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