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usr/lib64/python3.12/__pycache__/fractions.cpython-312.opt-1.pyc 0000644 00000107625 15220053760 0017777 0 ustar 00 ֦i d Z ddlmZ ddlZddlZddlZddlZddlZddlZdgZ ej j Z ej j Z ej d d Z ej" dej$ ej& z Zd d Zd Z ej" d ej. ej$ z j0 Z G d dej4 Zy)z/Fraction, infinite-precision, rational numbers. DecimalNFractioni @ )maxsizec t |dt }t t t | |z }| dk\ r|n| }|dk( rdS |S # t $ r t }Y $w xY w)Nr )pow_PyHASH_MODULUShashabs ValueError _PyHASH_INF) numerator denominatordinvhash_results "/usr/lib64/python3.12/fractions.py_hash_algorithmr se 2;O4( T#i.)D01 1nU5&F2 2)6)+ s A AAa \A\s* # optional whitespace at the start, (?P<sign>[-+]?) # an optional sign, then (?=\d|\.\d) # lookahead for digit or .digit (?P<num>\d*|\d+(_\d+)*) # numerator (possibly empty) (?: # followed by (?:\s*/\s*(?P<denom>\d+(_\d+)*))? # an optional denominator | # or (?:\.(?P<decimal>\d*|\d+(_\d+)*))? # an optional fractional part (?:E(?P<exp>[-+]?\d+(_\d+)*))? # and optional exponent ) \s*\Z # and optional whitespace to finish c |dk\ r |d|z z }n | d| z z } t | |dz z | \ }}|dk( r |dz dk( r|dz }|r|dk n| dk }|t | fS )aM Round a rational number to the nearest multiple of a given power of 10. Rounds the rational number n/d to the nearest integer multiple of 10**exponent, rounding to the nearest even integer multiple in the case of a tie. Returns a pair (sign: bool, significand: int) representing the rounded value (-1)**sign * significand * 10**exponent. If no_neg_zero is true, then the returned sign will always be False when the significand is zero. Otherwise, the sign reflects the sign of the input. d must be positive, but n and d need not be relatively prime. r r )divmodr )ndexponent no_neg_zeroqrsigns r _round_to_exponentr" J s| 1} R\ R(] !qAv, "DAqAv!a%1* R 1q5QUD Q< c | dk( rddd|z fS t t | t | }}t | t | z ||k z }||z }t | || \ }}t t | |dz k( r |dz }|dz }|||fS )a Round a rational number to a given number of significant figures. Rounds the rational number n/d to the given number of significant figures using the round-ties-to-even rule, and returns a triple (sign: bool, significand: int, exponent: int) representing the rounded value (-1)**sign * significand * 10**exponent. In the special case where n = 0, returns a significand of zero and an exponent of 1 - figures, for compatibility with formatting. Otherwise, the returned significand satisfies 10**(figures - 1) <= significand < 10**figures. d must be positive, but n and d need not be relatively prime. figures must be positive. r Fr r )strr lenr" ) r r figuresstr_nstr_dmr r! significands r _round_to_figuresr, g s " AvaW$$ s1v;A5E E SZ 5E>2A 7{H*1a:D+ 3{ ! + A h &&r# a (?: (?P<fill>.)? (?P<align>[<>=^]) )? (?P<sign>[-+ ]?) (?P<no_neg_zero>z)? (?P<alt>\#)? # A '0' that's *not* followed by another digit is parsed as a minimum width # rather than a zeropad flag. (?P<zeropad>0(?=[0-9]))? (?P<minimumwidth>0|[1-9][0-9]*)? (?P<thousands_sep>[,_])? (?:\.(?P<precision>0|[1-9][0-9]*))? (?P<presentation_type>[eEfFgG%]) c e Zd ZdZdZd, fd Zed Zed Ze fd Z d Z d Z d-d Z e d Ze d Zd Zd Zd Zd Zd Z eeej, \ ZZd Z eeej4 \ ZZ d Z ee ej< \ Z Z d Z! ee!ejD \ Z#Z$d Z% ee%ejL \ Z'Z(d Z) ee)e* \ Z+Z,d Z- ee-ej\ \ Z/Z0d Z1d Z2d Z3d Z4d Z5ejl fd Z7d Z8d Z9d Z:d.d Z;d! Z<d" Z=d# Z>d$ Z?d% Z@d& ZAd' ZBd( ZCd) ZDd* ZEd+ ZF xZGS )/r a] 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) _numerator _denominatorc B t t | | }|t | t u r||_ d|_ |S t |t j r$|j |_ |j |_ |S t |t t f r |j \ |_ |_ |S t |t rt j# | }|t% d|z t |j' d xs d }|j' d }|r t | }nd}|j' d }|r6|j) dd }d t+ | z }||z t | z }||z }|j' d }|r"t | }|d k\ r |d |z z }n |d | z z }|j' d d k( r| }nt- d t | t cxu r t | u rn nnrt |t j rMt |t j r3|j |j z |j |j z }}n t- d |d k( rt/ d|z t1 j2 || } |d k r| } || z }|| z }||_ ||_ |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) r z Invalid literal for Fraction: %rnum0denomdecimal_ r expr r! -z2argument should be a string or a Rational instancez+both arguments should be Rational instancesFraction(%s, 0))superr __new__typeintr/ r0 isinstancenumbersRationalr r floatr as_integer_ratior% _RATIONAL_FORMATmatchr groupreplacer& TypeErrorZeroDivisionErrormathgcd) clsr r selfr* r4 r5 scaler8 g __class__s r r< zFraction.__new__ s > Xs+C0 I#%"+$%! Iw'7'78"+"5"5$-$9$9! Iw'785>5O5O5Q2!2 Is+$**959$%G%.&/ 0 0 5# 6 ("%e*K"#K ggi 0G ")//#r": "CL 0$-$5G $D #u, ''%.C !#h !8 %S 0I '2t8 3K776?c)!* I !9 : : )_ 8tK'8 8 G$4$45 {G$4$4 5##k&=&==%% (=(== #I 1 2 2 ! #$5 $AB B HHY , ?Aa # ' r# c t |t j r | | S t |t s1t | j d|dt | j d | j |j S )zConverts a finite float to a rational number, exactly. Beware that Fraction.from_float(0.3) != Fraction(3, 10). z%.from_float() only takes floats, not ()) r? r@ IntegralrB rH __name__r= _from_coprime_intsrC )rL fs r from_floatzFraction.from_float# sm a)) *q6MAu% \\1d1g.>.> @ A A%s%%q'9'9';<<r# c ddl m} t |t j r |t | }n=t || s1t | j d|dt | j d | j |j S )zAConverts a finite Decimal instance to a rational number, exactly.r r z).from_decimal() only takes Decimals, not rR rS ) r5 r r? r@ rT r> rH rU r= rV rC )rL decr s r from_decimalzFraction.from_decimal1 st $ c7++ ,#c(#CC) sDI$6$689 9 &s%%s';';'=>>r# c J t t | | }||_ ||_ |S )zConvert a pair of ints to a rational number, for internal use. The ratio of integers should be in lowest terms and the denominator should be positive. )r; r r< r/ r0 )rL r r objrP s r rV zFraction._from_coprime_ints= s* Hc*3/"& r# c | j dk( S )z*Return True if the Fraction is an integer.r r0 rM s r is_integerzFraction.is_integerI s A%%r# c 2 | j | j fS )zReturn a pair of integers, whose ratio is equal to the original Fraction. The ratio is in lowest terms and has a positive denominator. r. r` s r rC zFraction.as_integer_ratioM s !2!233r# c |dk r t d | j |k r t | S d\ }}}}| j | j }} ||z }|||z z } | |kD rn |||||z z | f\ }}}}||||z z }}/||z |z } d|z || |z z z | j k rt j || S t j || |z z || |z z S )aW 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) r z$max_denominator should be at least 1)r r r r )r r0 r r/ rV ) rM max_denominatorp0q0p1q1r r aq2ks r limit_denominatorzFraction.limit_denominatorT s @ Q CD D /D> !#BB 1 111AAbDBO# R"Wb 0NBBa!eqA R " $ Q31R4=D - - -..r26 6..r!B$w1R4@ @r# c | j S N)r/ rj s r r zFraction.numerator s ||r# c | j S ro r_ rp s r r zFraction.denominator s ~~ r# c h | j j d| j d| j dS )z repr(self)(z, rS )rP rU r/ r0 r` s r __repr__zFraction.__repr__ s* #~~ 6 6 #0A0AC Cr# c | j dk( rt | j S | j d| j S )z str(self)r /)r0 r% r/ r` s r __str__zFraction.__str__ s4 !t' ' "oot/@/@A Ar# c ! |s t | S t | }|$t d|dt | j |d *|d %t d|dt | j d |d xs d}|d xs d }|d d k( rd n|d }t |d }t |d }t |d }t |d xs d } |d !t |d xs d } |d } | dv xr | } | } | dv rdnd}| dv r7| }| dk( r|dz }t | j | j || \ }}d }| }nY| dv r t | d n| d z }t | j | j | \ }}}| d v xs |d kD xs ||z d k }|r|d z n| }| dk( rd}n|r | ||z d!}nd }|d|d z d"}|rd n|}|dt | |z |t | |z d }| r|j d }| r|sd nd#}||z |z }|r8| t | z t | z } j !r d$|z d%z d z n| !rId t d z d$z z } d| d j !fd&t! | t d$ D z |z } || t | z t | z z } |d k( r| |z | z S |d'k( r|| z | z S |d(k( r t | dz } | d| |z | z | | d z S || z | z S ))zAFormat this fraction according to the given format specification.NzInvalid format specifier z for object of type alignzeropadz0; can't use explicit alignment when zero-paddingfill >r! r9 r7 r alt minimumwidthr3 thousands_sep precision6presentation_typegGEFGEezfF%%rd Fr eEr z+03dr . c 3 4 K | ] }||d z z yw)r N ).0posleadingr s r <genexpr>z&Fraction.__format__.<locals>.<genexpr> s) 4<C cAg 66<s <^)r% #_FLOAT_FORMAT_SPECIFICATION_MATCHERr r= rU boolr> r" r/ r0 maxr, r& rstripzfilljoinrange)"rM format_specrE r{ ry pos_signr alternate_formrz r r r trim_zeros trim_pointexponent_indicatorr negativer+ scientific point_posr' suffixdigitsr! frac_part separatortrailing min_leading first_posbodypaddinghalfr r s" @@r __format__zFraction.__format__ s t9 4K@ = +K? ;&&*4j&9&9%<> 7^ 'E),<,H +K? ;&&*4j&9&9%< =AA V}#g%# v #-25=5 /0 eEl+uY'(5 07C8 o. k*1c2 !"5 6&$.E~3E '' $5$>SC %!zH C'A $6!2!2Hk%K !Hk J!I %, Iq! ] /@!2!2G/= +Hk8 "T) ,a<,g%+ (2! yI #F *+Hy,@+FGFF )a- 12 sH23v;233v;245 !((-I$YBC y(61 &T2S]BK mm,9K1$q({G S\A - 22I jy)BGG 4 CL!<4 - G !,T2SY>? C<T>D( ( c\$;( ( c\w<1$D5D>D(4/'$%.@ @'>D( (r# c fd}dj z dz |_ j |_ fd}dj z dz |_ j |_ ||fS )a 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 t |t r | | S t |t r | t | S t |t r t | | S t |t r t | | S t S ro )r? r r> rB complexNotImplemented)rj bfallback_operatormonomorphic_operators r forwardz-Fraction._operator_fallbacks.<locals>.forwarde sq !X&+Aq11As#+Ax{;;Au%(q155Aw'(Q77%%r# __c < t |t j r t | | S t |t j r t | t | S t |t j r t | t | S t S ro ) r? r@ rA r RealrB Complexr r )r rj r r s r reversez-Fraction._operator_fallbacks.<locals>.reverses sp !W - -.+HQK;;Aw||,(q58<<Aw/(WQZ@@%%r# __r)rU __doc__)r r r r s `` r _operator_fallbacksz Fraction._operator_fallbacks si ` & "3"<"<<tC.66 & !#4#=#==D.66 r# c | j | j }}|j |j }}t j || }|dk( r"t j ||z ||z z ||z S ||z }|||z z ||z z }t j || } | dk( rt j |||z S t j || z ||| z z S )za + br r/ r0 rJ rK r rV rj r nadanbdbrO stg2s r _addz Fraction._add q~~B q~~B HHR 6..rBwb/@"r'J J !G "'NR!V # XXa^ 7..q!b&9 9**17ArNCCr# c | j | j }}|j |j }}t j || }|dk( r"t j ||z ||z z ||z S ||z }|||z z ||z z }t j || } | dk( rt j |||z S t j || z ||| z z S )za - br r r s r _subz Fraction._sub r r# c . | j | j }}|j |j }}t j || }|dkD r ||z }||z }t j || }|dkD r ||z }||z }t j ||z ||z S )za * br r )rj r r r r r g1r s r _mulz Fraction._mul s q~~B q~~B XXb" 6 2IB 2IB XXb" 6 2IB 2IB**27BG<<r# c r |j |j }}|dk( rt d|z | j | j }}t j || }|dkD r ||z }||z }t j || }|dkD r ||z }||z }||z ||z } }| dk r| | } }t j || S )za / br r: r )r/ r0 rI rJ rK r rV ) rj r r r r r r r r r s r _divz Fraction._div s q~~B 7#$5$:; ; q~~B XXb" 6 2IB 2IB XXb" 6 2IB 2IBBwR1 q52rqA**1a00r# c h | j |j z | j |j z z S )za // b)r r rj r s r _floordivzFraction._floordiv s' amm+ 1LMMr# c | j |j }}t | j |z ||j z \ }}|t |||z fS )z(a // b, a % b))r r r r )rj r r r divn_mods r _divmodzFraction._divmod sK BAKK" ,b1;;.>? UHUBG,,,r# c | j |j }}t | j |z |j |z z ||z S )za % b)r r r )rj r r r s r _modz Fraction._mod s; Br)akkB.>?bIIr# c t |t j r|j dk( r|j }|dk\ r0t j | j |z | j |z S | j dkD r2t j | j | z | j | z S | j dk( r t d| j | z z t j | j | z | j | z S t | t | z S t |t t f rt | |z S t S )za ** 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 r r: ) r? r@ rA r r r rV r/ r0 rI rB r r )rj r powers r __pow__zFraction.__pow__! s8 a)) *}}! A:#66q||u7L78~~7N P P\\A%#66q~~%7O78||v7M O O\\Q&+,=,-NNuf,D-E F F $66 UF7R9: 5&7P R R Qx58++ E7+ ,8q= ! !r# c . | j dk( r | j dk\ r|| j z S t |t j r#t |j |j | z S | j dk( r|| j z S |t | z S )za ** br r ) r0 r/ r? r@ rA r r r rB )r rj s r __rpow__zFraction.__rpow__A s{ >>Q 1<<1#4 $ $ a)) *AKK 71< < >>Q $ $E!H} r# c V t j | j | j S )z++a: Coerces a subclass instance to Fractionr rV r/ r0 rp s r __pos__zFraction.__pos__O s **1<< HHr# c X t j | j | j S )z-ar rp s r __neg__zFraction.__neg__S s **ALL=!..IIr# c h t j t | j | j S )zabs(a))r rV r r/ r0 rp s r __abs__zFraction.__abs__W s" **3q||+<annMMr# c | j dk r! || j | j z S || j | j z S )zint(a)r r. )rj _indexs r __int__zFraction.__int__[ sC <<! Q\\MQ^^ ;<= =!,,!..89 9r# c | j dk r| j | j z S | j | j z S )z math.trunc(a)r r. rp s r __trunc__zFraction.__trunc__b s9 <<! ll]ann45 5<<1>>1 1r# c 4 | j | j z S )z math.floor(a)r. rp s r __floor__zFraction.__floor__i s ||q~~--r# c 8 | j | j z S )z math.ceil(a)r. rp s r __ceil__zFraction.__ceil__m s ,, !..011r# c & |K| j }t | j | \ }}|dz |k r|S |dz |kD r|dz S |dz dk( r|S |dz S dt | z }|dkD rt t | |z | S t t | |z |z S )z?round(self, ndigits) Rounds half toward even. rd r r r )r0 r r/ r r round)rM ndigitsr floor remaindershifts r __round__zFraction.__round__r s ?!!A %dooq 9 E91}q Q " qy a qy CL Q;E$, /7 7E$, /% 78 8r# c B t | j | j S )z hash(self))r r/ r0 r` s r __hash__zFraction.__hash__ s t0A0ABBr# c t | t u r | j |k( xr | j dk( S t |t j r4| j |j k( xr | j |j k( S t |t j r|j dk( r |j }t |t rCt j | st j | rd|k( S | | j! | k( S t" S )za == br r )r= r> r/ r0 r? r@ rA r r r imagrealrB rJ isnanisinfrX r r s r __eq__zFraction.__eq__ s 7c><<1$< 1)< < a)) *LLAKK/ 4NNamm3 5 a )affkA a zz!} 1 axALLO++ " !r# c f t |t j r7 || j |j z | j |j z S t |t rKt j | st j | r |d| S || | j | S t S )ac 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. r ) r? r@ rA r/ r r0 r rB rJ r r rX r )rM otherops r _richcmpzFraction._richcmp s eW - - .doo(9(99''%//9; ; eU #zz% DJJu$5#u~%$ 677! !r# c B | j |t j S )za < b)r operatorltr s r __lt__zFraction.__lt__ zz!X[[))r# c B | j |t j S )za > b)r r gtr s r __gt__zFraction.__gt__ r r# c B | j |t j S )za <= b)r r ler s r __le__zFraction.__le__ r r# c B | j |t j S )za >= b)r r ger s r __ge__zFraction.__ge__ r r# c , t | j S )za != 0)r r/ rp s r __bool__zFraction.__bool__ s ALL!!r# c J | j | j | j ffS ro )rP r/ r0 r` s r __reduce__zFraction.__reduce__ s $2C2C DEEr# c v t | t k( r| S | j | j | j S ro r= r rP r/ r0 r` s r __copy__zFraction.__copy__ . : !K~~doot/@/@AAr# c v t | t k( r| S | j | j | j S ro r )rM memos r __deepcopy__zFraction.__deepcopy__ r r# )r N)i@B ro )HrU __module__ __qualname__r __slots__r< classmethodrX r[ rV ra rC rm propertyr r rt rw r r r r add__add____radd__r sub__sub____rsub__r mul__mul____rmul__r truediv __truediv__ __rtruediv__r floordiv __floordiv__ __rfloordiv__r r __divmod__ __rdivmod__r mod__mod____rmod__r r r r r indexr r r r r r r r r r r r r r r r __classcell__)rP s @r r r s ( /IgR = = ? ? &47Ar C Br)hk b D ,D(,,?GX D ,D(,,?GX = ,D(,,?GX1( !4D(:J:J K K N #6iARAR"S L-- 2'6 BJ J ,D(,,?GX "@ IJN #.. :2.2 94C"*",****"FB Br# )F) r r5 r functoolsrJ r@ r resys__all__ hash_infomodulusr infr lru_cacher compileVERBOSE IGNORECASErD r" r, DOTALL fullmatchr rA r r r# r <module>rG s 6 , --'' mm w' * ( *@ 2:: ZZ"-- ! ":$'R '1bjj 2 YY ' 'Y $$| Bw | Br#