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 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
73PyAPI_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
83PyAPI_FUNC(unsigned short) _Py_get_387controlword(void);
84PyAPI_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 intrinsics 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 */
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

source code of include/python3.10/pymath.h