cpython/Doc/library/math.rst

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:mod:`math` --- Mathematical functions
======================================
.. module:: math
:synopsis: Mathematical functions (sin() etc.).
.. testsetup::
from math import fsum
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This module is always available. It provides access to the mathematical
functions defined by the C standard.
These functions cannot be used with complex numbers; use the functions of the
same name from the :mod:`cmath` module if you require support for complex
numbers. The distinction between functions which support complex numbers and
those which don't is made since most users do not want to learn quite as much
mathematics as required to understand complex numbers. Receiving an exception
instead of a complex result allows earlier detection of the unexpected complex
number used as a parameter, so that the programmer can determine how and why it
was generated in the first place.
The following functions are provided by this module. Except when explicitly
noted otherwise, all return values are floats.
Merged revisions 67654,67676-67677,67681,67692,67725,67761,67784-67785,67787-67788,67802,67848-67850,67862-67864,67880,67882 via svnmerge from 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 ........
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Number-theoretic and representation functions
---------------------------------------------
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.. function:: ceil(x)
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Return the ceiling of *x*, the smallest integer greater than or equal to *x*.
If *x* is not a float, delegates to ``x.__ceil__()``, which should return an
:class:`~numbers.Integral` value.
Merged revisions 59666-59679 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59666 | christian.heimes | 2008-01-02 19:28:32 +0100 (Wed, 02 Jan 2008) | 1 line Made vs9to8 Unix compatible ........ r59669 | guido.van.rossum | 2008-01-02 20:00:46 +0100 (Wed, 02 Jan 2008) | 2 lines Patch #1696. Don't attempt to close None in dry-run mode. ........ r59671 | jeffrey.yasskin | 2008-01-03 03:21:52 +0100 (Thu, 03 Jan 2008) | 6 lines Backport PEP 3141 from the py3k branch to the trunk. This includes r50877 (just the complex_pow part), r56649, r56652, r56715, r57296, r57302, r57359, r57361, r57372, r57738, r57739, r58017, r58039, r58040, and r59390, and new documentation. The only significant difference is that round(x) returns a float to preserve backward-compatibility. See http://bugs.python.org/issue1689. ........ r59672 | christian.heimes | 2008-01-03 16:41:30 +0100 (Thu, 03 Jan 2008) | 1 line Issue #1726: Remove Python/atof.c from PCBuild/pythoncore.vcproj ........ r59675 | guido.van.rossum | 2008-01-03 20:12:44 +0100 (Thu, 03 Jan 2008) | 4 lines Issue #1700, reported by Nguyen Quan Son, fix by Fredruk Lundh: Regular Expression inline flags not handled correctly for some unicode characters. (Forward port from 2.5.2.) ........ r59676 | christian.heimes | 2008-01-03 21:23:15 +0100 (Thu, 03 Jan 2008) | 1 line Added math.isinf() and math.isnan() ........ r59677 | christian.heimes | 2008-01-03 22:14:48 +0100 (Thu, 03 Jan 2008) | 1 line Some build bots don't compile mathmodule. There is an issue with the long definition of pi and euler ........ r59678 | christian.heimes | 2008-01-03 23:16:32 +0100 (Thu, 03 Jan 2008) | 2 lines Modified PyImport_Import and PyImport_ImportModule to always use absolute imports by calling __import__ with an explicit level of 0 Added a new API function PyImport_ImportModuleNoBlock. It solves the problem with dead locks when mixing threads and imports ........ r59679 | christian.heimes | 2008-01-03 23:32:26 +0100 (Thu, 03 Jan 2008) | 1 line Added copysign(x, y) function to the math module ........
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.. function:: copysign(x, y)
Return a float with the magnitude (absolute value) of *x* but the sign of
*y*. On platforms that support signed zeros, ``copysign(1.0, -0.0)``
returns *-1.0*.
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.. function:: fabs(x)
Return the absolute value of *x*.
Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r64002 | travis.oliphant | 2008-06-07 00:33:21 +0200 (Sat, 07 Jun 2008) | 1 line Add long double check support to configure test. ........ r64003 | travis.oliphant | 2008-06-07 00:39:47 +0200 (Sat, 07 Jun 2008) | 1 line Remove locking part of new buffer protocol. ........ r64012 | facundo.batista | 2008-06-07 15:36:36 +0200 (Sat, 07 Jun 2008) | 4 lines Finished bug #2451. Fixed the retrying part to make it more robust. ........ r64036 | georg.brandl | 2008-06-08 10:54:40 +0200 (Sun, 08 Jun 2008) | 2 lines #3028: tokenize passes the physical line. ........ r64037 | georg.brandl | 2008-06-08 10:59:38 +0200 (Sun, 08 Jun 2008) | 2 lines Argh, I read it wrong. Reverted 64036 and added a clarifying remark. ........ r64047 | raymond.hettinger | 2008-06-09 03:28:30 +0200 (Mon, 09 Jun 2008) | 1 line Issue3065: Fixed pickling of named tuples. Added tests. ........ r64050 | raymond.hettinger | 2008-06-09 08:54:45 +0200 (Mon, 09 Jun 2008) | 1 line Issue #2138: Add math.factorial(). ........ r64051 | raymond.hettinger | 2008-06-09 10:33:37 +0200 (Mon, 09 Jun 2008) | 1 line Let set.union() and set.update() accept multiple inputs. ........ r64052 | raymond.hettinger | 2008-06-09 11:29:17 +0200 (Mon, 09 Jun 2008) | 1 line Address double-rounding scenarios by setting all variables to long doubles. ........ r64054 | raymond.hettinger | 2008-06-09 13:24:47 +0200 (Mon, 09 Jun 2008) | 1 line Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. ........ r64055 | raymond.hettinger | 2008-06-09 15:07:27 +0200 (Mon, 09 Jun 2008) | 1 line Let set.intersection() and set.intersection_update() take multiple input arguments. ........ r64066 | robert.schuppenies | 2008-06-10 12:10:31 +0200 (Tue, 10 Jun 2008) | 2 lines Issue 3048: Fixed sys.getsizeof for unicode objects. ........ r64071 | thomas.heller | 2008-06-10 16:07:12 +0200 (Tue, 10 Jun 2008) | 3 lines NEWS entry for: Add an optional 'offset' parameter to byref, defaulting to zero. ........
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.. function:: factorial(x)
Merged revisions 64365,64370,64406,64408-64409,64412,64416-64417,64420-64421,64425-64428 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r64365 | raymond.hettinger | 2008-06-17 19:56:57 -0500 (Tue, 17 Jun 2008) | 1 line Fix double decref. ........ r64370 | mark.dickinson | 2008-06-18 04:20:17 -0500 (Wed, 18 Jun 2008) | 2 lines Typo fix ........ r64406 | andrew.kuchling | 2008-06-19 09:02:30 -0500 (Thu, 19 Jun 2008) | 1 line Only include update_lines_cols() function when it's actually going to be used ........ r64408 | amaury.forgeotdarc | 2008-06-19 14:57:39 -0500 (Thu, 19 Jun 2008) | 2 lines test_macos can be skipped on non-mac platforms. ........ r64409 | andrew.kuchling | 2008-06-19 15:33:31 -0500 (Thu, 19 Jun 2008) | 1 line Put threading in front of thread ........ r64412 | amaury.forgeotdarc | 2008-06-19 16:17:12 -0500 (Thu, 19 Jun 2008) | 3 lines In test_site, correctly escape backslashes in path names. This allows the test to pass when the username begins with a lowercase 't'... ........ r64416 | vinay.sajip | 2008-06-19 17:40:17 -0500 (Thu, 19 Jun 2008) | 2 lines Bug #3136: fileConfig()'s disabling of old loggers is now conditional via an optional disable_existing_loggers parameter, but the default value is such that the old behaviour is preserved. Thanks to Leandro Lucarella for the patch. ........ r64417 | vinay.sajip | 2008-06-19 17:41:08 -0500 (Thu, 19 Jun 2008) | 1 line Updated with fix for #3136. ........ r64420 | andrew.kuchling | 2008-06-19 21:05:57 -0500 (Thu, 19 Jun 2008) | 1 line Various items ........ r64421 | andrew.kuchling | 2008-06-19 21:11:42 -0500 (Thu, 19 Jun 2008) | 1 line Fix comment typos ........ r64425 | andrew.kuchling | 2008-06-20 06:39:54 -0500 (Fri, 20 Jun 2008) | 1 line Various items ........ r64426 | mark.dickinson | 2008-06-20 09:53:43 -0500 (Fri, 20 Jun 2008) | 4 lines Issue #3004: Minor fix to slice.indices(). slice(-10).indices(9) now returns (0, 0, 1) instead of (0, -1, 1), and slice(None, 10, -1).indices(10) returns (9, 9, -1) instead of (9, 10, -1). ........ r64427 | mark.dickinson | 2008-06-20 10:17:41 -0500 (Fri, 20 Jun 2008) | 2 lines Fix outdated count of the number of new math module functions. ........ r64428 | mark.dickinson | 2008-06-20 10:26:19 -0500 (Fri, 20 Jun 2008) | 2 lines Fix another typo in math_sum comment ........
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Return *x* factorial. Raises :exc:`ValueError` if *x* is not integral or
Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r64002 | travis.oliphant | 2008-06-07 00:33:21 +0200 (Sat, 07 Jun 2008) | 1 line Add long double check support to configure test. ........ r64003 | travis.oliphant | 2008-06-07 00:39:47 +0200 (Sat, 07 Jun 2008) | 1 line Remove locking part of new buffer protocol. ........ r64012 | facundo.batista | 2008-06-07 15:36:36 +0200 (Sat, 07 Jun 2008) | 4 lines Finished bug #2451. Fixed the retrying part to make it more robust. ........ r64036 | georg.brandl | 2008-06-08 10:54:40 +0200 (Sun, 08 Jun 2008) | 2 lines #3028: tokenize passes the physical line. ........ r64037 | georg.brandl | 2008-06-08 10:59:38 +0200 (Sun, 08 Jun 2008) | 2 lines Argh, I read it wrong. Reverted 64036 and added a clarifying remark. ........ r64047 | raymond.hettinger | 2008-06-09 03:28:30 +0200 (Mon, 09 Jun 2008) | 1 line Issue3065: Fixed pickling of named tuples. Added tests. ........ r64050 | raymond.hettinger | 2008-06-09 08:54:45 +0200 (Mon, 09 Jun 2008) | 1 line Issue #2138: Add math.factorial(). ........ r64051 | raymond.hettinger | 2008-06-09 10:33:37 +0200 (Mon, 09 Jun 2008) | 1 line Let set.union() and set.update() accept multiple inputs. ........ r64052 | raymond.hettinger | 2008-06-09 11:29:17 +0200 (Mon, 09 Jun 2008) | 1 line Address double-rounding scenarios by setting all variables to long doubles. ........ r64054 | raymond.hettinger | 2008-06-09 13:24:47 +0200 (Mon, 09 Jun 2008) | 1 line Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. ........ r64055 | raymond.hettinger | 2008-06-09 15:07:27 +0200 (Mon, 09 Jun 2008) | 1 line Let set.intersection() and set.intersection_update() take multiple input arguments. ........ r64066 | robert.schuppenies | 2008-06-10 12:10:31 +0200 (Tue, 10 Jun 2008) | 2 lines Issue 3048: Fixed sys.getsizeof for unicode objects. ........ r64071 | thomas.heller | 2008-06-10 16:07:12 +0200 (Tue, 10 Jun 2008) | 3 lines NEWS entry for: Add an optional 'offset' parameter to byref, defaulting to zero. ........
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is negative.
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.. function:: floor(x)
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Return the floor of *x*, the largest integer less than or equal to *x*.
If *x* is not a float, delegates to ``x.__floor__()``, which should return an
:class:`~numbers.Integral` value.
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.. function:: fmod(x, y)
Return ``fmod(x, y)``, as defined by the platform C library. Note that the
Python expression ``x % y`` may not return the same result. The intent of the C
standard is that ``fmod(x, y)`` be exactly (mathematically; to infinite
precision) equal to ``x - n*y`` for some integer *n* such that the result has
the same sign as *x* and magnitude less than ``abs(y)``. Python's ``x % y``
returns a result with the sign of *y* instead, and may not be exactly computable
for float arguments. For example, ``fmod(-1e-100, 1e100)`` is ``-1e-100``, but
the result of Python's ``-1e-100 % 1e100`` is ``1e100-1e-100``, which cannot be
represented exactly as a float, and rounds to the surprising ``1e100``. For
this reason, function :func:`fmod` is generally preferred when working with
floats, while Python's ``x % y`` is preferred when working with integers.
.. function:: frexp(x)
Return the mantissa and exponent of *x* as the pair ``(m, e)``. *m* is a float
and *e* is an integer such that ``x == m * 2**e`` exactly. If *x* is zero,
returns ``(0.0, 0)``, otherwise ``0.5 <= abs(m) < 1``. This is used to "pick
apart" the internal representation of a float in a portable way.
Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r65258 | mark.dickinson | 2008-07-27 08:15:29 +0100 (Sun, 27 Jul 2008) | 4 lines Remove math.sum tests related to overflow, special values, and behaviour near the extremes of the floating-point range. (The behaviour of math.sum should be regarded as undefined in these cases.) ........ r65292 | mark.dickinson | 2008-07-29 19:45:38 +0100 (Tue, 29 Jul 2008) | 4 lines More modifications to tests for math.sum: replace the Python version of msum by a version using a different algorithm, and use the new float.fromhex method to specify test results exactly. ........ r65299 | mark.dickinson | 2008-07-30 13:01:41 +0100 (Wed, 30 Jul 2008) | 5 lines Fix special-value handling for math.sum. Also minor cleanups to the code: fix tabbing, remove trailing whitespace, and reformat to fit into 80 columns. ........ r65308 | mark.dickinson | 2008-07-30 17:20:10 +0100 (Wed, 30 Jul 2008) | 2 lines Rename math.sum to math.fsum ........ r65309 | mark.dickinson | 2008-07-30 17:25:16 +0100 (Wed, 30 Jul 2008) | 3 lines Replace math.sum with math.fsum in a couple of comments that were missed by r65308 ........ r65315 | mark.dickinson | 2008-07-30 21:23:15 +0100 (Wed, 30 Jul 2008) | 2 lines Add note about problems with math.fsum on x86 hardware. ........ r65326 | mark.dickinson | 2008-07-31 15:48:32 +0100 (Thu, 31 Jul 2008) | 2 lines Rename testSum to testFsum and move it to proper place in test_math.py ........
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.. function:: fsum(iterable)
Return an accurate floating point sum of values in the iterable. Avoids
loss of precision by tracking multiple intermediate partial sums::
>>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
0.9999999999999999
>>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
1.0
The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the
typical case where the rounding mode is half-even. On some non-Windows
builds, the underlying C library uses extended precision addition and may
occasionally double-round an intermediate sum causing it to be off in its
least significant bit.
Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r65258 | mark.dickinson | 2008-07-27 08:15:29 +0100 (Sun, 27 Jul 2008) | 4 lines Remove math.sum tests related to overflow, special values, and behaviour near the extremes of the floating-point range. (The behaviour of math.sum should be regarded as undefined in these cases.) ........ r65292 | mark.dickinson | 2008-07-29 19:45:38 +0100 (Tue, 29 Jul 2008) | 4 lines More modifications to tests for math.sum: replace the Python version of msum by a version using a different algorithm, and use the new float.fromhex method to specify test results exactly. ........ r65299 | mark.dickinson | 2008-07-30 13:01:41 +0100 (Wed, 30 Jul 2008) | 5 lines Fix special-value handling for math.sum. Also minor cleanups to the code: fix tabbing, remove trailing whitespace, and reformat to fit into 80 columns. ........ r65308 | mark.dickinson | 2008-07-30 17:20:10 +0100 (Wed, 30 Jul 2008) | 2 lines Rename math.sum to math.fsum ........ r65309 | mark.dickinson | 2008-07-30 17:25:16 +0100 (Wed, 30 Jul 2008) | 3 lines Replace math.sum with math.fsum in a couple of comments that were missed by r65308 ........ r65315 | mark.dickinson | 2008-07-30 21:23:15 +0100 (Wed, 30 Jul 2008) | 2 lines Add note about problems with math.fsum on x86 hardware. ........ r65326 | mark.dickinson | 2008-07-31 15:48:32 +0100 (Thu, 31 Jul 2008) | 2 lines Rename testSum to testFsum and move it to proper place in test_math.py ........
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For further discussion and two alternative approaches, see the `ASPN cookbook
recipes for accurate floating point summation
<http://code.activestate.com/recipes/393090/>`_\.
Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r65258 | mark.dickinson | 2008-07-27 08:15:29 +0100 (Sun, 27 Jul 2008) | 4 lines Remove math.sum tests related to overflow, special values, and behaviour near the extremes of the floating-point range. (The behaviour of math.sum should be regarded as undefined in these cases.) ........ r65292 | mark.dickinson | 2008-07-29 19:45:38 +0100 (Tue, 29 Jul 2008) | 4 lines More modifications to tests for math.sum: replace the Python version of msum by a version using a different algorithm, and use the new float.fromhex method to specify test results exactly. ........ r65299 | mark.dickinson | 2008-07-30 13:01:41 +0100 (Wed, 30 Jul 2008) | 5 lines Fix special-value handling for math.sum. Also minor cleanups to the code: fix tabbing, remove trailing whitespace, and reformat to fit into 80 columns. ........ r65308 | mark.dickinson | 2008-07-30 17:20:10 +0100 (Wed, 30 Jul 2008) | 2 lines Rename math.sum to math.fsum ........ r65309 | mark.dickinson | 2008-07-30 17:25:16 +0100 (Wed, 30 Jul 2008) | 3 lines Replace math.sum with math.fsum in a couple of comments that were missed by r65308 ........ r65315 | mark.dickinson | 2008-07-30 21:23:15 +0100 (Wed, 30 Jul 2008) | 2 lines Add note about problems with math.fsum on x86 hardware. ........ r65326 | mark.dickinson | 2008-07-31 15:48:32 +0100 (Thu, 31 Jul 2008) | 2 lines Rename testSum to testFsum and move it to proper place in test_math.py ........
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.. function:: isfinite(x)
Return ``True`` if *x* is neither an infinity nor a NaN, and
``False`` otherwise. (Note that ``0.0`` *is* considered finite.)
.. versionadded:: 3.2
Merged revisions 59666-59679 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59666 | christian.heimes | 2008-01-02 19:28:32 +0100 (Wed, 02 Jan 2008) | 1 line Made vs9to8 Unix compatible ........ r59669 | guido.van.rossum | 2008-01-02 20:00:46 +0100 (Wed, 02 Jan 2008) | 2 lines Patch #1696. Don't attempt to close None in dry-run mode. ........ r59671 | jeffrey.yasskin | 2008-01-03 03:21:52 +0100 (Thu, 03 Jan 2008) | 6 lines Backport PEP 3141 from the py3k branch to the trunk. This includes r50877 (just the complex_pow part), r56649, r56652, r56715, r57296, r57302, r57359, r57361, r57372, r57738, r57739, r58017, r58039, r58040, and r59390, and new documentation. The only significant difference is that round(x) returns a float to preserve backward-compatibility. See http://bugs.python.org/issue1689. ........ r59672 | christian.heimes | 2008-01-03 16:41:30 +0100 (Thu, 03 Jan 2008) | 1 line Issue #1726: Remove Python/atof.c from PCBuild/pythoncore.vcproj ........ r59675 | guido.van.rossum | 2008-01-03 20:12:44 +0100 (Thu, 03 Jan 2008) | 4 lines Issue #1700, reported by Nguyen Quan Son, fix by Fredruk Lundh: Regular Expression inline flags not handled correctly for some unicode characters. (Forward port from 2.5.2.) ........ r59676 | christian.heimes | 2008-01-03 21:23:15 +0100 (Thu, 03 Jan 2008) | 1 line Added math.isinf() and math.isnan() ........ r59677 | christian.heimes | 2008-01-03 22:14:48 +0100 (Thu, 03 Jan 2008) | 1 line Some build bots don't compile mathmodule. There is an issue with the long definition of pi and euler ........ r59678 | christian.heimes | 2008-01-03 23:16:32 +0100 (Thu, 03 Jan 2008) | 2 lines Modified PyImport_Import and PyImport_ImportModule to always use absolute imports by calling __import__ with an explicit level of 0 Added a new API function PyImport_ImportModuleNoBlock. It solves the problem with dead locks when mixing threads and imports ........ r59679 | christian.heimes | 2008-01-03 23:32:26 +0100 (Thu, 03 Jan 2008) | 1 line Added copysign(x, y) function to the math module ........
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.. function:: isinf(x)
Return ``True`` if *x* is a positive or negative infinity, and
``False`` otherwise.
Merged revisions 59666-59679 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59666 | christian.heimes | 2008-01-02 19:28:32 +0100 (Wed, 02 Jan 2008) | 1 line Made vs9to8 Unix compatible ........ r59669 | guido.van.rossum | 2008-01-02 20:00:46 +0100 (Wed, 02 Jan 2008) | 2 lines Patch #1696. Don't attempt to close None in dry-run mode. ........ r59671 | jeffrey.yasskin | 2008-01-03 03:21:52 +0100 (Thu, 03 Jan 2008) | 6 lines Backport PEP 3141 from the py3k branch to the trunk. This includes r50877 (just the complex_pow part), r56649, r56652, r56715, r57296, r57302, r57359, r57361, r57372, r57738, r57739, r58017, r58039, r58040, and r59390, and new documentation. The only significant difference is that round(x) returns a float to preserve backward-compatibility. See http://bugs.python.org/issue1689. ........ r59672 | christian.heimes | 2008-01-03 16:41:30 +0100 (Thu, 03 Jan 2008) | 1 line Issue #1726: Remove Python/atof.c from PCBuild/pythoncore.vcproj ........ r59675 | guido.van.rossum | 2008-01-03 20:12:44 +0100 (Thu, 03 Jan 2008) | 4 lines Issue #1700, reported by Nguyen Quan Son, fix by Fredruk Lundh: Regular Expression inline flags not handled correctly for some unicode characters. (Forward port from 2.5.2.) ........ r59676 | christian.heimes | 2008-01-03 21:23:15 +0100 (Thu, 03 Jan 2008) | 1 line Added math.isinf() and math.isnan() ........ r59677 | christian.heimes | 2008-01-03 22:14:48 +0100 (Thu, 03 Jan 2008) | 1 line Some build bots don't compile mathmodule. There is an issue with the long definition of pi and euler ........ r59678 | christian.heimes | 2008-01-03 23:16:32 +0100 (Thu, 03 Jan 2008) | 2 lines Modified PyImport_Import and PyImport_ImportModule to always use absolute imports by calling __import__ with an explicit level of 0 Added a new API function PyImport_ImportModuleNoBlock. It solves the problem with dead locks when mixing threads and imports ........ r59679 | christian.heimes | 2008-01-03 23:32:26 +0100 (Thu, 03 Jan 2008) | 1 line Added copysign(x, y) function to the math module ........
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.. function:: isnan(x)
Return ``True`` if *x* is a NaN (not a number), and ``False`` otherwise.
Merged revisions 59666-59679 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59666 | christian.heimes | 2008-01-02 19:28:32 +0100 (Wed, 02 Jan 2008) | 1 line Made vs9to8 Unix compatible ........ r59669 | guido.van.rossum | 2008-01-02 20:00:46 +0100 (Wed, 02 Jan 2008) | 2 lines Patch #1696. Don't attempt to close None in dry-run mode. ........ r59671 | jeffrey.yasskin | 2008-01-03 03:21:52 +0100 (Thu, 03 Jan 2008) | 6 lines Backport PEP 3141 from the py3k branch to the trunk. This includes r50877 (just the complex_pow part), r56649, r56652, r56715, r57296, r57302, r57359, r57361, r57372, r57738, r57739, r58017, r58039, r58040, and r59390, and new documentation. The only significant difference is that round(x) returns a float to preserve backward-compatibility. See http://bugs.python.org/issue1689. ........ r59672 | christian.heimes | 2008-01-03 16:41:30 +0100 (Thu, 03 Jan 2008) | 1 line Issue #1726: Remove Python/atof.c from PCBuild/pythoncore.vcproj ........ r59675 | guido.van.rossum | 2008-01-03 20:12:44 +0100 (Thu, 03 Jan 2008) | 4 lines Issue #1700, reported by Nguyen Quan Son, fix by Fredruk Lundh: Regular Expression inline flags not handled correctly for some unicode characters. (Forward port from 2.5.2.) ........ r59676 | christian.heimes | 2008-01-03 21:23:15 +0100 (Thu, 03 Jan 2008) | 1 line Added math.isinf() and math.isnan() ........ r59677 | christian.heimes | 2008-01-03 22:14:48 +0100 (Thu, 03 Jan 2008) | 1 line Some build bots don't compile mathmodule. There is an issue with the long definition of pi and euler ........ r59678 | christian.heimes | 2008-01-03 23:16:32 +0100 (Thu, 03 Jan 2008) | 2 lines Modified PyImport_Import and PyImport_ImportModule to always use absolute imports by calling __import__ with an explicit level of 0 Added a new API function PyImport_ImportModuleNoBlock. It solves the problem with dead locks when mixing threads and imports ........ r59679 | christian.heimes | 2008-01-03 23:32:26 +0100 (Thu, 03 Jan 2008) | 1 line Added copysign(x, y) function to the math module ........
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.. function:: ldexp(x, i)
Return ``x * (2**i)``. This is essentially the inverse of function
:func:`frexp`.
.. function:: modf(x)
Merged revisions 67654,67676-67677,67681,67692,67725,67761,67784-67785,67787-67788,67802,67848-67850,67862-67864,67880,67882 via svnmerge from 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 ........
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Return the fractional and integer parts of *x*. Both results carry the sign
of *x* and are floats.
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.. function:: trunc(x)
Return the :class:`~numbers.Real` value *x* truncated to an
:class:`~numbers.Integral` (usually an integer). Delegates to
``x.__trunc__()``.
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Note that :func:`frexp` and :func:`modf` have a different call/return pattern
than their C equivalents: they take a single argument and return a pair of
values, rather than returning their second return value through an 'output
parameter' (there is no such thing in Python).
For the :func:`ceil`, :func:`floor`, and :func:`modf` functions, note that *all*
floating-point numbers of sufficiently large magnitude are exact integers.
Python floats typically carry no more than 53 bits of precision (the same as the
platform C double type), in which case any float *x* with ``abs(x) >= 2**52``
necessarily has no fractional bits.
Merged revisions 67654,67676-67677,67681,67692,67725,67761,67784-67785,67787-67788,67802,67848-67850,67862-67864,67880,67882 via svnmerge from 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 ........
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Power and logarithmic functions
-------------------------------
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.. function:: exp(x)
Return ``e**x``.
.. function:: expm1(x)
Return ``e**x - 1``. For small floats *x*, the subtraction in ``exp(x) - 1``
can result in a `significant loss of precision
<http://en.wikipedia.org/wiki/Loss_of_significance>`_\; the :func:`expm1`
function provides a way to compute this quantity to full precision::
>>> from math import exp, expm1
>>> exp(1e-5) - 1 # gives result accurate to 11 places
1.0000050000069649e-05
>>> expm1(1e-5) # result accurate to full precision
1.0000050000166668e-05
.. versionadded:: 3.2
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.. function:: log(x[, base])
Merged revisions 74542,74544-74548,74550,74554-74555,74578,74588,74590,74603,74616-74618,74621 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r74542 | georg.brandl | 2009-08-23 23:28:56 +0200 (So, 23 Aug 2009) | 1 line Restore alphabetic order. ........ r74544 | georg.brandl | 2009-08-24 19:12:30 +0200 (Mo, 24 Aug 2009) | 1 line #6775: fix python.org URLs in README. ........ r74545 | georg.brandl | 2009-08-24 19:14:29 +0200 (Mo, 24 Aug 2009) | 1 line #6772: mention utf-8 as utf8 alias. ........ r74546 | georg.brandl | 2009-08-24 19:20:40 +0200 (Mo, 24 Aug 2009) | 1 line #6725: spell "namespace" consistently. ........ r74547 | georg.brandl | 2009-08-24 19:22:05 +0200 (Mo, 24 Aug 2009) | 1 line #6718: fix example. ........ r74548 | georg.brandl | 2009-08-24 19:24:27 +0200 (Mo, 24 Aug 2009) | 1 line #6677: mention "deleting" as an alias for removing files. ........ r74550 | georg.brandl | 2009-08-24 19:48:40 +0200 (Mo, 24 Aug 2009) | 1 line #6677: note that rmdir only removes empty directories. ........ r74554 | georg.brandl | 2009-08-27 20:59:02 +0200 (Do, 27 Aug 2009) | 1 line Typo fix. ........ r74555 | georg.brandl | 2009-08-27 21:02:43 +0200 (Do, 27 Aug 2009) | 1 line #6787: reference fix. ........ r74578 | tarek.ziade | 2009-08-29 15:33:21 +0200 (Sa, 29 Aug 2009) | 1 line fixed #6801: symmetric_difference_update also accepts pipe ........ r74588 | georg.brandl | 2009-08-30 10:35:01 +0200 (So, 30 Aug 2009) | 1 line #6803: fix old name. ........ r74590 | georg.brandl | 2009-08-30 13:51:53 +0200 (So, 30 Aug 2009) | 1 line #6801: fix copy-paste oversight. ........ r74603 | georg.brandl | 2009-08-31 08:38:29 +0200 (Mo, 31 Aug 2009) | 1 line other -> others where multiple arguments are accepted. ........ r74616 | georg.brandl | 2009-09-01 09:46:26 +0200 (Di, 01 Sep 2009) | 1 line #6808: clarification. ........ r74617 | georg.brandl | 2009-09-01 09:53:37 +0200 (Di, 01 Sep 2009) | 1 line #6765: hint that log(x, base) is not very sophisticated. ........ r74618 | georg.brandl | 2009-09-01 10:00:47 +0200 (Di, 01 Sep 2009) | 1 line #6810: add a link to the section about frame objects instead of just a description where to find it. ........ r74621 | georg.brandl | 2009-09-01 10:06:03 +0200 (Di, 01 Sep 2009) | 1 line #6638: fix wrong parameter name and markup a class. ........
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With one argument, return the natural logarithm of *x* (to base *e*).
With two arguments, return the logarithm of *x* to the given *base*,
calculated as ``log(x)/log(base)``.
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.. function:: log1p(x)
Return the natural logarithm of *1+x* (base *e*). The
result is calculated in a way which is accurate for *x* near zero.
.. function:: log2(x)
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Return the base-2 logarithm of *x*. This is usually more accurate than
``log(x, 2)``.
.. versionadded:: 3.3
.. seealso::
:meth:`int.bit_length` returns the number of bits necessary to represent
an integer in binary, excluding the sign and leading zeros.
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.. function:: log10(x)
Merged revisions 74542,74544-74548,74550,74554-74555,74578,74588,74590,74603,74616-74618,74621 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r74542 | georg.brandl | 2009-08-23 23:28:56 +0200 (So, 23 Aug 2009) | 1 line Restore alphabetic order. ........ r74544 | georg.brandl | 2009-08-24 19:12:30 +0200 (Mo, 24 Aug 2009) | 1 line #6775: fix python.org URLs in README. ........ r74545 | georg.brandl | 2009-08-24 19:14:29 +0200 (Mo, 24 Aug 2009) | 1 line #6772: mention utf-8 as utf8 alias. ........ r74546 | georg.brandl | 2009-08-24 19:20:40 +0200 (Mo, 24 Aug 2009) | 1 line #6725: spell "namespace" consistently. ........ r74547 | georg.brandl | 2009-08-24 19:22:05 +0200 (Mo, 24 Aug 2009) | 1 line #6718: fix example. ........ r74548 | georg.brandl | 2009-08-24 19:24:27 +0200 (Mo, 24 Aug 2009) | 1 line #6677: mention "deleting" as an alias for removing files. ........ r74550 | georg.brandl | 2009-08-24 19:48:40 +0200 (Mo, 24 Aug 2009) | 1 line #6677: note that rmdir only removes empty directories. ........ r74554 | georg.brandl | 2009-08-27 20:59:02 +0200 (Do, 27 Aug 2009) | 1 line Typo fix. ........ r74555 | georg.brandl | 2009-08-27 21:02:43 +0200 (Do, 27 Aug 2009) | 1 line #6787: reference fix. ........ r74578 | tarek.ziade | 2009-08-29 15:33:21 +0200 (Sa, 29 Aug 2009) | 1 line fixed #6801: symmetric_difference_update also accepts pipe ........ r74588 | georg.brandl | 2009-08-30 10:35:01 +0200 (So, 30 Aug 2009) | 1 line #6803: fix old name. ........ r74590 | georg.brandl | 2009-08-30 13:51:53 +0200 (So, 30 Aug 2009) | 1 line #6801: fix copy-paste oversight. ........ r74603 | georg.brandl | 2009-08-31 08:38:29 +0200 (Mo, 31 Aug 2009) | 1 line other -> others where multiple arguments are accepted. ........ r74616 | georg.brandl | 2009-09-01 09:46:26 +0200 (Di, 01 Sep 2009) | 1 line #6808: clarification. ........ r74617 | georg.brandl | 2009-09-01 09:53:37 +0200 (Di, 01 Sep 2009) | 1 line #6765: hint that log(x, base) is not very sophisticated. ........ r74618 | georg.brandl | 2009-09-01 10:00:47 +0200 (Di, 01 Sep 2009) | 1 line #6810: add a link to the section about frame objects instead of just a description where to find it. ........ r74621 | georg.brandl | 2009-09-01 10:06:03 +0200 (Di, 01 Sep 2009) | 1 line #6638: fix wrong parameter name and markup a class. ........
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Return the base-10 logarithm of *x*. This is usually more accurate
than ``log(x, 10)``.
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.. function:: pow(x, y)
Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r62386 | christian.heimes | 2008-04-19 04:23:57 +0200 (Sat, 19 Apr 2008) | 2 lines Added kill, terminate and send_signal to subprocess.Popen The bits and pieces for the Windows side were already in place. The POSIX side is trivial (as usual) and uses os.kill(). ........ r62387 | georg.brandl | 2008-04-19 10:23:59 +0200 (Sat, 19 Apr 2008) | 2 lines Fix-up docs for revision 62386. ........ r62389 | georg.brandl | 2008-04-19 18:57:43 +0200 (Sat, 19 Apr 2008) | 2 lines #2369: clarify that copyfile() doesn't take a target directory. ........ r62390 | georg.brandl | 2008-04-19 18:58:28 +0200 (Sat, 19 Apr 2008) | 2 lines #2634: clarify meaning of env parameter to spawn/exec*e. ........ r62391 | georg.brandl | 2008-04-19 18:58:49 +0200 (Sat, 19 Apr 2008) | 2 lines #2633: clarify meaning of env parameter. ........ r62392 | georg.brandl | 2008-04-19 18:59:16 +0200 (Sat, 19 Apr 2008) | 2 lines #2631: clarify IMPORT_NAME semantics. ........ r62393 | georg.brandl | 2008-04-19 19:00:14 +0200 (Sat, 19 Apr 2008) | 2 lines :func: et al. should *not* include the parens. ........ r62396 | mark.dickinson | 2008-04-19 20:51:48 +0200 (Sat, 19 Apr 2008) | 5 lines Additional tests for math.pow, and extra special-case handling code in math.pow, in the hope of making all tests pass on the alpha Tru64 buildbot. ........ r62400 | mark.dickinson | 2008-04-19 21:41:52 +0200 (Sat, 19 Apr 2008) | 3 lines Additional special-case handling for math.pow. Windows/VS2008 doesn't like (-1)**(+-inf). ........ r62401 | benjamin.peterson | 2008-04-19 21:47:34 +0200 (Sat, 19 Apr 2008) | 2 lines Complete documentation for errors argument of io's open and TextIOWrapper ........ r62402 | mark.dickinson | 2008-04-19 22:31:16 +0200 (Sat, 19 Apr 2008) | 2 lines Document updates to math and cmath modules. ........ r62407 | georg.brandl | 2008-04-19 23:28:38 +0200 (Sat, 19 Apr 2008) | 2 lines Update template for newest Sphinx. ........ r62409 | mark.dickinson | 2008-04-19 23:35:35 +0200 (Sat, 19 Apr 2008) | 5 lines Correct documentation for math.pow; 0**nan is nan, not 0. (But nan**0 and 1**nan are 1.) Also fix minor typo: 'quite NaN' -> 'quiet NaN' ........ r62410 | mark.dickinson | 2008-04-19 23:49:22 +0200 (Sat, 19 Apr 2008) | 4 lines Move asinh documentation to the proper place. Remove meaningless 'in radians' from inverse hyperbolic functions. ........ r62412 | mark.dickinson | 2008-04-20 03:22:30 +0200 (Sun, 20 Apr 2008) | 5 lines Report additional diagnostic information in test_math, to help track down debian-alpha buildbot failure. ........ r62413 | mark.dickinson | 2008-04-20 03:39:24 +0200 (Sun, 20 Apr 2008) | 3 lines FreeBSD doesn't follow C99 for modf(inf); so add explicit special-value handling to math.modf code. ........ r62414 | mark.dickinson | 2008-04-20 06:13:13 +0200 (Sun, 20 Apr 2008) | 5 lines Yet more explicit special case handling to make math.pow behave on alpha Tru64. All IEEE 754 special values are now handled directly; only the finite**finite case is handled by libm. ........ r62418 | mark.dickinson | 2008-04-20 18:13:17 +0200 (Sun, 20 Apr 2008) | 7 lines Issue 2662: Initialize special value tables dynamically (i.e. when cmath module is loaded) instead of statically. This fixes compile-time problems on platforms where HUGE_VAL is an extern variable rather than a constant. Thanks Hirokazu Yamamoto for the patch. ........ r62419 | andrew.kuchling | 2008-04-20 18:54:02 +0200 (Sun, 20 Apr 2008) | 1 line Move description of math module changes; various edits to description of cmath changes ........
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Return ``x`` raised to the power ``y``. Exceptional cases follow
Annex 'F' of the C99 standard as far as possible. In particular,
``pow(1.0, x)`` and ``pow(x, 0.0)`` always return ``1.0``, even
when ``x`` is a zero or a NaN. If both ``x`` and ``y`` are finite,
``x`` is negative, and ``y`` is not an integer then ``pow(x, y)``
is undefined, and raises :exc:`ValueError`.
Unlike the built-in ``**`` operator, :func:`math.pow` converts both
its arguments to type :class:`float`. Use ``**`` or the built-in
:func:`pow` function for computing exact integer powers.
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.. function:: sqrt(x)
Return the square root of *x*.
Merged revisions 67654,67676-67677,67681,67692,67725,67761,67784-67785,67787-67788,67802,67848-67850,67862-67864,67880,67882 via svnmerge from 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 ........
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Trigonometric functions
-----------------------
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.. function:: acos(x)
Return the arc cosine of *x*, in radians.
.. function:: asin(x)
Return the arc sine of *x*, in radians.
.. function:: atan(x)
Return the arc tangent of *x*, in radians.
.. function:: atan2(y, x)
Return ``atan(y / x)``, in radians. The result is between ``-pi`` and ``pi``.
The vector in the plane from the origin to point ``(x, y)`` makes this angle
with the positive X axis. The point of :func:`atan2` is that the signs of both
inputs are known to it, so it can compute the correct quadrant for the angle.
For example, ``atan(1)`` and ``atan2(1, 1)`` are both ``pi/4``, but ``atan2(-1,
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-1)`` is ``-3*pi/4``.
.. function:: cos(x)
Return the cosine of *x* radians.
.. function:: hypot(x, y)
Return the Euclidean norm, ``sqrt(x*x + y*y)``. This is the length of the vector
from the origin to point ``(x, y)``.
.. function:: sin(x)
Return the sine of *x* radians.
.. function:: tan(x)
Return the tangent of *x* radians.
Merged revisions 67654,67676-67677,67681,67692,67725,67761,67784-67785,67787-67788,67802,67848-67850,67862-67864,67880,67882 via svnmerge from 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 ........
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Angular conversion
------------------
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.. function:: degrees(x)
Converts angle *x* from radians to degrees.
.. function:: radians(x)
Converts angle *x* from degrees to radians.
Merged revisions 67654,67676-67677,67681,67692,67725,67761,67784-67785,67787-67788,67802,67848-67850,67862-67864,67880,67882 via svnmerge from 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 ........
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Hyperbolic functions
--------------------
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`Hyperbolic functions <http://en.wikipedia.org/wiki/Hyperbolic_function>`_
are analogs of trigonometric functions that are based on hyperbolas
instead of circles.
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Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r62386 | christian.heimes | 2008-04-19 04:23:57 +0200 (Sat, 19 Apr 2008) | 2 lines Added kill, terminate and send_signal to subprocess.Popen The bits and pieces for the Windows side were already in place. The POSIX side is trivial (as usual) and uses os.kill(). ........ r62387 | georg.brandl | 2008-04-19 10:23:59 +0200 (Sat, 19 Apr 2008) | 2 lines Fix-up docs for revision 62386. ........ r62389 | georg.brandl | 2008-04-19 18:57:43 +0200 (Sat, 19 Apr 2008) | 2 lines #2369: clarify that copyfile() doesn't take a target directory. ........ r62390 | georg.brandl | 2008-04-19 18:58:28 +0200 (Sat, 19 Apr 2008) | 2 lines #2634: clarify meaning of env parameter to spawn/exec*e. ........ r62391 | georg.brandl | 2008-04-19 18:58:49 +0200 (Sat, 19 Apr 2008) | 2 lines #2633: clarify meaning of env parameter. ........ r62392 | georg.brandl | 2008-04-19 18:59:16 +0200 (Sat, 19 Apr 2008) | 2 lines #2631: clarify IMPORT_NAME semantics. ........ r62393 | georg.brandl | 2008-04-19 19:00:14 +0200 (Sat, 19 Apr 2008) | 2 lines :func: et al. should *not* include the parens. ........ r62396 | mark.dickinson | 2008-04-19 20:51:48 +0200 (Sat, 19 Apr 2008) | 5 lines Additional tests for math.pow, and extra special-case handling code in math.pow, in the hope of making all tests pass on the alpha Tru64 buildbot. ........ r62400 | mark.dickinson | 2008-04-19 21:41:52 +0200 (Sat, 19 Apr 2008) | 3 lines Additional special-case handling for math.pow. Windows/VS2008 doesn't like (-1)**(+-inf). ........ r62401 | benjamin.peterson | 2008-04-19 21:47:34 +0200 (Sat, 19 Apr 2008) | 2 lines Complete documentation for errors argument of io's open and TextIOWrapper ........ r62402 | mark.dickinson | 2008-04-19 22:31:16 +0200 (Sat, 19 Apr 2008) | 2 lines Document updates to math and cmath modules. ........ r62407 | georg.brandl | 2008-04-19 23:28:38 +0200 (Sat, 19 Apr 2008) | 2 lines Update template for newest Sphinx. ........ r62409 | mark.dickinson | 2008-04-19 23:35:35 +0200 (Sat, 19 Apr 2008) | 5 lines Correct documentation for math.pow; 0**nan is nan, not 0. (But nan**0 and 1**nan are 1.) Also fix minor typo: 'quite NaN' -> 'quiet NaN' ........ r62410 | mark.dickinson | 2008-04-19 23:49:22 +0200 (Sat, 19 Apr 2008) | 4 lines Move asinh documentation to the proper place. Remove meaningless 'in radians' from inverse hyperbolic functions. ........ r62412 | mark.dickinson | 2008-04-20 03:22:30 +0200 (Sun, 20 Apr 2008) | 5 lines Report additional diagnostic information in test_math, to help track down debian-alpha buildbot failure. ........ r62413 | mark.dickinson | 2008-04-20 03:39:24 +0200 (Sun, 20 Apr 2008) | 3 lines FreeBSD doesn't follow C99 for modf(inf); so add explicit special-value handling to math.modf code. ........ r62414 | mark.dickinson | 2008-04-20 06:13:13 +0200 (Sun, 20 Apr 2008) | 5 lines Yet more explicit special case handling to make math.pow behave on alpha Tru64. All IEEE 754 special values are now handled directly; only the finite**finite case is handled by libm. ........ r62418 | mark.dickinson | 2008-04-20 18:13:17 +0200 (Sun, 20 Apr 2008) | 7 lines Issue 2662: Initialize special value tables dynamically (i.e. when cmath module is loaded) instead of statically. This fixes compile-time problems on platforms where HUGE_VAL is an extern variable rather than a constant. Thanks Hirokazu Yamamoto for the patch. ........ r62419 | andrew.kuchling | 2008-04-20 18:54:02 +0200 (Sun, 20 Apr 2008) | 1 line Move description of math module changes; various edits to description of cmath changes ........
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.. function:: acosh(x)
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Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r62386 | christian.heimes | 2008-04-19 04:23:57 +0200 (Sat, 19 Apr 2008) | 2 lines Added kill, terminate and send_signal to subprocess.Popen The bits and pieces for the Windows side were already in place. The POSIX side is trivial (as usual) and uses os.kill(). ........ r62387 | georg.brandl | 2008-04-19 10:23:59 +0200 (Sat, 19 Apr 2008) | 2 lines Fix-up docs for revision 62386. ........ r62389 | georg.brandl | 2008-04-19 18:57:43 +0200 (Sat, 19 Apr 2008) | 2 lines #2369: clarify that copyfile() doesn't take a target directory. ........ r62390 | georg.brandl | 2008-04-19 18:58:28 +0200 (Sat, 19 Apr 2008) | 2 lines #2634: clarify meaning of env parameter to spawn/exec*e. ........ r62391 | georg.brandl | 2008-04-19 18:58:49 +0200 (Sat, 19 Apr 2008) | 2 lines #2633: clarify meaning of env parameter. ........ r62392 | georg.brandl | 2008-04-19 18:59:16 +0200 (Sat, 19 Apr 2008) | 2 lines #2631: clarify IMPORT_NAME semantics. ........ r62393 | georg.brandl | 2008-04-19 19:00:14 +0200 (Sat, 19 Apr 2008) | 2 lines :func: et al. should *not* include the parens. ........ r62396 | mark.dickinson | 2008-04-19 20:51:48 +0200 (Sat, 19 Apr 2008) | 5 lines Additional tests for math.pow, and extra special-case handling code in math.pow, in the hope of making all tests pass on the alpha Tru64 buildbot. ........ r62400 | mark.dickinson | 2008-04-19 21:41:52 +0200 (Sat, 19 Apr 2008) | 3 lines Additional special-case handling for math.pow. Windows/VS2008 doesn't like (-1)**(+-inf). ........ r62401 | benjamin.peterson | 2008-04-19 21:47:34 +0200 (Sat, 19 Apr 2008) | 2 lines Complete documentation for errors argument of io's open and TextIOWrapper ........ r62402 | mark.dickinson | 2008-04-19 22:31:16 +0200 (Sat, 19 Apr 2008) | 2 lines Document updates to math and cmath modules. ........ r62407 | georg.brandl | 2008-04-19 23:28:38 +0200 (Sat, 19 Apr 2008) | 2 lines Update template for newest Sphinx. ........ r62409 | mark.dickinson | 2008-04-19 23:35:35 +0200 (Sat, 19 Apr 2008) | 5 lines Correct documentation for math.pow; 0**nan is nan, not 0. (But nan**0 and 1**nan are 1.) Also fix minor typo: 'quite NaN' -> 'quiet NaN' ........ r62410 | mark.dickinson | 2008-04-19 23:49:22 +0200 (Sat, 19 Apr 2008) | 4 lines Move asinh documentation to the proper place. Remove meaningless 'in radians' from inverse hyperbolic functions. ........ r62412 | mark.dickinson | 2008-04-20 03:22:30 +0200 (Sun, 20 Apr 2008) | 5 lines Report additional diagnostic information in test_math, to help track down debian-alpha buildbot failure. ........ r62413 | mark.dickinson | 2008-04-20 03:39:24 +0200 (Sun, 20 Apr 2008) | 3 lines FreeBSD doesn't follow C99 for modf(inf); so add explicit special-value handling to math.modf code. ........ r62414 | mark.dickinson | 2008-04-20 06:13:13 +0200 (Sun, 20 Apr 2008) | 5 lines Yet more explicit special case handling to make math.pow behave on alpha Tru64. All IEEE 754 special values are now handled directly; only the finite**finite case is handled by libm. ........ r62418 | mark.dickinson | 2008-04-20 18:13:17 +0200 (Sun, 20 Apr 2008) | 7 lines Issue 2662: Initialize special value tables dynamically (i.e. when cmath module is loaded) instead of statically. This fixes compile-time problems on platforms where HUGE_VAL is an extern variable rather than a constant. Thanks Hirokazu Yamamoto for the patch. ........ r62419 | andrew.kuchling | 2008-04-20 18:54:02 +0200 (Sun, 20 Apr 2008) | 1 line Move description of math module changes; various edits to description of cmath changes ........
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Return the inverse hyperbolic cosine of *x*.
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Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r62386 | christian.heimes | 2008-04-19 04:23:57 +0200 (Sat, 19 Apr 2008) | 2 lines Added kill, terminate and send_signal to subprocess.Popen The bits and pieces for the Windows side were already in place. The POSIX side is trivial (as usual) and uses os.kill(). ........ r62387 | georg.brandl | 2008-04-19 10:23:59 +0200 (Sat, 19 Apr 2008) | 2 lines Fix-up docs for revision 62386. ........ r62389 | georg.brandl | 2008-04-19 18:57:43 +0200 (Sat, 19 Apr 2008) | 2 lines #2369: clarify that copyfile() doesn't take a target directory. ........ r62390 | georg.brandl | 2008-04-19 18:58:28 +0200 (Sat, 19 Apr 2008) | 2 lines #2634: clarify meaning of env parameter to spawn/exec*e. ........ r62391 | georg.brandl | 2008-04-19 18:58:49 +0200 (Sat, 19 Apr 2008) | 2 lines #2633: clarify meaning of env parameter. ........ r62392 | georg.brandl | 2008-04-19 18:59:16 +0200 (Sat, 19 Apr 2008) | 2 lines #2631: clarify IMPORT_NAME semantics. ........ r62393 | georg.brandl | 2008-04-19 19:00:14 +0200 (Sat, 19 Apr 2008) | 2 lines :func: et al. should *not* include the parens. ........ r62396 | mark.dickinson | 2008-04-19 20:51:48 +0200 (Sat, 19 Apr 2008) | 5 lines Additional tests for math.pow, and extra special-case handling code in math.pow, in the hope of making all tests pass on the alpha Tru64 buildbot. ........ r62400 | mark.dickinson | 2008-04-19 21:41:52 +0200 (Sat, 19 Apr 2008) | 3 lines Additional special-case handling for math.pow. Windows/VS2008 doesn't like (-1)**(+-inf). ........ r62401 | benjamin.peterson | 2008-04-19 21:47:34 +0200 (Sat, 19 Apr 2008) | 2 lines Complete documentation for errors argument of io's open and TextIOWrapper ........ r62402 | mark.dickinson | 2008-04-19 22:31:16 +0200 (Sat, 19 Apr 2008) | 2 lines Document updates to math and cmath modules. ........ r62407 | georg.brandl | 2008-04-19 23:28:38 +0200 (Sat, 19 Apr 2008) | 2 lines Update template for newest Sphinx. ........ r62409 | mark.dickinson | 2008-04-19 23:35:35 +0200 (Sat, 19 Apr 2008) | 5 lines Correct documentation for math.pow; 0**nan is nan, not 0. (But nan**0 and 1**nan are 1.) Also fix minor typo: 'quite NaN' -> 'quiet NaN' ........ r62410 | mark.dickinson | 2008-04-19 23:49:22 +0200 (Sat, 19 Apr 2008) | 4 lines Move asinh documentation to the proper place. Remove meaningless 'in radians' from inverse hyperbolic functions. ........ r62412 | mark.dickinson | 2008-04-20 03:22:30 +0200 (Sun, 20 Apr 2008) | 5 lines Report additional diagnostic information in test_math, to help track down debian-alpha buildbot failure. ........ r62413 | mark.dickinson | 2008-04-20 03:39:24 +0200 (Sun, 20 Apr 2008) | 3 lines FreeBSD doesn't follow C99 for modf(inf); so add explicit special-value handling to math.modf code. ........ r62414 | mark.dickinson | 2008-04-20 06:13:13 +0200 (Sun, 20 Apr 2008) | 5 lines Yet more explicit special case handling to make math.pow behave on alpha Tru64. All IEEE 754 special values are now handled directly; only the finite**finite case is handled by libm. ........ r62418 | mark.dickinson | 2008-04-20 18:13:17 +0200 (Sun, 20 Apr 2008) | 7 lines Issue 2662: Initialize special value tables dynamically (i.e. when cmath module is loaded) instead of statically. This fixes compile-time problems on platforms where HUGE_VAL is an extern variable rather than a constant. Thanks Hirokazu Yamamoto for the patch. ........ r62419 | andrew.kuchling | 2008-04-20 18:54:02 +0200 (Sun, 20 Apr 2008) | 1 line Move description of math module changes; various edits to description of cmath changes ........
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.. function:: asinh(x)
Return the inverse hyperbolic sine of *x*.
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.. function:: atanh(x)
Return the inverse hyperbolic tangent of *x*.
.. function:: cosh(x)
Return the hyperbolic cosine of *x*.
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.. function:: sinh(x)
Return the hyperbolic sine of *x*.
.. function:: tanh(x)
Return the hyperbolic tangent of *x*.
Special functions
-----------------
.. function:: erf(x)
Return the `error function <http://en.wikipedia.org/wiki/Error_function>`_ at
*x*.
The :func:`erf` function can be used to compute traditional statistical
functions such as the `cumulative standard normal distribution
<http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function>`_::
def phi(x):
'Cumulative distribution function for the standard normal distribution'
return (1.0 + erf(x / sqrt(2.0))) / 2.0
.. versionadded:: 3.2
.. function:: erfc(x)
Return the complementary error function at *x*. The `complementary error
function <http://en.wikipedia.org/wiki/Error_function>`_ is defined as
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``1.0 - erf(x)``. It is used for large values of *x* where a subtraction
from one would cause a `loss of significance
<http://en.wikipedia.org/wiki/Loss_of_significance>`_\.
.. versionadded:: 3.2
.. function:: gamma(x)
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Return the `Gamma function <http://en.wikipedia.org/wiki/Gamma_function>`_ at
*x*.
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.. versionadded:: 3.2
.. function:: lgamma(x)
Return the natural logarithm of the absolute value of the Gamma
function at *x*.
.. versionadded:: 3.2
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Constants
---------
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.. data:: pi
The mathematical constant π = 3.141592..., to available precision.
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.. data:: e
The mathematical constant e = 2.718281..., to available precision.
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Merged revisions 75365,75394,75402-75403,75418,75459,75484,75592-75596,75600,75602-75607,75610-75613,75616-75617,75623,75627,75640,75647,75696,75795 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r75365 | georg.brandl | 2009-10-11 22:16:16 +0200 (So, 11 Okt 2009) | 1 line Fix broken links found by "make linkcheck". scipy.org seems to be done right now, so I could not verify links going there. ........ r75394 | georg.brandl | 2009-10-13 20:10:59 +0200 (Di, 13 Okt 2009) | 1 line Fix markup. ........ r75402 | georg.brandl | 2009-10-14 17:51:48 +0200 (Mi, 14 Okt 2009) | 1 line #7125: fix typo. ........ r75403 | georg.brandl | 2009-10-14 17:57:46 +0200 (Mi, 14 Okt 2009) | 1 line #7126: os.environ changes *do* take effect in subprocesses started with os.system(). ........ r75418 | georg.brandl | 2009-10-14 20:48:32 +0200 (Mi, 14 Okt 2009) | 1 line #7116: str.join() takes an iterable. ........ r75459 | georg.brandl | 2009-10-17 10:57:43 +0200 (Sa, 17 Okt 2009) | 1 line Fix refleaks in _ctypes PyCSimpleType_New, which fixes the refleak seen in test___all__. ........ r75484 | georg.brandl | 2009-10-18 09:58:12 +0200 (So, 18 Okt 2009) | 1 line Fix missing word. ........ r75592 | georg.brandl | 2009-10-22 09:05:48 +0200 (Do, 22 Okt 2009) | 1 line Fix punctuation. ........ r75593 | georg.brandl | 2009-10-22 09:06:49 +0200 (Do, 22 Okt 2009) | 1 line Revert unintended change. ........ r75594 | georg.brandl | 2009-10-22 09:56:02 +0200 (Do, 22 Okt 2009) | 1 line Fix markup. ........ r75595 | georg.brandl | 2009-10-22 09:56:56 +0200 (Do, 22 Okt 2009) | 1 line Fix duplicate target. ........ r75596 | georg.brandl | 2009-10-22 10:05:04 +0200 (Do, 22 Okt 2009) | 1 line Add a new directive marking up implementation details and start using it. ........ r75600 | georg.brandl | 2009-10-22 13:01:46 +0200 (Do, 22 Okt 2009) | 1 line Make it more robust. ........ r75602 | georg.brandl | 2009-10-22 13:28:06 +0200 (Do, 22 Okt 2009) | 1 line Document new directive. ........ r75603 | georg.brandl | 2009-10-22 13:28:23 +0200 (Do, 22 Okt 2009) | 1 line Allow short form with text as argument. ........ r75604 | georg.brandl | 2009-10-22 13:36:50 +0200 (Do, 22 Okt 2009) | 1 line Fix stylesheet for multi-paragraph impl-details. ........ r75605 | georg.brandl | 2009-10-22 13:48:10 +0200 (Do, 22 Okt 2009) | 1 line Use "impl-detail" directive where applicable. ........ r75606 | georg.brandl | 2009-10-22 17:00:06 +0200 (Do, 22 Okt 2009) | 1 line #6324: membership test tries iteration via __iter__. ........ r75607 | georg.brandl | 2009-10-22 17:04:09 +0200 (Do, 22 Okt 2009) | 1 line #7088: document new functions in signal as Unix-only. ........ r75610 | georg.brandl | 2009-10-22 17:27:24 +0200 (Do, 22 Okt 2009) | 1 line Reorder __slots__ fine print and add a clarification. ........ r75611 | georg.brandl | 2009-10-22 17:42:32 +0200 (Do, 22 Okt 2009) | 1 line #7035: improve docs of the various <method>_errors() functions, and give them docstrings. ........ r75612 | georg.brandl | 2009-10-22 17:52:15 +0200 (Do, 22 Okt 2009) | 1 line #7156: document curses as Unix-only. ........ r75613 | georg.brandl | 2009-10-22 17:54:35 +0200 (Do, 22 Okt 2009) | 1 line #6977: getopt does not support optional option arguments. ........ r75616 | georg.brandl | 2009-10-22 18:17:05 +0200 (Do, 22 Okt 2009) | 1 line Add proper references. ........ r75617 | georg.brandl | 2009-10-22 18:20:55 +0200 (Do, 22 Okt 2009) | 1 line Make printout margin important. ........ r75623 | georg.brandl | 2009-10-23 10:14:44 +0200 (Fr, 23 Okt 2009) | 1 line #7188: fix optionxform() docs. ........ r75627 | fred.drake | 2009-10-23 15:04:51 +0200 (Fr, 23 Okt 2009) | 2 lines add further note about what's passed to optionxform ........ r75640 | neil.schemenauer | 2009-10-23 21:58:17 +0200 (Fr, 23 Okt 2009) | 2 lines Improve some docstrings in the 'warnings' module. ........ r75647 | georg.brandl | 2009-10-24 12:04:19 +0200 (Sa, 24 Okt 2009) | 1 line Fix markup. ........ r75696 | georg.brandl | 2009-10-25 21:25:43 +0100 (So, 25 Okt 2009) | 1 line Fix a demo. ........ r75795 | georg.brandl | 2009-10-27 16:10:22 +0100 (Di, 27 Okt 2009) | 1 line Fix a strange mis-edit. ........
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.. impl-detail::
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The :mod:`math` module consists mostly of thin wrappers around the platform C
math library functions. Behavior in exceptional cases follows Annex F of
the C99 standard where appropriate. The current implementation will raise
:exc:`ValueError` for invalid operations like ``sqrt(-1.0)`` or ``log(0.0)``
(where C99 Annex F recommends signaling invalid operation or divide-by-zero),
and :exc:`OverflowError` for results that overflow (for example,
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``exp(1000.0)``). A NaN will not be returned from any of the functions
above unless one or more of the input arguments was a NaN; in that case,
most functions will return a NaN, but (again following C99 Annex F) there
are some exceptions to this rule, for example ``pow(float('nan'), 0.0)`` or
``hypot(float('nan'), float('inf'))``.
Note that Python makes no effort to distinguish signaling NaNs from
quiet NaNs, and behavior for signaling NaNs remains unspecified.
Typical behavior is to treat all NaNs as though they were quiet.
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.. seealso::
Module :mod:`cmath`
Complex number versions of many of these functions.