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Filename : pymath.h
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#ifndef Py_PYMATH_H
#define Py_PYMATH_H

#include "pyconfig.h" /* include for defines */

/**************************************************************************
Symbols and macros to supply platform-independent interfaces to mathematical
functions and constants
**************************************************************************/

/* Python provides implementations for copysign, round and hypot in
 * Python/pymath.c just in case your math library doesn't provide the
 * functions.
 *
 *Note: PC/pyconfig.h defines copysign as _copysign
 */
#ifndef HAVE_COPYSIGN
extern double copysign(double, double);
#endif

#ifndef HAVE_ROUND
extern double round(double);
#endif

#ifndef HAVE_HYPOT
extern double hypot(double, double);
#endif

/* extra declarations */
#ifndef _MSC_VER
#ifndef __STDC__
extern double fmod (double, double);
extern double frexp (double, int *);
extern double ldexp (double, int);
extern double modf (double, double *);
extern double pow(double, double);
#endif /* __STDC__ */
#endif /* _MSC_VER */

/* High precision definition of pi and e (Euler)
 * The values are taken from libc6's math.h.
 */
#ifndef Py_MATH_PIl
#define Py_MATH_PIl 3.1415926535897932384626433832795029L
#endif
#ifndef Py_MATH_PI
#define Py_MATH_PI 3.14159265358979323846
#endif

#ifndef Py_MATH_El
#define Py_MATH_El 2.7182818284590452353602874713526625L
#endif

#ifndef Py_MATH_E
#define Py_MATH_E 2.7182818284590452354
#endif

/* Tau (2pi) to 40 digits, taken from tauday.com/tau-digits. */
#ifndef Py_MATH_TAU
#define Py_MATH_TAU 6.2831853071795864769252867665590057683943L
#endif


/* On x86, Py_FORCE_DOUBLE forces a floating-point number out of an x87 FPU
   register and into a 64-bit memory location, rounding from extended
   precision to double precision in the process.  On other platforms it does
   nothing. */

/* we take double rounding as evidence of x87 usage */
#ifndef Py_LIMITED_API
#ifndef Py_FORCE_DOUBLE
#  ifdef X87_DOUBLE_ROUNDING
PyAPI_FUNC(double) _Py_force_double(double);
#    define Py_FORCE_DOUBLE(X) (_Py_force_double(X))
#  else
#    define Py_FORCE_DOUBLE(X) (X)
#  endif
#endif
#endif

#ifndef Py_LIMITED_API
#ifdef HAVE_GCC_ASM_FOR_X87
PyAPI_FUNC(unsigned short) _Py_get_387controlword(void);
PyAPI_FUNC(void) _Py_set_387controlword(unsigned short);
#endif
#endif

/* Py_IS_NAN(X)
 * Return 1 if float or double arg is a NaN, else 0.
 * Caution:
 *     X is evaluated more than once.
 *     This may not work on all platforms.  Each platform has *some*
 *     way to spell this, though -- override in pyconfig.h if you have
 *     a platform where it doesn't work.
 * Note: PC/pyconfig.h defines Py_IS_NAN as _isnan
 */
#ifndef Py_IS_NAN
#if defined HAVE_DECL_ISNAN && HAVE_DECL_ISNAN == 1
#define Py_IS_NAN(X) isnan(X)
#else
#define Py_IS_NAN(X) ((X) != (X))
#endif
#endif

/* Py_IS_INFINITY(X)
 * Return 1 if float or double arg is an infinity, else 0.
 * Caution:
 *    X is evaluated more than once.
 *    This implementation may set the underflow flag if |X| is very small;
 *    it really can't be implemented correctly (& easily) before C99.
 *    Override in pyconfig.h if you have a better spelling on your platform.
 *  Py_FORCE_DOUBLE is used to avoid getting false negatives from a
 *    non-infinite value v sitting in an 80-bit x87 register such that
 *    v becomes infinite when spilled from the register to 64-bit memory.
 * Note: PC/pyconfig.h defines Py_IS_INFINITY as _isinf
 */
#ifndef Py_IS_INFINITY
#  if defined HAVE_DECL_ISINF && HAVE_DECL_ISINF == 1
#    define Py_IS_INFINITY(X) isinf(X)
#  else
#    define Py_IS_INFINITY(X) ((X) &&                                   \
                               (Py_FORCE_DOUBLE(X)*0.5 == Py_FORCE_DOUBLE(X)))
#  endif
#endif

/* Py_IS_FINITE(X)
 * Return 1 if float or double arg is neither infinite nor NAN, else 0.
 * Some compilers (e.g. VisualStudio) have intrinsics for this, so a special
 * macro for this particular test is useful
 * Note: PC/pyconfig.h defines Py_IS_FINITE as _finite
 */
#ifndef Py_IS_FINITE
#if defined HAVE_DECL_ISFINITE && HAVE_DECL_ISFINITE == 1
#define Py_IS_FINITE(X) isfinite(X)
#elif defined HAVE_FINITE
#define Py_IS_FINITE(X) finite(X)
#else
#define Py_IS_FINITE(X) (!Py_IS_INFINITY(X) && !Py_IS_NAN(X))
#endif
#endif

/* HUGE_VAL is supposed to expand to a positive double infinity.  Python
 * uses Py_HUGE_VAL instead because some platforms are broken in this
 * respect.  We used to embed code in pyport.h to try to worm around that,
 * but different platforms are broken in conflicting ways.  If you're on
 * a platform where HUGE_VAL is defined incorrectly, fiddle your Python
 * config to #define Py_HUGE_VAL to something that works on your platform.
 */
#ifndef Py_HUGE_VAL
#define Py_HUGE_VAL HUGE_VAL
#endif

/* Py_NAN
 * A value that evaluates to a NaN. On IEEE 754 platforms INF*0 or
 * INF/INF works. Define Py_NO_NAN in pyconfig.h if your platform
 * doesn't support NaNs.
 */
#if !defined(Py_NAN) && !defined(Py_NO_NAN)
#if !defined(__INTEL_COMPILER)
    #define Py_NAN (Py_HUGE_VAL * 0.)
#else /* __INTEL_COMPILER */
    #if defined(ICC_NAN_STRICT)
        #pragma float_control(push)
        #pragma float_control(precise, on)
        #pragma float_control(except,  on)
        #if defined(_MSC_VER)
            __declspec(noinline)
        #else /* Linux */
            __attribute__((noinline))
        #endif /* _MSC_VER */
        static double __icc_nan()
        {
            return sqrt(-1.0);
        }
        #pragma float_control (pop)
        #define Py_NAN __icc_nan()
    #else /* ICC_NAN_RELAXED as default for Intel Compiler */
        static const union { unsigned char buf[8]; double __icc_nan; } __nan_store = {0,0,0,0,0,0,0xf8,0x7f};
        #define Py_NAN (__nan_store.__icc_nan)
    #endif /* ICC_NAN_STRICT */
#endif /* __INTEL_COMPILER */
#endif

/* Py_OVERFLOWED(X)
 * Return 1 iff a libm function overflowed.  Set errno to 0 before calling
 * a libm function, and invoke this macro after, passing the function
 * result.
 * Caution:
 *    This isn't reliable.  C99 no longer requires libm to set errno under
 *        any exceptional condition, but does require +- HUGE_VAL return
 *        values on overflow.  A 754 box *probably* maps HUGE_VAL to a
 *        double infinity, and we're cool if that's so, unless the input
 *        was an infinity and an infinity is the expected result.  A C89
 *        system sets errno to ERANGE, so we check for that too.  We're
 *        out of luck if a C99 754 box doesn't map HUGE_VAL to +Inf, or
 *        if the returned result is a NaN, or if a C89 box returns HUGE_VAL
 *        in non-overflow cases.
 *    X is evaluated more than once.
 * Some platforms have better way to spell this, so expect some #ifdef'ery.
 *
 * OpenBSD uses 'isinf()' because a compiler bug on that platform causes
 * the longer macro version to be mis-compiled. This isn't optimal, and
 * should be removed once a newer compiler is available on that platform.
 * The system that had the failure was running OpenBSD 3.2 on Intel, with
 * gcc 2.95.3.
 *
 * According to Tim's checkin, the FreeBSD systems use isinf() to work
 * around a FPE bug on that platform.
 */
#if defined(__FreeBSD__) || defined(__OpenBSD__)
#define Py_OVERFLOWED(X) isinf(X)
#else
#define Py_OVERFLOWED(X) ((X) != 0.0 && (errno == ERANGE ||    \
                                         (X) == Py_HUGE_VAL || \
                                         (X) == -Py_HUGE_VAL))
#endif

/* Return whether integral type *type* is signed or not. */
#define _Py_IntegralTypeSigned(type) ((type)(-1) < 0)
/* Return the maximum value of integral type *type*. */
#define _Py_IntegralTypeMax(type) ((_Py_IntegralTypeSigned(type)) ? (((((type)1 << (sizeof(type)*CHAR_BIT - 2)) - 1) << 1) + 1) : ~(type)0)
/* Return the minimum value of integral type *type*. */
#define _Py_IntegralTypeMin(type) ((_Py_IntegralTypeSigned(type)) ? -_Py_IntegralTypeMax(type) - 1 : 0)
/* Check whether *v* is in the range of integral type *type*. This is most
 * useful if *v* is floating-point, since demoting a floating-point *v* to an
 * integral type that cannot represent *v*'s integral part is undefined
 * behavior. */
#define _Py_InIntegralTypeRange(type, v) (_Py_IntegralTypeMin(type) <= v && v <= _Py_IntegralTypeMax(type))

/* Return the smallest integer k such that n < 2**k, or 0 if n == 0.
 * Equivalent to floor(log2(x))+1.  Also equivalent to: bitwidth_of_type -
 * count_leading_zero_bits(x)
 */
#ifndef Py_LIMITED_API
PyAPI_FUNC(unsigned int) _Py_bit_length(unsigned long d);
#endif

#endif /* Py_PYMATH_H */