phpOMS/Math/Number/Integer.php

<?php
class Integer implements Number 
{
	public static function isInteger($value) : bool
	{
		return is_int($value);
	}

	/**
     * Greatest common diviser.
     *
     * @param int $n Number one
     * @param int $m Number two
     *
     * @return int
     *
     * @since  1.0.0
     * @author Dennis Eichhorn
     */
    public static function greatestCommonDivisor(int $n, int $m) : int
    {
        while (true) {
            if ($n === $m) {
                return $m;
            } if ($n > $m) {
                $n -= $m;
            } else {
                $m -= $n;
            }
        }
    }

	public static function trialFactorization(int $value) 
	{
		if ($value < 2) {
			return [];
		}

		$factors = [];
		$primes = Prime::sieveOfEratosthenes((int) $value**0.5);

		for($primes as $prime) {
			if($prime*$prime > $value) {
				break;
			}

			while($value%$prime === 0) {
				$factors[] = $prime;
				$value /= $prime; 
			}
		}

		if($value > 1) {
			$factors[] = $value;
		}

		return $factors;
	}

	public static function pollardsRho($value, $x = 2, $factor = 1, $cycleSize = 2, $xFixed = 2) 
	{
		while($factor === 1) {
			for($i = 1; $i < $cycleSize && $factor <= 1; $i++) {
				$x = ($x*$x+1)%$value;
				$factor = self::greatestCommonDivisor($x-$xFixed, $value);
			}

			$cycleSize *= 2;
			$xFixed = $x;
		}

		return $factor;
	}

	public static function fermatFactor(int $value)
	{
		$a = $value;
		$b2 = $a*$a - $value;

		while(abs((int) round(sqrt($b2), 0) - sqrt($b2)) > 0.0001) {
			$a += 1;
			$b2 = $a*$a - $value;
		}

		return $a - sqrt($b2);
	}
}