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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)) #endif /* Py_PYMATH_H */