!23&M      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ Continued fractionsMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe q  Lucas sequencesMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafeA2Generating random natural numbers of a given widthMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe=Utility functionsMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe  An abstract ring typeMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafeU!"'&$#%()*+,-./01!"'&$#%()*+,-./01Polynomial arithmeticMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafeE23546789:;<=>?@ABCDEFGHIJKLMNOP23546789:;<=>?@ABCDEFGHIJKLMNOP2Modular arithmetic using Montgomery multiplicationMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe#RSUTVW^]\[ZYX_`abcdefghijklmnopqrst#VW^]\[ZYXRSUT_`abcdefghijklmnopqrstModular arithmeticMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe wxyz{|}~ wxyz{|}~ Natural number square rootMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafeq  Leftist heapsMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafeA !The genuine sieve of EratosphenesMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe  Generating random primesMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe! Factorized natural numbersMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe#!Williams p+1 factorization methodMIT Joe Leslie-Hurd <joe@gilith.com> provisionalportableSafe& !"#$%&'()*+,-.//0123456789:;<==>?@4ABCD5EFGHIJKLMN012O8P3QRSSTUVVWXYZ[\]^_`abcde456071829:;fghib0123Q789:;< j j k l m n o p q r s t u v w x y z { | } ~  0   0   5 2 : e !%arithmetic-1.3-6GTp4iK6zdW26ZYJUnETqWArithmetic.ContinuedFractionArithmetic.LucasArithmetic.RandomArithmetic.UtilityArithmetic.RingArithmetic.PolynomialArithmetic.MontgomeryArithmetic.ModularArithmetic.QuadraticArithmetic.Utility.HeapArithmetic.Prime.SieveArithmetic.PrimeArithmetic.Prime.FactorArithmetic.WilliamsContinuedFractionunContinuedFraction fromNatural goldenRationaturalLogarithmBase convergentsFn numerators denominators convergentsunstableConvergentsfractionalConvergentsrationalConvergentstoDouble fromRealFracinvert$fShowContinuedFraction$fEqContinuedFractionadvancesequence uSequence vSequencerandomPairWith randomPair randomMaybe randomFilter randomWidth randomOdd randomCoprime functionPowermultiplyExponential factorTwos factorOutRingaddnegatemultiplydividezeroonetwodoublesubtractsquareexpexp2divides Polynomialcarrier coefficientsfromCoefficientsisZeroconstant destConstant isConstantmultiplyByPowermonomial variablePowervariabledegreeleadingCoefficientnthCoefficientisMonicevaluateaddCoefficientsmultiplyByScalarquotientRemainderring$fShowPolynomial Montgomery pMontgomery nMontgomery Parameters nParameters wParameters sParameters kParameters rParameters r2Parameters zParametersaligncustomParametersalignedParametersstandardParameters normalize normalize1reduce toNaturalmodexpmodexp2$fShowParameters$fShowMontgomeryResidue NonResidueZero rootFloor rootCeilingrootContinuedFractionrootContinuedFractionPeriodic!rootContinuedFractionPeriodicTail jacobiSymbol isResidue isNonResidue nextResiduenextNonResiduerootModuloPrime3Mod4rootModuloPrime5Mod8rootModuloPrime $fEqResidue $fOrdResidue $fShowResidueHeapsizeisEmptyemptyremovetoList $fShowHeap $fShowNodeSieveunSieveinitialbump $fShowSieveprimesmillerRabinWitness millerRabinisPrime previousPrime nextPrimenextPrime3Mod4nextPrime5Mod8 randomPrimerandomPrime3Mod4randomPrime5Mod8FactorunFactor primePowersisOne primePowerdestPrimePower isPrimePowerprime destPrimedestRSAisRSArootdestRootisRootgcd trialDivision destSmoothisSmooth nextSmoothmultiplicativetotient factorPowerfactor randomRSA $fShowFactornthExpnthbasemethod