cpython/Lib/numbers.py

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# Copyright 2007 Google, Inc. All Rights Reserved.
# Licensed to PSF under a Contributor Agreement.
"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
TODO: Fill out more detailed documentation on the operators."""
############ Maintenance notes #########################################
#
# ABCs are different from other standard library modules in that they
# specify compliance tests. In general, once an ABC has been published,
# new methods (either abstract or concrete) cannot be added.
#
# Though classes that inherit from an ABC would automatically receive a
# new mixin method, registered classes would become non-compliant and
# violate the contract promised by ``isinstance(someobj, SomeABC)``.
#
# Though irritating, the correct procedure for adding new abstract or
# mixin methods is to create a new ABC as a subclass of the previous
# ABC.
#
# Because they are so hard to change, new ABCs should have their APIs
# carefully thought through prior to publication.
#
# Since ABCMeta only checks for the presence of methods, it is possible
# to alter the signature of a method by adding optional arguments
# or changing parameter names. This is still a bit dubious but at
# least it won't cause isinstance() to return an incorrect result.
#
#
#######################################################################
from abc import ABCMeta, abstractmethod
Merged revisions 61404-61407 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r61404 | raymond.hettinger | 2008-03-15 21:02:04 +0100 (Sat, 15 Mar 2008) | 17 lines Removed Exact/Inexact after discussion with Yasskin. Unlike Scheme where exactness is implemented as taints, the Python implementation associated exactness with data types. This created inheritance issues (making an exact subclass of floats would result in the subclass having both an explicit Exact registration and an inherited Inexact registration). This was a problem for the decimal module which was designed to span both exact and inexact arithmetic. There was also a question of use cases and no examples were found where ABCs for exactness could be used to improve code. One other issue was having separate tags for both the affirmative and negative cases. This is at odds with the approach taken elsewhere in the Python (i.e. we don't have an ABC both Hashable and Unhashable). ........ r61405 | raymond.hettinger | 2008-03-15 21:37:50 +0100 (Sat, 15 Mar 2008) | 1 line Zap one more use of Exact/Inexact. ........ r61406 | neal.norwitz | 2008-03-15 23:03:18 +0100 (Sat, 15 Mar 2008) | 9 lines Add a warning for code like: assert (0, 'message') An empty tuple does not create a warning. While questionable usage: assert (), 'message' should not display a warning. Tested manually. The warning message could be improved. Feel free to update it. ........ r61407 | neal.norwitz | 2008-03-15 23:36:01 +0100 (Sat, 15 Mar 2008) | 1 line Handle memory allocation failure. Found by Adam Olsen ........
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__all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
class Number(metaclass=ABCMeta):
"""All numbers inherit from this class.
If you just want to check if an argument x is a number, without
caring what kind, use isinstance(x, Number).
"""
__slots__ = ()
# Concrete numeric types must provide their own hash implementation
__hash__ = None
Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from 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. ........
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## Notes on Decimal
## ----------------
## Decimal has all of the methods specified by the Real abc, but it should
## not be registered as a Real because decimals do not interoperate with
Merged revisions 61404-61407 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r61404 | raymond.hettinger | 2008-03-15 21:02:04 +0100 (Sat, 15 Mar 2008) | 17 lines Removed Exact/Inexact after discussion with Yasskin. Unlike Scheme where exactness is implemented as taints, the Python implementation associated exactness with data types. This created inheritance issues (making an exact subclass of floats would result in the subclass having both an explicit Exact registration and an inherited Inexact registration). This was a problem for the decimal module which was designed to span both exact and inexact arithmetic. There was also a question of use cases and no examples were found where ABCs for exactness could be used to improve code. One other issue was having separate tags for both the affirmative and negative cases. This is at odds with the approach taken elsewhere in the Python (i.e. we don't have an ABC both Hashable and Unhashable). ........ r61405 | raymond.hettinger | 2008-03-15 21:37:50 +0100 (Sat, 15 Mar 2008) | 1 line Zap one more use of Exact/Inexact. ........ r61406 | neal.norwitz | 2008-03-15 23:03:18 +0100 (Sat, 15 Mar 2008) | 9 lines Add a warning for code like: assert (0, 'message') An empty tuple does not create a warning. While questionable usage: assert (), 'message' should not display a warning. Tested manually. The warning message could be improved. Feel free to update it. ........ r61407 | neal.norwitz | 2008-03-15 23:36:01 +0100 (Sat, 15 Mar 2008) | 1 line Handle memory allocation failure. Found by Adam Olsen ........
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## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But,
## abstract reals are expected to interoperate (i.e. R1 + R2 should be
## expected to work if R1 and R2 are both Reals).
Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60735-60751 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r60735 | raymond.hettinger | 2008-02-11 23:53:01 +0100 (Mon, 11 Feb 2008) | 1 line Add notes on how decimal fits into the model. ........ r60737 | raymond.hettinger | 2008-02-12 00:34:56 +0100 (Tue, 12 Feb 2008) | 1 line Fix markup ........ r60738 | raymond.hettinger | 2008-02-12 00:38:00 +0100 (Tue, 12 Feb 2008) | 1 line Backport ABC docs ........ r60739 | raymond.hettinger | 2008-02-12 01:15:32 +0100 (Tue, 12 Feb 2008) | 1 line Restore fractions.rst to the document tree. ........ r60740 | raymond.hettinger | 2008-02-12 01:48:20 +0100 (Tue, 12 Feb 2008) | 1 line Fix typo in comments ........ r60741 | raymond.hettinger | 2008-02-12 02:18:03 +0100 (Tue, 12 Feb 2008) | 1 line Bring decimal a bit closer to the spec for Reals. ........ r60743 | martin.v.loewis | 2008-02-12 14:47:26 +0100 (Tue, 12 Feb 2008) | 2 lines Patch #1736: Fix file name handling of _msi.FCICreate. ........ r60745 | kurt.kaiser | 2008-02-12 16:45:50 +0100 (Tue, 12 Feb 2008) | 2 lines what??! Correct r60225. ........ r60747 | martin.v.loewis | 2008-02-12 19:47:34 +0100 (Tue, 12 Feb 2008) | 4 lines Patch #1966: Break infinite loop in httplib when the servers implements the chunked encoding incorrectly. Will backport to 2.5. ........ r60749 | raymond.hettinger | 2008-02-12 20:05:36 +0100 (Tue, 12 Feb 2008) | 1 line dict.copy() rises from the ashes. Revert r60687. ........
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class Complex(Number):
"""Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, **, abs(), .conjugate, ==, and !=.
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If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
"""
__slots__ = ()
@abstractmethod
def __complex__(self):
"""Return a builtin complex instance. Called for complex(self)."""
def __bool__(self):
"""True if self != 0. Called for bool(self)."""
return self != 0
@property
@abstractmethod
def real(self):
"""Retrieve the real component of this number.
This should subclass Real.
"""
raise NotImplementedError
@property
@abstractmethod
def imag(self):
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"""Retrieve the imaginary component of this number.
This should subclass Real.
"""
raise NotImplementedError
@abstractmethod
def __add__(self, other):
"""self + other"""
raise NotImplementedError
@abstractmethod
def __radd__(self, other):
"""other + self"""
raise NotImplementedError
@abstractmethod
def __neg__(self):
"""-self"""
raise NotImplementedError
Merged revisions 59952-59984 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59952 | thomas.heller | 2008-01-14 02:35:28 -0800 (Mon, 14 Jan 2008) | 1 line Issue 1821: configure libffi for amd64 on FreeeBSD. ........ r59953 | andrew.kuchling | 2008-01-14 06:48:43 -0800 (Mon, 14 Jan 2008) | 1 line Update description of float_info ........ r59959 | raymond.hettinger | 2008-01-14 14:58:05 -0800 (Mon, 14 Jan 2008) | 1 line Fix 1698398: Zipfile.printdir() crashed because the format string expected a tuple object of length six instead of a time.struct_time object. ........ r59961 | andrew.kuchling | 2008-01-14 17:29:16 -0800 (Mon, 14 Jan 2008) | 1 line Typo fixes ........ r59962 | andrew.kuchling | 2008-01-14 17:29:44 -0800 (Mon, 14 Jan 2008) | 1 line Markup fix ........ r59963 | andrew.kuchling | 2008-01-14 17:47:32 -0800 (Mon, 14 Jan 2008) | 1 line Add many items ........ r59964 | andrew.kuchling | 2008-01-14 17:55:32 -0800 (Mon, 14 Jan 2008) | 1 line Repair unfinished sentence ........ r59967 | raymond.hettinger | 2008-01-14 19:02:37 -0800 (Mon, 14 Jan 2008) | 5 lines Issue 1820: structseq objects did not work with the % formatting operator or isinstance(t, tuple). Orignal patch (without tests) by Leif Walsh. ........ r59968 | raymond.hettinger | 2008-01-14 19:07:42 -0800 (Mon, 14 Jan 2008) | 1 line Tighten the definition of a named tuple. ........ r59969 | skip.montanaro | 2008-01-14 19:40:20 -0800 (Mon, 14 Jan 2008) | 3 lines Better (?) text describing the lack of guarantees provided by qsize(), empty() and full(). ........ r59970 | raymond.hettinger | 2008-01-14 21:39:59 -0800 (Mon, 14 Jan 2008) | 1 line Temporarily revert 59967 until GC can be added. ........ r59971 | raymond.hettinger | 2008-01-14 21:46:43 -0800 (Mon, 14 Jan 2008) | 1 line Small grammar nit ........ r59972 | georg.brandl | 2008-01-14 22:55:56 -0800 (Mon, 14 Jan 2008) | 2 lines Typo. ........ r59973 | georg.brandl | 2008-01-14 22:58:15 -0800 (Mon, 14 Jan 2008) | 2 lines Remove duplicate entry. ........ r59974 | jeffrey.yasskin | 2008-01-14 23:46:24 -0800 (Mon, 14 Jan 2008) | 12 lines Add rational.Rational as an implementation of numbers.Rational with infinite precision. This has been discussed at http://bugs.python.org/issue1682. It's useful primarily for teaching, but it also demonstrates how to implement a member of the numeric tower, including fallbacks for mixed-mode arithmetic. I expect to write a couple more patches in this area: * Rational.from_decimal() * Rational.trim/approximate() (maybe with different names) * Maybe remove the parentheses from Rational.__str__() * Maybe rename one of the Rational classes * Maybe make Rational('3/2') work. ........ r59978 | andrew.kuchling | 2008-01-15 06:38:05 -0800 (Tue, 15 Jan 2008) | 8 lines Restore description of sys.dont_write_bytecode. The duplication is intentional -- this paragraph is in a section describing additions to the sys module, and there's a later section that mentions the switch. I think most people scan the what's-new and don't read it in detail, so a bit of duplication is OK. ........ r59984 | guido.van.rossum | 2008-01-15 09:59:29 -0800 (Tue, 15 Jan 2008) | 3 lines Issue #1786 (by myself): pdb should use its own stdin/stdout around an exec call and when creating a recursive instance. ........
2008-01-15 17:44:53 -04:00
@abstractmethod
def __pos__(self):
"""+self"""
raise NotImplementedError
def __sub__(self, other):
"""self - other"""
return self + -other
def __rsub__(self, other):
"""other - self"""
return -self + other
@abstractmethod
def __mul__(self, other):
"""self * other"""
raise NotImplementedError
@abstractmethod
def __rmul__(self, other):
"""other * self"""
raise NotImplementedError
Merged revisions 59952-59984 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59952 | thomas.heller | 2008-01-14 02:35:28 -0800 (Mon, 14 Jan 2008) | 1 line Issue 1821: configure libffi for amd64 on FreeeBSD. ........ r59953 | andrew.kuchling | 2008-01-14 06:48:43 -0800 (Mon, 14 Jan 2008) | 1 line Update description of float_info ........ r59959 | raymond.hettinger | 2008-01-14 14:58:05 -0800 (Mon, 14 Jan 2008) | 1 line Fix 1698398: Zipfile.printdir() crashed because the format string expected a tuple object of length six instead of a time.struct_time object. ........ r59961 | andrew.kuchling | 2008-01-14 17:29:16 -0800 (Mon, 14 Jan 2008) | 1 line Typo fixes ........ r59962 | andrew.kuchling | 2008-01-14 17:29:44 -0800 (Mon, 14 Jan 2008) | 1 line Markup fix ........ r59963 | andrew.kuchling | 2008-01-14 17:47:32 -0800 (Mon, 14 Jan 2008) | 1 line Add many items ........ r59964 | andrew.kuchling | 2008-01-14 17:55:32 -0800 (Mon, 14 Jan 2008) | 1 line Repair unfinished sentence ........ r59967 | raymond.hettinger | 2008-01-14 19:02:37 -0800 (Mon, 14 Jan 2008) | 5 lines Issue 1820: structseq objects did not work with the % formatting operator or isinstance(t, tuple). Orignal patch (without tests) by Leif Walsh. ........ r59968 | raymond.hettinger | 2008-01-14 19:07:42 -0800 (Mon, 14 Jan 2008) | 1 line Tighten the definition of a named tuple. ........ r59969 | skip.montanaro | 2008-01-14 19:40:20 -0800 (Mon, 14 Jan 2008) | 3 lines Better (?) text describing the lack of guarantees provided by qsize(), empty() and full(). ........ r59970 | raymond.hettinger | 2008-01-14 21:39:59 -0800 (Mon, 14 Jan 2008) | 1 line Temporarily revert 59967 until GC can be added. ........ r59971 | raymond.hettinger | 2008-01-14 21:46:43 -0800 (Mon, 14 Jan 2008) | 1 line Small grammar nit ........ r59972 | georg.brandl | 2008-01-14 22:55:56 -0800 (Mon, 14 Jan 2008) | 2 lines Typo. ........ r59973 | georg.brandl | 2008-01-14 22:58:15 -0800 (Mon, 14 Jan 2008) | 2 lines Remove duplicate entry. ........ r59974 | jeffrey.yasskin | 2008-01-14 23:46:24 -0800 (Mon, 14 Jan 2008) | 12 lines Add rational.Rational as an implementation of numbers.Rational with infinite precision. This has been discussed at http://bugs.python.org/issue1682. It's useful primarily for teaching, but it also demonstrates how to implement a member of the numeric tower, including fallbacks for mixed-mode arithmetic. I expect to write a couple more patches in this area: * Rational.from_decimal() * Rational.trim/approximate() (maybe with different names) * Maybe remove the parentheses from Rational.__str__() * Maybe rename one of the Rational classes * Maybe make Rational('3/2') work. ........ r59978 | andrew.kuchling | 2008-01-15 06:38:05 -0800 (Tue, 15 Jan 2008) | 8 lines Restore description of sys.dont_write_bytecode. The duplication is intentional -- this paragraph is in a section describing additions to the sys module, and there's a later section that mentions the switch. I think most people scan the what's-new and don't read it in detail, so a bit of duplication is OK. ........ r59984 | guido.van.rossum | 2008-01-15 09:59:29 -0800 (Tue, 15 Jan 2008) | 3 lines Issue #1786 (by myself): pdb should use its own stdin/stdout around an exec call and when creating a recursive instance. ........
2008-01-15 17:44:53 -04:00
@abstractmethod
def __truediv__(self, other):
"""self / other: Should promote to float when necessary."""
Merged revisions 59952-59984 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r59952 | thomas.heller | 2008-01-14 02:35:28 -0800 (Mon, 14 Jan 2008) | 1 line Issue 1821: configure libffi for amd64 on FreeeBSD. ........ r59953 | andrew.kuchling | 2008-01-14 06:48:43 -0800 (Mon, 14 Jan 2008) | 1 line Update description of float_info ........ r59959 | raymond.hettinger | 2008-01-14 14:58:05 -0800 (Mon, 14 Jan 2008) | 1 line Fix 1698398: Zipfile.printdir() crashed because the format string expected a tuple object of length six instead of a time.struct_time object. ........ r59961 | andrew.kuchling | 2008-01-14 17:29:16 -0800 (Mon, 14 Jan 2008) | 1 line Typo fixes ........ r59962 | andrew.kuchling | 2008-01-14 17:29:44 -0800 (Mon, 14 Jan 2008) | 1 line Markup fix ........ r59963 | andrew.kuchling | 2008-01-14 17:47:32 -0800 (Mon, 14 Jan 2008) | 1 line Add many items ........ r59964 | andrew.kuchling | 2008-01-14 17:55:32 -0800 (Mon, 14 Jan 2008) | 1 line Repair unfinished sentence ........ r59967 | raymond.hettinger | 2008-01-14 19:02:37 -0800 (Mon, 14 Jan 2008) | 5 lines Issue 1820: structseq objects did not work with the % formatting operator or isinstance(t, tuple). Orignal patch (without tests) by Leif Walsh. ........ r59968 | raymond.hettinger | 2008-01-14 19:07:42 -0800 (Mon, 14 Jan 2008) | 1 line Tighten the definition of a named tuple. ........ r59969 | skip.montanaro | 2008-01-14 19:40:20 -0800 (Mon, 14 Jan 2008) | 3 lines Better (?) text describing the lack of guarantees provided by qsize(), empty() and full(). ........ r59970 | raymond.hettinger | 2008-01-14 21:39:59 -0800 (Mon, 14 Jan 2008) | 1 line Temporarily revert 59967 until GC can be added. ........ r59971 | raymond.hettinger | 2008-01-14 21:46:43 -0800 (Mon, 14 Jan 2008) | 1 line Small grammar nit ........ r59972 | georg.brandl | 2008-01-14 22:55:56 -0800 (Mon, 14 Jan 2008) | 2 lines Typo. ........ r59973 | georg.brandl | 2008-01-14 22:58:15 -0800 (Mon, 14 Jan 2008) | 2 lines Remove duplicate entry. ........ r59974 | jeffrey.yasskin | 2008-01-14 23:46:24 -0800 (Mon, 14 Jan 2008) | 12 lines Add rational.Rational as an implementation of numbers.Rational with infinite precision. This has been discussed at http://bugs.python.org/issue1682. It's useful primarily for teaching, but it also demonstrates how to implement a member of the numeric tower, including fallbacks for mixed-mode arithmetic. I expect to write a couple more patches in this area: * Rational.from_decimal() * Rational.trim/approximate() (maybe with different names) * Maybe remove the parentheses from Rational.__str__() * Maybe rename one of the Rational classes * Maybe make Rational('3/2') work. ........ r59978 | andrew.kuchling | 2008-01-15 06:38:05 -0800 (Tue, 15 Jan 2008) | 8 lines Restore description of sys.dont_write_bytecode. The duplication is intentional -- this paragraph is in a section describing additions to the sys module, and there's a later section that mentions the switch. I think most people scan the what's-new and don't read it in detail, so a bit of duplication is OK. ........ r59984 | guido.van.rossum | 2008-01-15 09:59:29 -0800 (Tue, 15 Jan 2008) | 3 lines Issue #1786 (by myself): pdb should use its own stdin/stdout around an exec call and when creating a recursive instance. ........
2008-01-15 17:44:53 -04:00
raise NotImplementedError
@abstractmethod
def __rtruediv__(self, other):
"""other / self"""
raise NotImplementedError
@abstractmethod
def __pow__(self, exponent):
"""self ** exponent; should promote to float or complex when necessary."""
raise NotImplementedError
@abstractmethod
def __rpow__(self, base):
"""base ** self"""
raise NotImplementedError
@abstractmethod
def __abs__(self):
"""Returns the Real distance from 0. Called for abs(self)."""
raise NotImplementedError
@abstractmethod
def conjugate(self):
"""(x+y*i).conjugate() returns (x-y*i)."""
raise NotImplementedError
@abstractmethod
def __eq__(self, other):
"""self == other"""
raise NotImplementedError
Complex.register(complex)
class Real(Complex):
"""To Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
"""
__slots__ = ()
@abstractmethod
def __float__(self):
"""Any Real can be converted to a native float object.
Called for float(self)."""
raise NotImplementedError
@abstractmethod
def __trunc__(self):
"""trunc(self): Truncates self to an Integral.
Returns an Integral i such that:
* i > 0 iff self > 0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
"""
raise NotImplementedError
@abstractmethod
def __floor__(self):
"""Finds the greatest Integral <= self."""
raise NotImplementedError
@abstractmethod
def __ceil__(self):
"""Finds the least Integral >= self."""
raise NotImplementedError
@abstractmethod
def __round__(self, ndigits=None):
"""Rounds self to ndigits decimal places, defaulting to 0.
If ndigits is omitted or None, returns an Integral, otherwise
returns a Real. Rounds half toward even.
"""
raise NotImplementedError
def __divmod__(self, other):
"""divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
"""
return (self // other, self % other)
def __rdivmod__(self, other):
"""divmod(other, self): The pair (other // self, other % self).
Sometimes this can be computed faster than the pair of
operations.
"""
return (other // self, other % self)
@abstractmethod
def __floordiv__(self, other):
"""self // other: The floor() of self/other."""
raise NotImplementedError
@abstractmethod
def __rfloordiv__(self, other):
"""other // self: The floor() of other/self."""
raise NotImplementedError
@abstractmethod
def __mod__(self, other):
"""self % other"""
raise NotImplementedError
@abstractmethod
def __rmod__(self, other):
"""other % self"""
raise NotImplementedError
@abstractmethod
def __lt__(self, other):
"""self < other
< on Reals defines a total ordering, except perhaps for NaN."""
raise NotImplementedError
@abstractmethod
def __le__(self, other):
"""self <= other"""
raise NotImplementedError
# Concrete implementations of Complex abstract methods.
def __complex__(self):
"""complex(self) == complex(float(self), 0)"""
return complex(float(self))
@property
def real(self):
"""Real numbers are their real component."""
return +self
@property
def imag(self):
"""Real numbers have no imaginary component."""
return 0
def conjugate(self):
"""Conjugate is a no-op for Reals."""
return +self
Real.register(float)
Merged revisions 61404-61407 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r61404 | raymond.hettinger | 2008-03-15 21:02:04 +0100 (Sat, 15 Mar 2008) | 17 lines Removed Exact/Inexact after discussion with Yasskin. Unlike Scheme where exactness is implemented as taints, the Python implementation associated exactness with data types. This created inheritance issues (making an exact subclass of floats would result in the subclass having both an explicit Exact registration and an inherited Inexact registration). This was a problem for the decimal module which was designed to span both exact and inexact arithmetic. There was also a question of use cases and no examples were found where ABCs for exactness could be used to improve code. One other issue was having separate tags for both the affirmative and negative cases. This is at odds with the approach taken elsewhere in the Python (i.e. we don't have an ABC both Hashable and Unhashable). ........ r61405 | raymond.hettinger | 2008-03-15 21:37:50 +0100 (Sat, 15 Mar 2008) | 1 line Zap one more use of Exact/Inexact. ........ r61406 | neal.norwitz | 2008-03-15 23:03:18 +0100 (Sat, 15 Mar 2008) | 9 lines Add a warning for code like: assert (0, 'message') An empty tuple does not create a warning. While questionable usage: assert (), 'message' should not display a warning. Tested manually. The warning message could be improved. Feel free to update it. ........ r61407 | neal.norwitz | 2008-03-15 23:36:01 +0100 (Sat, 15 Mar 2008) | 1 line Handle memory allocation failure. Found by Adam Olsen ........
2008-03-15 21:32:36 -03:00
class Rational(Real):
""".numerator and .denominator should be in lowest terms."""
__slots__ = ()
@property
@abstractmethod
def numerator(self):
raise NotImplementedError
@property
@abstractmethod
def denominator(self):
raise NotImplementedError
# Concrete implementation of Real's conversion to float.
def __float__(self):
2008-01-31 10:31:45 -04:00
"""float(self) = self.numerator / self.denominator
It's important that this conversion use the integer's "true"
division rather than casting one side to float before dividing
so that ratios of huge integers convert without overflowing.
"""
return self.numerator / self.denominator
class Integral(Rational):
"""Integral adds methods that work on integral numbers.
In short, these are conversion to int, pow with modulus, and the
bit-string operations.
"""
__slots__ = ()
@abstractmethod
def __int__(self):
"""int(self)"""
raise NotImplementedError
def __index__(self):
"""Called whenever an index is needed, such as in slicing"""
return int(self)
@abstractmethod
def __pow__(self, exponent, modulus=None):
"""self ** exponent % modulus, but maybe faster.
Accept the modulus argument if you want to support the
3-argument version of pow(). Raise a TypeError if exponent < 0
or any argument isn't Integral. Otherwise, just implement the
2-argument version described in Complex.
"""
raise NotImplementedError
@abstractmethod
def __lshift__(self, other):
"""self << other"""
raise NotImplementedError
@abstractmethod
def __rlshift__(self, other):
"""other << self"""
raise NotImplementedError
@abstractmethod
def __rshift__(self, other):
"""self >> other"""
raise NotImplementedError
@abstractmethod
def __rrshift__(self, other):
"""other >> self"""
raise NotImplementedError
@abstractmethod
def __and__(self, other):
"""self & other"""
raise NotImplementedError
@abstractmethod
def __rand__(self, other):
"""other & self"""
raise NotImplementedError
@abstractmethod
def __xor__(self, other):
"""self ^ other"""
raise NotImplementedError
@abstractmethod
def __rxor__(self, other):
"""other ^ self"""
raise NotImplementedError
@abstractmethod
def __or__(self, other):
"""self | other"""
raise NotImplementedError
@abstractmethod
def __ror__(self, other):
"""other | self"""
raise NotImplementedError
@abstractmethod
def __invert__(self):
"""~self"""
raise NotImplementedError
# Concrete implementations of Rational and Real abstract methods.
def __float__(self):
"""float(self) == float(int(self))"""
return float(int(self))
@property
def numerator(self):
"""Integers are their own numerators."""
return +self
@property
def denominator(self):
"""Integers have a denominator of 1."""
return 1
Integral.register(int)