diff options
Diffstat (limited to 'Lib/fractions.py')
| -rw-r--r--[-rwxr-xr-x] | Lib/fractions.py | 204 |
1 files changed, 135 insertions, 69 deletions
diff --git a/Lib/fractions.py b/Lib/fractions.py index 2d6f672569..a0d86a4393 100755..100644 --- a/Lib/fractions.py +++ b/Lib/fractions.py @@ -4,6 +4,7 @@ """Rational, infinite-precision, real numbers.""" from __future__ import division +from decimal import Decimal import math import numbers import operator @@ -30,74 +31,135 @@ _RATIONAL_FORMAT = re.compile(r""" (?P<sign>[-+]?) # an optional sign, then (?=\d|\.\d) # lookahead for digit or .digit (?P<num>\d*) # numerator (possibly empty) - (?: # followed by an optional - /(?P<denom>\d+) # / and denominator + (?: # followed by + (?:/(?P<denom>\d+))? # an optional denominator | # or - \.(?P<decimal>\d*) # decimal point and fractional part - )? + (?:\.(?P<decimal>\d*))? # an optional fractional part + (?:E(?P<exp>[-+]?\d+))? # and optional exponent + ) \s*\Z # and optional whitespace to finish -""", re.VERBOSE) +""", re.VERBOSE | re.IGNORECASE) class Fraction(Rational): """This class implements rational numbers. - Fraction(8, 6) will produce a rational number equivalent to - 4/3. Both arguments must be Integral. The numerator defaults to 0 - and the denominator defaults to 1 so that Fraction(3) == 3 and - Fraction() == 0. + In the two-argument form of the constructor, Fraction(8, 6) will + produce a rational number equivalent to 4/3. Both arguments must + be Rational. The numerator defaults to 0 and the denominator + defaults to 1 so that Fraction(3) == 3 and Fraction() == 0. - Fractions can also be constructed from strings of the form - '[-+]?[0-9]+((/|.)[0-9]+)?', optionally surrounded by spaces. + Fractions can also be constructed from: + + - numeric strings similar to those accepted by the + float constructor (for example, '-2.3' or '1e10') + + - strings of the form '123/456' + + - float and Decimal instances + + - other Rational instances (including integers) """ __slots__ = ('_numerator', '_denominator') # We're immutable, so use __new__ not __init__ - def __new__(cls, numerator=0, denominator=1): + def __new__(cls, numerator=0, denominator=None): """Constructs a Fraction. - Takes a string like '3/2' or '1.5', another Fraction, or a - numerator/denominator pair. + Takes a string like '3/2' or '1.5', another Rational instance, a + numerator/denominator pair, or a float. + + Examples + -------- + + >>> Fraction(10, -8) + Fraction(-5, 4) + >>> Fraction(Fraction(1, 7), 5) + Fraction(1, 35) + >>> Fraction(Fraction(1, 7), Fraction(2, 3)) + Fraction(3, 14) + >>> Fraction('314') + Fraction(314, 1) + >>> Fraction('-35/4') + Fraction(-35, 4) + >>> Fraction('3.1415') # conversion from numeric string + Fraction(6283, 2000) + >>> Fraction('-47e-2') # string may include a decimal exponent + Fraction(-47, 100) + >>> Fraction(1.47) # direct construction from float (exact conversion) + Fraction(6620291452234629, 4503599627370496) + >>> Fraction(2.25) + Fraction(9, 4) + >>> Fraction(Decimal('1.47')) + Fraction(147, 100) """ self = super(Fraction, cls).__new__(cls) - if type(numerator) not in (int, long) and denominator == 1: - if isinstance(numerator, basestring): + if denominator is None: + if isinstance(numerator, Rational): + self._numerator = numerator.numerator + self._denominator = numerator.denominator + return self + + elif isinstance(numerator, float): + # Exact conversion from float + value = Fraction.from_float(numerator) + self._numerator = value._numerator + self._denominator = value._denominator + return self + + elif isinstance(numerator, Decimal): + value = Fraction.from_decimal(numerator) + self._numerator = value._numerator + self._denominator = value._denominator + return self + + elif isinstance(numerator, basestring): # Handle construction from strings. - input = numerator - m = _RATIONAL_FORMAT.match(input) + m = _RATIONAL_FORMAT.match(numerator) if m is None: - raise ValueError('Invalid literal for Fraction: %r' % input) - numerator = m.group('num') - decimal = m.group('decimal') - if decimal: - # The literal is a decimal number. - numerator = int(numerator + decimal) - denominator = 10**len(decimal) + raise ValueError('Invalid literal for Fraction: %r' % + numerator) + numerator = int(m.group('num') or '0') + denom = m.group('denom') + if denom: + denominator = int(denom) else: - # The literal is an integer or fraction. - numerator = int(numerator) - # Default denominator to 1. - denominator = int(m.group('denom') or 1) - + denominator = 1 + decimal = m.group('decimal') + if decimal: + scale = 10**len(decimal) + numerator = numerator * scale + int(decimal) + denominator *= scale + exp = m.group('exp') + if exp: + exp = int(exp) + if exp >= 0: + numerator *= 10**exp + else: + denominator *= 10**-exp if m.group('sign') == '-': numerator = -numerator - elif isinstance(numerator, Rational): - # Handle copies from other rationals. Integrals get - # caught here too, but it doesn't matter because - # denominator is already 1. - other_rational = numerator - numerator = other_rational.numerator - denominator = other_rational.denominator + else: + raise TypeError("argument should be a string " + "or a Rational instance") + + elif (isinstance(numerator, Rational) and + isinstance(denominator, Rational)): + numerator, denominator = ( + numerator.numerator * denominator.denominator, + denominator.numerator * numerator.denominator + ) + else: + raise TypeError("both arguments should be " + "Rational instances") if denominator == 0: raise ZeroDivisionError('Fraction(%s, 0)' % numerator) - numerator = operator.index(numerator) - denominator = operator.index(denominator) g = gcd(numerator, denominator) self._numerator = numerator // g self._denominator = denominator // g @@ -470,54 +532,58 @@ class Fraction(Rational): if isinstance(b, numbers.Complex) and b.imag == 0: b = b.real if isinstance(b, float): - return a == a.from_float(b) + if math.isnan(b) or math.isinf(b): + # comparisons with an infinity or nan should behave in + # the same way for any finite a, so treat a as zero. + return 0.0 == b + else: + return a == a.from_float(b) else: - # XXX: If b.__eq__ is implemented like this method, it may - # give the wrong answer after float(a) changes a's - # value. Better ways of doing this are welcome. - return float(a) == b + # Since a doesn't know how to compare with b, let's give b + # a chance to compare itself with a. + return NotImplemented - def _subtractAndCompareToZero(a, b, op): - """Helper function for comparison operators. + def _richcmp(self, other, op): + """Helper for comparison operators, for internal use only. - Subtracts b from a, exactly if possible, and compares the - result with 0 using op, in such a way that the comparison - won't recurse. If the difference raises a TypeError, returns - NotImplemented instead. + Implement comparison between a Rational instance `self`, and + either another Rational instance or a float `other`. If + `other` is not a Rational instance or a float, return + NotImplemented. `op` should be one of the six standard + comparison operators. """ - if isinstance(b, numbers.Complex) and b.imag == 0: - b = b.real - if isinstance(b, float): - b = a.from_float(b) - try: - # XXX: If b <: Real but not <: Rational, this is likely - # to fall back to a float. If the actual values differ by - # less than MIN_FLOAT, this could falsely call them equal, - # which would make <= inconsistent with ==. Better ways of - # doing this are welcome. - diff = a - b - except TypeError: + # convert other to a Rational instance where reasonable. + if isinstance(other, Rational): + return op(self._numerator * other.denominator, + self._denominator * other.numerator) + # comparisons with complex should raise a TypeError, for consistency + # with int<->complex, float<->complex, and complex<->complex comparisons. + if isinstance(other, complex): + raise TypeError("no ordering relation is defined for complex numbers") + if isinstance(other, float): + if math.isnan(other) or math.isinf(other): + return op(0.0, other) + else: + return op(self, self.from_float(other)) + else: return NotImplemented - if isinstance(diff, Rational): - return op(diff.numerator, 0) - return op(diff, 0) def __lt__(a, b): """a < b""" - return a._subtractAndCompareToZero(b, operator.lt) + return a._richcmp(b, operator.lt) def __gt__(a, b): """a > b""" - return a._subtractAndCompareToZero(b, operator.gt) + return a._richcmp(b, operator.gt) def __le__(a, b): """a <= b""" - return a._subtractAndCompareToZero(b, operator.le) + return a._richcmp(b, operator.le) def __ge__(a, b): """a >= b""" - return a._subtractAndCompareToZero(b, operator.ge) + return a._richcmp(b, operator.ge) def __nonzero__(a): """a != 0""" |