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� z fc @ s� d Z d d l m Z d d l m Z d d l Z d d l Z d d l Z d d l Z d d g Z e j Z d � Z e j d e j e j B� Z d e f d � � YZ d S( s+ Rational, infinite-precision, real numbers.i����( t division( t DecimalNt Fractiont gcdc C s" x | r | | | } } q W| S( s� Calculate the Greatest Common Divisor of a and b. Unless b==0, the result will have the same sign as b (so that when b is divided by it, the result comes out positive). ( ( t at b( ( s! /usr/lib64/python2.7/fractions.pyR s sC \A\s* # optional whitespace at the start, then (?P<sign>[-+]?) # an optional sign, then (?=\d|\.\d) # lookahead for digit or .digit (?P<num>\d*) # numerator (possibly empty) (?: # followed by (?:/(?P<denom>\d+))? # an optional denominator | # or (?:\.(?P<decimal>\d*))? # an optional fractional part (?:E(?P<exp>[-+]?\d+))? # and optional exponent ) \s*\Z # and optional whitespace to finish c B s� e Z d Z d' Z d d( d � Z e d � � Z e d � � Z d d � Z e d � � Z e d � � Z d � Z d � Z d � Z d � Z e e e j � \ Z Z d � Z e e e j � \ Z Z d � Z e e e j � \ Z Z d � Z e e e j � \ Z Z e e e j! � \ Z" Z# d � Z$ d � Z% d � Z& d � Z' d � Z( d � Z) d � Z* d � Z+ d � Z, d � Z- d � Z. d � Z/ d � Z0 d � Z1 d � Z2 d! � Z3 d" � Z4 d# � Z5 d$ � Z6 d% � Z7 d& � Z8 RS() s] This class implements rational numbers. 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: - 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) t _numeratort _denominatori c C s� t t | � j | � } | d k r t | t � rO | j | _ | j | _ | St | t � r� t j | � } | j | _ | j | _ | St | t � r� t j | � } | j | _ | j | _ | St | t � r�t j | � } | d k r t d | � � n t | j d � pd � } | j d � } | r?t | � } n� d } | j d � } | r�d t | � } | | t | � } | | 9} n | j d � } | r�t | � } | d k r�| d | 9} q�| d | 9} n | j d � d k r | } q qZt d � � nN t | t � rNt | t � rN| j | j | j | j } } n t d � � | d k ryt d | � � n t | | � } | | | _ | | | _ | S( s� Constructs a Fraction. 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) s Invalid literal for Fraction: %rt numt 0t denomi t decimali t expi t signt -s2 argument should be a string or a Rational instances+ both arguments should be Rational instancess Fraction(%s, 0)N( t superR t __new__t Nonet isinstancet Rationalt numeratorR t denominatorR t floatt from_floatR t from_decimalt basestringt _RATIONAL_FORMATt matcht ValueErrort intt groupt lent TypeErrort ZeroDivisionErrorR ( t clsR R t selft valuet mR R t scaleR t g( ( s! /usr/lib64/python2.7/fractions.pyR D sf c C s� t | t j � r | | � St | t � sS t d | j | t | � j f � � n t j | � sq t j | � r� t d | | j f � � n | | j � � S( s� Converts a finite float to a rational number, exactly. Beware that Fraction.from_float(0.3) != Fraction(3, 10). s. %s.from_float() only takes floats, not %r (%s)s Cannot convert %r to %s.( R t numberst IntegralR R t __name__t typet matht isnant isinft as_integer_ratio( R" t f( ( s! /usr/lib64/python2.7/fractions.pyR � s " c C s d d l m } t | t j � r7 | t | � � } n7 t | | � sn t d | j | t | � j f � � n | j � s� t d | | j f � � n | j � \ } } } t d j t t | � � � } | r� | } n | d k r� | | d | � S| | d | � Sd S( sA Converts a finite Decimal instance to a rational number, exactly.i����( R s2 %s.from_decimal() only takes Decimals, not %r (%s)s Cannot convert %s to %s.t i i N( R R R R( R) R R R* R+ t is_finitet as_tuplet joint mapt str( R" t decR R t digitsR ( ( s! /usr/lib64/python2.7/fractions.pyR � s " i@B c C s1 | d k r t d � � n | j | k r4 t | � Sd \ } } } } | j | j } } xm t r� | | } | | | } | | k r� Pn | | | | | | f \ } } } } | | | | } } q\ W| | | } t | | | | | | � } t | | � } t | | � t | | � k r)| S| Sd S( sW Closest Fraction to self with denominator at most max_denominator. >>> Fraction('3.141592653589793').limit_denominator(10) Fraction(22, 7) >>> Fraction('3.141592653589793').limit_denominator(100) Fraction(311, 99) >>> Fraction(4321, 8765).limit_denominator(10000) Fraction(4321, 8765) i s$ max_denominator should be at least 1i N( i i i i ( R R R R t Truet abs( R# t max_denominatort p0t q0t p1t q1t nt dR t q2t kt bound1t bound2( ( s! /usr/lib64/python2.7/fractions.pyt limit_denominator� s& & c C s | j S( N( R ( R ( ( s! /usr/lib64/python2.7/fractions.pyR s c C s | j S( N( R ( R ( ( s! /usr/lib64/python2.7/fractions.pyR s c C s d | j | j f S( s repr(self)s Fraction(%s, %s)( R R ( R# ( ( s! /usr/lib64/python2.7/fractions.pyt __repr__ s c C s4 | j d k r t | j � Sd | j | j f Sd S( s str(self)i s %s/%sN( R R6 R ( R# ( ( s! /usr/lib64/python2.7/fractions.pyt __str__ s c sn � � f d � } d � j d | _ � j | _ � � f d � } d � j d | _ � j | _ | | f S( s� Generates forward and reverse operators given a purely-rational operator and a function from the operator module. Use this like: __op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op) In general, we want to implement the arithmetic operations so that mixed-mode operations either call an implementation whose author knew about the types of both arguments, or convert both to the nearest built in type and do the operation there. In Fraction, that means that we define __add__ and __radd__ as: def __add__(self, other): # Both types have numerators/denominator attributes, # so do the operation directly if isinstance(other, (int, long, Fraction)): return Fraction(self.numerator * other.denominator + other.numerator * self.denominator, self.denominator * other.denominator) # float and complex don't have those operations, but we # know about those types, so special case them. elif isinstance(other, float): return float(self) + other elif isinstance(other, complex): return complex(self) + other # Let the other type take over. return NotImplemented def __radd__(self, other): # radd handles more types than add because there's # nothing left to fall back to. if isinstance(other, Rational): return Fraction(self.numerator * other.denominator + other.numerator * self.denominator, self.denominator * other.denominator) elif isinstance(other, Real): return float(other) + float(self) elif isinstance(other, Complex): return complex(other) + complex(self) return NotImplemented There are 5 different cases for a mixed-type addition on Fraction. I'll refer to all of the above code that doesn't refer to Fraction, float, or complex as "boilerplate". 'r' will be an instance of Fraction, which is a subtype of Rational (r : Fraction <: Rational), and b : B <: Complex. The first three involve 'r + b': 1. If B <: Fraction, int, float, or complex, we handle that specially, and all is well. 2. If Fraction falls back to the boilerplate code, and it were to return a value from __add__, we'd miss the possibility that B defines a more intelligent __radd__, so the boilerplate should return NotImplemented from __add__. In particular, we don't handle Rational here, even though we could get an exact answer, in case the other type wants to do something special. 3. If B <: Fraction, Python tries B.__radd__ before Fraction.__add__. This is ok, because it was implemented with knowledge of Fraction, so it can handle those instances before delegating to Real or Complex. The next two situations describe 'b + r'. We assume that b didn't know about Fraction in its implementation, and that it uses similar boilerplate code: 4. If B <: Rational, then __radd_ converts both to the builtin rational type (hey look, that's us) and proceeds. 5. Otherwise, __radd__ tries to find the nearest common base ABC, and fall back to its builtin type. Since this class doesn't subclass a concrete type, there's no implementation to fall back to, so we need to try as hard as possible to return an actual value, or the user will get a TypeError. c sq t | t t t f � r% � | | � St | t � rG � t | � | � St | t � ri � t | � | � St Sd S( N( R R t longR R t complext NotImplemented( R R ( t fallback_operatort monomorphic_operator( s! /usr/lib64/python2.7/fractions.pyt forwardh s t __c sz t | t � r � | | � St | t j � rG � t | � t | � � St | t j � rr � t | � t | � � St Sd S( N( R R R( t RealR t ComplexRJ RK ( R R ( RL RM ( s! /usr/lib64/python2.7/fractions.pyt reverset s t __r( R* t __doc__( RM RL RN RR ( ( RL RM s! /usr/lib64/python2.7/fractions.pyt _operator_fallbacks s P c C s/ t | j | j | j | j | j | j � S( s a + b( R R R ( R R ( ( s! /usr/lib64/python2.7/fractions.pyt _add� s c C s/ t | j | j | j | j | j | j � S( s a - b( R R R ( R R ( ( s! /usr/lib64/python2.7/fractions.pyt _sub� s c C s! t | j | j | j | j � S( s a * b( R R R ( R R ( ( s! /usr/lib64/python2.7/fractions.pyt _mul� s c C s! t | j | j | j | j � S( s a / b( R R R ( R R ( ( s! /usr/lib64/python2.7/fractions.pyt _div� s c C s8 | | } t | t � r' | j | j St j | � Sd S( s a // bN( R R R R R, t floor( R R t div( ( s! /usr/lib64/python2.7/fractions.pyt __floordiv__� s c C s8 | | } t | t � r' | j | j St j | � Sd S( s a // bN( R R R R R, RZ ( R R R[ ( ( s! /usr/lib64/python2.7/fractions.pyt __rfloordiv__� s c C s | | } | | | S( s a % b( ( R R R[ ( ( s! /usr/lib64/python2.7/fractions.pyt __mod__� s c C s | | } | | | S( s a % b( ( R R R[ ( ( s! /usr/lib64/python2.7/fractions.pyt __rmod__� s c C s� t | t � r� | j d k rn | j } | d k rN t | j | | j | � St | j | | j | � Sq� t | � t | � Sn t | � | Sd S( s� a ** b If b is not an integer, the result will be a float or complex since roots are generally irrational. If b is an integer, the result will be rational. i i N( R R R R R R R R ( R R t power( ( s! /usr/lib64/python2.7/fractions.pyt __pow__� s c C sw | j d k r) | j d k r) | | j St | t � rO t | j | j � | S| j d k ri | | j S| t | � S( s a ** bi i ( R R R R R R R R ( R R ( ( s! /usr/lib64/python2.7/fractions.pyt __rpow__� s c C s t | j | j � S( s+ +a: Coerces a subclass instance to Fraction( R R R ( R ( ( s! /usr/lib64/python2.7/fractions.pyt __pos__� s c C s t | j | j � S( s -a( R R R ( R ( ( s! /usr/lib64/python2.7/fractions.pyt __neg__� s c C s t t | j � | j � S( s abs(a)( R R: R R ( R ( ( s! /usr/lib64/python2.7/fractions.pyt __abs__� s c C s1 | j d k r | j | j S| j | j Sd S( s trunc(a)i N( R R ( R ( ( s! /usr/lib64/python2.7/fractions.pyt __trunc__� s c C sX | j d k r t | j � S| t | � k r> t t | � � St | j | j f � Sd S( s� hash(self) Tricky because values that are exactly representable as a float must have the same hash as that float. i N( R t hashR R ( R# ( ( s! /usr/lib64/python2.7/fractions.pyt __hash__� s c C s� t | t � r1 | j | j k o0 | j | j k St | t j � r^ | j d k r^ | j } n t | t � r� t j | � s� t j | � r� d | k S| | j | � k Sn t Sd S( s a == bi g N( R R R R R R R( RQ t imagt realR R, R- R. R RK ( R R ( ( s! /usr/lib64/python2.7/fractions.pyt __eq__ s ! c C s� t | t � r0 | | j | j | j | j � St | t � rN t d � � n t | t � r� t j | � s{ t j | � r� | d | � S| | | j | � � Sn t Sd S( sc Helper for comparison operators, for internal use only. 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. s3 no ordering relation is defined for complex numbersg N( R R R R R R RJ R R R, R- R. R RK ( R# t othert op( ( s! /usr/lib64/python2.7/fractions.pyt _richcmp" s c C s | j | t j � S( s a < b( Rn t operatort lt( R R ( ( s! /usr/lib64/python2.7/fractions.pyt __lt__< s c C s | j | t j � S( s a > b( Rn Ro t gt( R R ( ( s! /usr/lib64/python2.7/fractions.pyt __gt__@ s c C s | j | t j � S( s a <= b( Rn Ro t le( R R ( ( s! /usr/lib64/python2.7/fractions.pyt __le__D s c C s | j | t j � S( s a >= b( Rn Ro t ge( R R ( ( s! /usr/lib64/python2.7/fractions.pyt __ge__H s c C s | j d k S( s a != 0i ( R ( R ( ( s! /usr/lib64/python2.7/fractions.pyt __nonzero__L s c C s | j t | � f f S( N( t __class__R6 ( R# ( ( s! /usr/lib64/python2.7/fractions.pyt __reduce__R s c C s, t | � t k r | S| j | j | j � S( N( R+ R Ry R R ( R# ( ( s! /usr/lib64/python2.7/fractions.pyt __copy__U s c C s, t | � t k r | S| j | j | j � S( N( R+ R Ry R R ( R# t memo( ( s! /usr/lib64/python2.7/fractions.pyt __deepcopy__Z s ( R R N(9 R* t __module__RT t __slots__R R t classmethodR R RF t propertyR R RG RH RU RV Ro t addt __add__t __radd__RW t subt __sub__t __rsub__RX t mult __mul__t __rmul__RY t truedivt __truediv__t __rtruediv__R[ t __div__t __rdiv__R\ R] R^ R_ Ra Rb Rc Rd Re Rf Rh Rk Rn Rq Rs Ru Rw Rx Rz R{ R} ( ( ( s! /usr/lib64/python2.7/fractions.pyR , sR d 7 k ( RT t __future__R R R R, R( Ro t ret __all__R R t compilet VERBOSEt IGNORECASER R ( ( ( s! /usr/lib64/python2.7/fractions.pyt <module> s