cpython/Doc/library/numbers.rst

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:mod:`numbers` --- Numeric abstract base classes
================================================
.. module:: numbers
:synopsis: Numeric abstract base classes (Complex, Real, Integral, etc.).
.. versionadded:: 2.6
The :mod:`numbers` module (:pep:`3141`) defines a hierarchy of numeric abstract
base classes which progressively define more operations. None of the types
defined in this module can be instantiated.
.. class:: Number
The root of the numeric hierarchy. If you just want to check if an argument
*x* is a number, without caring what kind, use ``isinstance(x, Number)``.
The numeric tower
-----------------
.. class:: Complex
Subclasses of this type describe complex numbers and include the operations
that work on the built-in :class:`complex` type. These are: conversions to
:class:`complex` and :class:`bool`, :attr:`.real`, :attr:`.imag`, ``+``,
``-``, ``*``, ``/``, :func:`abs`, :meth:`conjugate`, ``==``, and ``!=``. All
except ``-`` and ``!=`` are abstract.
.. attribute:: real
Abstract. Retrieves the :class:`Real` component of this number.
.. attribute:: imag
Abstract. Retrieves the :class:`Real` component of this number.
.. method:: conjugate()
Abstract. Returns the complex conjugate. For example, ``(1+3j).conjugate()
== (1-3j)``.
.. class:: Real
To :class:`Complex`, :class:`Real` adds the operations that work on real
numbers.
In short, those are: a conversion to :class:`float`, :func:`trunc`,
:func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`, ``//``,
``%``, ``<``, ``<=``, ``>``, and ``>=``.
Merged revisions 68133-68134,68141-68142,68145-68146,68148-68149,68159-68162,68166,68171-68174,68179,68195-68196,68210,68214-68215,68217-68222 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r68133 | antoine.pitrou | 2009-01-01 16:38:03 +0100 (Thu, 01 Jan 2009) | 1 line fill in actual issue number in tests ........ r68134 | hirokazu.yamamoto | 2009-01-01 16:45:39 +0100 (Thu, 01 Jan 2009) | 2 lines Issue #4797: IOError.filename was not set when _fileio.FileIO failed to open file with `str' filename on Windows. ........ r68141 | benjamin.peterson | 2009-01-01 17:43:12 +0100 (Thu, 01 Jan 2009) | 1 line fix highlighting ........ r68142 | benjamin.peterson | 2009-01-01 18:29:49 +0100 (Thu, 01 Jan 2009) | 2 lines welcome to 2009, Python! ........ r68145 | amaury.forgeotdarc | 2009-01-02 01:03:54 +0100 (Fri, 02 Jan 2009) | 5 lines #4801 _collections module fails to build on cygwin. _PyObject_GC_TRACK is the macro version of PyObject_GC_Track, and according to documentation it should not be used for extension modules. ........ r68146 | ronald.oussoren | 2009-01-02 11:44:46 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4472: "configure --enable-shared doesn't work on OSX" ........ r68148 | ronald.oussoren | 2009-01-02 11:48:31 +0100 (Fri, 02 Jan 2009) | 2 lines Forgot to add a NEWS item in my previous checkin ........ r68149 | ronald.oussoren | 2009-01-02 11:50:48 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4780 ........ r68159 | ronald.oussoren | 2009-01-02 15:48:17 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue 1627952 ........ r68160 | ronald.oussoren | 2009-01-02 15:52:09 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue r1737832 ........ r68161 | ronald.oussoren | 2009-01-02 16:00:05 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 1149804 ........ r68162 | ronald.oussoren | 2009-01-02 16:06:00 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 4472 is incompatible with Cygwin, this patch should fix that. ........ r68166 | benjamin.peterson | 2009-01-02 19:26:23 +0100 (Fri, 02 Jan 2009) | 1 line document PyMemberDef ........ r68171 | georg.brandl | 2009-01-02 21:25:14 +0100 (Fri, 02 Jan 2009) | 3 lines #4811: fix markup glitches (mostly remains of the conversion), found by Gabriel Genellina. ........ r68172 | martin.v.loewis | 2009-01-02 21:32:55 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4075: Use OutputDebugStringW in Py_FatalError. ........ r68173 | martin.v.loewis | 2009-01-02 21:40:14 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4051: Prevent conflict of UNICODE macros in cPickle. ........ r68174 | benjamin.peterson | 2009-01-02 21:47:27 +0100 (Fri, 02 Jan 2009) | 1 line fix compilation on non-Windows platforms ........ r68179 | raymond.hettinger | 2009-01-02 22:26:45 +0100 (Fri, 02 Jan 2009) | 1 line Issue #4615. Document how to use itertools for de-duping. ........ r68195 | georg.brandl | 2009-01-03 14:45:15 +0100 (Sat, 03 Jan 2009) | 2 lines Remove useless string literal. ........ r68196 | georg.brandl | 2009-01-03 15:29:53 +0100 (Sat, 03 Jan 2009) | 2 lines Fix indentation. ........ r68210 | georg.brandl | 2009-01-03 20:10:12 +0100 (Sat, 03 Jan 2009) | 2 lines Set eol-style correctly for mp_distributing.py. ........ r68214 | georg.brandl | 2009-01-03 20:44:48 +0100 (Sat, 03 Jan 2009) | 2 lines Make indentation consistent. ........ r68215 | georg.brandl | 2009-01-03 21:15:14 +0100 (Sat, 03 Jan 2009) | 2 lines Fix role name. ........ r68217 | georg.brandl | 2009-01-03 21:30:15 +0100 (Sat, 03 Jan 2009) | 2 lines Add rstlint, a little tool to find subtle markup problems and inconsistencies in the Doc sources. ........ r68218 | georg.brandl | 2009-01-03 21:38:59 +0100 (Sat, 03 Jan 2009) | 2 lines Recognize usage of the default role. ........ r68219 | georg.brandl | 2009-01-03 21:47:01 +0100 (Sat, 03 Jan 2009) | 2 lines Fix uses of the default role. ........ r68220 | georg.brandl | 2009-01-03 21:55:06 +0100 (Sat, 03 Jan 2009) | 2 lines Remove trailing whitespace. ........ r68221 | georg.brandl | 2009-01-03 22:04:55 +0100 (Sat, 03 Jan 2009) | 2 lines Remove tabs from the documentation. ........ r68222 | georg.brandl | 2009-01-03 22:11:58 +0100 (Sat, 03 Jan 2009) | 2 lines Disable the line length checker by default. ........
2009-01-03 17:55:17 -04:00
Real also provides defaults for :func:`complex`, :attr:`~Complex.real`,
:attr:`~Complex.imag`, and :meth:`~Complex.conjugate`.
.. class:: Rational
Subtypes :class:`Real` and adds
Merged revisions 68133-68134,68141-68142,68145-68146,68148-68149,68159-68162,68166,68171-68174,68179,68195-68196,68210,68214-68215,68217-68222 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r68133 | antoine.pitrou | 2009-01-01 16:38:03 +0100 (Thu, 01 Jan 2009) | 1 line fill in actual issue number in tests ........ r68134 | hirokazu.yamamoto | 2009-01-01 16:45:39 +0100 (Thu, 01 Jan 2009) | 2 lines Issue #4797: IOError.filename was not set when _fileio.FileIO failed to open file with `str' filename on Windows. ........ r68141 | benjamin.peterson | 2009-01-01 17:43:12 +0100 (Thu, 01 Jan 2009) | 1 line fix highlighting ........ r68142 | benjamin.peterson | 2009-01-01 18:29:49 +0100 (Thu, 01 Jan 2009) | 2 lines welcome to 2009, Python! ........ r68145 | amaury.forgeotdarc | 2009-01-02 01:03:54 +0100 (Fri, 02 Jan 2009) | 5 lines #4801 _collections module fails to build on cygwin. _PyObject_GC_TRACK is the macro version of PyObject_GC_Track, and according to documentation it should not be used for extension modules. ........ r68146 | ronald.oussoren | 2009-01-02 11:44:46 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4472: "configure --enable-shared doesn't work on OSX" ........ r68148 | ronald.oussoren | 2009-01-02 11:48:31 +0100 (Fri, 02 Jan 2009) | 2 lines Forgot to add a NEWS item in my previous checkin ........ r68149 | ronald.oussoren | 2009-01-02 11:50:48 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4780 ........ r68159 | ronald.oussoren | 2009-01-02 15:48:17 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue 1627952 ........ r68160 | ronald.oussoren | 2009-01-02 15:52:09 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue r1737832 ........ r68161 | ronald.oussoren | 2009-01-02 16:00:05 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 1149804 ........ r68162 | ronald.oussoren | 2009-01-02 16:06:00 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 4472 is incompatible with Cygwin, this patch should fix that. ........ r68166 | benjamin.peterson | 2009-01-02 19:26:23 +0100 (Fri, 02 Jan 2009) | 1 line document PyMemberDef ........ r68171 | georg.brandl | 2009-01-02 21:25:14 +0100 (Fri, 02 Jan 2009) | 3 lines #4811: fix markup glitches (mostly remains of the conversion), found by Gabriel Genellina. ........ r68172 | martin.v.loewis | 2009-01-02 21:32:55 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4075: Use OutputDebugStringW in Py_FatalError. ........ r68173 | martin.v.loewis | 2009-01-02 21:40:14 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4051: Prevent conflict of UNICODE macros in cPickle. ........ r68174 | benjamin.peterson | 2009-01-02 21:47:27 +0100 (Fri, 02 Jan 2009) | 1 line fix compilation on non-Windows platforms ........ r68179 | raymond.hettinger | 2009-01-02 22:26:45 +0100 (Fri, 02 Jan 2009) | 1 line Issue #4615. Document how to use itertools for de-duping. ........ r68195 | georg.brandl | 2009-01-03 14:45:15 +0100 (Sat, 03 Jan 2009) | 2 lines Remove useless string literal. ........ r68196 | georg.brandl | 2009-01-03 15:29:53 +0100 (Sat, 03 Jan 2009) | 2 lines Fix indentation. ........ r68210 | georg.brandl | 2009-01-03 20:10:12 +0100 (Sat, 03 Jan 2009) | 2 lines Set eol-style correctly for mp_distributing.py. ........ r68214 | georg.brandl | 2009-01-03 20:44:48 +0100 (Sat, 03 Jan 2009) | 2 lines Make indentation consistent. ........ r68215 | georg.brandl | 2009-01-03 21:15:14 +0100 (Sat, 03 Jan 2009) | 2 lines Fix role name. ........ r68217 | georg.brandl | 2009-01-03 21:30:15 +0100 (Sat, 03 Jan 2009) | 2 lines Add rstlint, a little tool to find subtle markup problems and inconsistencies in the Doc sources. ........ r68218 | georg.brandl | 2009-01-03 21:38:59 +0100 (Sat, 03 Jan 2009) | 2 lines Recognize usage of the default role. ........ r68219 | georg.brandl | 2009-01-03 21:47:01 +0100 (Sat, 03 Jan 2009) | 2 lines Fix uses of the default role. ........ r68220 | georg.brandl | 2009-01-03 21:55:06 +0100 (Sat, 03 Jan 2009) | 2 lines Remove trailing whitespace. ........ r68221 | georg.brandl | 2009-01-03 22:04:55 +0100 (Sat, 03 Jan 2009) | 2 lines Remove tabs from the documentation. ........ r68222 | georg.brandl | 2009-01-03 22:11:58 +0100 (Sat, 03 Jan 2009) | 2 lines Disable the line length checker by default. ........
2009-01-03 17:55:17 -04:00
:attr:`~Rational.numerator` and :attr:`~Rational.denominator` properties, which
should be in lowest terms. With these, it provides a default for
:func:`float`.
.. attribute:: numerator
Abstract.
.. attribute:: denominator
Abstract.
.. class:: Integral
Subtypes :class:`Rational` and adds a conversion to :class:`int`.
Merged revisions 68133-68134,68141-68142,68145-68146,68148-68149,68159-68162,68166,68171-68174,68179,68195-68196,68210,68214-68215,68217-68222 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r68133 | antoine.pitrou | 2009-01-01 16:38:03 +0100 (Thu, 01 Jan 2009) | 1 line fill in actual issue number in tests ........ r68134 | hirokazu.yamamoto | 2009-01-01 16:45:39 +0100 (Thu, 01 Jan 2009) | 2 lines Issue #4797: IOError.filename was not set when _fileio.FileIO failed to open file with `str' filename on Windows. ........ r68141 | benjamin.peterson | 2009-01-01 17:43:12 +0100 (Thu, 01 Jan 2009) | 1 line fix highlighting ........ r68142 | benjamin.peterson | 2009-01-01 18:29:49 +0100 (Thu, 01 Jan 2009) | 2 lines welcome to 2009, Python! ........ r68145 | amaury.forgeotdarc | 2009-01-02 01:03:54 +0100 (Fri, 02 Jan 2009) | 5 lines #4801 _collections module fails to build on cygwin. _PyObject_GC_TRACK is the macro version of PyObject_GC_Track, and according to documentation it should not be used for extension modules. ........ r68146 | ronald.oussoren | 2009-01-02 11:44:46 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4472: "configure --enable-shared doesn't work on OSX" ........ r68148 | ronald.oussoren | 2009-01-02 11:48:31 +0100 (Fri, 02 Jan 2009) | 2 lines Forgot to add a NEWS item in my previous checkin ........ r68149 | ronald.oussoren | 2009-01-02 11:50:48 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4780 ........ r68159 | ronald.oussoren | 2009-01-02 15:48:17 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue 1627952 ........ r68160 | ronald.oussoren | 2009-01-02 15:52:09 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue r1737832 ........ r68161 | ronald.oussoren | 2009-01-02 16:00:05 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 1149804 ........ r68162 | ronald.oussoren | 2009-01-02 16:06:00 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 4472 is incompatible with Cygwin, this patch should fix that. ........ r68166 | benjamin.peterson | 2009-01-02 19:26:23 +0100 (Fri, 02 Jan 2009) | 1 line document PyMemberDef ........ r68171 | georg.brandl | 2009-01-02 21:25:14 +0100 (Fri, 02 Jan 2009) | 3 lines #4811: fix markup glitches (mostly remains of the conversion), found by Gabriel Genellina. ........ r68172 | martin.v.loewis | 2009-01-02 21:32:55 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4075: Use OutputDebugStringW in Py_FatalError. ........ r68173 | martin.v.loewis | 2009-01-02 21:40:14 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4051: Prevent conflict of UNICODE macros in cPickle. ........ r68174 | benjamin.peterson | 2009-01-02 21:47:27 +0100 (Fri, 02 Jan 2009) | 1 line fix compilation on non-Windows platforms ........ r68179 | raymond.hettinger | 2009-01-02 22:26:45 +0100 (Fri, 02 Jan 2009) | 1 line Issue #4615. Document how to use itertools for de-duping. ........ r68195 | georg.brandl | 2009-01-03 14:45:15 +0100 (Sat, 03 Jan 2009) | 2 lines Remove useless string literal. ........ r68196 | georg.brandl | 2009-01-03 15:29:53 +0100 (Sat, 03 Jan 2009) | 2 lines Fix indentation. ........ r68210 | georg.brandl | 2009-01-03 20:10:12 +0100 (Sat, 03 Jan 2009) | 2 lines Set eol-style correctly for mp_distributing.py. ........ r68214 | georg.brandl | 2009-01-03 20:44:48 +0100 (Sat, 03 Jan 2009) | 2 lines Make indentation consistent. ........ r68215 | georg.brandl | 2009-01-03 21:15:14 +0100 (Sat, 03 Jan 2009) | 2 lines Fix role name. ........ r68217 | georg.brandl | 2009-01-03 21:30:15 +0100 (Sat, 03 Jan 2009) | 2 lines Add rstlint, a little tool to find subtle markup problems and inconsistencies in the Doc sources. ........ r68218 | georg.brandl | 2009-01-03 21:38:59 +0100 (Sat, 03 Jan 2009) | 2 lines Recognize usage of the default role. ........ r68219 | georg.brandl | 2009-01-03 21:47:01 +0100 (Sat, 03 Jan 2009) | 2 lines Fix uses of the default role. ........ r68220 | georg.brandl | 2009-01-03 21:55:06 +0100 (Sat, 03 Jan 2009) | 2 lines Remove trailing whitespace. ........ r68221 | georg.brandl | 2009-01-03 22:04:55 +0100 (Sat, 03 Jan 2009) | 2 lines Remove tabs from the documentation. ........ r68222 | georg.brandl | 2009-01-03 22:11:58 +0100 (Sat, 03 Jan 2009) | 2 lines Disable the line length checker by default. ........
2009-01-03 17:55:17 -04:00
Provides defaults for :func:`float`, :attr:`~Rational.numerator`, and
:attr:`~Rational.denominator`, and bit-string operations: ``<<``,
``>>``, ``&``, ``^``, ``|``, ``~``.
Notes for type implementors
---------------------------
Implementors should be careful to make equal numbers equal and hash
them to the same values. This may be subtle if there are two different
extensions of the real numbers. For example, :class:`fractions.Fraction`
implements :func:`hash` as follows::
def __hash__(self):
if self.denominator == 1:
# Get integers right.
return hash(self.numerator)
# Expensive check, but definitely correct.
if self == float(self):
return hash(float(self))
else:
# Use tuple's hash to avoid a high collision rate on
# simple fractions.
return hash((self.numerator, self.denominator))
Adding More Numeric ABCs
~~~~~~~~~~~~~~~~~~~~~~~~
There are, of course, more possible ABCs for numbers, and this would
be a poor hierarchy if it precluded the possibility of adding
those. You can add ``MyFoo`` between :class:`Complex` and
:class:`Real` with::
class MyFoo(Complex): ...
MyFoo.register(Real)
Implementing the arithmetic operations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We want to implement the arithmetic operations so that mixed-mode
operations either call an implementation whose author knew about the
types of both arguments, or convert both to the nearest built in type
and do the operation there. For subtypes of :class:`Integral`, this
means that :meth:`__add__` and :meth:`__radd__` should be defined as::
class MyIntegral(Integral):
def __add__(self, other):
if isinstance(other, MyIntegral):
return do_my_adding_stuff(self, other)
elif isinstance(other, OtherTypeIKnowAbout):
return do_my_other_adding_stuff(self, other)
else:
return NotImplemented
def __radd__(self, other):
if isinstance(other, MyIntegral):
return do_my_adding_stuff(other, self)
elif isinstance(other, OtherTypeIKnowAbout):
return do_my_other_adding_stuff(other, self)
elif isinstance(other, Integral):
return int(other) + int(self)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
else:
return NotImplemented
There are 5 different cases for a mixed-type operation on subclasses
of :class:`Complex`. I'll refer to all of the above code that doesn't
refer to ``MyIntegral`` and ``OtherTypeIKnowAbout`` as
"boilerplate". ``a`` will be an instance of ``A``, which is a subtype
of :class:`Complex` (``a : A <: Complex``), and ``b : B <:
Complex``. I'll consider ``a + b``:
1. If ``A`` defines an :meth:`__add__` which accepts ``b``, all is
well.
2. If ``A`` falls back to the boilerplate code, and it were to
return a value from :meth:`__add__`, we'd miss the possibility
that ``B`` defines a more intelligent :meth:`__radd__`, so the
boilerplate should return :const:`NotImplemented` from
:meth:`__add__`. (Or ``A`` may not implement :meth:`__add__` at
all.)
3. Then ``B``'s :meth:`__radd__` gets a chance. If it accepts
``a``, all is well.
4. If it falls back to the boilerplate, there are no more possible
methods to try, so this is where the default implementation
should live.
5. If ``B <: A``, Python tries ``B.__radd__`` before
``A.__add__``. This is ok, because it was implemented with
knowledge of ``A``, so it can handle those instances before
delegating to :class:`Complex`.
Merged revisions 68133-68134,68141-68142,68145-68146,68148-68149,68159-68162,68166,68171-68174,68179,68195-68196,68210,68214-68215,68217-68222 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r68133 | antoine.pitrou | 2009-01-01 16:38:03 +0100 (Thu, 01 Jan 2009) | 1 line fill in actual issue number in tests ........ r68134 | hirokazu.yamamoto | 2009-01-01 16:45:39 +0100 (Thu, 01 Jan 2009) | 2 lines Issue #4797: IOError.filename was not set when _fileio.FileIO failed to open file with `str' filename on Windows. ........ r68141 | benjamin.peterson | 2009-01-01 17:43:12 +0100 (Thu, 01 Jan 2009) | 1 line fix highlighting ........ r68142 | benjamin.peterson | 2009-01-01 18:29:49 +0100 (Thu, 01 Jan 2009) | 2 lines welcome to 2009, Python! ........ r68145 | amaury.forgeotdarc | 2009-01-02 01:03:54 +0100 (Fri, 02 Jan 2009) | 5 lines #4801 _collections module fails to build on cygwin. _PyObject_GC_TRACK is the macro version of PyObject_GC_Track, and according to documentation it should not be used for extension modules. ........ r68146 | ronald.oussoren | 2009-01-02 11:44:46 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4472: "configure --enable-shared doesn't work on OSX" ........ r68148 | ronald.oussoren | 2009-01-02 11:48:31 +0100 (Fri, 02 Jan 2009) | 2 lines Forgot to add a NEWS item in my previous checkin ........ r68149 | ronald.oussoren | 2009-01-02 11:50:48 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue4780 ........ r68159 | ronald.oussoren | 2009-01-02 15:48:17 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue 1627952 ........ r68160 | ronald.oussoren | 2009-01-02 15:52:09 +0100 (Fri, 02 Jan 2009) | 2 lines Fix for issue r1737832 ........ r68161 | ronald.oussoren | 2009-01-02 16:00:05 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 1149804 ........ r68162 | ronald.oussoren | 2009-01-02 16:06:00 +0100 (Fri, 02 Jan 2009) | 3 lines Fix for issue 4472 is incompatible with Cygwin, this patch should fix that. ........ r68166 | benjamin.peterson | 2009-01-02 19:26:23 +0100 (Fri, 02 Jan 2009) | 1 line document PyMemberDef ........ r68171 | georg.brandl | 2009-01-02 21:25:14 +0100 (Fri, 02 Jan 2009) | 3 lines #4811: fix markup glitches (mostly remains of the conversion), found by Gabriel Genellina. ........ r68172 | martin.v.loewis | 2009-01-02 21:32:55 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4075: Use OutputDebugStringW in Py_FatalError. ........ r68173 | martin.v.loewis | 2009-01-02 21:40:14 +0100 (Fri, 02 Jan 2009) | 2 lines Issue #4051: Prevent conflict of UNICODE macros in cPickle. ........ r68174 | benjamin.peterson | 2009-01-02 21:47:27 +0100 (Fri, 02 Jan 2009) | 1 line fix compilation on non-Windows platforms ........ r68179 | raymond.hettinger | 2009-01-02 22:26:45 +0100 (Fri, 02 Jan 2009) | 1 line Issue #4615. Document how to use itertools for de-duping. ........ r68195 | georg.brandl | 2009-01-03 14:45:15 +0100 (Sat, 03 Jan 2009) | 2 lines Remove useless string literal. ........ r68196 | georg.brandl | 2009-01-03 15:29:53 +0100 (Sat, 03 Jan 2009) | 2 lines Fix indentation. ........ r68210 | georg.brandl | 2009-01-03 20:10:12 +0100 (Sat, 03 Jan 2009) | 2 lines Set eol-style correctly for mp_distributing.py. ........ r68214 | georg.brandl | 2009-01-03 20:44:48 +0100 (Sat, 03 Jan 2009) | 2 lines Make indentation consistent. ........ r68215 | georg.brandl | 2009-01-03 21:15:14 +0100 (Sat, 03 Jan 2009) | 2 lines Fix role name. ........ r68217 | georg.brandl | 2009-01-03 21:30:15 +0100 (Sat, 03 Jan 2009) | 2 lines Add rstlint, a little tool to find subtle markup problems and inconsistencies in the Doc sources. ........ r68218 | georg.brandl | 2009-01-03 21:38:59 +0100 (Sat, 03 Jan 2009) | 2 lines Recognize usage of the default role. ........ r68219 | georg.brandl | 2009-01-03 21:47:01 +0100 (Sat, 03 Jan 2009) | 2 lines Fix uses of the default role. ........ r68220 | georg.brandl | 2009-01-03 21:55:06 +0100 (Sat, 03 Jan 2009) | 2 lines Remove trailing whitespace. ........ r68221 | georg.brandl | 2009-01-03 22:04:55 +0100 (Sat, 03 Jan 2009) | 2 lines Remove tabs from the documentation. ........ r68222 | georg.brandl | 2009-01-03 22:11:58 +0100 (Sat, 03 Jan 2009) | 2 lines Disable the line length checker by default. ........
2009-01-03 17:55:17 -04:00
If ``A <: Complex`` and ``B <: Real`` without sharing any other knowledge,
then the appropriate shared operation is the one involving the built
in :class:`complex`, and both :meth:`__radd__` s land there, so ``a+b
== b+a``.
Because most of the operations on any given type will be very similar,
it can be useful to define a helper function which generates the
forward and reverse instances of any given operator. For example,
:class:`fractions.Fraction` uses::
def _operator_fallbacks(monomorphic_operator, fallback_operator):
def forward(a, b):
if isinstance(b, (int, long, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
def _add(a, b):
"""a + b"""
return Fraction(a.numerator * b.denominator +
b.numerator * a.denominator,
a.denominator * b.denominator)
__add__, __radd__ = _operator_fallbacks(_add, operator.add)
# ...