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 Factor(p: SafeLong, next: SafeLong) extends Ordered[Factor] with Product with Serializable

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.

Linear Supertypes
Serializable, Serializable, Product, Equals, Ordered[Factor], Comparable[Factor], AnyRef, Any
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Inherited
  1. Factor
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. Ordered
  7. Comparable
  8. AnyRef
  9. Any
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Visibility
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Instance Constructors

  1. new Factor(p: SafeLong, next: SafeLong)

Value Members

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

Inherited from Comparable[Factor]

Inherited from AnyRef

Inherited from Any

Ungrouped