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svn+ssh://pythondev@svn.python.org/python/trunk ........ r60752 | mark.dickinson | 2008-02-12 22:31:59 +0100 (Tue, 12 Feb 2008) | 5 lines Implementation of Fraction.limit_denominator. Remove Fraction.to_continued_fraction and Fraction.from_continued_fraction ........ r60754 | mark.dickinson | 2008-02-12 22:40:53 +0100 (Tue, 12 Feb 2008) | 3 lines Revert change in r60712: turn alternate constructors back into classmethods instead of staticmethods. ........ r60755 | mark.dickinson | 2008-02-12 22:46:54 +0100 (Tue, 12 Feb 2008) | 4 lines Replace R=fractions.Fraction with F=fractions.Fraction in test_fractions.py. This should have been part of the name change from Rational to Fraction. ........ r60758 | georg.brandl | 2008-02-13 08:20:22 +0100 (Wed, 13 Feb 2008) | 3 lines #2063: correct order of utime and stime in os.times() result on Windows. ........ r60762 | jeffrey.yasskin | 2008-02-13 18:58:04 +0100 (Wed, 13 Feb 2008) | 7 lines Working on issue #1762: Brought ./python.exe -m timeit -s 'from fractions import Fraction; f = Fraction(3, 2)' 'isinstance(3, Fraction); isinstance(f, Fraction)' from 12.3 usec/loop to 3.44 usec/loop and ./python.exe -m timeit -s 'from fractions import Fraction' 'Fraction(3, 2)' from 48.8 usec to 23.6 usec by avoiding genexps and sets in __instancecheck__ and inlining the common case from __subclasscheck__. ........ r60765 | brett.cannon | 2008-02-13 20:15:44 +0100 (Wed, 13 Feb 2008) | 5 lines Fix --enable-universalsdk and its comment line so that zsh's flag completion works. Thanks to Jeroen Ruigrok van der Werven for the fix. ........ r60771 | kurt.kaiser | 2008-02-14 01:08:55 +0100 (Thu, 14 Feb 2008) | 2 lines Bring NEWS.txt up to date from check-in msgs. ........ r60772 | raymond.hettinger | 2008-02-14 02:08:02 +0100 (Thu, 14 Feb 2008) | 3 lines Update notes on Decimal. ........ r60773 | raymond.hettinger | 2008-02-14 03:41:22 +0100 (Thu, 14 Feb 2008) | 1 line Fix decimal repr which should have used single quotes like other reprs. ........ r60785 | jeffrey.yasskin | 2008-02-14 07:12:24 +0100 (Thu, 14 Feb 2008) | 11 lines Performance optimizations on Fraction's constructor. ./python.exe -m timeit -s 'from fractions import Fraction' 'Fraction(3)` 31.7 usec/loop -> 9.2 usec/loop ./python.exe -m timeit -s 'from fractions import Fraction' 'Fraction(3, 2)'` 27.7 usec/loop -> 9.32 usec/loop ./python.exe -m timeit -s 'from fractions import Fraction; f = Fraction(3, 2)' 'Fraction(f)' 31.9 usec/loop -> 14.3 usec/loop ........ r60786 | jeffrey.yasskin | 2008-02-14 08:49:25 +0100 (Thu, 14 Feb 2008) | 5 lines Change simple instances (in Fraction) of self.numerator and self.denominator to self._numerator and self._denominator. This speeds abs() up from 12.2us to 10.8us and trunc() from 2.07us to 1.11us. This doesn't change _add and friends because they're more complicated. ........
93 lines
2.9 KiB
ReStructuredText
93 lines
2.9 KiB
ReStructuredText
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:mod:`fractions` --- Rational numbers
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=====================================
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.. module:: fractions
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:synopsis: Rational numbers.
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.. moduleauthor:: Jeffrey Yasskin <jyasskin at gmail.com>
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.. sectionauthor:: Jeffrey Yasskin <jyasskin at gmail.com>
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.. versionadded:: 2.6
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The :mod:`fractions` module defines an immutable, infinite-precision
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Rational number class.
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.. class:: Fraction(numerator=0, denominator=1)
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Fraction(other_fraction)
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Fraction(string)
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The first version requires that *numerator* and *denominator* are
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instances of :class:`numbers.Integral` and returns a new
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``Fraction`` representing ``numerator/denominator``. If
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*denominator* is :const:`0`, raises a :exc:`ZeroDivisionError`. The
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second version requires that *other_fraction* is an instance of
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:class:`numbers.Fraction` and returns an instance of
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:class:`Rational` with the same value. The third version expects a
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string of the form ``[-+]?[0-9]+(/[0-9]+)?``, optionally surrounded
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by spaces.
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Implements all of the methods and operations from
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:class:`numbers.Rational` and is immutable and hashable.
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.. method:: Fraction.from_float(flt)
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This classmethod constructs a :class:`Fraction` representing the
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exact value of *flt*, which must be a :class:`float`. Beware that
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``Fraction.from_float(0.3)`` is not the same value as ``Rational(3,
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10)``
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.. method:: Fraction.from_decimal(dec)
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This classmethod constructs a :class:`Fraction` representing the
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exact value of *dec*, which must be a
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:class:`decimal.Decimal`.
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.. method:: Fraction.limit_denominator(max_denominator=1000000)
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Finds and returns the closest :class:`Fraction` to ``self`` that
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has denominator at most max_denominator. This method is useful for
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finding rational approximations to a given floating-point number::
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>>> Fraction('3.1415926535897932').limit_denominator(1000)
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Fraction(355, 113)
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or for recovering a rational number that's represented as a float::
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>>> from math import pi, cos
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>>> Fraction.from_float(cos(pi/3))
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Fraction(4503599627370497L, 9007199254740992L)
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>>> Fraction.from_float(cos(pi/3)).limit_denominator()
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Fraction(1, 2)
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.. method:: Fraction.__floor__()
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Returns the greatest :class:`int` ``<= self``. Will be accessible
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through :func:`math.floor` in Py3k.
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.. method:: Fraction.__ceil__()
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Returns the least :class:`int` ``>= self``. Will be accessible
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through :func:`math.ceil` in Py3k.
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.. method:: Fraction.__round__()
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Fraction.__round__(ndigits)
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The first version returns the nearest :class:`int` to ``self``,
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rounding half to even. The second version rounds ``self`` to the
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nearest multiple of ``Fraction(1, 10**ndigits)`` (logically, if
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``ndigits`` is negative), again rounding half toward even. Will be
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accessible through :func:`round` in Py3k.
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.. seealso::
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Module :mod:`numbers`
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The abstract base classes making up the numeric tower.
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