/*  math.h

    Definitions for the math floating point package.

*/

/*
 *      C/C++ Run Time Library - Version 24.0
 *
 *      Copyright (c) 1987, 2016 by Embarcadero Technologies, Inc.
 *      All Rights Reserved.
 *
 */

/* $Revision: 35726 $ */

#ifndef  __MATH_H
#define  __MATH_H

#if defined(__cplusplus)
#if defined(__clang__) && !defined(__clang_analyzer__) && defined(__USING_CNAME__)
#include <xtgmath.h>
#endif
#endif /* defined(__cplusplus) */

#include <_stddef.h>

#if !defined(RC_INVOKED)

#if defined(__STDC__)
#pragma warn -nak
#endif

#pragma pack(push, 1)

#endif  /* !RC_INVOKED */


#if !defined(__STDC__) /* NON-ANSI */

#ifdef __cplusplus
  extern "C" {
#endif

#if !defined(__clang__)
/* Intrinsic functions listed before any namespace */

double      _RTLENTRY __sin__ (double __x);
double      _RTLENTRY __cos__ (double __x);
long double _RTLENTRY __cosl__(long double __x);
long double _RTLENTRY __sinl__(long double __x);
int         _RTLENTRY __abs__ (int);
#endif

/* matherr and struct _exception must not be availible in __STDC__ nor
   can they be in namespace std since user's won't be able to override them
   there.
*/

#ifndef __STDC__
/* In "C" mode, (but not in standard C mode) we can allow the old name of
   'exception' for this structure.
 */
#ifndef __cplusplus
#define _exception exception
#endif
#endif /* __STDC__ */



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

struct  _exceptionl
{
    int type;
    char   _FAR *name;
    long double  arg1, arg2, retval;
};

typedef enum
{
    DOMAIN = 1,    /* argument domain error -- log (-1)        */
    SING,          /* argument singularity  -- pow (0,-2))     */
    OVERFLOW,      /* overflow range error  -- exp (1000)      */
    UNDERFLOW,     /* underflow range error -- exp (-1000)     */
    TLOSS,         /* total loss of significance -- sin(10e70) */
    PLOSS,         /* partial loss of signif. -- not used      */
    STACKFAULT     /* floating point unit stack overflow       */
}   _mexcep;

int         _RTLENTRY          _matherr(struct _exception  *__e);
int         _RTLENTRY          _matherrl(struct _exceptionl *__e);

#ifdef __cplusplus
}  // extern "C"
#endif

#ifdef __cplusplus
    /* use class complex instead of _cabs in C++ (now in STL 2.0) */
#else
struct complex      /* as used by "_cabs" function */
{
    double  x, y;
};

struct _complexl    /* as used by "_cabsl" function */
{
    long double  x, y;
};

#define cabs(z)     (hypot  ((z).x, (z).y))
#define cabsl(z)    (hypotl ((z).x, (z).y))
#endif /* __cplusplus */
#endif /* NON-ANSI */

#ifdef __cplusplus
  namespace std {
#endif


/* Constants rounded for 21 decimals. */
#define M_E         2.71828182845904523536
#define M_LOG2E     1.44269504088896340736
#define M_LOG10E    0.434294481903251827651
#define M_LN2       0.693147180559945309417
#define M_LN10      2.30258509299404568402
#define M_PI        3.14159265358979323846
#define M_PI_2      1.57079632679489661923
#define M_PI_4      0.785398163397448309616
#define M_1_PI      0.318309886183790671538
#define M_2_PI      0.636619772367581343076
#define M_1_SQRTPI  0.564189583547756286948
#define M_2_SQRTPI  1.12837916709551257390
#define M_SQRT2     1.41421356237309504880
#define M_SQRT_2    0.707106781186547524401

#define EDOM    33      /* Math argument */
#define ERANGE  34      /* Result too large */


#ifdef __cplusplus
extern "C" {
#endif

extern double _RTLENTRY _EXPDATA _huge_dble;
extern long double _RTLENTRY _EXPDATA _huge_ldble;

#if defined(__cplusplus) && defined(__USING_CNAME__)
#define HUGE_VAL    std::_huge_dble
#define _LHUGE_VAL   std::_huge_ldble
#else
#define HUGE_VAL    _huge_dble
#define _LHUGE_VAL   _huge_ldble
#endif

float       _RTLENTRY _EXPFUNC atan2f(float, float);
float       _RTLENTRY _EXPFUNC ceilf(float);
float       _RTLENTRY _EXPFUNC cosf(float);
float       _RTLENTRY _EXPFUNC expf(float);
float       _RTLENTRY _EXPFUNC floorf(float);
float       _RTLENTRY _EXPFUNC ldexpf(float, int);
float       _RTLENTRY _EXPFUNC logf(float);
float       _RTLENTRY _EXPFUNC powf(float, float);
float       _RTLENTRY _EXPFUNC sinf(float);
float       _RTLENTRY _EXPFUNC sqrtf(float);
float       _RTLENTRY _EXPFUNC tanf(float);

#if defined(__clang__)
float       _EXPFUNC acosf(float);
float       _EXPFUNC asinf(float);
float       _EXPFUNC atanf(float);
float       _EXPFUNC coshf(float);
float       _EXPFUNC fabsf(float);
float       _EXPFUNC fmodf(float, float);
float       _EXPFUNC frexpf(float, int *);
float       _EXPFUNC hypotf(float, float);
float       _EXPFUNC log10f(float);
float       _EXPFUNC modff(float, float *);
float       _EXPFUNC sinhf(float);
float       _EXPFUNC tanhf(float);

float       _EXPFUNC nanf(const char*);
double      _EXPFUNC nan(const char*);
long double _EXPFUNC nanl(const char*);

float       _EXPFUNC roundf(float);
double      _EXPFUNC round(double);
long double _EXPFUNC roundl(long double);

float       _EXPFUNC acoshf(float);
float       _EXPFUNC asinhf(float);
float       _EXPFUNC atanhf(float);
double      _EXPFUNC acosh(double);
double      _EXPFUNC asinh(double);
double      _EXPFUNC atanh(double);
long double _EXPFUNC acoshl(long double);
long double _EXPFUNC asinhl(long double);
long double _EXPFUNC atanhl(long double);

float       _RTLENTRY _EXPFUNC exp2f(float __x);
double      _RTLENTRY _EXPFUNC exp2(double __x);
long double _RTLENTRY _EXPFUNC exp2l(long double __x);

float       _RTLENTRY _EXPFUNC expm1f  (float __x);
double      _RTLENTRY _EXPFUNC expm1   (double __x);
long double _RTLENTRY _EXPFUNC expm1l  (long double __x);

float       _RTLENTRY _EXPFUNC log2f(float);
double      _RTLENTRY _EXPFUNC log2(double);
long double _RTLENTRY _EXPFUNC log2l(long double);

float       _RTLENTRY _EXPFUNC log1pf(float);
double      _RTLENTRY _EXPFUNC log1p(double);
long double _RTLENTRY _EXPFUNC log1pl(long double);

float       _RTLENTRY _EXPFUNC copysignf(float, float);
double      _RTLENTRY _EXPFUNC copysign(double, double);
long double _RTLENTRY _EXPFUNC copysignl(long double, long double);


#endif  /* __clang__ */

double      _RTLENTRY _EXPFUNC acos    (double __x);
double      _RTLENTRY _EXPFUNC asin    (double __x);
double      _RTLENTRY _EXPFUNC atan    (double __x);
double      _RTLENTRY _EXPFUNC atan2   (double __y, double __x);
double      _RTLENTRY _EXPFUNC ceil    (double __x);
double      _RTLENTRY _EXPFUNC cos     (double __x);
double      _RTLENTRY _EXPFUNC cosh    (double __x);
double      _RTLENTRY _EXPFUNC exp     (double __x);
double      _RTLENTRY _EXPFUNC fabs    (double __x);
double      _RTLENTRY _EXPFUNC floor   (double __x);
double      _RTLENTRY _EXPFUNC fmod    (double __x, double __y);
double      _RTLENTRY _EXPFUNC frexp   (double __x, int * __exponent);
double      _RTLENTRY _EXPFUNC hypot   (double __x, double __y);
double      _RTLENTRY _EXPFUNC ldexp   (double __x, int __exponent);
double      _RTLENTRY _EXPFUNC log     (double __x);
double      _RTLENTRY _EXPFUNC log10   (double __x);
double      _RTLENTRY _EXPFUNC modf    (double __x, double * __ipart);
double      _RTLENTRY _EXPFUNC pow     (double __x, double __y);
double      _RTLENTRY _EXPFUNC sin     (double __x);
double      _RTLENTRY _EXPFUNC sinh    (double __x);
double      _RTLENTRY _EXPFUNC sqrt    (double __x);
double      _RTLENTRY _EXPFUNC tan     (double __x);
double      _RTLENTRY _EXPFUNC tanh    (double __x);

long double _RTLENTRY _EXPFUNC acosl  (long double __x);
long double _RTLENTRY _EXPFUNC asinl  (long double __x);
long double _RTLENTRY _EXPFUNC atan2l (long double __x, long double __y);
long double _RTLENTRY _EXPFUNC atanl  (long double __x);
long double _RTLENTRY _EXPFUNC ceill  (long double __x);
long double _RTLENTRY _EXPFUNC coshl  (long double __x);
long double _RTLENTRY _EXPFUNC cosl   (long double __x);
long double _RTLENTRY _EXPFUNC expl   (long double __x);
long double _RTLENTRY _EXPFUNC fabsl  (long double __x);
long double _RTLENTRY _EXPFUNC floorl (long double __x);
long double _RTLENTRY _EXPFUNC fmodl  (long double __x, long double __y);
long double _RTLENTRY _EXPFUNC frexpl (long double __x, int * __exponent);
long double _RTLENTRY _EXPFUNC hypotl (long double __x, long double __y);
long double _RTLENTRY _EXPFUNC ldexpl (long double __x, int __exponent);
long double _RTLENTRY _EXPFUNC log10l (long double __x);
long double _RTLENTRY _EXPFUNC logl   (long double __x);
long double _RTLENTRY _EXPFUNC modfl  (long double __x, long double * __ipart);
long double _RTLENTRY _EXPFUNC powl   (long double __x, long double __y);
long double _RTLENTRY _EXPFUNC sinhl  (long double __x);
long double _RTLENTRY _EXPFUNC sinl   (long double __x);
long double _RTLENTRY _EXPFUNC sqrtl  (long double __x);
long double _RTLENTRY _EXPFUNC tanhl  (long double __x);
long double _RTLENTRY _EXPFUNC tanl   (long double __x);

double      _RTLENTRY _EXPFUNC atof    (const char * __s);

#if !defined(__STDC__) /* NON_ANSI */

#if !defined(__clang__)
#if !defined(__ABS_DEFINED)
#define __ABS_DEFINED
#ifdef __cplusplus
inline int _RTLENTRY  abs(int __x) { return __abs__(__x); }
#else
int         _RTLENTRY _EXPFUNC abs(int __x);
#  define abs(x)   __abs__(x)
#endif /* __cplusplus */
#endif /* __ABS_DEFINED */
#else /* __clang__ */
int         _RTLENTRY _EXPFUNC abs(int __x);
#endif /* __clang__ */

long        _RTLENTRY _EXPFUNC labs    (long __x);
double      _RTLENTRY _EXPFUNC pow10   (int __p);

long double _RTLENTRY _EXPFUNC _atold  (const char * __s);


double      _RTLENTRY _EXPFUNC poly    (double __x, int __degree, double __coeffs []);
long double _RTLENTRY _EXPFUNC polyl   (long double __x, int __degree, long double __coeffs []);
long double _RTLENTRY _EXPFUNC pow10l  (int __p);

#if defined (_INTEGRAL_MAX_BITS) && (_INTEGRAL_MAX_BITS >= 64)
__int64     _RTLENTRY _EXPFUNC   _atoi64(const char * __s);
char *      _RTLENTRY   _EXPFUNC _i64toa(__int64 __value, char *__strP, int __radix);
char *      _RTLENTRY   _EXPFUNC _ui64toa(unsigned __int64 __value, char *__strP, int __radix);
__int64     _RTLENTRY _EXPFUNC   _wtoi64(const wchar_t * __s);
wchar_t *   _RTLENTRY   _EXPFUNC _i64tow(__int64 __value, wchar_t *__strP, int __radix);
wchar_t *   _RTLENTRY   _EXPFUNC _ui64tow(unsigned __int64 __value, wchar_t *__strP, int __radix);
#endif
double      _RTLENTRY _EXPFUNC   _wtof(const wchar_t * __s);
int         _RTLENTRY _EXPFUNC   _wtoi(const wchar_t * __s);
long        _RTLENTRY _EXPFUNC   _wtol(const wchar_t * __s);
long double _RTLENTRY _EXPFUNC   _wtold(const wchar_t * __s);

#endif  /* !__STDC__ */

/* Add overloaded functions from 26.5 here */
#if defined(__cplusplus)

extern "C++" {

#if defined(_WIN64)
inline float abs (float __x) { return fabsf(__x); }
inline float acos (float __x) { return acosf(__x); }
inline float acosh (float __x) { return acoshf(__x); }
inline float asin (float __x) { return asinf(__x); }
inline float asinh (float __x) { return asinhf(__x); }
inline float atan (float __x) { return atanf(__x); }
inline float atan2(float __x, float __y) { return atan2f(__x, __y); }
inline float atanh (float __x) { return atanhf(__x); }
inline float ceil (float __x) { return ceilf(__x); }
inline float cos (float __x) { return cosf(__x); }
inline float cosh (float __x) { return coshf(__x); }
inline float exp (float __x) { return expf(__x); }
inline float fabs (float __x) { return fabsf(__x); }
inline float floor(float __x) { return floorf(__x); }
inline float fmod (float __x, float __y) { return fmodf(__x, __y); }
inline float frexp(float __x, int *__y) { return frexpf(__x,__y); }
inline float hypot(float __x, float __y) { return hypotf(__x,__y); }
inline float ldexp(float __x, int __y) { return ldexpf(__x,__y); }
inline float log (float __x) { return logf(__x); }
inline float log10(float __x) { return log10f(__x); }
inline float modf (float __x, float *__y) { return modff(__x, __y); }
inline float pow (float __x, float __y) { return powf(__x,__y); }
inline float sin (float __x) { return sinf(__x); }
inline float sinh (float __x) { return sinhf(__x); }
inline float sqrt (float __x) { return sqrtf(__x); }
inline float tan (float __x) { return tanf(__x); }
inline float tanh (float __x) { return tanhf(__x); }

inline double abs(double __x) { return fabs(__x); }

inline long double abs (long double __x) { return fabsl(__x); }
inline long double acos (long double __x) { return acosl(__x); }
inline long double acosh (long double __x) { return acoshl(__x); }
inline long double asin (long double __x) { return asinl(__x); }
inline long double asinh (long double __x) { return asinhl(__x); }
inline long double atan (long double __x) { return atanl(__x); }
inline long double atan2(long double __x, long double __y) { return atan2l(__x,__y); }
inline long double atanh (long double __x) { return atanhl(__x); }
inline long double ceil (long double __x) { return ceill(__x); }
inline long double cos (long double __x) { return cosl(__x); }
inline long double cosh (long double __x) { return coshl(__x); }
inline long double exp (long double __x) { return expl(__x); }
inline long double fabs (long double __x) { return fabsl(__x); }
inline long double floor(long double __x) { return floorl(__x); }
inline long double fmod (long double __x, long double __y) { return fmodl(__x,__y); }
inline long double frexp(long double __x, int *__y) { return frexpl(__x,__y); }
inline long double hypot(long double __x, long double __y) { return hypotl(__x,__y); }
inline long double ldexp(long double __x, int __y) { return ldexpl(__x,__y); }
inline long double log (long double __x) { return logl(__x); }
inline long double log10(long double __x) { return log10l(__x); }
inline long double modf (long double __x, long double *__y) { return modfl(__x,__y); }
inline long double pow (long double __x, long double __y) { return powl(__x,__y); }
inline long double sin (long double __x) { return sinl(__x); }
inline long double sinh (long double __x) { return sinhl(__x); }
inline long double sqrt (long double __x) { return sqrtl(__x); }
inline long double tan (long double __x) { return tanl(__x); }
inline long double tanh (long double __x) { return tanhl(__x); }
#else
inline float abs (float __x) { return (float)fabs((double)__x); }
inline float acos (float __x) { return (float)acos((double)__x); }
inline float asin (float __x) { return (float)asin((double)__x); }
inline float atan (float __x) { return (float)atan((double)__x); }
inline float atan2(float __x, float __y) { return (float)atan2((double)__x,(double)__y); }
inline float ceil (float __x) { return (float)ceil((double)__x); }
inline float cos (float __x) { return (float)cos((double)__x); }
inline float cosh (float __x) { return (float)cosh((double)__x); }
inline float exp (float __x) { return (float)exp((double)__x); }
inline float fabs (float __x) { return (float)fabs((double)__x); }
inline float floor(float __x) { return (float)floor((double)__x); }
inline float fmod (float __x, float __y) { return (float)fmod((double) __x,(double) __y); }
inline float frexp(float __x, int *__y) { return (float)frexp((double)__x,__y); }
inline float hypot(float __x, float __y) { return (float)hypot((double) __x,(double) __y); }
inline float ldexp(float __x, int __y) { return (float)ldexp((double)__x,__y); }
inline float log (float __x) { return (float)log((double)__x); }
inline float log10(float __x) { return (float)log10((double)__x); }
inline float pow (float __x, float __y) { return (float)pow((double)__x,(double)__y); }
inline float pow (float __x, int __y) { return (float)pow((double)__x,(double)__y); }
inline float sin (float __x) { return (float)sin((double)__x); }
inline float sinh (float __x) { return (float)sinh((double)__x); }
inline float sqrt (float __x) { return (float)sqrt((double)__x); }
inline float tan (float __x) { return (float)tan((double)__x); }
inline float tanh (float __x) { return (float)tanh((double)__x); }

inline float modf (float __x, float *__y) 
{ 
  double __d;
  float __f = (float)modf((double)__x, &__d); 
  *__y = (float) __d;
  return __f;
}

inline double abs(double __x) { return fabs(__x); }
inline double pow(double __x, int __y) { return pow(__x,(double)__y); }

inline long double abs (long double __x) { return fabsl(__x); }
inline long double acos (long double __x) { return acosl(__x); }
inline long double asin (long double __x) { return asinl(__x); }
inline long double atan (long double __x) { return atanl(__x); }
inline long double atan2(long double __x, long double __y) { return atan2l(__x,__y); }
inline long double ceil (long double __x) { return ceill(__x); }
inline long double cos (long double __x) { return cosl(__x); }
inline long double cosh (long double __x) { return coshl(__x); }
inline long double exp (long double __x) { return expl(__x); }
inline long double fabs (long double __x) { return fabsl(__x); }
inline long double floor(long double __x) { return floorl(__x); }
inline long double fmod (long double __x, long double __y) { return fmodl(__x,__y); }
inline long double hypot(long double __x, long double __y) { return hypotl(__x,__y); }
inline long double frexp(long double __x, int *__y) { return frexpl(__x,__y); }
inline long double ldexp(long double __x, int __y) { return ldexpl(__x,__y); }
inline long double log (long double __x) { return logl(__x); }
inline long double log10(long double __x) { return log10l(__x); }
inline long double modf (long double __x, long double *__y) { return modfl(__x,__y); }
inline long double pow (long double __x, long double __y) { return powl(__x,__y); }
inline long double pow (long double __x, int __y) { return powl(__x,(double)__y); }
inline long double sin (long double __x) { return sinl(__x); }
inline long double sinh (long double __x) { return sinhl(__x); }
inline long double sqrt (long double __x) { return sqrtl(__x); }
inline long double tan (long double __x) { return tanl(__x); }
inline long double tanh (long double __x) { return tanhl(__x); }
#endif /* _WIN64 */

}

#endif /* __cplusplus */

#ifdef __cplusplus
} // extern "C"
} // std
#endif /* __cplusplus */

#if !defined(RC_INVOKED)

/* restore default packing */
#pragma pack(pop)

#if defined(__STDC__)
#pragma warn .nak
#endif

#endif  /* !RC_INVOKED */
#endif  /* __MATH_H */

#if defined(__cplusplus) && !defined(__USING_CNAME__) && !defined(__MATH_H_USING_LIST)
#define __MATH_H_USING_LIST
    using std::_huge_dble;
    using std::_huge_ldble;
    using std::acos;
    using std::asin;
    using std::atan;
    using std::atan2;
    using std::ceil;
    using std::cosh;
    using std::exp;
    using std::fabs;
    using std::floor;
    using std::fmod;
    using std::frexp;
    using std::hypot;
    using std::ldexp;
    using std::log;
    using std::log10;
    using std::modf;
    using std::pow;
    using std::sinh;
    using std::sqrt;
    using std::tan;
    using std::tanh;
    using std::acosl;
    using std::asinl;
    using std::atan2l;
    using std::atanl;
    using std::ceill;
    using std::coshl;
    using std::expl;
    using std::fabsl;
    using std::floorl;
    using std::fmodl;
    using std::frexpl;
    using std::hypotl;
    using std::ldexpl;
    using std::log10l;
    using std::logl;
    using std::modfl;
    using std::powl;
    using std::sinhl;
    using std::sqrtl;
    using std::tanhl;
    using std::tanl;
    using std::atof;

    using std::atan2f;
    using std::ceilf;
    using std::cosf;
    using std::expf;
    using std::floorf;
    using std::ldexpf;
    using std::logf;
    using std::powf;
    using std::sinf;
    using std::sqrtf;
    using std::tanf;

#if defined(_WIN64)
    using std::acosf;
    using std::asinf;
    using std::atanf;
    using std::coshf;
    using std::fabsf;
    using std::fmodf;
    using std::frexpf;
    using std::hypotf;
    using std::log10f;
    using std::modff;
    using std::sinhf;
    using std::tanhf;

    using std::nan;
    using std::nanf;
    using std::nanl;
    using std::round;
    using std::roundf;
    using std::roundl;
    using std::acoshf;
    using std::asinhf;
    using std::atanhf;
    using std::acosh;
    using std::asinh;
    using std::atanh;
    using std::acoshl;
    using std::asinhl;
    using std::atanhl;

#endif

/*
   Handle intrinsics specially.  If intrinsics are on, the compiler creates
   a macro of the normal function mapping to the __ intrinsic version, ie:
     #define strcpy __strcpy__
   Thus, we can test the normal name as a macro to see if it's defined, and
   only preform a using statement if it's not an intrinsic
*/

#   ifndef sin
      using std::sin;
#   endif // ifndef sin
#   ifndef cos
      using std::cos;
#   endif // ifndef cos
#   ifndef sinl
      using std::sinl;
#   endif // ifndef sinl
#   ifndef cosl
      using std::cosl;
#   endif // ifndef cosl

# if !defined(__STDC__) /* NON_ANSI */
#   ifndef abs
      using std::abs;
#   endif // ifndef abs

    using std::labs;
    using std::pow10;
    using std::_atold;
    using std::poly;
    using std::polyl;
    using std::pow10l;

# if defined (_INTEGRAL_MAX_BITS) && (_INTEGRAL_MAX_BITS >= 64)
    using std::_atoi64;
    using std::_i64toa;
    using std::_ui64toa;
    using std::_wtoi64;
    using std::_i64tow;
    using std::_ui64tow;
    using std::_wtof;
    using std::_wtoi;
    using std::_wtol;
    using std::_wtold;
# endif // _INTEGRAL_MAX_BITS
# endif // !__STDC__
#endif /* __USING_CNAME__ */

#if defined(_FM_USE_FASTMATH) && !defined(__FASTMATH_H)
#   include <fastmath.h>
#endif /* _FM_USE_FASTMATH */