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<?php |
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/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */ |
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/** |
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* Pure-PHP arbitrary precision integer arithmetic library. |
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* |
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* Supports base-2, base-10, base-16, and base-256 numbers. Uses the GMP or BCMath extensions, if available, |
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* and an internal implementation, otherwise. |
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* |
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* PHP versions 4 and 5 |
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* |
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* {@internal (all DocBlock comments regarding implementation - such as the one that follows - refer to the |
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* {@link MATH_BIGINTEGER_MODE_INTERNAL MATH_BIGINTEGER_MODE_INTERNAL} mode) |
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* |
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* Math_BigInteger uses base-2**26 to perform operations such as multiplication and division and |
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* base-2**52 (ie. two base 2**26 digits) to perform addition and subtraction. Because the largest possible |
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* value when multiplying two base-2**26 numbers together is a base-2**52 number, double precision floating |
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* point numbers - numbers that should be supported on most hardware and whose significand is 53 bits - are |
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* used. As a consequence, bitwise operators such as >> and << cannot be used, nor can the modulo operator %, |
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* which only supports integers. Although this fact will slow this library down, the fact that such a high |
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* base is being used should more than compensate. |
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* |
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* When PHP version 6 is officially released, we'll be able to use 64-bit integers. This should, once again, |
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* allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition / |
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* subtraction). |
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* |
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* Useful resources are as follows: |
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* |
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* - {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf Handbook of Applied Cryptography (HAC)} |
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* - {@link http://math.libtomcrypt.com/files/tommath.pdf Multi-Precision Math (MPM)} |
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* - Java's BigInteger classes. See /j2se/src/share/classes/java/math in jdk-1_5_0-src-jrl.zip |
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* |
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* One idea for optimization is to use the comba method to reduce the number of operations performed. |
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* MPM uses this quite extensively. The following URL elaborates: |
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* |
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* {@link http://www.everything2.com/index.pl?node_id=1736418}}} |
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* |
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* Here's an example of how to use this library: |
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* <code> |
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* <?php |
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* include('Math/BigInteger.php'); |
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* |
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* $a = new Math_BigInteger(2); |
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* $b = new Math_BigInteger(3); |
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* |
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* $c = $a->add($b); |
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* |
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* echo $c->toString(); // outputs 5 |
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* ?> |
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* </code> |
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* |
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* LICENSE: This library is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Lesser General Public |
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* License as published by the Free Software Foundation; either |
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* version 2.1 of the License, or (at your option) any later version. |
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* |
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* This library is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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* Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public |
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* License along with this library; if not, write to the Free Software |
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, |
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* MA 02111-1307 USA |
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* |
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* @category Math |
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* @package Math_BigInteger |
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* @author Jim Wigginton <terrafrost@php.net> |
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* @copyright MMVI Jim Wigginton |
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* @license http://www.gnu.org/licenses/lgpl.txt |
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* @version $Id: BigInteger.php,v 1.18 2009/12/04 19:12:18 terrafrost Exp $ |
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* @link http://pear.php.net/package/Math_BigInteger |
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*/ |
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/**#@+ |
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* @access private |
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* @see Math_BigInteger::_slidingWindow() |
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*/ |
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/** |
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* @see Math_BigInteger::_montgomery() |
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* @see Math_BigInteger::_prepMontgomery() |
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*/ |
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define('MATH_BIGINTEGER_MONTGOMERY', 0); |
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/** |
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* @see Math_BigInteger::_barrett() |
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*/ |
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define('MATH_BIGINTEGER_BARRETT', 1); |
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/** |
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* @see Math_BigInteger::_mod2() |
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*/ |
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define('MATH_BIGINTEGER_POWEROF2', 2); |
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/** |
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* @see Math_BigInteger::_remainder() |
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*/ |
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define('MATH_BIGINTEGER_CLASSIC', 3); |
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/** |
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* @see Math_BigInteger::__clone() |
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*/ |
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define('MATH_BIGINTEGER_NONE', 4); |
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/**#@-*/ |
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/**#@+ |
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* @access private |
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* @see Math_BigInteger::_montgomery() |
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* @see Math_BigInteger::_barrett() |
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*/ |
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/** |
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* $cache[MATH_BIGINTEGER_VARIABLE] tells us whether or not the cached data is still valid. |
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*/ |
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define('MATH_BIGINTEGER_VARIABLE', 0); |
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/** |
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* $cache[MATH_BIGINTEGER_DATA] contains the cached data. |
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*/ |
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define('MATH_BIGINTEGER_DATA', 1); |
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/**#@-*/ |
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/**#@+ |
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* @access private |
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* @see Math_BigInteger::Math_BigInteger() |
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*/ |
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/** |
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* To use the pure-PHP implementation |
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*/ |
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define('MATH_BIGINTEGER_MODE_INTERNAL', 1); |
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/** |
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* To use the BCMath library |
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* |
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* (if enabled; otherwise, the internal implementation will be used) |
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*/ |
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define('MATH_BIGINTEGER_MODE_BCMATH', 2); |
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/** |
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* To use the GMP library |
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* |
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* (if present; otherwise, either the BCMath or the internal implementation will be used) |
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*/ |
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define('MATH_BIGINTEGER_MODE_GMP', 3); |
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/**#@-*/ |
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/** |
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* The largest digit that may be used in addition / subtraction |
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* |
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* (we do pow(2, 52) instead of using 4503599627370496, directly, because some PHP installations |
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* will truncate 4503599627370496) |
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* |
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* @access private |
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*/ |
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define('MATH_BIGINTEGER_MAX_DIGIT52', pow(2, 52)); |
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/** |
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* Karatsuba Cutoff |
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* |
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* At what point do we switch between Karatsuba multiplication and schoolbook long multiplication? |
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* |
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* @access private |
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*/ |
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define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 15); |
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/** |
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* Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256 |
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* numbers. |
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* |
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* @author Jim Wigginton <terrafrost@php.net> |
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* @version 1.0.0RC3 |
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* @access public |
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* @package Math_BigInteger |
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*/ |
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class Math_BigInteger { |
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/** |
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* Holds the BigInteger's value. |
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* |
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* @var Array |
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* @access private |
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*/ |
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var $value; |
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/** |
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* Holds the BigInteger's magnitude. |
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* |
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* @var Boolean |
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* @access private |
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*/ |
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var $is_negative = false; |
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/** |
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* Random number generator function |
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* |
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* @see setRandomGenerator() |
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* @access private |
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*/ |
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var $generator = 'mt_rand'; |
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/** |
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* Precision |
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* |
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* @see setPrecision() |
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* @access private |
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*/ |
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var $precision = -1; |
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/** |
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* Precision Bitmask |
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* |
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* @see setPrecision() |
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* @access private |
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*/ |
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var $bitmask = false; |
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/** |
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* Converts base-2, base-10, base-16, and binary strings (eg. base-256) to BigIntegers. |
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* |
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* If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using |
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* two's compliment. The sole exception to this is -10, which is treated the same as 10 is. |
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* |
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* Here's an example: |
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* <code> |
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* <?php |
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* include('Math/BigInteger.php'); |
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* |
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* $a = new Math_BigInteger('0x32', 16); // 50 in base-16 |
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* |
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* echo $a->toString(); // outputs 50 |
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* ?> |
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* </code> |
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* |
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* @param optional $x base-10 number or base-$base number if $base set. |
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* @param optional integer $base |
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* @return Math_BigInteger |
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* @access public |
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*/ |
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function Math_BigInteger($x = 0, $base = 10) |
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{ |
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if ( !defined('MATH_BIGINTEGER_MODE') ) { |
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switch (true) { |
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case extension_loaded('gmp'): |
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define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_GMP); |
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break; |
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case extension_loaded('bcmath'): |
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define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_BCMATH); |
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break; |
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default: |
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define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_INTERNAL); |
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} |
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} |
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switch ( MATH_BIGINTEGER_MODE ) { |
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case MATH_BIGINTEGER_MODE_GMP: |
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if (is_resource($x) && get_resource_type($x) == 'GMP integer') { |
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$this->value = $x; |
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return; |
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} |
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$this->value = gmp_init(0); |
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break; |
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case MATH_BIGINTEGER_MODE_BCMATH: |
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$this->value = '0'; |
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break; |
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default: |
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$this->value = array(); |
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} |
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if ($x === 0) { |
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return; |
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} |
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switch ($base) { |
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case -256: |
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if (ord($x[0]) & 0x80) { |
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$x = ~$x; |
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$this->is_negative = true; |
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} |
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case 256: |
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switch ( MATH_BIGINTEGER_MODE ) { |
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case MATH_BIGINTEGER_MODE_GMP: |
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$sign = $this->is_negative ? '-' : ''; |
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$this->value = gmp_init($sign . '0x' . bin2hex($x)); |
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break; |
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case MATH_BIGINTEGER_MODE_BCMATH: |
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// round $len to the nearest 4 (thanks, DavidMJ!) |
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$len = (strlen($x) + 3) & 0xFFFFFFFC; |
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$x = str_pad($x, $len, chr(0), STR_PAD_LEFT); |
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for ($i = 0; $i < $len; $i+= 4) { |
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$this->value = bcmul($this->value, '4294967296'); // 4294967296 == 2**32 |
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$this->value = bcadd($this->value, 0x1000000 * ord($x[$i]) + ((ord($x[$i + 1]) << 16) | (ord($x[$i + 2]) << 8) | ord($x[$i + 3]))); |
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} |
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if ($this->is_negative) { |
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$this->value = '-' . $this->value; |
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} |
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break; |
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// converts a base-2**8 (big endian / msb) number to base-2**26 (little endian / lsb) |
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default: |
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while (strlen($x)) { |
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$this->value[] = $this->_bytes2int($this->_base256_rshift($x, 26)); |
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} |
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} |
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if ($this->is_negative) { |
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if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) { |
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$this->is_negative = false; |
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} |
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$temp = $this->add(new Math_BigInteger('-1')); |
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$this->value = $temp->value; |
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} |
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break; |
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case 16: |
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case -16: |
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if ($base > 0 && $x[0] == '-') { |
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$this->is_negative = true; |
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$x = substr($x, 1); |
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} |
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$x = preg_replace('#^(?:0x)?([A-Fa-f0-9]*).*#', '$1', $x); |
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$is_negative = false; |
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if ($base < 0 && hexdec($x[0]) >= 8) { |
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$this->is_negative = $is_negative = true; |
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$x = bin2hex(~pack('H*', $x)); |
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} |
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switch ( MATH_BIGINTEGER_MODE ) { |
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case MATH_BIGINTEGER_MODE_GMP: |
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$temp = $this->is_negative ? '-0x' . $x : '0x' . $x; |
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$this->value = gmp_init($temp); |
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$this->is_negative = false; |
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break; |
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case MATH_BIGINTEGER_MODE_BCMATH: |
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$x = ( strlen($x) & 1 ) ? '0' . $x : $x; |
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$temp = new Math_BigInteger(pack('H*', $x), 256); |
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$this->value = $this->is_negative ? '-' . $temp->value : $temp->value; |
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$this->is_negative = false; |
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break; |
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default: |
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$x = ( strlen($x) & 1 ) ? '0' . $x : $x; |
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$temp = new Math_BigInteger(pack('H*', $x), 256); |
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$this->value = $temp->value; |
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} |
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if ($is_negative) { |
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$temp = $this->add(new Math_BigInteger('-1')); |
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$this->value = $temp->value; |
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} |
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break; |
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case 10: |
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case -10: |
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$x = preg_replace('#^(-?[0-9]*).*#', '$1', $x); |
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switch ( MATH_BIGINTEGER_MODE ) { |
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case MATH_BIGINTEGER_MODE_GMP: |
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$this->value = gmp_init($x); |
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break; |
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case MATH_BIGINTEGER_MODE_BCMATH: |
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// explicitly casting $x to a string is necessary, here, since doing $x[0] on -1 yields different |
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// results then doing it on '-1' does (modInverse does $x[0]) |
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$this->value = (string) $x; |
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break; |
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default: |
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$temp = new Math_BigInteger(); |
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// array(10000000) is 10**7 in base-2**26. 10**7 is the closest to 2**26 we can get without passing it. |
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$multiplier = new Math_BigInteger(); |
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$multiplier->value = array(10000000); |
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if ($x[0] == '-') { |
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$this->is_negative = true; |
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$x = substr($x, 1); |
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} |
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$x = str_pad($x, strlen($x) + (6 * strlen($x)) % 7, 0, STR_PAD_LEFT); |
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while (strlen($x)) { |
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$temp = $temp->multiply($multiplier); |
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$temp = $temp->add(new Math_BigInteger($this->_int2bytes(substr($x, 0, 7)), 256)); |
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$x = substr($x, 7); |
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} |
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$this->value = $temp->value; |
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} |
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break; |
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case 2: // base-2 support originally implemented by Lluis Pamies - thanks! |
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case -2: |
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if ($base > 0 && $x[0] == '-') { |
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$this->is_negative = true; |
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$x = substr($x, 1); |
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} |
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$x = preg_replace('#^([01]*).*#', '$1', $x); |
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$x = str_pad($x, strlen($x) + (3 * strlen($x)) % 4, 0, STR_PAD_LEFT); |
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$str = '0x'; |
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while (strlen($x)) { |
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$part = substr($x, 0, 4); |
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$str.= dechex(bindec($part)); |
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$x = substr($x, 4); |
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} |
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if ($this->is_negative) { |
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$str = '-' . $str; |
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} |
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$temp = new Math_BigInteger($str, 8 * $base); // ie. either -16 or +16 |
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$this->value = $temp->value; |
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$this->is_negative = $temp->is_negative; |
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break; |
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default: |
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// base not supported, so we'll let $this == 0 |
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} |
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} |
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/** |
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* Converts a BigInteger to a byte string (eg. base-256). |
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* |
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* Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're |
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* saved as two's compliment. |
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* |
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* Here's an example: |
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* <code> |
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* <?php |
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* include('Math/BigInteger.php'); |
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* |
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* $a = new Math_BigInteger('65'); |
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* |
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* echo $a->toBytes(); // outputs chr(65) |
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* ?> |
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* </code> |
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* |
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* @param Boolean $twos_compliment |
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* @return String |
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* @access public |
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* @internal Converts a base-2**26 number to base-2**8 |
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*/ |
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function toBytes($twos_compliment = false) |
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{ |
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if ($twos_compliment) { |
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$comparison = $this->compare(new Math_BigInteger()); |
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if ($comparison == 0) { |
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return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : ''; |
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} |
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$temp = $comparison < 0 ? $this->add(new Math_BigInteger(1)) : $this->copy(); |
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$bytes = $temp->toBytes(); |
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if (empty($bytes)) { // eg. if the number we're trying to convert is -1 |
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$bytes = chr(0); |
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} |
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if (ord($bytes[0]) & 0x80) { |
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$bytes = chr(0) . $bytes; |
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} |
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return $comparison < 0 ? ~$bytes : $bytes; |
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} |
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switch ( MATH_BIGINTEGER_MODE ) { |
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case MATH_BIGINTEGER_MODE_GMP: |
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if (gmp_cmp($this->value, gmp_init(0)) == 0) { |
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return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : ''; |
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} |
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$temp = gmp_strval(gmp_abs($this->value), 16); |
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$temp = ( strlen($temp) & 1 ) ? '0' . $temp : $temp; |
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$temp = pack('H*', $temp); |
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|
|
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); |
|
|
} |
|
|
|
|
|
// we don't do four bytes at a time because then numbers larger than 1<<31 would be negative |
|
|
// two's complimented numbers, which would break chr. |
|
|
while (bccomp($current, '0') > 0) { |
|
|
$temp = bcmod($current, 0x1000000); |
|
|
$value = chr($temp >> 16) . chr($temp >> 8) . chr($temp) . $value; |
|
|
$current = bcdiv($current, 0x1000000); |
|
|
} |
|
|
|
|
|
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 $this->precision > 0 ? |
|
|
substr(str_pad($result, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) : |
|
|
$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; $i < strlen($hex); $i+=8) { |
|
|
$bits.= str_pad(decbin(hexdec(substr($hex, $i, 8))), 32, '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); |
|
|
$result = str_pad($mod->value[0], 7, '0', STR_PAD_LEFT) . $result; |
|
|
} |
|
|
$result = ltrim($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(); |
|
|
} |
|
|
|
|
|
/** |
|
|
* 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); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$this_size = count($this->value); |
|
|
$y_size = count($y->value); |
|
|
|
|
|
if ($this_size == 0) { |
|
|
return $y->copy(); |
|
|
} else if ($y_size == 0) { |
|
|
return $this->copy(); |
|
|
} |
|
|
|
|
|
// subtract, if appropriate |
|
|
if ( $this->is_negative != $y->is_negative ) { |
|
|
// is $y the negative number? |
|
|
$y_negative = $this->compare($y) > 0; |
|
|
|
|
|
$temp = $this->copy(); |
|
|
$y = $y->copy(); |
|
|
$temp->is_negative = $y->is_negative = false; |
|
|
|
|
|
$diff = $temp->compare($y); |
|
|
if ( !$diff ) { |
|
|
$temp = new Math_BigInteger(); |
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$temp = $temp->subtract($y); |
|
|
|
|
|
$temp->is_negative = ($diff > 0) ? !$y_negative : $y_negative; |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$result = new Math_BigInteger(); |
|
|
$carry = 0; |
|
|
|
|
|
$size = max($this_size, $y_size); |
|
|
$size+= $size & 1; // rounds $size to the nearest 2. |
|
|
|
|
|
$x = array_pad($this->value, $size, 0); |
|
|
$y = array_pad($y->value, $size, 0); |
|
|
|
|
|
for ($i = 0; $i < $size - 1; $i+=2) { |
|
|
$sum = $x[$i + 1] * 0x4000000 + $x[$i] + $y[$i + 1] * 0x4000000 + $y[$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; |
|
|
|
|
|
$temp = floor($sum / 0x4000000); |
|
|
|
|
|
$result->value[] = $sum - 0x4000000 * $temp; // eg. a faster alternative to fmod($sum, 0x4000000) |
|
|
$result->value[] = $temp; |
|
|
} |
|
|
|
|
|
if ($carry) { |
|
|
$result->value[] = (int) $carry; |
|
|
} |
|
|
|
|
|
$result->is_negative = $this->is_negative; |
|
|
|
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* 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); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$this_size = count($this->value); |
|
|
$y_size = count($y->value); |
|
|
|
|
|
if ($this_size == 0) { |
|
|
$temp = $y->copy(); |
|
|
$temp->is_negative = !$temp->is_negative; |
|
|
return $temp; |
|
|
} else if ($y_size == 0) { |
|
|
return $this->copy(); |
|
|
} |
|
|
|
|
|
// add, if appropriate (ie. -$x - +$y or +$x - -$y) |
|
|
if ( $this->is_negative != $y->is_negative ) { |
|
|
$is_negative = $y->compare($this) > 0; |
|
|
|
|
|
$temp = $this->copy(); |
|
|
$y = $y->copy(); |
|
|
$temp->is_negative = $y->is_negative = false; |
|
|
|
|
|
$temp = $temp->add($y); |
|
|
|
|
|
$temp->is_negative = $is_negative; |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$diff = $this->compare($y); |
|
|
|
|
|
if ( !$diff ) { |
|
|
$temp = new Math_BigInteger(); |
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
// switch $this and $y around, if appropriate. |
|
|
if ( (!$this->is_negative && $diff < 0) || ($this->is_negative && $diff > 0) ) { |
|
|
$is_negative = $y->is_negative; |
|
|
|
|
|
$temp = $this->copy(); |
|
|
$y = $y->copy(); |
|
|
$temp->is_negative = $y->is_negative = false; |
|
|
|
|
|
$temp = $y->subtract($temp); |
|
|
$temp->is_negative = !$is_negative; |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$result = new Math_BigInteger(); |
|
|
$carry = 0; |
|
|
|
|
|
$size = max($this_size, $y_size); |
|
|
$size+= $size % 2; |
|
|
|
|
|
$x = array_pad($this->value, $size, 0); |
|
|
$y = array_pad($y->value, $size, 0); |
|
|
|
|
|
for ($i = 0; $i < $size - 1; $i+=2) { |
|
|
$sum = $x[$i + 1] * 0x4000000 + $x[$i] - $y[$i + 1] * 0x4000000 - $y[$i] + $carry; |
|
|
$carry = $sum < 0 ? -1 : 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1 |
|
|
$sum = $carry ? $sum + MATH_BIGINTEGER_MAX_DIGIT52 : $sum; |
|
|
|
|
|
$temp = floor($sum / 0x4000000); |
|
|
|
|
|
$result->value[] = $sum - 0x4000000 * $temp; |
|
|
$result->value[] = $temp; |
|
|
} |
|
|
|
|
|
// $carry shouldn't be anything other than zero, at this point, since we already made sure that $this |
|
|
// was bigger than $y. |
|
|
|
|
|
$result->is_negative = $this->is_negative; |
|
|
|
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* 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); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
static $cutoff = false; |
|
|
if ($cutoff === false) { |
|
|
$cutoff = 2 * MATH_BIGINTEGER_KARATSUBA_CUTOFF; |
|
|
} |
|
|
|
|
|
if ( $this->equals($x) ) { |
|
|
return $this->_square(); |
|
|
} |
|
|
|
|
|
$this_length = count($this->value); |
|
|
$x_length = count($x->value); |
|
|
|
|
|
if ( !$this_length || !$x_length ) { // a 0 is being multiplied |
|
|
$temp = new Math_BigInteger(); |
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
$product = min($this_length, $x_length) < $cutoff ? $this->_multiply($x) : $this->_karatsuba($x); |
|
|
|
|
|
$product->is_negative = $this->is_negative != $x->is_negative; |
|
|
|
|
|
return $this->_normalize($product); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Performs long multiplication up to $stop digits |
|
|
* |
|
|
* If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved. |
|
|
* |
|
|
* @see _barrett() |
|
|
* @param Math_BigInteger $x |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _multiplyLower($x, $stop) |
|
|
{ |
|
|
$this_length = count($this->value); |
|
|
$x_length = count($x->value); |
|
|
|
|
|
if ( !$this_length || !$x_length ) { // a 0 is being multiplied |
|
|
return new Math_BigInteger(); |
|
|
} |
|
|
|
|
|
if ( $this_length < $x_length ) { |
|
|
return $x->_multiplyLower($this, $stop); |
|
|
} |
|
|
|
|
|
$product = new Math_BigInteger(); |
|
|
$product->value = $this->_array_repeat(0, $this_length + $x_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 < $this_length; $j++) { // ie. $i = 0, $k = $i |
|
|
$temp = $this->value[$j] * $x->value[0] + $carry; // $product->value[$k] == 0 |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$product->value[$j] = $temp - 0x4000000 * $carry; |
|
|
} |
|
|
|
|
|
if ($j < $stop) { |
|
|
$product->value[$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 < $x_length; $i++) { |
|
|
$carry = 0; |
|
|
|
|
|
for ($j = 0, $k = $i; $j < $this_length && $k < $stop; $j++, $k++) { |
|
|
$temp = $product->value[$k] + $this->value[$j] * $x->value[$i] + $carry; |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$product->value[$k] = $temp - 0x4000000 * $carry; |
|
|
} |
|
|
|
|
|
if ($k < $stop) { |
|
|
$product->value[$k] = $carry; |
|
|
} |
|
|
} |
|
|
|
|
|
$product->is_negative = $this->is_negative != $x->is_negative; |
|
|
|
|
|
return $product; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Performs long multiplication on two BigIntegers |
|
|
* |
|
|
* Modeled after 'multiply' in MutableBigInteger.java. |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _multiply($x) |
|
|
{ |
|
|
$this_length = count($this->value); |
|
|
$x_length = count($x->value); |
|
|
|
|
|
if ( !$this_length || !$x_length ) { // a 0 is being multiplied |
|
|
return new Math_BigInteger(); |
|
|
} |
|
|
|
|
|
if ( $this_length < $x_length ) { |
|
|
return $x->_multiply($this); |
|
|
} |
|
|
|
|
|
$product = new Math_BigInteger(); |
|
|
$product->value = $this->_array_repeat(0, $this_length + $x_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 < $this_length; $j++) { // ie. $i = 0 |
|
|
$temp = $this->value[$j] * $x->value[0] + $carry; // $product->value[$k] == 0 |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$product->value[$j] = $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 < $x_length; $i++) { |
|
|
$carry = 0; |
|
|
|
|
|
for ($j = 0, $k = $i; $j < $this_length; $j++, $k++) { |
|
|
$temp = $product->value[$k] + $this->value[$j] * $x->value[$i] + $carry; |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$product->value[$k] = $temp - 0x4000000 * $carry; |
|
|
} |
|
|
|
|
|
$product->value[$k] = $carry; |
|
|
} |
|
|
|
|
|
$product->is_negative = $this->is_negative != $x->is_negative; |
|
|
|
|
|
return $this->_normalize($product); |
|
|
} |
|
|
|
|
|
/** |
|
|
* 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 Math_BigInteger $y |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _karatsuba($y) |
|
|
{ |
|
|
$x = $this->copy(); |
|
|
|
|
|
$m = min(count($x->value) >> 1, count($y->value) >> 1); |
|
|
|
|
|
if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) { |
|
|
return $x->_multiply($y); |
|
|
} |
|
|
|
|
|
$x1 = new Math_BigInteger(); |
|
|
$x0 = new Math_BigInteger(); |
|
|
$y1 = new Math_BigInteger(); |
|
|
$y0 = new Math_BigInteger(); |
|
|
|
|
|
$x1->value = array_slice($x->value, $m); |
|
|
$x0->value = array_slice($x->value, 0, $m); |
|
|
$y1->value = array_slice($y->value, $m); |
|
|
$y0->value = array_slice($y->value, 0, $m); |
|
|
|
|
|
$z2 = $x1->_karatsuba($y1); |
|
|
$z0 = $x0->_karatsuba($y0); |
|
|
|
|
|
$z1 = $x1->add($x0); |
|
|
$z1 = $z1->_karatsuba($y1->add($y0)); |
|
|
$z1 = $z1->subtract($z2->add($z0)); |
|
|
|
|
|
$z2->value = array_merge(array_fill(0, 2 * $m, 0), $z2->value); |
|
|
$z1->value = array_merge(array_fill(0, $m, 0), $z1->value); |
|
|
|
|
|
$xy = $z2->add($z1); |
|
|
$xy = $xy->add($z0); |
|
|
|
|
|
return $xy; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Squares a BigInteger |
|
|
* |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _square() |
|
|
{ |
|
|
static $cutoff = false; |
|
|
if ($cutoff === false) { |
|
|
$cutoff = 2 * MATH_BIGINTEGER_KARATSUBA_CUTOFF; |
|
|
} |
|
|
|
|
|
return count($this->value) < $cutoff ? $this->_baseSquare() : $this->_karatsubaSquare(); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Performs traditional squaring on two BigIntegers |
|
|
* |
|
|
* Squaring can be done faster than multiplying a number by itself can be. See |
|
|
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=7 HAC 14.2.4} / |
|
|
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=141 MPM 5.3} for more information. |
|
|
* |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _baseSquare() |
|
|
{ |
|
|
if ( empty($this->value) ) { |
|
|
return new Math_BigInteger(); |
|
|
} |
|
|
|
|
|
$square = new Math_BigInteger(); |
|
|
$square->value = $this->_array_repeat(0, 2 * count($this->value)); |
|
|
|
|
|
for ($i = 0, $max_index = count($this->value) - 1; $i <= $max_index; $i++) { |
|
|
$i2 = 2 * $i; |
|
|
|
|
|
$temp = $square->value[$i2] + $this->value[$i] * $this->value[$i]; |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$square->value[$i2] = $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 * $this->value[$j] * $this->value[$i] + $carry; |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$square->value[$k] = $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; |
|
|
} |
|
|
|
|
|
/** |
|
|
* 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 Math_BigInteger $y |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _karatsubaSquare() |
|
|
{ |
|
|
$m = count($this->value) >> 1; |
|
|
|
|
|
if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) { |
|
|
return $this->_square(); |
|
|
} |
|
|
|
|
|
$x1 = new Math_BigInteger(); |
|
|
$x0 = new Math_BigInteger(); |
|
|
|
|
|
$x1->value = array_slice($this->value, $m); |
|
|
$x0->value = array_slice($this->value, 0, $m); |
|
|
|
|
|
$z2 = $x1->_karatsubaSquare(); |
|
|
$z0 = $x0->_karatsubaSquare(); |
|
|
|
|
|
$z1 = $x1->add($x0); |
|
|
$z1 = $z1->_karatsubaSquare(); |
|
|
$z1 = $z1->subtract($z2->add($z0)); |
|
|
|
|
|
$z2->value = array_merge(array_fill(0, 2 * $m, 0), $z2->value); |
|
|
$z1->value = array_merge(array_fill(0, $m, 0), $z1->value); |
|
|
|
|
|
$xx = $z2->add($z1); |
|
|
$xx = $xx->add($z0); |
|
|
|
|
|
return $xx; |
|
|
} |
|
|
|
|
|
/** |
|
|
* 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); |
|
|
$remainder->value = bcmod($this->value, $y->value); |
|
|
|
|
|
if ($remainder->value[0] == '-') { |
|
|
$remainder->value = bcadd($remainder->value, $y->value[0] == '-' ? substr($y->value, 1) : $y->value); |
|
|
} |
|
|
|
|
|
return array($this->_normalize($quotient), $this->_normalize($remainder)); |
|
|
} |
|
|
|
|
|
if (count($y->value) == 1) { |
|
|
$temp = $this->_divide_digit($y->value[0]); |
|
|
$temp[0]->is_negative = $this->is_negative != $y->is_negative; |
|
|
return array($this->_normalize($temp[0]), $this->_normalize($temp[1])); |
|
|
} |
|
|
|
|
|
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); |
|
|
|
|
|
$x_max = count($x->value) - 1; |
|
|
$y_max = count($y->value) - 1; |
|
|
|
|
|
$quotient = new Math_BigInteger(); |
|
|
$quotient->value = $this->_array_repeat(0, $x_max - $y_max + 1); |
|
|
|
|
|
// $temp = $y << ($x_max - $y_max-1) in base 2**26 |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array_merge($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 = array( |
|
|
$x->value[$i], |
|
|
( $i > 0 ) ? $x->value[$i - 1] : 0, |
|
|
( $i > 1 ) ? $x->value[$i - 2] : 0 |
|
|
); |
|
|
$y_value = array( |
|
|
$y->value[$y_max], |
|
|
( $y_max > 0 ) ? $y->value[$y_max - 1] : 0 |
|
|
); |
|
|
|
|
|
$q_index = $i - $y_max - 1; |
|
|
if ($x_value[0] == $y_value[0]) { |
|
|
$quotient->value[$q_index] = 0x3FFFFFF; |
|
|
} else { |
|
|
$quotient->value[$q_index] = floor( |
|
|
($x_value[0] * 0x4000000 + $x_value[1]) |
|
|
/ |
|
|
$y_value[0] |
|
|
); |
|
|
} |
|
|
|
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array($y_value[1], $y_value[0]); |
|
|
|
|
|
$lhs = new Math_BigInteger(); |
|
|
$lhs->value = array($quotient->value[$q_index]); |
|
|
$lhs = $lhs->multiply($temp); |
|
|
|
|
|
$rhs = new Math_BigInteger(); |
|
|
$rhs->value = array($x_value[2], $x_value[1], $x_value[0]); |
|
|
|
|
|
while ( $lhs->compare($rhs) > 0 ) { |
|
|
$quotient->value[$q_index]--; |
|
|
|
|
|
$lhs = new Math_BigInteger(); |
|
|
$lhs->value = array($quotient->value[$q_index]); |
|
|
$lhs = $lhs->multiply($temp); |
|
|
} |
|
|
|
|
|
$adjust = $this->_array_repeat(0, $q_index); |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array($quotient->value[$q_index]); |
|
|
$temp = $temp->multiply($y); |
|
|
$temp->value = array_merge($adjust, $temp->value); |
|
|
|
|
|
$x = $x->subtract($temp); |
|
|
|
|
|
if ($x->compare($zero) < 0) { |
|
|
$temp->value = array_merge($adjust, $y->value); |
|
|
$x = $x->add($temp); |
|
|
|
|
|
$quotient->value[$q_index]--; |
|
|
} |
|
|
|
|
|
$x_max = count($x->value) - 1; |
|
|
} |
|
|
|
|
|
// unnormalize the remainder |
|
|
$x->_rshift($shift); |
|
|
|
|
|
$quotient->is_negative = $x_sign != $y_sign; |
|
|
|
|
|
// calculate the "common residue", if appropriate |
|
|
if ( $x_sign ) { |
|
|
$y->_rshift($shift); |
|
|
$x = $y->subtract($x); |
|
|
} |
|
|
|
|
|
return array($this->_normalize($quotient), $this->_normalize($x)); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Divides a BigInteger by a regular integer |
|
|
* |
|
|
* abc / x = a00 / x + b0 / x + c / x |
|
|
* |
|
|
* @param Math_BigInteger $divisor |
|
|
* @return Array |
|
|
* @access public |
|
|
*/ |
|
|
function _divide_digit($divisor) |
|
|
{ |
|
|
$carry = 0; |
|
|
$result = new Math_BigInteger(); |
|
|
|
|
|
for ($i = count($this->value) - 1; $i >= 0; $i--) { |
|
|
$temp = 0x4000000 * $carry + $this->value[$i]; |
|
|
$result->value[$i] = floor($temp / $divisor); |
|
|
$carry = fmod($temp, $divisor); |
|
|
} |
|
|
|
|
|
$remainder = new Math_BigInteger(); |
|
|
$remainder->value = array($carry); |
|
|
|
|
|
return array($result, $remainder); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Performs modular exponentiation. |
|
|
* |
|
|
* Here's an example: |
|
|
* <code> |
|
|
* <?php |
|
|
* include('Math/BigInteger.php'); |
|
|
* |
|
|
* $a = new Math_BigInteger('10'); |
|
|
* $b = new Math_BigInteger('20'); |
|
|
* $c = new Math_BigInteger('30'); |
|
|
* |
|
|
* $c = $a->modPow($b, $c); |
|
|
* |
|
|
* echo $c->toString(); // outputs 10 |
|
|
* ?> |
|
|
* </code> |
|
|
* |
|
|
* @param Math_BigInteger $e |
|
|
* @param Math_BigInteger $n |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
* @internal The most naive approach to modular exponentiation has very unreasonable requirements, and |
|
|
* and although the approach involving repeated squaring does vastly better, it, too, is impractical |
|
|
* for our purposes. The reason being that division - by far the most complicated and time-consuming |
|
|
* of the basic operations (eg. +,-,*,/) - occurs multiple times within it. |
|
|
* |
|
|
* Modular reductions resolve this issue. Although an individual modular reduction takes more time |
|
|
* then an individual division, when performed in succession (with the same modulo), they're a lot faster. |
|
|
* |
|
|
* The two most commonly used modular reductions are Barrett and Montgomery reduction. Montgomery reduction, |
|
|
* although faster, only works when the gcd of the modulo and of the base being used is 1. In RSA, when the |
|
|
* base is a power of two, the modulo - a product of two primes - is always going to have a gcd of 1 (because |
|
|
* the product of two odd numbers is odd), but what about when RSA isn't used? |
|
|
* |
|
|
* In contrast, Barrett reduction has no such constraint. As such, some bigint implementations perform a |
|
|
* Barrett reduction after every operation in the modpow function. Others perform Barrett reductions when the |
|
|
* modulo is even and Montgomery reductions when the modulo is odd. BigInteger.java's modPow method, however, |
|
|
* uses a trick involving the Chinese Remainder Theorem to factor the even modulo into two numbers - one odd and |
|
|
* the other, a power of two - and recombine them, later. This is the method that this modPow function uses. |
|
|
* {@link http://islab.oregonstate.edu/papers/j34monex.pdf Montgomery Reduction with Even Modulus} elaborates. |
|
|
*/ |
|
|
function modPow($e, $n) |
|
|
{ |
|
|
$n = $this->bitmask !== false && $this->bitmask->compare($n) < 0 ? $this->bitmask : $n->abs(); |
|
|
|
|
|
if ($e->compare(new Math_BigInteger()) < 0) { |
|
|
$e = $e->abs(); |
|
|
|
|
|
$temp = $this->modInverse($n); |
|
|
if ($temp === false) { |
|
|
return false; |
|
|
} |
|
|
|
|
|
return $this->_normalize($temp->modPow($e, $n)); |
|
|
} |
|
|
|
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = gmp_powm($this->value, $e->value, $n->value); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = bcpowmod($this->value, $e->value, $n->value); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
if ( empty($e->value) ) { |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array(1); |
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
if ( $e->value == array(1) ) { |
|
|
list(, $temp) = $this->divide($n); |
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
if ( $e->value == array(2) ) { |
|
|
$temp = $this->_square(); |
|
|
list(, $temp) = $temp->divide($n); |
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
return $this->_normalize($this->_slidingWindow($e, $n, MATH_BIGINTEGER_BARRETT)); |
|
|
|
|
|
// is the modulo odd? |
|
|
if ( $n->value[0] & 1 ) { |
|
|
return $this->_normalize($this->_slidingWindow($e, $n, MATH_BIGINTEGER_MONTGOMERY)); |
|
|
} |
|
|
// if it's not, it's even |
|
|
|
|
|
// find the lowest set bit (eg. the max pow of 2 that divides $n) |
|
|
for ($i = 0; $i < count($n->value); $i++) { |
|
|
if ( $n->value[$i] ) { |
|
|
$temp = decbin($n->value[$i]); |
|
|
$j = strlen($temp) - strrpos($temp, '1') - 1; |
|
|
$j+= 26 * $i; |
|
|
break; |
|
|
} |
|
|
} |
|
|
// at this point, 2^$j * $n/(2^$j) == $n |
|
|
|
|
|
$mod1 = $n->copy(); |
|
|
$mod1->_rshift($j); |
|
|
$mod2 = new Math_BigInteger(); |
|
|
$mod2->value = array(1); |
|
|
$mod2->_lshift($j); |
|
|
|
|
|
$part1 = ( $mod1->value != array(1) ) ? $this->_slidingWindow($e, $mod1, MATH_BIGINTEGER_MONTGOMERY) : new Math_BigInteger(); |
|
|
$part2 = $this->_slidingWindow($e, $mod2, MATH_BIGINTEGER_POWEROF2); |
|
|
|
|
|
$y1 = $mod2->modInverse($mod1); |
|
|
$y2 = $mod1->modInverse($mod2); |
|
|
|
|
|
$result = $part1->multiply($mod2); |
|
|
$result = $result->multiply($y1); |
|
|
|
|
|
$temp = $part2->multiply($mod1); |
|
|
$temp = $temp->multiply($y2); |
|
|
|
|
|
$result = $result->add($temp); |
|
|
list(, $result) = $result->divide($n); |
|
|
|
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Performs modular exponentiation. |
|
|
* |
|
|
* Alias for Math_BigInteger::modPow() |
|
|
* |
|
|
* @param Math_BigInteger $e |
|
|
* @param Math_BigInteger $n |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
*/ |
|
|
function powMod($e, $n) |
|
|
{ |
|
|
return $this->modPow($e, $n); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Sliding Window k-ary Modular Exponentiation |
|
|
* |
|
|
* Based on {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=27 HAC 14.85} / |
|
|
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=210 MPM 7.7}. In a departure from those algorithims, |
|
|
* however, this function performs a modular reduction after every multiplication and squaring operation. |
|
|
* As such, this function has the same preconditions that the reductions being used do. |
|
|
* |
|
|
* @param Math_BigInteger $e |
|
|
* @param Math_BigInteger $n |
|
|
* @param Integer $mode |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _slidingWindow($e, $n, $mode) |
|
|
{ |
|
|
static $window_ranges = array(7, 25, 81, 241, 673, 1793); // from BigInteger.java's oddModPow function |
|
|
//static $window_ranges = array(0, 7, 36, 140, 450, 1303, 3529); // from MPM 7.3.1 |
|
|
|
|
|
$e_length = count($e->value) - 1; |
|
|
$e_bits = decbin($e->value[$e_length]); |
|
|
for ($i = $e_length - 1; $i >= 0; $i--) { |
|
|
$e_bits.= str_pad(decbin($e->value[$i]), 26, '0', STR_PAD_LEFT); |
|
|
} |
|
|
|
|
|
$e_length = strlen($e_bits); |
|
|
|
|
|
// calculate the appropriate window size. |
|
|
// $window_size == 3 if $window_ranges is between 25 and 81, for example. |
|
|
for ($i = 0, $window_size = 1; $e_length > $window_ranges[$i] && $i < count($window_ranges); $window_size++, $i++); |
|
|
switch ($mode) { |
|
|
case MATH_BIGINTEGER_MONTGOMERY: |
|
|
$reduce = '_montgomery'; |
|
|
$prep = '_prepMontgomery'; |
|
|
break; |
|
|
case MATH_BIGINTEGER_BARRETT: |
|
|
$reduce = '_barrett'; |
|
|
$prep = '_barrett'; |
|
|
break; |
|
|
case MATH_BIGINTEGER_POWEROF2: |
|
|
$reduce = '_mod2'; |
|
|
$prep = '_mod2'; |
|
|
break; |
|
|
case MATH_BIGINTEGER_CLASSIC: |
|
|
$reduce = '_remainder'; |
|
|
$prep = '_remainder'; |
|
|
break; |
|
|
case MATH_BIGINTEGER_NONE: |
|
|
// ie. do no modular reduction. useful if you want to just do pow as opposed to modPow. |
|
|
$reduce = 'copy'; |
|
|
$prep = 'copy'; |
|
|
break; |
|
|
default: |
|
|
// an invalid $mode was provided |
|
|
} |
|
|
|
|
|
// precompute $this^0 through $this^$window_size |
|
|
$powers = array(); |
|
|
$powers[1] = $this->$prep($n); |
|
|
$powers[2] = $powers[1]->_square(); |
|
|
$powers[2] = $powers[2]->$reduce($n); |
|
|
|
|
|
// we do every other number since substr($e_bits, $i, $j+1) (see below) is supposed to end |
|
|
// in a 1. ie. it's supposed to be odd. |
|
|
$temp = 1 << ($window_size - 1); |
|
|
for ($i = 1; $i < $temp; $i++) { |
|
|
$powers[2 * $i + 1] = $powers[2 * $i - 1]->multiply($powers[2]); |
|
|
$powers[2 * $i + 1] = $powers[2 * $i + 1]->$reduce($n); |
|
|
} |
|
|
|
|
|
$result = new Math_BigInteger(); |
|
|
$result->value = array(1); |
|
|
$result = $result->$prep($n); |
|
|
|
|
|
for ($i = 0; $i < $e_length; ) { |
|
|
if ( !$e_bits[$i] ) { |
|
|
$result = $result->_square(); |
|
|
$result = $result->$reduce($n); |
|
|
$i++; |
|
|
} else { |
|
|
for ($j = $window_size - 1; $j > 0; $j--) { |
|
|
if ( !empty($e_bits[$i + $j]) ) { |
|
|
break; |
|
|
} |
|
|
} |
|
|
|
|
|
for ($k = 0; $k <= $j; $k++) {// eg. the length of substr($e_bits, $i, $j+1) |
|
|
$result = $result->_square(); |
|
|
$result = $result->$reduce($n); |
|
|
} |
|
|
|
|
|
$result = $result->multiply($powers[bindec(substr($e_bits, $i, $j + 1))]); |
|
|
$result = $result->$reduce($n); |
|
|
|
|
|
$i+=$j + 1; |
|
|
} |
|
|
} |
|
|
|
|
|
$result = $result->$reduce($n); |
|
|
|
|
|
return $result; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Remainder |
|
|
* |
|
|
* A wrapper for the divide function. |
|
|
* |
|
|
* @see divide() |
|
|
* @see _slidingWindow() |
|
|
* @access private |
|
|
* @param Math_BigInteger |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function _remainder($n) |
|
|
{ |
|
|
list(, $temp) = $this->divide($n); |
|
|
return $temp; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Modulos for Powers of Two |
|
|
* |
|
|
* Calculates $x%$n, where $n = 2**$e, for some $e. Since this is basically the same as doing $x & ($n-1), |
|
|
* we'll just use this function as a wrapper for doing that. |
|
|
* |
|
|
* @see _slidingWindow() |
|
|
* @access private |
|
|
* @param Math_BigInteger |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function _mod2($n) |
|
|
{ |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array(1); |
|
|
return $this->bitwise_and($n->subtract($temp)); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Barrett Modular Reduction |
|
|
* |
|
|
* See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=14 HAC 14.3.3} / |
|
|
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=165 MPM 6.2.5} for more information. Modified slightly, |
|
|
* so as not to require negative numbers (initially, this script didn't support negative numbers). |
|
|
* |
|
|
* @see _slidingWindow() |
|
|
* @access private |
|
|
* @param Math_BigInteger |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function _barrett($n) |
|
|
{ |
|
|
static $cache = array( |
|
|
MATH_BIGINTEGER_VARIABLE => array(), |
|
|
MATH_BIGINTEGER_DATA => array() |
|
|
); |
|
|
|
|
|
$n_length = count($n->value); |
|
|
|
|
|
if (count($this->value) > 2 * $n_length) { |
|
|
list(, $temp) = $this->divide($n); |
|
|
return $temp; |
|
|
} |
|
|
|
|
|
if ( ($key = array_search($n->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) { |
|
|
$key = count($cache[MATH_BIGINTEGER_VARIABLE]); |
|
|
$cache[MATH_BIGINTEGER_VARIABLE][] = $n->value; |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = $this->_array_repeat(0, 2 * $n_length); |
|
|
$temp->value[] = 1; |
|
|
list($cache[MATH_BIGINTEGER_DATA][], ) = $temp->divide($n); |
|
|
} |
|
|
|
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array_slice($this->value, $n_length - 1); |
|
|
$temp = $temp->multiply($cache[MATH_BIGINTEGER_DATA][$key]); |
|
|
$temp->value = array_slice($temp->value, $n_length + 1); |
|
|
|
|
|
$result = new Math_BigInteger(); |
|
|
$result->value = array_slice($this->value, 0, $n_length + 1); |
|
|
$temp = $temp->_multiplyLower($n, $n_length + 1); |
|
|
// $temp->value == array_slice($temp->multiply($n)->value, 0, $n_length + 1) |
|
|
|
|
|
if ($result->compare($temp) < 0) { |
|
|
$corrector = new Math_BigInteger(); |
|
|
$corrector->value = $this->_array_repeat(0, $n_length + 1); |
|
|
$corrector->value[] = 1; |
|
|
$result = $result->add($corrector); |
|
|
} |
|
|
|
|
|
$result = $result->subtract($temp); |
|
|
while ($result->compare($n) > 0) { |
|
|
$result = $result->subtract($n); |
|
|
} |
|
|
|
|
|
return $result; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Montgomery Modular Reduction |
|
|
* |
|
|
* ($this->_prepMontgomery($n))->_montgomery($n) yields $x%$n. |
|
|
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=170 MPM 6.3} provides insights on how this can be |
|
|
* improved upon (basically, by using the comba method). gcd($n, 2) must be equal to one for this function |
|
|
* to work correctly. |
|
|
* |
|
|
* @see _prepMontgomery() |
|
|
* @see _slidingWindow() |
|
|
* @access private |
|
|
* @param Math_BigInteger |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function _montgomery($n) |
|
|
{ |
|
|
static $cache = array( |
|
|
MATH_BIGINTEGER_VARIABLE => array(), |
|
|
MATH_BIGINTEGER_DATA => array() |
|
|
); |
|
|
|
|
|
if ( ($key = array_search($n->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) { |
|
|
$key = count($cache[MATH_BIGINTEGER_VARIABLE]); |
|
|
$cache[MATH_BIGINTEGER_VARIABLE][] = $n->value; |
|
|
$cache[MATH_BIGINTEGER_DATA][] = $n->_modInverse67108864(); |
|
|
} |
|
|
|
|
|
$k = count($n->value); |
|
|
|
|
|
$result = $this->copy(); |
|
|
|
|
|
for ($i = 0; $i < $k; $i++) { |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array( |
|
|
($result->value[$i] * $cache[MATH_BIGINTEGER_DATA][$key]) & 0x3FFFFFF |
|
|
); |
|
|
|
|
|
$temp = $temp->multiply($n); |
|
|
$temp->value = array_merge($this->_array_repeat(0, $i), $temp->value); |
|
|
$result = $result->add($temp); |
|
|
} |
|
|
|
|
|
$result->value = array_slice($result->value, $k); |
|
|
|
|
|
if ($result->compare($n) >= 0) { |
|
|
$result = $result->subtract($n); |
|
|
} |
|
|
|
|
|
return $result; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Prepare a number for use in Montgomery Modular Reductions |
|
|
* |
|
|
* @see _montgomery() |
|
|
* @see _slidingWindow() |
|
|
* @access private |
|
|
* @param Math_BigInteger |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function _prepMontgomery($n) |
|
|
{ |
|
|
$k = count($n->value); |
|
|
|
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = array_merge($this->_array_repeat(0, $k), $this->value); |
|
|
|
|
|
list(, $temp) = $temp->divide($n); |
|
|
return $temp; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Modular Inverse of a number mod 2**26 (eg. 67108864) |
|
|
* |
|
|
* Based off of the bnpInvDigit function implemented and justified in the following URL: |
|
|
* |
|
|
* {@link http://www-cs-students.stanford.edu/~tjw/jsbn/jsbn.js} |
|
|
* |
|
|
* The following URL provides more info: |
|
|
* |
|
|
* {@link http://groups.google.com/group/sci.crypt/msg/7a137205c1be7d85} |
|
|
* |
|
|
* As for why we do all the bitmasking... strange things can happen when converting from floats to ints. For |
|
|
* instance, on some computers, var_dump((int) -4294967297) yields int(-1) and on others, it yields |
|
|
* int(-2147483648). To avoid problems stemming from this, we use bitmasks to guarantee that ints aren't |
|
|
* auto-converted to floats. The outermost bitmask is present because without it, there's no guarantee that |
|
|
* the "residue" returned would be the so-called "common residue". We use fmod, in the last step, because the |
|
|
* maximum possible $x is 26 bits and the maximum $result is 16 bits. Thus, we have to be able to handle up to |
|
|
* 40 bits, which only 64-bit floating points will support. |
|
|
* |
|
|
* Thanks to Pedro Gimeno Fortea for input! |
|
|
* |
|
|
* @see _montgomery() |
|
|
* @access private |
|
|
* @return Integer |
|
|
*/ |
|
|
function _modInverse67108864() // 2**26 == 67108864 |
|
|
{ |
|
|
$x = -$this->value[0]; |
|
|
$result = $x & 0x3; // x**-1 mod 2**2 |
|
|
$result = ($result * (2 - $x * $result)) & 0xF; // x**-1 mod 2**4 |
|
|
$result = ($result * (2 - ($x & 0xFF) * $result)) & 0xFF; // x**-1 mod 2**8 |
|
|
$result = ($result * ((2 - ($x & 0xFFFF) * $result) & 0xFFFF)) & 0xFFFF; // x**-1 mod 2**16 |
|
|
$result = fmod($result * (2 - fmod($x * $result, 0x4000000)), 0x4000000); // x**-1 mod 2**26 |
|
|
return $result & 0x3FFFFFF; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Calculates modular inverses. |
|
|
* |
|
|
* Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses. |
|
|
* |
|
|
* Here's an example: |
|
|
* <code> |
|
|
* <?php |
|
|
* include('Math/BigInteger.php'); |
|
|
* |
|
|
* $a = new Math_BigInteger(30); |
|
|
* $b = new Math_BigInteger(17); |
|
|
* |
|
|
* $c = $a->modInverse($b); |
|
|
* echo $c->toString(); // outputs 4 |
|
|
* |
|
|
* echo "\r\n"; |
|
|
* |
|
|
* $d = $a->multiply($c); |
|
|
* list(, $d) = $d->divide($b); |
|
|
* echo $d; // outputs 1 (as per the definition of modular inverse) |
|
|
* ?> |
|
|
* </code> |
|
|
* |
|
|
* @param Math_BigInteger $n |
|
|
* @return mixed false, if no modular inverse exists, Math_BigInteger, otherwise. |
|
|
* @access public |
|
|
* @internal See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=21 HAC 14.64} for more information. |
|
|
*/ |
|
|
function modInverse($n) |
|
|
{ |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = gmp_invert($this->value, $n->value); |
|
|
|
|
|
return ( $temp->value === false ) ? false : $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
static $zero, $one; |
|
|
if (!isset($zero)) { |
|
|
$zero = new Math_BigInteger(); |
|
|
$one = new Math_BigInteger(1); |
|
|
} |
|
|
|
|
|
// $x mod $n == $x mod -$n. |
|
|
$n = $n->abs(); |
|
|
|
|
|
if ($this->compare($zero) < 0) { |
|
|
$temp = $this->abs(); |
|
|
$temp = $temp->modInverse($n); |
|
|
return $negated === false ? false : $this->_normalize($n->subtract($temp)); |
|
|
} |
|
|
|
|
|
extract($this->extendedGCD($n)); |
|
|
|
|
|
if (!$gcd->equals($one)) { |
|
|
return false; |
|
|
} |
|
|
|
|
|
$x = $x->compare($zero) < 0 ? $x->add($n) : $x; |
|
|
|
|
|
return $this->compare($zero) < 0 ? $this->_normalize($n->subtract($x)) : $this->_normalize($x); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Calculates the greatest common divisor and B<EFBFBD>zout's identity. |
|
|
* |
|
|
* Say you have 693 and 609. The GCD is 21. B<EFBFBD>zout's identity states that there exist integers x and y such that |
|
|
* 693*x + 609*y == 21. In point of fact, there are actually an infinite number of x and y combinations and which |
|
|
* combination is returned is dependant upon which mode is in use. See |
|
|
* {@link http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity B<EFBFBD>zout's identity - Wikipedia} for more information. |
|
|
* |
|
|
* Here's an example: |
|
|
* <code> |
|
|
* <?php |
|
|
* include('Math/BigInteger.php'); |
|
|
* |
|
|
* $a = new Math_BigInteger(693); |
|
|
* $b = new Math_BigInteger(609); |
|
|
* |
|
|
* extract($a->extendedGCD($b)); |
|
|
* |
|
|
* echo $gcd->toString() . "\r\n"; // outputs 21 |
|
|
* echo $a->toString() * $x->toString() + $b->toString() * $y->toString(); // outputs 21 |
|
|
* ?> |
|
|
* </code> |
|
|
* |
|
|
* @param Math_BigInteger $n |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
* @internal Calculates the GCD using the binary xGCD algorithim described in |
|
|
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=19 HAC 14.61}. As the text above 14.61 notes, |
|
|
* the more traditional algorithim requires "relatively costly multiple-precision divisions". |
|
|
*/ |
|
|
function extendedGCD($n) { |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
extract(gmp_gcdext($this->value, $n->value)); |
|
|
|
|
|
return array( |
|
|
'gcd' => $this->_normalize(new Math_BigInteger($g)), |
|
|
'x' => $this->_normalize(new Math_BigInteger($s)), |
|
|
'y' => $this->_normalize(new Math_BigInteger($t)) |
|
|
); |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
// it might be faster to use the binary xGCD algorithim here, as well, but (1) that algorithim works |
|
|
// best when the base is a power of 2 and (2) i don't think it'd make much difference, anyway. as is, |
|
|
// the basic extended euclidean algorithim is what we're using. |
|
|
|
|
|
$u = $this->value; |
|
|
$v = $n->value; |
|
|
|
|
|
$a = '1'; |
|
|
$b = '0'; |
|
|
$c = '0'; |
|
|
$d = '1'; |
|
|
|
|
|
while (bccomp($v, '0') != 0) { |
|
|
$q = bcdiv($u, $v); |
|
|
|
|
|
$temp = $u; |
|
|
$u = $v; |
|
|
$v = bcsub($temp, bcmul($v, $q)); |
|
|
|
|
|
$temp = $a; |
|
|
$a = $c; |
|
|
$c = bcsub($temp, bcmul($a, $q)); |
|
|
|
|
|
$temp = $b; |
|
|
$b = $d; |
|
|
$d = bcsub($temp, bcmul($b, $q)); |
|
|
} |
|
|
|
|
|
return array( |
|
|
'gcd' => $this->_normalize(new Math_BigInteger($u)), |
|
|
'x' => $this->_normalize(new Math_BigInteger($a)), |
|
|
'y' => $this->_normalize(new Math_BigInteger($b)) |
|
|
); |
|
|
} |
|
|
|
|
|
$y = $n->copy(); |
|
|
$x = $this->copy(); |
|
|
$g = new Math_BigInteger(); |
|
|
$g->value = array(1); |
|
|
|
|
|
while ( !(($x->value[0] & 1)|| ($y->value[0] & 1)) ) { |
|
|
$x->_rshift(1); |
|
|
$y->_rshift(1); |
|
|
$g->_lshift(1); |
|
|
} |
|
|
|
|
|
$u = $x->copy(); |
|
|
$v = $y->copy(); |
|
|
|
|
|
$a = new Math_BigInteger(); |
|
|
$b = new Math_BigInteger(); |
|
|
$c = new Math_BigInteger(); |
|
|
$d = new Math_BigInteger(); |
|
|
|
|
|
$a->value = $d->value = $g->value = array(1); |
|
|
|
|
|
while ( !empty($u->value) ) { |
|
|
while ( !($u->value[0] & 1) ) { |
|
|
$u->_rshift(1); |
|
|
if ( ($a->value[0] & 1) || ($b->value[0] & 1) ) { |
|
|
$a = $a->add($y); |
|
|
$b = $b->subtract($x); |
|
|
} |
|
|
$a->_rshift(1); |
|
|
$b->_rshift(1); |
|
|
} |
|
|
|
|
|
while ( !($v->value[0] & 1) ) { |
|
|
$v->_rshift(1); |
|
|
if ( ($c->value[0] & 1) || ($d->value[0] & 1) ) { |
|
|
$c = $c->add($y); |
|
|
$d = $d->subtract($x); |
|
|
} |
|
|
$c->_rshift(1); |
|
|
$d->_rshift(1); |
|
|
} |
|
|
|
|
|
if ($u->compare($v) >= 0) { |
|
|
$u = $u->subtract($v); |
|
|
$a = $a->subtract($c); |
|
|
$b = $b->subtract($d); |
|
|
} else { |
|
|
$v = $v->subtract($u); |
|
|
$c = $c->subtract($a); |
|
|
$d = $d->subtract($b); |
|
|
} |
|
|
} |
|
|
|
|
|
return array( |
|
|
'gcd' => $this->_normalize($g->multiply($v)), |
|
|
'x' => $this->_normalize($c), |
|
|
'y' => $this->_normalize($d) |
|
|
); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Calculates the greatest common divisor |
|
|
* |
|
|
* Say you have 693 and 609. The GCD is 21. |
|
|
* |
|
|
* Here's an example: |
|
|
* <code> |
|
|
* <?php |
|
|
* include('Math/BigInteger.php'); |
|
|
* |
|
|
* $a = new Math_BigInteger(693); |
|
|
* $b = new Math_BigInteger(609); |
|
|
* |
|
|
* $gcd = a->extendedGCD($b); |
|
|
* |
|
|
* echo $gcd->toString() . "\r\n"; // outputs 21 |
|
|
* ?> |
|
|
* </code> |
|
|
* |
|
|
* @param Math_BigInteger $n |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
*/ |
|
|
function gcd($n) |
|
|
{ |
|
|
extract($this->extendedGCD($n)); |
|
|
return $gcd; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Absolute value. |
|
|
* |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
*/ |
|
|
function abs() |
|
|
{ |
|
|
$temp = new Math_BigInteger(); |
|
|
|
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
$temp->value = gmp_abs($this->value); |
|
|
break; |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$temp->value = (bccomp($this->value, '0') < 0) ? substr($this->value, 1) : $this->value; |
|
|
break; |
|
|
default: |
|
|
$temp->value = $this->value; |
|
|
} |
|
|
|
|
|
return $temp; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Compares two numbers. |
|
|
* |
|
|
* Although one might think !$x->compare($y) means $x != $y, it, in fact, means the opposite. The reason for this is |
|
|
* demonstrated thusly: |
|
|
* |
|
|
* $x > $y: $x->compare($y) > 0 |
|
|
* $x < $y: $x->compare($y) < 0 |
|
|
* $x == $y: $x->compare($y) == 0 |
|
|
* |
|
|
* Note how the same comparison operator is used. If you want to test for equality, use $x->equals($y). |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @return Integer < 0 if $this is less than $x; > 0 if $this is greater than $x, and 0 if they are equal. |
|
|
* @access public |
|
|
* @see equals() |
|
|
* @internal Could return $this->sub($x), but that's not as fast as what we do do. |
|
|
*/ |
|
|
function compare($y) |
|
|
{ |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
return gmp_cmp($this->value, $y->value); |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
return bccomp($this->value, $y->value); |
|
|
} |
|
|
|
|
|
$x = $this->_normalize($this->copy()); |
|
|
$y = $this->_normalize($y); |
|
|
|
|
|
if ( $x->is_negative != $y->is_negative ) { |
|
|
return ( !$x->is_negative && $y->is_negative ) ? 1 : -1; |
|
|
} |
|
|
|
|
|
$result = $x->is_negative ? -1 : 1; |
|
|
|
|
|
if ( count($x->value) != count($y->value) ) { |
|
|
return ( count($x->value) > count($y->value) ) ? $result : -$result; |
|
|
} |
|
|
|
|
|
for ($i = count($x->value) - 1; $i >= 0; $i--) { |
|
|
if ($x->value[$i] != $y->value[$i]) { |
|
|
return ( $x->value[$i] > $y->value[$i] ) ? $result : -$result; |
|
|
} |
|
|
} |
|
|
|
|
|
return 0; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Tests the equality of two numbers. |
|
|
* |
|
|
* If you need to see if one number is greater than or less than another number, use Math_BigInteger::compare() |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @return Boolean |
|
|
* @access public |
|
|
* @see compare() |
|
|
*/ |
|
|
function equals($x) |
|
|
{ |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
return gmp_cmp($this->value, $x->value) == 0; |
|
|
default: |
|
|
return $this->value == $x->value && $this->is_negative == $x->is_negative; |
|
|
} |
|
|
} |
|
|
|
|
|
/** |
|
|
* Set Precision |
|
|
* |
|
|
* Some bitwise operations give different results depending on the precision being used. Examples include left |
|
|
* shift, not, and rotates. |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @access public |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function setPrecision($bits) |
|
|
{ |
|
|
$this->precision = $bits; |
|
|
if ( MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_BCMATH ) { |
|
|
$this->bitmask = new Math_BigInteger(chr((1 << ($bits & 0x7)) - 1) . str_repeat(chr(0xFF), $bits >> 3), 256); |
|
|
} else { |
|
|
$this->bitmask = new Math_BigInteger(bcpow('2', $bits)); |
|
|
} |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical And |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @access public |
|
|
* @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat> |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function bitwise_and($x) |
|
|
{ |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = gmp_and($this->value, $x->value); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$left = $this->toBytes(); |
|
|
$right = $x->toBytes(); |
|
|
|
|
|
$length = max(strlen($left), strlen($right)); |
|
|
|
|
|
$left = str_pad($left, $length, chr(0), STR_PAD_LEFT); |
|
|
$right = str_pad($right, $length, chr(0), STR_PAD_LEFT); |
|
|
|
|
|
return $this->_normalize(new Math_BigInteger($left & $right, 256)); |
|
|
} |
|
|
|
|
|
$result = $this->copy(); |
|
|
|
|
|
$length = min(count($x->value), count($this->value)); |
|
|
|
|
|
$result->value = array_slice($result->value, 0, $length); |
|
|
|
|
|
for ($i = 0; $i < $length; $i++) { |
|
|
$result->value[$i] = $result->value[$i] & $x->value[$i]; |
|
|
} |
|
|
|
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Or |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @access public |
|
|
* @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat> |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function bitwise_or($x) |
|
|
{ |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = gmp_or($this->value, $x->value); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$left = $this->toBytes(); |
|
|
$right = $x->toBytes(); |
|
|
|
|
|
$length = max(strlen($left), strlen($right)); |
|
|
|
|
|
$left = str_pad($left, $length, chr(0), STR_PAD_LEFT); |
|
|
$right = str_pad($right, $length, chr(0), STR_PAD_LEFT); |
|
|
|
|
|
return $this->_normalize(new Math_BigInteger($left | $right, 256)); |
|
|
} |
|
|
|
|
|
$length = max(count($this->value), count($x->value)); |
|
|
$result = $this->copy(); |
|
|
$result->value = array_pad($result->value, 0, $length); |
|
|
$x->value = array_pad($x->value, 0, $length); |
|
|
|
|
|
for ($i = 0; $i < $length; $i++) { |
|
|
$result->value[$i] = $this->value[$i] | $x->value[$i]; |
|
|
} |
|
|
|
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Exclusive-Or |
|
|
* |
|
|
* @param Math_BigInteger $x |
|
|
* @access public |
|
|
* @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat> |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function bitwise_xor($x) |
|
|
{ |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
$temp = new Math_BigInteger(); |
|
|
$temp->value = gmp_xor($this->value, $x->value); |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$left = $this->toBytes(); |
|
|
$right = $x->toBytes(); |
|
|
|
|
|
$length = max(strlen($left), strlen($right)); |
|
|
|
|
|
$left = str_pad($left, $length, chr(0), STR_PAD_LEFT); |
|
|
$right = str_pad($right, $length, chr(0), STR_PAD_LEFT); |
|
|
|
|
|
return $this->_normalize(new Math_BigInteger($left ^ $right, 256)); |
|
|
} |
|
|
|
|
|
$length = max(count($this->value), count($x->value)); |
|
|
$result = $this->copy(); |
|
|
$result->value = array_pad($result->value, 0, $length); |
|
|
$x->value = array_pad($x->value, 0, $length); |
|
|
|
|
|
for ($i = 0; $i < $length; $i++) { |
|
|
$result->value[$i] = $this->value[$i] ^ $x->value[$i]; |
|
|
} |
|
|
|
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Not |
|
|
* |
|
|
* @access public |
|
|
* @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat> |
|
|
* @return Math_BigInteger |
|
|
*/ |
|
|
function bitwise_not() |
|
|
{ |
|
|
// calculuate "not" without regard to $this->precision |
|
|
// (will always result in a smaller number. ie. ~1 isn't 1111 1110 - it's 0) |
|
|
$temp = $this->toBytes(); |
|
|
$pre_msb = decbin(ord($temp[0])); |
|
|
$temp = ~$temp; |
|
|
$msb = decbin(ord($temp[0])); |
|
|
if (strlen($msb) == 8) { |
|
|
$msb = substr($msb, strpos($msb, '0')); |
|
|
} |
|
|
$temp[0] = chr(bindec($msb)); |
|
|
|
|
|
// see if we need to add extra leading 1's |
|
|
$current_bits = strlen($pre_msb) + 8 * strlen($temp) - 8; |
|
|
$new_bits = $this->precision - $current_bits; |
|
|
if ($new_bits <= 0) { |
|
|
return $this->_normalize(new Math_BigInteger($temp, 256)); |
|
|
} |
|
|
|
|
|
// generate as many leading 1's as we need to. |
|
|
$leading_ones = chr((1 << ($new_bits & 0x7)) - 1) . str_repeat(chr(0xFF), $new_bits >> 3); |
|
|
$this->_base256_lshift($leading_ones, $current_bits); |
|
|
|
|
|
$temp = str_pad($temp, ceil($this->bits / 8), chr(0), STR_PAD_LEFT); |
|
|
|
|
|
return $this->_normalize(new Math_BigInteger($leading_ones | $temp, 256)); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Right Shift |
|
|
* |
|
|
* Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift. |
|
|
* |
|
|
* @param Integer $shift |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
* @internal The only version that yields any speed increases is the internal version. |
|
|
*/ |
|
|
function bitwise_rightShift($shift) |
|
|
{ |
|
|
$temp = new Math_BigInteger(); |
|
|
|
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
static $two; |
|
|
|
|
|
if (empty($two)) { |
|
|
$two = gmp_init('2'); |
|
|
} |
|
|
|
|
|
$temp->value = gmp_div_q($this->value, gmp_pow($two, $shift)); |
|
|
|
|
|
break; |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$temp->value = bcdiv($this->value, bcpow('2', $shift)); |
|
|
|
|
|
break; |
|
|
default: // could just replace _lshift with this, but then all _lshift() calls would need to be rewritten |
|
|
// and I don't want to do that... |
|
|
$temp->value = $this->value; |
|
|
$temp->_rshift($shift); |
|
|
} |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Left Shift |
|
|
* |
|
|
* Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift. |
|
|
* |
|
|
* @param Integer $shift |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
* @internal The only version that yields any speed increases is the internal version. |
|
|
*/ |
|
|
function bitwise_leftShift($shift) |
|
|
{ |
|
|
$temp = new Math_BigInteger(); |
|
|
|
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
static $two; |
|
|
|
|
|
if (empty($two)) { |
|
|
$two = gmp_init('2'); |
|
|
} |
|
|
|
|
|
$temp->value = gmp_mul($this->value, gmp_pow($two, $shift)); |
|
|
|
|
|
break; |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
$temp->value = bcmul($this->value, bcpow('2', $shift)); |
|
|
|
|
|
break; |
|
|
default: // could just replace _rshift with this, but then all _lshift() calls would need to be rewritten |
|
|
// and I don't want to do that... |
|
|
$temp->value = $this->value; |
|
|
$temp->_lshift($shift); |
|
|
} |
|
|
|
|
|
return $this->_normalize($temp); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Left Rotate |
|
|
* |
|
|
* Instead of the top x bits being dropped they're appended to the shifted bit string. |
|
|
* |
|
|
* @param Integer $shift |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
*/ |
|
|
function bitwise_leftRotate($shift) |
|
|
{ |
|
|
$bits = $this->toBytes(); |
|
|
|
|
|
if ($this->precision > 0) { |
|
|
$precision = $this->precision; |
|
|
if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH ) { |
|
|
$mask = $this->bitmask->subtract(new Math_BigInteger(1)); |
|
|
$mask = $mask->toBytes(); |
|
|
} else { |
|
|
$mask = $this->bitmask->toBytes(); |
|
|
} |
|
|
} else { |
|
|
$temp = ord($bits[0]); |
|
|
for ($i = 0; $temp >> $i; $i++); |
|
|
$precision = 8 * strlen($bits) - 8 + $i; |
|
|
$mask = chr((1 << ($precision & 0x7)) - 1) . str_repeat(chr(0xFF), $precision >> 3); |
|
|
} |
|
|
|
|
|
if ($shift < 0) { |
|
|
$shift+= $precision; |
|
|
} |
|
|
$shift%= $precision; |
|
|
|
|
|
if (!$shift) { |
|
|
return $this->copy(); |
|
|
} |
|
|
|
|
|
$left = $this->bitwise_leftShift($shift); |
|
|
$left = $left->bitwise_and(new Math_BigInteger($mask, 256)); |
|
|
$right = $this->bitwise_rightShift($precision - $shift); |
|
|
$result = MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_BCMATH ? $left->bitwise_or($right) : $left->add($right); |
|
|
return $this->_normalize($result); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Right Rotate |
|
|
* |
|
|
* Instead of the bottom x bits being dropped they're prepended to the shifted bit string. |
|
|
* |
|
|
* @param Integer $shift |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
*/ |
|
|
function bitwise_rightRotate($shift) |
|
|
{ |
|
|
return $this->bitwise_leftRotate(-$shift); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Set random number generator function |
|
|
* |
|
|
* $generator should be the name of a random generating function whose first parameter is the minimum |
|
|
* value and whose second parameter is the maximum value. If this function needs to be seeded, it should |
|
|
* be seeded prior to calling Math_BigInteger::random() or Math_BigInteger::randomPrime() |
|
|
* |
|
|
* If the random generating function is not explicitly set, it'll be assumed to be mt_rand(). |
|
|
* |
|
|
* @see random() |
|
|
* @see randomPrime() |
|
|
* @param optional String $generator |
|
|
* @access public |
|
|
*/ |
|
|
function setRandomGenerator($generator) |
|
|
{ |
|
|
$this->generator = $generator; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Generate a random number |
|
|
* |
|
|
* @param optional Integer $min |
|
|
* @param optional Integer $max |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
*/ |
|
|
function random($min = false, $max = false) |
|
|
{ |
|
|
if ($min === false) { |
|
|
$min = new Math_BigInteger(0); |
|
|
} |
|
|
|
|
|
if ($max === false) { |
|
|
$max = new Math_BigInteger(0x7FFFFFFF); |
|
|
} |
|
|
|
|
|
$compare = $max->compare($min); |
|
|
|
|
|
if (!$compare) { |
|
|
return $this->_normalize($min); |
|
|
} else if ($compare < 0) { |
|
|
// if $min is bigger then $max, swap $min and $max |
|
|
$temp = $max; |
|
|
$max = $min; |
|
|
$min = $temp; |
|
|
} |
|
|
|
|
|
$generator = $this->generator; |
|
|
|
|
|
$max = $max->subtract($min); |
|
|
$max = ltrim($max->toBytes(), chr(0)); |
|
|
$size = strlen($max) - 1; |
|
|
$random = ''; |
|
|
|
|
|
$bytes = $size & 1; |
|
|
for ($i = 0; $i < $bytes; $i++) { |
|
|
$random.= chr($generator(0, 255)); |
|
|
} |
|
|
|
|
|
$blocks = $size >> 1; |
|
|
for ($i = 0; $i < $blocks; $i++) { |
|
|
// mt_rand(-2147483648, 0x7FFFFFFF) always produces -2147483648 on some systems |
|
|
$random.= pack('n', $generator(0, 0xFFFF)); |
|
|
} |
|
|
|
|
|
$temp = new Math_BigInteger($random, 256); |
|
|
if ($temp->compare(new Math_BigInteger(substr($max, 1), 256)) > 0) { |
|
|
$random = chr($generator(0, ord($max[0]) - 1)) . $random; |
|
|
} else { |
|
|
$random = chr($generator(0, ord($max[0]) )) . $random; |
|
|
} |
|
|
|
|
|
$random = new Math_BigInteger($random, 256); |
|
|
|
|
|
return $this->_normalize($random->add($min)); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Generate a random prime number. |
|
|
* |
|
|
* If there's not a prime within the given range, false will be returned. If more than $timeout seconds have elapsed, |
|
|
* give up and return false. |
|
|
* |
|
|
* @param optional Integer $min |
|
|
* @param optional Integer $max |
|
|
* @param optional Integer $timeout |
|
|
* @return Math_BigInteger |
|
|
* @access public |
|
|
* @internal See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=15 HAC 4.44}. |
|
|
*/ |
|
|
function randomPrime($min = false, $max = false, $timeout = false) |
|
|
{ |
|
|
// gmp_nextprime() requires PHP 5 >= 5.2.0 per <http://php.net/gmp-nextprime>. |
|
|
if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_GMP && function_exists('gmp_nextprime') ) { |
|
|
// we don't rely on Math_BigInteger::random()'s min / max when gmp_nextprime() is being used since this function |
|
|
// does its own checks on $max / $min when gmp_nextprime() is used. When gmp_nextprime() is not used, however, |
|
|
// the same $max / $min checks are not performed. |
|
|
if ($min === false) { |
|
|
$min = new Math_BigInteger(0); |
|
|
} |
|
|
|
|
|
if ($max === false) { |
|
|
$max = new Math_BigInteger(0x7FFFFFFF); |
|
|
} |
|
|
|
|
|
$compare = $max->compare($min); |
|
|
|
|
|
if (!$compare) { |
|
|
return $min; |
|
|
} else if ($compare < 0) { |
|
|
// if $min is bigger then $max, swap $min and $max |
|
|
$temp = $max; |
|
|
$max = $min; |
|
|
$min = $temp; |
|
|
} |
|
|
|
|
|
$x = $this->random($min, $max); |
|
|
|
|
|
$x->value = gmp_nextprime($x->value); |
|
|
|
|
|
if ($x->compare($max) <= 0) { |
|
|
return $x; |
|
|
} |
|
|
|
|
|
$x->value = gmp_nextprime($min->value); |
|
|
|
|
|
if ($x->compare($max) <= 0) { |
|
|
return $x; |
|
|
} |
|
|
|
|
|
return false; |
|
|
} |
|
|
|
|
|
$repeat1 = $repeat2 = array(); |
|
|
|
|
|
$one = new Math_BigInteger(1); |
|
|
$two = new Math_BigInteger(2); |
|
|
|
|
|
$start = time(); |
|
|
|
|
|
do { |
|
|
if ($timeout !== false && time() - $start > $timeout) { |
|
|
return false; |
|
|
} |
|
|
|
|
|
$x = $this->random($min, $max); |
|
|
if ($x->equals($two)) { |
|
|
return $x; |
|
|
} |
|
|
|
|
|
// make the number odd |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
gmp_setbit($x->value, 0); |
|
|
break; |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
if ($x->value[strlen($x->value) - 1] % 2 == 0) { |
|
|
$x = $x->add($one); |
|
|
} |
|
|
break; |
|
|
default: |
|
|
$x->value[0] |= 1; |
|
|
} |
|
|
|
|
|
// if we've seen this number twice before, assume there are no prime numbers within the given range |
|
|
if (in_array($x->value, $repeat1)) { |
|
|
if (in_array($x->value, $repeat2)) { |
|
|
return false; |
|
|
} else { |
|
|
$repeat2[] = $x->value; |
|
|
} |
|
|
} else { |
|
|
$repeat1[] = $x->value; |
|
|
} |
|
|
} while (!$x->isPrime()); |
|
|
|
|
|
return $x; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Checks a numer to see if it's prime |
|
|
* |
|
|
* Assuming the $t parameter is not set, this functoin has an error rate of 2**-80. The main motivation for the |
|
|
* $t parameter is distributability. Math_BigInteger::randomPrime() can be distributed accross multiple pageloads |
|
|
* on a website instead of just one. |
|
|
* |
|
|
* @param optional Integer $t |
|
|
* @return Boolean |
|
|
* @access public |
|
|
* @internal Uses the |
|
|
* {@link http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test Miller<EFBFBD>Rabin primality test}. See |
|
|
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=8 HAC 4.24}. |
|
|
*/ |
|
|
function isPrime($t = false) |
|
|
{ |
|
|
$length = strlen($this->toBytes()); |
|
|
|
|
|
if (!$t) { |
|
|
// see HAC 4.49 "Note (controlling the error probability)" |
|
|
if ($length >= 163) { $t = 2; } // floor(1300 / 8) |
|
|
else if ($length >= 106) { $t = 3; } // floor( 850 / 8) |
|
|
else if ($length >= 81 ) { $t = 4; } // floor( 650 / 8) |
|
|
else if ($length >= 68 ) { $t = 5; } // floor( 550 / 8) |
|
|
else if ($length >= 56 ) { $t = 6; } // floor( 450 / 8) |
|
|
else if ($length >= 50 ) { $t = 7; } // floor( 400 / 8) |
|
|
else if ($length >= 43 ) { $t = 8; } // floor( 350 / 8) |
|
|
else if ($length >= 37 ) { $t = 9; } // floor( 300 / 8) |
|
|
else if ($length >= 31 ) { $t = 12; } // floor( 250 / 8) |
|
|
else if ($length >= 25 ) { $t = 15; } // floor( 200 / 8) |
|
|
else if ($length >= 18 ) { $t = 18; } // floor( 150 / 8) |
|
|
else { $t = 27; } |
|
|
} |
|
|
|
|
|
// ie. gmp_testbit($this, 0) |
|
|
// ie. isEven() or !isOdd() |
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
return gmp_prob_prime($this->value, $t) != 0; |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
if ($this->value == '2') { |
|
|
return true; |
|
|
} |
|
|
if ($this->value[strlen($this->value) - 1] % 2 == 0) { |
|
|
return false; |
|
|
} |
|
|
break; |
|
|
default: |
|
|
if ($this->value == array(2)) { |
|
|
return true; |
|
|
} |
|
|
if (~$this->value[0] & 1) { |
|
|
return false; |
|
|
} |
|
|
} |
|
|
|
|
|
static $primes, $zero, $one, $two; |
|
|
|
|
|
if (!isset($primes)) { |
|
|
$primes = array( |
|
|
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, |
|
|
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, |
|
|
139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, |
|
|
229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, |
|
|
317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, |
|
|
421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, |
|
|
521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, |
|
|
619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, |
|
|
733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, |
|
|
839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, |
|
|
953, 967, 971, 977, 983, 991, 997 |
|
|
); |
|
|
|
|
|
for ($i = 0; $i < count($primes); $i++) { |
|
|
$primes[$i] = new Math_BigInteger($primes[$i]); |
|
|
} |
|
|
|
|
|
$zero = new Math_BigInteger(); |
|
|
$one = new Math_BigInteger(1); |
|
|
$two = new Math_BigInteger(2); |
|
|
} |
|
|
|
|
|
// see HAC 4.4.1 "Random search for probable primes" |
|
|
for ($i = 0; $i < count($primes); $i++) { |
|
|
list(, $r) = $this->divide($primes[$i]); |
|
|
if ($r->equals($zero)) { |
|
|
return false; |
|
|
} |
|
|
} |
|
|
|
|
|
$n = $this->copy(); |
|
|
$n_1 = $n->subtract($one); |
|
|
$n_2 = $n->subtract($two); |
|
|
|
|
|
$r = $n_1->copy(); |
|
|
// ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s)); |
|
|
if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH ) { |
|
|
$s = 0; |
|
|
while ($r->value[strlen($r->value) - 1] % 2 == 0) { |
|
|
$r->value = bcdiv($r->value, 2); |
|
|
$s++; |
|
|
} |
|
|
} else { |
|
|
for ($i = 0; $i < count($r->value); $i++) { |
|
|
$temp = ~$r->value[$i] & 0xFFFFFF; |
|
|
for ($j = 1; ($temp >> $j) & 1; $j++); |
|
|
if ($j != 25) { |
|
|
break; |
|
|
} |
|
|
} |
|
|
$s = 26 * $i + $j - 1; |
|
|
$r->_rshift($s); |
|
|
} |
|
|
|
|
|
for ($i = 0; $i < $t; $i++) { |
|
|
$a = new Math_BigInteger(); |
|
|
$a = $a->random($two, $n_2); |
|
|
$y = $a->modPow($r, $n); |
|
|
|
|
|
if (!$y->equals($one) && !$y->equals($n_1)) { |
|
|
for ($j = 1; $j < $s && !$y->equals($n_1); $j++) { |
|
|
$y = $y->modPow($two, $n); |
|
|
if ($y->equals($one)) { |
|
|
return false; |
|
|
} |
|
|
} |
|
|
|
|
|
if (!$y->equals($n_1)) { |
|
|
return false; |
|
|
} |
|
|
} |
|
|
} |
|
|
return true; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Left Shift |
|
|
* |
|
|
* Shifts BigInteger's by $shift bits. |
|
|
* |
|
|
* @param Integer $shift |
|
|
* @access private |
|
|
*/ |
|
|
function _lshift($shift) |
|
|
{ |
|
|
if ( $shift == 0 ) { |
|
|
return; |
|
|
} |
|
|
|
|
|
$num_digits = floor($shift / 26); |
|
|
$shift %= 26; |
|
|
$shift = 1 << $shift; |
|
|
|
|
|
$carry = 0; |
|
|
|
|
|
for ($i = 0; $i < count($this->value); $i++) { |
|
|
$temp = $this->value[$i] * $shift + $carry; |
|
|
$carry = floor($temp / 0x4000000); |
|
|
$this->value[$i] = $temp - $carry * 0x4000000; |
|
|
} |
|
|
|
|
|
if ( $carry ) { |
|
|
$this->value[] = $carry; |
|
|
} |
|
|
|
|
|
while ($num_digits--) { |
|
|
array_unshift($this->value, 0); |
|
|
} |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Right Shift |
|
|
* |
|
|
* Shifts BigInteger's by $shift bits. |
|
|
* |
|
|
* @param Integer $shift |
|
|
* @access private |
|
|
*/ |
|
|
function _rshift($shift) |
|
|
{ |
|
|
if ($shift == 0) { |
|
|
return; |
|
|
} |
|
|
|
|
|
$num_digits = floor($shift / 26); |
|
|
$shift %= 26; |
|
|
$carry_shift = 26 - $shift; |
|
|
$carry_mask = (1 << $shift) - 1; |
|
|
|
|
|
if ( $num_digits ) { |
|
|
$this->value = array_slice($this->value, $num_digits); |
|
|
} |
|
|
|
|
|
$carry = 0; |
|
|
|
|
|
for ($i = count($this->value) - 1; $i >= 0; $i--) { |
|
|
$temp = $this->value[$i] >> $shift | $carry; |
|
|
$carry = ($this->value[$i] & $carry_mask) << $carry_shift; |
|
|
$this->value[$i] = $temp; |
|
|
} |
|
|
} |
|
|
|
|
|
/** |
|
|
* Normalize |
|
|
* |
|
|
* Deletes leading zeros and truncates (if necessary) to maintain the appropriate precision |
|
|
* |
|
|
* @return Math_BigInteger |
|
|
* @access private |
|
|
*/ |
|
|
function _normalize($result) |
|
|
{ |
|
|
$result->precision = $this->precision; |
|
|
$result->bitmask = $this->bitmask; |
|
|
|
|
|
switch ( MATH_BIGINTEGER_MODE ) { |
|
|
case MATH_BIGINTEGER_MODE_GMP: |
|
|
if (!empty($result->bitmask->value)) { |
|
|
$result->value = gmp_and($result->value, $result->bitmask->value); |
|
|
} |
|
|
|
|
|
return $result; |
|
|
case MATH_BIGINTEGER_MODE_BCMATH: |
|
|
if (!empty($result->bitmask->value)) { |
|
|
$result->value = bcmod($result->value, $result->bitmask->value); |
|
|
} |
|
|
|
|
|
return $result; |
|
|
} |
|
|
|
|
|
if ( !count($result->value) ) { |
|
|
return $result; |
|
|
} |
|
|
|
|
|
for ($i = count($result->value) - 1; $i >= 0; $i--) { |
|
|
if ( $result->value[$i] ) { |
|
|
break; |
|
|
} |
|
|
unset($result->value[$i]); |
|
|
} |
|
|
|
|
|
if (!empty($result->bitmask->value)) { |
|
|
$length = min(count($result->value), count($this->bitmask->value)); |
|
|
$result->value = array_slice($result->value, 0, $length); |
|
|
|
|
|
for ($i = 0; $i < $length; $i++) { |
|
|
$result->value[$i] = $result->value[$i] & $this->bitmask->value[$i]; |
|
|
} |
|
|
} |
|
|
|
|
|
return $result; |
|
|
} |
|
|
|
|
|
/** |
|
|
* Array Repeat |
|
|
* |
|
|
* @param $input Array |
|
|
* @param $multiplier mixed |
|
|
* @return Array |
|
|
* @access private |
|
|
*/ |
|
|
function _array_repeat($input, $multiplier) |
|
|
{ |
|
|
return ($multiplier) ? array_fill(0, $multiplier, $input) : array(); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Left Shift |
|
|
* |
|
|
* Shifts binary strings $shift bits, essentially multiplying by 2**$shift. |
|
|
* |
|
|
* @param $x String |
|
|
* @param $shift Integer |
|
|
* @return String |
|
|
* @access private |
|
|
*/ |
|
|
function _base256_lshift(&$x, $shift) |
|
|
{ |
|
|
if ($shift == 0) { |
|
|
return; |
|
|
} |
|
|
|
|
|
$num_bytes = $shift >> 3; // eg. floor($shift/8) |
|
|
$shift &= 7; // eg. $shift % 8 |
|
|
|
|
|
$carry = 0; |
|
|
for ($i = strlen($x) - 1; $i >= 0; $i--) { |
|
|
$temp = ord($x[$i]) << $shift | $carry; |
|
|
$x[$i] = chr($temp); |
|
|
$carry = $temp >> 8; |
|
|
} |
|
|
$carry = ($carry != 0) ? chr($carry) : ''; |
|
|
$x = $carry . $x . str_repeat(chr(0), $num_bytes); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Logical Right Shift |
|
|
* |
|
|
* Shifts binary strings $shift bits, essentially dividing by 2**$shift and returning the remainder. |
|
|
* |
|
|
* @param $x String |
|
|
* @param $shift Integer |
|
|
* @return String |
|
|
* @access private |
|
|
*/ |
|
|
function _base256_rshift(&$x, $shift) |
|
|
{ |
|
|
if ($shift == 0) { |
|
|
$x = ltrim($x, chr(0)); |
|
|
return ''; |
|
|
} |
|
|
|
|
|
$num_bytes = $shift >> 3; // eg. floor($shift/8) |
|
|
$shift &= 7; // eg. $shift % 8 |
|
|
|
|
|
$remainder = ''; |
|
|
if ($num_bytes) { |
|
|
$start = $num_bytes > strlen($x) ? -strlen($x) : -$num_bytes; |
|
|
$remainder = substr($x, $start); |
|
|
$x = substr($x, 0, -$num_bytes); |
|
|
} |
|
|
|
|
|
$carry = 0; |
|
|
$carry_shift = 8 - $shift; |
|
|
for ($i = 0; $i < strlen($x); $i++) { |
|
|
$temp = (ord($x[$i]) >> $shift) | $carry; |
|
|
$carry = (ord($x[$i]) << $carry_shift) & 0xFF; |
|
|
$x[$i] = chr($temp); |
|
|
} |
|
|
$x = ltrim($x, chr(0)); |
|
|
|
|
|
$remainder = chr($carry >> $carry_shift) . $remainder; |
|
|
|
|
|
return ltrim($remainder, chr(0)); |
|
|
} |
|
|
|
|
|
// one quirk about how the following functions are implemented is that PHP defines N to be an unsigned long |
|
|
// at 32-bits, while java's longs are 64-bits. |
|
|
|
|
|
/** |
|
|
* Converts 32-bit integers to bytes. |
|
|
* |
|
|
* @param Integer $x |
|
|
* @return String |
|
|
* @access private |
|
|
*/ |
|
|
function _int2bytes($x) |
|
|
{ |
|
|
return ltrim(pack('N', $x), chr(0)); |
|
|
} |
|
|
|
|
|
/** |
|
|
* Converts bytes to 32-bit integers |
|
|
* |
|
|
* @param String $x |
|
|
* @return Integer |
|
|
* @access private |
|
|
*/ |
|
|
function _bytes2int($x) |
|
|
{ |
|
|
$temp = unpack('Nint', str_pad($x, 4, chr(0), STR_PAD_LEFT)); |
|
|
return $temp['int']; |
|
|
} |
|
|
} |