10c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_PYMATH_H 20c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_PYMATH_H 30c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 40c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#include "pyconfig.h" /* include for defines */ 50c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 60c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/************************************************************************** 70c5958b1636c47ed7c284f859c8e805fd06a0e6Bill YiSymbols and macros to supply platform-independent interfaces to mathematical 80c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yifunctions and constants 90c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi**************************************************************************/ 100c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 110c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* Python provides implementations for copysign, round and hypot in 120c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Python/pymath.c just in case your math library doesn't provide the 130c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * functions. 140c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * 150c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi *Note: PC/pyconfig.h defines copysign as _copysign 160c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 170c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef HAVE_COPYSIGN 180c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double copysign(double, double); 190c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 200c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 210c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef HAVE_ROUND 220c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double round(double); 230c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 240c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 250c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef HAVE_HYPOT 260c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double hypot(double, double); 270c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 280c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 290c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* extra declarations */ 300c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef _MSC_VER 310c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef __STDC__ 320c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double fmod (double, double); 330c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double frexp (double, int *); 340c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double ldexp (double, int); 350c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double modf (double, double *); 360c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double pow(double, double); 370c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif /* __STDC__ */ 380c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif /* _MSC_VER */ 390c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 400c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifdef _OSF_SOURCE 410c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* OSF1 5.1 doesn't make these available with XOPEN_SOURCE_EXTENDED defined */ 420c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern int finite(double); 430c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yiextern double copysign(double, double); 440c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 450c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 460c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* High precision defintion of pi and e (Euler) 470c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * The values are taken from libc6's math.h. 480c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 490c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_MATH_PIl 500c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_MATH_PIl 3.1415926535897932384626433832795029L 510c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 520c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_MATH_PI 530c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_MATH_PI 3.14159265358979323846 540c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 550c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 560c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_MATH_El 570c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_MATH_El 2.7182818284590452353602874713526625L 580c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 590c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 600c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_MATH_E 610c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_MATH_E 2.7182818284590452354 620c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 630c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 640c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* On x86, Py_FORCE_DOUBLE forces a floating-point number out of an x87 FPU 650c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi register and into a 64-bit memory location, rounding from extended 660c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi precision to double precision in the process. On other platforms it does 670c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi nothing. */ 680c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 690c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* we take double rounding as evidence of x87 usage */ 700c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_FORCE_DOUBLE 710c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# ifdef X87_DOUBLE_ROUNDING 720c5958b1636c47ed7c284f859c8e805fd06a0e6Bill YiPyAPI_FUNC(double) _Py_force_double(double); 730c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# define Py_FORCE_DOUBLE(X) (_Py_force_double(X)) 740c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# else 750c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# define Py_FORCE_DOUBLE(X) (X) 760c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# endif 770c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 780c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 790c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifdef HAVE_GCC_ASM_FOR_X87 800c5958b1636c47ed7c284f859c8e805fd06a0e6Bill YiPyAPI_FUNC(unsigned short) _Py_get_387controlword(void); 810c5958b1636c47ed7c284f859c8e805fd06a0e6Bill YiPyAPI_FUNC(void) _Py_set_387controlword(unsigned short); 820c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 830c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 840c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* Py_IS_NAN(X) 850c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Return 1 if float or double arg is a NaN, else 0. 860c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Caution: 870c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * X is evaluated more than once. 880c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * This may not work on all platforms. Each platform has *some* 890c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * way to spell this, though -- override in pyconfig.h if you have 900c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * a platform where it doesn't work. 910c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Note: PC/pyconfig.h defines Py_IS_NAN as _isnan 920c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 930c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_IS_NAN 940c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#if defined HAVE_DECL_ISNAN && HAVE_DECL_ISNAN == 1 950c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_IS_NAN(X) isnan(X) 960c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#else 970c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_IS_NAN(X) ((X) != (X)) 980c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 990c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1000c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 1010c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* Py_IS_INFINITY(X) 1020c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Return 1 if float or double arg is an infinity, else 0. 1030c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Caution: 1040c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * X is evaluated more than once. 1050c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * This implementation may set the underflow flag if |X| is very small; 1060c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * it really can't be implemented correctly (& easily) before C99. 1070c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Override in pyconfig.h if you have a better spelling on your platform. 1080c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Py_FORCE_DOUBLE is used to avoid getting false negatives from a 1090c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * non-infinite value v sitting in an 80-bit x87 register such that 1100c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * v becomes infinite when spilled from the register to 64-bit memory. 1110c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Note: PC/pyconfig.h defines Py_IS_INFINITY as _isinf 1120c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * FIXME: PC/pyconfig.h defines Py_IS_INFINITY as (!_finite(X) && !_isnan(X)) 1130c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * so that above note isn't correct !!! 1140c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 1150c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_IS_INFINITY 1160c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# if defined HAVE_DECL_ISINF && HAVE_DECL_ISINF == 1 1170c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# define Py_IS_INFINITY(X) isinf(X) 1180c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# else 1190c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# define Py_IS_INFINITY(X) ((X) && \ 1200c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi (Py_FORCE_DOUBLE(X)*0.5 == Py_FORCE_DOUBLE(X))) 1210c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi# endif 1220c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1230c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 1240c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* Py_IS_FINITE(X) 1250c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Return 1 if float or double arg is neither infinite nor NAN, else 0. 1260c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Some compilers (e.g. VisualStudio) have intrisics for this, so a special 1270c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * macro for this particular test is useful 1280c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Note: PC/pyconfig.h defines Py_IS_FINITE as _finite 1290c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 1300c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_IS_FINITE 1310c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#if defined HAVE_DECL_ISFINITE && HAVE_DECL_ISFINITE == 1 1320c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_IS_FINITE(X) isfinite(X) 1330c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#elif defined HAVE_FINITE 1340c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_IS_FINITE(X) finite(X) 1350c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#else 1360c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_IS_FINITE(X) (!Py_IS_INFINITY(X) && !Py_IS_NAN(X)) 1370c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1380c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1390c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 1400c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* HUGE_VAL is supposed to expand to a positive double infinity. Python 1410c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * uses Py_HUGE_VAL instead because some platforms are broken in this 1420c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * respect. We used to embed code in pyport.h to try to worm around that, 1430c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * but different platforms are broken in conflicting ways. If you're on 1440c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * a platform where HUGE_VAL is defined incorrectly, fiddle your Python 1450c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * config to #define Py_HUGE_VAL to something that works on your platform. 1460c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 1470c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#ifndef Py_HUGE_VAL 1480c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_HUGE_VAL HUGE_VAL 1490c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1500c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 1510c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* Py_NAN 1520c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * A value that evaluates to a NaN. On IEEE 754 platforms INF*0 or 1530c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * INF/INF works. Define Py_NO_NAN in pyconfig.h if your platform 1540c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * doesn't support NaNs. 1550c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 1560c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#if !defined(Py_NAN) && !defined(Py_NO_NAN) 1570c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_NAN (Py_HUGE_VAL * 0.) 1580c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1590c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 1600c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi/* Py_OVERFLOWED(X) 1610c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Return 1 iff a libm function overflowed. Set errno to 0 before calling 1620c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * a libm function, and invoke this macro after, passing the function 1630c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * result. 1640c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Caution: 1650c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * This isn't reliable. C99 no longer requires libm to set errno under 1660c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * any exceptional condition, but does require +- HUGE_VAL return 1670c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * values on overflow. A 754 box *probably* maps HUGE_VAL to a 1680c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * double infinity, and we're cool if that's so, unless the input 1690c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * was an infinity and an infinity is the expected result. A C89 1700c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * system sets errno to ERANGE, so we check for that too. We're 1710c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * out of luck if a C99 754 box doesn't map HUGE_VAL to +Inf, or 1720c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * if the returned result is a NaN, or if a C89 box returns HUGE_VAL 1730c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * in non-overflow cases. 1740c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * X is evaluated more than once. 1750c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * Some platforms have better way to spell this, so expect some #ifdef'ery. 1760c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * 1770c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * OpenBSD uses 'isinf()' because a compiler bug on that platform causes 1780c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * the longer macro version to be mis-compiled. This isn't optimal, and 1790c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * should be removed once a newer compiler is available on that platform. 1800c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * The system that had the failure was running OpenBSD 3.2 on Intel, with 1810c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * gcc 2.95.3. 1820c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * 1830c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * According to Tim's checkin, the FreeBSD systems use isinf() to work 1840c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi * around a FPE bug on that platform. 1850c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi */ 1860c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#if defined(__FreeBSD__) || defined(__OpenBSD__) 1870c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_OVERFLOWED(X) isinf(X) 1880c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#else 1890c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#define Py_OVERFLOWED(X) ((X) != 0.0 && (errno == ERANGE || \ 1900c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi (X) == Py_HUGE_VAL || \ 1910c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi (X) == -Py_HUGE_VAL)) 1920c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif 1930c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi 1940c5958b1636c47ed7c284f859c8e805fd06a0e6Bill Yi#endif /* Py_PYMATH_H */ 195