1352 lines
42 KiB
PHP
1352 lines
42 KiB
PHP
<?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\Exception\RoundingNecessaryException;
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use Brick\Math\Internal\Calculator;
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use Brick\Math\Internal\CalculatorRegistry;
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use InvalidArgumentException;
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use LogicException;
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use Override;
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use function assert;
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use function bin2hex;
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use function chr;
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use function count_chars;
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use function filter_var;
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use function func_num_args;
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use function hex2bin;
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use function in_array;
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use function intdiv;
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use function ltrim;
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use function ord;
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use function preg_match;
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use function preg_quote;
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use function random_bytes;
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use function sprintf;
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use function str_repeat;
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use function strlen;
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use function strtolower;
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use function substr;
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use function trigger_error;
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use const E_USER_DEPRECATED;
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use const FILTER_VALIDATE_INT;
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/**
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* An arbitrarily large integer number.
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*
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* This class is immutable.
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*/
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final readonly 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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private string $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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* @pure
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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 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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* @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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* @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 must not 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 ($number === '') {
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throw new NumberFormatException('The number must not be empty.');
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}
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$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 = CalculatorRegistry::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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* This method is byte-oriented: the alphabet is interpreted as a sequence of single-byte characters.
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* Multibyte UTF-8 characters are not supported.
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*
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* Because this method accepts any single-byte 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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* @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, or contains duplicates.
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*
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* @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 must not be empty.');
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}
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$base = strlen($alphabet);
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if ($base < 2) {
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throw new InvalidArgumentException('The alphabet must contain at least 2 chars.');
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}
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if (strlen(count_chars($alphabet, 3)) !== $base) {
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throw new InvalidArgumentException('The alphabet must not contain duplicate chars.');
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}
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$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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$number = CalculatorRegistry::get()->fromArbitraryBase($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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* @throws NumberFormatException If the string is empty.
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*
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* @pure
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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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* @param int $numBits The number of bits.
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* @param (callable(int): string)|null $randomBytesGenerator A function that accepts a number of bytes, and returns
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* a string of random bytes of the given length. Defaults
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* to the `random_bytes()` function.
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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 must not 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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/** @var int<1, max> $byteLength */
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$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`, inclusive.
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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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* @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(int): string)|null $randomBytesGenerator A function that accepts a number of bytes, and returns
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* a string of random bytes of the given length. Defaults
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* to the `random_bytes()` function.
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*
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* @throws MathException If one of the parameters cannot be converted to a BigInteger,
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* or `$min` is greater than `$max`.
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*/
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public static function randomRange(
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BigNumber|int|float|string $min,
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BigNumber|int|float|string $max,
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?callable $randomBytesGenerator = null,
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): BigInteger {
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$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 must be less than or equal to $max.');
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}
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if ($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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* @pure
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*/
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public static function zero(): BigInteger
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{
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/** @var BigInteger|null $zero */
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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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* @pure
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*/
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public static function one(): BigInteger
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{
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/** @var BigInteger|null $one */
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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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* @pure
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||
*/
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public static function ten(): BigInteger
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||
{
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||
/** @var BigInteger|null $ten */
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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 greatest common divisor of the given numbers.
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*
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* The GCD is always positive, unless all numbers are zero, in which case it is zero.
|
||
*
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||
* @param BigNumber|int|float|string $a The first number. Must be convertible to a BigInteger.
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* @param BigNumber|int|float|string ...$n The additional numbers. Each number must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If one of the parameters cannot be converted to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public static function gcdAll(BigNumber|int|float|string $a, BigNumber|int|float|string ...$n): BigInteger
|
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{
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$result = BigInteger::of($a)->abs();
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foreach ($n as $next) {
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$result = $result->gcd(BigInteger::of($next));
|
||
|
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if ($result->isEqualTo(1)) {
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return $result;
|
||
}
|
||
}
|
||
|
||
return $result;
|
||
}
|
||
|
||
/**
|
||
* Returns the least common multiple of the given numbers.
|
||
*
|
||
* The LCM is always positive, unless one of the numbers is zero, in which case it is zero.
|
||
*
|
||
* @param BigNumber|int|float|string $a The first number. Must be convertible to a BigInteger.
|
||
* @param BigNumber|int|float|string ...$n The additional numbers. Each number must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If one of the parameters cannot be converted to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public static function lcmAll(BigNumber|int|float|string $a, BigNumber|int|float|string ...$n): BigInteger
|
||
{
|
||
$result = BigInteger::of($a)->abs();
|
||
|
||
foreach ($n as $next) {
|
||
$result = $result->lcm(BigInteger::of($next));
|
||
|
||
if ($result->isZero()) {
|
||
return $result;
|
||
}
|
||
}
|
||
|
||
return $result;
|
||
}
|
||
|
||
/**
|
||
* @deprecated Use gcdAll() instead.
|
||
*
|
||
* @param BigNumber|int|float|string $a The first number. Must be convertible to a BigInteger.
|
||
* @param BigNumber|int|float|string ...$n The subsequent numbers. Must be convertible to BigInteger.
|
||
*/
|
||
public static function gcdMultiple(BigNumber|int|float|string $a, BigNumber|int|float|string ...$n): BigInteger
|
||
{
|
||
trigger_error(
|
||
'BigInteger::gcdMultiple() is deprecated and will be removed in version 0.15. Use gcdAll() instead.',
|
||
E_USER_DEPRECATED,
|
||
);
|
||
|
||
return self::gcdAll($a, ...$n);
|
||
}
|
||
|
||
/**
|
||
* Returns the sum of this number and the given one.
|
||
*
|
||
* @param BigNumber|int|float|string $that The number to add. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the number is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function plus(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '0') {
|
||
return $this;
|
||
}
|
||
|
||
if ($this->value === '0') {
|
||
return $that;
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->add($this->value, $that->value);
|
||
|
||
return new BigInteger($value);
|
||
}
|
||
|
||
/**
|
||
* Returns the difference of this number and the given one.
|
||
*
|
||
* @param BigNumber|int|float|string $that The number to subtract. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the number is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function minus(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '0') {
|
||
return $this;
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->sub($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.
|
||
*
|
||
* @throws MathException If the multiplier is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function multipliedBy(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '1') {
|
||
return $this;
|
||
}
|
||
|
||
if ($this->value === '1') {
|
||
return $that;
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->mul($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 RoundingMode $roundingMode An optional rounding mode, defaults to Unnecessary.
|
||
*
|
||
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
|
||
* @throws DivisionByZeroException If the divisor is zero.
|
||
* @throws RoundingNecessaryException If RoundingMode::Unnecessary is used and the remainder is not zero.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function dividedBy(BigNumber|int|float|string $that, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '1') {
|
||
return $this;
|
||
}
|
||
|
||
if ($that->value === '0') {
|
||
throw DivisionByZeroException::divisionByZero();
|
||
}
|
||
|
||
$result = CalculatorRegistry::get()->divRound($this->value, $that->value, $roundingMode);
|
||
|
||
return new BigInteger($result);
|
||
}
|
||
|
||
/**
|
||
* Returns this number exponentiated to the given value.
|
||
*
|
||
* @throws InvalidArgumentException If the exponent is not in the range 0 to 1,000,000.
|
||
*
|
||
* @pure
|
||
*/
|
||
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.',
|
||
$exponent,
|
||
Calculator::MAX_POWER,
|
||
));
|
||
}
|
||
|
||
return new BigInteger(CalculatorRegistry::get()->pow($this->value, $exponent));
|
||
}
|
||
|
||
/**
|
||
* Returns the quotient of the division of this number by the given one.
|
||
*
|
||
* Examples:
|
||
*
|
||
* - `7` quotient `3` returns `2`
|
||
* - `7` quotient `-3` returns `-2`
|
||
* - `-7` quotient `3` returns `-2`
|
||
* - `-7` quotient `-3` returns `2`
|
||
*
|
||
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
|
||
* @throws DivisionByZeroException If the divisor is zero.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function quotient(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '1') {
|
||
return $this;
|
||
}
|
||
|
||
if ($that->value === '0') {
|
||
throw DivisionByZeroException::divisionByZero();
|
||
}
|
||
|
||
$quotient = CalculatorRegistry::get()->divQ($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.
|
||
*
|
||
* Examples:
|
||
*
|
||
* - `7` remainder `3` returns `1`
|
||
* - `7` remainder `-3` returns `1`
|
||
* - `-7` remainder `3` returns `-1`
|
||
* - `-7` remainder `-3` returns `-1`
|
||
*
|
||
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
|
||
* @throws DivisionByZeroException If the divisor is zero.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function remainder(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '1') {
|
||
return BigInteger::zero();
|
||
}
|
||
|
||
if ($that->value === '0') {
|
||
throw DivisionByZeroException::divisionByZero();
|
||
}
|
||
|
||
$remainder = CalculatorRegistry::get()->divR($this->value, $that->value);
|
||
|
||
return new BigInteger($remainder);
|
||
}
|
||
|
||
/**
|
||
* Returns the quotient and remainder of the division of this number by the given one.
|
||
*
|
||
* Examples:
|
||
*
|
||
* - `7` quotientAndRemainder `3` returns [`2`, `1`]
|
||
* - `7` quotientAndRemainder `-3` returns [`-2`, `1`]
|
||
* - `-7` quotientAndRemainder `3` returns [`-2`, `-1`]
|
||
* - `-7` quotientAndRemainder `-3` returns [`2`, `-1`]
|
||
*
|
||
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
|
||
*
|
||
* @return array{BigInteger, BigInteger} An array containing the quotient and the remainder.
|
||
*
|
||
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
|
||
* @throws DivisionByZeroException If the divisor is zero.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function quotientAndRemainder(BigNumber|int|float|string $that): array
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '0') {
|
||
throw DivisionByZeroException::divisionByZero();
|
||
}
|
||
|
||
[$quotient, $remainder] = CalculatorRegistry::get()->divQR($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.
|
||
*
|
||
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
|
||
* @throws DivisionByZeroException If the divisor is zero.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function mod(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->isZero()) {
|
||
throw DivisionByZeroException::modulusMustNotBeZero();
|
||
}
|
||
|
||
if ($that->isNegative()) {
|
||
// @phpstan-ignore-next-line
|
||
trigger_error(
|
||
'Passing a negative modulus to BigInteger::mod() is deprecated and will throw a NegativeNumberException in 0.15.',
|
||
E_USER_DEPRECATED,
|
||
);
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->mod($this->value, $that->value);
|
||
|
||
return new BigInteger($value);
|
||
}
|
||
|
||
/**
|
||
* Returns the modular multiplicative inverse of this BigInteger modulo $m.
|
||
*
|
||
* @param BigNumber|int|float|string $m The modulus. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the modulus is not valid, or is not convertible to a 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).
|
||
*
|
||
* @pure
|
||
*/
|
||
public function modInverse(BigNumber|int|float|string $m): BigInteger
|
||
{
|
||
$m = BigInteger::of($m);
|
||
|
||
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();
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->modInverse($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 requires a non-negative exponent and a strictly positive modulus.
|
||
*
|
||
* @param BigNumber|int|float|string $exp The exponent. Must be convertible to a BigInteger.
|
||
* @param BigNumber|int|float|string $mod The modulus. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the exponent or modulus is not valid, or is not convertible to a BigInteger.
|
||
* @throws NegativeNumberException If the exponent or modulus is negative.
|
||
* @throws DivisionByZeroException If the modulus is zero.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function modPow(BigNumber|int|float|string $exp, BigNumber|int|float|string $mod): BigInteger
|
||
{
|
||
$exp = BigInteger::of($exp);
|
||
$mod = BigInteger::of($mod);
|
||
|
||
if ($exp->isNegative()) {
|
||
throw new NegativeNumberException('The exponent cannot be negative.');
|
||
}
|
||
|
||
if ($mod->isNegative()) {
|
||
throw new NegativeNumberException('The modulus cannot be negative.');
|
||
}
|
||
|
||
if ($mod->isZero()) {
|
||
throw DivisionByZeroException::modulusMustNotBeZero();
|
||
}
|
||
|
||
$result = CalculatorRegistry::get()->modPow($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 a BigInteger.
|
||
*
|
||
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function gcd(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($that->value === '0' && $this->value[0] !== '-') {
|
||
return $this;
|
||
}
|
||
|
||
if ($this->value === '0' && $that->value[0] !== '-') {
|
||
return $that;
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->gcd($this->value, $that->value);
|
||
|
||
return new BigInteger($value);
|
||
}
|
||
|
||
/**
|
||
* Returns the least common multiple of this number and the given one.
|
||
*
|
||
* The LCM is always positive, unless at least one operand is zero, in which case it is zero.
|
||
*
|
||
* @param BigNumber|int|float|string $that The operand. Must be convertible to a BigInteger.
|
||
*
|
||
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function lcm(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
if ($this->isZero() || $that->isZero()) {
|
||
return BigInteger::zero();
|
||
}
|
||
|
||
$value = CalculatorRegistry::get()->lcm($this->value, $that->value);
|
||
|
||
return new BigInteger($value);
|
||
}
|
||
|
||
/**
|
||
* Returns the integer square root of this number, rounded according to the given rounding mode.
|
||
*
|
||
* @param RoundingMode $roundingMode The rounding mode to use, defaults to Down.
|
||
* ⚠️ WARNING: the default rounding mode was kept as Down for backward
|
||
* compatibility, but will change to Unnecessary in version 0.15. Pass a rounding
|
||
* mode explicitly to avoid this upcoming breaking change.
|
||
*
|
||
* @throws NegativeNumberException If this number is negative.
|
||
* @throws RoundingNecessaryException If RoundingMode::Unnecessary is used, and the number is not a perfect square.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function sqrt(RoundingMode $roundingMode = RoundingMode::Down): BigInteger
|
||
{
|
||
if (func_num_args() === 0) {
|
||
// @phpstan-ignore-next-line
|
||
trigger_error(
|
||
'The default rounding mode of BigInteger::sqrt() will change from Down to Unnecessary in version 0.15. ' .
|
||
'Pass a rounding mode explicitly to avoid this breaking change.',
|
||
E_USER_DEPRECATED,
|
||
);
|
||
}
|
||
|
||
if ($this->value[0] === '-') {
|
||
throw new NegativeNumberException('Cannot calculate the square root of a negative number.');
|
||
}
|
||
|
||
$calculator = CalculatorRegistry::get();
|
||
|
||
$sqrt = $calculator->sqrt($this->value);
|
||
|
||
// For Down and Floor (equivalent for non-negative numbers), return floor sqrt
|
||
if ($roundingMode === RoundingMode::Down || $roundingMode === RoundingMode::Floor) {
|
||
return new BigInteger($sqrt);
|
||
}
|
||
|
||
// Check if the sqrt is exact
|
||
$s2 = $calculator->mul($sqrt, $sqrt);
|
||
$remainder = $calculator->sub($this->value, $s2);
|
||
|
||
if ($remainder === '0') {
|
||
// sqrt is exact
|
||
return new BigInteger($sqrt);
|
||
}
|
||
|
||
// sqrt is not exact
|
||
if ($roundingMode === RoundingMode::Unnecessary) {
|
||
throw RoundingNecessaryException::roundingNecessary();
|
||
}
|
||
|
||
// For Up and Ceiling (equivalent for non-negative numbers), round up
|
||
if ($roundingMode === RoundingMode::Up || $roundingMode === RoundingMode::Ceiling) {
|
||
return new BigInteger($calculator->add($sqrt, '1'));
|
||
}
|
||
|
||
// For Half* modes, compare our number to the midpoint of the interval [s², (s+1)²[.
|
||
// The midpoint is s² + s + 0.5. Comparing n >= s² + s + 0.5 with remainder = n − s²
|
||
// is equivalent to comparing 2*remainder >= 2*s + 1.
|
||
$twoRemainder = $calculator->mul($remainder, '2');
|
||
$threshold = $calculator->add($calculator->mul($sqrt, '2'), '1');
|
||
$cmp = $calculator->cmp($twoRemainder, $threshold);
|
||
|
||
// We're supposed to increment (round up) when:
|
||
// - HalfUp, HalfCeiling => $cmp >= 0
|
||
// - HalfDown, HalfFloor => $cmp > 0
|
||
// - HalfEven => $cmp > 0 || ($cmp === 0 && $sqrt % 2 === 1)
|
||
// But 2*remainder is always even and 2*s + 1 is always odd, so $cmp is never zero.
|
||
// Therefore, all Half* modes simplify to:
|
||
if ($cmp > 0) {
|
||
$sqrt = $calculator->add($sqrt, '1');
|
||
}
|
||
|
||
return new BigInteger($sqrt);
|
||
}
|
||
|
||
#[Override]
|
||
public function negated(): static
|
||
{
|
||
return new BigInteger(CalculatorRegistry::get()->neg($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 a BigInteger.
|
||
*
|
||
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function and(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
return new BigInteger(CalculatorRegistry::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 a BigInteger.
|
||
*
|
||
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function or(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
return new BigInteger(CalculatorRegistry::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 a BigInteger.
|
||
*
|
||
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function xor(BigNumber|int|float|string $that): BigInteger
|
||
{
|
||
$that = BigInteger::of($that);
|
||
|
||
return new BigInteger(CalculatorRegistry::get()->xor($this->value, $that->value));
|
||
}
|
||
|
||
/**
|
||
* Returns the bitwise-not of this BigInteger.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function not(): BigInteger
|
||
{
|
||
return $this->negated()->minus(1);
|
||
}
|
||
|
||
/**
|
||
* Returns the integer left shifted by a given number of bits.
|
||
*
|
||
* @throws InvalidArgumentException If the number of bits is out of range.
|
||
*
|
||
* @pure
|
||
*/
|
||
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.
|
||
*
|
||
* @throws InvalidArgumentException If the number of bits is out of range.
|
||
*
|
||
* @pure
|
||
*/
|
||
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))).
|
||
*
|
||
* @pure
|
||
*/
|
||
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.
|
||
*
|
||
* @pure
|
||
*/
|
||
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 true if and only if the designated bit is set.
|
||
*
|
||
* Computes ((this & (1<<n)) != 0).
|
||
*
|
||
* @param int $n The bit to test, 0-based.
|
||
*
|
||
* @throws InvalidArgumentException If the bit to test is negative.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function isBitSet(int $n): bool
|
||
{
|
||
if ($n < 0) {
|
||
throw new InvalidArgumentException('The bit to test cannot be negative.');
|
||
}
|
||
|
||
return $this->shiftedRight($n)->isOdd();
|
||
}
|
||
|
||
/**
|
||
* Returns whether this number is even.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function isEven(): bool
|
||
{
|
||
return in_array($this->value[-1], ['0', '2', '4', '6', '8'], true);
|
||
}
|
||
|
||
/**
|
||
* Returns whether this number is odd.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function isOdd(): bool
|
||
{
|
||
return in_array($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).
|
||
*
|
||
* @deprecated Use isBitSet().
|
||
*
|
||
* @param int $n The bit to test, 0-based.
|
||
*
|
||
* @throws InvalidArgumentException If the bit to test is negative.
|
||
*/
|
||
public function testBit(int $n): bool
|
||
{
|
||
trigger_error(
|
||
'The BigInteger::testBit() method is deprecated, use isBitSet() instead.',
|
||
E_USER_DEPRECATED,
|
||
);
|
||
|
||
return $this->isBitSet($n);
|
||
}
|
||
|
||
#[Override]
|
||
public function compareTo(BigNumber|int|float|string $that): int
|
||
{
|
||
$that = BigNumber::of($that);
|
||
|
||
if ($that instanceof BigInteger) {
|
||
return CalculatorRegistry::get()->cmp($this->value, $that->value);
|
||
}
|
||
|
||
return -$that->compareTo($this);
|
||
}
|
||
|
||
#[Override]
|
||
public function getSign(): int
|
||
{
|
||
return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);
|
||
}
|
||
|
||
#[Override]
|
||
public function toBigInteger(): BigInteger
|
||
{
|
||
return $this;
|
||
}
|
||
|
||
#[Override]
|
||
public function toBigDecimal(): BigDecimal
|
||
{
|
||
return self::newBigDecimal($this->value);
|
||
}
|
||
|
||
#[Override]
|
||
public function toBigRational(): BigRational
|
||
{
|
||
return self::newBigRational($this, BigInteger::one(), false);
|
||
}
|
||
|
||
#[Override]
|
||
public function toScale(int $scale, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigDecimal
|
||
{
|
||
return $this->toBigDecimal()->toScale($scale, $roundingMode);
|
||
}
|
||
|
||
#[Override]
|
||
public function toInt(): int
|
||
{
|
||
$intValue = filter_var($this->value, FILTER_VALIDATE_INT);
|
||
|
||
if ($intValue === false) {
|
||
throw IntegerOverflowException::toIntOverflow($this);
|
||
}
|
||
|
||
return $intValue;
|
||
}
|
||
|
||
#[Override]
|
||
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.
|
||
*
|
||
* @throws InvalidArgumentException If the base is out of range.
|
||
*
|
||
* @pure
|
||
*/
|
||
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]', $base));
|
||
}
|
||
|
||
return CalculatorRegistry::get()->toBase($this->value, $base);
|
||
}
|
||
|
||
/**
|
||
* Returns a string representation of this number in an arbitrary base with a custom alphabet.
|
||
*
|
||
* This method is byte-oriented: the alphabet is interpreted as a sequence of single-byte characters.
|
||
* Multibyte UTF-8 characters are not supported.
|
||
*
|
||
* Because this method accepts any single-byte 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.
|
||
*
|
||
* @throws NegativeNumberException If this number is negative.
|
||
* @throws InvalidArgumentException If the alphabet does not contain at least 2 chars, or contains duplicates.
|
||
*
|
||
* @pure
|
||
*/
|
||
public function toArbitraryBase(string $alphabet): string
|
||
{
|
||
$base = strlen($alphabet);
|
||
|
||
if ($base < 2) {
|
||
throw new InvalidArgumentException('The alphabet must contain at least 2 chars.');
|
||
}
|
||
|
||
if (strlen(count_chars($alphabet, 3)) !== $base) {
|
||
throw new InvalidArgumentException('The alphabet must not contain duplicate chars.');
|
||
}
|
||
|
||
if ($this->value[0] === '-') {
|
||
throw new NegativeNumberException(__FUNCTION__ . '() does not support negative numbers.');
|
||
}
|
||
|
||
return CalculatorRegistry::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.
|
||
*
|
||
* @throws NegativeNumberException If $signed is false, and the number is negative.
|
||
*
|
||
* @pure
|
||
*/
|
||
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;
|
||
}
|
||
}
|
||
}
|
||
|
||
$result = hex2bin($hex);
|
||
assert($result !== false);
|
||
|
||
return $result;
|
||
}
|
||
|
||
/**
|
||
* @return numeric-string
|
||
*/
|
||
#[Override]
|
||
public function toString(): string
|
||
{
|
||
/** @var numeric-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
|
||
*
|
||
* @param array{value: string} $data
|
||
*
|
||
* @throws LogicException
|
||
*/
|
||
public function __unserialize(array $data): void
|
||
{
|
||
/** @phpstan-ignore isset.initializedProperty */
|
||
if (isset($this->value)) {
|
||
throw new LogicException('__unserialize() is an internal function, it must not be called directly.');
|
||
}
|
||
|
||
/** @phpstan-ignore deadCode.unreachable */
|
||
$this->value = $data['value'];
|
||
}
|
||
|
||
#[Override]
|
||
protected static function from(BigNumber $number): static
|
||
{
|
||
return $number->toBigInteger();
|
||
}
|
||
}
|