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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\InvalidArgumentException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NegativeNumberException;
use Brick\Math\Exception\NoInverseException;
use Brick\Math\Exception\NumberFormatException;
use Brick\Math\Exception\RandomSourceException;
use Brick\Math\Exception\RoundingNecessaryException;
use Brick\Math\Internal\Calculator;
use Brick\Math\Internal\CalculatorRegistry;
use Brick\Math\Internal\Safe;
use LogicException;
use Override;
use Throwable;
use function array_map;
use function assert;
use function bin2hex;
use function chr;
use function count_chars;
use function filter_var;
use function hex2bin;
use function in_array;
use function intdiv;
use function is_string;
use function ltrim;
use function ord;
use function preg_match;
use function preg_quote;
use function random_bytes;
use function str_repeat;
use function strlen;
use function substr;
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 non-empty-string $number The number to convert, in the given base.
* @param int<2, 36> $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 $base): BigInteger
{
if ($base < 2 || $base > 36) { // @phpstan-ignore smaller.alwaysFalse, greater.alwaysFalse, booleanOr.alwaysFalse
throw InvalidArgumentException::baseOutOfRange($base);
}
if ($number === '') { // @phpstan-ignore identical.alwaysFalse
throw NumberFormatException::emptyNumber();
}
$originalNumber = $number;
if ($number[0] === '-') {
$sign = '-';
$number = substr($number, 1);
} elseif ($number[0] === '+') {
$sign = '';
$number = substr($number, 1);
} else {
$sign = '';
}
if ($number === '') {
throw NumberFormatException::invalidFormat($originalNumber);
}
$number = ltrim($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, $base) . ']/i';
if (preg_match($pattern, $number, $matches) === 1) {
throw NumberFormatException::charNotValidInBase($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 non-empty-string $number The number to parse.
* @param non-empty-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
{
$base = strlen($alphabet);
if ($base < 2) {
throw InvalidArgumentException::alphabetTooShort();
}
if (strlen(count_chars($alphabet, 3)) !== $base) {
throw InvalidArgumentException::duplicateCharsInAlphabet();
}
if ($number === '') { // @phpstan-ignore identical.alwaysFalse
throw NumberFormatException::emptyNumber();
}
$pattern = '/[^' . preg_quote($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 non-empty-string $bytes 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 $bytes, bool $signed = true): BigInteger
{
if ($bytes === '') { // @phpstan-ignore identical.alwaysFalse
throw NumberFormatException::emptyByteString();
}
$twosComplement = false;
if ($signed) {
$x = ord($bytes[0]);
if (($twosComplement = ($x >= 0x80))) {
$bytes = ~$bytes;
}
}
$number = self::fromBase(bin2hex($bytes), 16);
if ($twosComplement) {
return $number->plus(1)->negated();
}
return $number;
}
/**
* Generates a pseudo-random number in the range 0 to 2^bitCount - 1.
*
* Using the default random bytes generator, this method is suitable for cryptographic use.
*
* @param non-negative-int $bitCount 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 $bitCount is negative.
* @throws RandomSourceException If random byte generation fails.
*/
public static function randomBits(int $bitCount, ?callable $randomBytesGenerator = null): BigInteger
{
if ($bitCount < 0) { // @phpstan-ignore smaller.alwaysFalse
throw InvalidArgumentException::negativeBitCount();
}
if ($bitCount === 0) {
return BigInteger::zero();
}
/** @var int<1, max> $byteLength */
$byteLength = intdiv($bitCount - 1, 8) + 1;
$extraBits = ($byteLength * 8 - $bitCount);
$bitmask = chr(0xFF >> $extraBits);
$randomBytes = self::randomBytes($byteLength, $randomBytesGenerator);
$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|string $min The lower bound. Must be convertible to a BigInteger.
* @param BigNumber|int|string $max The upper bound. Must be convertible to a BigInteger.
* @param (callable(int): string)|null $randomBytesGenerator A function that accepts a number of bytes, and returns
* a string of random bytes of the given length. Defaults
* to the `random_bytes()` function.
*
* @throws MathException If one of the parameters cannot be converted to a BigInteger.
* @throws InvalidArgumentException If `$min` is greater than `$max`.
* @throws RandomSourceException If random byte generation fails.
*/
public static function randomRange(
BigNumber|int|string $min,
BigNumber|int|string $max,
?callable $randomBytesGenerator = null,
): BigInteger {
$min = BigInteger::of($min);
$max = BigInteger::of($max);
if ($min->isGreaterThan($max)) {
throw InvalidArgumentException::minGreaterThanMax();
}
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|string $a The first number. Must be convertible to a BigInteger.
* @param BigNumber|int|string ...$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|string $a, BigNumber|int|string ...$n): BigInteger
{
$result = BigInteger::of($a)->abs();
$n = array_map(BigInteger::of(...), $n); // @phpstan-ignore possiblyImpure.functionCall
foreach ($n as $next) {
$result = $result->gcd($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|string $a The first number. Must be convertible to a BigInteger.
* @param BigNumber|int|string ...$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|string $a, BigNumber|int|string ...$n): BigInteger
{
$result = BigInteger::of($a)->abs();
$n = array_map(BigInteger::of(...), $n); // @phpstan-ignore possiblyImpure.functionCall
foreach ($n as $next) {
$result = $result->lcm($next);
if ($result->isZero()) {
return $result;
}
}
return $result;
}
/**
* Returns the sum of this number and the given one.
*
* @param BigNumber|int|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|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
return $this;
}
if ($this->isZero()) {
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|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|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
return $this;
}
if ($this->isZero()) {
return $that->negated();
}
$value = CalculatorRegistry::get()->sub($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the product of this number and the given one.
*
* @param BigNumber|int|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|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isOne()) {
return $this;
}
if ($this->isOne()) {
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|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|string $that, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
if ($that->isOne()) {
return $this;
}
if ($that->isMinusOne()) {
return $this->negated();
}
$result = CalculatorRegistry::get()->divRound($this->value, $that->value, $roundingMode);
if ($result === null) {
throw RoundingNecessaryException::integerDivisionNotExact();
}
return new BigInteger($result);
}
/**
* Returns this number exponentiated to the given value.
*
* @param non-negative-int $exponent
*
* @throws InvalidArgumentException If the exponent is negative.
*
* @pure
*/
public function power(int $exponent): BigInteger
{
if ($exponent === 0) {
return BigInteger::one();
}
if ($exponent === 1) {
return $this;
}
if ($exponent < 0) { // @phpstan-ignore smaller.alwaysFalse
throw InvalidArgumentException::negativeExponent();
}
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|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|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
if ($that->isOne()) {
return $this;
}
if ($that->isMinusOne()) {
return $this->negated();
}
$quotient = CalculatorRegistry::get()->divQ($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|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|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
if ($that->isOne() || $that->isMinusOne()) {
return BigInteger::zero();
}
$remainder = CalculatorRegistry::get()->divR($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|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|string $that): array
{
$that = BigInteger::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
if ($that->isOne()) {
return [$this, BigInteger::zero()];
}
if ($that->isMinusOne()) {
return [$this->negated(), BigInteger::zero()];
}
[$quotient, $remainder] = CalculatorRegistry::get()->divQR($this->value, $that->value);
return [
new BigInteger($quotient),
new BigInteger($remainder),
];
}
/**
* Returns this number modulo the given one.
*
* The result is always non-negative, and is the unique value `r` such that `0 <= r < m`
* and `this - r` is a multiple of `m`.
*
* This is also known as Euclidean modulo. Unlike `remainder()`, which can return negative values
* when the dividend is negative, `mod()` always returns a non-negative result.
*
* Examples:
*
* - `7` mod `3` returns `1`
* - `-7` mod `3` returns `2`
*
* @param BigNumber|int|string $modulus The modulus. Must be convertible to a BigInteger.
*
* @throws MathException If the modulus is not valid, or is not convertible to a BigInteger.
* @throws InvalidArgumentException If the modulus is negative.
* @throws DivisionByZeroException If the modulus is zero.
*
* @pure
*/
public function mod(BigNumber|int|string $modulus): BigInteger
{
$modulus = BigInteger::of($modulus);
if ($modulus->isZero()) {
throw DivisionByZeroException::zeroModulus();
}
if ($modulus->isNegative()) {
throw InvalidArgumentException::negativeModulus();
}
$value = CalculatorRegistry::get()->mod($this->value, $modulus->value);
return new BigInteger($value);
}
/**
* Returns the modular multiplicative inverse of this BigInteger modulo $modulus.
*
* @param BigNumber|int|string $modulus The modulus. Must be convertible to a BigInteger.
*
* @throws MathException If the modulus is not valid, or is not convertible to a BigInteger.
* @throws InvalidArgumentException If the modulus is negative.
* @throws DivisionByZeroException If the modulus is zero.
* @throws NoInverseException 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|string $modulus): BigInteger
{
$modulus = BigInteger::of($modulus);
if ($modulus->isZero()) {
throw DivisionByZeroException::zeroModulus();
}
if ($modulus->isNegative()) {
throw InvalidArgumentException::negativeModulus();
}
if ($modulus->isOne()) {
return BigInteger::zero();
}
$value = CalculatorRegistry::get()->modInverse($this->value, $modulus->value);
if ($value === null) {
throw NoInverseException::noModularInverse();
}
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|string $exponent The exponent. Must be convertible to a BigInteger.
* @param BigNumber|int|string $modulus 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 InvalidArgumentException If the exponent or modulus is negative.
* @throws DivisionByZeroException If the modulus is zero.
*
* @pure
*/
public function modPow(BigNumber|int|string $exponent, BigNumber|int|string $modulus): BigInteger
{
$exponent = BigInteger::of($exponent);
$modulus = BigInteger::of($modulus);
if ($modulus->isZero()) {
throw DivisionByZeroException::zeroModulus();
}
if ($modulus->isNegative()) {
throw InvalidArgumentException::negativeModulus();
}
if ($exponent->isNegative()) {
throw InvalidArgumentException::negativeExponent();
}
$result = CalculatorRegistry::get()->modPow($this->value, $exponent->value, $modulus->value);
return new BigInteger($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|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|string $that): BigInteger
{
$that = BigInteger::of($that);
if ($that->isZero()) {
return $this->abs();
}
if ($this->isZero()) {
return $that->abs();
}
$value = CalculatorRegistry::get()->gcd($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|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|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 An optional rounding mode, defaults to Unnecessary.
*
* @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 $roundingMode = RoundingMode::Unnecessary): BigInteger
{
if ($this->isNegative()) {
throw NegativeNumberException::squareRootOfNegativeNumber();
}
$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::integerSquareRootNotExact();
}
// 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);
}
/**
* Returns the integer nth root of this number, rounded according to the given rounding mode.
*
* For odd $n, the operation is defined for negative inputs: the sign is preserved and the
* magnitude of the root is |$this|^(1/$n).
*
* @param positive-int $n The root degree. Must be a strictly positive integer.
* @param RoundingMode $roundingMode An optional rounding mode, defaults to Unnecessary.
*
* @throws InvalidArgumentException If $n is less than 1.
* @throws NegativeNumberException If this number is negative and $n is even.
* @throws RoundingNecessaryException If RoundingMode::Unnecessary is used, and this number is not a perfect nth power.
*
* @pure
*/
public function nthRoot(int $n, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigInteger
{
if ($n < 1) { // @phpstan-ignore smaller.alwaysFalse
throw InvalidArgumentException::nonPositiveNthRootDegree();
}
if ($n === 1) {
return $this;
}
$isNegative = $this->isNegative();
if ($isNegative && $n % 2 === 0) {
throw NegativeNumberException::nthRootOfNegativeNumber();
}
$calculator = CalculatorRegistry::get();
// Truncation toward zero: for positive $this this is the floor root, for negative $this
// with odd $n this is the ceiling of the true root (i.e., the root of smaller magnitude).
$truncatedRoot = $calculator->nthRoot($this->value, $n);
$rootPow = $calculator->pow($truncatedRoot, $n);
if ($rootPow === $this->value) {
return new BigInteger($truncatedRoot);
}
if ($roundingMode === RoundingMode::Unnecessary) {
throw RoundingNecessaryException::integerNthRootNotExact();
}
$isPositive = ! $isNegative;
// The next-step root is one unit further from zero than the truncated root.
$nextStep = $isPositive
? $calculator->add($truncatedRoot, '1')
: $calculator->sub($truncatedRoot, '1');
if ($roundingMode === RoundingMode::Up) {
$increment = true;
} elseif ($roundingMode === RoundingMode::Down) {
$increment = false;
} elseif ($roundingMode === RoundingMode::Ceiling) {
$increment = $isPositive;
} elseif ($roundingMode === RoundingMode::Floor) {
$increment = ! $isPositive;
} else {
// Half* modes: increment iff |$this| > (|truncated| + 0.5)^n, equivalently
// 2^n * |$this| > (2*|truncated| + 1)^n. The rhs is odd while the lhs is even
// (n ≥ 2 here, so 2^n is even), so a midpoint tie is impossible and all five
// Half* modes collapse to the same comparison.
$absValue = $calculator->abs($this->value);
$absTruncated = $calculator->abs($truncatedRoot);
$twoAbsRootPlus1 = $calculator->add($calculator->mul($absTruncated, '2'), '1');
$lhs = $calculator->mul($calculator->pow('2', $n), $absValue);
$rhs = $calculator->pow($twoAbsRootPlus1, $n);
$increment = $calculator->cmp($lhs, $rhs) > 0;
}
return new BigInteger($increment ? $nextStep : $truncatedRoot);
}
#[Override]
public function negated(): static
{
return new BigInteger(CalculatorRegistry::get()->neg($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|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|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|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|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|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|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.
*
* If $bits is negative, the integer is shifted right by the absolute value instead.
*
* @pure
*/
public function shiftedLeft(int $bits): BigInteger
{
if ($bits === 0) {
return $this;
}
if ($bits < 0) {
return $this->shiftedRight(Safe::neg($bits));
}
return $this->multipliedBy(BigInteger::of(2)->power($bits));
}
/**
* Returns the integer right shifted by a given number of bits.
*
* If $bits is negative, the integer is shifted left by the absolute value instead.
*
* @pure
*/
public function shiftedRight(int $bits): BigInteger
{
if ($bits === 0) {
return $this;
}
if ($bits < 0) {
return $this->shiftedLeft(Safe::neg($bits));
}
$operand = BigInteger::of(2)->power($bits);
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 non-negative-int
*
* @pure
*/
public function getBitLength(): int
{
if ($this->isZero()) {
return 0;
}
if ($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 null if this BigInteger is zero.
*
* @return non-negative-int|null
*
* @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 null;
}
/**
* Returns true if and only if the designated bit is set.
*
* Computes ((this & (1<<bitIndex)) != 0).
*
* @param non-negative-int $bitIndex The bit to test, 0-based.
*
* @throws InvalidArgumentException If the bit to test is negative.
*
* @pure
*/
public function isBitSet(int $bitIndex): bool
{
if ($bitIndex < 0) { // @phpstan-ignore smaller.alwaysFalse
throw InvalidArgumentException::negativeBitIndex();
}
return $this->shiftedRight($bitIndex)->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);
}
#[Override]
public function compareTo(BigNumber|int|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, 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 ($intValue === false) {
throw IntegerOverflowException::integerOutOfRange($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.
*
* @param int<2, 36> $base
*
* @return non-empty-string
*
* @throws InvalidArgumentException If the base is out of range.
*
* @pure
*/
public function toBase(int $base): string
{
if ($base === 10) {
/** @var non-empty-string */
return $this->value;
}
if ($base < 2 || $base > 36) { // @phpstan-ignore smaller.alwaysFalse, greater.alwaysFalse, booleanOr.alwaysFalse
throw InvalidArgumentException::baseOutOfRange($base);
}
/** @var non-empty-string */
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 non-empty-string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8.
*
* @return non-empty-string
*
* @throws InvalidArgumentException If the alphabet does not contain at least 2 chars, or contains duplicates.
* @throws NegativeNumberException If this number is negative.
*
* @pure
*/
public function toArbitraryBase(string $alphabet): string
{
$base = strlen($alphabet);
if ($base < 2) {
throw InvalidArgumentException::alphabetTooShort();
}
if (strlen(count_chars($alphabet, 3)) !== $base) {
throw InvalidArgumentException::duplicateCharsInAlphabet();
}
if ($this->isNegative()) {
throw NegativeNumberException::toArbitraryBaseOfNegativeNumber();
}
/** @var non-empty-string */
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.
*
* @return non-empty-string
*
* @throws NegativeNumberException If $signed is false, and the number is negative.
*
* @pure
*/
public function toBytes(bool $signed = true): string
{
if (! $signed && $this->isNegative()) {
throw NegativeNumberException::unsignedBytesOfNegativeNumber();
}
$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);
/** @var non-empty-string $hex */
$hex = bin2hex(~$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);
/** @var non-empty-string */
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();
}
/**
* Returns random bytes from the provided generator or from random_bytes().
*
* @param int $byteLength The number of requested bytes.
* @param (callable(int): string)|null $randomBytesGenerator The random bytes generator, or null to use random_bytes().
*
* @throws RandomSourceException If random byte generation fails.
*/
private static function randomBytes(int $byteLength, ?callable $randomBytesGenerator): string
{
if ($randomBytesGenerator === null) {
$randomBytesGenerator = random_bytes(...);
}
try {
$randomBytes = $randomBytesGenerator($byteLength);
} catch (Throwable $e) {
throw RandomSourceException::randomSourceFailure($e);
}
/** @phpstan-ignore function.alreadyNarrowedType (Defensive runtime check for user-provided callbacks) */
if (! is_string($randomBytes)) {
throw RandomSourceException::invalidRandomBytesType($randomBytes);
}
if (strlen($randomBytes) !== $byteLength) {
throw RandomSourceException::invalidRandomBytesLength($byteLength, strlen($randomBytes));
}
return $randomBytes;
}
/**
* @pure
*/
private function isOne(): bool
{
return $this->value === '1';
}
/**
* @pure
*/
private function isMinusOne(): bool
{
return $this->value === '-1';
}
}