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  • package spire
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  • package math
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    spire
  • package prime

    Basic tools for prime factorization.

    Basic tools for prime factorization.

    This package is intended to provide tools for factoring numbers, checking primality, generating prime numbers, etc. For now, its main contributions are a method for factoring integers (spire.math.prime.factor) and a type for representing prime factors and their exponents (spire.math.prime.Factors).

    The factorization currently happens via an implementation of Pollard-Rho with Brent's optimization. This technique works very well for composites with small prime factors (up to 10 decimal digits or so) and can support semiprimes (products of two similarly-sized primes) of 20-40 digits.

    The implementation does cheat, using BigInteger.isProbablePrime(40) to test basic primality. This has a roughly 1-in-1,000,000,000,000 chance of being wrong.

    Since Pollard-Rho uses random primes, its performance is somewhat non-deterministic. On this machine, factoring 20-digit semiprimes seem to average about 1.5s and factoring 30-digit semiprimes seem to average about 20s. Much larger numbers can be factored provided they are either prime or composites with smallish factors.

    Definition Classes
    math
  • BitSet
  • FactorHeap
  • Factors
  • SieveSegment
  • SieveUtil
  • Siever
o

spire.math.prime

SieveUtil

object SieveUtil

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  1. case class Factor (p: SafeLong, next: SafeLong) extends Ordered[Factor] with Product with Serializable

    Represents a prime factor which we need to keep track of.

    Represents a prime factor which we need to keep track of.

    The first field 'p' is the prime itself. The 'next' field is the next multiple of the prime that we expect to see.

    We use a slightly non-standard compare() function so that the factor with the smallest 'next' field will be the largest.

  2. case class FastFactor (p: Int, m: SafeLong) extends Product with Serializable

    Reprsents a prime factor which we need to keep track of.

    Reprsents a prime factor which we need to keep track of.

    Similar to Factor, but in this case the prime is small enough that it fits in an Int. This means that each of our sieve segments will contain at least one multiple of 'p' if not more. So we can use a slightly more compact data structure.

  3. case class FastFactors (arr: Array[FastFactor]) extends Product with Serializable

    This class simply wraps an Array[FastFactor].

    This class simply wraps an Array[FastFactor]. Its only real purpose is to allow us to lazily initialize our fast factors (which we can only do after constructing our first sieve segment).

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  20. object FastFactors extends Serializable

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