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<?php
/**
* Pure-PHP arbitrary precision integer arithmetic library.
*
* Supports base-2, base-10, base-16, and base-256 numbers. Uses the GMP or BCMath extensions, if available,
* and an internal implementation, otherwise.
*
* PHP version 5 and 7
*
* Here's an example of how to use this library:
* <code>
* <?php
* $a = new \phpseclib3\Math\BigInteger(2);
* $b = new \phpseclib3\Math\BigInteger(3);
*
* $c = $a->add($b);
*
* echo $c->toString(); // outputs 5
* ?>
* </code>
*
* @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
*/
namespace phpseclib3\Math;
use phpseclib3\Exception\BadConfigurationException;
use phpseclib3\Math\BigInteger\Engines\Engine;
/**
* Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256
* numbers.
*
* @package BigInteger
* @author Jim Wigginton <terrafrost@php.net>
* @access public
*/
class BigInteger implements \JsonSerializable
{
/**
* Main Engine
*
* @var class-string<Engine>
*/
private static $mainEngine;
/**
* Selected Engines
*
* @var list<string>
*/
private static $engines;
/**
* The actual BigInteger object
*
* @var object
*/
private $value;
/**
* Mode independent value used for serialization.
*
* @see self::__sleep()
* @see self::__wakeup()
* @var string
*/
private $hex;
/**
* Precision (used only for serialization)
*
* @see self::__sleep()
* @see self::__wakeup()
* @var int
*/
private $precision;
/**
* Sets engine type.
*
* Throws an exception if the type is invalid
*
* @param string $main
* @param list<string> $modexps optional
* @return void
*/
public static function setEngine($main, array $modexps = ['DefaultEngine'])
{
self::$engines = [];
$fqmain = 'phpseclib3\\Math\\BigInteger\\Engines\\' . $main;
if (!class_exists($fqmain) || !method_exists($fqmain, 'isValidEngine')) {
throw new \InvalidArgumentException("$main is not a valid engine");
}
if (!$fqmain::isValidEngine()) {
throw new BadConfigurationException("$main is not setup correctly on this system");
}
/** @var class-string<Engine> $fqmain */
self::$mainEngine = $fqmain;
if (!in_array('Default', $modexps)) {
$modexps[] = 'DefaultEngine';
}
$found = false;
foreach ($modexps as $modexp) {
try {
$fqmain::setModExpEngine($modexp);
$found = true;
break;
} catch (\Exception $e) {
}
}
if (!$found) {
throw new BadConfigurationException("No valid modular exponentiation engine found for $main");
}
self::$engines = [$main, $modexp];
}
/**
* Returns the engine type
*
* @return string[]
*/
public static function getEngine()
{
self::initialize_static_variables();
return self::$engines;
}
/**
* Initialize static variables
*/
private static function initialize_static_variables()
{
if (!isset(self::$mainEngine)) {
$engines = [
['GMP'],
['PHP64', ['OpenSSL']],
['BCMath', ['OpenSSL']],
['PHP32', ['OpenSSL']]
];
foreach ($engines as $engine) {
try {
self::setEngine($engine[0], isset($engine[1]) ? $engine[1] : []);
break;
} catch (\Exception $e) {
}
}
}
}
/**
* Converts base-2, base-10, base-16, and binary strings (base-256) to BigIntegers.
*
* If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using
* two's compliment. The sole exception to this is -10, which is treated the same as 10 is.
*
* @param string|int|BigInteger\Engines\Engine $x Base-10 number or base-$base number if $base set.
* @param int $base
*/
public function __construct($x = 0, $base = 10)
{
self::initialize_static_variables();
if ($x instanceof self::$mainEngine) {
$this->value = clone $x;
} elseif ($x instanceof BigInteger\Engines\Engine) {
$this->value = new static("$x");
$this->value->setPrecision($x->getPrecision());
} else {
$this->value = new self::$mainEngine($x, $base);
}
}
/**
* Converts a BigInteger to a base-10 number.
*
* @return string
*/
public function toString()
{
return $this->value->toString();
}
/**
* __toString() magic method
*/
public function __toString()
{
return (string)$this->value;
}
/**
* __debugInfo() magic method
*
* Will be called, automatically, when print_r() or var_dump() are called
*/
public function __debugInfo()
{
return $this->value->__debugInfo();
}
/**
* Converts a BigInteger to a byte string (eg. base-256).
*
* @param bool $twos_compliment
* @return string
*/
public function toBytes($twos_compliment = false)
{
return $this->value->toBytes($twos_compliment);
}
/**
* Converts a BigInteger to a hex string (eg. base-16).
*
* @param bool $twos_compliment
* @return string
*/
public function toHex($twos_compliment = false)
{
return $this->value->toHex($twos_compliment);
}
/**
* Converts a BigInteger to a bit string (eg. base-2).
*
* Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
* saved as two's compliment.
*
* @param bool $twos_compliment
* @return string
*/
public function toBits($twos_compliment = false)
{
return $this->value->toBits($twos_compliment);
}
/**
* Adds two BigIntegers.
*
* @param BigInteger $y
* @return BigInteger
*/
public function add(BigInteger $y)
{
return new static($this->value->add($y->value));
}
/**
* Subtracts two BigIntegers.
*
* @param BigInteger $y
* @return BigInteger
*/
public function subtract(BigInteger $y)
{
return new static($this->value->subtract($y->value));
}
/**
* Multiplies two BigIntegers
*
* @param BigInteger $x
* @return BigInteger
*/
public function multiply(BigInteger $x)
{
return new static($this->value->multiply($x->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).
*
* Here's an example:
* <code>
* <?php
* $a = new \phpseclib3\Math\BigInteger('10');
* $b = new \phpseclib3\Math\BigInteger('20');
*
* list($quotient, $remainder) = $a->divide($b);
*
* echo $quotient->toString(); // outputs 0
* echo "\r\n";
* echo $remainder->toString(); // outputs 10
* ?>
* </code>
*
* @param BigInteger $y
* @return BigInteger[]
*/
public function divide(BigInteger $y)
{
list($q, $r) = $this->value->divide($y->value);
return [
new static($q),
new static($r)
];
}
/**
* Calculates modular inverses.
*
* Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
*
* @param BigInteger $n
* @return BigInteger
*/
public function modInverse(BigInteger $n)
{
return new static($this->value->modInverse($n->value));
}
/**
* Calculates modular inverses.
*
* Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
*
* @param BigInteger $n
* @return BigInteger[]
*/
public function extendedGCD(BigInteger $n)
{
extract($this->value->extendedGCD($n->value));
/**
* @var BigInteger $gcd
* @var BigInteger $x
* @var BigInteger $y
*/
return [
'gcd' => new static($gcd),
'x' => new static($x),
'y' => new static($y)
];
}
/**
* Calculates the greatest common divisor
*
* Say you have 693 and 609. The GCD is 21.
*
* @param BigInteger $n
* @return BigInteger
*/
public function gcd(BigInteger $n)
{
return new static($this->value->gcd($n->value));
}
/**
* Absolute value.
*
* @return BigInteger
* @access public
*/
public function abs()
{
return new static($this->value->abs());
}
/**
* Set Precision
*
* Some bitwise operations give different results depending on the precision being used. Examples include left
* shift, not, and rotates.
*
* @param int $bits
*/
public function setPrecision($bits)
{
$this->value->setPrecision($bits);
}
/**
* Get Precision
*
* Returns the precision if it exists, false if it doesn't
*
* @return int|bool
*/
public function getPrecision()
{
return $this->value->getPrecision();
}
/**
* Serialize
*
* Will be called, automatically, when serialize() is called on a BigInteger object.
*
* __sleep() / __wakeup() have been around since PHP 4.0
*
* \Serializable was introduced in PHP 5.1 and deprecated in PHP 8.1:
* https://wiki.php.net/rfc/phase_out_serializable
*
* __serialize() / __unserialize() were introduced in PHP 7.4:
* https://wiki.php.net/rfc/custom_object_serialization
*
* @return array
*/
public function __sleep()
{
$this->hex = $this->toHex(true);
$vars = ['hex'];
if ($this->getPrecision() > 0) {
$vars[] = 'precision';
}
return $vars;
}
/**
* Serialize
*
* Will be called, automatically, when unserialize() is called on a BigInteger object.
*/
public function __wakeup()
{
$temp = new static($this->hex, -16);
$this->value = $temp->value;
if ($this->precision > 0) {
// recalculate $this->bitmask
$this->setPrecision($this->precision);
}
}
/**
* JSON Serialize
*
* Will be called, automatically, when json_encode() is called on a BigInteger object.
*/
#[\ReturnTypeWillChange]
public function jsonSerialize()
{
$result = ['hex' => $this->toHex(true)];
if ($this->precision > 0) {
$result['precision'] = $this->getPrecision();
}
return $result;
}
/**
* Performs modular exponentiation.
*
* @param BigInteger $e
* @param BigInteger $n
* @return BigInteger
*/
public function powMod(BigInteger $e, BigInteger $n)
{
return new static($this->value->powMod($e->value, $n->value));
}
/**
* Performs modular exponentiation.
*
* @param BigInteger $e
* @param BigInteger $n
* @return BigInteger
*/
public function modPow(BigInteger $e, BigInteger $n)
{
return new static($this->value->modPow($e->value, $n->value));
}
/**
* Compares two numbers.
*
* Although one might think !$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 BigInteger $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.
* @access public
* @see self::equals()
*/
public function compare(BigInteger $y)
{
return $this->value->compare($y->value);
}
/**
* 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 BigInteger $x
* @return bool
*/
public function equals(BigInteger $x)
{
return $this->value->equals($x->value);
}
/**
* Logical Not
*
* @return BigInteger
*/
public function bitwise_not()
{
return new static($this->value->bitwise_not());
}
/**
* Logical And
*
* @param BigInteger $x
* @return BigInteger
*/
public function bitwise_and(BigInteger $x)
{
return new static($this->value->bitwise_and($x->value));
}
/**
* Logical Or
*
* @param BigInteger $x
* @return BigInteger
*/
public function bitwise_or(BigInteger $x)
{
return new static($this->value->bitwise_or($x->value));
}
/**
* Logical Exclusive Or
*
* @param BigInteger $x
* @return BigInteger
*/
public function bitwise_xor(BigInteger $x)
{
return new static($this->value->bitwise_xor($x->value));
}
/**
* Logical Right Shift
*
* Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.
*
* @param int $shift
* @return BigInteger
*/
public function bitwise_rightShift($shift)
{
return new static($this->value->bitwise_rightShift($shift));
}
/**
* Logical Left Shift
*
* Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.
*
* @param int $shift
* @return BigInteger
*/
public function bitwise_leftShift($shift)
{
return new static($this->value->bitwise_leftShift($shift));
}
/**
* Logical Left Rotate
*
* Instead of the top x bits being dropped they're appended to the shifted bit string.
*
* @param int $shift
* @return BigInteger
*/
public function bitwise_leftRotate($shift)
{
return new static($this->value->bitwise_leftRotate($shift));
}
/**
* Logical Right Rotate
*
* Instead of the bottom x bits being dropped they're prepended to the shifted bit string.
*
* @param int $shift
* @return BigInteger
*/
public function bitwise_rightRotate($shift)
{
return new static($this->value->bitwise_rightRotate($shift));
}
/**
* Returns the smallest and largest n-bit number
*
* @param int $bits
* @return BigInteger[]
*/
public static function minMaxBits($bits)
{
self::initialize_static_variables();
$class = self::$mainEngine;
extract($class::minMaxBits($bits));
/** @var BigInteger $min
* @var BigInteger $max
*/
return [
'min' => new static($min),
'max' => new static($max)
];
}
/**
* Return the size of a BigInteger in bits
*
* @return int
*/
public function getLength()
{
return $this->value->getLength();
}
/**
* Return the size of a BigInteger in bytes
*
* @return int
*/
public function getLengthInBytes()
{
return $this->value->getLengthInBytes();
}
/**
* Generates a random number of a certain size
*
* Bit length is equal to $size
*
* @param int $size
* @return BigInteger
*/
public static function random($size)
{
self::initialize_static_variables();
$class = self::$mainEngine;
return new static($class::random($size));
}
/**
* Generates a random prime number of a certain size
*
* Bit length is equal to $size
*
* @param int $size
* @return BigInteger
*/
public static function randomPrime($size)
{
self::initialize_static_variables();
$class = self::$mainEngine;
return new static($class::randomPrime($size));
}
/**
* Generate a random prime number between a range
*
* If there's not a prime within the given range, false will be returned.
*
* @param BigInteger $min
* @param BigInteger $max
* @return false|BigInteger
*/
public static function randomRangePrime(BigInteger $min, BigInteger $max)
{
$class = self::$mainEngine;
return new static($class::randomRangePrime($min->value, $max->value));
}
/**
* 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 BigInteger $min
* @param BigInteger $max
* @return BigInteger
*/
public static function randomRange(BigInteger $min, BigInteger $max)
{
$class = self::$mainEngine;
return new static($class::randomRange($min->value, $max->value));
}
/**
* Checks a numer to see if it's prime
*
* Assuming the $t parameter is not set, this function has an error rate of 2**-80. The main motivation for the
* $t parameter is distributability. BigInteger::randomPrime() can be distributed across multiple pageloads
* on a website instead of just one.
*
* @param int|bool $t
* @return bool
*/
public function isPrime($t = false)
{
return $this->value->isPrime($t);
}
/**
* Calculates the nth root of a biginteger.
*
* Returns the nth root of a positive biginteger, where n defaults to 2
*
* @param int $n optional
* @return BigInteger
*/
public function root($n = 2)
{
return new static($this->value->root($n));
}
/**
* Performs exponentiation.
*
* @param BigInteger $n
* @return BigInteger
*/
public function pow(BigInteger $n)
{
return new static($this->value->pow($n->value));
}
/**
* Return the minimum BigInteger between an arbitrary number of BigIntegers.
*
* @param BigInteger ...$nums
* @return BigInteger
*/
public static function min(BigInteger ...$nums)
{
$class = self::$mainEngine;
$nums = array_map(function ($num) {
return $num->value;
}, $nums);
return new static($class::min(...$nums));
}
/**
* Return the maximum BigInteger between an arbitrary number of BigIntegers.
*
* @param BigInteger ...$nums
* @return BigInteger
*/
public static function max(BigInteger ...$nums)
{
$class = self::$mainEngine;
$nums = array_map(function ($num) {
return $num->value;
}, $nums);
return new static($class::max(...$nums));
}
/**
* Tests BigInteger to see if it is between two integers, inclusive
*
* @param BigInteger $min
* @param BigInteger $max
* @return bool
*/
public function between(BigInteger $min, BigInteger $max)
{
return $this->value->between($min->value, $max->value);
}
/**
* Clone
*/
public function __clone()
{
$this->value = clone $this->value;
}
/**
* Is Odd?
*
* @return bool
*/
public function isOdd()
{
return $this->value->isOdd();
}
/**
* Tests if a bit is set
*
* @param int $x
* @return bool
*/
public function testBit($x)
{
return $this->value->testBit($x);
}
/**
* Is Negative?
*
* @return bool
*/
public function isNegative()
{
return $this->value->isNegative();
}
/**
* Negate
*
* Given $k, returns -$k
*
* @return BigInteger
*/
public function negate()
{
return new static($this->value->negate());
}
/**
* 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 BigInteger $r
* @return int
*/
public static function scan1divide(BigInteger $r)
{
$class = self::$mainEngine;
return $class::scan1divide($r->value);
}
/**
* Create Recurring Modulo Function
*
* Sometimes it may be desirable to do repeated modulos with the same number outside of
* modular exponentiation
*
* @return callable
*/
public function createRecurringModuloFunction()
{
$func = $this->value->createRecurringModuloFunction();
return function (BigInteger $x) use ($func) {
return new static($func($x->value));
};
}
/**
* Bitwise Split
*
* Splits BigInteger's into chunks of $split bits
*
* @param int $split
* @return BigInteger[]
*/
public function bitwise_split($split)
{
return array_map(function ($val) {
return new static($val);
}, $this->value->bitwise_split($split));
}
}