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<?php

/**

 * PHP Barrett Modular Exponentiation 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\PHP\Reductions;

use phpseclib3\Math\BigInteger\Engines\PHP;

use phpseclib3\Math\BigInteger\Engines\PHP\Base;

/**

 * PHP Barrett Modular Exponentiation Engine

 *

 * @package PHP

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

 * @access  public

 */

abstract class Barrett extends Base

{

    /**

     * 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).

     *

     * Employs "folding", as described at

     * {@link http://www.cosic.esat.kuleuven.be/publications/thesis-149.pdf#page=66 thesis-149.pdf#page=66}.  To quote from

     * it, "the idea [behind folding] is to find a value x' such that x (mod m) = x' (mod m), with x' being smaller than x."

     *

     * Unfortunately, the "Barrett Reduction with Folding" algorithm described in thesis-149.pdf is not, as written, all that

     * usable on account of (1) its not using reasonable radix points as discussed in

     * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=162 MPM 6.2.2} and (2) the fact that, even with reasonable

     * radix points, it only works when there are an even number of digits in the denominator.  The reason for (2) is that

     * (x >> 1) + (x >> 1) != x / 2 + x / 2.  If x is even, they're the same, but if x is odd, they're not.  See the in-line

     * comments for details.

     *

     * @param array $n

     * @param array $m

     * @param class-string<PHP> $class

     * @return array

     */

    protected static function reduce(array $n, array $m, $class)

    {

        static $cache = [

            self::VARIABLE => [],

            self::DATA => []

        ];

        $m_length = count($m);

        // if (self::compareHelper($n, $static::square($m)) >= 0) {

        if (count($n) > 2 * $m_length) {

            $lhs = new $class();

            $rhs = new $class();

            $lhs->value = $n;

            $rhs->value = $m;

            list(, $temp) = $lhs->divide($rhs);

            return $temp->value;

        }

        // if (m.length >> 1) + 2 <= m.length then m is too small and n can't be reduced

        if ($m_length < 5) {

            return self::regularBarrett($n, $m, $class);

        }

        // n = 2 * m.length

        if (($key = array_search($m, $cache[self::VARIABLE])) === false) {

            $key = count($cache[self::VARIABLE]);

            $cache[self::VARIABLE][] = $m;

            $lhs = new $class();

            $lhs_value = &$lhs->value;

            $lhs_value = self::array_repeat(0, $m_length + ($m_length >> 1));

            $lhs_value[] = 1;

            $rhs = new $class();

            $rhs->value = $m;

            list($u, $m1) = $lhs->divide($rhs);

            $u = $u->value;

            $m1 = $m1->value;

            $cache[self::DATA][] = [

                'u' => $u, // m.length >> 1 (technically (m.length >> 1) + 1)

                'm1' => $m1 // m.length

            ];

        } else {

            extract($cache[self::DATA][$key]);

        }

        $cutoff = $m_length + ($m_length >> 1);

        $lsd = array_slice($n, 0, $cutoff); // m.length + (m.length >> 1)

        $msd = array_slice($n, $cutoff);    // m.length >> 1

        $lsd = self::trim($lsd);

        $temp = $class::multiplyHelper($msd, false, $m1, false); // m.length + (m.length >> 1)

        $n = $class::addHelper($lsd, false, $temp[self::VALUE], false); // m.length + (m.length >> 1) + 1 (so basically we're adding two same length numbers)

        //if ($m_length & 1) {

        //    return self::regularBarrett($n[self::VALUE], $m, $class);

        //}

        // (m.length + (m.length >> 1) + 1) - (m.length - 1) == (m.length >> 1) + 2

        $temp = array_slice($n[self::VALUE], $m_length - 1);

        // if even: ((m.length >> 1) + 2) + (m.length >> 1) == m.length + 2

        // if odd:  ((m.length >> 1) + 2) + (m.length >> 1) == (m.length - 1) + 2 == m.length + 1

        $temp = $class::multiplyHelper($temp, false, $u, false);

        // if even: (m.length + 2) - ((m.length >> 1) + 1) = m.length - (m.length >> 1) + 1

        // if odd:  (m.length + 1) - ((m.length >> 1) + 1) = m.length - (m.length >> 1)

        $temp = array_slice($temp[self::VALUE], ($m_length >> 1) + 1);

        // if even: (m.length - (m.length >> 1) + 1) + m.length = 2 * m.length - (m.length >> 1) + 1

        // if odd:  (m.length - (m.length >> 1)) + m.length     = 2 * m.length - (m.length >> 1)

        $temp = $class::multiplyHelper($temp, false, $m, false);

        // at this point, if m had an odd number of digits, we'd be subtracting a 2 * m.length - (m.length >> 1) digit

        // number from a m.length + (m.length >> 1) + 1 digit number.  ie. there'd be an extra digit and the while loop

        // following this comment would loop a lot (hence our calling _regularBarrett() in that situation).

        $result = $class::subtractHelper($n[self::VALUE], false, $temp[self::VALUE], false);

        while (self::compareHelper($result[self::VALUE], $result[self::SIGN], $m, false) >= 0) {

            $result = $class::subtractHelper($result[self::VALUE], $result[self::SIGN], $m, false);

        }

        return $result[self::VALUE];

    }

    /**

     * (Regular) Barrett Modular Reduction

     *

     * For numbers with more than four digits BigInteger::_barrett() is faster.  The difference between that and this

     * is that this function does not fold the denominator into a smaller form.

     *

     * @param array $x

     * @param array $n

     * @param string $class

     * @return array

     */

    private static function regularBarrett(array $x, array $n, $class)

    {

        static $cache = [

            self::VARIABLE => [],

            self::DATA => []

        ];

        $n_length = count($n);

        if (count($x) > 2 * $n_length) {

            $lhs = new $class();

            $rhs = new $class();

            $lhs->value = $x;

            $rhs->value = $n;

            list(, $temp) = $lhs->divide($rhs);

            return $temp->value;

        }

        if (($key = array_search($n, $cache[self::VARIABLE])) === false) {

            $key = count($cache[self::VARIABLE]);

            $cache[self::VARIABLE][] = $n;

            $lhs = new $class();

            $lhs_value = &$lhs->value;

            $lhs_value = self::array_repeat(0, 2 * $n_length);

            $lhs_value[] = 1;

            $rhs = new $class();

            $rhs->value = $n;

            list($temp, ) = $lhs->divide($rhs); // m.length

            $cache[self::DATA][] = $temp->value;

        }

        // 2 * m.length - (m.length - 1) = m.length + 1

        $temp = array_slice($x, $n_length - 1);

        // (m.length + 1) + m.length = 2 * m.length + 1

        $temp = $class::multiplyHelper($temp, false, $cache[self::DATA][$key], false);

        // (2 * m.length + 1) - (m.length - 1) = m.length + 2

        $temp = array_slice($temp[self::VALUE], $n_length + 1);

        // m.length + 1

        $result = array_slice($x, 0, $n_length + 1);

        // m.length + 1

        $temp = self::multiplyLower($temp, false, $n, false, $n_length + 1, $class);

        // $temp == array_slice($class::regularMultiply($temp, false, $n, false)->value, 0, $n_length + 1)

        if (self::compareHelper($result, false, $temp[self::VALUE], $temp[self::SIGN]) < 0) {

            $corrector_value = self::array_repeat(0, $n_length + 1);

            $corrector_value[count($corrector_value)] = 1;

            $result = $class::addHelper($result, false, $corrector_value, false);

            $result = $result[self::VALUE];

        }

        // at this point, we're subtracting a number with m.length + 1 digits from another number with m.length + 1 digits

        $result = $class::subtractHelper($result, false, $temp[self::VALUE], $temp[self::SIGN]);

        while (self::compareHelper($result[self::VALUE], $result[self::SIGN], $n, false) > 0) {

            $result = $class::subtractHelper($result[self::VALUE], $result[self::SIGN], $n, false);

        }

        return $result[self::VALUE];

    }

    /**

     * 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 self::regularBarrett()

     * @param array $x_value

     * @param bool $x_negative

     * @param array $y_value

     * @param bool $y_negative

     * @param int $stop

     * @param string $class

     * @return array

     */

    private static function multiplyLower(array $x_value, $x_negative, array $y_value, $y_negative, $stop, $class)

    {

        $x_length = count($x_value);

        $y_length = count($y_value);

        if (!$x_length || !$y_length) { // a 0 is being multiplied

            return [

                self::VALUE => [],

                self::SIGN => false

            ];

        }

        if ($x_length < $y_length) {

            $temp = $x_value;

            $x_value = $y_value;

            $y_value = $temp;

            $x_length = count($x_value);

            $y_length = count($y_value);

        }

        $product_value = self::array_repeat(0, $x_length + $y_length);

        // the following for loop could be removed if the for loop following it

        // (the one with nested for loops) initially set $i to 0, but

        // doing so would also make the result in one set of unnecessary adds,

        // since on the outermost loops first pass, $product->value[$k] is going

        // to always be 0

        $carry = 0;

        for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0, $k = $i

            $temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0

            $carry = $class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);

            $product_value[$j] = (int) ($temp - $class::BASE_FULL * $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 < $y_length; ++$i) {

            $carry = 0;

            for ($j = 0, $k = $i; $j < $x_length && $k < $stop; ++$j, ++$k) {

                $temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;

                $carry = $class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);

                $product_value[$k] = (int) ($temp - $class::BASE_FULL * $carry);

            }

            if ($k < $stop) {

                $product_value[$k] = $carry;

            }

        }

        return [

            self::VALUE => self::trim($product_value),

            self::SIGN => $x_negative != $y_negative

        ];

    }

}