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<?php
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declare(strict_types=1);
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namespace Brick\Math;
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use Brick\Math\Exception\DivisionByZeroException;
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use Brick\Math\Exception\IntegerOverflowException;
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use Brick\Math\Exception\MathException;
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use Brick\Math\Exception\NegativeNumberException;
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use Brick\Math\Exception\NumberFormatException;
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use Brick\Math\Internal\Calculator;
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/**
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* An arbitrary-size integer.
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*
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* All methods accepting a number as a parameter accept either a BigInteger instance,
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* an integer, or a string representing an arbitrary size integer.
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*
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* @psalm-immutable
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*/
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final class BigInteger extends BigNumber
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{
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/**
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* The value, as a string of digits with optional leading minus sign.
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*
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* No leading zeros must be present.
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* No leading minus sign must be present if the number is zero.
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*
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* @var string
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*/
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private $value;
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/**
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* Protected constructor. Use a factory method to obtain an instance.
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*
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* @param string $value A string of digits, with optional leading minus sign.
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*/
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protected function __construct(string $value)
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{
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$this->value = $value;
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}
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/**
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* Creates a BigInteger of the given value.
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*
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* @param BigNumber|int|float|string $value
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*
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* @return BigInteger
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*
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* @throws MathException If the value cannot be converted to a BigInteger.
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*
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* @psalm-pure
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*/
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public static function of($value) : BigNumber
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{
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return parent::of($value)->toBigInteger();
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}
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/**
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* Creates a number from a string in a given base.
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*
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* The string can optionally be prefixed with the `+` or `-` sign.
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*
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* Bases greater than 36 are not supported by this method, as there is no clear consensus on which of the lowercase
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* or uppercase characters should come first. Instead, this method accepts any base up to 36, and does not
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* differentiate lowercase and uppercase characters, which are considered equal.
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*
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* For bases greater than 36, and/or custom alphabets, use the fromArbitraryBase() method.
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*
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* @param string $number The number to convert, in the given base.
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* @param int $base The base of the number, between 2 and 36.
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*
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* @return BigInteger
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*
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* @throws NumberFormatException If the number is empty, or contains invalid chars for the given base.
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* @throws \InvalidArgumentException If the base is out of range.
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*
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* @psalm-pure
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*/
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public static function fromBase(string $number, int $base) : BigInteger
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{
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if ($number === '') {
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throw new NumberFormatException('The number cannot be empty.');
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}
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if ($base < 2 || $base > 36) {
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throw new \InvalidArgumentException(\sprintf('Base %d is not in range 2 to 36.', $base));
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}
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if ($number[0] === '-') {
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$sign = '-';
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$number = \substr($number, 1);
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} elseif ($number[0] === '+') {
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$sign = '';
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$number = \substr($number, 1);
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} else {
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$sign = '';
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}
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if ($number === '') {
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throw new NumberFormatException('The number cannot be empty.');
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}
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$number = \ltrim($number, '0');
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if ($number === '') {
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// The result will be the same in any base, avoid further calculation.
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return BigInteger::zero();
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}
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if ($number === '1') {
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// The result will be the same in any base, avoid further calculation.
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return new BigInteger($sign . '1');
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}
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$pattern = '/[^' . \substr(Calculator::ALPHABET, 0, $base) . ']/';
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if (\preg_match($pattern, \strtolower($number), $matches) === 1) {
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throw new NumberFormatException(\sprintf('"%s" is not a valid character in base %d.', $matches[0], $base));
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}
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if ($base === 10) {
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// The number is usable as is, avoid further calculation.
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return new BigInteger($sign . $number);
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}
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$result = Calculator::get()->fromBase($number, $base);
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return new BigInteger($sign . $result);
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}
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/**
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* Parses a string containing an integer in an arbitrary base, using a custom alphabet.
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*
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* Because this method accepts an alphabet with any character, including dash, it does not handle negative numbers.
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*
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* @param string $number The number to parse.
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* @param string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8.
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*
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* @return BigInteger
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*
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* @throws NumberFormatException If the given number is empty or contains invalid chars for the given alphabet.
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* @throws \InvalidArgumentException If the alphabet does not contain at least 2 chars.
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*
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* @psalm-pure
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*/
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public static function fromArbitraryBase(string $number, string $alphabet) : BigInteger
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{
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if ($number === '') {
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throw new NumberFormatException('The number cannot be empty.');
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}
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$base = \strlen($alphabet);
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if ($base < 2) {
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throw new \InvalidArgumentException('The alphabet must contain at least 2 chars.');
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}
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$pattern = '/[^' . \preg_quote($alphabet, '/') . ']/';
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if (\preg_match($pattern, $number, $matches) === 1) {
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throw NumberFormatException::charNotInAlphabet($matches[0]);
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}
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$number = Calculator::get()->fromArbitraryBase($number, $alphabet, $base);
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return new BigInteger($number);
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}
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/**
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* Translates a string of bytes containing the binary representation of a BigInteger into a BigInteger.
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*
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* The input string is assumed to be in big-endian byte-order: the most significant byte is in the zeroth element.
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*
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* If `$signed` is true, the input is assumed to be in two's-complement representation, and the leading bit is
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* interpreted as a sign bit. If `$signed` is false, the input is interpreted as an unsigned number, and the
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* resulting BigInteger will always be positive or zero.
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*
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* This method can be used to retrieve a number exported by `toBytes()`, as long as the `$signed` flags match.
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*
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* @param string $value The byte string.
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* @param bool $signed Whether to interpret as a signed number in two's-complement representation with a leading
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* sign bit.
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*
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* @return BigInteger
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*
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* @throws NumberFormatException If the string is empty.
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*/
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public static function fromBytes(string $value, bool $signed = true) : BigInteger
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{
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if ($value === '') {
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throw new NumberFormatException('The byte string must not be empty.');
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}
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$twosComplement = false;
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if ($signed) {
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$x = \ord($value[0]);
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if (($twosComplement = ($x >= 0x80))) {
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$value = ~$value;
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}
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}
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$number = self::fromBase(\bin2hex($value), 16);
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if ($twosComplement) {
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return $number->plus(1)->negated();
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}
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return $number;
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}
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/**
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* Generates a pseudo-random number in the range 0 to 2^numBits - 1.
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*
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* Using the default random bytes generator, this method is suitable for cryptographic use.
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*
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* @psalm-param callable(int): string $randomBytesGenerator
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*
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* @param int $numBits The number of bits.
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* @param callable|null $randomBytesGenerator A function that accepts a number of bytes as an integer, and returns a
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* string of random bytes of the given length. Defaults to the
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* `random_bytes()` function.
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*
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* @return BigInteger
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*
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* @throws \InvalidArgumentException If $numBits is negative.
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*/
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public static function randomBits(int $numBits, ?callable $randomBytesGenerator = null) : BigInteger
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{
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if ($numBits < 0) {
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throw new \InvalidArgumentException('The number of bits cannot be negative.');
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}
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if ($numBits === 0) {
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return BigInteger::zero();
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}
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if ($randomBytesGenerator === null) {
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$randomBytesGenerator = 'random_bytes';
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}
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$byteLength = \intdiv($numBits - 1, 8) + 1;
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$extraBits = ($byteLength * 8 - $numBits);
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$bitmask = \chr(0xFF >> $extraBits);
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$randomBytes = $randomBytesGenerator($byteLength);
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$randomBytes[0] = $randomBytes[0] & $bitmask;
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return self::fromBytes($randomBytes, false);
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}
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/**
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* Generates a pseudo-random number between `$min` and `$max`.
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*
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* Using the default random bytes generator, this method is suitable for cryptographic use.
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*
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* @psalm-param (callable(int): string)|null $randomBytesGenerator
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*
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* @param BigNumber|int|float|string $min The lower bound. Must be convertible to a BigInteger.
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* @param BigNumber|int|float|string $max The upper bound. Must be convertible to a BigInteger.
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* @param callable|null $randomBytesGenerator A function that accepts a number of bytes as an integer,
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* and returns a string of random bytes of the given length.
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* Defaults to the `random_bytes()` function.
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*
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* @return BigInteger
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*
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* @throws MathException If one of the parameters cannot be converted to a BigInteger,
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* or `$min` is greater than `$max`.
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*/
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public static function randomRange($min, $max, ?callable $randomBytesGenerator = null) : BigInteger
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{
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$min = BigInteger::of($min);
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$max = BigInteger::of($max);
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if ($min->isGreaterThan($max)) {
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throw new MathException('$min cannot be greater than $max.');
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}
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if ($min->isEqualTo($max)) {
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return $min;
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}
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$diff = $max->minus($min);
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$bitLength = $diff->getBitLength();
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// try until the number is in range (50% to 100% chance of success)
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do {
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$randomNumber = self::randomBits($bitLength, $randomBytesGenerator);
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} while ($randomNumber->isGreaterThan($diff));
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return $randomNumber->plus($min);
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}
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/**
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* Returns a BigInteger representing zero.
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*
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* @return BigInteger
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*
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* @psalm-pure
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*/
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public static function zero() : BigInteger
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{
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/**
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* @psalm-suppress ImpureStaticVariable
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* @var BigInteger|null $zero
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*/
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static $zero;
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if ($zero === null) {
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$zero = new BigInteger('0');
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}
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return $zero;
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}
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/**
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* Returns a BigInteger representing one.
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*
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* @return BigInteger
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*
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* @psalm-pure
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*/
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public static function one() : BigInteger
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{
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/**
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* @psalm-suppress ImpureStaticVariable
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* @var BigInteger|null $one
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*/
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static $one;
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if ($one === null) {
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$one = new BigInteger('1');
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}
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return $one;
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}
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/**
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* Returns a BigInteger representing ten.
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*
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* @return BigInteger
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*
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* @psalm-pure
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*/
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public static function ten() : BigInteger
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{
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/**
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* @psalm-suppress ImpureStaticVariable
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* @var BigInteger|null $ten
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*/
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static $ten;
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if ($ten === null) {
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$ten = new BigInteger('10');
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}
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return $ten;
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}
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/**
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* Returns the sum of this number and the given one.
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*
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* @param BigNumber|int|float|string $that The number to add. Must be convertible to a BigInteger.
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*
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* @return BigInteger The result.
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*
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* @throws MathException If the number is not valid, or is not convertible to a BigInteger.
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*/
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public function plus($that) : BigInteger
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{
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$that = BigInteger::of($that);
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if ($that->value === '0') {
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return $this;
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}
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if ($this->value === '0') {
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return $that;
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}
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$value = Calculator::get()->add($this->value, $that->value);
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return new BigInteger($value);
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}
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/**
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* Returns the difference of this number and the given one.
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*
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* @param BigNumber|int|float|string $that The number to subtract. Must be convertible to a BigInteger.
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*
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* @return BigInteger The result.
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*
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* @throws MathException If the number is not valid, or is not convertible to a BigInteger.
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*/
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public function minus($that) : BigInteger
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{
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$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '0') {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
$value = Calculator::get()->sub($this->value, $that->value);
|
|
|
|
|
|
|
|
return new BigInteger($value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the product of this number and the given one.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The multiplier. Must be convertible to a BigInteger.
|
|
|
|
*
|
|
|
|
* @return BigInteger The result.
|
|
|
|
*
|
|
|
|
* @throws MathException If the multiplier is not a valid number, or is not convertible to a BigInteger.
|
|
|
|
*/
|
|
|
|
public function multipliedBy($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '1') {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($this->value === '1') {
|
|
|
|
return $that;
|
|
|
|
}
|
|
|
|
|
|
|
|
$value = Calculator::get()->mul($this->value, $that->value);
|
|
|
|
|
|
|
|
return new BigInteger($value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the result of the division of this number by the given one.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
|
|
|
* @param int $roundingMode An optional rounding mode.
|
|
|
|
*
|
|
|
|
* @return BigInteger The result.
|
|
|
|
*
|
|
|
|
* @throws MathException If the divisor is not a valid number, is not convertible to a BigInteger, is zero,
|
|
|
|
* or RoundingMode::UNNECESSARY is used and the remainder is not zero.
|
|
|
|
*/
|
|
|
|
public function dividedBy($that, int $roundingMode = RoundingMode::UNNECESSARY) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '1') {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($that->value === '0') {
|
|
|
|
throw DivisionByZeroException::divisionByZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
$result = Calculator::get()->divRound($this->value, $that->value, $roundingMode);
|
|
|
|
|
|
|
|
return new BigInteger($result);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns this number exponentiated to the given value.
|
|
|
|
*
|
|
|
|
* @param int $exponent The exponent.
|
|
|
|
*
|
|
|
|
* @return BigInteger The result.
|
|
|
|
*
|
|
|
|
* @throws \InvalidArgumentException If the exponent is not in the range 0 to 1,000,000.
|
|
|
|
*/
|
|
|
|
public function power(int $exponent) : BigInteger
|
|
|
|
{
|
|
|
|
if ($exponent === 0) {
|
|
|
|
return BigInteger::one();
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($exponent === 1) {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($exponent < 0 || $exponent > Calculator::MAX_POWER) {
|
|
|
|
throw new \InvalidArgumentException(\sprintf(
|
|
|
|
'The exponent %d is not in the range 0 to %d.',
|
|
|
|
$exponent,
|
|
|
|
Calculator::MAX_POWER
|
|
|
|
));
|
|
|
|
}
|
|
|
|
|
|
|
|
return new BigInteger(Calculator::get()->pow($this->value, $exponent));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the quotient of the division of this number by the given one.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*
|
|
|
|
* @throws DivisionByZeroException If the divisor is zero.
|
|
|
|
*/
|
|
|
|
public function quotient($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '1') {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($that->value === '0') {
|
|
|
|
throw DivisionByZeroException::divisionByZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
$quotient = Calculator::get()->divQ($this->value, $that->value);
|
|
|
|
|
|
|
|
return new BigInteger($quotient);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the remainder of the division of this number by the given one.
|
|
|
|
*
|
|
|
|
* The remainder, when non-zero, has the same sign as the dividend.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*
|
|
|
|
* @throws DivisionByZeroException If the divisor is zero.
|
|
|
|
*/
|
|
|
|
public function remainder($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '1') {
|
|
|
|
return BigInteger::zero();
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($that->value === '0') {
|
|
|
|
throw DivisionByZeroException::divisionByZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
$remainder = Calculator::get()->divR($this->value, $that->value);
|
|
|
|
|
|
|
|
return new BigInteger($remainder);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the quotient and remainder of the division of this number by the given one.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
|
|
|
*
|
|
|
|
* @return BigInteger[] An array containing the quotient and the remainder.
|
|
|
|
*
|
|
|
|
* @throws DivisionByZeroException If the divisor is zero.
|
|
|
|
*/
|
|
|
|
public function quotientAndRemainder($that) : array
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '0') {
|
|
|
|
throw DivisionByZeroException::divisionByZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
[$quotient, $remainder] = Calculator::get()->divQR($this->value, $that->value);
|
|
|
|
|
|
|
|
return [
|
|
|
|
new BigInteger($quotient),
|
|
|
|
new BigInteger($remainder)
|
|
|
|
];
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the modulo of this number and the given one.
|
|
|
|
*
|
|
|
|
* The modulo operation yields the same result as the remainder operation when both operands are of the same sign,
|
|
|
|
* and may differ when signs are different.
|
|
|
|
*
|
|
|
|
* The result of the modulo operation, when non-zero, has the same sign as the divisor.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*
|
|
|
|
* @throws DivisionByZeroException If the divisor is zero.
|
|
|
|
*/
|
|
|
|
public function mod($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '0') {
|
|
|
|
throw DivisionByZeroException::modulusMustNotBeZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
$value = Calculator::get()->mod($this->value, $that->value);
|
|
|
|
|
|
|
|
return new BigInteger($value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the modular multiplicative inverse of this BigInteger modulo $m.
|
|
|
|
*
|
|
|
|
* @param BigInteger $m
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*
|
|
|
|
* @throws DivisionByZeroException If $m is zero.
|
|
|
|
* @throws NegativeNumberException If $m is negative.
|
|
|
|
* @throws MathException If this BigInteger has no multiplicative inverse mod m (that is, this BigInteger
|
|
|
|
* is not relatively prime to m).
|
|
|
|
*/
|
|
|
|
public function modInverse(BigInteger $m) : BigInteger
|
|
|
|
{
|
|
|
|
if ($m->value === '0') {
|
|
|
|
throw DivisionByZeroException::modulusMustNotBeZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($m->isNegative()) {
|
|
|
|
throw new NegativeNumberException('Modulus must not be negative.');
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($m->value === '1') {
|
|
|
|
return BigInteger::zero();
|
|
|
|
}
|
|
|
|
|
|
|
|
$value = Calculator::get()->modInverse($this->value, $m->value);
|
|
|
|
|
|
|
|
if ($value === null) {
|
|
|
|
throw new MathException('Unable to compute the modInverse for the given modulus.');
|
|
|
|
}
|
|
|
|
|
|
|
|
return new BigInteger($value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns this number raised into power with modulo.
|
|
|
|
*
|
|
|
|
* This operation only works on positive numbers.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $exp The exponent. Must be positive or zero.
|
|
|
|
* @param BigNumber|int|float|string $mod The modulus. Must be strictly positive.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*
|
|
|
|
* @throws NegativeNumberException If any of the operands is negative.
|
|
|
|
* @throws DivisionByZeroException If the modulus is zero.
|
|
|
|
*/
|
|
|
|
public function modPow($exp, $mod) : BigInteger
|
|
|
|
{
|
|
|
|
$exp = BigInteger::of($exp);
|
|
|
|
$mod = BigInteger::of($mod);
|
|
|
|
|
|
|
|
if ($this->isNegative() || $exp->isNegative() || $mod->isNegative()) {
|
|
|
|
throw new NegativeNumberException('The operands cannot be negative.');
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($mod->isZero()) {
|
|
|
|
throw DivisionByZeroException::modulusMustNotBeZero();
|
|
|
|
}
|
|
|
|
|
|
|
|
$result = Calculator::get()->modPow($this->value, $exp->value, $mod->value);
|
|
|
|
|
|
|
|
return new BigInteger($result);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the greatest common divisor of this number and the given one.
|
|
|
|
*
|
|
|
|
* The GCD is always positive, unless both operands are zero, in which case it is zero.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function gcd($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
if ($that->value === '0' && $this->value[0] !== '-') {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($this->value === '0' && $that->value[0] !== '-') {
|
|
|
|
return $that;
|
|
|
|
}
|
|
|
|
|
|
|
|
$value = Calculator::get()->gcd($this->value, $that->value);
|
|
|
|
|
|
|
|
return new BigInteger($value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the integer square root number of this number, rounded down.
|
|
|
|
*
|
|
|
|
* The result is the largest x such that x² ≤ n.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*
|
|
|
|
* @throws NegativeNumberException If this number is negative.
|
|
|
|
*/
|
|
|
|
public function sqrt() : BigInteger
|
|
|
|
{
|
|
|
|
if ($this->value[0] === '-') {
|
|
|
|
throw new NegativeNumberException('Cannot calculate the square root of a negative number.');
|
|
|
|
}
|
|
|
|
|
|
|
|
$value = Calculator::get()->sqrt($this->value);
|
|
|
|
|
|
|
|
return new BigInteger($value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the absolute value of this number.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function abs() : BigInteger
|
|
|
|
{
|
|
|
|
return $this->isNegative() ? $this->negated() : $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the inverse of this number.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function negated() : BigInteger
|
|
|
|
{
|
|
|
|
return new BigInteger(Calculator::get()->neg($this->value));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the integer bitwise-and combined with another integer.
|
|
|
|
*
|
|
|
|
* This method returns a negative BigInteger if and only if both operands are negative.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function and($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
return new BigInteger(Calculator::get()->and($this->value, $that->value));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the integer bitwise-or combined with another integer.
|
|
|
|
*
|
|
|
|
* This method returns a negative BigInteger if and only if either of the operands is negative.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function or($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
return new BigInteger(Calculator::get()->or($this->value, $that->value));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the integer bitwise-xor combined with another integer.
|
|
|
|
*
|
|
|
|
* This method returns a negative BigInteger if and only if exactly one of the operands is negative.
|
|
|
|
*
|
|
|
|
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function xor($that) : BigInteger
|
|
|
|
{
|
|
|
|
$that = BigInteger::of($that);
|
|
|
|
|
|
|
|
return new BigInteger(Calculator::get()->xor($this->value, $that->value));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the bitwise-not of this BigInteger.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function not() : BigInteger
|
|
|
|
{
|
|
|
|
return $this->negated()->minus(1);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the integer left shifted by a given number of bits.
|
|
|
|
*
|
|
|
|
* @param int $distance The distance to shift.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function shiftedLeft(int $distance) : BigInteger
|
|
|
|
{
|
|
|
|
if ($distance === 0) {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($distance < 0) {
|
|
|
|
return $this->shiftedRight(- $distance);
|
|
|
|
}
|
|
|
|
|
|
|
|
return $this->multipliedBy(BigInteger::of(2)->power($distance));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the integer right shifted by a given number of bits.
|
|
|
|
*
|
|
|
|
* @param int $distance The distance to shift.
|
|
|
|
*
|
|
|
|
* @return BigInteger
|
|
|
|
*/
|
|
|
|
public function shiftedRight(int $distance) : BigInteger
|
|
|
|
{
|
|
|
|
if ($distance === 0) {
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($distance < 0) {
|
|
|
|
return $this->shiftedLeft(- $distance);
|
|
|
|
}
|
|
|
|
|
|
|
|
$operand = BigInteger::of(2)->power($distance);
|
|
|
|
|
|
|
|
if ($this->isPositiveOrZero()) {
|
|
|
|
return $this->quotient($operand);
|
|
|
|
}
|
|
|
|
|
|
|
|
return $this->dividedBy($operand, RoundingMode::UP);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.
|
|
|
|
*
|
|
|
|
* For positive BigIntegers, this is equivalent to the number of bits in the ordinary binary representation.
|
|
|
|
* Computes (ceil(log2(this < 0 ? -this : this+1))).
|
|
|
|
*
|
|
|
|
* @return int
|
|
|
|
*/
|
|
|
|
public function getBitLength() : int
|
|
|
|
{
|
|
|
|
if ($this->value === '0') {
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($this->isNegative()) {
|
|
|
|
return $this->abs()->minus(1)->getBitLength();
|
|
|
|
}
|
|
|
|
|
|
|
|
return \strlen($this->toBase(2));
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns the index of the rightmost (lowest-order) one bit in this BigInteger.
|
|
|
|
*
|
|
|
|
* Returns -1 if this BigInteger contains no one bits.
|
|
|
|
*
|
|
|
|
* @return int
|
|
|
|
*/
|
|
|
|
public function getLowestSetBit() : int
|
|
|
|
{
|
|
|
|
$n = $this;
|
|
|
|
$bitLength = $this->getBitLength();
|
|
|
|
|
|
|
|
for ($i = 0; $i <= $bitLength; $i++) {
|
|
|
|
if ($n->isOdd()) {
|
|
|
|
return $i;
|
|
|
|
}
|
|
|
|
|
|
|
|
$n = $n->shiftedRight(1);
|
|
|
|
}
|
|
|
|
|
|
|
|
return -1;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns whether this number is even.
|
|
|
|
*
|
|
|
|
* @return bool
|
|
|
|
*/
|
|
|
|
public function isEven() : bool
|
|
|
|
{
|
|
|
|
return \in_array($this->value[-1], ['0', '2', '4', '6', '8'], true);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns whether this number is odd.
|
|
|
|
*
|
|
|
|
* @return bool
|
|
|
|
*/
|
|
|
|
public function isOdd() : bool
|
|
|
|
{
|
|
|
|
return \in_array($this->value[-1], ['1', '3', '5', '7', '9'], true);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns true if and only if the designated bit is set.
|
|
|
|
*
|
|
|
|
* Computes ((this & (1<<n)) != 0).
|
|
|
|
*
|
|
|
|
* @param int $n The bit to test, 0-based.
|
|
|
|
*
|
|
|
|
* @return bool
|
|
|
|
*
|
|
|
|
* @throws \InvalidArgumentException If the bit to test is negative.
|
|
|
|
*/
|
|
|
|
public function testBit(int $n) : bool
|
|
|
|
{
|
|
|
|
if ($n < 0) {
|
|
|
|
throw new \InvalidArgumentException('The bit to test cannot be negative.');
|
|
|
|
}
|
|
|
|
|
|
|
|
return $this->shiftedRight($n)->isOdd();
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function compareTo($that) : int
|
|
|
|
{
|
|
|
|
$that = BigNumber::of($that);
|
|
|
|
|
|
|
|
if ($that instanceof BigInteger) {
|
|
|
|
return Calculator::get()->cmp($this->value, $that->value);
|
|
|
|
}
|
|
|
|
|
|
|
|
return - $that->compareTo($this);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function getSign() : int
|
|
|
|
{
|
|
|
|
return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function toBigInteger() : BigInteger
|
|
|
|
{
|
|
|
|
return $this;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function toBigDecimal() : BigDecimal
|
|
|
|
{
|
|
|
|
return BigDecimal::create($this->value);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function toBigRational() : BigRational
|
|
|
|
{
|
|
|
|
return BigRational::create($this, BigInteger::one(), false);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
|
|
|
|
{
|
|
|
|
return $this->toBigDecimal()->toScale($scale, $roundingMode);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function toInt() : int
|
|
|
|
{
|
|
|
|
$intValue = (int) $this->value;
|
|
|
|
|
|
|
|
if ($this->value !== (string) $intValue) {
|
|
|
|
throw IntegerOverflowException::toIntOverflow($this);
|
|
|
|
}
|
|
|
|
|
|
|
|
return $intValue;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function toFloat() : float
|
|
|
|
{
|
|
|
|
return (float) $this->value;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns a string representation of this number in the given base.
|
|
|
|
*
|
|
|
|
* The output will always be lowercase for bases greater than 10.
|
|
|
|
*
|
|
|
|
* @param int $base
|
|
|
|
*
|
|
|
|
* @return string
|
|
|
|
*
|
|
|
|
* @throws \InvalidArgumentException If the base is out of range.
|
|
|
|
*/
|
|
|
|
public function toBase(int $base) : string
|
|
|
|
{
|
|
|
|
if ($base === 10) {
|
|
|
|
return $this->value;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($base < 2 || $base > 36) {
|
|
|
|
throw new \InvalidArgumentException(\sprintf('Base %d is out of range [2, 36]', $base));
|
|
|
|
}
|
|
|
|
|
|
|
|
return Calculator::get()->toBase($this->value, $base);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns a string representation of this number in an arbitrary base with a custom alphabet.
|
|
|
|
*
|
|
|
|
* Because this method accepts an alphabet with any character, including dash, it does not handle negative numbers;
|
|
|
|
* a NegativeNumberException will be thrown when attempting to call this method on a negative number.
|
|
|
|
*
|
|
|
|
* @param string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8.
|
|
|
|
*
|
|
|
|
* @return string
|
|
|
|
*
|
|
|
|
* @throws NegativeNumberException If this number is negative.
|
|
|
|
* @throws \InvalidArgumentException If the given alphabet does not contain at least 2 chars.
|
|
|
|
*/
|
|
|
|
public function toArbitraryBase(string $alphabet) : string
|
|
|
|
{
|
|
|
|
$base = \strlen($alphabet);
|
|
|
|
|
|
|
|
if ($base < 2) {
|
|
|
|
throw new \InvalidArgumentException('The alphabet must contain at least 2 chars.');
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($this->value[0] === '-') {
|
|
|
|
throw new NegativeNumberException(__FUNCTION__ . '() does not support negative numbers.');
|
|
|
|
}
|
|
|
|
|
|
|
|
return Calculator::get()->toArbitraryBase($this->value, $alphabet, $base);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* Returns a string of bytes containing the binary representation of this BigInteger.
|
|
|
|
*
|
|
|
|
* The string is in big-endian byte-order: the most significant byte is in the zeroth element.
|
|
|
|
*
|
|
|
|
* If `$signed` is true, the output will be in two's-complement representation, and a sign bit will be prepended to
|
|
|
|
* the output. If `$signed` is false, no sign bit will be prepended, and this method will throw an exception if the
|
|
|
|
* number is negative.
|
|
|
|
*
|
|
|
|
* The string will contain the minimum number of bytes required to represent this BigInteger, including a sign bit
|
|
|
|
* if `$signed` is true.
|
|
|
|
*
|
|
|
|
* This representation is compatible with the `fromBytes()` factory method, as long as the `$signed` flags match.
|
|
|
|
*
|
|
|
|
* @param bool $signed Whether to output a signed number in two's-complement representation with a leading sign bit.
|
|
|
|
*
|
|
|
|
* @return string
|
|
|
|
*
|
|
|
|
* @throws NegativeNumberException If $signed is false, and the number is negative.
|
|
|
|
*/
|
|
|
|
public function toBytes(bool $signed = true) : string
|
|
|
|
{
|
|
|
|
if (! $signed && $this->isNegative()) {
|
|
|
|
throw new NegativeNumberException('Cannot convert a negative number to a byte string when $signed is false.');
|
|
|
|
}
|
|
|
|
|
|
|
|
$hex = $this->abs()->toBase(16);
|
|
|
|
|
|
|
|
if (\strlen($hex) % 2 !== 0) {
|
|
|
|
$hex = '0' . $hex;
|
|
|
|
}
|
|
|
|
|
|
|
|
$baseHexLength = \strlen($hex);
|
|
|
|
|
|
|
|
if ($signed) {
|
|
|
|
if ($this->isNegative()) {
|
|
|
|
$bin = \hex2bin($hex);
|
|
|
|
assert($bin !== false);
|
|
|
|
|
|
|
|
$hex = \bin2hex(~$bin);
|
|
|
|
$hex = self::fromBase($hex, 16)->plus(1)->toBase(16);
|
|
|
|
|
|
|
|
$hexLength = \strlen($hex);
|
|
|
|
|
|
|
|
if ($hexLength < $baseHexLength) {
|
|
|
|
$hex = \str_repeat('0', $baseHexLength - $hexLength) . $hex;
|
|
|
|
}
|
|
|
|
|
|
|
|
if ($hex[0] < '8') {
|
|
|
|
$hex = 'FF' . $hex;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
if ($hex[0] >= '8') {
|
|
|
|
$hex = '00' . $hex;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
return \hex2bin($hex);
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* {@inheritdoc}
|
|
|
|
*/
|
|
|
|
public function __toString() : string
|
|
|
|
{
|
|
|
|
return $this->value;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* This method is required for serializing the object and SHOULD NOT be accessed directly.
|
|
|
|
*
|
|
|
|
* @internal
|
|
|
|
*
|
|
|
|
* @return array{value: string}
|
|
|
|
*/
|
|
|
|
public function __serialize(): array
|
|
|
|
{
|
|
|
|
return ['value' => $this->value];
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* This method is only here to allow unserializing the object and cannot be accessed directly.
|
|
|
|
*
|
|
|
|
* @internal
|
|
|
|
* @psalm-suppress RedundantPropertyInitializationCheck
|
|
|
|
*
|
|
|
|
* @param array{value: string} $data
|
|
|
|
*
|
|
|
|
* @return void
|
|
|
|
*
|
|
|
|
* @throws \LogicException
|
|
|
|
*/
|
|
|
|
public function __unserialize(array $data): void
|
|
|
|
{
|
|
|
|
if (isset($this->value)) {
|
|
|
|
throw new \LogicException('__unserialize() is an internal function, it must not be called directly.');
|
|
|
|
}
|
|
|
|
|
|
|
|
$this->value = $data['value'];
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* This method is required by interface Serializable and SHOULD NOT be accessed directly.
|
|
|
|
*
|
|
|
|
* @internal
|
|
|
|
*
|
|
|
|
* @return string
|
|
|
|
*/
|
|
|
|
public function serialize() : string
|
|
|
|
{
|
|
|
|
return $this->value;
|
|
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
|
|
* This method is only here to implement interface Serializable and cannot be accessed directly.
|
|
|
|
*
|
|
|
|
* @internal
|
|
|
|
* @psalm-suppress RedundantPropertyInitializationCheck
|
|
|
|
*
|
|
|
|
* @param string $value
|
|
|
|
*
|
|
|
|
* @return void
|
|
|
|
*
|
|
|
|
* @throws \LogicException
|
|
|
|
*/
|
|
|
|
public function unserialize($value) : void
|
|
|
|
{
|
|
|
|
if (isset($this->value)) {
|
|
|
|
throw new \LogicException('unserialize() is an internal function, it must not be called directly.');
|
|
|
|
}
|
|
|
|
|
|
|
|
$this->value = $value;
|
|
|
|
}
|
|
|
|
} |
