Subversion-Projekte lars-tiefland.laravel_shop

<?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.

     */

    private string $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.

     *

     * @throws MathException If the value cannot be converted to a BigInteger.

     *

     * @psalm-pure

     */

    public static function of(BigNumber|int|float|string $value) : BigInteger

    {

        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.

     *

     * @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.

     *

     * @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.

     *

     * @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.

     *

     * @psalm-param (callable(int): string)|null $randomBytesGenerator

     *

     * @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.

     *

     * @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.

     *

     * @psalm-param (callable(int): string)|null $randomBytesGenerator

     *

     * @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.

     *

     * @throws MathException If one of the parameters cannot be converted to a BigInteger,

     *                       or `$min` is greater than `$max`.

     */

    public static function randomRange(

        BigNumber|int|float|string $min,

        BigNumber|int|float|string $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.

     *

     * @psalm-pure

     */

    public static function zero() : BigInteger

    {

        /**

         * @psalm-suppress ImpureStaticVariable

         * @var BigInteger|null $zero

         */

        static $zero;

        if ($zero === null) {

            $zero = new BigInteger('0');

        }

        return $zero;

    }

    /**

     * Returns a BigInteger representing one.

     *

     * @psalm-pure

     */

    public static function one() : BigInteger

    {

        /**

         * @psalm-suppress ImpureStaticVariable

         * @var BigInteger|null $one

         */

        static $one;

        if ($one === null) {

            $one = new BigInteger('1');

        }

        return $one;

    }

    /**

     * Returns a BigInteger representing ten.

     *

     * @psalm-pure

     */

    public static function ten() : BigInteger

    {

        /**

         * @psalm-suppress ImpureStaticVariable

         * @var BigInteger|null $ten

         */

        static $ten;

        if ($ten === null) {

            $ten = new BigInteger('10');

        }

        return $ten;

    }

    public static function gcdMultiple(BigInteger $a, BigInteger ...$n): BigInteger

    {

        $result = $a;

        foreach ($n as $next) {

            $result = $result->gcd($next);

            if ($result->isEqualTo(1)) {

                return $result;

            }

        }

        return $result;

    }

    /**

     * 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.

     */

    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;

        }

        $value = Calculator::get()->add($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.

     *

     * @throws MathException If the number is not valid, or is not convertible to a BigInteger.

     */

    public function minus(BigNumber|int|float|string $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.

     *

     * @throws MathException If the multiplier is not a valid number, or is not convertible to a BigInteger.

     */

    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;

        }

        $value = Calculator::get()->mul($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.

     *

     * @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(BigNumber|int|float|string $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.

     *

     * @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.

     *

     * @throws DivisionByZeroException If the divisor is zero.

     */

    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();

        }

        $quotient = Calculator::get()->divQ($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.

     *

     * @throws DivisionByZeroException If the divisor is zero.

     */

    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();

        }

        $remainder = Calculator::get()->divR($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(BigNumber|int|float|string $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.

     *

     * @throws DivisionByZeroException If the divisor is zero.

     */

    public function mod(BigNumber|int|float|string $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.

     *

     * @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.

     *

     * @throws NegativeNumberException If any of the operands is negative.

     * @throws DivisionByZeroException If the modulus is zero.

     */

    public function modPow(BigNumber|int|float|string $exp, BigNumber|int|float|string $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.

     */

    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;

        }

        $value = Calculator::get()->gcd($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.

     *

     * @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.

     */

    public function abs() : BigInteger

    {

        return $this->isNegative() ? $this->negated() : $this;

    }

    /**

     * Returns the inverse of this number.

     */

    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.

     */

    public function and(BigNumber|int|float|string $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.

     */

    public function or(BigNumber|int|float|string $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.

     */

    public function xor(BigNumber|int|float|string $that) : BigInteger

    {

        $that = BigInteger::of($that);

        return new BigInteger(Calculator::get()->xor($this->value, $that->value));

    }

    /**

     * Returns the bitwise-not of this BigInteger.

     */

    public function not() : BigInteger

    {

        return $this->negated()->minus(1);

    }

    /**

     * Returns the integer left shifted by a given number of bits.

     */

    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.

     */

    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))).

     */

    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.

     */

    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.

     */

    public function isEven() : bool

    {

        return \in_array($this->value[-1], ['0', '2', '4', '6', '8'], true);

    }

    /**

     * Returns whether this number is odd.

     */

    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.

     *

     * @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();

    }

    public function compareTo(BigNumber|int|float|string $that) : int

    {

        $that = BigNumber::of($that);

        if ($that instanceof BigInteger) {

            return Calculator::get()->cmp($this->value, $that->value);

        }

        return - $that->compareTo($this);

    }

    public function getSign() : int

    {

        return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);

    }

    public function toBigInteger() : BigInteger

    {

        return $this;

    }

    public function toBigDecimal() : BigDecimal

    {

        return self::newBigDecimal($this->value);

    }

    public function toBigRational() : BigRational

    {

        return self::newBigRational($this, BigInteger::one(), false);

    }

    public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal

    {

        return $this->toBigDecimal()->toScale($scale, $roundingMode);

    }

    public function toInt() : int

    {

        $intValue = (int) $this->value;

        if ($this->value !== (string) $intValue) {

            throw IntegerOverflowException::toIntOverflow($this);

        }

        return $intValue;

    }

    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.

     */

    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.

     *

     * @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.

     *

     * @throws NegativeNumberException If $signed is false, and the number is negative.

     */

    public function toBytes(bool $signed = true) : string

    {

        if (! $signed && $this->isNegative()) {

            throw new NegativeNumberException('Cannot convert a negative number to a byte string when $signed is false.');

        }

        $hex = $this->abs()->toBase(16);

        if (\strlen($hex) % 2 !== 0) {

            $hex = '0' . $hex;

        }

        $baseHexLength = \strlen($hex);

        if ($signed) {

            if ($this->isNegative()) {

                $bin = \hex2bin($hex);

                assert($bin !== false);

                $hex = \bin2hex(~$bin);

                $hex = self::fromBase($hex, 16)->plus(1)->toBase(16);

                $hexLength = \strlen($hex);

                if ($hexLength < $baseHexLength) {

                    $hex = \str_repeat('0', $baseHexLength - $hexLength) . $hex;

                }