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<?php
/**
* BCMath 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 ParagonIE\ConstantTime\Hex;
use phpseclib3\Exception\BadConfigurationException;
/**
* BCMath Engine.
*
* @package BCMath
* @author Jim Wigginton <terrafrost@php.net>
* @access public
*/
class BCMath extends Engine
{
/**
* Can Bitwise operations be done fast?
*
* @see parent::bitwise_leftRotate()
* @see parent::bitwise_rightRotate()
* @access protected
*/
const FAST_BITWISE = false;
/**
* Engine Directory
*
* @see parent::setModExpEngine
* @access protected
*/
const ENGINE_DIR = 'BCMath';
/**
* Modular Exponentiation Engine
*
* @var string
*/
protected static $modexpEngine;
/**
* Engine Validity Flag
*
* @var bool
*/
protected static $isValidEngine;
/**
* BigInteger(0)
*
* @var \phpseclib3\Math\BigInteger\Engines\BCMath
*/
protected static $zero;
/**
* BigInteger(1)
*
* @var \phpseclib3\Math\BigInteger\Engines\BCMath
*/
protected static $one;
/**
* BigInteger(2)
*
* @var \phpseclib3\Math\BigInteger\Engines\BCMath
*/
protected static $two;
/**
* Primes > 2 and < 1000
*
* @var array
*/
protected static $primes;
/**
* Test for engine validity
*
* @see parent::__construct()
* @return bool
*/
public static function isValidEngine()
{
return extension_loaded('bcmath');
}
/**
* Default constructor
*
* @param mixed $x integer Base-10 number or base-$base number if $base set.
* @param int $base
* @see parent::__construct()
* @return \phpseclib3\Math\BigInteger\Engines\BCMath
*/
public function __construct($x = 0, $base = 10)
{
if (!isset(self::$isValidEngine)) {
self::$isValidEngine = self::isValidEngine();
}
if (!self::$isValidEngine) {
throw new BadConfigurationException('BCMath is not setup correctly on this system');
}
$this->value = '0';
parent::__construct($x, $base);
}
/**
* Initialize a BCMath BigInteger Engine instance
*
* @param int $base
* @see parent::__construct()
*/
protected function initialize($base)
{
switch (abs($base)) {
case 256:
// round $len to the nearest 4
$len = (strlen($this->value) + 3) & 0xFFFFFFFC;
$x = str_pad($this->value, $len, chr(0), STR_PAD_LEFT);
$this->value = '0';
for ($i = 0; $i < $len; $i+= 4) {
$this->value = bcmul($this->value, '4294967296', 0); // 4294967296 == 2**32
$this->value = bcadd($this->value, 0x1000000 * ord($x[$i]) + ((ord($x[$i + 1]) << 16) | (ord($x[$i + 2]) << 8) | ord($x[$i + 3])), 0);
}
if ($this->is_negative) {
$this->value = '-' . $this->value;
}
break;
case 16:
$x = (strlen($this->value) & 1) ? '0' . $this->value : $this->value;
$temp = new self(Hex::decode($x), 256);
$this->value = $this->is_negative ? '-' . $temp->value : $temp->value;
$this->is_negative = false;
break;
case 10:
// explicitly casting $x to a string is necessary, here, since doing $x[0] on -1 yields different
// results then doing it on '-1' does (modInverse does $x[0])
$this->value = $this->value === '-' ? '0' : (string) $this->value;
}
}
/**
* Converts a BigInteger to a base-10 number.
*
* @return string
*/
public function toString()
{
if ($this->value === '0') {
return '0';
}
return ltrim($this->value, '0');
}
/**
* Converts a BigInteger to a byte string (eg. base-256).
*
* @param bool $twos_compliment
* @return string
*/
function toBytes($twos_compliment = false)
{
if ($twos_compliment) {
return $this->toBytesHelper();
}
$value = '';
$current = $this->value;
if ($current[0] == '-') {
$current = substr($current, 1);
}
while (bccomp($current, '0', 0) > 0) {
$temp = bcmod($current, '16777216');
$value = chr($temp >> 16) . chr($temp >> 8) . chr($temp) . $value;
$current = bcdiv($current, '16777216', 0);
}
return $this->precision > 0 ?
substr(str_pad($value, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) :
ltrim($value, chr(0));
}
/**
* Adds two BigIntegers.
*
* @param BCMath $y
* @return BCMath
*/
public function add(BCMath $y)
{
$temp = new self();
$temp->value = bcadd($this->value, $y->value);
return $this->normalize($temp);
}
/**
* Subtracts two BigIntegers.
*
* @param BCMath $y
* @return BCMath
*/
public function subtract(BCMath $y)
{
$temp = new self();
$temp->value = bcsub($this->value, $y->value);
return $this->normalize($temp);
}
/**
* Multiplies two BigIntegers.
*
* @param BCMath $x
* @return BCMath
*/
public function multiply(BCMath $x)
{
$temp = new self();
$temp->value = bcmul($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 BCMath $y
* @return BCMath
*/
public function divide(BCMath $y)
{
$quotient = new self();
$remainder = new self();
$quotient->value = bcdiv($this->value, $y->value, 0);
$remainder->value = bcmod($this->value, $y->value);
if ($remainder->value[0] == '-') {
$remainder->value = bcadd($remainder->value, $y->value[0] == '-' ? substr($y->value, 1) : $y->value, 0);
}
return [$this->normalize($quotient), $this->normalize($remainder)];
}
/**
* Calculates modular inverses.
*
* Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
*
* @return false|BCMath
* @param \phpseclib3\Math\BigInteger\Engines\BCMath $n
*/
public function modInverse(BCMath $n)
{
return $this->modInverseHelper($n);
}
/**
* 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 BCMath $n
* @return BCMath
*/
public function extendedGCD(BCMath $n)
{
// it might be faster to use the binary xGCD algorithim here, as well, but (1) that algorithim works
// best when the base is a power of 2 and (2) i don't think it'd make much difference, anyway. as is,
// the basic extended euclidean algorithim is what we're using.
$u = $this->value;
$v = $n->value;
$a = '1';
$b = '0';
$c = '0';
$d = '1';
while (bccomp($v, '0', 0) != 0) {
$q = bcdiv($u, $v, 0);
$temp = $u;
$u = $v;
$v = bcsub($temp, bcmul($v, $q, 0), 0);
$temp = $a;
$a = $c;
$c = bcsub($temp, bcmul($a, $q, 0), 0);
$temp = $b;
$b = $d;
$d = bcsub($temp, bcmul($b, $q, 0), 0);
}
return [
'gcd' => $this->normalize(new static($u)),
'x' => $this->normalize(new static($a)),
'y' => $this->normalize(new static($b))
];
}
/**
* Calculates the greatest common divisor
*
* Say you have 693 and 609. The GCD is 21.
*
* @param BCMath $n
* @return BCMath
*/
public function gcd(BCMath $n)
{
extract($this->extendedGCD($n));
/** @var BCMath $gcd */
return $gcd;
}
/**
* Absolute value.
*
* @return \phpseclib3\Math\BigInteger\Engines\BCMath
*/
public function abs()
{
$temp = new static();
$temp->value = strlen($this->value) && $this->value[0] == '-' ?
substr($this->value, 1) :
$this->value;
return $temp;
}
/**
* Logical And
*
* @param BCMath $x
* @return BCMath
*/
public function bitwise_and(BCMath $x)
{
return $this->bitwiseAndHelper($x);
}
/**
* Logical Or
*
* @param BCMath $x
* @return BCMath
*/
public function bitwise_or(BCMath $x)
{
return $this->bitwiseXorHelper($x);
}
/**
* Logical Exclusive Or
*
* @param BCMath $x
* @return BCMath
*/
public function bitwise_xor(BCMath $x)
{
return $this->bitwiseXorHelper($x);
}
/**
* Logical Right Shift
*
* Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.
*
* @param int $shift
* @return \phpseclib3\Math\BigInteger\Engines\BCMath
*/
public function bitwise_rightShift($shift)
{
$temp = new static();
$temp->value = bcdiv($this->value, bcpow('2', $shift, 0), 0);
return $this->normalize($temp);
}
/**
* Logical Left Shift
*
* Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.
*
* @param int $shift
* @return \phpseclib3\Math\BigInteger\Engines\BCMath
*/
public function bitwise_leftShift($shift)
{
$temp = new static();
$temp->value = bcmul($this->value, bcpow('2', $shift, 0), 0);
return $this->normalize($temp);
}
/**
* 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 BCMath $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.
* @see self::equals()
*/
public function compare(BCMath $y)
{
return bccomp($this->value, $y->value, 0);
}
/**
* 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 BCMath $x
* @return bool
*/
public function equals(BCMath $x)
{
return $this->value == $x->value;
}
/**
* Performs modular exponentiation.
*
* @param BCMath $e
* @param BCMath $n
* @return BCMath
*/
public function modPow(BCMath $e, BCMath $n)
{
return $this->powModOuter($e, $n);
}
/**
* Performs modular exponentiation.
*
* Alias for modPow().
*
* @param BCMath $e
* @param BCMath $n
* @return BCMath
*/
public function powMod(BCMath $e, BCMath $n)
{
return $this->powModOuter($e, $n);
}
/**
* Performs modular exponentiation.
*
* @param BCMath $e
* @param BCMath $n
* @return BCMath
*/
protected function powModInner(BCMath $e, BCMath $n)
{
try {
$class = self::$modexpEngine;
return $class::powModHelper($this, $e, $n, static::class);
} catch (\Exception $err) {
return BCMath\DefaultEngine::powModHelper($this, $e, $n, static::class);
}
}
/**
* Normalize
*
* Removes leading zeros and truncates (if necessary) to maintain the appropriate precision
*
* @param BCMath $result
* @return BCMath
*/
protected function normalize(BCMath $result)
{
unset($result->reduce);
$result->precision = $this->precision;
$result->bitmask = $this->bitmask;
if ($result->bitmask !== false) {
$result->value = bcmod($result->value, $result->bitmask->value);
}
return $result;
}
/**
* Generate a random prime number between a range
*
* If there's not a prime within the given range, false will be returned.
*
* @param BCMath $min
* @param BCMath $max
* @return false|BCMath
*/
public static function randomRangePrime(BCMath $min, BCMath $max)
{
return self::randomRangePrimeOuter($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 BCMath $min
* @param BCMath $max
* @return BCMath
*/
public static function randomRange(BCMath $min, BCMath $max)
{
return self::randomRangeHelper($min, $max);
}
/**
* Make the current number odd
*
* If the current number is odd it'll be unchanged. If it's even, one will be added to it.
*
* @see self::randomPrime()
*/
protected function make_odd()
{
if (!$this->isOdd()) {
$this->value = bcadd($this->value, '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 ($this->value[strlen($this->value) - 1] % 2 == 0) {
return false;
}
$value = $this->value;
foreach (self::$primes as $prime) {
$r = bcmod($this->value, $prime);
if ($r == '0') {
return $this->value == $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));
*
* @see self::isPrime()
* @param BCMath $r
* @return int
*/
public static function scan1divide(BCMath $r)
{
$r_value = &$r->value;
$s = 0;
// if $n was 1, $r would be 0 and this would be an infinite loop, hence our $this->equals(static::$one) check earlier
while ($r_value[strlen($r_value) - 1] % 2 == 0) {
$r_value = bcdiv($r_value, '2', 0);
++$s;
}
return $s;
}
/**
* Performs exponentiation.
*
* @param BCMath $n
* @return BCMath
*/
public function pow(BCMath $n)
{
$temp = new self();
$temp->value = bcpow($this->value, $n->value);
return $this->normalize($temp);
}
/**
* Return the minimum BigInteger between an arbitrary number of BigIntegers.
*
* @param BCMath ...$nums
* @return BCMath
*/
public static function min(BCMath ...$nums)
{
return self::minHelper($nums);
}
/**
* Return the maximum BigInteger between an arbitrary number of BigIntegers.
*
* @param BCMath ...$nums
* @return BCMath
*/
public static function max(BCMath ...$nums)
{
return self::maxHelper($nums);
}
/**
* Tests BigInteger to see if it is between two integers, inclusive
*
* @param BCMath $min
* @param BCMath $max
* @return bool
*/
public function between(BCMath $min, BCMath $max)
{
return $this->compare($min) >= 0 && $this->compare($max) <= 0;
}
/**
* Set Bitmask
*
* @return Engine
* @param int $bits
* @see self::setPrecision()
*/
protected static function setBitmask($bits)
{
$temp = parent::setBitmask($bits);
return $temp->add(static::$one);
}
/**
* Is Odd?
*
* @return boolean
*/
public function isOdd()
{
return $this->value[strlen($this->value) - 1] % 2 == 1;
}
/**
* Tests if a bit is set
*
* @return boolean
*/
public function testBit($x)
{
return bccomp(
bcmod($this->value, bcpow('2', $x + 1, 0), 0),
bcpow('2', $x, 0),
0
) >= 0;
}
/**
* Is Negative?
*
* @return boolean
*/
public function isNegative()
{
return strlen($this->value) && $this->value[0] == '-';
}
/**
* Negate
*
* Given $k, returns -$k
*
* @return BCMath
*/
public function negate()
{
$temp = clone $this;
if (!strlen($temp->value)) {
return $temp;
}
$temp->value = $temp->value[0] == '-' ?
substr($this->value, 1) :
'-' . $this->value;
return $temp;
}
}
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