Файл: vendor/brick/math/src/BigInteger.php
Строк: 2011
<?php
declare(strict_types=1);
namespace BrickMath;
use BrickMathExceptionDivisionByZeroException;
use BrickMathExceptionIntegerOverflowException;
use BrickMathExceptionMathException;
use BrickMathExceptionNegativeNumberException;
use BrickMathExceptionNumberFormatException;
use BrickMathExceptionRoundingNecessaryException;
use BrickMathInternalCalculator;
use BrickMathInternalCalculatorRegistry;
use InvalidArgumentException;
use LogicException;
use Override;
use function assert;
use function bin2hex;
use function chr;
use function count_chars;
use function filter_var;
use function func_num_args;
use function hex2bin;
use function in_array;
use function intdiv;
use function ltrim;
use function ord;
use function preg_match;
use function preg_quote;
use function random_bytes;
use function sprintf;
use function str_repeat;
use function strlen;
use function strtolower;
use function substr;
use function trigger_error;
use const E_USER_DEPRECATED;
use const FILTER_VALIDATE_INT;
/**
* An arbitrarily large integer number.
*
* This class is immutable.
*/
final readonly 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.
*
* @pure
*/
protected function __construct(string $value)
{
$this->value = $value;
}
/**
* 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.
*
* @pure
*/
public static function fromBase(string $number, int $base): BigInteger
{
if ($number === '') {
throw new NumberFormatException('The number must not 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 must not 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);
}
$result = CalculatorRegistry::get()->fromBase($number, $base);
return new BigInteger($sign . $result);
}
/**
* Parses a string containing an integer in an arbitrary base, using a custom alphabet.
*
* This method is byte-oriented: the alphabet is interpreted as a sequence of single-byte characters.
* Multibyte UTF-8 characters are not supported.
*
* Because this method accepts any single-byte 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, or contains duplicates.
*
* @pure
*/
public static function fromArbitraryBase(string $number, string $alphabet): BigInteger
{
if ($number === '') {
throw new NumberFormatException('The number must not be empty.');
}
$base = strlen($alphabet);
if ($base < 2) {
throw new InvalidArgumentException('The alphabet must contain at least 2 chars.');
}
if (strlen(count_chars($alphabet, 3)) !== $base) {
throw new InvalidArgumentException('The alphabet must not contain duplicate chars.');
}
$pattern = '/[^' . preg_quote($alphabet, '/') . ']/';
if (preg_match($pattern, $number, $matches) === 1) {
throw NumberFormatException::charNotInAlphabet($matches[0]);
}
$number = CalculatorRegistry::get()->fromArbitraryBase($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.
*
* @pure
*/
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(int): string)|null $randomBytesGenerator A function that accepts a number of bytes, 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 must not be negative.');
}
if ($numBits === 0) {
return BigInteger::zero();
}
if ($randomBytesGenerator === null) {
$randomBytesGenerator = random_bytes(...);
}
/** @var int<1, max> $byteLength */
$byteLength = intdiv($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`, inclusive.
*
* 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(int): string)|null $randomBytesGenerator A function that accepts a number of bytes, and returns
* a string of random bytes of the given length. Defaults
* to the `random_bytes()` function.
*
* @throws MathException If one of the parameters cannot be converted to a BigInteger,
* or `$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 must be less than or equal to $max.');
}
if ($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.
*
* @pure
*/
public static function zero(): BigInteger
{
/** @var BigInteger|null $zero */
static $zero;
if ($zero === null) {
$zero = new BigInteger('0');
}
return $zero;
}
/**
* Returns a BigInteger representing one.
*
* @pure
*/
public static function one(): BigInteger
{
/** @var BigInteger|null $one */
static $one;
if ($one === null) {
$one = new BigInteger('1');
}
return $one;
}
/**
* Returns a BigInteger representing ten.
*
* @pure
*/
public static function ten(): BigInteger
{
/** @var BigInteger|null $ten */
static $ten;
if ($ten === null) {
$ten = new BigInteger('10');
}
return $ten;
}
/**
* Returns the greatest common divisor of the given numbers.
*
* The GCD is always positive, unless all numbers are zero, in which case it is zero.
*
* @param BigNumber|int|float|string $a The first number. Must be convertible to a BigInteger.
* @param BigNumber|int|float|string ...$n The additional numbers. Each number must be convertible to a BigInteger.
*
* @throws MathException If one of the parameters cannot be converted to a BigInteger.
*
* @pure
*/
public static function gcdAll(BigNumber|int|float|string $a, BigNumber|int|float|string ...$n): BigInteger
{
$result = BigInteger::of($a)->abs();
foreach ($n as $next) {
$result = $result->gcd(BigInteger::of($next));
if ($result->isEqualTo(1)) {
return $result;
}
}
return $result;
}
/**
* Returns the least common multiple of the given numbers.
*
* The LCM is always positive, unless one of the numbers is zero, in which case it is zero.
*
* @param BigNumber|int|float|string $a The first number. Must be convertible to a BigInteger.
* @param BigNumber|int|float|string ...$n The additional numbers. Each number must be convertible to a BigInteger.
*
* @throws MathException If one of the parameters cannot be converted to a BigInteger.
*
* @pure
*/
public static function lcmAll(BigNumber|int|float|string $a, BigNumber|int|float|string ...$n): BigInteger
{
$result = BigInteger::of($a)->abs();
foreach ($n as $next) {
$result = $result->lcm(BigInteger::of($next));
if ($result->isZero()) {
return $result;
}
}
return $result;
}
/**
* @deprecated Use gcdAll() instead.
*
* @param BigNumber|int|float|string $a The first number. Must be convertible to a BigInteger.
* @param BigNumber|int|float|string ...$n The subsequent numbers. Must be convertible to BigInteger.
*/
public static function gcdMultiple(BigNumber|int|float|string $a, BigNumber|int|float|string ...$n): BigInteger
{
trigger_error(
'BigInteger::gcdMultiple() is deprecated and will be removed in version 0.15. Use gcdAll() instead.',
E_USER_DEPRECATED,
);
return self::gcdAll($a, ...$n);
}
/**
* 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.
*
* @pure
*/
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;
}
$value = CalculatorRegistry::get()->add($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.
*
* @pure
*/
public function minus(BigNumber|int|float|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '0') {
return $this;
}
$value = CalculatorRegistry::get()->sub($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 valid, or is not convertible to a BigInteger.
*
* @pure
*/
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;
}
$value = CalculatorRegistry::get()->mul($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 RoundingMode $roundingMode An optional rounding mode, defaults to Unnecessary.
*
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
* @throws DivisionByZeroException If the divisor is zero.
* @throws RoundingNecessaryException If RoundingMode::Unnecessary is used and the remainder is not zero.
*
* @pure
*/
public function dividedBy(BigNumber|int|float|string $that, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '1') {
return $this;
}
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
$result = CalculatorRegistry::get()->divRound($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.
*
* @pure
*/
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.',
$exponent,
Calculator::MAX_POWER,
));
}
return new BigInteger(CalculatorRegistry::get()->pow($this->value, $exponent));
}
/**
* Returns the quotient of the division of this number by the given one.
*
* Examples:
*
* - `7` quotient `3` returns `2`
* - `7` quotient `-3` returns `-2`
* - `-7` quotient `3` returns `-2`
* - `-7` quotient `-3` returns `2`
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
* @throws DivisionByZeroException If the divisor is zero.
*
* @pure
*/
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();
}
$quotient = CalculatorRegistry::get()->divQ($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.
*
* Examples:
*
* - `7` remainder `3` returns `1`
* - `7` remainder `-3` returns `1`
* - `-7` remainder `3` returns `-1`
* - `-7` remainder `-3` returns `-1`
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
* @throws DivisionByZeroException If the divisor is zero.
*
* @pure
*/
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();
}
$remainder = CalculatorRegistry::get()->divR($this->value, $that->value);
return new BigInteger($remainder);
}
/**
* Returns the quotient and remainder of the division of this number by the given one.
*
* Examples:
*
* - `7` quotientAndRemainder `3` returns [`2`, `1`]
* - `7` quotientAndRemainder `-3` returns [`-2`, `1`]
* - `-7` quotientAndRemainder `3` returns [`-2`, `-1`]
* - `-7` quotientAndRemainder `-3` returns [`2`, `-1`]
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @return array{BigInteger, BigInteger} An array containing the quotient and the remainder.
*
* @throws MathException If the divisor is not valid, or is not convertible to a BigInteger.
* @throws DivisionByZeroException If the divisor is zero.
*
* @pure
*/
public function quotientAndRemainder(BigNumber|int|float|string $that): array
{
$that = BigInteger::of($that);
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
[$quotient, $remainder] = CalculatorRegistry::get()->divQR($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 MathException If the divisor is not valid, or is not convertible to a BigInteger.
* @throws DivisionByZeroException If the divisor is zero.
*
* @pure
*/
public function mod(BigNumber|int|float|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::modulusMustNotBeZero();
}
if ($that->isNegative()) {
// @phpstan-ignore-next-line
trigger_error(
'Passing a negative modulus to BigInteger::mod() is deprecated and will throw a NegativeNumberException in 0.15.',
E_USER_DEPRECATED,
);
}
$value = CalculatorRegistry::get()->mod($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the modular multiplicative inverse of this BigInteger modulo $m.
*
* @param BigNumber|int|float|string $m The modulus. Must be convertible to a BigInteger.
*
* @throws MathException If the modulus is not valid, or is not convertible to a 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).
*
* @pure
*/
public function modInverse(BigNumber|int|float|string $m): BigInteger
{
$m = BigInteger::of($m);
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();
}
$value = CalculatorRegistry::get()->modInverse($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 requires a non-negative exponent and a strictly positive modulus.
*
* @param BigNumber|int|float|string $exp The exponent. Must be convertible to a BigInteger.
* @param BigNumber|int|float|string $mod The modulus. Must be convertible to a BigInteger.
*
* @throws MathException If the exponent or modulus is not valid, or is not convertible to a BigInteger.
* @throws NegativeNumberException If the exponent or modulus is negative.
* @throws DivisionByZeroException If the modulus is zero.
*
* @pure
*/
public function modPow(BigNumber|int|float|string $exp, BigNumber|int|float|string $mod): BigInteger
{
$exp = BigInteger::of($exp);
$mod = BigInteger::of($mod);
if ($exp->isNegative()) {
throw new NegativeNumberException('The exponent cannot be negative.');
}
if ($mod->isNegative()) {
throw new NegativeNumberException('The modulus cannot be negative.');
}
if ($mod->isZero()) {
throw DivisionByZeroException::modulusMustNotBeZero();
}
$result = CalculatorRegistry::get()->modPow($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 a BigInteger.
*
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
*
* @pure
*/
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;
}
$value = CalculatorRegistry::get()->gcd($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the least common multiple of this number and the given one.
*
* The LCM is always positive, unless at least one operand is zero, in which case it is zero.
*
* @param BigNumber|int|float|string $that The operand. Must be convertible to a BigInteger.
*
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
*
* @pure
*/
public function lcm(BigNumber|int|float|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($this->isZero() || $that->isZero()) {
return BigInteger::zero();
}
$value = CalculatorRegistry::get()->lcm($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the integer square root of this number, rounded according to the given rounding mode.
*
* @param RoundingMode $roundingMode The rounding mode to use, defaults to Down.
* ⚠️ WARNING: the default rounding mode was kept as Down for backward
* compatibility, but will change to Unnecessary in version 0.15. Pass a rounding
* mode explicitly to avoid this upcoming breaking change.
*
* @throws NegativeNumberException If this number is negative.
* @throws RoundingNecessaryException If RoundingMode::Unnecessary is used, and the number is not a perfect square.
*
* @pure
*/
public function sqrt(RoundingMode $roundingMode = RoundingMode::Down): BigInteger
{
if (func_num_args() === 0) {
// @phpstan-ignore-next-line
trigger_error(
'The default rounding mode of BigInteger::sqrt() will change from Down to Unnecessary in version 0.15. ' .
'Pass a rounding mode explicitly to avoid this breaking change.',
E_USER_DEPRECATED,
);
}
if ($this->value[0] === '-') {
throw new NegativeNumberException('Cannot calculate the square root of a negative number.');
}
$calculator = CalculatorRegistry::get();
$sqrt = $calculator->sqrt($this->value);
// For Down and Floor (equivalent for non-negative numbers), return floor sqrt
if ($roundingMode === RoundingMode::Down || $roundingMode === RoundingMode::Floor) {
return new BigInteger($sqrt);
}
// Check if the sqrt is exact
$s2 = $calculator->mul($sqrt, $sqrt);
$remainder = $calculator->sub($this->value, $s2);
if ($remainder === '0') {
// sqrt is exact
return new BigInteger($sqrt);
}
// sqrt is not exact
if ($roundingMode === RoundingMode::Unnecessary) {
throw RoundingNecessaryException::roundingNecessary();
}
// For Up and Ceiling (equivalent for non-negative numbers), round up
if ($roundingMode === RoundingMode::Up || $roundingMode === RoundingMode::Ceiling) {
return new BigInteger($calculator->add($sqrt, '1'));
}
// For Half* modes, compare our number to the midpoint of the interval [s², (s+1)²[.
// The midpoint is s² + s + 0.5. Comparing n >= s² + s + 0.5 with remainder = n − s²
// is equivalent to comparing 2*remainder >= 2*s + 1.
$twoRemainder = $calculator->mul($remainder, '2');
$threshold = $calculator->add($calculator->mul($sqrt, '2'), '1');
$cmp = $calculator->cmp($twoRemainder, $threshold);
// We're supposed to increment (round up) when:
// - HalfUp, HalfCeiling => $cmp >= 0
// - HalfDown, HalfFloor => $cmp > 0
// - HalfEven => $cmp > 0 || ($cmp === 0 && $sqrt % 2 === 1)
// But 2*remainder is always even and 2*s + 1 is always odd, so $cmp is never zero.
// Therefore, all Half* modes simplify to:
if ($cmp > 0) {
$sqrt = $calculator->add($sqrt, '1');
}
return new BigInteger($sqrt);
}
#[Override]
public function negated(): static
{
return new BigInteger(CalculatorRegistry::get()->neg($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 a BigInteger.
*
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
*
* @pure
*/
public function and(BigNumber|int|float|string $that): BigInteger
{
$that = BigInteger::of($that);
return new BigInteger(CalculatorRegistry::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 a BigInteger.
*
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
*
* @pure
*/
public function or(BigNumber|int|float|string $that): BigInteger
{
$that = BigInteger::of($that);
return new BigInteger(CalculatorRegistry::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 a BigInteger.
*
* @throws MathException If the operand is not valid, or is not convertible to a BigInteger.
*
* @pure
*/
public function xor(BigNumber|int|float|string $that): BigInteger
{
$that = BigInteger::of($that);
return new BigInteger(CalculatorRegistry::get()->xor($this->value, $that->value));
}
/**
* Returns the bitwise-not of this BigInteger.
*
* @pure
*/
public function not(): BigInteger
{
return $this->negated()->minus(1);
}
/**
* Returns the integer left shifted by a given number of bits.
*
* @throws InvalidArgumentException If the number of bits is out of range.
*
* @pure
*/
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.
*
* @throws InvalidArgumentException If the number of bits is out of range.
*
* @pure
*/
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))).
*
* @pure
*/
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.
*
* @pure
*/
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 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.
*
* @pure
*/
public function isBitSet(int $n): bool
{
if ($n < 0) {
throw new InvalidArgumentException('The bit to test cannot be negative.');
}
return $this->shiftedRight($n)->isOdd();
}
/**
* Returns whether this number is even.
*
* @pure
*/
public function isEven(): bool
{
return in_array($this->value[-1], ['0', '2', '4', '6', '8'], true);
}
/**
* Returns whether this number is odd.
*
* @pure
*/
public function isOdd(): bool
{
return in_array($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).
*
* @deprecated Use isBitSet().
*
* @param int $n The bit to test, 0-based.
*
* @throws InvalidArgumentException If the bit to test is negative.
*/
public function testBit(int $n): bool
{
trigger_error(
'The BigInteger::testBit() method is deprecated, use isBitSet() instead.',
E_USER_DEPRECATED,
);
return $this->isBitSet($n);
}
#[Override]
public function compareTo(BigNumber|int|float|string $that): int
{
$that = BigNumber::of($that);
if ($that instanceof BigInteger) {
return CalculatorRegistry::get()->cmp($this->value, $that->value);
}
return -$that->compareTo($this);
}
#[Override]
public function getSign(): int
{
return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);
}
#[Override]
public function toBigInteger(): BigInteger
{
return $this;
}
#[Override]
public function toBigDecimal(): BigDecimal
{
return self::newBigDecimal($this->value);
}
#[Override]
public function toBigRational(): BigRational
{
return self::newBigRational($this, BigInteger::one(), false);
}
#[Override]
public function toScale(int $scale, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigDecimal
{
return $this->toBigDecimal()->toScale($scale, $roundingMode);
}
#[Override]
public function toInt(): int
{
$intValue = filter_var($this->value, FILTER_VALIDATE_INT);
if ($intValue === false) {
throw IntegerOverflowException::toIntOverflow($this);
}
return $intValue;
}
#[Override]
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.
*
* @pure
*/
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]', $base));
}
return CalculatorRegistry::get()->toBase($this->value, $base);
}
/**
* Returns a string representation of this number in an arbitrary base with a custom alphabet.
*
* This method is byte-oriented: the alphabet is interpreted as a sequence of single-byte characters.
* Multibyte UTF-8 characters are not supported.
*
* Because this method accepts any single-byte 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 alphabet does not contain at least 2 chars, or contains duplicates.
*
* @pure
*/
public function toArbitraryBase(string $alphabet): string
{
$base = strlen($alphabet);
if ($base < 2) {
throw new InvalidArgumentException('The alphabet must contain at least 2 chars.');
}
if (strlen(count_chars($alphabet, 3)) !== $base) {
throw new InvalidArgumentException('The alphabet must not contain duplicate chars.');
}
if ($this->value[0] === '-') {
throw new NegativeNumberException(__FUNCTION__ . '() does not support negative numbers.');
}
return CalculatorRegistry::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.
*
* @pure
*/
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) . $hex;
}
if ($hex[0] < '8') {
$hex = 'FF' . $hex;
}
} else {
if ($hex[0] >= '8') {
$hex = '00' . $hex;
}
}
}
$result = hex2bin($hex);
assert($result !== false);
return $result;
}
/**
* @return numeric-string
*/
#[Override]
public function toString(): string
{
/** @var numeric-string */
return $this->value;
}
/**
* This method is required for serializing the object and SHOULD NOT be accessed directly.
*
* @internal
*
* @return array{value: string}
*/
public function __serialize(): array
{
return ['value' => $this->value];
}
/**
* This method is only here to allow unserializing the object and cannot be accessed directly.
*
* @internal
*
* @param array{value: string} $data
*
* @throws LogicException
*/
public function __unserialize(array $data): void
{
/** @phpstan-ignore isset.initializedProperty */
if (isset($this->value)) {
throw new LogicException('__unserialize() is an internal function, it must not be called directly.');
}
/** @phpstan-ignore deadCode.unreachable */
$this->value = $data['value'];
}
#[Override]
protected static function from(BigNumber $number): static
{
return $number->toBigInteger();
}
}