":h4ddlmZddlmZddlZGddeZGddeZGdd eZd Z d Z d Z d Z dZ dZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZgdZday) )division)reduceNceZdZdZy)Errorz)Base class for exceptions in this module.N)__name__ __module__ __qualname____doc__e/var/www/html/turnos/venv/lib/python3.12/site-packages/ccxt/static_dependencies/ecdsa/numbertheory.pyrrs3r rc eZdZy)SquareRootErrorNrrr r r r rrr rc eZdZy)NegativeExponentErrorNrr r r rrrr rcB|dkrtd|zt|||S)z+Raise base to exponent, reducing by modulusrz#Negative exponents (%d) not allowed)rpow)baseexponentmoduluss r modular_expr s0!|#$I&.%/0 0 tXw ''r c |ddk(sJt|dkDsJt|t|k\r\|ddk7r7tdt|dzD]}|| |d|| zz |z|| <|dd}t|t|k\r\|S)zReduce poly by polymod, integer arithmetic modulo p. Polynomials are represented as lists of coefficients of increasing powers of x.r)lenrange)polypolymodpis r polynomial_reduce_modr$2s 2;!   wucvcudvdqs r inverse_modrLs 1uQ E aqANBB q&A,!%1aa"fb1r6k2r9BB q& 6M6 Av Av r c|r ||z|}}|r |S)z1Greatest common divisor using Euclid's algorithm.r r6r?s r gcd2rOs 1ua1 Hr ct|dkDrtt|St|ddrtt|dS|dS)zLGreatest common divisor. Usage: gcd([ 2, 4, 6 ]) or: gcd(2, 4, 6) rr__iter__)rrrOhasattrr6s r gcdrTC 1vzdAqtZ dAaD!! Q4Kr c&||zt||zS)z&Least common multiple of two integers.rTrNs r lcm2rXs Ec!Qi r ct|dkDrtt|St|ddrtt|dS|dS)zJLeast common multiple. Usage: lcm([ 3, 4, 5 ]) or: lcm(3, 4, 5) rrrQ)rrrXrRrSs r lcmrZrUr c^t|tsJ|dkrgSg}d}tD]Z}||kDrnSt||\}}|dk(sd}||kr"|}t||\}}|dk7rn |dz}||kr"|j ||f\|tdkDrt |r|j |df|Std} |dz}t||\}}||krnD|dk(r>d}|}||kr"t||\}}|dk7rn |}|dz}||kr"|j ||f^|dkDr|j |df|S)z2Decompose n into a list of (prime,exponent) pairs.rrrr) isinstanceint smallprimesrDappendis_prime)r7resultr>rKrcounts r factorizationrd s a  1u F A & q5 a|1 6Eq&a|16  q& MM1e* % &" ;r? A; MM1a& !* M'BAEa|1q56EAq&%a|16! %  q& MM1e*-1u q!f% Mr ct|tsJ|dkryd}t|}|D]/}|d}|dkDr||d|dz zz|ddz z}%||ddz z}1|S)z'Return the Euler totient function of n.r1rr)r\r]rd)r7rarAr@r9s r phirfAs a  1u F q B ) aD q5adq1uo-1:Fqtax(F ) Mr c*tt|S)zReturn Carmichael function of n. Carmichael(n) is the smallest integer x such that m**x = 1 mod n for all m relatively prime to n. )carmichael_of_factorizedrd)r7s r carmichaelriTs $M!$4 55r ct|dkryt|d}tdt|D]}t|t||}|S)zhReturn the Carmichael function of a number that is represented as a list of (prime,exponent) pairs. rr)rcarmichael_of_ppowerrrZ)f_listrar#s r rhrh^sW  6{Q !&) ,F 1c&k ">V1&)<=> Mr cL|\}}|dk(r |dkDrd|dz zS|dz ||dz zzS)z=Carmichael function of the given power of the given prime. rrr )ppr"r6s r rkrkms? DAqAv!a%QU|Aq1u%%r cl|dkryt||dk(sJ|}d}|dk7r||z|z}|dz}|dk7r|S)z;Return the order of x in the multiplicative group mod m. rrrW)xrEzras r order_modrrxsW Av q!9>> A F q& UaK! q& Mr cd t||}|dkr |S|} t||\}}|dkDrn|}0)z8Return the largest factor of a relatively prime to b. rr)rTrD)r6r?r>rKrbs r largest_factor_relatively_primertsU 1I 6  H !Q>r cda|tdkr |tvryyt|ddk7ryd}dtt j |dz}d D]\}}||krn|}d}|dz }|dzdk(r|dz}|dz}|dzdk(rt |D]w}t|}t|||} | dk7s| |dz k7s(d} | |dz kr7| |dz k7r/t| d|} | dk(r|dzay| dz} | |dz kr | |dz k7r/| |dz k7sr|dzayy) a*Return True if x is prime, False otherwise. We use the Miller-Rabin test, as given in Menezes et al. p. 138. This test is not exact: there are composite values n for which it returns True. In testing the odd numbers from 10000001 to 19999999, about 66 composites got past the first test, 5 got past the second test, and none got past the third. Since factors of 2, 3, 5, 7, and 11 were detected during preliminary screening, the number of numbers tested by Miller-Rabin was (19999999 - 10000001)*(2/3)*(4/5)*(6/7) = 4.57 million. rrTFi r(r) )d))) )i, )i^r2)ir3)i)i&r;)ir4)iRr1)ir)miller_rabin_test_countr^rTr]mathlogrr) r7tn_bitsr-ttr.rbr#r6yr)s r r`r`so& KO  1 !Q& A TXXa^$ $F 2 A:  & A AA q5Q, E F q5Q,1X  N 1a  6a1q5jAq1u*a!e1a(6./!e+ E q1u*a!e AEz*+a%'  r cZ|dkry|dzdz}t|s|dz}t|s|S)z9Return the smallest prime larger than the starting value.rr)r`)starting_valueras r next_primers>q A %Fv!v Mr )rr1r;r3 %)+/5;=CGIOSYaegkmqiii iiiii%i3i7i9i=iKiQi[i]iaigioiui{iiiiiiiiiiiiiiiiiiiiiii i ii#i-i3i9i;iAiKiQiWiYi_ieiiikiwiiiiiiiiiiiiiiiiiiiiiiiii)i+i5i7i;i=iGiUiYi[i_imiqisiwiiiiiiiiiiiiiiiiiiii iiii%i'i-i?iCiEiIiOiUi]iciiiiiiiiiiiiii) __future__r functoolsrr Exceptionrrrrr$r*r/r5rBrLrOrTrXrZrdrfrirhrkrrrtrvr`rr^rr r r rs   I  e  E ($.30 @"<&&R0   5p&6 &( "?JZE *r