tgseclib/phpseclib/Math/BigInteger/Engines/PHP/Reductions/EvalBarrett.php

<?php

/**
 * PHP Dynamic 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\Base;
use phpseclib3\Math\BigInteger\Engines\PHP;

/**
 * PHP Dynamic Barrett Modular Exponentiation Engine
 *
 * @package PHP
 * @author  Jim Wigginton <terrafrost@php.net>
 * @access  public
 */
abstract class EvalBarrett extends Base
{
    /**
     * Custom Reduction Function
     *
     * @see self::generateCustomReduction
     */
    private static $custom_reduction;

    /**
     * Barrett Modular Reduction
     *
     * This calls a dynamically generated loop unrolled function that's specific to a given modulo.
     * Array lookups are avoided as are if statements testing for how many bits the host OS supports, etc.
     *
     * @param array $n
     * @param array $m
     * @param string $class
     * @return array
     */
    protected static function reduce(array $n, array $m, $class)
    {
        $inline = self::$custom_reduction;
        return $inline($n);
    }

    /**
     * Generate Custom Reduction
     *
     * @param PHP $m
     * @param string $class
     * @return callable
     */
    protected static function generateCustomReduction(PHP $m, $class)
    {
        if (isset($n->reduce)) {
            self::$custom_reduction = $n->reduce;
            return $n->reduce;
        }

        $m_length = count($m->value);

        if ($m_length < 5) {
            $code = '
                $lhs = new ' . $class . '();
                $lhs->value = $x;
                $rhs = new ' . $class . '();
                $rhs->value = [' .
                implode(',', array_map('self::float2string', $m->value)) . '];
                list(, $temp) = $lhs->divide($rhs);
                return $temp->value;
            ';
            eval('$func = function ($x) { ' . $code . '};');
            self::$custom_reduction = $func;
            //self::$custom_reduction = \Closure::bind($func, $m, $class);
            return $func;
        }

        $lhs = new $class();
        $lhs_value = &$lhs->value;

        $lhs_value = self::array_repeat(0, $m_length + ($m_length >> 1));
        $lhs_value[] = 1;
        $rhs = new $class();

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

        if ($class::BASE != 26) {
            $u = $u->value;
        } else {
            $lhs_value = self::array_repeat(0, 2 * $m_length);
            $lhs_value[] = 1;
            $rhs = new $class();

            list($u) = $lhs->divide($m);
            $u = $u->value;
        }

        $m = $m->value;
        $m1 = $m1->value;

        $cutoff = count($m) + (count($m) >> 1);

        $code = '
            if (count($n) > ' . (2 * count($m)) . ') {
                $lhs = new ' . $class . '();
                $rhs = new ' . $class . '();
                $lhs->value = $n;
                $rhs->value = [' .
                implode(',', array_map('self::float2string', $m)) . '];
                list(, $temp) = $lhs->divide($rhs);
                return $temp->value;
            }

            $lsd = array_slice($n, 0, ' . $cutoff . ');
            $msd = array_slice($n, ' . $cutoff . ');';

        $code.= self::generateInlineTrim('msd');
        $code.= self::generateInlineMultiply('msd', $m1, 'temp', $class);
        $code.= self::generateInlineAdd('lsd', 'temp', 'n', $class);

        $code.= '$temp = array_slice($n, ' . (count($m) - 1) . ');';
        $code.= self::generateInlineMultiply('temp', $u, 'temp2', $class);
        $code.= self::generateInlineTrim('temp2');

        $code.= $class::BASE == 26 ?
            '$temp = array_slice($temp2, ' . (count($m) + 1) . ');' :
            '$temp = array_slice($temp2, ' . ((count($m) >> 1) + 1) . ');';
        $code.= self::generateInlineMultiply('temp', $m, 'temp2', $class);
        $code.= self::generateInlineTrim('temp2');

        /*
        if ($class::BASE == 26) {
            $code.= '$n = array_slice($n, 0, ' . (count($m) + 1) . ');
                     $temp2 = array_slice($temp2, 0, ' . (count($m) + 1) . ');';
        }
        */

        $code.= self::generateInlineSubtract2('n', 'temp2', 'temp', $class);

        $subcode = self::generateInlineSubtract1('temp', $m, 'temp2', $class);
        $subcode.= '$temp = $temp2;';

        $code.= self::generateInlineCompare($m, 'temp', $subcode);

        $code.= 'return $temp;';

        eval('$func = function ($n) { ' . $code . '};');

        self::$custom_reduction = $func;

        return $func;

        //self::$custom_reduction = \Closure::bind($func, $m, $class);
    }

    /**
     * Inline Trim
     *
     * Removes leading zeros
     *
     * @param string $name
     * @return string
     */
    private static function generateInlineTrim($name)
    {
        return '
            for ($i = count($' . $name . ') - 1; $i >= 0; --$i) {
                if ($' . $name . '[$i]) {
                    break;
                }
                unset($' . $name . '[$i]);
            }';
    }

    /**
     * Inline Multiply (unknown, known)
     *
     * @param string $input
     * @param array $arr
     * @param string $output
     * @param string $class
     * @return string
     */
    private static function generateInlineMultiply($input, array $arr, $output, $class)
    {
        if (!count($arr)) {
            return 'return [];';
        }

        $regular = '
            $length = count($' . $input . ');
            if (!$length) {
                $' . $output . ' = [];
            }else{
            $' . $output . ' = array_fill(0, $length + ' . count($arr) . ', 0);
            $carry = 0;';

            for ($i = 0; $i < count($arr); $i++) {
            $regular.= '
                $subtemp = $' . $input . '[0] * ' . $arr[$i];
            $regular.= $i ? ' + $carry;' : ';';

            $regular.= '$carry = ';
            $regular.= $class::BASE === 26 ?
                'intval($subtemp / 0x4000000);' :
                '$subtemp >> 31;';
            $regular.=
                '$' . $output . '[' . $i . '] = ';
            if ($class::BASE === 26) {
                $regular.= '(int) (';
            }
            $regular.= '$subtemp - ' . $class::BASE_FULL . ' * $carry';
            $regular.= $class::BASE === 26 ? ');' : ';';
        }

        $regular.= '$' . $output . '[' . count($arr) . '] = $carry;';

        $regular.= '
            for ($i = 1; $i < $length; ++$i) {';

        for ($j = 0; $j < count($arr); $j++) {
            $regular.= $j ? '$k++;' : '$k = $i;';
            $regular.= '
                $subtemp = $' . $output . '[$k] + $' . $input . '[$i] * ' . $arr[$j];
            $regular.= $j ? ' + $carry;' : ';';

            $regular.= '$carry = ';
            $regular.= $class::BASE === 26 ?
                'intval($subtemp / 0x4000000);' :
                '$subtemp >> 31;';
            $regular.=
                '$' . $output . '[$k] = ';
            if ($class::BASE === 26) {
                $regular.= '(int) (';
            }
            $regular.= '$subtemp - ' . $class::BASE_FULL . ' * $carry';
            $regular.= $class::BASE === 26 ? ');' : ';';
        }

        $regular.= '$' . $output. '[++$k] = $carry; $carry = 0;';

        $regular.= '}}';

        //if (count($arr) < 2 * self::KARATSUBA_CUTOFF) {
        //}

        return $regular;
    }

    /**
     * Inline Addition
     *
     * @param string $x
     * @param string $y
     * @param string $result
     * @param string $class
     * @return string
     */
    private static function generateInlineAdd($x, $y, $result, $class)
    {
        $code = '
            $length = max(count($' . $x . '), count($' . $y . '));
            $' . $result . ' = array_pad($' . $x . ', $length + 1, 0);
            $_' . $y . ' = array_pad($' . $y . ', $length, 0);
            $carry = 0;
            for ($i = 0, $j = 1; $j < $length; $i+=2, $j+=2) {
                $sum = ($' . $result . '[$j] + $_' . $y . '[$j]) * ' . $class::BASE_FULL . '
                           + $' . $result . '[$i] + $_' . $y . '[$i] +
                           $carry;
                $carry = $sum >= ' . self::float2string($class::MAX_DIGIT2) . ';
                $sum = $carry ? $sum - ' . self::float2string($class::MAX_DIGIT2) . ' : $sum;';

            $code.= $class::BASE === 26 ?
                '$upper = intval($sum / 0x4000000); $' . $result . '[$i] = (int) ($sum - ' . $class::BASE_FULL . ' * $upper);' :
                '$upper = $sum >> 31; $' . $result . '[$i] = $sum - ' . $class::BASE_FULL . ' * $upper;';
            $code.= '
                $' . $result . '[$j] = $upper;
            }
            if ($j == $length) {
                $sum = $' . $result . '[$i] + $_' . $y . '[$i] + $carry;
                $carry = $sum >= ' . self::float2string($class::BASE_FULL) . ';
                $' . $result . '[$i] = $carry ? $sum - ' . self::float2string($class::BASE_FULL) . ' : $sum;
            }
            if ($carry) {
                for (; $' . $result . '[$i] == ' . $class::MAX_DIGIT . '; ++$i) {
                    $' . $result . '[$i] = 0;
                }
                ++$' . $result . '[$i];
            }';
            $code.= self::generateInlineTrim($result);

            return $code;
    }

    /**
     * Inline Subtraction 2
     *
     * For when $known is more digits than $unknown. This is the harder use case to optimize for.
     *
     * @param string $known
     * @param string $unknown
     * @param string $result
     * @param string $class
     * @return string
     */
    private static function generateInlineSubtract2($known, $unknown, $result, $class)
    {
        $code = '
            $' . $result .' = $' . $known . ';
            $carry = 0;
            $size = count($' . $unknown . ');
            for ($i = 0, $j = 1; $j < $size; $i+= 2, $j+= 2) {
                $sum = ($' . $known . '[$j] - $' . $unknown . '[$j]) * ' . $class::BASE_FULL . ' + $' . $known . '[$i]
                    - $' . $unknown . '[$i]
                    - $carry;
                $carry = $sum < 0;
                if ($carry) {
                    $sum+= ' . self::float2string($class::MAX_DIGIT2) . ';
                }
                $subtemp = ';
        $code.= $class::BASE === 26 ?
            'intval($sum / 0x4000000);' :
            '$sum >> 31;';
        $code.= '$' . $result . '[$i] = ';
        if ($class::BASE === 26) {
            $code.= '(int) (';
        }
        $code.= '$sum - ' . $class::BASE_FULL . ' * $subtemp';
        if ($class::BASE === 26) {
            $code.= ')';
        }
        $code.= ';
                $' . $result . '[$j] = $subtemp;
            }
            if ($j == $size) {
                $sum = $' . $known . '[$i] - $' . $unknown . '[$i] - $carry;
                $carry = $sum < 0;
                $' . $result . '[$i] = $carry ? $sum + ' . $class::BASE_FULL . ' : $sum;
                ++$i;
            }

            if ($carry) {
                for (; !$' . $result . '[$i]; ++$i) {
                    $' . $result . '[$i] = ' . $class::MAX_DIGIT . ';
                }
                --$' . $result . '[$i];
            }';

        $code.= self::generateInlineTrim($result);

        return $code;
    }

    /**
     * Inline Subtraction 1
     *
     * For when $unknown is more digits than $known. This is the easier use case to optimize for.
     *
     * @param string $unknown
     * @param array $known
     * @param string $result
     * @param string $class
     * @return string
     */
    private static function generateInlineSubtract1($unknown, array $known, $result, $class)
    {
        $code = '$' . $result . ' = $' . $unknown . ';';
        for ($i = 0, $j = 1; $j < count($known); $i+=2, $j+=2) {
            $code.= '$sum = $' . $unknown . '[' . $j . '] * ' . $class::BASE_FULL . ' + $' . $unknown . '[' . $i . '] - ';
            $code.= self::float2string($known[$j] * $class::BASE_FULL + $known[$i]);
            if ($i != 0) {
                $code.= ' - $carry';
            }

            $code.= ';
                if ($carry = $sum < 0) {
                    $sum+= ' . self::float2string($class::MAX_DIGIT2) . ';
                }
                $subtemp = ';
            $code.= $class::BASE === 26 ?
                'intval($sum / 0x4000000);' :
                '$sum >> 31;';
            $code.= '
                $' . $result . '[' . $i . '] = ';
            if ($class::BASE === 26) {
                $code.= ' (int) (';
            }
            $code.= '$sum - ' . $class::BASE_FULL . ' * $subtemp';
            if ($class::BASE === 26) {
                $code.= ')';
            }
            $code.= ';
                $' . $result . '[' . $j . '] = $subtemp;';
        }

        $code.= '$i = ' . $i . ';';

        if ($j == count($known)) {
            $code.= '
                $sum = $' . $unknown . '[' . $i . '] - ' . $known[$i] . ' - $carry;
                $carry = $sum < 0;
                $' . $result . '[' . $i . '] = $carry ? $sum + ' . $class::BASE_FULL . ' : $sum;
                ++$i;';
        }

        $code.= '
            if ($carry) {
                for (; !$' . $result . '[$i]; ++$i) {
                    $' . $result . '[$i] = ' . $class::MAX_DIGIT . ';
                }
                --$' . $result . '[$i];
            }';
        $code.= self::generateInlineTrim($result);

        return $code;
    }

    /**
     * Inline Comparison
     *
     * If $unknown >= $known then loop
     *
     * @param array $known
     * @param string $unknown
     * @param string $subcode
     * @return string
     */
    private static function generateInlineCompare(array $known, $unknown, $subcode)
    {
        $uniqid = uniqid();
        $code = 'loop_' . $uniqid . ':
            $clength = count($' . $unknown . ');
            switch (true) {
                case $clength < ' . count($known) . ':
                    goto end_' . $uniqid . ';
                case $clength > ' . count($known) . ':';
        for ($i = count($known) - 1; $i >= 0; $i--) {
            $code.= '
                case $' . $unknown . '[' . $i . '] > ' . $known[$i] . ':
                    goto subcode_' . $uniqid . ';
                case $' . $unknown . '[' . $i . '] < ' . $known[$i] . ':
                    goto end_' . $uniqid . ';';
        }
        $code.= '
                default:
                    // do subcode
            }

            subcode_' . $uniqid . ':' . $subcode . '
            goto loop_' . $uniqid . ';

            end_' . $uniqid . ':';

        return $code;
    }

    /**
     * Convert a float to a string
     *
     * If you do echo floatval(pow(2, 52)) you'll get 4.6116860184274E+18. It /can/ be displayed without a loss of
     * precision but displayed in this way there will be precision loss, hence the need for this method.
     *
     * @param int|float $num
     * @return string
     */
    private static function float2string($num)
    {
        if (!is_float($num)) {
            return $num;
        }

        if ($num < 0) {
            return '-' . self::float2string(abs($num));
        }

        $temp = '';
        while ($num) {
            $temp = fmod($num, 10) . $temp;
            $num = floor($num / 10);
        }

        return $temp;
    }
}