1 #ifndef Py_PYMATH_H 2 #define Py_PYMATH_H 3 4 #include "pyconfig.h" /* include for defines */ 5 6 /************************************************************************** 7 Symbols and macros to supply platform-independent interfaces to mathematical 8 functions and constants 9 **************************************************************************/ 10 11 /* Python provides implementations for copysign, round and hypot in 12 * Python/pymath.c just in case your math library doesn't provide the 13 * functions. 14 * 15 *Note: PC/pyconfig.h defines copysign as _copysign 16 */ 17 #ifndef HAVE_COPYSIGN 18 extern double copysign(double, double); 19 #endif 20 21 #ifndef HAVE_ROUND 22 extern double round(double); 23 #endif 24 25 #ifndef HAVE_HYPOT 26 extern double hypot(double, double); 27 #endif 28 29 /* extra declarations */ 30 #ifndef _MSC_VER 31 #ifndef __STDC__ 32 extern double fmod (double, double); 33 extern double frexp (double, int *); 34 extern double ldexp (double, int); 35 extern double modf (double, double *); 36 extern double pow(double, double); 37 #endif /* __STDC__ */ 38 #endif /* _MSC_VER */ 39 40 /* High precision definition of pi and e (Euler) 41 * The values are taken from libc6's math.h. 42 */ 43 #ifndef Py_MATH_PIl 44 #define Py_MATH_PIl 3.1415926535897932384626433832795029L 45 #endif 46 #ifndef Py_MATH_PI 47 #define Py_MATH_PI 3.14159265358979323846 48 #endif 49 50 #ifndef Py_MATH_El 51 #define Py_MATH_El 2.7182818284590452353602874713526625L 52 #endif 53 54 #ifndef Py_MATH_E 55 #define Py_MATH_E 2.7182818284590452354 56 #endif 57 58 /* Tau (2pi) to 40 digits, taken from tauday.com/tau-digits. */ 59 #ifndef Py_MATH_TAU 60 #define Py_MATH_TAU 6.2831853071795864769252867665590057683943L 61 #endif 62 63 64 /* On x86, Py_FORCE_DOUBLE forces a floating-point number out of an x87 FPU 65 register and into a 64-bit memory location, rounding from extended 66 precision to double precision in the process. On other platforms it does 67 nothing. */ 68 69 /* we take double rounding as evidence of x87 usage */ 70 #ifndef Py_LIMITED_API 71 #ifndef Py_FORCE_DOUBLE 72 # ifdef X87_DOUBLE_ROUNDING 73 PyAPI_FUNC(double) _Py_force_double(double); 74 # define Py_FORCE_DOUBLE(X) (_Py_force_double(X)) 75 # else 76 # define Py_FORCE_DOUBLE(X) (X) 77 # endif 78 #endif 79 #endif 80 81 #ifndef Py_LIMITED_API 82 #ifdef HAVE_GCC_ASM_FOR_X87 83 PyAPI_FUNC(unsigned short) _Py_get_387controlword(void); 84 PyAPI_FUNC(void) _Py_set_387controlword(unsigned short); 85 #endif 86 #endif 87 88 /* Py_IS_NAN(X) 89 * Return 1 if float or double arg is a NaN, else 0. 90 * Caution: 91 * X is evaluated more than once. 92 * This may not work on all platforms. Each platform has *some* 93 * way to spell this, though -- override in pyconfig.h if you have 94 * a platform where it doesn't work. 95 * Note: PC/pyconfig.h defines Py_IS_NAN as _isnan 96 */ 97 #ifndef Py_IS_NAN 98 #if defined HAVE_DECL_ISNAN && HAVE_DECL_ISNAN == 1 99 #define Py_IS_NAN(X) isnan(X) 100 #else 101 #define Py_IS_NAN(X) ((X) != (X)) 102 #endif 103 #endif 104 105 /* Py_IS_INFINITY(X) 106 * Return 1 if float or double arg is an infinity, else 0. 107 * Caution: 108 * X is evaluated more than once. 109 * This implementation may set the underflow flag if |X| is very small; 110 * it really can't be implemented correctly (& easily) before C99. 111 * Override in pyconfig.h if you have a better spelling on your platform. 112 * Py_FORCE_DOUBLE is used to avoid getting false negatives from a 113 * non-infinite value v sitting in an 80-bit x87 register such that 114 * v becomes infinite when spilled from the register to 64-bit memory. 115 * Note: PC/pyconfig.h defines Py_IS_INFINITY as _isinf 116 */ 117 #ifndef Py_IS_INFINITY 118 # if defined HAVE_DECL_ISINF && HAVE_DECL_ISINF == 1 119 # define Py_IS_INFINITY(X) isinf(X) 120 # else 121 # define Py_IS_INFINITY(X) ((X) && \ 122 (Py_FORCE_DOUBLE(X)*0.5 == Py_FORCE_DOUBLE(X))) 123 # endif 124 #endif 125 126 /* Py_IS_FINITE(X) 127 * Return 1 if float or double arg is neither infinite nor NAN, else 0. 128 * Some compilers (e.g. VisualStudio) have intrisics for this, so a special 129 * macro for this particular test is useful 130 * Note: PC/pyconfig.h defines Py_IS_FINITE as _finite 131 */ 132 #ifndef Py_IS_FINITE 133 #if defined HAVE_DECL_ISFINITE && HAVE_DECL_ISFINITE == 1 134 #define Py_IS_FINITE(X) isfinite(X) 135 #elif defined HAVE_FINITE 136 #define Py_IS_FINITE(X) finite(X) 137 #else 138 #define Py_IS_FINITE(X) (!Py_IS_INFINITY(X) && !Py_IS_NAN(X)) 139 #endif 140 #endif 141 142 /* HUGE_VAL is supposed to expand to a positive double infinity. Python 143 * uses Py_HUGE_VAL instead because some platforms are broken in this 144 * respect. We used to embed code in pyport.h to try to worm around that, 145 * but different platforms are broken in conflicting ways. If you're on 146 * a platform where HUGE_VAL is defined incorrectly, fiddle your Python 147 * config to #define Py_HUGE_VAL to something that works on your platform. 148 */ 149 #ifndef Py_HUGE_VAL 150 #define Py_HUGE_VAL HUGE_VAL 151 #endif 152 153 /* Py_NAN 154 * A value that evaluates to a NaN. On IEEE 754 platforms INF*0 or 155 * INF/INF works. Define Py_NO_NAN in pyconfig.h if your platform 156 * doesn't support NaNs. 157 */ 158 #if !defined(Py_NAN) && !defined(Py_NO_NAN) 159 #if !defined(__INTEL_COMPILER) 160 #define Py_NAN (Py_HUGE_VAL * 0.) 161 #else /* __INTEL_COMPILER */ 162 #if defined(ICC_NAN_STRICT) 163 #pragma float_control(push) 164 #pragma float_control(precise, on) 165 #pragma float_control(except, on) 166 #if defined(_MSC_VER) 167 __declspec(noinline) 168 #else /* Linux */ 169 __attribute__((noinline)) 170 #endif /* _MSC_VER */ __icc_nan()171 static double __icc_nan() 172 { 173 return sqrt(-1.0); 174 } 175 #pragma float_control (pop) 176 #define Py_NAN __icc_nan() 177 #else /* ICC_NAN_RELAXED as default for Intel Compiler */ 178 static const union { unsigned char buf[8]; double __icc_nan; } __nan_store = {0,0,0,0,0,0,0xf8,0x7f}; 179 #define Py_NAN (__nan_store.__icc_nan) 180 #endif /* ICC_NAN_STRICT */ 181 #endif /* __INTEL_COMPILER */ 182 #endif 183 184 /* Py_OVERFLOWED(X) 185 * Return 1 iff a libm function overflowed. Set errno to 0 before calling 186 * a libm function, and invoke this macro after, passing the function 187 * result. 188 * Caution: 189 * This isn't reliable. C99 no longer requires libm to set errno under 190 * any exceptional condition, but does require +- HUGE_VAL return 191 * values on overflow. A 754 box *probably* maps HUGE_VAL to a 192 * double infinity, and we're cool if that's so, unless the input 193 * was an infinity and an infinity is the expected result. A C89 194 * system sets errno to ERANGE, so we check for that too. We're 195 * out of luck if a C99 754 box doesn't map HUGE_VAL to +Inf, or 196 * if the returned result is a NaN, or if a C89 box returns HUGE_VAL 197 * in non-overflow cases. 198 * X is evaluated more than once. 199 * Some platforms have better way to spell this, so expect some #ifdef'ery. 200 * 201 * OpenBSD uses 'isinf()' because a compiler bug on that platform causes 202 * the longer macro version to be mis-compiled. This isn't optimal, and 203 * should be removed once a newer compiler is available on that platform. 204 * The system that had the failure was running OpenBSD 3.2 on Intel, with 205 * gcc 2.95.3. 206 * 207 * According to Tim's checkin, the FreeBSD systems use isinf() to work 208 * around a FPE bug on that platform. 209 */ 210 #if defined(__FreeBSD__) || defined(__OpenBSD__) 211 #define Py_OVERFLOWED(X) isinf(X) 212 #else 213 #define Py_OVERFLOWED(X) ((X) != 0.0 && (errno == ERANGE || \ 214 (X) == Py_HUGE_VAL || \ 215 (X) == -Py_HUGE_VAL)) 216 #endif 217 218 /* Return whether integral type *type* is signed or not. */ 219 #define _Py_IntegralTypeSigned(type) ((type)(-1) < 0) 220 /* Return the maximum value of integral type *type*. */ 221 #define _Py_IntegralTypeMax(type) ((_Py_IntegralTypeSigned(type)) ? (((((type)1 << (sizeof(type)*CHAR_BIT - 2)) - 1) << 1) + 1) : ~(type)0) 222 /* Return the minimum value of integral type *type*. */ 223 #define _Py_IntegralTypeMin(type) ((_Py_IntegralTypeSigned(type)) ? -_Py_IntegralTypeMax(type) - 1 : 0) 224 /* Check whether *v* is in the range of integral type *type*. This is most 225 * useful if *v* is floating-point, since demoting a floating-point *v* to an 226 * integral type that cannot represent *v*'s integral part is undefined 227 * behavior. */ 228 #define _Py_InIntegralTypeRange(type, v) (_Py_IntegralTypeMin(type) <= v && v <= _Py_IntegralTypeMax(type)) 229 230 #endif /* Py_PYMATH_H */ 231