Merge branch '5.2RC'5.2

1 files changed, 1134 insertions, 0 deletions

diff --git a/vendor/brick/math/src/BigInteger.php b/vendor/brick/math/src/BigInteger.php
new file mode 100644
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+++ b/vendor/brick/math/src/BigInteger.php
@@ -0,0 +1,1134 @@
+<?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;
+    }
+}