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Diffstat (limited to 'vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/PHP.php')
| -rw-r--r-- | vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/PHP.php | 1344 |
1 files changed, 1344 insertions, 0 deletions
diff --git a/vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/PHP.php b/vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/PHP.php new file mode 100644 index 0000000..7e85783 --- /dev/null +++ b/vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/PHP.php @@ -0,0 +1,1344 @@ +<?php + +/** + * Pure-PHP BigInteger Engine + * + * PHP version 5 and 7 + * + * @author Jim Wigginton <[email protected]> + * @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\Common\Functions\Strings; +use phpseclib3\Exception\BadConfigurationException; + +/** + * Pure-PHP Engine. + * + * @author Jim Wigginton <[email protected]> + */ +abstract class PHP extends Engine +{ + /**#@+ + * Array constants + * + * Rather than create a thousands and thousands of new BigInteger objects in repeated function calls to add() and + * multiply() or whatever, we'll just work directly on arrays, taking them in as parameters and returning them. + * + */ + /** + * $result[self::VALUE] contains the value. + */ + const VALUE = 0; + /** + * $result[self::SIGN] contains the sign. + */ + const SIGN = 1; + /**#@-*/ + + /** + * Karatsuba Cutoff + * + * At what point do we switch between Karatsuba multiplication and schoolbook long multiplication? + * + */ + const KARATSUBA_CUTOFF = 25; + + /** + * Can Bitwise operations be done fast? + * + * @see parent::bitwise_leftRotate() + * @see parent::bitwise_rightRotate() + */ + const FAST_BITWISE = true; + + /** + * Engine Directory + * + * @see parent::setModExpEngine + */ + const ENGINE_DIR = 'PHP'; + + /** + * Default constructor + * + * @param mixed $x integer Base-10 number or base-$base number if $base set. + * @param int $base + * @return PHP + * @see parent::__construct() + */ + public function __construct($x = 0, $base = 10) + { + if (!isset(static::$isValidEngine[static::class])) { + static::$isValidEngine[static::class] = static::isValidEngine(); + } + if (!static::$isValidEngine[static::class]) { + throw new BadConfigurationException(static::class . ' is not setup correctly on this system'); + } + + $this->value = []; + parent::__construct($x, $base); + } + + /** + * Initialize a PHP BigInteger Engine instance + * + * @param int $base + * @see parent::__construct() + */ + protected function initialize($base) + { + switch (abs($base)) { + case 16: + $x = (strlen($this->value) & 1) ? '0' . $this->value : $this->value; + $temp = new static(Strings::hex2bin($x), 256); + $this->value = $temp->value; + break; + case 10: + $temp = new static(); + + $multiplier = new static(); + $multiplier->value = [static::MAX10]; + + $x = $this->value; + + if ($x[0] == '-') { + $this->is_negative = true; + $x = substr($x, 1); + } + + $x = str_pad( + $x, + strlen($x) + ((static::MAX10LEN - 1) * strlen($x)) % static::MAX10LEN, + 0, + STR_PAD_LEFT + ); + while (strlen($x)) { + $temp = $temp->multiply($multiplier); + $temp = $temp->add(new static($this->int2bytes(substr($x, 0, static::MAX10LEN)), 256)); + $x = substr($x, static::MAX10LEN); + } + + $this->value = $temp->value; + } + } + + /** + * Pads strings so that unpack may be used on them + * + * @param string $str + * @return string + */ + protected function pad($str) + { + $length = strlen($str); + + $pad = 4 - (strlen($str) % 4); + + return str_pad($str, $length + $pad, "\0", STR_PAD_LEFT); + } + + /** + * Converts a BigInteger to a base-10 number. + * + * @return string + */ + public function toString() + { + if (!count($this->value)) { + return '0'; + } + + $temp = clone $this; + $temp->bitmask = false; + $temp->is_negative = false; + + $divisor = new static(); + $divisor->value = [static::MAX10]; + $result = ''; + while (count($temp->value)) { + list($temp, $mod) = $temp->divide($divisor); + $result = str_pad( + isset($mod->value[0]) ? $mod->value[0] : '', + static::MAX10LEN, + '0', + STR_PAD_LEFT + ) . $result; + } + $result = ltrim($result, '0'); + if (empty($result)) { + $result = '0'; + } + + if ($this->is_negative) { + $result = '-' . $result; + } + + return $result; + } + + /** + * 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 $this->toBytesHelper(); + } + + if (!count($this->value)) { + return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : ''; + } + + $result = $this->bitwise_small_split(8); + $result = implode('', array_map('chr', $result)); + + return $this->precision > 0 ? + str_pad( + substr($result, -(($this->precision + 7) >> 3)), + ($this->precision + 7) >> 3, + chr(0), + STR_PAD_LEFT + ) : + $result; + } + + /** + * Performs addition. + * + * @param array $x_value + * @param bool $x_negative + * @param array $y_value + * @param bool $y_negative + * @return array + */ + protected static function addHelper(array $x_value, $x_negative, array $y_value, $y_negative) + { + $x_size = count($x_value); + $y_size = count($y_value); + + if ($x_size == 0) { + return [ + self::VALUE => $y_value, + self::SIGN => $y_negative + ]; + } elseif ($y_size == 0) { + return [ + self::VALUE => $x_value, + self::SIGN => $x_negative + ]; + } + + // subtract, if appropriate + if ($x_negative != $y_negative) { + if ($x_value == $y_value) { + return [ + self::VALUE => [], + self::SIGN => false + ]; + } + + $temp = self::subtractHelper($x_value, false, $y_value, false); + $temp[self::SIGN] = self::compareHelper($x_value, false, $y_value, false) > 0 ? + $x_negative : $y_negative; + + return $temp; + } + + if ($x_size < $y_size) { + $size = $x_size; + $value = $y_value; + } else { + $size = $y_size; + $value = $x_value; + } + + $value[count($value)] = 0; // just in case the carry adds an extra digit + + $carry = 0; + for ($i = 0, $j = 1; $j < $size; $i += 2, $j += 2) { + //$sum = $x_value[$j] * static::BASE_FULL + $x_value[$i] + $y_value[$j] * static::BASE_FULL + $y_value[$i] + $carry; + $sum = ($x_value[$j] + $y_value[$j]) * static::BASE_FULL + $x_value[$i] + $y_value[$i] + $carry; + $carry = $sum >= static::MAX_DIGIT2; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1 + $sum = $carry ? $sum - static::MAX_DIGIT2 : $sum; + + $temp = static::BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31); + + $value[$i] = (int)($sum - static::BASE_FULL * $temp); // eg. a faster alternative to fmod($sum, 0x4000000) + $value[$j] = $temp; + } + + if ($j == $size) { // ie. if $y_size is odd + $sum = $x_value[$i] + $y_value[$i] + $carry; + $carry = $sum >= static::BASE_FULL; + $value[$i] = $carry ? $sum - static::BASE_FULL : $sum; + ++$i; // ie. let $i = $j since we've just done $value[$i] + } + + if ($carry) { + for (; $value[$i] == static::MAX_DIGIT; ++$i) { + $value[$i] = 0; + } + ++$value[$i]; + } + + return [ + self::VALUE => self::trim($value), + self::SIGN => $x_negative + ]; + } + + /** + * Performs subtraction. + * + * @param array $x_value + * @param bool $x_negative + * @param array $y_value + * @param bool $y_negative + * @return array + */ + public static function subtractHelper(array $x_value, $x_negative, array $y_value, $y_negative) + { + $x_size = count($x_value); + $y_size = count($y_value); + + if ($x_size == 0) { + return [ + self::VALUE => $y_value, + self::SIGN => !$y_negative + ]; + } elseif ($y_size == 0) { + return [ + self::VALUE => $x_value, + self::SIGN => $x_negative + ]; + } + + // add, if appropriate (ie. -$x - +$y or +$x - -$y) + if ($x_negative != $y_negative) { + $temp = self::addHelper($x_value, false, $y_value, false); + $temp[self::SIGN] = $x_negative; + + return $temp; + } + + $diff = self::compareHelper($x_value, $x_negative, $y_value, $y_negative); + + if (!$diff) { + return [ + self::VALUE => [], + self::SIGN => false + ]; + } + + // switch $x and $y around, if appropriate. + if ((!$x_negative && $diff < 0) || ($x_negative && $diff > 0)) { + $temp = $x_value; + $x_value = $y_value; + $y_value = $temp; + + $x_negative = !$x_negative; + + $x_size = count($x_value); + $y_size = count($y_value); + } + + // at this point, $x_value should be at least as big as - if not bigger than - $y_value + + $carry = 0; + for ($i = 0, $j = 1; $j < $y_size; $i += 2, $j += 2) { + $sum = ($x_value[$j] - $y_value[$j]) * static::BASE_FULL + $x_value[$i] - $y_value[$i] - $carry; + + $carry = $sum < 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1 + $sum = $carry ? $sum + static::MAX_DIGIT2 : $sum; + + $temp = static::BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31); + + $x_value[$i] = (int)($sum - static::BASE_FULL * $temp); + $x_value[$j] = $temp; + } + + if ($j == $y_size) { // ie. if $y_size is odd + $sum = $x_value[$i] - $y_value[$i] - $carry; + $carry = $sum < 0; + $x_value[$i] = $carry ? $sum + static::BASE_FULL : $sum; + ++$i; + } + + if ($carry) { + for (; !$x_value[$i]; ++$i) { + $x_value[$i] = static::MAX_DIGIT; + } + --$x_value[$i]; + } + + return [ + self::VALUE => self::trim($x_value), + self::SIGN => $x_negative + ]; + } + + /** + * Performs multiplication. + * + * @param array $x_value + * @param bool $x_negative + * @param array $y_value + * @param bool $y_negative + * @return array + */ + protected static function multiplyHelper(array $x_value, $x_negative, array $y_value, $y_negative) + { + //if ( $x_value == $y_value ) { + // return [ + // self::VALUE => self::square($x_value), + // self::SIGN => $x_sign != $y_value + // ]; + //} + + $x_length = count($x_value); + $y_length = count($y_value); + + if (!$x_length || !$y_length) { // a 0 is being multiplied + return [ + self::VALUE => [], + self::SIGN => false + ]; + } + + return [ + self::VALUE => min($x_length, $y_length) < 2 * self::KARATSUBA_CUTOFF ? + self::trim(self::regularMultiply($x_value, $y_value)) : + self::trim(self::karatsuba($x_value, $y_value)), + self::SIGN => $x_negative != $y_negative + ]; + } + + /** + * 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 array $x_value + * @param array $y_value + * @return array + */ + private static function karatsuba(array $x_value, array $y_value) + { + $m = min(count($x_value) >> 1, count($y_value) >> 1); + + if ($m < self::KARATSUBA_CUTOFF) { + return self::regularMultiply($x_value, $y_value); + } + + $x1 = array_slice($x_value, $m); + $x0 = array_slice($x_value, 0, $m); + $y1 = array_slice($y_value, $m); + $y0 = array_slice($y_value, 0, $m); + + $z2 = self::karatsuba($x1, $y1); + $z0 = self::karatsuba($x0, $y0); + + $z1 = self::addHelper($x1, false, $x0, false); + $temp = self::addHelper($y1, false, $y0, false); + $z1 = self::karatsuba($z1[self::VALUE], $temp[self::VALUE]); + $temp = self::addHelper($z2, false, $z0, false); + $z1 = self::subtractHelper($z1, false, $temp[self::VALUE], false); + + $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2); + $z1[self::VALUE] = array_merge(array_fill(0, $m, 0), $z1[self::VALUE]); + + $xy = self::addHelper($z2, false, $z1[self::VALUE], $z1[self::SIGN]); + $xy = self::addHelper($xy[self::VALUE], $xy[self::SIGN], $z0, false); + + return $xy[self::VALUE]; + } + + /** + * Performs long multiplication on two BigIntegers + * + * Modeled after 'multiply' in MutableBigInteger.java. + * + * @param array $x_value + * @param array $y_value + * @return array + */ + protected static function regularMultiply(array $x_value, array $y_value) + { + $x_length = count($x_value); + $y_length = count($y_value); + + if (!$x_length || !$y_length) { // a 0 is being multiplied + return []; + } + + $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 + $temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0 + $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); + $product_value[$j] = (int)($temp - static::BASE_FULL * $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 < $y_length; ++$i) { + $carry = 0; + + for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) { + $temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry; + $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); + $product_value[$k] = (int)($temp - static::BASE_FULL * $carry); + } + + $product_value[$k] = $carry; + } + + return $product_value; + } + + /** + * 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). + * + * @return array{static, static} + * @internal This function is based off of + * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=9 HAC 14.20}. + */ + protected function divideHelper(PHP $y) + { + if (count($y->value) == 1) { + list($q, $r) = $this->divide_digit($this->value, $y->value[0]); + $quotient = new static(); + $remainder = new static(); + $quotient->value = $q; + $remainder->value = [$r]; + $quotient->is_negative = $this->is_negative != $y->is_negative; + return [$this->normalize($quotient), $this->normalize($remainder)]; + } + + $x = clone $this; + $y = clone $y; + + $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 static(); + $temp->value = [1]; + $temp->is_negative = $x_sign != $y_sign; + return [$this->normalize($temp), $this->normalize(static::$zero[static::class])]; + } + + if ($diff < 0) { + // if $x is negative, "add" $y. + if ($x_sign) { + $x = $y->subtract($x); + } + return [$this->normalize(static::$zero[static::class]), $this->normalize($x)]; + } + + // normalize $x and $y as described in HAC 14.23 / 14.24 + $msb = $y->value[count($y->value) - 1]; + for ($shift = 0; !($msb & static::MSB); ++$shift) { + $msb <<= 1; + } + $x->lshift($shift); + $y->lshift($shift); + $y_value = &$y->value; + + $x_max = count($x->value) - 1; + $y_max = count($y->value) - 1; + + $quotient = new static(); + $quotient_value = &$quotient->value; + $quotient_value = self::array_repeat(0, $x_max - $y_max + 1); + + static $temp, $lhs, $rhs; + if (!isset($temp)) { + $temp = new static(); + $lhs = new static(); + $rhs = new static(); + } + if (static::class != get_class($temp)) { + $temp = new static(); + $lhs = new static(); + $rhs = new static(); + } + $temp_value = &$temp->value; + $rhs_value = &$rhs->value; + + // $temp = $y << ($x_max - $y_max-1) in base 2**26 + $temp_value = array_merge(self::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) { + $x_value = &$x->value; + $x_window = [ + isset($x_value[$i]) ? $x_value[$i] : 0, + isset($x_value[$i - 1]) ? $x_value[$i - 1] : 0, + isset($x_value[$i - 2]) ? $x_value[$i - 2] : 0 + ]; + $y_window = [ + $y_value[$y_max], + ($y_max > 0) ? $y_value[$y_max - 1] : 0 + ]; + + $q_index = $i - $y_max - 1; + if ($x_window[0] == $y_window[0]) { + $quotient_value[$q_index] = static::MAX_DIGIT; + } else { + $quotient_value[$q_index] = self::safe_divide( + $x_window[0] * static::BASE_FULL + $x_window[1], + $y_window[0] + ); + } + + $temp_value = [$y_window[1], $y_window[0]]; + + $lhs->value = [$quotient_value[$q_index]]; + $lhs = $lhs->multiply($temp); + + $rhs_value = [$x_window[2], $x_window[1], $x_window[0]]; + + while ($lhs->compare($rhs) > 0) { + --$quotient_value[$q_index]; + + $lhs->value = [$quotient_value[$q_index]]; + $lhs = $lhs->multiply($temp); + } + + $adjust = self::array_repeat(0, $q_index); + $temp_value = [$quotient_value[$q_index]]; + $temp = $temp->multiply($y); + $temp_value = &$temp->value; + if (count($temp_value)) { + $temp_value = array_merge($adjust, $temp_value); + } + + $x = $x->subtract($temp); + + if ($x->compare(static::$zero[static::class]) < 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 [$this->normalize($quotient), $this->normalize($x)]; + } + + /** + * Divides a BigInteger by a regular integer + * + * abc / x = a00 / x + b0 / x + c / x + * + * @param array $dividend + * @param int $divisor + * @return array + */ + private static function divide_digit(array $dividend, $divisor) + { + $carry = 0; + $result = []; + + for ($i = count($dividend) - 1; $i >= 0; --$i) { + $temp = static::BASE_FULL * $carry + $dividend[$i]; + $result[$i] = self::safe_divide($temp, $divisor); + $carry = (int)($temp - $divisor * $result[$i]); + } + + return [$result, $carry]; + } + + /** + * Single digit division + * + * Even if int64 is being used the division operator will return a float64 value + * if the dividend is not evenly divisible by the divisor. Since a float64 doesn't + * have the precision of int64 this is a problem so, when int64 is being used, + * we'll guarantee that the dividend is divisible by first subtracting the remainder. + * + * @param int $x + * @param int $y + * @return int + */ + private static function safe_divide($x, $y) + { + if (static::BASE === 26) { + return (int)($x / $y); + } + + // static::BASE === 31 + /** @var int */ + return ($x - ($x % $y)) / $y; + } + + /** + * Convert an array / boolean to a PHP BigInteger object + * + * @param array $arr + * @return static + */ + protected function convertToObj(array $arr) + { + $result = new static(); + $result->value = $arr[self::VALUE]; + $result->is_negative = $arr[self::SIGN]; + + return $this->normalize($result); + } + + /** + * Normalize + * + * Removes leading zeros and truncates (if necessary) to maintain the appropriate precision + * + * @param PHP $result + * @return static + */ + protected function normalize(PHP $result) + { + $result->precision = $this->precision; + $result->bitmask = $this->bitmask; + + $value = &$result->value; + + if (!count($value)) { + $result->is_negative = false; + return $result; + } + + $value = static::trim($value); + + if (!empty($result->bitmask->value)) { + $length = min(count($value), count($result->bitmask->value)); + $value = array_slice($value, 0, $length); + + for ($i = 0; $i < $length; ++$i) { + $value[$i] = $value[$i] & $result->bitmask->value[$i]; + } + + $value = static::trim($value); + } + + return $result; + } + + /** + * Compares two numbers. + * + * @param array $x_value + * @param bool $x_negative + * @param array $y_value + * @param bool $y_negative + * @return int + * @see static::compare() + */ + protected static function compareHelper(array $x_value, $x_negative, array $y_value, $y_negative) + { + if ($x_negative != $y_negative) { + return (!$x_negative && $y_negative) ? 1 : -1; + } + + $result = $x_negative ? -1 : 1; + + if (count($x_value) != count($y_value)) { + return (count($x_value) > count($y_value)) ? $result : -$result; + } + $size = max(count($x_value), count($y_value)); + + $x_value = array_pad($x_value, $size, 0); + $y_value = array_pad($y_value, $size, 0); + + for ($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; + } + + /** + * Absolute value. + * + * @return PHP + */ + public function abs() + { + $temp = new static(); + $temp->value = $this->value; + + return $temp; + } + + /** + * Trim + * + * Removes leading zeros + * + * @param list<static> $value + * @return list<static> + */ + protected static function trim(array $value) + { + for ($i = count($value) - 1; $i >= 0; --$i) { + if ($value[$i]) { + break; + } + unset($value[$i]); + } + + return $value; + } + + /** + * Logical Right Shift + * + * Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift. + * + * @param int $shift + * @return PHP + */ + public function bitwise_rightShift($shift) + { + $temp = new static(); + + // 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 int $shift + * @return PHP + */ + public function bitwise_leftShift($shift) + { + $temp = new static(); + // 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); + } + + /** + * Converts 32-bit integers to bytes. + * + * @param int $x + * @return string + */ + private static function int2bytes($x) + { + return ltrim(pack('N', $x), chr(0)); + } + + /** + * Array Repeat + * + * @param int $input + * @param int $multiplier + * @return array + */ + protected static function array_repeat($input, $multiplier) + { + return $multiplier ? array_fill(0, $multiplier, $input) : []; + } + + /** + * Logical Left Shift + * + * Shifts BigInteger's by $shift bits. + * + * @param int $shift + */ + protected function lshift($shift) + { + if ($shift == 0) { + return; + } + + $num_digits = (int)($shift / static::BASE); + $shift %= static::BASE; + $shift = 1 << $shift; + + $carry = 0; + + for ($i = 0; $i < count($this->value); ++$i) { + $temp = $this->value[$i] * $shift + $carry; + $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); + $this->value[$i] = (int)($temp - $carry * static::BASE_FULL); + } + + if ($carry) { + $this->value[count($this->value)] = $carry; + } + + while ($num_digits--) { + array_unshift($this->value, 0); + } + } + + /** + * Logical Right Shift + * + * Shifts BigInteger's by $shift bits. + * + * @param int $shift + */ + protected function rshift($shift) + { + if ($shift == 0) { + return; + } + + $num_digits = (int)($shift / static::BASE); + $shift %= static::BASE; + $carry_shift = static::BASE - $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; + } + + $this->value = static::trim($this->value); + } + + /** + * Performs modular exponentiation. + * + * @param PHP $e + * @param PHP $n + * @return PHP + */ + protected function powModInner(PHP $e, PHP $n) + { + try { + $class = static::$modexpEngine[static::class]; + return $class::powModHelper($this, $e, $n, static::class); + } catch (\Exception $err) { + return PHP\DefaultEngine::powModHelper($this, $e, $n, static::class); + } + } + + /** + * Performs squaring + * + * @param list<static> $x + * @return list<static> + */ + protected static function square(array $x) + { + return count($x) < 2 * self::KARATSUBA_CUTOFF ? + self::trim(self::baseSquare($x)) : + self::trim(self::karatsubaSquare($x)); + } + + /** + * 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. + * + * @param array $value + * @return array + */ + protected static function baseSquare(array $value) + { + if (empty($value)) { + return []; + } + $square_value = self::array_repeat(0, 2 * count($value)); + + for ($i = 0, $max_index = count($value) - 1; $i <= $max_index; ++$i) { + $i2 = $i << 1; + + $temp = $square_value[$i2] + $value[$i] * $value[$i]; + $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); + $square_value[$i2] = (int)($temp - static::BASE_FULL * $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 * $value[$j] * $value[$i] + $carry; + $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); + $square_value[$k] = (int)($temp - static::BASE_FULL * $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_value; + } + + /** + * 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 array $value + * @return array + */ + protected static function karatsubaSquare(array $value) + { + $m = count($value) >> 1; + + if ($m < self::KARATSUBA_CUTOFF) { + return self::baseSquare($value); + } + + $x1 = array_slice($value, $m); + $x0 = array_slice($value, 0, $m); + + $z2 = self::karatsubaSquare($x1); + $z0 = self::karatsubaSquare($x0); + + $z1 = self::addHelper($x1, false, $x0, false); + $z1 = self::karatsubaSquare($z1[self::VALUE]); + $temp = self::addHelper($z2, false, $z0, false); + $z1 = self::subtractHelper($z1, false, $temp[self::VALUE], false); + + $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2); + $z1[self::VALUE] = array_merge(array_fill(0, $m, 0), $z1[self::VALUE]); + + $xx = self::addHelper($z2, false, $z1[self::VALUE], $z1[self::SIGN]); + $xx = self::addHelper($xx[self::VALUE], $xx[self::SIGN], $z0, false); + + return $xx[self::VALUE]; + } + + /** + * 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() + { + $this->value[0] |= 1; + } + + /** + * Test the number against small primes. + * + * @see self::isPrime() + */ + protected function testSmallPrimes() + { + if ($this->value == [1]) { + return false; + } + if ($this->value == [2]) { + return true; + } + if (~$this->value[0] & 1) { + return false; + } + + $value = $this->value; + foreach (static::PRIMES as $prime) { + list(, $r) = self::divide_digit($value, $prime); + if (!$r) { + return count($value) == 1 && $value[0] == $prime; + } + } + + return true; + } + + /** + * 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 PHP $r + * @return int + * @see self::isPrime() + */ + public static function scan1divide(PHP $r) + { + $r_value = &$r->value; + for ($i = 0, $r_length = count($r_value); $i < $r_length; ++$i) { + $temp = ~$r_value[$i] & static::MAX_DIGIT; + for ($j = 1; ($temp >> $j) & 1; ++$j) { + } + if ($j <= static::BASE) { + break; + } + } + $s = static::BASE * $i + $j; + $r->rshift($s); + return $s; + } + + /** + * Performs exponentiation. + * + * @param PHP $n + * @return PHP + */ + protected function powHelper(PHP $n) + { + if ($n->compare(static::$zero[static::class]) == 0) { + return new static(1); + } // n^0 = 1 + + $temp = clone $this; + while (!$n->equals(static::$one[static::class])) { + $temp = $temp->multiply($this); + $n = $n->subtract(static::$one[static::class]); + } + + return $temp; + } + + /** + * Is Odd? + * + * @return bool + */ + public function isOdd() + { + return (bool)($this->value[0] & 1); + } + + /** + * Tests if a bit is set + * + * @return bool + */ + public function testBit($x) + { + $digit = (int) floor($x / static::BASE); + $bit = $x % static::BASE; + + if (!isset($this->value[$digit])) { + return false; + } + + return (bool)($this->value[$digit] & (1 << $bit)); + } + + /** + * Is Negative? + * + * @return bool + */ + public function isNegative() + { + return $this->is_negative; + } + + /** + * Negate + * + * Given $k, returns -$k + * + * @return static + */ + public function negate() + { + $temp = clone $this; + $temp->is_negative = !$temp->is_negative; + + return $temp; + } + + /** + * Bitwise Split + * + * Splits BigInteger's into chunks of $split bits + * + * @param int $split + * @return list<static> + */ + public function bitwise_split($split) + { + if ($split < 1) { + throw new \RuntimeException('Offset must be greater than 1'); + } + + $width = (int)($split / static::BASE); + if (!$width) { + $arr = $this->bitwise_small_split($split); + return array_map(function ($digit) { + $temp = new static(); + $temp->value = $digit != 0 ? [$digit] : []; + return $temp; + }, $arr); + } + + $vals = []; + $val = $this->value; + + $i = $overflow = 0; + $len = count($val); + while ($i < $len) { + $digit = []; + if (!$overflow) { + $digit = array_slice($val, $i, $width); + $i += $width; + $overflow = $split % static::BASE; + if ($overflow) { + $mask = (1 << $overflow) - 1; + $temp = isset($val[$i]) ? $val[$i] : 0; + $digit[] = $temp & $mask; + } + } else { + $remaining = static::BASE - $overflow; + $tempsplit = $split - $remaining; + $tempwidth = (int)($tempsplit / static::BASE + 1); + $digit = array_slice($val, $i, $tempwidth); + $i += $tempwidth; + $tempoverflow = $tempsplit % static::BASE; + if ($tempoverflow) { + $tempmask = (1 << $tempoverflow) - 1; + $temp = isset($val[$i]) ? $val[$i] : 0; + $digit[] = $temp & $tempmask; + } + $newbits = 0; + for ($j = count($digit) - 1; $j >= 0; $j--) { + $temp = $digit[$j] & $mask; + $digit[$j] = ($digit[$j] >> $overflow) | ($newbits << $remaining); + $newbits = $temp; + } + $overflow = $tempoverflow; + $mask = $tempmask; + } + $temp = new static(); + $temp->value = static::trim($digit); + $vals[] = $temp; + } + + return array_reverse($vals); + } + + /** + * Bitwise Split where $split < static::BASE + * + * @param int $split + * @return list<int> + */ + private function bitwise_small_split($split) + { + $vals = []; + $val = $this->value; + + $mask = (1 << $split) - 1; + + $i = $overflow = 0; + $len = count($val); + $val[] = 0; + $remaining = static::BASE; + while ($i != $len) { + $digit = $val[$i] & $mask; + $val[$i] >>= $split; + if (!$overflow) { + $remaining -= $split; + $overflow = $split <= $remaining ? 0 : $split - $remaining; + + if (!$remaining) { + $i++; + $remaining = static::BASE; + $overflow = 0; + } + } elseif (++$i != $len) { + $tempmask = (1 << $overflow) - 1; + $digit |= ($val[$i] & $tempmask) << $remaining; + $val[$i] >>= $overflow; + $remaining = static::BASE - $overflow; + $overflow = $split <= $remaining ? 0 : $split - $remaining; + } + + $vals[] = $digit; + } + + while ($vals[count($vals) - 1] == 0) { + unset($vals[count($vals) - 1]); + } + + return array_reverse($vals); + } + + /** + * @return bool + */ + protected static function testJITOnWindows() + { + // see https://github.com/php/php-src/issues/11917 + if (strtoupper(substr(PHP_OS, 0, 3)) === 'WIN' && function_exists('opcache_get_status') && PHP_VERSION_ID < 80213 && !defined('PHPSECLIB_ALLOW_JIT')) { + $status = opcache_get_status(); + if ($status && isset($status['jit']) && $status['jit']['enabled'] && $status['jit']['on']) { + return true; + } + } + return false; + } +} |