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+<?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;
+ }
+}