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6ebe78f5cc
svn+ssh://pythondev@svn.python.org/python/trunk ........ r67654 | georg.brandl | 2008-12-07 16:42:09 -0600 (Sun, 07 Dec 2008) | 2 lines #4457: rewrite __import__() documentation. ........ r67676 | benjamin.peterson | 2008-12-08 20:03:03 -0600 (Mon, 08 Dec 2008) | 1 line specify how things are copied ........ r67677 | benjamin.peterson | 2008-12-08 20:05:11 -0600 (Mon, 08 Dec 2008) | 1 line revert unrelated change to installer script ........ r67681 | jeremy.hylton | 2008-12-09 15:03:10 -0600 (Tue, 09 Dec 2008) | 2 lines Add simple unittests for Request ........ r67692 | amaury.forgeotdarc | 2008-12-10 18:03:42 -0600 (Wed, 10 Dec 2008) | 2 lines #1030250: correctly pass the dry_run option to the mkpath() function. ........ r67725 | benjamin.peterson | 2008-12-12 22:02:20 -0600 (Fri, 12 Dec 2008) | 1 line fix incorrect example ........ r67761 | benjamin.peterson | 2008-12-14 11:26:04 -0600 (Sun, 14 Dec 2008) | 1 line fix missing bracket ........ r67784 | georg.brandl | 2008-12-15 02:33:58 -0600 (Mon, 15 Dec 2008) | 2 lines #4446: document "platforms" argument for setup(). ........ r67785 | georg.brandl | 2008-12-15 02:36:11 -0600 (Mon, 15 Dec 2008) | 2 lines #4611: fix typo. ........ r67787 | georg.brandl | 2008-12-15 02:58:59 -0600 (Mon, 15 Dec 2008) | 2 lines #4578: fix has_key() usage in compiler package. ........ r67788 | georg.brandl | 2008-12-15 03:07:39 -0600 (Mon, 15 Dec 2008) | 2 lines #4568: remove limitation in varargs callback example. ........ r67802 | amaury.forgeotdarc | 2008-12-15 16:29:14 -0600 (Mon, 15 Dec 2008) | 4 lines #3632: the "pyo" macro from gdbinit can now run when the GIL is released. Patch by haypo. ........ r67848 | benjamin.peterson | 2008-12-18 20:28:56 -0600 (Thu, 18 Dec 2008) | 1 line fix typo ........ r67849 | benjamin.peterson | 2008-12-18 20:31:35 -0600 (Thu, 18 Dec 2008) | 1 line _call_method -> _callmethod and _get_value to _getvalue ........ r67850 | raymond.hettinger | 2008-12-19 03:06:07 -0600 (Fri, 19 Dec 2008) | 9 lines Fix-up and clean-up docs for int.bit_length(). * Replace dramatic footnote with in-line comment about possible round-off errors in logarithms of large numbers. * Add comments to the pure python code equivalent. * replace floor() with int() in the mathematical equivalent so the type is correct (should be an int, not a float). * add abs() to the mathematical equivalent so that it matches the previous line that it is supposed to be equivalent to. * make one combined example with a negative input. ........ r67862 | benjamin.peterson | 2008-12-19 20:48:02 -0600 (Fri, 19 Dec 2008) | 1 line copy sentence from docstring ........ r67863 | benjamin.peterson | 2008-12-19 20:51:26 -0600 (Fri, 19 Dec 2008) | 1 line add headings ........ r67864 | benjamin.peterson | 2008-12-19 20:57:19 -0600 (Fri, 19 Dec 2008) | 1 line beef up docstring ........ r67880 | benjamin.peterson | 2008-12-20 16:49:24 -0600 (Sat, 20 Dec 2008) | 1 line remove redundant sentence ........ r67882 | benjamin.peterson | 2008-12-20 16:59:49 -0600 (Sat, 20 Dec 2008) | 1 line add some recent releases to the list ........
1205 lines
34 KiB
C
1205 lines
34 KiB
C
/* Math module -- standard C math library functions, pi and e */
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/* Here are some comments from Tim Peters, extracted from the
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discussion attached to http://bugs.python.org/issue1640. They
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describe the general aims of the math module with respect to
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special values, IEEE-754 floating-point exceptions, and Python
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exceptions.
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These are the "spirit of 754" rules:
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1. If the mathematical result is a real number, but of magnitude too
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large to approximate by a machine float, overflow is signaled and the
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result is an infinity (with the appropriate sign).
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2. If the mathematical result is a real number, but of magnitude too
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small to approximate by a machine float, underflow is signaled and the
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result is a zero (with the appropriate sign).
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3. At a singularity (a value x such that the limit of f(y) as y
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approaches x exists and is an infinity), "divide by zero" is signaled
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and the result is an infinity (with the appropriate sign). This is
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complicated a little by that the left-side and right-side limits may
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not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
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from the positive or negative directions. In that specific case, the
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sign of the zero determines the result of 1/0.
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4. At a point where a function has no defined result in the extended
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reals (i.e., the reals plus an infinity or two), invalid operation is
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signaled and a NaN is returned.
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And these are what Python has historically /tried/ to do (but not
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always successfully, as platform libm behavior varies a lot):
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For #1, raise OverflowError.
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For #2, return a zero (with the appropriate sign if that happens by
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accident ;-)).
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For #3 and #4, raise ValueError. It may have made sense to raise
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Python's ZeroDivisionError in #3, but historically that's only been
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raised for division by zero and mod by zero.
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*/
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/*
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In general, on an IEEE-754 platform the aim is to follow the C99
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standard, including Annex 'F', whenever possible. Where the
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standard recommends raising the 'divide-by-zero' or 'invalid'
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floating-point exceptions, Python should raise a ValueError. Where
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the standard recommends raising 'overflow', Python should raise an
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OverflowError. In all other circumstances a value should be
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returned.
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*/
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#include "Python.h"
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#include "longintrepr.h" /* just for SHIFT */
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#ifdef _OSF_SOURCE
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/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
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extern double copysign(double, double);
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#endif
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/* Call is_error when errno != 0, and where x is the result libm
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* returned. is_error will usually set up an exception and return
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* true (1), but may return false (0) without setting up an exception.
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*/
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static int
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is_error(double x)
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{
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int result = 1; /* presumption of guilt */
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assert(errno); /* non-zero errno is a precondition for calling */
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if (errno == EDOM)
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PyErr_SetString(PyExc_ValueError, "math domain error");
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else if (errno == ERANGE) {
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/* ANSI C generally requires libm functions to set ERANGE
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* on overflow, but also generally *allows* them to set
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* ERANGE on underflow too. There's no consistency about
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* the latter across platforms.
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* Alas, C99 never requires that errno be set.
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* Here we suppress the underflow errors (libm functions
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* should return a zero on underflow, and +- HUGE_VAL on
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* overflow, so testing the result for zero suffices to
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* distinguish the cases).
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*
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* On some platforms (Ubuntu/ia64) it seems that errno can be
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* set to ERANGE for subnormal results that do *not* underflow
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* to zero. So to be safe, we'll ignore ERANGE whenever the
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* function result is less than one in absolute value.
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*/
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if (fabs(x) < 1.0)
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result = 0;
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else
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PyErr_SetString(PyExc_OverflowError,
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"math range error");
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}
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else
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/* Unexpected math error */
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PyErr_SetFromErrno(PyExc_ValueError);
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return result;
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}
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/*
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wrapper for atan2 that deals directly with special cases before
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delegating to the platform libm for the remaining cases. This
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is necessary to get consistent behaviour across platforms.
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Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
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always follow C99.
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*/
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static double
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m_atan2(double y, double x)
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{
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if (Py_IS_NAN(x) || Py_IS_NAN(y))
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return Py_NAN;
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if (Py_IS_INFINITY(y)) {
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if (Py_IS_INFINITY(x)) {
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if (copysign(1., x) == 1.)
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/* atan2(+-inf, +inf) == +-pi/4 */
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return copysign(0.25*Py_MATH_PI, y);
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else
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/* atan2(+-inf, -inf) == +-pi*3/4 */
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return copysign(0.75*Py_MATH_PI, y);
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}
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/* atan2(+-inf, x) == +-pi/2 for finite x */
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return copysign(0.5*Py_MATH_PI, y);
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}
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if (Py_IS_INFINITY(x) || y == 0.) {
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if (copysign(1., x) == 1.)
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/* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
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return copysign(0., y);
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else
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/* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
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return copysign(Py_MATH_PI, y);
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}
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return atan2(y, x);
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}
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/*
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Various platforms (Solaris, OpenBSD) do nonstandard things for log(0),
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log(-ve), log(NaN). Here are wrappers for log and log10 that deal with
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special values directly, passing positive non-special values through to
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the system log/log10.
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*/
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static double
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m_log(double x)
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{
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if (Py_IS_FINITE(x)) {
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if (x > 0.0)
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return log(x);
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errno = EDOM;
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if (x == 0.0)
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return -Py_HUGE_VAL; /* log(0) = -inf */
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else
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return Py_NAN; /* log(-ve) = nan */
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}
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else if (Py_IS_NAN(x))
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return x; /* log(nan) = nan */
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else if (x > 0.0)
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return x; /* log(inf) = inf */
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else {
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errno = EDOM;
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return Py_NAN; /* log(-inf) = nan */
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}
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}
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static double
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m_log10(double x)
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{
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if (Py_IS_FINITE(x)) {
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if (x > 0.0)
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return log10(x);
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errno = EDOM;
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if (x == 0.0)
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return -Py_HUGE_VAL; /* log10(0) = -inf */
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else
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return Py_NAN; /* log10(-ve) = nan */
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}
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else if (Py_IS_NAN(x))
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return x; /* log10(nan) = nan */
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else if (x > 0.0)
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return x; /* log10(inf) = inf */
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else {
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errno = EDOM;
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return Py_NAN; /* log10(-inf) = nan */
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}
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}
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/*
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math_1 is used to wrap a libm function f that takes a double
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arguments and returns a double.
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The error reporting follows these rules, which are designed to do
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the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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platforms.
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- a NaN result from non-NaN inputs causes ValueError to be raised
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- an infinite result from finite inputs causes OverflowError to be
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raised if can_overflow is 1, or raises ValueError if can_overflow
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is 0.
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- if the result is finite and errno == EDOM then ValueError is
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raised
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- if the result is finite and nonzero and errno == ERANGE then
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OverflowError is raised
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The last rule is used to catch overflow on platforms which follow
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C89 but for which HUGE_VAL is not an infinity.
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For the majority of one-argument functions these rules are enough
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to ensure that Python's functions behave as specified in 'Annex F'
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of the C99 standard, with the 'invalid' and 'divide-by-zero'
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floating-point exceptions mapping to Python's ValueError and the
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'overflow' floating-point exception mapping to OverflowError.
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math_1 only works for functions that don't have singularities *and*
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the possibility of overflow; fortunately, that covers everything we
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care about right now.
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*/
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static PyObject *
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math_1_to_whatever(PyObject *arg, double (*func) (double),
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PyObject *(*from_double_func) (double),
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int can_overflow)
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{
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double x, r;
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x = PyFloat_AsDouble(arg);
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if (x == -1.0 && PyErr_Occurred())
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return NULL;
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errno = 0;
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PyFPE_START_PROTECT("in math_1", return 0);
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r = (*func)(x);
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PyFPE_END_PROTECT(r);
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if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
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PyErr_SetString(PyExc_ValueError,
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"math domain error"); /* invalid arg */
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return NULL;
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}
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if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
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if (can_overflow)
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PyErr_SetString(PyExc_OverflowError,
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"math range error"); /* overflow */
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else
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PyErr_SetString(PyExc_ValueError,
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"math domain error"); /* singularity */
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return NULL;
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}
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if (Py_IS_FINITE(r) && errno && is_error(r))
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/* this branch unnecessary on most platforms */
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return NULL;
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return (*from_double_func)(r);
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}
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/*
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math_2 is used to wrap a libm function f that takes two double
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arguments and returns a double.
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The error reporting follows these rules, which are designed to do
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the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
|
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platforms.
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- a NaN result from non-NaN inputs causes ValueError to be raised
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- an infinite result from finite inputs causes OverflowError to be
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raised.
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- if the result is finite and errno == EDOM then ValueError is
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raised
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- if the result is finite and nonzero and errno == ERANGE then
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OverflowError is raised
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The last rule is used to catch overflow on platforms which follow
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C89 but for which HUGE_VAL is not an infinity.
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For most two-argument functions (copysign, fmod, hypot, atan2)
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these rules are enough to ensure that Python's functions behave as
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specified in 'Annex F' of the C99 standard, with the 'invalid' and
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'divide-by-zero' floating-point exceptions mapping to Python's
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ValueError and the 'overflow' floating-point exception mapping to
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OverflowError.
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*/
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static PyObject *
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math_1(PyObject *arg, double (*func) (double), int can_overflow)
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{
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return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
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}
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static PyObject *
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math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
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{
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return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
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}
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static PyObject *
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math_2(PyObject *args, double (*func) (double, double), char *funcname)
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{
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PyObject *ox, *oy;
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double x, y, r;
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if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
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return NULL;
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x = PyFloat_AsDouble(ox);
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y = PyFloat_AsDouble(oy);
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if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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return NULL;
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errno = 0;
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PyFPE_START_PROTECT("in math_2", return 0);
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r = (*func)(x, y);
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PyFPE_END_PROTECT(r);
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if (Py_IS_NAN(r)) {
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if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
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errno = EDOM;
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else
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errno = 0;
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}
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else if (Py_IS_INFINITY(r)) {
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if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
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errno = ERANGE;
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else
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errno = 0;
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}
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if (errno && is_error(r))
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return NULL;
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else
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return PyFloat_FromDouble(r);
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}
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#define FUNC1(funcname, func, can_overflow, docstring) \
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static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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return math_1(args, func, can_overflow); \
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}\
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PyDoc_STRVAR(math_##funcname##_doc, docstring);
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#define FUNC2(funcname, func, docstring) \
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static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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return math_2(args, func, #funcname); \
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}\
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PyDoc_STRVAR(math_##funcname##_doc, docstring);
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FUNC1(acos, acos, 0,
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"acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
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FUNC1(acosh, acosh, 0,
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"acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
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FUNC1(asin, asin, 0,
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"asin(x)\n\nReturn the arc sine (measured in radians) of x.")
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FUNC1(asinh, asinh, 0,
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"asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
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FUNC1(atan, atan, 0,
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"atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
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FUNC2(atan2, m_atan2,
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"atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
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"Unlike atan(y/x), the signs of both x and y are considered.")
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FUNC1(atanh, atanh, 0,
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"atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
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static PyObject * math_ceil(PyObject *self, PyObject *number) {
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static PyObject *ceil_str = NULL;
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PyObject *method;
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if (ceil_str == NULL) {
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ceil_str = PyUnicode_InternFromString("__ceil__");
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if (ceil_str == NULL)
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return NULL;
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}
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method = _PyType_Lookup(Py_TYPE(number), ceil_str);
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if (method == NULL)
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return math_1_to_int(number, ceil, 0);
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else
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return PyObject_CallFunction(method, "O", number);
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}
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PyDoc_STRVAR(math_ceil_doc,
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"ceil(x)\n\nReturn the ceiling of x as an int.\n"
|
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"This is the smallest integral value >= x.");
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FUNC2(copysign, copysign,
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"copysign(x,y)\n\nReturn x with the sign of y.")
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FUNC1(cos, cos, 0,
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"cos(x)\n\nReturn the cosine of x (measured in radians).")
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FUNC1(cosh, cosh, 1,
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"cosh(x)\n\nReturn the hyperbolic cosine of x.")
|
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FUNC1(exp, exp, 1,
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"exp(x)\n\nReturn e raised to the power of x.")
|
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FUNC1(fabs, fabs, 0,
|
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"fabs(x)\n\nReturn the absolute value of the float x.")
|
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|
|
static PyObject * math_floor(PyObject *self, PyObject *number) {
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static PyObject *floor_str = NULL;
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PyObject *method;
|
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|
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if (floor_str == NULL) {
|
|
floor_str = PyUnicode_InternFromString("__floor__");
|
|
if (floor_str == NULL)
|
|
return NULL;
|
|
}
|
|
|
|
method = _PyType_Lookup(Py_TYPE(number), floor_str);
|
|
if (method == NULL)
|
|
return math_1_to_int(number, floor, 0);
|
|
else
|
|
return PyObject_CallFunction(method, "O", number);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_floor_doc,
|
|
"floor(x)\n\nReturn the floor of x as an int.\n"
|
|
"This is the largest integral value <= x.");
|
|
|
|
FUNC1(log1p, log1p, 1,
|
|
"log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n\
|
|
The result is computed in a way which is accurate for x near zero.")
|
|
FUNC1(sin, sin, 0,
|
|
"sin(x)\n\nReturn the sine of x (measured in radians).")
|
|
FUNC1(sinh, sinh, 1,
|
|
"sinh(x)\n\nReturn the hyperbolic sine of x.")
|
|
FUNC1(sqrt, sqrt, 0,
|
|
"sqrt(x)\n\nReturn the square root of x.")
|
|
FUNC1(tan, tan, 0,
|
|
"tan(x)\n\nReturn the tangent of x (measured in radians).")
|
|
FUNC1(tanh, tanh, 0,
|
|
"tanh(x)\n\nReturn the hyperbolic tangent of x.")
|
|
|
|
/* Precision summation function as msum() by Raymond Hettinger in
|
|
<http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
|
|
enhanced with the exact partials sum and roundoff from Mark
|
|
Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
|
|
See those links for more details, proofs and other references.
|
|
|
|
Note 1: IEEE 754R floating point semantics are assumed,
|
|
but the current implementation does not re-establish special
|
|
value semantics across iterations (i.e. handling -Inf + Inf).
|
|
|
|
Note 2: No provision is made for intermediate overflow handling;
|
|
therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
|
|
sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
|
|
overflow of the first partial sum.
|
|
|
|
Note 3: The intermediate values lo, yr, and hi are declared volatile so
|
|
aggressive compilers won't algebraically reduce lo to always be exactly 0.0.
|
|
Also, the volatile declaration forces the values to be stored in memory as
|
|
regular doubles instead of extended long precision (80-bit) values. This
|
|
prevents double rounding because any addition or subtraction of two doubles
|
|
can be resolved exactly into double-sized hi and lo values. As long as the
|
|
hi value gets forced into a double before yr and lo are computed, the extra
|
|
bits in downstream extended precision operations (x87 for example) will be
|
|
exactly zero and therefore can be losslessly stored back into a double,
|
|
thereby preventing double rounding.
|
|
|
|
Note 4: A similar implementation is in Modules/cmathmodule.c.
|
|
Be sure to update both when making changes.
|
|
|
|
Note 5: The signature of math.fsum() differs from __builtin__.sum()
|
|
because the start argument doesn't make sense in the context of
|
|
accurate summation. Since the partials table is collapsed before
|
|
returning a result, sum(seq2, start=sum(seq1)) may not equal the
|
|
accurate result returned by sum(itertools.chain(seq1, seq2)).
|
|
*/
|
|
|
|
#define NUM_PARTIALS 32 /* initial partials array size, on stack */
|
|
|
|
/* Extend the partials array p[] by doubling its size. */
|
|
static int /* non-zero on error */
|
|
_fsum_realloc(double **p_ptr, Py_ssize_t n,
|
|
double *ps, Py_ssize_t *m_ptr)
|
|
{
|
|
void *v = NULL;
|
|
Py_ssize_t m = *m_ptr;
|
|
|
|
m += m; /* double */
|
|
if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
|
|
double *p = *p_ptr;
|
|
if (p == ps) {
|
|
v = PyMem_Malloc(sizeof(double) * m);
|
|
if (v != NULL)
|
|
memcpy(v, ps, sizeof(double) * n);
|
|
}
|
|
else
|
|
v = PyMem_Realloc(p, sizeof(double) * m);
|
|
}
|
|
if (v == NULL) { /* size overflow or no memory */
|
|
PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
|
|
return 1;
|
|
}
|
|
*p_ptr = (double*) v;
|
|
*m_ptr = m;
|
|
return 0;
|
|
}
|
|
|
|
/* Full precision summation of a sequence of floats.
|
|
|
|
def msum(iterable):
|
|
partials = [] # sorted, non-overlapping partial sums
|
|
for x in iterable:
|
|
i = 0
|
|
for y in partials:
|
|
if abs(x) < abs(y):
|
|
x, y = y, x
|
|
hi = x + y
|
|
lo = y - (hi - x)
|
|
if lo:
|
|
partials[i] = lo
|
|
i += 1
|
|
x = hi
|
|
partials[i:] = [x]
|
|
return sum_exact(partials)
|
|
|
|
Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
|
|
are exactly equal to x+y. The inner loop applies hi/lo summation to each
|
|
partial so that the list of partial sums remains exact.
|
|
|
|
Sum_exact() adds the partial sums exactly and correctly rounds the final
|
|
result (using the round-half-to-even rule). The items in partials remain
|
|
non-zero, non-special, non-overlapping and strictly increasing in
|
|
magnitude, but possibly not all having the same sign.
|
|
|
|
Depends on IEEE 754 arithmetic guarantees and half-even rounding.
|
|
*/
|
|
|
|
static PyObject*
|
|
math_fsum(PyObject *self, PyObject *seq)
|
|
{
|
|
PyObject *item, *iter, *sum = NULL;
|
|
Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
|
|
double x, y, t, ps[NUM_PARTIALS], *p = ps;
|
|
double xsave, special_sum = 0.0, inf_sum = 0.0;
|
|
volatile double hi, yr, lo;
|
|
|
|
iter = PyObject_GetIter(seq);
|
|
if (iter == NULL)
|
|
return NULL;
|
|
|
|
PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
|
|
|
|
for(;;) { /* for x in iterable */
|
|
assert(0 <= n && n <= m);
|
|
assert((m == NUM_PARTIALS && p == ps) ||
|
|
(m > NUM_PARTIALS && p != NULL));
|
|
|
|
item = PyIter_Next(iter);
|
|
if (item == NULL) {
|
|
if (PyErr_Occurred())
|
|
goto _fsum_error;
|
|
break;
|
|
}
|
|
x = PyFloat_AsDouble(item);
|
|
Py_DECREF(item);
|
|
if (PyErr_Occurred())
|
|
goto _fsum_error;
|
|
|
|
xsave = x;
|
|
for (i = j = 0; j < n; j++) { /* for y in partials */
|
|
y = p[j];
|
|
if (fabs(x) < fabs(y)) {
|
|
t = x; x = y; y = t;
|
|
}
|
|
hi = x + y;
|
|
yr = hi - x;
|
|
lo = y - yr;
|
|
if (lo != 0.0)
|
|
p[i++] = lo;
|
|
x = hi;
|
|
}
|
|
|
|
n = i; /* ps[i:] = [x] */
|
|
if (x != 0.0) {
|
|
if (! Py_IS_FINITE(x)) {
|
|
/* a nonfinite x could arise either as
|
|
a result of intermediate overflow, or
|
|
as a result of a nan or inf in the
|
|
summands */
|
|
if (Py_IS_FINITE(xsave)) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"intermediate overflow in fsum");
|
|
goto _fsum_error;
|
|
}
|
|
if (Py_IS_INFINITY(xsave))
|
|
inf_sum += xsave;
|
|
special_sum += xsave;
|
|
/* reset partials */
|
|
n = 0;
|
|
}
|
|
else if (n >= m && _fsum_realloc(&p, n, ps, &m))
|
|
goto _fsum_error;
|
|
else
|
|
p[n++] = x;
|
|
}
|
|
}
|
|
|
|
if (special_sum != 0.0) {
|
|
if (Py_IS_NAN(inf_sum))
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"-inf + inf in fsum");
|
|
else
|
|
sum = PyFloat_FromDouble(special_sum);
|
|
goto _fsum_error;
|
|
}
|
|
|
|
hi = 0.0;
|
|
if (n > 0) {
|
|
hi = p[--n];
|
|
/* sum_exact(ps, hi) from the top, stop when the sum becomes
|
|
inexact. */
|
|
while (n > 0) {
|
|
x = hi;
|
|
y = p[--n];
|
|
assert(fabs(y) < fabs(x));
|
|
hi = x + y;
|
|
yr = hi - x;
|
|
lo = y - yr;
|
|
if (lo != 0.0)
|
|
break;
|
|
}
|
|
/* Make half-even rounding work across multiple partials.
|
|
Needed so that sum([1e-16, 1, 1e16]) will round-up the last
|
|
digit to two instead of down to zero (the 1e-16 makes the 1
|
|
slightly closer to two). With a potential 1 ULP rounding
|
|
error fixed-up, math.fsum() can guarantee commutativity. */
|
|
if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
|
|
(lo > 0.0 && p[n-1] > 0.0))) {
|
|
y = lo * 2.0;
|
|
x = hi + y;
|
|
yr = x - hi;
|
|
if (y == yr)
|
|
hi = x;
|
|
}
|
|
}
|
|
sum = PyFloat_FromDouble(hi);
|
|
|
|
_fsum_error:
|
|
PyFPE_END_PROTECT(hi)
|
|
Py_DECREF(iter);
|
|
if (p != ps)
|
|
PyMem_Free(p);
|
|
return sum;
|
|
}
|
|
|
|
#undef NUM_PARTIALS
|
|
|
|
PyDoc_STRVAR(math_fsum_doc,
|
|
"sum(iterable)\n\n\
|
|
Return an accurate floating point sum of values in the iterable.\n\
|
|
Assumes IEEE-754 floating point arithmetic.");
|
|
|
|
static PyObject *
|
|
math_factorial(PyObject *self, PyObject *arg)
|
|
{
|
|
long i, x;
|
|
PyObject *result, *iobj, *newresult;
|
|
|
|
if (PyFloat_Check(arg)) {
|
|
double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
|
|
if (dx != floor(dx)) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"factorial() only accepts integral values");
|
|
return NULL;
|
|
}
|
|
}
|
|
|
|
x = PyLong_AsLong(arg);
|
|
if (x == -1 && PyErr_Occurred())
|
|
return NULL;
|
|
if (x < 0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"factorial() not defined for negative values");
|
|
return NULL;
|
|
}
|
|
|
|
result = (PyObject *)PyLong_FromLong(1);
|
|
if (result == NULL)
|
|
return NULL;
|
|
for (i=1 ; i<=x ; i++) {
|
|
iobj = (PyObject *)PyLong_FromLong(i);
|
|
if (iobj == NULL)
|
|
goto error;
|
|
newresult = PyNumber_Multiply(result, iobj);
|
|
Py_DECREF(iobj);
|
|
if (newresult == NULL)
|
|
goto error;
|
|
Py_DECREF(result);
|
|
result = newresult;
|
|
}
|
|
return result;
|
|
|
|
error:
|
|
Py_DECREF(result);
|
|
return NULL;
|
|
}
|
|
|
|
PyDoc_STRVAR(math_factorial_doc,
|
|
"factorial(x) -> Integral\n"
|
|
"\n"
|
|
"Find x!. Raise a ValueError if x is negative or non-integral.");
|
|
|
|
static PyObject *
|
|
math_trunc(PyObject *self, PyObject *number)
|
|
{
|
|
static PyObject *trunc_str = NULL;
|
|
PyObject *trunc;
|
|
|
|
if (Py_TYPE(number)->tp_dict == NULL) {
|
|
if (PyType_Ready(Py_TYPE(number)) < 0)
|
|
return NULL;
|
|
}
|
|
|
|
if (trunc_str == NULL) {
|
|
trunc_str = PyUnicode_InternFromString("__trunc__");
|
|
if (trunc_str == NULL)
|
|
return NULL;
|
|
}
|
|
|
|
trunc = _PyType_Lookup(Py_TYPE(number), trunc_str);
|
|
if (trunc == NULL) {
|
|
PyErr_Format(PyExc_TypeError,
|
|
"type %.100s doesn't define __trunc__ method",
|
|
Py_TYPE(number)->tp_name);
|
|
return NULL;
|
|
}
|
|
return PyObject_CallFunctionObjArgs(trunc, number, NULL);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_trunc_doc,
|
|
"trunc(x:Real) -> Integral\n"
|
|
"\n"
|
|
"Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
|
|
|
|
static PyObject *
|
|
math_frexp(PyObject *self, PyObject *arg)
|
|
{
|
|
int i;
|
|
double x = PyFloat_AsDouble(arg);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
/* deal with special cases directly, to sidestep platform
|
|
differences */
|
|
if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
|
|
i = 0;
|
|
}
|
|
else {
|
|
PyFPE_START_PROTECT("in math_frexp", return 0);
|
|
x = frexp(x, &i);
|
|
PyFPE_END_PROTECT(x);
|
|
}
|
|
return Py_BuildValue("(di)", x, i);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_frexp_doc,
|
|
"frexp(x)\n"
|
|
"\n"
|
|
"Return the mantissa and exponent of x, as pair (m, e).\n"
|
|
"m is a float and e is an int, such that x = m * 2.**e.\n"
|
|
"If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
|
|
|
|
static PyObject *
|
|
math_ldexp(PyObject *self, PyObject *args)
|
|
{
|
|
double x, r;
|
|
PyObject *oexp;
|
|
long exp;
|
|
if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
|
|
return NULL;
|
|
|
|
if (PyLong_Check(oexp)) {
|
|
/* on overflow, replace exponent with either LONG_MAX
|
|
or LONG_MIN, depending on the sign. */
|
|
exp = PyLong_AsLong(oexp);
|
|
if (exp == -1 && PyErr_Occurred()) {
|
|
if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
|
|
if (Py_SIZE(oexp) < 0) {
|
|
exp = LONG_MIN;
|
|
}
|
|
else {
|
|
exp = LONG_MAX;
|
|
}
|
|
PyErr_Clear();
|
|
}
|
|
else {
|
|
/* propagate any unexpected exception */
|
|
return NULL;
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
PyErr_SetString(PyExc_TypeError,
|
|
"Expected an int or long as second argument "
|
|
"to ldexp.");
|
|
return NULL;
|
|
}
|
|
|
|
if (x == 0. || !Py_IS_FINITE(x)) {
|
|
/* NaNs, zeros and infinities are returned unchanged */
|
|
r = x;
|
|
errno = 0;
|
|
} else if (exp > INT_MAX) {
|
|
/* overflow */
|
|
r = copysign(Py_HUGE_VAL, x);
|
|
errno = ERANGE;
|
|
} else if (exp < INT_MIN) {
|
|
/* underflow to +-0 */
|
|
r = copysign(0., x);
|
|
errno = 0;
|
|
} else {
|
|
errno = 0;
|
|
PyFPE_START_PROTECT("in math_ldexp", return 0);
|
|
r = ldexp(x, (int)exp);
|
|
PyFPE_END_PROTECT(r);
|
|
if (Py_IS_INFINITY(r))
|
|
errno = ERANGE;
|
|
}
|
|
|
|
if (errno && is_error(r))
|
|
return NULL;
|
|
return PyFloat_FromDouble(r);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_ldexp_doc,
|
|
"ldexp(x, i) -> x * (2**i)");
|
|
|
|
static PyObject *
|
|
math_modf(PyObject *self, PyObject *arg)
|
|
{
|
|
double y, x = PyFloat_AsDouble(arg);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
/* some platforms don't do the right thing for NaNs and
|
|
infinities, so we take care of special cases directly. */
|
|
if (!Py_IS_FINITE(x)) {
|
|
if (Py_IS_INFINITY(x))
|
|
return Py_BuildValue("(dd)", copysign(0., x), x);
|
|
else if (Py_IS_NAN(x))
|
|
return Py_BuildValue("(dd)", x, x);
|
|
}
|
|
|
|
errno = 0;
|
|
PyFPE_START_PROTECT("in math_modf", return 0);
|
|
x = modf(x, &y);
|
|
PyFPE_END_PROTECT(x);
|
|
return Py_BuildValue("(dd)", x, y);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_modf_doc,
|
|
"modf(x)\n"
|
|
"\n"
|
|
"Return the fractional and integer parts of x. Both results carry the sign\n"
|
|
"of x and are floats.");
|
|
|
|
/* A decent logarithm is easy to compute even for huge longs, but libm can't
|
|
do that by itself -- loghelper can. func is log or log10, and name is
|
|
"log" or "log10". Note that overflow isn't possible: a long can contain
|
|
no more than INT_MAX * SHIFT bits, so has value certainly less than
|
|
2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
|
|
small enough to fit in an IEEE single. log and log10 are even smaller.
|
|
*/
|
|
|
|
static PyObject*
|
|
loghelper(PyObject* arg, double (*func)(double), char *funcname)
|
|
{
|
|
/* If it is long, do it ourselves. */
|
|
if (PyLong_Check(arg)) {
|
|
double x;
|
|
int e;
|
|
x = _PyLong_AsScaledDouble(arg, &e);
|
|
if (x <= 0.0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"math domain error");
|
|
return NULL;
|
|
}
|
|
/* Value is ~= x * 2**(e*PyLong_SHIFT), so the log ~=
|
|
log(x) + log(2) * e * PyLong_SHIFT.
|
|
CAUTION: e*PyLong_SHIFT may overflow using int arithmetic,
|
|
so force use of double. */
|
|
x = func(x) + (e * (double)PyLong_SHIFT) * func(2.0);
|
|
return PyFloat_FromDouble(x);
|
|
}
|
|
|
|
/* Else let libm handle it by itself. */
|
|
return math_1(arg, func, 0);
|
|
}
|
|
|
|
static PyObject *
|
|
math_log(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *arg;
|
|
PyObject *base = NULL;
|
|
PyObject *num, *den;
|
|
PyObject *ans;
|
|
|
|
if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
|
|
return NULL;
|
|
|
|
num = loghelper(arg, m_log, "log");
|
|
if (num == NULL || base == NULL)
|
|
return num;
|
|
|
|
den = loghelper(base, m_log, "log");
|
|
if (den == NULL) {
|
|
Py_DECREF(num);
|
|
return NULL;
|
|
}
|
|
|
|
ans = PyNumber_TrueDivide(num, den);
|
|
Py_DECREF(num);
|
|
Py_DECREF(den);
|
|
return ans;
|
|
}
|
|
|
|
PyDoc_STRVAR(math_log_doc,
|
|
"log(x[, base]) -> the logarithm of x to the given base.\n\
|
|
If the base not specified, returns the natural logarithm (base e) of x.");
|
|
|
|
static PyObject *
|
|
math_log10(PyObject *self, PyObject *arg)
|
|
{
|
|
return loghelper(arg, m_log10, "log10");
|
|
}
|
|
|
|
PyDoc_STRVAR(math_log10_doc,
|
|
"log10(x) -> the base 10 logarithm of x.");
|
|
|
|
static PyObject *
|
|
math_fmod(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *ox, *oy;
|
|
double r, x, y;
|
|
if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
|
|
return NULL;
|
|
x = PyFloat_AsDouble(ox);
|
|
y = PyFloat_AsDouble(oy);
|
|
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
|
|
return NULL;
|
|
/* fmod(x, +/-Inf) returns x for finite x. */
|
|
if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
|
|
return PyFloat_FromDouble(x);
|
|
errno = 0;
|
|
PyFPE_START_PROTECT("in math_fmod", return 0);
|
|
r = fmod(x, y);
|
|
PyFPE_END_PROTECT(r);
|
|
if (Py_IS_NAN(r)) {
|
|
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
|
|
errno = EDOM;
|
|
else
|
|
errno = 0;
|
|
}
|
|
if (errno && is_error(r))
|
|
return NULL;
|
|
else
|
|
return PyFloat_FromDouble(r);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_fmod_doc,
|
|
"fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
|
|
" x % y may differ.");
|
|
|
|
static PyObject *
|
|
math_hypot(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *ox, *oy;
|
|
double r, x, y;
|
|
if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
|
|
return NULL;
|
|
x = PyFloat_AsDouble(ox);
|
|
y = PyFloat_AsDouble(oy);
|
|
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
|
|
return NULL;
|
|
/* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
|
|
if (Py_IS_INFINITY(x))
|
|
return PyFloat_FromDouble(fabs(x));
|
|
if (Py_IS_INFINITY(y))
|
|
return PyFloat_FromDouble(fabs(y));
|
|
errno = 0;
|
|
PyFPE_START_PROTECT("in math_hypot", return 0);
|
|
r = hypot(x, y);
|
|
PyFPE_END_PROTECT(r);
|
|
if (Py_IS_NAN(r)) {
|
|
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
|
|
errno = EDOM;
|
|
else
|
|
errno = 0;
|
|
}
|
|
else if (Py_IS_INFINITY(r)) {
|
|
if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
|
|
errno = ERANGE;
|
|
else
|
|
errno = 0;
|
|
}
|
|
if (errno && is_error(r))
|
|
return NULL;
|
|
else
|
|
return PyFloat_FromDouble(r);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_hypot_doc,
|
|
"hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
|
|
|
|
/* pow can't use math_2, but needs its own wrapper: the problem is
|
|
that an infinite result can arise either as a result of overflow
|
|
(in which case OverflowError should be raised) or as a result of
|
|
e.g. 0.**-5. (for which ValueError needs to be raised.)
|
|
*/
|
|
|
|
static PyObject *
|
|
math_pow(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *ox, *oy;
|
|
double r, x, y;
|
|
int odd_y;
|
|
|
|
if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
|
|
return NULL;
|
|
x = PyFloat_AsDouble(ox);
|
|
y = PyFloat_AsDouble(oy);
|
|
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
|
|
return NULL;
|
|
|
|
/* deal directly with IEEE specials, to cope with problems on various
|
|
platforms whose semantics don't exactly match C99 */
|
|
r = 0.; /* silence compiler warning */
|
|
if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
|
|
errno = 0;
|
|
if (Py_IS_NAN(x))
|
|
r = y == 0. ? 1. : x; /* NaN**0 = 1 */
|
|
else if (Py_IS_NAN(y))
|
|
r = x == 1. ? 1. : y; /* 1**NaN = 1 */
|
|
else if (Py_IS_INFINITY(x)) {
|
|
odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
|
|
if (y > 0.)
|
|
r = odd_y ? x : fabs(x);
|
|
else if (y == 0.)
|
|
r = 1.;
|
|
else /* y < 0. */
|
|
r = odd_y ? copysign(0., x) : 0.;
|
|
}
|
|
else if (Py_IS_INFINITY(y)) {
|
|
if (fabs(x) == 1.0)
|
|
r = 1.;
|
|
else if (y > 0. && fabs(x) > 1.0)
|
|
r = y;
|
|
else if (y < 0. && fabs(x) < 1.0) {
|
|
r = -y; /* result is +inf */
|
|
if (x == 0.) /* 0**-inf: divide-by-zero */
|
|
errno = EDOM;
|
|
}
|
|
else
|
|
r = 0.;
|
|
}
|
|
}
|
|
else {
|
|
/* let libm handle finite**finite */
|
|
errno = 0;
|
|
PyFPE_START_PROTECT("in math_pow", return 0);
|
|
r = pow(x, y);
|
|
PyFPE_END_PROTECT(r);
|
|
/* a NaN result should arise only from (-ve)**(finite
|
|
non-integer); in this case we want to raise ValueError. */
|
|
if (!Py_IS_FINITE(r)) {
|
|
if (Py_IS_NAN(r)) {
|
|
errno = EDOM;
|
|
}
|
|
/*
|
|
an infinite result here arises either from:
|
|
(A) (+/-0.)**negative (-> divide-by-zero)
|
|
(B) overflow of x**y with x and y finite
|
|
*/
|
|
else if (Py_IS_INFINITY(r)) {
|
|
if (x == 0.)
|
|
errno = EDOM;
|
|
else
|
|
errno = ERANGE;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (errno && is_error(r))
|
|
return NULL;
|
|
else
|
|
return PyFloat_FromDouble(r);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_pow_doc,
|
|
"pow(x,y)\n\nReturn x**y (x to the power of y).");
|
|
|
|
static const double degToRad = Py_MATH_PI / 180.0;
|
|
static const double radToDeg = 180.0 / Py_MATH_PI;
|
|
|
|
static PyObject *
|
|
math_degrees(PyObject *self, PyObject *arg)
|
|
{
|
|
double x = PyFloat_AsDouble(arg);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
return PyFloat_FromDouble(x * radToDeg);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_degrees_doc,
|
|
"degrees(x) -> converts angle x from radians to degrees");
|
|
|
|
static PyObject *
|
|
math_radians(PyObject *self, PyObject *arg)
|
|
{
|
|
double x = PyFloat_AsDouble(arg);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
return PyFloat_FromDouble(x * degToRad);
|
|
}
|
|
|
|
PyDoc_STRVAR(math_radians_doc,
|
|
"radians(x) -> converts angle x from degrees to radians");
|
|
|
|
static PyObject *
|
|
math_isnan(PyObject *self, PyObject *arg)
|
|
{
|
|
double x = PyFloat_AsDouble(arg);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
return PyBool_FromLong((long)Py_IS_NAN(x));
|
|
}
|
|
|
|
PyDoc_STRVAR(math_isnan_doc,
|
|
"isnan(x) -> bool\n\
|
|
Checks if float x is not a number (NaN)");
|
|
|
|
static PyObject *
|
|
math_isinf(PyObject *self, PyObject *arg)
|
|
{
|
|
double x = PyFloat_AsDouble(arg);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
return PyBool_FromLong((long)Py_IS_INFINITY(x));
|
|
}
|
|
|
|
PyDoc_STRVAR(math_isinf_doc,
|
|
"isinf(x) -> bool\n\
|
|
Checks if float x is infinite (positive or negative)");
|
|
|
|
static PyMethodDef math_methods[] = {
|
|
{"acos", math_acos, METH_O, math_acos_doc},
|
|
{"acosh", math_acosh, METH_O, math_acosh_doc},
|
|
{"asin", math_asin, METH_O, math_asin_doc},
|
|
{"asinh", math_asinh, METH_O, math_asinh_doc},
|
|
{"atan", math_atan, METH_O, math_atan_doc},
|
|
{"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
|
|
{"atanh", math_atanh, METH_O, math_atanh_doc},
|
|
{"ceil", math_ceil, METH_O, math_ceil_doc},
|
|
{"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
|
|
{"cos", math_cos, METH_O, math_cos_doc},
|
|
{"cosh", math_cosh, METH_O, math_cosh_doc},
|
|
{"degrees", math_degrees, METH_O, math_degrees_doc},
|
|
{"exp", math_exp, METH_O, math_exp_doc},
|
|
{"fabs", math_fabs, METH_O, math_fabs_doc},
|
|
{"factorial", math_factorial, METH_O, math_factorial_doc},
|
|
{"floor", math_floor, METH_O, math_floor_doc},
|
|
{"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
|
|
{"frexp", math_frexp, METH_O, math_frexp_doc},
|
|
{"fsum", math_fsum, METH_O, math_fsum_doc},
|
|
{"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
|
|
{"isinf", math_isinf, METH_O, math_isinf_doc},
|
|
{"isnan", math_isnan, METH_O, math_isnan_doc},
|
|
{"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
|
|
{"log", math_log, METH_VARARGS, math_log_doc},
|
|
{"log1p", math_log1p, METH_O, math_log1p_doc},
|
|
{"log10", math_log10, METH_O, math_log10_doc},
|
|
{"modf", math_modf, METH_O, math_modf_doc},
|
|
{"pow", math_pow, METH_VARARGS, math_pow_doc},
|
|
{"radians", math_radians, METH_O, math_radians_doc},
|
|
{"sin", math_sin, METH_O, math_sin_doc},
|
|
{"sinh", math_sinh, METH_O, math_sinh_doc},
|
|
{"sqrt", math_sqrt, METH_O, math_sqrt_doc},
|
|
{"tan", math_tan, METH_O, math_tan_doc},
|
|
{"tanh", math_tanh, METH_O, math_tanh_doc},
|
|
{"trunc", math_trunc, METH_O, math_trunc_doc},
|
|
{NULL, NULL} /* sentinel */
|
|
};
|
|
|
|
|
|
PyDoc_STRVAR(module_doc,
|
|
"This module is always available. It provides access to the\n"
|
|
"mathematical functions defined by the C standard.");
|
|
|
|
|
|
static struct PyModuleDef mathmodule = {
|
|
PyModuleDef_HEAD_INIT,
|
|
"math",
|
|
module_doc,
|
|
-1,
|
|
math_methods,
|
|
NULL,
|
|
NULL,
|
|
NULL,
|
|
NULL
|
|
};
|
|
|
|
PyMODINIT_FUNC
|
|
PyInit_math(void)
|
|
{
|
|
PyObject *m;
|
|
|
|
m = PyModule_Create(&mathmodule);
|
|
if (m == NULL)
|
|
goto finally;
|
|
|
|
PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
|
|
PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
|
|
|
|
finally:
|
|
return m;
|
|
}
|