ */

/* 7.12.6.12  Double in C89 */
extern float __cdecl modff (float, float*);
extern long double __cdecl modfl (long double, long double*);

/* 7.12.6.13 */
extern double __cdecl scalbn (double, int);
extern float __cdecl scalbnf (float, int);
extern long double __cdecl scalbnl (long double, int);

extern double __cdecl scalbln (double, long);
extern float __cdecl scalblnf (float, long);
extern long double __cdecl scalblnl (long double, long);

/* 7.12.7.1 */
/* Implementations adapted from Cephes versions */
extern double __cdecl cbrt (double);
extern float __cdecl cbrtf (float);
extern long double __cdecl cbrtl (long double);

/* 7.12.7.2 The fabs functions: Double in C89 */
extern  float __cdecl fabsf (float x);
extern long double __cdecl fabsl (long double x);

/* 7.12.7.3  */
extern double __cdecl hypot (double, double); /* in libmoldname.a */
extern float __cdecl hypotf (float, float);
extern long double __cdecl hypotl (long double, long double);

/* 7.12.7.4 The pow functions. Double in C89 */
extern float __cdecl powf (float, float);
extern long double __cdecl powl (long double, long double);

/* 7.12.7.5 The sqrt functions. Double in C89. */
extern float __cdecl sqrtf (float);
extern long double __cdecl sqrtl (long double);

/* 7.12.8.1 The erf functions  */
extern double __cdecl erf (double);
extern float __cdecl erff (float);
extern long double __cdecl erfl (long double);

/* 7.12.8.2 The erfc functions  */
extern double __cdecl erfc (double);
extern float __cdecl erfcf (float);
extern long double __cdecl erfcl (long double);

/* 7.12.8.3 The lgamma functions */
extern double __cdecl lgamma (double);
extern float __cdecl lgammaf (float);
extern long double __cdecl lgammal (long double);

/* 7.12.8.4 The tgamma functions */
extern double __cdecl tgamma (double);
extern float __cdecl tgammaf (float);
extern long double __cdecl tgammal (long double);

/* 7.12.9.1 Double in C89 */
extern float __cdecl ceilf (float);
extern long double __cdecl ceill (long double);

/* 7.12.9.2 Double in C89 */
extern float __cdecl floorf (float);
extern long double __cdecl floorl (long double);

/* 7.12.9.3 */
extern double __cdecl nearbyint ( double);
extern float __cdecl nearbyintf (float);
extern long double __cdecl nearbyintl (long double);

/* 7.12.9.4 */
/* round, using fpu control word settings */
extern double __cdecl rint (double);
extern float __cdecl rintf (float);
extern long double __cdecl rintl (long double);

/* 7.12.9.5 */
extern long __cdecl lrint (double);
extern long __cdecl lrintf (float);
extern long __cdecl lrintl (long double);

extern long long __cdecl llrint (double);
extern long long __cdecl llrintf (float);
extern long long __cdecl llrintl (long double);

/* Inline versions of above.
 * GCC 4.0+ can do a better fast-math job with __builtins.
 */
#ifndef __NO_INLINE__
#if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
__CRT_INLINE double __cdecl rint (double x)
{
  double retval;
  __asm__ ("frndint;": "=t" (retval) : "0" (x));
  return retval;
}

__CRT_INLINE float __cdecl rintf (float x)
{
  float retval;
  __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
  return retval;
}

__CRT_INLINE long double __cdecl rintl (long double x)
{
  long double retval;
  __asm__ ("frndint;" : "=t" (retval) : "0" (x) );
  return retval;
}

__CRT_INLINE long __cdecl lrint (double x)
{
  long retval;
  __asm__ __volatile__
    ("fistpl %0"  : "=m" (retval) : "t" (x) : "st");
  return retval;
}

__CRT_INLINE long __cdecl lrintf (float x)
{
  long retval;
  __asm__ __volatile__
    ("fistpl %0"  : "=m" (retval) : "t" (x) : "st");
  return retval;
}

__CRT_INLINE long __cdecl lrintl (long double x)
{
  long retval;
  __asm__ __volatile__
    ("fistpl %0"  : "=m" (retval) : "t" (x) : "st");
  return retval;
}

__CRT_INLINE long long __cdecl llrint (double x)
{
  long long retval;
  __asm__ __volatile__
    ("fistpll %0"  : "=m" (retval) : "t" (x) : "st");
  return retval;
}

__CRT_INLINE long long __cdecl llrintf (float x)
{
  long long retval;
  __asm__ __volatile__
    ("fistpll %0"  : "=m" (retval) : "t" (x) : "st");
  return retval;
}

__CRT_INLINE long long __cdecl llrintl (long double x)
{
  long long retval;
  __asm__ __volatile__
    ("fistpll %0"  : "=m" (retval) : "t" (x) : "st");
  return retval;
}
#endif	/* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4,0) */
#endif	/* !__NO_INLINE__ */

/* 7.12.9.6 */
/* round away from zero, regardless of fpu control word settings */
extern double __cdecl round (double);
extern float __cdecl roundf (float);
extern long double __cdecl roundl (long double);

/* 7.12.9.7  */
extern long __cdecl lround (double);
extern long __cdecl lroundf (float);
extern long __cdecl lroundl (long double);

extern long long __cdecl llround (double);
extern long long __cdecl llroundf (float);
extern long long __cdecl llroundl (long double);

/* 7.12.9.8 */
/* round towards zero, regardless of fpu control word settings */
extern double __cdecl trunc (double);
extern float __cdecl truncf (float);
extern long double __cdecl truncl (long double);

/* 7.12.10.1 Double in C89 */
extern float __cdecl fmodf (float, float);
extern long double __cdecl fmodl (long double, long double);

/* 7.12.10.2 */
extern double __cdecl remainder (double, double);
extern float __cdecl remainderf (float, float);
extern long double __cdecl remainderl (long double, long double);

/* 7.12.10.3 */
extern double __cdecl remquo(double, double, int *);
extern float __cdecl remquof(float, float, int *);
extern long double __cdecl remquol(long double, long double, int *);

/* 7.12.11.1 */
extern double __cdecl copysign (double, double); /* in libmoldname.a */
extern float __cdecl copysignf (float, float);
extern long double __cdecl copysignl (long double, long double);

/* 7.12.11.2 Return a NaN */
extern double __cdecl nan(const char *tagp);
extern float __cdecl nanf(const char *tagp);
extern long double __cdecl nanl(const char *tagp);

#ifndef __STRICT_ANSI__
#define _nan()   nan("")
#define _nanf()  nanf("")
#define _nanl()  nanl("")
#endif

/* 7.12.11.3 */
extern double __cdecl nextafter (double, double); /* in libmoldname.a */
extern float __cdecl nextafterf (float, float);
extern long double __cdecl nextafterl (long double, long double);

/* 7.12.11.4 The nexttoward functions */
extern double __cdecl nexttoward (double,  long double);
extern float __cdecl nexttowardf (float,  long double);
extern long double __cdecl nexttowardl (long double, long double);

/* 7.12.12.1 */
/*  x > y ? (x - y) : 0.0  */
extern double __cdecl fdim (double x, double y);
extern float __cdecl fdimf (float x, float y);
extern long double __cdecl 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 __cdecl fmax  (double, double);
extern float __cdecl fmaxf (float, float);
extern long double __cdecl fmaxl (long double, long double);

/* 7.12.12.3 */
extern double __cdecl fmin (double, double);
extern float __cdecl fminf (float, float);
extern long double __cdecl fminl (long double, long double);

/* 7.12.13.1 */
/* return x * y + z as a ternary op */
extern double __cdecl fma (double, double, double);
extern float __cdecl fmaf (float, float, float);
extern long double __cdecl 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	/* __GNUC__ < 3 */
/*  helper  */
extern int  __cdecl __fp_unordered_compare (long double, long double);
#ifndef __NO_INLINE__
__CRT_INLINE int  __cdecl
__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;
}
#endif	/* !__NO_INLINE__ */

#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	/* __GNUC__ < 3 */
#endif	/* __cplusplus || _ISOC99_SOURCE */

_END_C_DECLS

#endif	/* ! RC_INVOKED */
#endif	/* !_MATH_H: $RCSfile: math.h,v $: end of file */
