org.apache.commons.math3.primes

Class PollardRho

java.lang.Object

org.apache.commons.math3.primes.PollardRho

 class PollardRho
extends java.lang.Object

Implementation of the Pollard's rho factorization algorithm.

Since:

3.2

Constructor Summary

Constructors

Modifier	Constructor and Description
private	PollardRho() Hide utility class.

Method Summary

Methods

Modifier and Type	Method and Description
(package private) static int	gcdPositive(int a, int b) Gcd between two positive numbers.
static java.util.List<java.lang.Integer>	primeFactors(int n) Factorization using Pollard's rho algorithm.
(package private) static int	rhoBrent(int n) Implementation of the Pollard's rho factorization algorithm.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PollardRho

private PollardRho()

Hide utility class.

Method Detail

primeFactors

public static java.util.List<java.lang.Integer> primeFactors(int n)

Factorization using Pollard's rho algorithm.

Parameters:

n - number to factors, must be > 0

Returns:

the list of prime factors of n.

rhoBrent

static int rhoBrent(int n)

Implementation of the Pollard's rho factorization algorithm.

This implementation follows the paper "An improved Monte Carlo factorization algorithm" by Richard P. Brent. This avoids the triple computation of f(x) typically found in Pollard's rho implementations. It also batches several gcd computation into 1.

The backtracking is not implemented as we deal only with semi-primes.

Parameters:

n - number to factor, must be semi-prime.

Returns:

a prime factor of n.

gcdPositive

static int gcdPositive(int a,
              int b)

Gcd between two positive numbers.

Gets the greatest common divisor of two numbers, using the "binary gcd" method, which avoids division and modulo operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef Stein (1961).

Special cases:

• The result of gcd(x, x), gcd(0, x) and gcd(x, 0) is the value of x.
• The invocation gcd(0, 0) is the only one which returns 0.

Parameters:

a - first number, must be ≥ 0

b - second number, must be ≥ 0

Returns:

gcd(a,b)