src/Biz/Util/Phpsec/Math/BigInteger.php

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<?php

/**
 * Pure-PHP arbitrary precision integer arithmetic library.
 *
 * Supports base-2, base-10, base-16, and base-256 numbers.  Uses the GMP or BCMath extensions, if available,
 * and an internal implementation, otherwise.
 *
 * PHP version 5
 *
 * {@internal (all DocBlock comments regarding implementation - such as the one that follows - refer to the
 * {@link self::MODE_INTERNAL self::MODE_INTERNAL} mode)
 *
 * BigInteger uses base-2**26 to perform operations such as multiplication and division and
 * base-2**52 (ie. two base 2**26 digits) to perform addition and subtraction.  Because the largest possible
 * value when multiplying two base-2**26 numbers together is a base-2**52 number, double precision floating
 * point numbers - numbers that should be supported on most hardware and whose significand is 53 bits - are
 * used.  As a consequence, bitwise operators such as >> and << cannot be used, nor can the modulo operator %,
 * which only supports integers.  Although this fact will slow this library down, the fact that such a high
 * base is being used should more than compensate.
 *
 * Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian} format.  ie.
 * (new \Biz\Util\Phpsec\Math\BigInteger(pow(2, 26)))->value = array(0, 1)
 *
 * Useful resources are as follows:
 *
 *  - {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf Handbook of Applied Cryptography (HAC)}
 *  - {@link http://math.libtomcrypt.com/files/tommath.pdf Multi-Precision Math (MPM)}
 *  - Java's BigInteger classes.  See /j2se/src/share/classes/java/math in jdk-1_5_0-src-jrl.zip
 *
 * Here's an example of how to use this library:
 * <code>
 * <?php
 *    $a = new \Biz\Util\Phpsec\Math\BigInteger(2);
 *    $b = new \Biz\Util\Phpsec\Math\BigInteger(3);
 *
 *    $c = $a->add($b);
 *
 *    echo $c->toString(); // outputs 5
 * ?>
 * </code>
 *
 * @category  Math
 *
 * @author    Jim Wigginton <terrafrost@php.net>
 * @copyright 2006 Jim Wigginton
 * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
 *
 * @see      http://pear.php.net/package/Math_BigInteger
 */

namespace Biz\Util\Phpsec\Math;

use Biz\Util\Phpsec\Crypt\Random;

/**
 * Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256
 * numbers.
 *
 *