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� �� f�Y c @ s� d Z d d l m Z d d l Z d d l Z d d l Z d d l Z d d l Z d d g Z d d � Z e j j Z e j j Z e j d e j e j B� Z Gd d � d e j � Z d S( u+ Fraction, infinite-precision, real numbers.i ( u DecimalNu Fractionu gcdc C s" x | r | | | } } q W| S( u� 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). ( ( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu gcd s uC \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 sf | Ee Z d Z d Z dP Z d dQ � f d d � Z e d d � � Z e d d � � Z d d d � Z e d d � � Z e d d � � Z d d � Z d d � Z d d � Z d d � Z e e e j � \ Z Z d d � Z e e e j � \ Z Z d d � Z e e e j � \ Z Z d d � Z e e e j � \ Z Z! d d! � Z" d" d# � Z# d$ d% � Z$ d& d' � Z% d( d) � Z& d* d+ � Z' d, d- � Z( d. d/ � Z) d0 d1 � Z* d2 d3 � Z+ d4 d5 � Z, d6 d7 � Z- dQ d8 d9 � Z. d: d; � Z/ d< d= � Z0 d> d? � Z1 d@ dA � Z2 dB dC � Z3 dD dE � Z4 dF dG � Z5 dH dI � Z6 dJ dK � Z7 dL dM � Z8 dN dO � Z9 � S(R u Fractionu] 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) u _numeratoru _denominatori c s� t t | � j | � } | d k rt | t j � rR | j | _ | j | _ | St | t � r� t j | � } | j | _ | j | _ | St | t � r� t j | � } | j | _ | j | _ | St | t � r t j | � } | d k rt d | � � n t | j d � pd � } | j d � } | rBt | � } 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 qct d � � nT t | t j � rWt | t j � rW| j | j | j | j } } n t d � � | d k r�t d | � � n t | | � } | | | _ | | | _ | S( u� Constructs a Rational. 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) u Invalid literal for Fraction: %ru numu 0u denomi u decimali u expi u signu -u2 argument should be a string or a Rational instanceu+ both arguments should be Rational instancesu Fraction(%s, 0)N( u superu Fractionu __new__u Noneu isinstanceu numbersu Rationalu numeratoru _numeratoru denominatoru _denominatoru floatu from_floatu Decimalu from_decimalu stru _RATIONAL_FORMATu matchu ValueErroru intu groupu lenu TypeErroru ZeroDivisionErroru gcd( u clsu numeratoru denominatoru selfu valueu mu denomu decimalu scaleu expu g( u __class__( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __new__I sf u Fraction.__new__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( u� Converts a finite float to a rational number, exactly. Beware that Fraction.from_float(0.3) != Fraction(3, 10). u. %s.from_float() only takes floats, not %r (%s)u Cannot convert %r to %s.( u isinstanceu numbersu Integralu floatu TypeErroru __name__u typeu mathu isnanu isinfu as_integer_ratio( u clsu f( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu from_float� s " u Fraction.from_floatc 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( uA Converts a finite Decimal instance to a rational number, exactly.i ( u Decimalu2 %s.from_decimal() only takes Decimals, not %r (%s)u Cannot convert %s to %s.u i N( u decimalu Decimalu isinstanceu numbersu Integralu intu TypeErroru __name__u typeu is_finiteu as_tupleu joinu mapu str( u clsu decu Decimalu signu digitsu exp( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu from_decimal� s " u Fraction.from_decimali@B c C s* | d k r t d � � n | j | k r4 t | � Sd \ } } } } | j | j } } xf | | } | | | } | | k r� Pn | | | | | | f \ } } } } | | | | } } q\ | | | } t | | | | | | � } t | | � } t | | � t | | � k r"| S| Sd S( uW 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 u$ max_denominator should be at least 1i N( i i i i ( u ValueErroru _denominatoru Fractionu _numeratoru abs( u selfu max_denominatoru p0u q0u p1u q1u nu du au q2u ku bound1u bound2( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu limit_denominator� s& & u Fraction.limit_denominatorc C s | j S( N( u _numerator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu numerator s u Fraction.numeratorc C s | j S( N( u _denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu denominator s u Fraction.denominatorc C s d | j | j f S( u repr(self)u Fraction(%s, %s)( u _numeratoru _denominator( u self( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __repr__ s u Fraction.__repr__c C s4 | j d k r t | j � Sd | j | j f Sd S( u str(self)i u %s/%sN( u _denominatoru stru _numerator( u self( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __str__ s u Fraction.__str__c st � � f d d � } d � j d | _ � j | _ � � f d d � } d � j d | _ � j | _ | | f S( u� 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, 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, numbers.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 sn t | t t f � r" � | | � St | t � rD � t | � | � St | t � rf � t | � | � St Sd S( N( u isinstanceu intu Fractionu floatu complexu NotImplemented( u au b( u fallback_operatoru monomorphic_operator( u. /opt/alt/python33/lib64/python3.3/fractions.pyu forwardm s u- Fraction._operator_fallbacks.<locals>.forwardu __c s} t | t j � r � | | � St | t j � rJ � t | � t | � � St | t j � ru � t | � t | � � St Sd S( N( u isinstanceu numbersu Rationalu Realu floatu Complexu complexu NotImplemented( u bu a( u fallback_operatoru monomorphic_operator( u. /opt/alt/python33/lib64/python3.3/fractions.pyu reversey s u- Fraction._operator_fallbacks.<locals>.reverseu __r( u __name__u __doc__( u monomorphic_operatoru fallback_operatoru forwardu reverse( ( u fallback_operatoru monomorphic_operatoru. /opt/alt/python33/lib64/python3.3/fractions.pyu _operator_fallbacks s P u Fraction._operator_fallbacksc C s/ t | j | j | j | j | j | j � S( u a + b( u Fractionu numeratoru denominator( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu _add� s u Fraction._addc C s/ t | j | j | j | j | j | j � S( u a - b( u Fractionu numeratoru denominator( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu _sub� s u Fraction._subc C s! t | j | j | j | j � S( u a * b( u Fractionu numeratoru denominator( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu _mul� s u Fraction._mulc C s! t | j | j | j | j � S( u a / b( u Fractionu numeratoru denominator( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu _div� s u Fraction._divc C s t j | | � S( u a // b( u mathu floor( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __floordiv__� s u Fraction.__floordiv__c C s t j | | � S( u a // b( u mathu floor( u bu a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __rfloordiv__� s u Fraction.__rfloordiv__c C s | | } | | | S( u a % b( ( u au bu div( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __mod__� s u Fraction.__mod__c C s | | } | | | S( u a % b( ( u bu au div( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __rmod__� s u Fraction.__rmod__c C s� t | t j � r� | j d k rq | j } | d k rQ t | j | | j | � St | j | | j | � Sq� t | � t | � Sn t | � | Sd S( u� 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( u isinstanceu numbersu Rationalu denominatoru numeratoru Fractionu _numeratoru _denominatoru float( u au bu power( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __pow__� s u Fraction.__pow__c C sz | j d k r) | j d k r) | | j St | t j � rR t | j | j � | S| j d k rl | | j S| t | � S( u a ** bi i ( u _denominatoru _numeratoru isinstanceu numbersu Rationalu Fractionu numeratoru denominatoru float( u bu a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __rpow__� s u Fraction.__rpow__c C s t | j | j � S( u+ +a: Coerces a subclass instance to Fraction( u Fractionu _numeratoru _denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __pos__� s u Fraction.__pos__c C s t | j | j � S( u -a( u Fractionu _numeratoru _denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __neg__� s u Fraction.__neg__c C s t t | j � | j � S( u abs(a)( u Fractionu absu _numeratoru _denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __abs__� s u Fraction.__abs__c C s1 | j d k r | j | j S| j | j Sd S( u trunc(a)i N( u _numeratoru _denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __trunc__� s u Fraction.__trunc__c C s | j | j S( u Will be math.floor(a) in 3.0.( u numeratoru denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __floor__� s u Fraction.__floor__c C s | j | j S( u Will be math.ceil(a) in 3.0.( u numeratoru denominator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __ceil__� s u Fraction.__ceil__c C s� | d k rx t | j | j � \ } } | d | j k r> | S| d | j k rY | d S| d d k rm | S| d Sn d t | � } | d k r� t t | | � | � St t | | � | � Sd S( uO Will be round(self, ndigits) in 3.0. Rounds half toward even. i i i i N( u Noneu divmodu numeratoru denominatoru absu Fractionu round( u selfu ndigitsu flooru remainderu shift( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __round__� s u Fraction.__round__c C sl t | j t d t � } | s( t } n t | j � | t } | d k rQ | n | } | d k rh d S| S( u hash(self)i i i i����i����( u powu _denominatoru _PyHASH_MODULUSu _PyHASH_INFu absu _numerator( u selfu dinvu hash_u result( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __hash__ s u Fraction.__hash__c C s� t | t j � r4 | j | j k o3 | j | j k St | t j � ra | j d k ra | j } n t | t � r� t j | � s� t j | � r� d | k S| | j | � k Sn t Sd S( u a == bi g N( u isinstanceu numbersu Rationalu _numeratoru numeratoru _denominatoru denominatoru Complexu imagu realu floatu mathu isnanu isinfu from_floatu NotImplemented( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __eq__( s ! u Fraction.__eq__c C s� t | t j � r3 | | j | j | j | j � St | t � r� t j | � s` t j | � rm | d | � S| | | j | � � Sn t Sd S( uc 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. g N( u isinstanceu numbersu Rationalu _numeratoru denominatoru _denominatoru numeratoru floatu mathu isnanu isinfu from_floatu NotImplemented( u selfu otheru op( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu _richcmp; s u Fraction._richcmpc C s | j | t j � S( u a < b( u _richcmpu operatoru lt( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __lt__Q s u Fraction.__lt__c C s | j | t j � S( u a > b( u _richcmpu operatoru gt( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __gt__U s u Fraction.__gt__c C s | j | t j � S( u a <= b( u _richcmpu operatoru le( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __le__Y s u Fraction.__le__c C s | j | t j � S( u a >= b( u _richcmpu operatoru ge( u au b( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __ge__] s u Fraction.__ge__c C s | j d k S( u a != 0i ( u _numerator( u a( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __bool__a s u Fraction.__bool__c C s | j t | � f f S( N( u __class__u str( u self( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __reduce__g s u Fraction.__reduce__c C s, t | � t k r | S| j | j | j � S( N( u typeu Fractionu __class__u _numeratoru _denominator( u self( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __copy__j s u Fraction.__copy__c C s, t | � t k r | S| j | j | j � S( N( u typeu Fractionu __class__u _numeratoru _denominator( u selfu memo( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu __deepcopy__o s u Fraction.__deepcopy__( u _numeratoru _denominatorN(: u __name__u __module__u __qualname__u __doc__u __slots__u Noneu __new__u classmethodu from_floatu from_decimalu limit_denominatoru propertyu numeratoru denominatoru __repr__u __str__u _operator_fallbacksu _addu operatoru addu __add__u __radd__u _subu subu __sub__u __rsub__u _mulu mulu __mul__u __rmul__u _divu truedivu __truediv__u __rtruediv__u __floordiv__u __rfloordiv__u __mod__u __rmod__u __pow__u __rpow__u __pos__u __neg__u __abs__u __trunc__u __floor__u __ceil__u __round__u __hash__u __eq__u _richcmpu __lt__u __gt__u __le__u __ge__u __bool__u __reduce__u __copy__u __deepcopy__( u __locals__( ( u __class__u. /opt/alt/python33/lib64/python3.3/fractions.pyu Fraction1 sV d7 k ( u __doc__u decimalu Decimalu mathu numbersu operatoru reu sysu __all__u gcdu hash_infou modulusu _PyHASH_MODULUSu infu _PyHASH_INFu compileu VERBOSEu IGNORECASEu _RATIONAL_FORMATu Rationalu Fraction( ( ( u. /opt/alt/python33/lib64/python3.3/fractions.pyu <module> s
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