î ¼ê[£Zã@s»dZddlmZddlZddlZddlZddlZddlZddgZdd„Z ej j Z ej j ZejdejejBƒZGdd„dejƒZdS) z+Fraction, infinite-precision, real numbers.é)ÚDecimalNÚFractionÚgcdcCs"x|r|||}}qW|S)z¶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). ©)ÚaÚbrrú/usr/lib/python3.4/fractions.pyrs aC \A\s* # optional whitespace at the start, then (?P[-+]?) # an optional sign, then (?=\d|\.\d) # lookahead for digit or .digit (?P\d*) # numerator (possibly empty) (?: # followed by (?:/(?P\d+))? # an optional denominator | # or (?:\.(?P\d*))? # an optional fractional part (?:E(?P[-+]?\d+))? # and optional exponent ) \s*\Z # and optional whitespace to finish csbeZdZdZdQZdd‡fdd†Zedd „ƒZed d „ƒZd d d„Z e dd„ƒZ e dd„ƒZ dd„Z dd„Zdd„Zdd„Zeeejƒ\ZZdd„Zeeejƒ\ZZdd„Zeeejƒ\ZZdd „Zeeejƒ\ZZ d!d"„Z!d#d$„Z"d%d&„Z#d'd(„Z$d)d*„Z%d+d,„Z&d-d.„Z'd/d0„Z(d1d2„Z)d3d4„Z*d5d6„Z+d7d8„Z,dd9d:„Z-d;d<„Z.d=d>„Z/d?d@„Z0dAdB„Z1dCdD„Z2dEdF„Z3dGdH„Z4dIdJ„Z5dKdL„Z6dMdN„Z7dOdP„Z8‡S)Rra]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) Ú _numeratorÚ _denominatorrNc s¯tt|ƒj|ƒ}|dkrt|tjƒrR|j|_|j|_ |St|t ƒrŒtj |ƒ}|j|_|j |_ |St|t ƒrÆtj |ƒ}|j|_|j |_ |St|tƒrtj|ƒ}|dkrtd|ƒ‚nt|jdƒpdƒ}|jdƒ}|rBt|ƒ}nœd}|jdƒ}|rŽdt|ƒ}||t|ƒ}||9}n|jd ƒ} | rÞt| ƒ} | d krÌ|d| 9}qÞ|d| 9}n|jd ƒd kr | }q qctd ƒ‚nTt|tjƒrWt|tjƒrW|j|j|j|j}}n tdƒ‚|d kr‚td|ƒ‚nt||ƒ} || |_|| |_ |S)a£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) Nz Invalid literal for Fraction: %rZnumÚ0ÚdenoméÚdecimalé ÚexprÚsignú-z2argument should be a string or a Rational instancez+both arguments should be Rational instanceszFraction(%s, 0))ÚsuperrÚ__new__Ú isinstanceÚnumbersÚRationalÚ numeratorr Ú denominatorr ÚfloatÚ from_floatrÚ from_decimalÚstrÚ_RATIONAL_FORMATÚmatchÚ ValueErrorÚintÚgroupÚlenÚ TypeErrorÚZeroDivisionErrorr) ÚclsrrÚselfÚvalueÚmr rZscalerÚg)Ú __class__rrrIsf                  zFraction.__new__cCs¹t|tjƒr||ƒSt|tƒsStd|j|t|ƒjfƒ‚ntj|ƒr~t d||jfƒ‚ntj |ƒr©t d||jfƒ‚n||j ƒŒS)z‚Converts a finite float to a rational number, exactly. Beware that Fraction.from_float(0.3) != Fraction(3, 10). z.%s.from_float() only takes floats, not %r (%s)zCannot convert %r to %s.) rrÚIntegralrr$Ú__name__ÚtypeÚmathÚisnanr ÚisinfÚ OverflowErrorÚas_integer_ratio)r&Úfrrrr­s "zFraction.from_floatcCs5ddlm}t|tjƒr7|t|ƒƒ}n7t||ƒsntd|j|t|ƒjfƒ‚n|j ƒr–t d||jfƒ‚n|j ƒr¾t d||jfƒ‚n|j ƒ\}}}tdjtt|ƒƒƒ}|r| }n|dkr||d|ƒS||d| ƒSdS)zAConverts a finite Decimal instance to a rational number, exactly.r)rz2%s.from_decimal() only takes Decimals, not %r (%s)zCannot convert %s to %s.ÚrN)rrrrr,r!r$r-r.Z is_infiniter2Zis_nanr Zas_tupleÚjoinÚmapr)r&ZdecrrZdigitsrrrrr¿s&"    zFraction.from_decimali@Bc Cs+|dkrtdƒ‚n|j|kr4t|ƒSd\}}}}|j|j}}xg||}|||} | |kr„Pn|||||| f\}}}}||||}}q\W|||} t|| ||| |ƒ} t||ƒ} t| |ƒt| |ƒkr#| S| SdS)aWClosest 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) r z$max_denominator should be at least 1rN)rr r r)r r rr Úabs) r'Zmax_denominatorZp0Zq0Zp1Zq1ÚnÚdrZq2ÚkZbound1Zbound2rrrÚlimit_denominator×s&    & zFraction.limit_denominatorcCs|jS)N)r )rrrrrszFraction.numeratorcCs|jS)N)r )rrrrrszFraction.denominatorcCsd|j|jfS)z repr(self)zFraction(%s, %s))r r )r'rrrÚ__repr__szFraction.__repr__cCs4|jdkrt|jƒSd|j|jfSdS)z str(self)r z%s/%sN)r rr )r'rrrÚ__str__s zFraction.__str__cst‡‡fdd†}dˆjd|_ˆj|_‡‡fdd†}dˆjd|_ˆj|_||fS)aÕGenerates 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. csnt|ttfƒr"ˆ||ƒSt|tƒrDˆt|ƒ|ƒSt|tƒrfˆt|ƒ|ƒStSdS)N)rr!rrÚcomplexÚNotImplemented)rr)Úfallback_operatorÚmonomorphic_operatorrrÚforwardqs z-Fraction._operator_fallbacks..forwardÚ__cs}t|tjƒrˆ||ƒSt|tjƒrJˆt|ƒt|ƒƒSt|tjƒruˆt|ƒt|ƒƒStSdS)N)rrrZRealrÚComplexr?r@)rr)rArBrrÚreverse}s z-Fraction._operator_fallbacks..reverseZ__r)r-Ú__doc__)rBrArCrFr)rArBrÚ_operator_fallbacks!sP    zFraction._operator_fallbackscCs/t|j|j|j|j|j|jƒS)za + b)rrr)rrrrrÚ_addŒsz Fraction._addcCs/t|j|j|j|j|j|jƒS)za - b)rrr)rrrrrÚ_sub”sz Fraction._subcCs!t|j|j|j|jƒS)za * b)rrr)rrrrrÚ_mulœsz Fraction._mulcCs!t|j|j|j|jƒS)za / b)rrr)rrrrrÚ_div¢sz Fraction._divcCstj||ƒS)za // b)r/Úfloor)rrrrrÚ __floordiv__©szFraction.__floordiv__cCstj||ƒS)za // b)r/rM)rrrrrÚ __rfloordiv__­szFraction.__rfloordiv__cCs||}|||S)za % br)rrÚdivrrrÚ__mod__±s zFraction.__mod__cCs||}|||S)za % br)rrrPrrrÚ__rmod__¶s zFraction.__rmod__cCsšt|tjƒrˆ|jdkrq|j}|dkrQt|j||j|ƒSt|j| |j| ƒSq–t|ƒt|ƒSnt|ƒ|SdS)z¾a ** 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. r rN) rrrrrrr r r)rrZpowerrrrÚ__pow__»s   zFraction.__pow__cCsz|jdkr)|jdkr)||jSt|tjƒrRt|j|jƒ|S|jdkrl||jS|t|ƒS)za ** br r) r r rrrrrrr)rrrrrÚ__rpow__Ós  zFraction.__rpow__cCst|j|jƒS)z++a: Coerces a subclass instance to Fraction)rr r )rrrrÚ__pos__ászFraction.__pos__cCst|j |jƒS)z-a)rr r )rrrrÚ__neg__åszFraction.__neg__cCstt|jƒ|jƒS)zabs(a))rr8r r )rrrrÚ__abs__észFraction.__abs__cCs1|jdkr|j |j S|j|jSdS)ztrunc(a)rN)r r )rrrrÚ __trunc__íszFraction.__trunc__cCs|j|jS)zWill be math.floor(a) in 3.0.)rr)rrrrÚ __floor__ôszFraction.__floor__cCs|j |j S)zWill be math.ceil(a) in 3.0.)rr)rrrrÚ__ceil__øszFraction.__ceil__cCsÇ|dkrxt|j|jƒ\}}|d|jkr>|S|d|jkrY|dS|ddkrm|S|dSndt|ƒ}|dkr«tt||ƒ|ƒStt||ƒ|ƒSdS)zOWill be round(self, ndigits) in 3.0. Rounds half toward even. Nér rr)Údivmodrrr8rÚround)r'ZndigitsrMZ remainderZshiftrrrÚ __round__ýs   zFraction.__round__cCslt|jtdtƒ}|s(t}nt|jƒ|t}|dkrQ|n| }|dkrhdS|S)z hash(self)r[rr éÿÿÿÿéþÿÿÿ)Úpowr Ú_PyHASH_MODULUSÚ _PyHASH_INFr8r )r'ZdinvZhash_ÚresultrrrÚ__hash__s  zFraction.__hash__cCs¶t|tjƒr4|j|jko3|j|jkSt|tjƒra|jdkra|j }nt|t ƒr®t j |ƒsŽt j |ƒr˜d|kS||j|ƒkSntSdS)za == brgN)rrrr rr rrEÚimagÚrealrr/r0r1rr@)rrrrrÚ__eq__,s!  zFraction.__eq__cCsŽt|tjƒr3||j|j|j|jƒSt|tƒr†tj |ƒs`tj |ƒrm|d|ƒS|||j |ƒƒSnt SdS)acHelper 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. gN) rrrr rr rrr/r0r1rr@)r'ÚotherÚoprrrÚ_richcmp?s  zFraction._richcmpcCs|j|tjƒS)za < b)rkÚoperatorÚlt)rrrrrÚ__lt__UszFraction.__lt__cCs|j|tjƒS)za > b)rkrlÚgt)rrrrrÚ__gt__YszFraction.__gt__cCs|j|tjƒS)za <= b)rkrlÚle)rrrrrÚ__le__]szFraction.__le__cCs|j|tjƒS)za >= b)rkrlÚge)rrrrrÚ__ge__aszFraction.__ge__cCs |jdkS)za != 0r)r )rrrrÚ__bool__eszFraction.__bool__cCs|jt|ƒffS)N)r+r)r'rrrÚ __reduce__kszFraction.__reduce__cCs,t|ƒtkr|S|j|j|jƒS)N)r.rr+r r )r'rrrÚ__copy__nszFraction.__copy__cCs,t|ƒtkr|S|j|j|jƒS)N)r.rr+r r )r'ÚmemorrrÚ __deepcopy__sszFraction.__deepcopy__)z _numeratorz _denominator)9r-Ú __module__Ú __qualname__rGÚ __slots__rÚ classmethodrrr<Úpropertyrrr=r>rHrIrlÚaddÚ__add__Ú__radd__rJÚsubÚ__sub__Ú__rsub__rKÚmulÚ__mul__Ú__rmul__rLÚtruedivÚ __truediv__Ú __rtruediv__rNrOrQrRrSrTrUrVrWrXrYrZr^rerhrkrnrprrrtrurvrwryrr)r+rr1sV d7   k                          )rGrrr/rrlÚreÚsysÚ__all__rÚ hash_infoÚmodulusrbÚinfrcÚcompileÚVERBOSEÚ IGNORECASErrrrrrrÚs