grthtrhthjhtyjytjytkergtrhtrjytjerhrfh4:24 29/09/2026+ pw)Rt^RIt^RIt^RItRRRR/Rlt]P !4P4t]P]n ]P]n ]P]n^]P]P &RtRtRt]P+R 4t^R IHt]!]4tAR ^/R ltR tRtRtRtRt Rt!Rt"Rt#Rt$R# ]dRtLi;i)aPython 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.Nneed_hiFshowcL\4p\4pV0pV'dVP4pW9gW8:dK&VPV4V^, pW, p V'dT MTp VPV 4VPV 4W8wgK~VPW , 4KVP4p \4p V 'dj\ V 4pV P V4V^, pW8gK5V^, V 9gKEW9gKMV PV4V PV4KqV'g V 'dQh/p \ Wl,4FpV^, pW, p V^, V 9d-V'd\RRR7W^, ,V,pMW9dfV'd\RRR7W,W,,pW8wd5V'd\RRR7^V,^,V8XgQhW,pMV'd\RRR7W,pV'd\RYV9dRMR 4WV&K WmP48:gQhV P4V, ;p'dV'gQhVFpWK V #) z* base)endsquarez * basepowz atneededextra) setpopaddcopymaxremovesortedprintkeys)wbase more_thanrrseenneedwslohiwhichcandsr dnresultexcesss&&&$$ ./opt/alt/python314/lib64/python3.14/_pylong.pycompute_powersr$9s 5D 5D B FFH 9   !V V2  u 8 FF19  IIKE EE  J Q !V >ac.2? IIbM IIbM %  A DL ! !V V Q3!8hB'sVd]F WhB'UQU]Fx),2vzQ&e$YF  %T Hw ?!1"4 668  D v wA Hc8aaaa^RIHo^oVVVV3Rlo\P!\4;_uu_4VP 4p\ VS!^4S4oV^8dRpV)pMRpS!W4pV'dV)pRRR4V# +'giX#;i)z6Asymptotically fast conversion of an 'int' to Decimal.)Decimalc<VS8:d S!V4#V^, pW, pV^V,^, ,pS!WB4S!W1V, 4SV,,,#r) r rw2rrBITLIMDinnerw2pows && r#r.int_to_decimal..innersV ;Q4K !V W 17a- R}uRR059<<.innersQ ;q6M !V59%RR 5=#6#6r#:::r%gyPD?-r0)r4_decimalr:r7intr$itemslstrip) r rkvsignsr=r.r>s & @@@r#int_to_decimal_stringrJs A7{x+>!$%%F; A" "Q &'A 1a (E 6a1u B a Ats{q HHSM 8Or%cpaaaaRoVVVV3Rlo\\S4^S4oS!^\S44#)z6Asymptotically fast conversion of a 'str' to an 'int'.ic<W, S8:d\SW4#W,^,^, pS!W!4S!W4SW, ,,W, ,,#r))rC)abmidr=r.rIw5pows&& r#r. _str_to_int_inner..innersW 5F?qv; uqyQc !ME!'N2!" #r%)r$len)rIr=r.rPsf@@@r#_str_to_int_innerrSs9F## 3q61f -E CF r%z0x1.a934f0979a371p-2) defaultdictGUARDc xaa a a aaRo \Pp\4oS^8gQhV VV V VV3Rlo VP4pV\,p\ V4pV^,WE, R8,pVP 4^.8d\RV R24h\P!\4;_uu_4o V!R4p\WgS RR7o\V^V, S RR7p^S P\P&\PS nSP4F6wrV P!4S,^,S nWV ,53SV &K8 ?\P$S nS !V!V4V4RRR4\ P'S4# +'giL%;i) ic<VS 8:d5SP\\V44PV44R#V^, pW, pST,wrg\ TP 4TP 4, ^4S ,S nT5T5,p\PS nTP4pYT,, pT^8gQh^pYV8d1^pYV,pT^, pYV8dRp\ YV4wrYI, p\T;;,^, uu&S !YB4?S !YS4R#)Ni) extendrCr:to_bytesr;radjustedprecr1MAX_PRECto_integral_value_spread)r rw1r+rrp256recipcounthi2BYTELIMrUctxr.pow256r!s&& r#r.$_dec_str_to_int_inner..inners < MM#c!f+..q1 2  !V V !*KD 1::<$--/91=ECHufB''CH%%'B$YB7N7Ez a:  E$R.GCIB ENa N b  b r%g?zcannot convert string of len z to intT)rN)r1r' bytearray__len___LOG_10_BASE_256rCr4 ValueErrorr2r3r$trapsInexact ROUND_DOWNroundingrDrZr[r\ from_bytes)rIrUr-lenSlog_ub log_ub_as_intrD256rpow256rFrGrdrer.rfr!s&d @@@@@r#_dec_str_to_int_innerrwsh GA [F 19977L 99;D $ $FKMV3c9:A  ||~8gFGG   4 5 5v$? AHgtD &' '//")) LLNDA zz|e+a/CHAJ;F1I# ## adA- 6. >>& !!/ 6 5s >CF)) F9 cVP4PRR4p\p\V4R8d\e\ pV!V4#)zkAsymptotically fast version of PyLong_FromString(), conversion of a string of decimal digits into an 'int'._ri)rstripreplacerSrRrBrw)rIfuncs& r#int_from_stringr}s@  3#A D 1vx3$ 7Nr%c\P!RV4pV'g \R4h\VP ^44pVP ^4R8XdV)pV#)zBAsymptotically fast version of decimal string to 'int' conversion.z\s*([+-]?)([0-9_]+)\s*z&invalid literal for int() with base 10r@)rematchrlr}group)rImrGs& r# str_to_intrsR *A.A ABB #AwwqzS B Hr%icVP4V, \8:d \W4#V^,pV'dV^,pV^,pV^, pV^, p^V,^, pW, W,rv\W, W, V,WWt4wr\WV,WWt4wrV'd V ^,p W,V ,V 3#)a2Divide 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. )r4 _DIV_LIMITr;_div3n2n) rMrNr padhalf_nmaskb1b2q1rq2s &&& r#_div2n1nrs ||~Z'a| a%C  a a Q !VF K1 D [!( QVakT11" EEB QD! 4EB  a <" a r%cW, V8Xd'^V,^, WV,, V,rvM\WV4wrgWu,V,Wd,, pV^8dV^,pWr, pKWg3#)zAHelper function for _div2n1n; not intended to be called directly.)r)a12a3rNrrr qrs&&&&&& r#rrsc x2~Q!|S!G_r11# "A a% Q  4Kr%caaa^.VP4S,^, S,,oVVV3RloV'dS!V^\S44S#)a2Decompose 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. c<V^,V8XdVSV&R#W,^, pW1, S ,pW, pWV,, pS!WaV4S!WSV4R#)rNr*) xLRrOshiftupperlowera_digitsr.r s &&& r#r._int2digits..innersW q5A:HQK ulA  e^$ e e!r%)r4rR)rMr rr.s&f@@r# _int2digitsrsEsq||~)A-!34H   aCM" Or%cPaaaVVV3RloS'dS!^\S44#^#)zxCombine base-2**n digits into an int. This function is the inverse of `_int2digits`. For more details, see _int2digits. c<V^,V8Xd SV,#W,^, pW , S,pS!W!4V,S!W4,#r)r*)rrrOrdigitsr.r s&& r#r._digits2int..innersF q5A:!9 ulA c &%-77r%)rR)rr r.sff@r# _digits2intrs" 8%+5CK 11r%cVP4p\W4p^p.p\V4F/p\WB,V,W4wrtVP V4K1 VP 4\ WR4pW3#)zWDivide a non-negative integer a by a positive integer b, giving quotient and remainder.)r4rreversedrappendreverser) rMrNr rrq_digitsa_digitq_digitrs && r# _divmod_posrsr A1 H AHH%qv0!7  & H A 4Kr%cV^8Xd \R4hV^8d\V)V)4wr#W#)3#V^8d\V(V4wr#V(W(,3#\W4#)zyAsymptotically fast replacement for divmod, for 'int'. Its time complexity is O(n**1.58), where n = #bits(a) + #bits(b). zdivision by zero)ZeroDivisionError int_divmodr)rMrNrrs&& r#rrsk Av 233 Q1"qb!"u Q1"a r1r6z1  r%),__doc__rr1rB ImportErrorr$ getcontextrr3r\r[MAX_EMAXEmaxMIN_EMINEminrmrnr7rJrSfloatfromhexrk collectionsrTrCr^rwr}rrrrrrrrconsumer itertoolschainrlimitrangerr*r%r#rs > NJ %J eJ X!++-224%..%..%..01W__-%N+ZJ==!78$ c t"at"l   "  < > 2" !b]HsC CC