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
  • object SieveUtil
    Definition Classes
    prime
  • Factor
  • FastFactor
  • FastFactors

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

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.

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Serializable, Serializable, Product, Equals, AnyRef, Any
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Instance Constructors

  1. new FastFactor(p: Int, m: SafeLong)

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  7. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  8. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  9. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  10. var m: SafeLong
  11. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. final def notify(): Unit
    Definition Classes
    AnyRef
  13. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  14. val p: Int
  15. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  16. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  17. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  18. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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Inherited from AnyRef

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