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<?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;
}
}
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