/drupal/profiles/medienlabor/modules/contrib/aes/phpseclib/Math/BigInteger.php
PHP | 3553 lines | 1866 code | 466 blank | 1221 comment | 372 complexity | 80b9e0cdd6b4fa97b897901a7c92db6a MD5 | raw file
Possible License(s): GPL-2.0, AGPL-1.0, LGPL-2.1
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- <?php
- /* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
-
- /**
- * 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 versions 4 and 5
- *
- * {@internal (all DocBlock comments regarding implementation - such as the one that follows - refer to the
- * {@link MATH_BIGINTEGER_MODE_INTERNAL MATH_BIGINTEGER_MODE_INTERNAL} mode)
- *
- * Math_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.
- *
- * When PHP version 6 is officially released, we'll be able to use 64-bit integers. This should, once again,
- * allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition /
- * subtraction).
- *
- * Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian} format. ie.
- * (new 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
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger(2);
- * $b = new Math_BigInteger(3);
- *
- * $c = $a->add($b);
- *
- * echo $c->toString(); // outputs 5
- * ?>
- * </code>
- *
- * LICENSE: Permission is hereby granted, free of charge, to any person obtaining a copy
- * of this software and associated documentation files (the "Software"), to deal
- * in the Software without restriction, including without limitation the rights
- * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
- * copies of the Software, and to permit persons to whom the Software is
- * furnished to do so, subject to the following conditions:
- *
- * The above copyright notice and this permission notice shall be included in
- * all copies or substantial portions of the Software.
- *
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
- * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
- * THE SOFTWARE.
- *
- * @category Math
- * @package Math_BigInteger
- * @author Jim Wigginton <terrafrost@php.net>
- * @copyright MMVI Jim Wigginton
- * @license http://www.opensource.org/licenses/mit-license.html MIT License
- * @version $Id: BigInteger.php 326530 2012-07-07 22:05:25Z terrafrost $
- * @link http://pear.php.net/package/Math_BigInteger
- */
-
- /**#@+
- * Reduction constants
- *
- * @access private
- * @see Math_BigInteger::_reduce()
- */
- /**
- * @see Math_BigInteger::_montgomery()
- * @see Math_BigInteger::_prepMontgomery()
- */
- define('MATH_BIGINTEGER_MONTGOMERY', 0);
- /**
- * @see Math_BigInteger::_barrett()
- */
- define('MATH_BIGINTEGER_BARRETT', 1);
- /**
- * @see Math_BigInteger::_mod2()
- */
- define('MATH_BIGINTEGER_POWEROF2', 2);
- /**
- * @see Math_BigInteger::_remainder()
- */
- define('MATH_BIGINTEGER_CLASSIC', 3);
- /**
- * @see Math_BigInteger::__clone()
- */
- define('MATH_BIGINTEGER_NONE', 4);
- /**#@-*/
-
- /**#@+
- * Array constants
- *
- * Rather than create a thousands and thousands of new Math_BigInteger objects in repeated function calls to add() and
- * multiply() or whatever, we'll just work directly on arrays, taking them in as parameters and returning them.
- *
- * @access private
- */
- /**
- * $result[MATH_BIGINTEGER_VALUE] contains the value.
- */
- define('MATH_BIGINTEGER_VALUE', 0);
- /**
- * $result[MATH_BIGINTEGER_SIGN] contains the sign.
- */
- define('MATH_BIGINTEGER_SIGN', 1);
- /**#@-*/
-
- /**#@+
- * @access private
- * @see Math_BigInteger::_montgomery()
- * @see Math_BigInteger::_barrett()
- */
- /**
- * Cache constants
- *
- * $cache[MATH_BIGINTEGER_VARIABLE] tells us whether or not the cached data is still valid.
- */
- define('MATH_BIGINTEGER_VARIABLE', 0);
- /**
- * $cache[MATH_BIGINTEGER_DATA] contains the cached data.
- */
- define('MATH_BIGINTEGER_DATA', 1);
- /**#@-*/
-
- /**#@+
- * Mode constants.
- *
- * @access private
- * @see Math_BigInteger::Math_BigInteger()
- */
- /**
- * To use the pure-PHP implementation
- */
- define('MATH_BIGINTEGER_MODE_INTERNAL', 1);
- /**
- * To use the BCMath library
- *
- * (if enabled; otherwise, the internal implementation will be used)
- */
- define('MATH_BIGINTEGER_MODE_BCMATH', 2);
- /**
- * To use the GMP library
- *
- * (if present; otherwise, either the BCMath or the internal implementation will be used)
- */
- define('MATH_BIGINTEGER_MODE_GMP', 3);
- /**#@-*/
-
- /**
- * The largest digit that may be used in addition / subtraction
- *
- * (we do pow(2, 52) instead of using 4503599627370496, directly, because some PHP installations
- * will truncate 4503599627370496)
- *
- * @access private
- */
- define('MATH_BIGINTEGER_MAX_DIGIT52', pow(2, 52));
-
- /**
- * Karatsuba Cutoff
- *
- * At what point do we switch between Karatsuba multiplication and schoolbook long multiplication?
- *
- * @access private
- */
- define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 25);
-
- /**
- * Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256
- * numbers.
- *
- * @author Jim Wigginton <terrafrost@php.net>
- * @version 1.0.0RC4
- * @access public
- * @package Math_BigInteger
- */
- class Math_BigInteger {
- /**
- * Holds the BigInteger's value.
- *
- * @var Array
- * @access private
- */
- var $value;
-
- /**
- * Holds the BigInteger's magnitude.
- *
- * @var Boolean
- * @access private
- */
- var $is_negative = false;
-
- /**
- * Random number generator function
- *
- * @see setRandomGenerator()
- * @access private
- */
- var $generator = 'mt_rand';
-
- /**
- * Precision
- *
- * @see setPrecision()
- * @access private
- */
- var $precision = -1;
-
- /**
- * Precision Bitmask
- *
- * @see setPrecision()
- * @access private
- */
- var $bitmask = false;
-
- /**
- * Mode independant value used for serialization.
- *
- * If the bcmath or gmp extensions are installed $this->value will be a non-serializable resource, hence the need for
- * a variable that'll be serializable regardless of whether or not extensions are being used. Unlike $this->value,
- * however, $this->hex is only calculated when $this->__sleep() is called.
- *
- * @see __sleep()
- * @see __wakeup()
- * @var String
- * @access private
- */
- var $hex;
-
- /**
- * Converts base-2, base-10, base-16, and binary strings (eg. base-256) to BigIntegers.
- *
- * If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using
- * two's compliment. The sole exception to this is -10, which is treated the same as 10 is.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('0x32', 16); // 50 in base-16
- *
- * echo $a->toString(); // outputs 50
- * ?>
- * </code>
- *
- * @param optional $x base-10 number or base-$base number if $base set.
- * @param optional integer $base
- * @return Math_BigInteger
- * @access public
- */
- function Math_BigInteger($x = 0, $base = 10)
- {
- if ( !defined('MATH_BIGINTEGER_MODE') ) {
- switch (true) {
- case extension_loaded('gmp'):
- define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_GMP);
- break;
- case extension_loaded('bcmath'):
- define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_BCMATH);
- break;
- default:
- define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_INTERNAL);
- }
- }
-
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- if (is_resource($x) && get_resource_type($x) == 'GMP integer') {
- $this->value = $x;
- return;
- }
- $this->value = gmp_init(0);
- break;
- case MATH_BIGINTEGER_MODE_BCMATH:
- $this->value = '0';
- break;
- default:
- $this->value = array();
- }
-
- // '0' counts as empty() but when the base is 256 '0' is equal to ord('0') or 48
- // '0' is the only value like this per http://php.net/empty
- if (empty($x) && (abs($base) != 256 || $x !== '0')) {
- return;
- }
-
- switch ($base) {
- case -256:
- if (ord($x[0]) & 0x80) {
- $x = ~$x;
- $this->is_negative = true;
- }
- case 256:
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $sign = $this->is_negative ? '-' : '';
- $this->value = gmp_init($sign . '0x' . bin2hex($x));
- break;
- case MATH_BIGINTEGER_MODE_BCMATH:
- // round $len to the nearest 4 (thanks, DavidMJ!)
- $len = (strlen($x) + 3) & 0xFFFFFFFC;
-
- $x = str_pad($x, $len, chr(0), STR_PAD_LEFT);
-
- for ($i = 0; $i < $len; $i+= 4) {
- $this->value = bcmul($this->value, '4294967296', 0); // 4294967296 == 2**32
- $this->value = bcadd($this->value, 0x1000000 * ord($x[$i]) + ((ord($x[$i + 1]) << 16) | (ord($x[$i + 2]) << 8) | ord($x[$i + 3])), 0);
- }
-
- if ($this->is_negative) {
- $this->value = '-' . $this->value;
- }
-
- break;
- // converts a base-2**8 (big endian / msb) number to base-2**26 (little endian / lsb)
- default:
- while (strlen($x)) {
- $this->value[] = $this->_bytes2int($this->_base256_rshift($x, 26));
- }
- }
-
- if ($this->is_negative) {
- if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) {
- $this->is_negative = false;
- }
- $temp = $this->add(new Math_BigInteger('-1'));
- $this->value = $temp->value;
- }
- break;
- case 16:
- case -16:
- if ($base > 0 && $x[0] == '-') {
- $this->is_negative = true;
- $x = substr($x, 1);
- }
-
- $x = preg_replace('#^(?:0x)?([A-Fa-f0-9]*).*#', '$1', $x);
-
- $is_negative = false;
- if ($base < 0 && hexdec($x[0]) >= 8) {
- $this->is_negative = $is_negative = true;
- $x = bin2hex(~pack('H*', $x));
- }
-
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $temp = $this->is_negative ? '-0x' . $x : '0x' . $x;
- $this->value = gmp_init($temp);
- $this->is_negative = false;
- break;
- case MATH_BIGINTEGER_MODE_BCMATH:
- $x = ( strlen($x) & 1 ) ? '0' . $x : $x;
- $temp = new Math_BigInteger(pack('H*', $x), 256);
- $this->value = $this->is_negative ? '-' . $temp->value : $temp->value;
- $this->is_negative = false;
- break;
- default:
- $x = ( strlen($x) & 1 ) ? '0' . $x : $x;
- $temp = new Math_BigInteger(pack('H*', $x), 256);
- $this->value = $temp->value;
- }
-
- if ($is_negative) {
- $temp = $this->add(new Math_BigInteger('-1'));
- $this->value = $temp->value;
- }
- break;
- case 10:
- case -10:
- $x = preg_replace('#^(-?[0-9]*).*#', '$1', $x);
-
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $this->value = gmp_init($x);
- break;
- case MATH_BIGINTEGER_MODE_BCMATH:
- // explicitly casting $x to a string is necessary, here, since doing $x[0] on -1 yields different
- // results then doing it on '-1' does (modInverse does $x[0])
- $this->value = (string) $x;
- break;
- default:
- $temp = new Math_BigInteger();
-
- // array(10000000) is 10**7 in base-2**26. 10**7 is the closest to 2**26 we can get without passing it.
- $multiplier = new Math_BigInteger();
- $multiplier->value = array(10000000);
-
- if ($x[0] == '-') {
- $this->is_negative = true;
- $x = substr($x, 1);
- }
-
- $x = str_pad($x, strlen($x) + (6 * strlen($x)) % 7, 0, STR_PAD_LEFT);
-
- while (strlen($x)) {
- $temp = $temp->multiply($multiplier);
- $temp = $temp->add(new Math_BigInteger($this->_int2bytes(substr($x, 0, 7)), 256));
- $x = substr($x, 7);
- }
-
- $this->value = $temp->value;
- }
- break;
- case 2: // base-2 support originally implemented by Lluis Pamies - thanks!
- case -2:
- if ($base > 0 && $x[0] == '-') {
- $this->is_negative = true;
- $x = substr($x, 1);
- }
-
- $x = preg_replace('#^([01]*).*#', '$1', $x);
- $x = str_pad($x, strlen($x) + (3 * strlen($x)) % 4, 0, STR_PAD_LEFT);
-
- $str = '0x';
- while (strlen($x)) {
- $part = substr($x, 0, 4);
- $str.= dechex(bindec($part));
- $x = substr($x, 4);
- }
-
- if ($this->is_negative) {
- $str = '-' . $str;
- }
-
- $temp = new Math_BigInteger($str, 8 * $base); // ie. either -16 or +16
- $this->value = $temp->value;
- $this->is_negative = $temp->is_negative;
-
- break;
- default:
- // base not supported, so we'll let $this == 0
- }
- }
-
- /**
- * Converts a BigInteger to a byte string (eg. base-256).
- *
- * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
- * saved as two's compliment.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('65');
- *
- * echo $a->toBytes(); // outputs chr(65)
- * ?>
- * </code>
- *
- * @param Boolean $twos_compliment
- * @return String
- * @access public
- * @internal Converts a base-2**26 number to base-2**8
- */
- function toBytes($twos_compliment = false)
- {
- if ($twos_compliment) {
- $comparison = $this->compare(new Math_BigInteger());
- if ($comparison == 0) {
- return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
- }
-
- $temp = $comparison < 0 ? $this->add(new Math_BigInteger(1)) : $this->copy();
- $bytes = $temp->toBytes();
-
- if (empty($bytes)) { // eg. if the number we're trying to convert is -1
- $bytes = chr(0);
- }
-
- if (ord($bytes[0]) & 0x80) {
- $bytes = chr(0) . $bytes;
- }
-
- return $comparison < 0 ? ~$bytes : $bytes;
- }
-
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- if (gmp_cmp($this->value, gmp_init(0)) == 0) {
- return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
- }
-
- $temp = gmp_strval(gmp_abs($this->value), 16);
- $temp = ( strlen($temp) & 1 ) ? '0' . $temp : $temp;
- $temp = pack('H*', $temp);
-
- return $this->precision > 0 ?
- substr(str_pad($temp, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) :
- ltrim($temp, chr(0));
- case MATH_BIGINTEGER_MODE_BCMATH:
- if ($this->value === '0') {
- return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
- }
-
- $value = '';
- $current = $this->value;
-
- if ($current[0] == '-') {
- $current = substr($current, 1);
- }
-
- while (bccomp($current, '0', 0) > 0) {
- $temp = bcmod($current, '16777216');
- $value = chr($temp >> 16) . chr($temp >> 8) . chr($temp) . $value;
- $current = bcdiv($current, '16777216', 0);
- }
-
- return $this->precision > 0 ?
- substr(str_pad($value, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) :
- ltrim($value, chr(0));
- }
-
- if (!count($this->value)) {
- return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
- }
- $result = $this->_int2bytes($this->value[count($this->value) - 1]);
-
- $temp = $this->copy();
-
- for ($i = count($temp->value) - 2; $i >= 0; --$i) {
- $temp->_base256_lshift($result, 26);
- $result = $result | str_pad($temp->_int2bytes($temp->value[$i]), strlen($result), chr(0), STR_PAD_LEFT);
- }
-
- return $this->precision > 0 ?
- str_pad(substr($result, -(($this->precision + 7) >> 3)), ($this->precision + 7) >> 3, chr(0), STR_PAD_LEFT) :
- $result;
- }
-
- /**
- * Converts a BigInteger to a hex string (eg. base-16)).
- *
- * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
- * saved as two's compliment.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('65');
- *
- * echo $a->toHex(); // outputs '41'
- * ?>
- * </code>
- *
- * @param Boolean $twos_compliment
- * @return String
- * @access public
- * @internal Converts a base-2**26 number to base-2**8
- */
- function toHex($twos_compliment = false)
- {
- return bin2hex($this->toBytes($twos_compliment));
- }
-
- /**
- * Converts a BigInteger to a bit string (eg. base-2).
- *
- * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
- * saved as two's compliment.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('65');
- *
- * echo $a->toBits(); // outputs '1000001'
- * ?>
- * </code>
- *
- * @param Boolean $twos_compliment
- * @return String
- * @access public
- * @internal Converts a base-2**26 number to base-2**2
- */
- function toBits($twos_compliment = false)
- {
- $hex = $this->toHex($twos_compliment);
- $bits = '';
- for ($i = 0, $end = strlen($hex) & 0xFFFFFFF8; $i < $end; $i+=8) {
- $bits.= str_pad(decbin(hexdec(substr($hex, $i, 8))), 32, '0', STR_PAD_LEFT);
- }
- if ($end != strlen($hex)) { // hexdec('') == 0
- $bits.= str_pad(decbin(hexdec(substr($hex, $end))), strlen($hex) & 7, '0', STR_PAD_LEFT);
- }
- return $this->precision > 0 ? substr($bits, -$this->precision) : ltrim($bits, '0');
- }
-
- /**
- * Converts a BigInteger to a base-10 number.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('50');
- *
- * echo $a->toString(); // outputs 50
- * ?>
- * </code>
- *
- * @return String
- * @access public
- * @internal Converts a base-2**26 number to base-10**7 (which is pretty much base-10)
- */
- function toString()
- {
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- return gmp_strval($this->value);
- case MATH_BIGINTEGER_MODE_BCMATH:
- if ($this->value === '0') {
- return '0';
- }
-
- return ltrim($this->value, '0');
- }
-
- if (!count($this->value)) {
- return '0';
- }
-
- $temp = $this->copy();
- $temp->is_negative = false;
-
- $divisor = new Math_BigInteger();
- $divisor->value = array(10000000); // eg. 10**7
- $result = '';
- while (count($temp->value)) {
- list($temp, $mod) = $temp->divide($divisor);
- $result = str_pad(isset($mod->value[0]) ? $mod->value[0] : '', 7, '0', STR_PAD_LEFT) . $result;
- }
- $result = ltrim($result, '0');
- if (empty($result)) {
- $result = '0';
- }
-
- if ($this->is_negative) {
- $result = '-' . $result;
- }
-
- return $result;
- }
-
- /**
- * Copy an object
- *
- * PHP5 passes objects by reference while PHP4 passes by value. As such, we need a function to guarantee
- * that all objects are passed by value, when appropriate. More information can be found here:
- *
- * {@link http://php.net/language.oop5.basic#51624}
- *
- * @access public
- * @see __clone()
- * @return Math_BigInteger
- */
- function copy()
- {
- $temp = new Math_BigInteger();
- $temp->value = $this->value;
- $temp->is_negative = $this->is_negative;
- $temp->generator = $this->generator;
- $temp->precision = $this->precision;
- $temp->bitmask = $this->bitmask;
- return $temp;
- }
-
- /**
- * __toString() magic method
- *
- * Will be called, automatically, if you're supporting just PHP5. If you're supporting PHP4, you'll need to call
- * toString().
- *
- * @access public
- * @internal Implemented per a suggestion by Techie-Michael - thanks!
- */
- function __toString()
- {
- return $this->toString();
- }
-
- /**
- * __clone() magic method
- *
- * Although you can call Math_BigInteger::__toString() directly in PHP5, you cannot call Math_BigInteger::__clone()
- * directly in PHP5. You can in PHP4 since it's not a magic method, but in PHP5, you have to call it by using the PHP5
- * only syntax of $y = clone $x. As such, if you're trying to write an application that works on both PHP4 and PHP5,
- * call Math_BigInteger::copy(), instead.
- *
- * @access public
- * @see copy()
- * @return Math_BigInteger
- */
- function __clone()
- {
- return $this->copy();
- }
-
- /**
- * __sleep() magic method
- *
- * Will be called, automatically, when serialize() is called on a Math_BigInteger object.
- *
- * @see __wakeup()
- * @access public
- */
- function __sleep()
- {
- $this->hex = $this->toHex(true);
- $vars = array('hex');
- if ($this->generator != 'mt_rand') {
- $vars[] = 'generator';
- }
- if ($this->precision > 0) {
- $vars[] = 'precision';
- }
- return $vars;
-
- }
-
- /**
- * __wakeup() magic method
- *
- * Will be called, automatically, when unserialize() is called on a Math_BigInteger object.
- *
- * @see __sleep()
- * @access public
- */
- function __wakeup()
- {
- $temp = new Math_BigInteger($this->hex, -16);
- $this->value = $temp->value;
- $this->is_negative = $temp->is_negative;
- $this->setRandomGenerator($this->generator);
- if ($this->precision > 0) {
- // recalculate $this->bitmask
- $this->setPrecision($this->precision);
- }
- }
-
- /**
- * Adds two BigIntegers.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('10');
- * $b = new Math_BigInteger('20');
- *
- * $c = $a->add($b);
- *
- * echo $c->toString(); // outputs 30
- * ?>
- * </code>
- *
- * @param Math_BigInteger $y
- * @return Math_BigInteger
- * @access public
- * @internal Performs base-2**52 addition
- */
- function add($y)
- {
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $temp = new Math_BigInteger();
- $temp->value = gmp_add($this->value, $y->value);
-
- return $this->_normalize($temp);
- case MATH_BIGINTEGER_MODE_BCMATH:
- $temp = new Math_BigInteger();
- $temp->value = bcadd($this->value, $y->value, 0);
-
- return $this->_normalize($temp);
- }
-
- $temp = $this->_add($this->value, $this->is_negative, $y->value, $y->is_negative);
-
- $result = new Math_BigInteger();
- $result->value = $temp[MATH_BIGINTEGER_VALUE];
- $result->is_negative = $temp[MATH_BIGINTEGER_SIGN];
-
- return $this->_normalize($result);
- }
-
- /**
- * Performs addition.
- *
- * @param Array $x_value
- * @param Boolean $x_negative
- * @param Array $y_value
- * @param Boolean $y_negative
- * @return Array
- * @access private
- */
- function _add($x_value, $x_negative, $y_value, $y_negative)
- {
- $x_size = count($x_value);
- $y_size = count($y_value);
-
- if ($x_size == 0) {
- return array(
- MATH_BIGINTEGER_VALUE => $y_value,
- MATH_BIGINTEGER_SIGN => $y_negative
- );
- } else if ($y_size == 0) {
- return array(
- MATH_BIGINTEGER_VALUE => $x_value,
- MATH_BIGINTEGER_SIGN => $x_negative
- );
- }
-
- // subtract, if appropriate
- if ( $x_negative != $y_negative ) {
- if ( $x_value == $y_value ) {
- return array(
- MATH_BIGINTEGER_VALUE => array(),
- MATH_BIGINTEGER_SIGN => false
- );
- }
-
- $temp = $this->_subtract($x_value, false, $y_value, false);
- $temp[MATH_BIGINTEGER_SIGN] = $this->_compare($x_value, false, $y_value, false) > 0 ?
- $x_negative : $y_negative;
-
- return $temp;
- }
-
- if ($x_size < $y_size) {
- $size = $x_size;
- $value = $y_value;
- } else {
- $size = $y_size;
- $value = $x_value;
- }
-
- $value[] = 0; // just in case the carry adds an extra digit
-
- $carry = 0;
- for ($i = 0, $j = 1; $j < $size; $i+=2, $j+=2) {
- $sum = $x_value[$j] * 0x4000000 + $x_value[$i] + $y_value[$j] * 0x4000000 + $y_value[$i] + $carry;
- $carry = $sum >= MATH_BIGINTEGER_MAX_DIGIT52; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
- $sum = $carry ? $sum - MATH_BIGINTEGER_MAX_DIGIT52 : $sum;
-
- $temp = (int) ($sum / 0x4000000);
-
- $value[$i] = (int) ($sum - 0x4000000 * $temp); // eg. a faster alternative to fmod($sum, 0x4000000)
- $value[$j] = $temp;
- }
-
- if ($j == $size) { // ie. if $y_size is odd
- $sum = $x_value[$i] + $y_value[$i] + $carry;
- $carry = $sum >= 0x4000000;
- $value[$i] = $carry ? $sum - 0x4000000 : $sum;
- ++$i; // ie. let $i = $j since we've just done $value[$i]
- }
-
- if ($carry) {
- for (; $value[$i] == 0x3FFFFFF; ++$i) {
- $value[$i] = 0;
- }
- ++$value[$i];
- }
-
- return array(
- MATH_BIGINTEGER_VALUE => $this->_trim($value),
- MATH_BIGINTEGER_SIGN => $x_negative
- );
- }
-
- /**
- * Subtracts two BigIntegers.
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('10');
- * $b = new Math_BigInteger('20');
- *
- * $c = $a->subtract($b);
- *
- * echo $c->toString(); // outputs -10
- * ?>
- * </code>
- *
- * @param Math_BigInteger $y
- * @return Math_BigInteger
- * @access public
- * @internal Performs base-2**52 subtraction
- */
- function subtract($y)
- {
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $temp = new Math_BigInteger();
- $temp->value = gmp_sub($this->value, $y->value);
-
- return $this->_normalize($temp);
- case MATH_BIGINTEGER_MODE_BCMATH:
- $temp = new Math_BigInteger();
- $temp->value = bcsub($this->value, $y->value, 0);
-
- return $this->_normalize($temp);
- }
-
- $temp = $this->_subtract($this->value, $this->is_negative, $y->value, $y->is_negative);
-
- $result = new Math_BigInteger();
- $result->value = $temp[MATH_BIGINTEGER_VALUE];
- $result->is_negative = $temp[MATH_BIGINTEGER_SIGN];
-
- return $this->_normalize($result);
- }
-
- /**
- * Performs subtraction.
- *
- * @param Array $x_value
- * @param Boolean $x_negative
- * @param Array $y_value
- * @param Boolean $y_negative
- * @return Array
- * @access private
- */
- function _subtract($x_value, $x_negative, $y_value, $y_negative)
- {
- $x_size = count($x_value);
- $y_size = count($y_value);
-
- if ($x_size == 0) {
- return array(
- MATH_BIGINTEGER_VALUE => $y_value,
- MATH_BIGINTEGER_SIGN => !$y_negative
- );
- } else if ($y_size == 0) {
- return array(
- MATH_BIGINTEGER_VALUE => $x_value,
- MATH_BIGINTEGER_SIGN => $x_negative
- );
- }
-
- // add, if appropriate (ie. -$x - +$y or +$x - -$y)
- if ( $x_negative != $y_negative ) {
- $temp = $this->_add($x_value, false, $y_value, false);
- $temp[MATH_BIGINTEGER_SIGN] = $x_negative;
-
- return $temp;
- }
-
- $diff = $this->_compare($x_value, $x_negative, $y_value, $y_negative);
-
- if ( !$diff ) {
- return array(
- MATH_BIGINTEGER_VALUE => array(),
- MATH_BIGINTEGER_SIGN => false
- );
- }
-
- // switch $x and $y around, if appropriate.
- if ( (!$x_negative && $diff < 0) || ($x_negative && $diff > 0) ) {
- $temp = $x_value;
- $x_value = $y_value;
- $y_value = $temp;
-
- $x_negative = !$x_negative;
-
- $x_size = count($x_value);
- $y_size = count($y_value);
- }
-
- // at this point, $x_value should be at least as big as - if not bigger than - $y_value
-
- $carry = 0;
- for ($i = 0, $j = 1; $j < $y_size; $i+=2, $j+=2) {
- $sum = $x_value[$j] * 0x4000000 + $x_value[$i] - $y_value[$j] * 0x4000000 - $y_value[$i] - $carry;
- $carry = $sum < 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
- $sum = $carry ? $sum + MATH_BIGINTEGER_MAX_DIGIT52 : $sum;
-
- $temp = (int) ($sum / 0x4000000);
-
- $x_value[$i] = (int) ($sum - 0x4000000 * $temp);
- $x_value[$j] = $temp;
- }
-
- if ($j == $y_size) { // ie. if $y_size is odd
- $sum = $x_value[$i] - $y_value[$i] - $carry;
- $carry = $sum < 0;
- $x_value[$i] = $carry ? $sum + 0x4000000 : $sum;
- ++$i;
- }
-
- if ($carry) {
- for (; !$x_value[$i]; ++$i) {
- $x_value[$i] = 0x3FFFFFF;
- }
- --$x_value[$i];
- }
-
- return array(
- MATH_BIGINTEGER_VALUE => $this->_trim($x_value),
- MATH_BIGINTEGER_SIGN => $x_negative
- );
- }
-
- /**
- * Multiplies two BigIntegers
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('10');
- * $b = new Math_BigInteger('20');
- *
- * $c = $a->multiply($b);
- *
- * echo $c->toString(); // outputs 200
- * ?>
- * </code>
- *
- * @param Math_BigInteger $x
- * @return Math_BigInteger
- * @access public
- */
- function multiply($x)
- {
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $temp = new Math_BigInteger();
- $temp->value = gmp_mul($this->value, $x->value);
-
- return $this->_normalize($temp);
- case MATH_BIGINTEGER_MODE_BCMATH:
- $temp = new Math_BigInteger();
- $temp->value = bcmul($this->value, $x->value, 0);
-
- return $this->_normalize($temp);
- }
-
- $temp = $this->_multiply($this->value, $this->is_negative, $x->value, $x->is_negative);
-
- $product = new Math_BigInteger();
- $product->value = $temp[MATH_BIGINTEGER_VALUE];
- $product->is_negative = $temp[MATH_BIGINTEGER_SIGN];
-
- return $this->_normalize($product);
- }
-
- /**
- * Performs multiplication.
- *
- * @param Array $x_value
- * @param Boolean $x_negative
- * @param Array $y_value
- * @param Boolean $y_negative
- * @return Array
- * @access private
- */
- function _multiply($x_value, $x_negative, $y_value, $y_negative)
- {
- //if ( $x_value == $y_value ) {
- // return array(
- // MATH_BIGINTEGER_VALUE => $this->_square($x_value),
- // MATH_BIGINTEGER_SIGN => $x_sign != $y_value
- // );
- //}
-
- $x_length = count($x_value);
- $y_length = count($y_value);
-
- if ( !$x_length || !$y_length ) { // a 0 is being multiplied
- return array(
- MATH_BIGINTEGER_VALUE => array(),
- MATH_BIGINTEGER_SIGN => false
- );
- }
-
- return array(
- MATH_BIGINTEGER_VALUE => min($x_length, $y_length) < 2 * MATH_BIGINTEGER_KARATSUBA_CUTOFF ?
- $this->_trim($this->_regularMultiply($x_value, $y_value)) :
- $this->_trim($this->_karatsuba($x_value, $y_value)),
- MATH_BIGINTEGER_SIGN => $x_negative != $y_negative
- );
- }
-
- /**
- * Performs long multiplication on two BigIntegers
- *
- * Modeled after 'multiply' in MutableBigInteger.java.
- *
- * @param Array $x_value
- * @param Array $y_value
- * @return Array
- * @access private
- */
- function _regularMultiply($x_value, $y_value)
- {
- $x_length = count($x_value);
- $y_length = count($y_value);
-
- if ( !$x_length || !$y_length ) { // a 0 is being multiplied
- return array();
- }
-
- if ( $x_length < $y_length ) {
- $temp = $x_value;
- $x_value = $y_value;
- $y_value = $temp;
-
- $x_length = count($x_value);
- $y_length = count($y_value);
- }
-
- $product_value = $this->_array_repeat(0, $x_length + $y_length);
-
- // the following for loop could be removed if the for loop following it
- // (the one with nested for loops) initially set $i to 0, but
- // doing so would also make the result in one set of unnecessary adds,
- // since on the outermost loops first pass, $product->value[$k] is going
- // to always be 0
-
- $carry = 0;
-
- for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0
- $temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
- $carry = (int) ($temp / 0x4000000);
- $product_value[$j] = (int) ($temp - 0x4000000 * $carry);
- }
-
- $product_value[$j] = $carry;
-
- // the above for loop is what the previous comment was talking about. the
- // following for loop is the "one with nested for loops"
- for ($i = 1; $i < $y_length; ++$i) {
- $carry = 0;
-
- for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) {
- $temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
- $carry = (int) ($temp / 0x4000000);
- $product_value[$k] = (int) ($temp - 0x4000000 * $carry);
- }
-
- $product_value[$k] = $carry;
- }
-
- return $product_value;
- }
-
- /**
- * Performs Karatsuba multiplication on two BigIntegers
- *
- * See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and
- * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=120 MPM 5.2.3}.
- *
- * @param Array $x_value
- * @param Array $y_value
- * @return Array
- * @access private
- */
- function _karatsuba($x_value, $y_value)
- {
- $m = min(count($x_value) >> 1, count($y_value) >> 1);
-
- if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) {
- return $this->_regularMultiply($x_value, $y_value);
- }
-
- $x1 = array_slice($x_value, $m);
- $x0 = array_slice($x_value, 0, $m);
- $y1 = array_slice($y_value, $m);
- $y0 = array_slice($y_value, 0, $m);
-
- $z2 = $this->_karatsuba($x1, $y1);
- $z0 = $this->_karatsuba($x0, $y0);
-
- $z1 = $this->_add($x1, false, $x0, false);
- $temp = $this->_add($y1, false, $y0, false);
- $z1 = $this->_karatsuba($z1[MATH_BIGINTEGER_VALUE], $temp[MATH_BIGINTEGER_VALUE]);
- $temp = $this->_add($z2, false, $z0, false);
- $z1 = $this->_subtract($z1, false, $temp[MATH_BIGINTEGER_VALUE], false);
-
- $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2);
- $z1[MATH_BIGINTEGER_VALUE] = array_merge(array_fill(0, $m, 0), $z1[MATH_BIGINTEGER_VALUE]);
-
- $xy = $this->_add($z2, false, $z1[MATH_BIGINTEGER_VALUE], $z1[MATH_BIGINTEGER_SIGN]);
- $xy = $this->_add($xy[MATH_BIGINTEGER_VALUE], $xy[MATH_BIGINTEGER_SIGN], $z0, false);
-
- return $xy[MATH_BIGINTEGER_VALUE];
- }
-
- /**
- * Performs squaring
- *
- * @param Array $x
- * @return Array
- * @access private
- */
- function _square($x = false)
- {
- return count($x) < 2 * MATH_BIGINTEGER_KARATSUBA_CUTOFF ?
- $this->_trim($this->_baseSquare($x)) :
- $this->_trim($this->_karatsubaSquare($x));
- }
-
- /**
- * Performs traditional squaring on two BigIntegers
- *
- * Squaring can be done faster than multiplying a number by itself can be. See
- * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=7 HAC 14.2.4} /
- * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=141 MPM 5.3} for more information.
- *
- * @param Array $value
- * @return Array
- * @access private
- */
- function _baseSquare($value)
- {
- if ( empty($value) ) {
- return array();
- }
- $square_value = $this->_array_repeat(0, 2 * count($value));
-
- for ($i = 0, $max_index = count($value) - 1; $i <= $max_index; ++$i) {
- $i2 = $i << 1;
-
- $temp = $square_value[$i2] + $value[$i] * $value[$i];
- $carry = (int) ($temp / 0x4000000);
- $square_value[$i2] = (int) ($temp - 0x4000000 * $carry);
-
- // note how we start from $i+1 instead of 0 as we do in multiplication.
- for ($j = $i + 1, $k = $i2 + 1; $j <= $max_index; ++$j, ++$k) {
- $temp = $square_value[$k] + 2 * $value[$j] * $value[$i] + $carry;
- $carry = (int) ($temp / 0x4000000);
- $square_value[$k] = (int) ($temp - 0x4000000 * $carry);
- }
-
- // the following line can yield values larger 2**15. at this point, PHP should switch
- // over to floats.
- $square_value[$i + $max_index + 1] = $carry;
- }
-
- return $square_value;
- }
-
- /**
- * Performs Karatsuba "squaring" on two BigIntegers
- *
- * See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and
- * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=151 MPM 5.3.4}.
- *
- * @param Array $value
- * @return Array
- * @access private
- */
- function _karatsubaSquare($value)
- {
- $m = count($value) >> 1;
-
- if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) {
- return $this->_baseSquare($value);
- }
-
- $x1 = array_slice($value, $m);
- $x0 = array_slice($value, 0, $m);
-
- $z2 = $this->_karatsubaSquare($x1);
- $z0 = $this->_karatsubaSquare($x0);
-
- $z1 = $this->_add($x1, false, $x0, false);
- $z1 = $this->_karatsubaSquare($z1[MATH_BIGINTEGER_VALUE]);
- $temp = $this->_add($z2, false, $z0, false);
- $z1 = $this->_subtract($z1, false, $temp[MATH_BIGINTEGER_VALUE], false);
-
- $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2);
- $z1[MATH_BIGINTEGER_VALUE] = array_merge(array_fill(0, $m, 0), $z1[MATH_BIGINTEGER_VALUE]);
-
- $xx = $this->_add($z2, false, $z1[MATH_BIGINTEGER_VALUE], $z1[MATH_BIGINTEGER_SIGN]);
- $xx = $this->_add($xx[MATH_BIGINTEGER_VALUE], $xx[MATH_BIGINTEGER_SIGN], $z0, false);
-
- return $xx[MATH_BIGINTEGER_VALUE];
- }
-
- /**
- * Divides two BigIntegers.
- *
- * Returns an array whose first element contains the quotient and whose second element contains the
- * "common residue". If the remainder would be positive, the "common residue" and the remainder are the
- * same. If the remainder would be negative, the "common residue" is equal to the sum of the remainder
- * and the divisor (basically, the "common residue" is the first positive modulo).
- *
- * Here's an example:
- * <code>
- * <?php
- * include('Math/BigInteger.php');
- *
- * $a = new Math_BigInteger('10');
- * $b = new Math_BigInteger('20');
- *
- * list($quotient, $remainder) = $a->divide($b);
- *
- * echo $quotient->toString(); // outputs 0
- * echo "\r\n";
- * echo $remainder->toString(); // outputs 10
- * ?>
- * </code>
- *
- * @param Math_BigInteger $y
- * @return Array
- * @access public
- * @internal This function is based off of {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=9 HAC 14.20}.
- */
- function divide($y)
- {
- switch ( MATH_BIGINTEGER_MODE ) {
- case MATH_BIGINTEGER_MODE_GMP:
- $quotient = new Math_BigInteger();
- $remainder = new Math_BigInteger();
-
- list($quotient->value, $remainder->value) = gmp_div_qr($this->value, $y->value);
-
- if (gmp_sign($remainder->value) < 0) {
- $remainder->value = gmp_add($remainder->value, gmp_abs($y->value));
- }
-
- return array($this->_normalize($quotient), $this->_normalize($remainder));
- case MATH_BIGINTEGER_MODE_BCMATH:
- $quotient = new Math_BigInteger();
- $remainder = new Math_BigInteger();
-
- $quotient->value = bcdiv($this->value, $y->value, 0);
- $remainder->value = bcmod($this->value, $y->value);
-
- if ($remainder->value[0] == '-') {
- $remainder->value = bcadd($remainder->value, $y->value[0] == '-' ? substr($y->value, 1) : $y->value, 0);
- }
-
- return array($this->_normalize($quotient), $this->_normalize($remainder));
- }
-
- if (count($y->value) == 1) {
- list($q, $r) = $this->_divide_digit($this->value, $y->value[0]);
- $quotient = new Math_BigInteger();
- $remainder = new Math_BigInteger();
- $quotient->value = $q;
- $remainder->value = array($r);
- $quotient->is_negative = $this->is_negative != $y->is_negative;
- return array($this->_normalize($quotient), $this->_normalize($remainder));
- }
-
- static $zero;
- if ( !isset($zero) ) {
- $zero = new Math_BigInteger();
- }
-
- $x = $this->copy();
- $y = $y->copy();
-
- $x_sign = $x->is_negative;
- $y_sign = $y->is_negative;
-
- $x->is_negative = $y->is_negative = false;
-
- $diff = $x->compare($y);
-
- if ( !$diff ) {
- $temp = new Math_BigInteger();
- $temp->value = array(1);
- $temp->is_negative = $x_sign != $y_sign;
- return array($this->_normalize($temp), $this->_normalize(new Math_BigInteger()));
- }
-
- if ( $diff < 0 ) {
- // if $x is negative, "add" $y.
- if ( $x_sign ) {
- $x = $y->subtract($x);
- }
- return array($this->_normalize(new Math_BigInteger()), $this->_normalize($x));
- }
-
- // normalize $x and $y as described in HAC 14.23 / 14.24
- $msb = $y->value[count($y->value) - 1];
- for ($shift = 0; !($msb & 0x2000000); ++$shift) {
- $msb <<= 1;
- }
- $x->_lshift($shift);
- $y->_lshift($shift);
- $y_value = &$y->value;
-
- $x_max = count($x->value) - 1;
- $y_max = count($y->value) - 1;
-
- $quotient = new Math_BigInteger();
- $quotient_value = &$quotient->value;
- $quotient_value = $this->_array_repeat(0, $x_max - $y_max + 1);
-
- static $temp, $lhs, $rhs;
- if (!isset($temp)) {
- $temp = new Math_BigInteger();
- $lhs = new Math_BigInteger();
- $rhs = new Math_BigInteger();
- }
- $temp_value = &$temp->value;
- $rhs_value = &$rhs->value;
-
- // $temp = $y << ($x_max - $y_max-1) in base 2**26
- $temp_value = array_merge($this->_array_repeat(0, $x_max - $y_max), $y_value);
-
- while ( $x->compare($temp) >= 0 ) {
- // calculate the "common residue"
- ++$quotient_value[$x_max - $y_max];
- $x = $x->subtract($temp);
- $x_max = count($x->value) - 1;
- }
-
- for ($i = $x_max; $i >= $y_max + 1; --$i) {
- $x_value = &$x->value;
- $x_window = array(
- isset($x_value[$i]) ? $x_value[$i] : 0,
- isset($x_value[$i - 1]) ? $x_value[$i - 1] : 0,
- isset($x_value[$i - 2]) ? $x_value[$i - 2] : 0
- );
- $y_window = array(
- $y_value[$y_max],
- ( $y_max > 0 ) ? $y_value[$y_max - 1] : 0
- );
-
- $q_index = $i - $y_max - 1;
- if ($x_window[0] == $y_window[0]) {
- $quotient_value[$q_index] = 0x3FFFFFF;
- } else {
- $quotient_value[$q_index] = (int) (
- ($x_window[0] * 0x4000000 + $x_window[1])
- /
- $y_window[0]
- );
- }
-
- $temp_value = array($y_window[1], $y_window[0]);
-
- $lhs->value = array($quotient_v…
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