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_pylong.cpython-312.pyc
CRh&* d Z ddlZddlZ ddlZd Zd Zd Zd Zd Z dZ d Z d Z d Z d Zd Zd Zy# e$ r dZY -w xY w)a Python implementations of some algorithms for use by longobject.c. The goal is to provide asymptotically faster algorithms that can be used for operations on integers with many digits. In those cases, the performance overhead of the Python implementation is not significant since the asymptotic behavior is what dominates runtime. Functions provided by this module should be considered private and not part of any public API. Note: for ease of maintainability, please prefer clear code and avoid "micro-optimizations". This module will only be imported and used for integers with a huge number of digits. Saving a few microseconds with tricky or non-obvious code is not worth it. For people looking for maximum performance, they should use something like gmpy2. Nc t j d di fd fdt j 5 }t j |_ t j |_ t j |_ d|j t j < | dk rd}| } nd} | | j }|r| }d d d |S # 1 sw Y S xY w) z6Asymptotically fast conversion of an 'int' to Decimal. c j | x}>| k r| z }n.| dz v r| dz x}|z }n| dz } | | |z z }|| < |S )zReturn D(2)**w and store the result. Also possibly save some intermediate results. In context, these are likely to be reused across various levels of the conversion to Decimal. get)wresulttw2BITLIMD2memw2pows /usr/lib/python3.12/_pylong.pyr z int_to_decimal.<locals>.w2pow+ sx ggaj F )F{QQ# "1q5z/!Q.!V rU1r6]2CF c |k r | S |dz }| |z }| ||z z } || |||z | z z S Nr ) nr r hilor Dinnerr s r r z int_to_decimal.<locals>.inner> sW ;Q4K !V "W "(^R}uRR 059 <<<r r r TFN) decimalDecimal localcontextMAX_PRECprecMAX_EMAXEmaxMIN_EMINEmintrapsInexact bit_length) r ctxnegater r r r r r r s @@@@@@r int_to_decimalr* s A 1B F C&= 3######%& '//" q5FAFq!,,.) WF M Ms BCC!c | j }|dkD rt t t | S fdt |dz dz }i | dk r| } d}nd} | | }|d dk( r| r|j d }||z S ) z?Asymptotically fast conversion of an 'int' to a decimal string.i c |dk r t | S |dz }j | }| d|z |z x}|< t | | \ }} |||z || j | z S )Ni r )strr divmodzfill)r r r dr r r pow10_caches r r z$int_to_decimal_string.<locals>.innerd s{ 9q6M !V OOB 9"#R%2+ -A B1 BRR 5R=#6#6r#:::r gyPD?r r - 0)r' _decimalr. r* intlstrip)r r signsr r2 s @@r int_to_decimal_stringr; W s A7{x+ >!$%% ;" A" "Q &'AK1u B a Ats{q HHSM !8Or c V di fd fd dt S )z6Asymptotically fast conversion of a 'str' to an 'int'.i c j | x}<| k rd| z }n,| dz v r | dz dz }n| dz } | | |z z }|| < |S )zReturn 5**w and store the result. Also possibly save some intermediate results. In context, these are likely to be reused across various levels of the conversion to 'int'. r- r r )r r r DIGLIMr w5pows r r? z _str_to_int_inner.<locals>.w5pow ss ggaj F )F{AQ# QUa !V rU1r6]2CF r c || z k rt | | S | |z dz dz } || | | ||z z ||z z z S r )r7 )abmidr> r r: r? s r r z _str_to_int_inner.<locals>.inner s] q5F?q1v; 1uqyQ S!}q# q3w !?QW MNNr r len)r: r> r r r? s `@@@@r _str_to_int_innerrF s- F C*O CF r c X | j j dd } t | S )zoAsymptotically fast version of PyLong_FromString(), conversion of a string of decimal digits into an 'int'._r4 )rstripreplacerF )r: s r int_from_stringrK s' 3#A Q r c t j d| }|s t d t |j d }|j d dk( r| }|S )zBAsymptotically fast version of decimal string to 'int' conversion.z\s*([+-]?)([0-9_]+)\s*z&invalid literal for int() with base 10r r r3 )rematch ValueErrorrK group)r: mvs r str_to_intrS sR *A.A ABB #AwwqzS B Hr i c . | j |z t k r t | | S |dz }|r| dz } |dz }|dz }|dz }d|z dz }||z ||z }}t | |z | |z |z |||| \ }} t | | |z |||| \ } } |r| dz } ||z | z | fS )aR Divide a 2n-bit nonnegative integer a by an n-bit positive integer b, using a recursive divide-and-conquer algorithm. Inputs: n is a positive integer b is a positive integer with exactly n bits a is a nonnegative integer such that a < 2**n * b Output: (q, r) such that a = b*q+r and 0 <= r < b. r )r' _DIV_LIMITr/ _div3n2n) rA rB r padhalf_nmaskb1b2q1rq2s r _div2n1nr_ s ||~Z'a| a%C a a Q !VF K1 D &[!d(B Q!Va6kT 11b"f EEB QD!RV 4EB a <" a r c | |z |k( rd|z dz | ||z z |z }}nt | || \ }}||z |z ||z z }|dk r|dz }||z }|dk r||fS )zAHelper function for _div2n1n; not intended to be called directly.r r )r_ )a12a3rB rZ r[ r qr] s r rV rV s ax2~Q!|SB!G_r 11R#1 a"B A a% Q Q a% a4Kr c ~ dg| j z dz z z fd| r | dt S )aR Decompose non-negative int a into base 2**n Input: a is a non-negative integer Output: List of the digits of a in base 2**n in little-endian order, meaning the most significant digit is last. The most significant digit is guaranteed to be non-zero. If a is 0 then the output is an empty list. r r c |dz |k( r| |< y ||z dz }||z z }| |z }| ||z z } ||| ||| y r r ) xLRrC shiftupperlowera_digitsr r s r r z_int2digits.<locals>.inner sc q5A:HQK 1ulqA U Ue^$ eQ eS! r )r' rE )rA r rl r s `@@r _int2digitsrm sE sq||~)A-!34H aCM" Or c B fd r dt S dS )zCombine base-2**n digits into an int. This function is the inverse of `_int2digits`. For more details, see _int2digits. c j | dz |k( r| S | |z dz }|| z z } || |z | | z S r r )rg rh rC ri digitsr r s r r z_digits2int.<locals>.inner! sN q5A:!9 1ulqA c1 &%3-77r r rD )rp r r s ``@r _digits2intrq s" 8 %+5CK 11r c |j }t | | }d}g }t | D ]) }t ||z |z || \ }}|j | + |j t || }||fS )z[Divide a non-negative integer a by a positive integer b, giving quotient and remainder.r )r' rm reversedr_ appendreverserq ) rA rB r rl r] q_digitsa_digitq_digitrc s r _divmod_posry + s~ A1a H AHH% qAv 0!Q7 & Ha A a4Kr c |dk( rt |dk rt | | \ }}|| fS | dk rt | | \ }}| || z fS t | | S )zAsymptotically fast replacement for divmod, for 'int'. Its time complexity is O(n**1.58), where n = #bits(a) + #bits(b). r )ZeroDivisionError int_divmodry )rA rB rc r] s r r| r| < so Av Q1"qb!11"u Q1"a 1r1r6z1a r )__doc__rM r r6 ImportErrorr* r; rF rK rS rU r_ rV rm rq ry r| r r r <module>r sr > =@*Z, ^ " < > 2 " !S Hs 4 >>