cpython-lru_cache-weakref: Doc/library/math.rst annotate

annotate Doc/library/math.rst @ 54294:dba767bc3155 legacy-trunk

remove mention of old ctypes version

author	Benjamin Peterson <benjamin@python.org>
date	Sat, 23 May 2009 20:59:09 +0000
parents	9800ab236c09
children	e157ceb54a43

rev	line source
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	1
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	2 :mod:`math` --- Mathematical functions
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	3 ======================================
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	4
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	5 .. module:: math
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	6 :synopsis: Mathematical functions (sin() etc.).
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	7
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	8
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	9 This module is always available. It provides access to the mathematical
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	10 functions defined by the C standard.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	11
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	12 These functions cannot be used with complex numbers; use the functions of the
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	13 same name from the :mod:`cmath` module if you require support for complex
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	14 numbers. The distinction between functions which support complex numbers and
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	15 those which don't is made since most users do not want to learn quite as much
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	16 mathematics as required to understand complex numbers. Receiving an exception
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	17 instead of a complex result allows earlier detection of the unexpected complex
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	18 number used as a parameter, so that the programmer can determine how and why it
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	19 was generated in the first place.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	20
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	21 The following functions are provided by this module. Except when explicitly
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	22 noted otherwise, all return values are floats.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	23
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	24
50235 0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	25 Number-theoretic and representation functions
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	26 ---------------------------------------------
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	27
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	28 .. function:: ceil(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	29
44488 94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44480 diff changeset	30 Return the ceiling of x as a float, the smallest integer value greater than or
94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44480 diff changeset	31 equal to x.
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	32
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	33
44440 6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	34 .. function:: copysign(x, y)
6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	35
6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	36 Return x with the sign of y. ``copysign`` copies the sign bit of an IEEE
6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	37 754 float, ``copysign(1, -0.0)`` returns -1.0.
6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	38
44480 57c7d42f6cde Fix markup Andrew M. Kuchling <amk@amk.ca> parents: 44440 diff changeset	39 .. versionadded:: 2.6
44440 6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	40
6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	41
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	42 .. function:: fabs(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	43
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	44 Return the absolute value of x.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	45
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	46
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47215 diff changeset	47 .. function:: factorial(x)
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47215 diff changeset	48
47758 ab12e3ad2e66 Typo fix Mark Dickinson <dickinsm@gmail.com> parents: 47529 diff changeset	49 Return x factorial. Raises :exc:`ValueError` if x is not integral or
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47215 diff changeset	50 is negative.
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	51
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	52 .. versionadded:: 2.6
b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	53
b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	54
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	55 .. function:: floor(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	56
44488 94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44480 diff changeset	57 Return the floor of x as a float, the largest integer value less than or equal
94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44480 diff changeset	58 to x.
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	59
44495 0c0aebc6656f Remove with_statement future imports from 2.6 docs. Georg Brandl <georg@python.org> parents: 44488 diff changeset	60 .. versionchanged:: 2.6
0c0aebc6656f Remove with_statement future imports from 2.6 docs. Georg Brandl <georg@python.org> parents: 44488 diff changeset	61 Added :meth:`__floor__` delegation.
0c0aebc6656f Remove with_statement future imports from 2.6 docs. Georg Brandl <georg@python.org> parents: 44488 diff changeset	62
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	63
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	64 .. function:: fmod(x, y)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	65
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	66 Return ``fmod(x, y)``, as defined by the platform C library. Note that the
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	67 Python expression ``x % y`` may not return the same result. The intent of the C
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	68 standard is that ``fmod(x, y)`` be exactly (mathematically; to infinite
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	69 precision) equal to ``x - ny`` for some integer n* such that the result has
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	70 the same sign as x and magnitude less than ``abs(y)``. Python's ``x % y``
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	71 returns a result with the sign of y instead, and may not be exactly computable
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	72 for float arguments. For example, ``fmod(-1e-100, 1e100)`` is ``-1e-100``, but
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	73 the result of Python's ``-1e-100 % 1e100`` is ``1e100-1e-100``, which cannot be
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	74 represented exactly as a float, and rounds to the surprising ``1e100``. For
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	75 this reason, function :func:`fmod` is generally preferred when working with
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	76 floats, while Python's ``x % y`` is preferred when working with integers.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	77
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	78
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	79 .. function:: frexp(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	80
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	81 Return the mantissa and exponent of x as the pair ``(m, e)``. m is a float
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	82 and e is an integer such that ``x == m * 2*e`` exactly. If x* is zero,
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	83 returns ``(0.0, 0)``, otherwise ``0.5 <= abs(m) < 1``. This is used to "pick
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	84 apart" the internal representation of a float in a portable way.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	85
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	86
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	87 .. function:: fsum(iterable)
8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	88
8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	89 Return an accurate floating point sum of values in the iterable. Avoids
51728 559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	90 loss of precision by tracking multiple intermediate partial sums::
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	91
51728 559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	92 >>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	93 0.99999999999999989
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	94 >>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	95 1.0
48105 67d177aab8a7 Add note about problems with math.fsum on x86 hardware. Mark Dickinson <dickinsm@gmail.com> parents: 48101 diff changeset	96
51728 559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	97 The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	98 typical case where the rounding mode is half-even. On some non-Windows
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	99 builds, the underlying C library uses extended precision addition and may
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	100 occasionally double-round an intermediate sum causing it to be off in its
559e4fc31c8a Add an example for math.fsum() and elaborate on the accurary note. Raymond Hettinger <python@rcn.com> parents: 50508 diff changeset	101 least significant bit.
48105 67d177aab8a7 Add note about problems with math.fsum on x86 hardware. Mark Dickinson <dickinsm@gmail.com> parents: 48101 diff changeset	102
51732 9800ab236c09 Add links to helpful external resources. Raymond Hettinger <python@rcn.com> parents: 51728 diff changeset	103 For further discussion and two alternative approaches, see the `ASPN cookbook
9800ab236c09 Add links to helpful external resources. Raymond Hettinger <python@rcn.com> parents: 51728 diff changeset	104 recipes for accurate floating point summation
9800ab236c09 Add links to helpful external resources. Raymond Hettinger <python@rcn.com> parents: 51728 diff changeset	105 <http://code.activestate.com/recipes/393090/>`_\.
9800ab236c09 Add links to helpful external resources. Raymond Hettinger <python@rcn.com> parents: 51728 diff changeset	106
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	107 .. versionadded:: 2.6
8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	108
8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 47759 diff changeset	109
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	110 .. function:: isinf(x)
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	111
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	112 Checks if the float x is positive or negative infinite.
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	113
44480 57c7d42f6cde Fix markup Andrew M. Kuchling <amk@amk.ca> parents: 44440 diff changeset	114 .. versionadded:: 2.6
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	115
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	116
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	117 .. function:: isnan(x)
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	118
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	119 Checks if the float x is a NaN (not a number). NaNs are part of the
50508 c52177f36852 Remove trailing whitespace. Georg Brandl <georg@python.org> parents: 50243 diff changeset	120 IEEE 754 standards. Operation like but not limited to ``inf * 0``,
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	121 ``inf / inf`` or any operation involving a NaN, e.g. ``nan * 1``, return
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	122 a NaN.
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	123
44480 57c7d42f6cde Fix markup Andrew M. Kuchling <amk@amk.ca> parents: 44440 diff changeset	124 .. versionadded:: 2.6
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	125
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	126
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	127 .. function:: ldexp(x, i)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	128
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	129 Return ``x * (2**i)``. This is essentially the inverse of function
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	130 :func:`frexp`.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	131
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	132
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	133 .. function:: modf(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	134
50234 9fb2a23eac43 copy sentence from docstring Benjamin Peterson <benjamin@python.org> parents: 48904 diff changeset	135 Return the fractional and integer parts of x. Both results carry the sign
50243 589edf615adb remove redundant sentence Benjamin Peterson <benjamin@python.org> parents: 50235 diff changeset	136 of x and are floats.
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	137
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	138
45079 492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	139 .. function:: trunc(x)
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	140
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	141 Return the :class:`Real` value x truncated to an :class:`Integral` (usually
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	142 a long integer). Delegates to ``x.__trunc__()``.
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	143
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	144 .. versionadded:: 2.6
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44495 diff changeset	145
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	146
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	147 Note that :func:`frexp` and :func:`modf` have a different call/return pattern
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	148 than their C equivalents: they take a single argument and return a pair of
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	149 values, rather than returning their second return value through an 'output
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	150 parameter' (there is no such thing in Python).
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	151
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	152 For the :func:`ceil`, :func:`floor`, and :func:`modf` functions, note that all
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	153 floating-point numbers of sufficiently large magnitude are exact integers.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	154 Python floats typically carry no more than 53 bits of precision (the same as the
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	155 platform C double type), in which case any float x with ``abs(x) >= 2**52``
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	156 necessarily has no fractional bits.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	157
50235 0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	158
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	159 Power and logarithmic functions
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	160 -------------------------------
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	161
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	162 .. function:: exp(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	163
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	164 Return ``e**x``.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	165
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	166
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	167 .. function:: log(x[, base])
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	168
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	169 Return the logarithm of x to the given base. If the base is not specified,
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	170 return the natural logarithm of x (that is, the logarithm to base e).
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	171
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	172 .. versionchanged:: 2.3
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	173 base argument added.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	174
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	175
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	176 .. function:: log1p(x)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	177
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	178 Return the natural logarithm of 1+x (base e). The
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	179 result is calculated in a way which is accurate for x near zero.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	180
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	181 .. versionadded:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	182
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	183
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	184 .. function:: log10(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	185
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	186 Return the base-10 logarithm of x.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	187
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	188
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	189 .. function:: pow(x, y)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	190
46495 f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	191 Return ``x`` raised to the power ``y``. Exceptional cases follow
f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	192 Annex 'F' of the C99 standard as far as possible. In particular,
f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	193 ``pow(1.0, x)`` and ``pow(x, 0.0)`` always return ``1.0``, even
f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	194 when ``x`` is a zero or a NaN. If both ``x`` and ``y`` are finite,
f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	195 ``x`` is negative, and ``y`` is not an integer then ``pow(x, y)``
f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	196 is undefined, and raises :exc:`ValueError`.
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	197
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	198 .. versionchanged:: 2.6
46495 f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	199 The outcome of ``1nan`` and ``nan0`` was undefined.
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	200
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	201
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	202 .. function:: sqrt(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	203
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	204 Return the square root of x.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	205
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	206
50235 0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	207 Trigonometric functions
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	208 -----------------------
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	209
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	210 .. function:: acos(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	211
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	212 Return the arc cosine of x, in radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	213
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	214
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	215 .. function:: asin(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	216
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	217 Return the arc sine of x, in radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	218
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	219
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	220 .. function:: atan(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	221
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	222 Return the arc tangent of x, in radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	223
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	224
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	225 .. function:: atan2(y, x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	226
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	227 Return ``atan(y / x)``, in radians. The result is between ``-pi`` and ``pi``.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	228 The vector in the plane from the origin to point ``(x, y)`` makes this angle
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	229 with the positive X axis. The point of :func:`atan2` is that the signs of both
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	230 inputs are known to it, so it can compute the correct quadrant for the angle.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	231 For example, ``atan(1``) and ``atan2(1, 1)`` are both ``pi/4``, but ``atan2(-1,
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	232 -1)`` is ``-3*pi/4``.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	233
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	234
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	235 .. function:: cos(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	236
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	237 Return the cosine of x radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	238
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	239
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	240 .. function:: hypot(x, y)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	241
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	242 Return the Euclidean norm, ``sqrt(xx + yy)``. This is the length of the vector
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	243 from the origin to point ``(x, y)``.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	244
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	245
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	246 .. function:: sin(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	247
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	248 Return the sine of x radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	249
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	250
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	251 .. function:: tan(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	252
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	253 Return the tangent of x radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	254
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	255
50235 0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	256 Angular conversion
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	257 ------------------
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	258
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	259 .. function:: degrees(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	260
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	261 Converts angle x from radians to degrees.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	262
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	263
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	264 .. function:: radians(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	265
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	266 Converts angle x from degrees to radians.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	267
47759 b4d823483421 Add versionadded tags to new math functions. Georg Brandl <georg@python.org> parents: 47758 diff changeset	268
50235 0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	269 Hyperbolic functions
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	270 --------------------
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	271
46496 35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	272 .. function:: acosh(x)
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	273
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	274 Return the inverse hyperbolic cosine of x.
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	275
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	276 .. versionadded:: 2.6
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	277
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	278
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	279 .. function:: asinh(x)
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	280
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	281 Return the inverse hyperbolic sine of x.
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	282
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	283 .. versionadded:: 2.6
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	284
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	285
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	286 .. function:: atanh(x)
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	287
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	288 Return the inverse hyperbolic tangent of x.
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	289
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	290 .. versionadded:: 2.6
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	291
35bf8012a376 Move asinh documentation to the proper place. Mark Dickinson <dickinsm@gmail.com> parents: 46495 diff changeset	292
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	293 .. function:: cosh(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	294
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	295 Return the hyperbolic cosine of x.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	296
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	297
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	298 .. function:: sinh(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	299
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	300 Return the hyperbolic sine of x.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	301
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	302
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	303 .. function:: tanh(x)
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	304
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	305 Return the hyperbolic tangent of x.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	306
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	307
50235 0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	308 Constants
0647948be840 add headings Benjamin Peterson <benjamin@python.org> parents: 50234 diff changeset	309 ---------
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	310
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	311 .. data:: pi
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	312
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	313 The mathematical constant pi.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	314
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	315
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	316 .. data:: e
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	317
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	318 The mathematical constant e.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	319
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	320
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	321 .. note::
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	322
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	323 The :mod:`math` module consists mostly of thin wrappers around the platform C
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	324 math library functions. Behavior in exceptional cases is loosely specified
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	325 by the C standards, and Python inherits much of its math-function
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	326 error-reporting behavior from the platform C implementation. As a result,
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	327 the specific exceptions raised in error cases (and even whether some
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	328 arguments are considered to be exceptional at all) are not defined in any
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	329 useful cross-platform or cross-release way. For example, whether
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	330 ``math.log(0)`` returns ``-Inf`` or raises :exc:`ValueError` or
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	331 :exc:`OverflowError` isn't defined, and in cases where ``math.log(0)`` raises
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	332 :exc:`OverflowError`, ``math.log(0L)`` may raise :exc:`ValueError` instead.
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	333
46495 f641e505fff4 Correct documentation for math.pow; Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	334 All functions return a quiet NaN if at least one of the args is NaN.
48904 f67963cd4395 Fix markup. Georg Brandl <georg@python.org> parents: 48123 diff changeset	335 Signaling NaN\s raise an exception. The exception type still depends on the
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	336 platform and libm implementation. It's usually :exc:`ValueError` for EDOM
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	337 and :exc:`OverflowError` for errno ERANGE.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	338
46958 e64039bbfe26 Fix markup. Georg Brandl <georg@python.org> parents: 46496 diff changeset	339 .. versionchanged:: 2.6
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	340 In earlier versions of Python the outcome of an operation with NaN as
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	341 input depended on platform and libm implementation.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45079 diff changeset	342
42604 9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	343
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	344 .. seealso::
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	345
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	346 Module :mod:`cmath`
9e1529bf0442 Move the 3k reST doc tree in place. Georg Brandl <georg@python.org> parents: diff changeset	347 Complex number versions of many of these functions.

Mercurial > cpython-lru_cache-weakref

annotate Doc/library/math.rst @ 54294:dba767bc3155 legacy-trunk