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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> * * @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. * * @author Jim Wigginton <terrafrost@php.net> */ 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; $found = false; foreach ($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)) { $engines = [ ['GMP'], ['PHP64', ['OpenSSL']], ['BCMath', ['OpenSSL']], ['PHP32', ['OpenSSL']], ['PHP64', ['DefaultEngine']], ['PHP32', ['DefaultEngine']] ]; foreach ($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($n->value)); } /** * Absolute value. * * @return BigInteger */ public function abs() { return new static($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. * * @return array{hex: string, precision?: int] */ #[\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. * @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)); } }