+ oiGRt^RIt!RR]4tRRltRRltRR ltR R ltR R ltRRlt ] R8Xd^RI t ] P!4R#R#)z/Common functionality shared by several modules.NcBaa]tRt^toRV3RlV3RllltRtVtV;t#)NotRelativePrimeErrorc 6<V^8dQhRS[RS[RS[RS[RR/#)abdmsgreturnN)intstr)format __classdict__s"m/Users/tonyclaw/.openclaw/workspace/scripts/youtube-playlists/venv/lib/python3.14/site-packages/rsa/common.py __annotate__"NotRelativePrimeError.__annotate__s0###Ccp<\ST`T;'g RWV3,4WnW nW0nR#)z.%d and %d are not relatively prime, divider=%iN)super__init__rrr)selfrrrr __class__s&&&&&rrNotRelativePrimeError.__init__s4 \\ PTUZ[S\ \]r)rrr))__name__ __module__ __qualname____firstlineno__r__static_attributes____classdictcell__ __classcell__)rrs@@rrrsrrc0V^8dQhR\R\/#)rnumr r )r s"rrrs\\#\#\rcVP4# \d"p\R\T4,4ThRp?ii;i)a Number of bits needed to represent a integer excluding any prefix 0 bits. Usage:: >>> bit_size(1023) 10 >>> bit_size(1024) 11 >>> bit_size(1025) 11 :param num: Integer value. If num is 0, returns 0. Only the absolute value of the number is considered. Therefore, signed integers will be abs(num) before the number's bit length is determined. :returns: Returns the number of bits in the integer. z,bit_size(num) only supports integers, not %rN) bit_lengthAttributeError TypeErrortype)r"exs& rbit_sizer*s?,\~~ \FcRSY[[\s >9>c0V^8dQhR\R\/#)rnumberr r#)r s"rrr8s))c)c)rc>V^8Xd^#\\V4^4#)a\ Returns the number of bytes required to hold a specific long number. The number of bytes is rounded up. Usage:: >>> byte_size(1 << 1023) 128 >>> byte_size((1 << 1024) - 1) 128 >>> byte_size(1 << 1024) 129 :param number: An unsigned integer :returns: The number of bytes required to hold a specific long number. )ceil_divr*)r,s&r byte_sizer/8s ({ HV$a ((rc<V^8dQhR\R\R\/#)rr"divr r#)r s"rrrQs!#CCrcB\W4wr#V'd V^, pV#)aF Returns the ceiling function of a division between `num` and `div`. Usage:: >>> ceil_div(100, 7) 15 >>> ceil_div(100, 10) 10 >>> ceil_div(1, 4) 1 :param num: Division's numerator, a number :param div: Division's divisor, a number :return: Rounded up result of the division between the parameters. )divmod)r"r1quantamods&& rr.r.Qs!$"KF !  Mrc |V^8dQhR\R\R\P\\\3,/#)rrrr )r typingTuple)r s"rrris0CCFLLc3$?rc^p^p^p^pTpTpV^8wd4W,pYV,rWHV,, TrBWXV,, TrSK:V^8d WG, pV^8d WV, pWV3#)z;Returns a tuple (r, i, j) such that r = gcd(a, b) = ia + jb) rrxylxlyoaobqs && r extended_gcdrBisy A A B B B B q& FUAa%L1Ba%L1B Av  Av  "9rc<V^8dQhR\R\R\/#)rr;nr r#)r s"rrrs!sssrcH\W4wr#pV^8wd \WV4hV#)z}Returns the inverse of x % n under multiplication, a.k.a x^-1 (mod n) >>> inverse(7, 4) 3 >>> (inverse(143, 4) * 143) % 4 1 )rBr)r;rDdividerinv_s&& rinverserIs,%Q*W1!|#A'22 JrcV^8dQhR\P\,R\P\,R\/#)ra_values modulo_valuesr )r7Iterabler )r s"rrrs4   &//#&  vs7K  PS  rc^p^pVF pW$,pK \W4F5wrVW%,p\Wu4pW6V,V,,V,pK7 V#)aYChinese Remainder Theorem. Calculates x such that x = a[i] (mod m[i]) for each i. :param a_values: the a-values of the above equation :param modulo_values: the m-values of the above equation :returns: x such that x = a[i] (mod m[i]) for each i >>> crt([2, 3], [3, 5]) 8 >>> crt([2, 3, 2], [3, 5, 7]) 23 >>> crt([2, 3, 0], [7, 11, 15]) 135 )ziprI) rKrLmr;modulom_ia_iM_irGs && rcrtrUs_( A A  -2 hc sS A % 3 Hr__main__) __doc__r7 ValueErrorrr*r/r.rBrIrUrdoctesttestmodr:rrr[sU6 J\8)200"  F z OOr