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

case class SieveSegment(start: SafeLong, primes: BitSet, cutoff: SafeLong) extends Product with Serializable

Linear Supertypes
Serializable, Serializable, Product, Equals, AnyRef, Any
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  1. SieveSegment
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. AnyRef
  7. Any
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Visibility
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Instance Constructors

  1. new SieveSegment(start: SafeLong, primes: BitSet, cutoff: 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. val cutoff: SafeLong
  7. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  8. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  9. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  10. def init(fastq: FastFactors, slowq: FactorHeap): Unit
  11. def initFirst(fastq: FastFactors, slowq: FactorHeap): Unit
  12. def initMod30(): Unit
  13. def initRest(slowq: FactorHeap): Unit
  14. def isComposite(n: SafeLong): Boolean
  15. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  16. def isPrime(n: SafeLong): Boolean
  17. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  18. def nextAfter(n: SafeLong): SafeLong
  19. final def notify(): Unit
    Definition Classes
    AnyRef
  20. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  21. val primes: BitSet
  22. def set(n: SafeLong): Unit
  23. val start: SafeLong
  24. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  25. def unset(n: SafeLong): Unit
  26. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  27. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  28. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

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