Subversion Repositories oidplus

<?php

/**

 * GMP BigInteger Engine

 *

 * PHP version 5 and 7

 *

 * @category  Math

 * @package   BigInteger

 * @author    Jim Wigginton <terrafrost@php.net>

 * @copyright 2017 Jim Wigginton

 * @license   http://www.opensource.org/licenses/mit-license.html  MIT License

 * @link      http://pear.php.net/package/Math_BigInteger

 */

namespace phpseclib3\Math\BigInteger\Engines;

use phpseclib3\Exception\BadConfigurationException;

/**

 * GMP Engine.

 *

 * @package GMP

 * @author  Jim Wigginton <terrafrost@php.net>

 * @access  public

 */

class GMP extends Engine

{

    /**

     * Can Bitwise operations be done fast?

     *

     * @see parent::bitwise_leftRotate()

     * @see parent::bitwise_rightRotate()

     * @access protected

     */

    const FAST_BITWISE = true;

    /**

     * Engine Directory

     *

     * @see parent::setModExpEngine

     * @access protected

     */

    const ENGINE_DIR = 'GMP';

    /**

     * Test for engine validity

     *

     * @return bool

     * @see parent::__construct()

     */

    public static function isValidEngine()

    {

        return extension_loaded('gmp');

    }

    /**

     * Default constructor

     *

     * @param mixed $x integer Base-10 number or base-$base number if $base set.

     * @param int $base

     * @see parent::__construct()

     */

    public function __construct($x = 0, $base = 10)

    {

        if (!isset(static::$isValidEngine[static::class])) {

            static::$isValidEngine[static::class] = self::isValidEngine();

        }

        if (!static::$isValidEngine[static::class]) {

            throw new BadConfigurationException('GMP is not setup correctly on this system');

        }

        if ($x instanceof \GMP) {

            $this->value = $x;

            return;

        }

        $this->value = gmp_init(0);

        parent::__construct($x, $base);

    }

    /**

     * Initialize a GMP BigInteger Engine instance

     *

     * @param int $base

     * @see parent::__construct()

     */

    protected function initialize($base)

    {

        switch (abs($base)) {

            case 256:

                $this->value = gmp_import($this->value);

                if ($this->is_negative) {

                    $this->value = -$this->value;

                }

                break;

            case 16:

                $temp = $this->is_negative ? '-0x' . $this->value : '0x' . $this->value;

                $this->value = gmp_init($temp);

                break;

            case 10:

                $this->value = gmp_init(isset($this->value) ? $this->value : '0');

        }

    }

    /**

     * Converts a BigInteger to a base-10 number.

     *

     * @return string

     */

    public function toString()

    {

        return (string)$this->value;

    }

    /**

     * 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.

     *

     * @param bool $twos_compliment

     * @return string

     */

    public function toBits($twos_compliment = false)

    {

        $hex = $this->toHex($twos_compliment);

        $bits = gmp_strval(gmp_init($hex, 16), 2);

        if ($this->precision > 0) {

            $bits = substr($bits, -$this->precision);

        }

        if ($twos_compliment && $this->compare(new static()) > 0 && $this->precision <= 0) {

            return '0' . $bits;

        }

        return $bits;

    }

    /**

     * Converts a BigInteger to a byte string (eg. base-256).

     *

     * @param bool $twos_compliment

     * @return string

     */

    public function toBytes($twos_compliment = false)

    {

        if ($twos_compliment) {

            return $this->toBytesHelper();

        }

        if (gmp_cmp($this->value, gmp_init(0)) == 0) {

            return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';

        }

        $temp = gmp_export($this->value);

        return $this->precision > 0 ?

            substr(str_pad($temp, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) :

            ltrim($temp, chr(0));

    }

    /**

     * Adds two BigIntegers.

     *

     * @param GMP $y

     * @return GMP

     */

    public function add(GMP $y)

    {

        $temp = new self();

        $temp->value = $this->value + $y->value;

        return $this->normalize($temp);

    }

    /**

     * Subtracts two BigIntegers.

     *

     * @param GMP $y

     * @return GMP

     */

    public function subtract(GMP $y)

    {

        $temp = new self();

        $temp->value = $this->value - $y->value;

        return $this->normalize($temp);

    }

    /**

     * Multiplies two BigIntegers.

     *

     * @param GMP $x

     * @return GMP

     */

    public function multiply(GMP $x)

    {

        $temp = new self();

        $temp->value = $this->value * $x->value;

        return $this->normalize($temp);

    }

    /**

     * 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).

     *

     * @param GMP $y

     * @return array{GMP, GMP}

     */

    public function divide(GMP $y)

    {

        $quotient = new self();

        $remainder = new self();

        list($quotient->value, $remainder->value) = gmp_div_qr($this->value, $y->value);

        if (gmp_sign($remainder->value) < 0) {

            $remainder->value = $remainder->value + gmp_abs($y->value);

        }

        return [$this->normalize($quotient), $this->normalize($remainder)];

    }

    /**

     * 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).

     *

     * {@internal Could return $this->subtract($x), but that's not as fast as what we do do.}

     *

     * @param GMP $y

     * @return int in case < 0 if $this is less than $y; > 0 if $this is greater than $y, and 0 if they are equal.

     * @access public

     * @see self::equals()

     */

    public function compare(GMP $y)

    {

        $r = gmp_cmp($this->value, $y->value);

        if ($r < -1) {

            $r = -1;

        }

        if ($r > 1) {

            $r = 1;

        }

        return $r;

    }

    /**

     * Tests the equality of two numbers.

     *

     * If you need to see if one number is greater than or less than another number, use BigInteger::compare()

     *

     * @param GMP $x

     * @return bool

     */

    public function equals(GMP $x)

    {

        return $this->value == $x->value;

    }

    /**

     * Calculates modular inverses.

     *

     * Say you have (30 mod 17 * x mod 17) mod 17 == 1.  x can be found using modular inverses.

     *

     * @param GMP $n

     * @return false|GMP

     */

    public function modInverse(GMP $n)

    {

        $temp = new self();

        $temp->value = gmp_invert($this->value, $n->value);

        return $temp->value === false ? false : $this->normalize($temp);

    }

    /**

     * Calculates the greatest common divisor and Bezout's identity.

     *

     * Say you have 693 and 609.  The GCD is 21.  Bezout'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 dependent upon which mode is in use.  See

     * {@link http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity Bezout's identity - Wikipedia} for more information.

     *

     * @param GMP $n

     * @return GMP[]

     */

    public function extendedGCD(GMP $n)

    {

        extract(gmp_gcdext($this->value, $n->value));

        return [

            'gcd' => $this->normalize(new self($g)),

            'x' => $this->normalize(new self($s)),

            'y' => $this->normalize(new self($t))

        ];

    }

    /**

     * Calculates the greatest common divisor

     *

     * Say you have 693 and 609.  The GCD is 21.

     *

     * @param GMP $n

     * @return GMP

     */

    public function gcd(GMP $n)

    {

        $r = gmp_gcd($this->value, $n->value);

        return $this->normalize(new self($r));

    }

    /**

     * Absolute value.

     *

     * @return GMP

     * @access public

     */

    public function abs()

    {

        $temp = new self();

        $temp->value = gmp_abs($this->value);

        return $temp;

    }

    /**

     * Logical And

     *

     * @param GMP $x

     * @return GMP

     */

    public function bitwise_and(GMP $x)

    {

        $temp = new self();

        $temp->value = $this->value & $x->value;

        return $this->normalize($temp);

    }

    /**

     * Logical Or

     *

     * @param GMP $x

     * @return GMP

     */

    public function bitwise_or(GMP $x)

    {

        $temp = new self();

        $temp->value = $this->value | $x->value;

        return $this->normalize($temp);

    }

    /**

     * Logical Exclusive Or

     *

     * @param GMP $x

     * @return GMP

     */

    public function bitwise_xor(GMP $x)

    {

        $temp = new self();

        $temp->value = $this->value ^ $x->value;

        return $this->normalize($temp);

    }

    /**

     * Logical Right Shift

     *

     * Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.

     *

     * @param int $shift

     * @return GMP

     */

    public function bitwise_rightShift($shift)

    {

        // 0xFFFFFFFF >> 2 == -1 (on 32-bit systems)

        // gmp_init('0xFFFFFFFF') >> 2 == gmp_init('0x3FFFFFFF')

        $temp = new self();

        $temp->value = $this->value >> $shift;

        return $this->normalize($temp);

    }

    /**

     * Logical Left Shift

     *

     * Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.

     *

     * @param int $shift

     * @return GMP

     */

    public function bitwise_leftShift($shift)

    {

        $temp = new self();

        $temp->value = $this->value << $shift;

        return $this->normalize($temp);

    }

    /**

     * Performs modular exponentiation.

     *

     * @param GMP $e

     * @param GMP $n

     * @return GMP

     */

    public function modPow(GMP $e, GMP $n)

    {

        return $this->powModOuter($e, $n);

    }

    /**

     * Performs modular exponentiation.

     *

     * Alias for modPow().

     *

     * @param GMP $e

     * @param GMP $n

     * @return GMP

     */

    public function powMod(GMP $e, GMP $n)

    {

        return $this->powModOuter($e, $n);

    }

    /**

     * Performs modular exponentiation.

     *

     * @param GMP $e

     * @param GMP $n

     * @return GMP

     */

    protected function powModInner(GMP $e, GMP $n)

    {

        $class = static::$modexpEngine[static::class];

        return $class::powModHelper($this, $e, $n);

    }

    /**

     * Normalize

     *

     * Removes leading zeros and truncates (if necessary) to maintain the appropriate precision

     *

     * @param GMP $result

     * @return GMP

     */

    protected function normalize(GMP $result)

    {

        $result->precision = $this->precision;

        $result->bitmask = $this->bitmask;

        if ($result->bitmask !== false) {

            $flip = $result->value < 0;

            if ($flip) {

                $result->value = -$result->value;

            }

            $result->value = $result->value & $result->bitmask->value;

            if ($flip) {

                $result->value = -$result->value;

            }

        }

        return $result;

    }

    /**

     * Performs some post-processing for randomRangePrime

     *

     * @param Engine $x

     * @param Engine $min

     * @param Engine $max

     * @return GMP

     */

    protected static function randomRangePrimeInner(Engine $x, Engine $min, Engine $max)

    {

        $p = gmp_nextprime($x->value);

        if ($p <= $max->value) {

            return new self($p);

        }

        if ($min->value != $x->value) {

            $x = new self($x->value - 1);

        }

        return self::randomRangePrime($min, $x);

    }

    /**

     * Generate a random prime number between a range

     *

     * If there's not a prime within the given range, false will be returned.

     *

     * @param GMP $min

     * @param GMP $max

     * @return false|GMP

     */

    public static function randomRangePrime(GMP $min, GMP $max)

    {

        return self::randomRangePrimeOuter($min, $max);

    }

    /**

     * Generate a random number between a range

     *

     * Returns a random number between $min and $max where $min and $max

     * can be defined using one of the two methods:

     *

     * BigInteger::randomRange($min, $max)

     * BigInteger::randomRange($max, $min)

     *

     * @param GMP $min

     * @param GMP $max

     * @return GMP

     */

    public static function randomRange(GMP $min, GMP $max)

    {

        return self::randomRangeHelper($min, $max);

    }

    /**

     * Make the current number odd

     *

     * If the current number is odd it'll be unchanged.  If it's even, one will be added to it.

     *

     * @see self::randomPrime()

     */

    protected function make_odd()

    {

        gmp_setbit($this->value, 0);

    }

    /**

     * Tests Primality

     *

     * @param int $t

     * @return bool

     */

    protected function testPrimality($t)

    {

        return gmp_prob_prime($this->value, $t) != 0;

    }

    /**

     * Calculates the nth root of a biginteger.

     *

     * Returns the nth root of a positive biginteger, where n defaults to 2

     *

     * @param int $n

     * @return GMP

     */

    protected function rootInner($n)

    {

        $root = new self();

        $root->value = gmp_root($this->value, $n);

        return $this->normalize($root);

    }

    /**

     * Performs exponentiation.

     *

     * @param GMP $n

     * @return GMP

     */

    public function pow(GMP $n)

    {

        $temp = new self();

        $temp->value = $this->value ** $n->value;

        return $this->normalize($temp);

    }

    /**

     * Return the minimum BigInteger between an arbitrary number of BigIntegers.

     *

     * @param GMP ...$nums

     * @return GMP

     */

    public static function min(GMP ...$nums)

    {

        return self::minHelper($nums);

    }

    /**

     * Return the maximum BigInteger between an arbitrary number of BigIntegers.

     *

     * @param GMP ...$nums

     * @return GMP

     */

    public static function max(GMP ...$nums)

    {

        return self::maxHelper($nums);

    }

    /**

     * Tests BigInteger to see if it is between two integers, inclusive

     *

     * @param GMP $min

     * @param GMP $max

     * @return bool

     */

    public function between(GMP $min, GMP $max)

    {

        return $this->compare($min) >= 0 && $this->compare($max) <= 0;

    }

    /**

     * Create Recurring Modulo Function

     *

     * Sometimes it may be desirable to do repeated modulos with the same number outside of

     * modular exponentiation

     *

     * @return callable

     */

    public function createRecurringModuloFunction()

    {

        $temp = $this->value;

        return function (GMP $x) use ($temp) {

            return new GMP($x->value % $temp);

        };

    }

    /**

     * Scan for 1 and right shift by that amount

     *

     * ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));

     *

     * @param GMP $r

     * @return int

     */

    public static function scan1divide(GMP $r)

    {

        $s = gmp_scan1($r->value, 0);

        $r->value >>= $s;

        return $s;

    }

    /**

     * Is Odd?

     *

     * @return bool

     */

    public function isOdd()

    {

        return gmp_testbit($this->value, 0);

    }

    /**

     * Tests if a bit is set

     *

     * @return bool

     */

    public function testBit($x)

    {

        return gmp_testbit($this->value, $x);

    }

    /**

     * Is Negative?

     *

     * @return bool

     */

    public function isNegative()

    {

        return gmp_sign($this->value) == -1;

    }

    /**

     * Negate

     *

     * Given $k, returns -$k

     *

     * @return GMP

     */

    public function negate()

    {

        $temp = clone $this;

        $temp->value = -$this->value;

        return $temp;

    }

}