cpython-lru_cache-weakref: Lib/fractions.py annotate

annotate Lib/fractions.py @ 58925:eecf1bef052d 2.6

Merged revisions 78207 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r78207 | ezio.melotti | 2010-02-17 01:26:09 +0200 (Wed, 17 Feb 2010) | 1 line #7930: fix stripid ........

author	Ezio Melotti <ezio.melotti@gmail.com>
date	Tue, 16 Feb 2010 23:29:44 +0000
parents	0869e1ab572e
children	b36cb4602e21

rev	line source
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	1 # Originally contributed by Sjoerd Mullender.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	2 # Significantly modified by Jeffrey Yasskin <jyasskin at gmail.com>.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	3
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	4 """Rational, infinite-precision, real numbers."""
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	5
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	6 from __future__ import division
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	7 import math
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	8 import numbers
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	9 import operator
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	10 import re
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	11
46727 0e76a8f34769 The __all__ variable forgot to expose the gcd() function. Raymond Hettinger <python@rcn.com> parents: 45332 diff changeset	12 __all__ = ['Fraction', 'gcd']
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	13
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	14 Rational = numbers.Rational
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	15
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	16
44993 4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	17 def gcd(a, b):
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	18 """Calculate the Greatest Common Divisor of a and b.
945 465b9841770e Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	19
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	20 Unless b==0, the result will have the same sign as b (so that when
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	21 b is divided by it, the result comes out positive).
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	22 """
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	23 while b:
558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	24 a, b = b, a%b
558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	25 return a
945 465b9841770e Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	26
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	27
45113 04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	28 _RATIONAL_FORMAT = re.compile(r"""
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	29 \A\s* # optional whitespace at the start, then
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	30 (?P<sign>[-+]?) # an optional sign, then
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	31 (?=\d\|\.\d) # lookahead for digit or .digit
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	32 (?P<num>\d*) # numerator (possibly empty)
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	33 (?: # followed by an optional
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	34 /(?P<denom>\d+) # / and denominator
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	35 \| # or
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	36 \.(?P<decimal>\d*) # decimal point and fractional part
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	37 )?
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	38 \s*\Z # and optional whitespace to finish
04653f92664f Make the Rational constructor accept '3.' and '.2' as well as '3.2'. Mark Dickinson <dickinsm@gmail.com> parents: 45080 diff changeset	39 """, re.VERBOSE)
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	40
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	41
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	42 class Fraction(Rational):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	43 """This class implements rational numbers.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	44
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	45 Fraction(8, 6) will produce a rational number equivalent to
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	46 4/3. Both arguments must be Integral. The numerator defaults to 0
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	47 and the denominator defaults to 1 so that Fraction(3) == 3 and
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	48 Fraction() == 0.
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	49
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	50 Fractions can also be constructed from strings of the form
44993 4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	51 '[-+]?[0-9]+((/\|.)[0-9]+)?', optionally surrounded by spaces.
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	52
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	53 """
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	54
45080 678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	55 __slots__ = ('_numerator', '_denominator')
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	56
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	57 # We're immutable, so use __new__ not __init__
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	58 def __new__(cls, numerator=0, denominator=1):
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	59 """Constructs a Fraction.
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	60
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	61 Takes a string like '3/2' or '1.5', another Fraction, or a
44993 4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	62 numerator/denominator pair.
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	63
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	64 """
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	65 self = super(Fraction, cls).__new__(cls)
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	66
45331 c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	67 if type(numerator) not in (int, long) and denominator == 1:
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	68 if isinstance(numerator, basestring):
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	69 # Handle construction from strings.
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	70 input = numerator
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	71 m = _RATIONAL_FORMAT.match(input)
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	72 if m is None:
47793 ac6eab2473c5 Use repr() for bad input strings; this makes the empty string or binary characters more visible Andrew M. Kuchling <amk@amk.ca> parents: 46727 diff changeset	73 raise ValueError('Invalid literal for Fraction: %r' % input)
44993 4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	74 numerator = m.group('num')
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	75 decimal = m.group('decimal')
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	76 if decimal:
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	77 # The literal is a decimal number.
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	78 numerator = int(numerator + decimal)
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	79 denominator = 10**len(decimal)
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	80 else:
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	81 # The literal is an integer or fraction.
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	82 numerator = int(numerator)
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	83 # Default denominator to 1.
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	84 denominator = int(m.group('denom') or 1)
4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	85
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	86 if m.group('sign') == '-':
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	87 numerator = -numerator
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	88
45331 c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	89 elif isinstance(numerator, Rational):
c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	90 # Handle copies from other rationals. Integrals get
c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	91 # caught here too, but it doesn't matter because
c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	92 # denominator is already 1.
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	93 other_rational = numerator
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	94 numerator = other_rational.numerator
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	95 denominator = other_rational.denominator
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	96
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	97 if denominator == 0:
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	98 raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
47917 c32e91650c14 Use operator.index() instead of n.__index__(). Raymond Hettinger <python@rcn.com> parents: 47916 diff changeset	99 numerator = operator.index(numerator)
c32e91650c14 Use operator.index() instead of n.__index__(). Raymond Hettinger <python@rcn.com> parents: 47916 diff changeset	100 denominator = operator.index(denominator)
44993 4dd0fcf3daf7 Make rational.gcd() public and allow Rational to take decimal strings, per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44937 diff changeset	101 g = gcd(numerator, denominator)
45331 c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	102 self._numerator = numerator // g
c7e683d52b3b Performance optimizations on Fraction's constructor. Jeffrey Yasskin <jyasskin@gmail.com> parents: 45305 diff changeset	103 self._denominator = denominator // g
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	104 return self
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	105
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	106 @classmethod
d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	107 def from_float(cls, f):
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	108 """Converts a finite float to a rational number, exactly.
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	109
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	110 Beware that Fraction.from_float(0.3) != Fraction(3, 10).
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	111
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	112 """
47920 bd435e8b2e28 Issue 3285: Fractions from_float() and from_decimal() accept Integral arguments. Raymond Hettinger <python@rcn.com> parents: 47917 diff changeset	113 if isinstance(f, numbers.Integral):
50476 c45fed03f747 Fractions.from_float() no longer loses precision with large integer inputs. Raymond Hettinger <python@rcn.com> parents: 47920 diff changeset	114 return cls(f)
47920 bd435e8b2e28 Issue 3285: Fractions from_float() and from_decimal() accept Integral arguments. Raymond Hettinger <python@rcn.com> parents: 47917 diff changeset	115 elif not isinstance(f, float):
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	116 raise TypeError("%s.from_float() only takes floats, not %r (%s)" %
d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	117 (cls.__name__, f, type(f).__name__))
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	118 if math.isnan(f) or math.isinf(f):
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	119 raise TypeError("Cannot convert %r to %s." % (f, cls.__name__))
d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	120 return cls(*f.as_integer_ratio())
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	121
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	122 @classmethod
d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	123 def from_decimal(cls, dec):
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	124 """Converts a finite Decimal instance to a rational number, exactly."""
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	125 from decimal import Decimal
47920 bd435e8b2e28 Issue 3285: Fractions from_float() and from_decimal() accept Integral arguments. Raymond Hettinger <python@rcn.com> parents: 47917 diff changeset	126 if isinstance(dec, numbers.Integral):
bd435e8b2e28 Issue 3285: Fractions from_float() and from_decimal() accept Integral arguments. Raymond Hettinger <python@rcn.com> parents: 47917 diff changeset	127 dec = Decimal(int(dec))
bd435e8b2e28 Issue 3285: Fractions from_float() and from_decimal() accept Integral arguments. Raymond Hettinger <python@rcn.com> parents: 47917 diff changeset	128 elif not isinstance(dec, Decimal):
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	129 raise TypeError(
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	130 "%s.from_decimal() only takes Decimals, not %r (%s)" %
d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	131 (cls.__name__, dec, type(dec).__name__))
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	132 if not dec.is_finite():
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	133 # Catches infinities and nans.
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	134 raise TypeError("Cannot convert %s to %s." % (dec, cls.__name__))
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	135 sign, digits, exp = dec.as_tuple()
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	136 digits = int(''.join(map(str, digits)))
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	137 if sign:
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	138 digits = -digits
c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	139 if exp >= 0:
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	140 return cls(digits * 10 ** exp)
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	141 else:
45305 d319f40cd000 Revert change in r60712: turn alternate constructors back into Mark Dickinson <dickinsm@gmail.com> parents: 45303 diff changeset	142 return cls(digits, 10 ** -exp)
44757 c4709b81abde Several tweaks: add construction from strings and .from_decimal(), change Jeffrey Yasskin <jyasskin@gmail.com> parents: 44691 diff changeset	143
45303 d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	144 def limit_denominator(self, max_denominator=1000000):
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	145 """Closest Fraction to self with denominator at most max_denominator.
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	146
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	147 >>> Fraction('3.141592653589793').limit_denominator(10)
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	148 Fraction(22, 7)
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	149 >>> Fraction('3.141592653589793').limit_denominator(100)
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	150 Fraction(311, 99)
57404 0869e1ab572e Merged revisions 76456 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50476 diff changeset	151 >>> Fraction(4321, 8765).limit_denominator(10000)
0869e1ab572e Merged revisions 76456 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50476 diff changeset	152 Fraction(4321, 8765)
44899 cdc4aecedd4c Add first-cut at an approximation function (still needs rounding tweaks). Add continued fraction conversions. Raymond Hettinger <python@rcn.com> parents: 44757 diff changeset	153
45303 d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	154 """
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	155 # Algorithm notes: For any real number x, define a *best upper
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	156 # approximation* to x to be a rational number p/q such that:
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	157 #
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	158 # (1) p/q >= x, and
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	159 # (2) if p/q > r/s >= x then s > q, for any rational r/s.
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	160 #
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	161 # Define best lower approximation similarly. Then it can be
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	162 # proved that a rational number is a best upper or lower
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	163 # approximation to x if, and only if, it is a convergent or
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	164 # semiconvergent of the (unique shortest) continued fraction
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	165 # associated to x.
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	166 #
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	167 # To find a best rational approximation with denominator <= M,
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	168 # we find the best upper and lower approximations with
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	169 # denominator <= M and take whichever of these is closer to x.
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	170 # In the event of a tie, the bound with smaller denominator is
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	171 # chosen. If both denominators are equal (which can happen
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	172 # only when max_denominator == 1 and self is midway between
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	173 # two integers) the lower bound---i.e., the floor of self, is
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	174 # taken.
44899 cdc4aecedd4c Add first-cut at an approximation function (still needs rounding tweaks). Add continued fraction conversions. Raymond Hettinger <python@rcn.com> parents: 44757 diff changeset	175
45303 d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	176 if max_denominator < 1:
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	177 raise ValueError("max_denominator should be at least 1")
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	178 if self._denominator <= max_denominator:
45303 d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	179 return Fraction(self)
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	180
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	181 p0, q0, p1, q1 = 0, 1, 1, 0
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	182 n, d = self._numerator, self._denominator
45303 d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	183 while True:
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	184 a = n//d
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	185 q2 = q0+a*q1
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	186 if q2 > max_denominator:
44899 cdc4aecedd4c Add first-cut at an approximation function (still needs rounding tweaks). Add continued fraction conversions. Raymond Hettinger <python@rcn.com> parents: 44757 diff changeset	187 break
45303 d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	188 p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	189 n, d = d, n-a*d
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	190
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	191 k = (max_denominator-q0)//q1
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	192 bound1 = Fraction(p0+kp1, q0+kq1)
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	193 bound2 = Fraction(p1, q1)
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	194 if abs(bound2 - self) <= abs(bound1-self):
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	195 return bound2
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	196 else:
d673d003b6ca Implementation of Fraction.limit_denominator. Mark Dickinson <dickinsm@gmail.com> parents: 45277 diff changeset	197 return bound1
44899 cdc4aecedd4c Add first-cut at an approximation function (still needs rounding tweaks). Add continued fraction conversions. Raymond Hettinger <python@rcn.com> parents: 44757 diff changeset	198
45080 678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	199 @property
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	200 def numerator(a):
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	201 return a._numerator
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	202
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	203 @property
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	204 def denominator(a):
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	205 return a._denominator
678509f9a03f Roll back r60248. It's useful to encourage users not to change Rational Jeffrey Yasskin <jyasskin@gmail.com> parents: 45075 diff changeset	206
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	207 def __repr__(self):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	208 """repr(self)"""
47839 43f6bb0eacb2 Remove trailing 'L's from numerator and denominator in the Mark Dickinson <dickinsm@gmail.com> parents: 47793 diff changeset	209 return ('Fraction(%s, %s)' % (self._numerator, self._denominator))
1966 dd7be8128410 adapted to new overloading scheme Guido van Rossum <guido@python.org> parents: 1427 diff changeset	210
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	211 def __str__(self):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	212 """str(self)"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	213 if self._denominator == 1:
4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	214 return str(self._numerator)
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	215 else:
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	216 return '%s/%s' % (self._numerator, self._denominator)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	217
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	218 def _operator_fallbacks(monomorphic_operator, fallback_operator):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	219 """Generates forward and reverse operators given a purely-rational
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	220 operator and a function from the operator module.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	221
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	222 Use this like:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	223 __op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	224
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	225 In general, we want to implement the arithmetic operations so
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	226 that mixed-mode operations either call an implementation whose
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	227 author knew about the types of both arguments, or convert both
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	228 to the nearest built in type and do the operation there. In
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	229 Fraction, that means that we define __add__ and __radd__ as:
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	230
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	231 def __add__(self, other):
45075 8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	232 # Both types have numerators/denominator attributes,
8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	233 # so do the operation directly
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	234 if isinstance(other, (int, long, Fraction)):
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	235 return Fraction(self.numerator * other.denominator +
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	236 other.numerator * self.denominator,
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	237 self.denominator * other.denominator)
45075 8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	238 # float and complex don't have those operations, but we
8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	239 # know about those types, so special case them.
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	240 elif isinstance(other, float):
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	241 return float(self) + other
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	242 elif isinstance(other, complex):
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	243 return complex(self) + other
45075 8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	244 # Let the other type take over.
8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	245 return NotImplemented
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	246
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	247 def __radd__(self, other):
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	248 # radd handles more types than add because there's
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	249 # nothing left to fall back to.
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	250 if isinstance(other, Rational):
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	251 return Fraction(self.numerator * other.denominator +
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	252 other.numerator * self.denominator,
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	253 self.denominator * other.denominator)
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	254 elif isinstance(other, Real):
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	255 return float(other) + float(self)
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	256 elif isinstance(other, Complex):
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	257 return complex(other) + complex(self)
45075 8659e52614da Minor wordsmithing on docstring Raymond Hettinger <python@rcn.com> parents: 45073 diff changeset	258 return NotImplemented
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	259
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	260
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	261 There are 5 different cases for a mixed-type addition on
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	262 Fraction. I'll refer to all of the above code that doesn't
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	263 refer to Fraction, float, or complex as "boilerplate". 'r'
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	264 will be an instance of Fraction, which is a subtype of
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	265 Rational (r : Fraction <: Rational), and b : B <:
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	266 Complex. The first three involve 'r + b':
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	267
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	268 1. If B <: Fraction, int, float, or complex, we handle
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	269 that specially, and all is well.
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	270 2. If Fraction falls back to the boilerplate code, and it
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	271 were to return a value from __add__, we'd miss the
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	272 possibility that B defines a more intelligent __radd__,
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	273 so the boilerplate should return NotImplemented from
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	274 __add__. In particular, we don't handle Rational
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	275 here, even though we could get an exact answer, in case
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	276 the other type wants to do something special.
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	277 3. If B <: Fraction, Python tries B.__radd__ before
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	278 Fraction.__add__. This is ok, because it was
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	279 implemented with knowledge of Fraction, so it can
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	280 handle those instances before delegating to Real or
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	281 Complex.
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	282
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	283 The next two situations describe 'b + r'. We assume that b
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	284 didn't know about Fraction in its implementation, and that it
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	285 uses similar boilerplate code:
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	286
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	287 4. If B <: Rational, then __radd_ converts both to the
45070 03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	288 builtin rational type (hey look, that's us) and
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	289 proceeds.
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	290 5. Otherwise, __radd__ tries to find the nearest common
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	291 base ABC, and fall back to its builtin type. Since this
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	292 class doesn't subclass a concrete type, there's no
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	293 implementation to fall back to, so we need to try as
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	294 hard as possible to return an actual value, or the user
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	295 will get a TypeError.
03e4a36a56bb Added more documentation on how mixed-mode arithmetic should be implemented. I Jeffrey Yasskin <jyasskin@gmail.com> parents: 45024 diff changeset	296
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	297 """
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	298 def forward(a, b):
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	299 if isinstance(b, (int, long, Fraction)):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	300 return monomorphic_operator(a, b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	301 elif isinstance(b, float):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	302 return fallback_operator(float(a), b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	303 elif isinstance(b, complex):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	304 return fallback_operator(complex(a), b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	305 else:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	306 return NotImplemented
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	307 forward.__name__ = '__' + fallback_operator.__name__ + '__'
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	308 forward.__doc__ = monomorphic_operator.__doc__
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	309
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	310 def reverse(b, a):
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	311 if isinstance(a, Rational):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	312 # Includes ints.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	313 return monomorphic_operator(a, b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	314 elif isinstance(a, numbers.Real):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	315 return fallback_operator(float(a), float(b))
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	316 elif isinstance(a, numbers.Complex):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	317 return fallback_operator(complex(a), complex(b))
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	318 else:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	319 return NotImplemented
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	320 reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	321 reverse.__doc__ = monomorphic_operator.__doc__
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	322
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	323 return forward, reverse
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	324
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	325 def _add(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	326 """a + b"""
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	327 return Fraction(a.numerator * b.denominator +
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	328 b.numerator * a.denominator,
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	329 a.denominator * b.denominator)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	330
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	331 __add__, __radd__ = _operator_fallbacks(_add, operator.add)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	332
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	333 def _sub(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	334 """a - b"""
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	335 return Fraction(a.numerator * b.denominator -
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	336 b.numerator * a.denominator,
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	337 a.denominator * b.denominator)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	338
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	339 __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	340
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	341 def _mul(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	342 """a * b"""
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	343 return Fraction(a.numerator * b.numerator, a.denominator * b.denominator)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	344
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	345 __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	346
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	347 def _div(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	348 """a / b"""
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	349 return Fraction(a.numerator * b.denominator,
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	350 a.denominator * b.numerator)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	351
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	352 __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	353 __div__, __rdiv__ = _operator_fallbacks(_div, operator.div)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	354
44932 ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	355 def __floordiv__(a, b):
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	356 """a // b"""
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	357 # Will be math.floor(a / b) in 3.0.
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	358 div = a / b
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	359 if isinstance(div, Rational):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	360 # trunc(math.floor(div)) doesn't work if the rational is
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	361 # more precise than a float because the intermediate
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	362 # rounding may cross an integer boundary.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	363 return div.numerator // div.denominator
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	364 else:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	365 return math.floor(div)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	366
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	367 def __rfloordiv__(b, a):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	368 """a // b"""
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	369 # Will be math.floor(a / b) in 3.0.
44932 ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	370 div = a / b
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	371 if isinstance(div, Rational):
44932 ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	372 # trunc(math.floor(div)) doesn't work if the rational is
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	373 # more precise than a float because the intermediate
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	374 # rounding may cross an integer boundary.
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	375 return div.numerator // div.denominator
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	376 else:
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	377 return math.floor(div)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	378
44932 ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	379 def __mod__(a, b):
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	380 """a % b"""
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	381 div = a // b
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	382 return a - b * div
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	383
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	384 def __rmod__(b, a):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	385 """a % b"""
44932 ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	386 div = a // b
ce159d01ee32 More code cleanup. Remove unnecessary indirection to useless class methods. Raymond Hettinger <python@rcn.com> parents: 44925 diff changeset	387 return a - b * div
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	388
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	389 def __pow__(a, b):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	390 """a ** b
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	391
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	392 If b is not an integer, the result will be a float or complex
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	393 since roots are generally irrational. If b is an integer, the
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	394 result will be rational.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	395
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	396 """
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	397 if isinstance(b, Rational):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	398 if b.denominator == 1:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	399 power = b.numerator
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	400 if power >= 0:
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	401 return Fraction(a._numerator ** power,
4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	402 a._denominator ** power)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	403 else:
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	404 return Fraction(a._denominator ** -power,
4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	405 a._numerator ** -power)
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	406 else:
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	407 # A fractional power will generally produce an
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	408 # irrational number.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	409 return float(a) ** float(b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	410 else:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	411 return float(a) ** b
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	412
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	413 def __rpow__(b, a):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	414 """a ** b"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	415 if b._denominator == 1 and b._numerator >= 0:
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	416 # If a is an int, keep it that way if possible.
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	417 return a ** b._numerator
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	418
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	419 if isinstance(a, Rational):
a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	420 return Fraction(a.numerator, a.denominator) ** b
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	421
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	422 if b._denominator == 1:
4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	423 return a ** b._numerator
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	424
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	425 return a ** float(b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	426
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	427 def __pos__(a):
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	428 """+a: Coerces a subclass instance to Fraction"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	429 return Fraction(a._numerator, a._denominator)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	430
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	431 def __neg__(a):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	432 """-a"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	433 return Fraction(-a._numerator, a._denominator)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	434
28788 558689b6d7f0 Run these demo scripts through reindent.py to give them 4-space indents. I've verified that their output is unchanged. Andrew M. Kuchling <amk@amk.ca> parents: 28787 diff changeset	435 def __abs__(a):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	436 """abs(a)"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	437 return Fraction(abs(a._numerator), a._denominator)
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	438
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	439 def __trunc__(a):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	440 """trunc(a)"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	441 if a._numerator < 0:
4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	442 return -(-a._numerator // a._denominator)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	443 else:
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	444 return a._numerator // a._denominator
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	445
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	446 def __hash__(self):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	447 """hash(self)
945 465b9841770e Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	448
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	449 Tricky because values that are exactly representable as a
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	450 float must have the same hash as that float.
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	451
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	452 """
44934 3bd19c8af2b1 Mark todos and review comments. Raymond Hettinger <python@rcn.com> parents: 44933 diff changeset	453 # XXX since this method is expensive, consider caching the result
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	454 if self._denominator == 1:
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	455 # Get integers right.
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	456 return hash(self._numerator)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	457 # Expensive check, but definitely correct.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	458 if self == float(self):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	459 return hash(float(self))
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	460 else:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	461 # Use tuple's hash to avoid a high collision rate on
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	462 # simple fractions.
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	463 return hash((self._numerator, self._denominator))
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	464
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	465 def __eq__(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	466 """a == b"""
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	467 if isinstance(b, Rational):
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	468 return (a._numerator == b.numerator and
4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	469 a._denominator == b.denominator)
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	470 if isinstance(b, numbers.Complex) and b.imag == 0:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	471 b = b.real
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	472 if isinstance(b, float):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	473 return a == a.from_float(b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	474 else:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	475 # XXX: If b.__eq__ is implemented like this method, it may
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	476 # give the wrong answer after float(a) changes a's
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	477 # value. Better ways of doing this are welcome.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	478 return float(a) == b
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	479
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	480 def _subtractAndCompareToZero(a, b, op):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	481 """Helper function for comparison operators.
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	482
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	483 Subtracts b from a, exactly if possible, and compares the
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	484 result with 0 using op, in such a way that the comparison
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	485 won't recurse. If the difference raises a TypeError, returns
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	486 NotImplemented instead.
5503 ba005e4db4c5 A completely new Rat.py by Sjoerd. Guido van Rossum <guido@python.org> parents: 1966 diff changeset	487
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	488 """
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	489 if isinstance(b, numbers.Complex) and b.imag == 0:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	490 b = b.real
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	491 if isinstance(b, float):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	492 b = a.from_float(b)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	493 try:
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	494 # XXX: If b <: Real but not <: Rational, this is likely
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	495 # to fall back to a float. If the actual values differ by
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	496 # less than MIN_FLOAT, this could falsely call them equal,
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	497 # which would make <= inconsistent with ==. Better ways of
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	498 # doing this are welcome.
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	499 diff = a - b
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	500 except TypeError:
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	501 return NotImplemented
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	502 if isinstance(diff, Rational):
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	503 return op(diff.numerator, 0)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	504 return op(diff, 0)
28786 8a6e4c92bd7f Avoid TypeError by not comparing complex numbers Andrew M. Kuchling <amk@amk.ca> parents: 9077 diff changeset	505
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	506 def __lt__(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	507 """a < b"""
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	508 return a._subtractAndCompareToZero(b, operator.lt)
945 465b9841770e Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	509
44691 46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	510 def __gt__(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	511 """a > b"""
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	512 return a._subtractAndCompareToZero(b, operator.gt)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	513
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	514 def __le__(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	515 """a <= b"""
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	516 return a._subtractAndCompareToZero(b, operator.le)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	517
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	518 def __ge__(a, b):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	519 """a >= b"""
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	520 return a._subtractAndCompareToZero(b, operator.ge)
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	521
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	522 def __nonzero__(a):
46e731bb6a85 Add rational.Rational as an implementation of numbers.Rational with infinite Jeffrey Yasskin <jyasskin@gmail.com> parents: 28788 diff changeset	523 """a != 0"""
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	524 return a._numerator != 0
44933 6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	525
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	526 # support for pickling, copy, and deepcopy
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	527
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	528 def __reduce__(self):
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	529 return (self.__class__, (str(self),))
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	530
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	531 def __copy__(self):
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	532 if type(self) == Fraction:
44933 6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	533 return self # I'm immutable; therefore I am my own clone
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	534 return self.__class__(self._numerator, self._denominator)
44933 6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	535
6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	536 def __deepcopy__(self, memo):
45275 a50c1fb7d920 Rename rational.Rational to fractions.Fraction, to avoid name clash Mark Dickinson <dickinsm@gmail.com> parents: 45266 diff changeset	537 if type(self) == Fraction:
44933 6da0eea36783 Add support for copy, deepcopy, and pickle. Raymond Hettinger <python@rcn.com> parents: 44932 diff changeset	538 return self # My components are also immutable
45332 4fcb700115d8 Change simple instances (in Fraction) of self.numerator and self.denominator to Jeffrey Yasskin <jyasskin@gmail.com> parents: 45331 diff changeset	539 return self.__class__(self._numerator, self._denominator)

Mercurial > cpython-lru_cache-weakref

annotate Lib/fractions.py @ 58925:eecf1bef052d 2.6