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Edit File : BigInteger.php \| Size : 32.60 KB
<?php declare(strict_types=1); namespace Brick\Math; use Brick\Math\Exception\DivisionByZeroException; use Brick\Math\Exception\IntegerOverflowException; use Brick\Math\Exception\MathException; use Brick\Math\Exception\NegativeNumberException; use Brick\Math\Exception\NumberFormatException; use Brick\Math\Internal\Calculator; /** * An arbitrary-size integer. * * All methods accepting a number as a parameter accept either a BigInteger instance, * an integer, or a string representing an arbitrary size integer. * * @psalm-immutable / final class BigInteger extends BigNumber { /* * The value, as a string of digits with optional leading minus sign. * * No leading zeros must be present. * No leading minus sign must be present if the number is zero. * * @var string / private $value; /* * Protected constructor. Use a factory method to obtain an instance. * * @param string $value A string of digits, with optional leading minus sign. / protected function __construct(string $value) { $this->value = $value; } /* * Creates a BigInteger of the given value. * * @param BigNumber\|int\|float\|string $value * * @return BigInteger * * @throws MathException If the value cannot be converted to a BigInteger. * * @psalm-pure / public static function of($value) : BigNumber { return parent::of($value)->toBigInteger(); } /* * Creates a number from a string in a given base. * * The string can optionally be prefixed with the `+` or `-` sign. * * Bases greater than 36 are not supported by this method, as there is no clear consensus on which of the lowercase * or uppercase characters should come first. Instead, this method accepts any base up to 36, and does not * differentiate lowercase and uppercase characters, which are considered equal. * * For bases greater than 36, and/or custom alphabets, use the fromArbitraryBase() method. * * @param string $number The number to convert, in the given base. * @param int $base The base of the number, between 2 and 36. * * @return BigInteger * * @throws NumberFormatException If the number is empty, or contains invalid chars for the given base. * @throws \InvalidArgumentException If the base is out of range. * * @psalm-pure / public static function fromBase(string $number, int $base) : BigInteger { if ($number === '') { throw new NumberFormatException('The number cannot be empty.'); } if ($base < 2 \|\| $base > 36) { throw new \InvalidArgumentException(\sprintf('Base %d is not in range 2 to 36.', $base)); } if ($number[0] === '-') { $sign = '-'; $number = \substr($number, 1); } elseif ($number[0] === '+') { $sign = ''; $number = \substr($number, 1); } else { $sign = ''; } if ($number === '') { throw new NumberFormatException('The number cannot be empty.'); } $number = \ltrim($number, '0'); if ($number === '') { // The result will be the same in any base, avoid further calculation. return BigInteger::zero(); } if ($number === '1') { // The result will be the same in any base, avoid further calculation. return new BigInteger($sign . '1'); } $pattern = '/[^' . \substr(Calculator::ALPHABET, 0, $base) . ']/'; if (\preg_match($pattern, \strtolower($number), $matches) === 1) { throw new NumberFormatException(\sprintf('"%s" is not a valid character in base %d.', $matches[0], $base)); } if ($base === 10) { // The number is usable as is, avoid further calculation. return new BigInteger($sign . $number); } $result = Calculator::get()->fromBase($number, $base); return new BigInteger($sign . $result); } /* * Parses a string containing an integer in an arbitrary base, using a custom alphabet. * * Because this method accepts an alphabet with any character, including dash, it does not handle negative numbers. * * @param string $number The number to parse. * @param string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8. * * @return BigInteger * * @throws NumberFormatException If the given number is empty or contains invalid chars for the given alphabet. * @throws \InvalidArgumentException If the alphabet does not contain at least 2 chars. * * @psalm-pure / public static function fromArbitraryBase(string $number, string $alphabet) : BigInteger { if ($number === '') { throw new NumberFormatException('The number cannot be empty.'); } $base = \strlen($alphabet); if ($base < 2) { throw new \InvalidArgumentException('The alphabet must contain at least 2 chars.'); } $pattern = '/[^' . \preg_quote($alphabet, '/') . ']/'; if (\preg_match($pattern, $number, $matches) === 1) { throw NumberFormatException::charNotInAlphabet($matches[0]); } $number = Calculator::get()->fromArbitraryBase($number, $alphabet, $base); return new BigInteger($number); } /* * Translates a string of bytes containing the binary representation of a BigInteger into a BigInteger. * * The input string is assumed to be in big-endian byte-order: the most significant byte is in the zeroth element. * * If `$signed` is true, the input is assumed to be in two's-complement representation, and the leading bit is * interpreted as a sign bit. If `$signed` is false, the input is interpreted as an unsigned number, and the * resulting BigInteger will always be positive or zero. * * This method can be used to retrieve a number exported by `toBytes()`, as long as the `$signed` flags match. * * @param string $value The byte string. * @param bool $signed Whether to interpret as a signed number in two's-complement representation with a leading * sign bit. * * @return BigInteger * * @throws NumberFormatException If the string is empty. / public static function fromBytes(string $value, bool $signed = true) : BigInteger { if ($value === '') { throw new NumberFormatException('The byte string must not be empty.'); } $twosComplement = false; if ($signed) { $x = \ord($value[0]); if (($twosComplement = ($x >= 0x80))) { $value = ~$value; } } $number = self::fromBase(\bin2hex($value), 16); if ($twosComplement) { return $number->plus(1)->negated(); } return $number; } /* * Generates a pseudo-random number in the range 0 to 2^numBits - 1. * * Using the default random bytes generator, this method is suitable for cryptographic use. * * @param int $numBits The number of bits. * @param callable\|null $randomBytesGenerator A function that accepts a number of bytes as an integer, and returns a * string of random bytes of the given length. Defaults to the * `random_bytes()` function. * * @return BigInteger * * @throws \InvalidArgumentException If $numBits is negative. / public static function randomBits(int $numBits, ?callable $randomBytesGenerator = null) : BigInteger { if ($numBits < 0) { throw new \InvalidArgumentException('The number of bits cannot be negative.'); } if ($numBits === 0) { return BigInteger::zero(); } if ($randomBytesGenerator === null) { $randomBytesGenerator = 'random_bytes'; } $byteLength = \intdiv($numBits - 1, 8) + 1; $extraBits = ($byteLength 8 - $numBits); $bitmask = \chr(0xFF >> $extraBits); $randomBytes = $randomBytesGenerator($byteLength); $randomBytes[0] = $randomBytes[0] & $bitmask; return self::fromBytes($randomBytes, false); } /** * Generates a pseudo-random number between `$min` and `$max`. * * Using the default random bytes generator, this method is suitable for cryptographic use. * * @param BigNumber\|int\|float\|string $min The lower bound. Must be convertible to a BigInteger. * @param BigNumber\|int\|float\|string $max The upper bound. Must be convertible to a BigInteger. * @param callable\|null $randomBytesGenerator A function that accepts a number of bytes as an integer, * and returns a string of random bytes of the given length. * Defaults to the `random_bytes()` function. * * @return BigInteger * * @throws MathException If one of the parameters cannot be converted to a BigInteger, * or `$min` is greater than `$max`. / public static function randomRange($min, $max, ?callable $randomBytesGenerator = null) : BigInteger { $min = BigInteger::of($min); $max = BigInteger::of($max); if ($min->isGreaterThan($max)) { throw new MathException('$min cannot be greater than $max.'); } if ($min->isEqualTo($max)) { return $min; } $diff = $max->minus($min); $bitLength = $diff->getBitLength(); // try until the number is in range (50% to 100% chance of success) do { $randomNumber = self::randomBits($bitLength, $randomBytesGenerator); } while ($randomNumber->isGreaterThan($diff)); return $randomNumber->plus($min); } /* * Returns a BigInteger representing zero. * * @return BigInteger * * @psalm-pure / public static function zero() : BigInteger { /* @psalm-suppress ImpureStaticVariable / static $zero; if ($zero === null) { $zero = new BigInteger('0'); } return $zero; } /* * Returns a BigInteger representing one. * * @return BigInteger * * @psalm-pure / public static function one() : BigInteger { /* @psalm-suppress ImpureStaticVariable / static $one; if ($one === null) { $one = new BigInteger('1'); } return $one; } /* * Returns a BigInteger representing ten. * * @return BigInteger * * @psalm-pure / public static function ten() : BigInteger { /* @psalm-suppress ImpureStaticVariable / static $ten; if ($ten === null) { $ten = new BigInteger('10'); } return $ten; } /* * Returns the sum of this number and the given one. * * @param BigNumber\|int\|float\|string $that The number to add. Must be convertible to a BigInteger. * * @return BigInteger The result. * * @throws MathException If the number is not valid, or is not convertible to a BigInteger. / public function plus($that) : BigInteger { $that = BigInteger::of($that); if ($that->value === '0') { return $this; } if ($this->value === '0') { return $that; } $value = Calculator::get()->add($this->value, $that->value); return new BigInteger($value); } /* * Returns the difference of this number and the given one. * * @param BigNumber\|int\|float\|string $that The number to subtract. Must be convertible to a BigInteger. * * @return BigInteger The result. * * @throws MathException If the number is not valid, or is not convertible to a BigInteger. / public function minus($that) : BigInteger { $that = BigInteger::of($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()) { $hex = \bin2hex(~\hex2bin($hex)); $hex = self::fromBase($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 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 * * @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; } } Back

Edit File : BigInteger.php | Size : 32.60 KB

<?php

declare(strict_types=1);

namespace Brick\Math;

use Brick\Math\Exception\DivisionByZeroException;
use Brick\Math\Exception\IntegerOverflowException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NegativeNumberException;
use Brick\Math\Exception\NumberFormatException;
use Brick\Math\Internal\Calculator;

/**
 * An arbitrary-size integer.
 *
 * All methods accepting a number as a parameter accept either a BigInteger instance,
 * an integer, or a string representing an arbitrary size integer.
 *
 * @psalm-immutable
 */
final class BigInteger extends BigNumber
{
    /**
     * The value, as a string of digits with optional leading minus sign.
     *
     * No leading zeros must be present.
     * No leading minus sign must be present if the number is zero.
     *
     * @var string
     */
    private $value;

/**
     * Protected constructor. Use a factory method to obtain an instance.
     *
     * @param string $value A string of digits, with optional leading minus sign.
     */
    protected function __construct(string $value)
    {
        $this->value = $value;
    }

/**
     * Creates a BigInteger of the given value.
     *
     * @param BigNumber|int|float|string $value
     *
     * @return BigInteger
     *
     * @throws MathException If the value cannot be converted to a BigInteger.
     *
     * @psalm-pure
     */
    public static function of($value) : BigNumber
    {
        return parent::of($value)->toBigInteger();
    }

/**
     * Creates a number from a string in a given base.
     *
     * The string can optionally be prefixed with the `+` or `-` sign.
     *
     * Bases greater than 36 are not supported by this method, as there is no clear consensus on which of the lowercase
     * or uppercase characters should come first. Instead, this method accepts any base up to 36, and does not
     * differentiate lowercase and uppercase characters, which are considered equal.
     *
     * For bases greater than 36, and/or custom alphabets, use the fromArbitraryBase() method.
     *
     * @param string $number The number to convert, in the given base.
     * @param int    $base   The base of the number, between 2 and 36.
     *
     * @return BigInteger
     *
     * @throws NumberFormatException     If the number is empty, or contains invalid chars for the given base.
     * @throws \InvalidArgumentException If the base is out of range.
     *
     * @psalm-pure
     */
    public static function fromBase(string $number, int $base) : BigInteger
    {
        if ($number === '') {
            throw new NumberFormatException('The number cannot be empty.');
        }

if ($base < 2 || $base > 36) {
            throw new \InvalidArgumentException(\sprintf('Base %d is not in range 2 to 36.', $base));
        }

if ($number[0] === '-') {
            $sign = '-';
            $number = \substr($number, 1);
        } elseif ($number[0] === '+') {
            $sign = '';
            $number = \substr($number, 1);
        } else {
            $sign = '';
        }

if ($number === '') {
            throw new NumberFormatException('The number cannot be empty.');
        }

$number = \ltrim($number, '0');

if ($number === '') {
            // The result will be the same in any base, avoid further calculation.
            return BigInteger::zero();
        }

if ($number === '1') {
            // The result will be the same in any base, avoid further calculation.
            return new BigInteger($sign . '1');
        }

$pattern = '/[^' . \substr(Calculator::ALPHABET, 0, $base) . ']/';

if (\preg_match($pattern, \strtolower($number), $matches) === 1) {
            throw new NumberFormatException(\sprintf('"%s" is not a valid character in base %d.', $matches[0], $base));
        }

if ($base === 10) {
            // The number is usable as is, avoid further calculation.
            return new BigInteger($sign . $number);
        }

$result = Calculator::get()->fromBase($number, $base);

return new BigInteger($sign . $result);
    }

/**
     * Parses a string containing an integer in an arbitrary base, using a custom alphabet.
     *
     * Because this method accepts an alphabet with any character, including dash, it does not handle negative numbers.
     *
     * @param string $number   The number to parse.
     * @param string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8.
     *
     * @return BigInteger
     *
     * @throws NumberFormatException     If the given number is empty or contains invalid chars for the given alphabet.
     * @throws \InvalidArgumentException If the alphabet does not contain at least 2 chars.
     *
     * @psalm-pure
     */
    public static function fromArbitraryBase(string $number, string $alphabet) : BigInteger
    {
        if ($number === '') {
            throw new NumberFormatException('The number cannot be empty.');
        }

$base = \strlen($alphabet);

if ($base < 2) {
            throw new \InvalidArgumentException('The alphabet must contain at least 2 chars.');
        }

$pattern = '/[^' . \preg_quote($alphabet, '/') . ']/';

if (\preg_match($pattern, $number, $matches) === 1) {
            throw NumberFormatException::charNotInAlphabet($matches[0]);
        }

$number = Calculator::get()->fromArbitraryBase($number, $alphabet, $base);

return new BigInteger($number);
    }

/**
     * Translates a string of bytes containing the binary representation of a BigInteger into a BigInteger.
     *
     * The input string is assumed to be in big-endian byte-order: the most significant byte is in the zeroth element.
     *
     * If `$signed` is true, the input is assumed to be in two's-complement representation, and the leading bit is
     * interpreted as a sign bit. If `$signed` is false, the input is interpreted as an unsigned number, and the
     * resulting BigInteger will always be positive or zero.
     *
     * This method can be used to retrieve a number exported by `toBytes()`, as long as the `$signed` flags match.
     *
     * @param string $value  The byte string.
     * @param bool   $signed Whether to interpret as a signed number in two's-complement representation with a leading
     *                       sign bit.
     *
     * @return BigInteger
     *
     * @throws NumberFormatException If the string is empty.
     */
    public static function fromBytes(string $value, bool $signed = true) : BigInteger
    {
        if ($value === '') {
            throw new NumberFormatException('The byte string must not be empty.');
        }

$twosComplement = false;

if ($signed) {
            $x = \ord($value[0]);

if (($twosComplement = ($x >= 0x80))) {
                $value = ~$value;
            }
        }

$number = self::fromBase(\bin2hex($value), 16);

if ($twosComplement) {
            return $number->plus(1)->negated();
        }

return $number;
    }

/**
     * Generates a pseudo-random number in the range 0 to 2^numBits - 1.
     *
     * Using the default random bytes generator, this method is suitable for cryptographic use.
     *
     * @param int           $numBits              The number of bits.
     * @param callable|null $randomBytesGenerator A function that accepts a number of bytes as an integer, and returns a
     *                                            string of random bytes of the given length. Defaults to the
     *                                            `random_bytes()` function.
     *
     * @return BigInteger
     *
     * @throws \InvalidArgumentException If $numBits is negative.
     */
    public static function randomBits(int $numBits, ?callable $randomBytesGenerator = null) : BigInteger
    {
        if ($numBits < 0) {
            throw new \InvalidArgumentException('The number of bits cannot be negative.');
        }

if ($numBits === 0) {
            return BigInteger::zero();
        }

if ($randomBytesGenerator === null) {
            $randomBytesGenerator = 'random_bytes';
        }

$byteLength = \intdiv($numBits - 1, 8) + 1;

$extraBits = ($byteLength * 8 - $numBits);
        $bitmask   = \chr(0xFF >> $extraBits);

$randomBytes    = $randomBytesGenerator($byteLength);
        $randomBytes[0] = $randomBytes[0] & $bitmask;

return self::fromBytes($randomBytes, false);
    }

/**
     * Generates a pseudo-random number between `$min` and `$max`.
     *
     * Using the default random bytes generator, this method is suitable for cryptographic use.
     *
     * @param BigNumber|int|float|string $min                  The lower bound. Must be convertible to a BigInteger.
     * @param BigNumber|int|float|string $max                  The upper bound. Must be convertible to a BigInteger.
     * @param callable|null              $randomBytesGenerator A function that accepts a number of bytes as an integer,
     *                                                         and returns a string of random bytes of the given length.
     *                                                         Defaults to the `random_bytes()` function.
     *
     * @return BigInteger
     *
     * @throws MathException If one of the parameters cannot be converted to a BigInteger,
     *                       or `$min` is greater than `$max`.
     */
    public static function randomRange($min, $max, ?callable $randomBytesGenerator = null) : BigInteger
    {
        $min = BigInteger::of($min);
        $max = BigInteger::of($max);

if ($min->isGreaterThan($max)) {
            throw new MathException('$min cannot be greater than $max.');
        }

if ($min->isEqualTo($max)) {
            return $min;
        }

$diff      = $max->minus($min);
        $bitLength = $diff->getBitLength();

// try until the number is in range (50% to 100% chance of success)
        do {
            $randomNumber = self::randomBits($bitLength, $randomBytesGenerator);
        } while ($randomNumber->isGreaterThan($diff));

return $randomNumber->plus($min);
    }

/**
     * Returns a BigInteger representing zero.
     *
     * @return BigInteger
     *
     * @psalm-pure
     */
    public static function zero() : BigInteger
    {
        /** @psalm-suppress ImpureStaticVariable */
        static $zero;

if ($zero === null) {
            $zero = new BigInteger('0');
        }

return $zero;
    }

/**
     * Returns a BigInteger representing one.
     *
     * @return BigInteger
     *
     * @psalm-pure
     */
    public static function one() : BigInteger
    {
        /** @psalm-suppress ImpureStaticVariable */
        static $one;

if ($one === null) {
            $one = new BigInteger('1');
        }

return $one;
    }

/**
     * Returns a BigInteger representing ten.
     *
     * @return BigInteger
     *
     * @psalm-pure
     */
    public static function ten() : BigInteger
    {
        /** @psalm-suppress ImpureStaticVariable */
        static $ten;

if ($ten === null) {
            $ten = new BigInteger('10');
        }

return $ten;
    }

/**
     * Returns the sum of this number and the given one.
     *
     * @param BigNumber|int|float|string $that The number to add. Must be convertible to a BigInteger.
     *
     * @return BigInteger The result.
     *
     * @throws MathException If the number is not valid, or is not convertible to a BigInteger.
     */
    public function plus($that) : BigInteger
    {
        $that = BigInteger::of($that);

if ($that->value === '0') {
            return $this;
        }

if ($this->value === '0') {
            return $that;
        }

$value = Calculator::get()->add($this->value, $that->value);

return new BigInteger($value);
    }

/**
     * Returns the difference of this number and the given one.
     *
     * @param BigNumber|int|float|string $that The number to subtract. Must be convertible to a BigInteger.
     *
     * @return BigInteger The result.
     *
     * @throws MathException If the number is not valid, or is not convertible to a BigInteger.
     */
    public function minus($that) : BigInteger
    {
        $that = BigInteger::of($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()) {
                $hex = \bin2hex(~\hex2bin($hex));
                $hex = self::fromBase($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 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
     *
     * @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;
    }
}

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