Packages

  • package root
    Definition Classes
    root
  • package spire
    Definition Classes
    root
  • package math
    Definition Classes
    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

object BitSet extends Serializable

Fast BitSet implementation.

This bitset is just intended to be a little bit faster than Scala's, and to support accessing its internals, which we do in some cases.

The max length (~2B) is a current limit to how big individual sieve segments can get. Until our sieving is more efficient, we don't want segments that big anyway, so this is OK.

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