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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();
}
/**
* Parses a string containing an integer in an arbitrary base.
*
* @deprecated will be removed in version 0.9 - use fromBase() instead
*
* The string can optionally be prefixed with the `+` or `-` sign.
* For bases greater than 10, both uppercase and lowercase letters are allowed.
*
* @param string $number The number to parse.
* @param int $base The base of the number, between 2 and 36.
*
* @return BigInteger
*
* @throws \InvalidArgumentException If the number is invalid or the base is out of range.
*/
public static function parse(string $number, int $base = 10) : BigInteger
{
try {
return self::fromBase($number, $base);
} catch (NumberFormatException $e) {
throw new \InvalidArgumentException($e->getMessage(), 0, $e);
}
}
/**
* 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 positive exponent.
* @param BigNumber|int|float|string $mod The modulus. Must not be zero.
*
* @return BigInteger
*
* @throws NegativeNumberException If any of the operands is negative.
* @throws DivisionByZeroException If the modulus is zero.
*/
public function modPow($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 this number raised into power with modulo.
*
* @deprecated Use modPow() instead.
*
* @param BigNumber|int|float|string $exp The positive exponent.
* @param BigNumber|int|float|string $mod The modulus. Must not be zero.
*
* @return BigInteger
*
* @throws NegativeNumberException If any of the operands is negative.
* @throws DivisionByZeroException If the modulus is zero.
*/
public function powerMod($exp, $mod) : BigInteger
{
return $this->modPow($exp, $mod);
}
/**
* 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 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;
}
}