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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. */ 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. */ protected function __construct(string $value) { $this->value = $value; } /** * Creates a BigInteger of the given value. * * @throws MathException If the value cannot be converted to a BigInteger. * * @psalm-pure */ public static function of(BigNumber|int|float|string $value) : BigInteger { return parent::of($value)->toBigInteger(); } /** * Creates a number from a string in a given base. * * The string can optionally be prefixed with the `+` or `-` sign. * * Bases greater than 36 are not supported by this method, as there is no clear consensus on which of the lowercase * or uppercase characters should come first. Instead, this method accepts any base up to 36, and does not * differentiate lowercase and uppercase characters, which are considered equal. * * For bases greater than 36, and/or custom alphabets, use the fromArbitraryBase() method. * * @param string $number The number to convert, in the given base. * @param int $base The base of the number, between 2 and 36. * * @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. * * @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. * * @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. * * @psalm-param (callable(int): string)|null $randomBytesGenerator * * @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. * * @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. * * @psalm-param (callable(int): string)|null $randomBytesGenerator * * @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 $randomBytesGenerator A function that accepts a number of bytes as an integer, * and returns a string of random bytes of the given length. * Defaults to the `random_bytes()` function. * * @throws MathException If one of the parameters cannot be converted to a BigInteger, * or `$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 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. * * @psalm-pure */ public static function zero() : BigInteger { /** * @psalm-suppress ImpureStaticVariable * @var BigInteger|null $zero */ static $zero; if ($zero === null) { $zero = new BigInteger('0'); } return $zero; } /** * Returns a BigInteger representing one. * * @psalm-pure */ public static function one() : BigInteger { /** * @psalm-suppress ImpureStaticVariable * @var BigInteger|null $one */ static $one; if ($one === null) { $one = new BigInteger('1'); } return $one; } /** * Returns a BigInteger representing ten. * * @psalm-pure */ public static function ten() : BigInteger { /** * @psalm-suppress ImpureStaticVariable * @var BigInteger|null $ten */ static $ten; if ($ten === null) { $ten = new BigInteger('10'); } return $ten; } public static function gcdMultiple(BigInteger $a, BigInteger ...$n): BigInteger { $result = $a; foreach ($n as $next) { $result = $result->gcd($next); if ($result->isEqualTo(1)) { return $result; } } return $result; } /** * 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. */ 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; } $value = Calculator::get()->add($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. * * @throws MathException If the number is not valid, or is not convertible to a BigInteger. */ public function minus(BigNumber|int|float|string $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. * * @throws MathException If the multiplier is not a valid number, or is not convertible to a BigInteger. */ 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; } $value = Calculator::get()->mul($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. * * @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(BigNumber|int|float|string $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. * * @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. * * @throws DivisionByZeroException If the divisor is zero. */ 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(); } $quotient = Calculator::get()->divQ($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. * * @throws DivisionByZeroException If the divisor is zero. */ 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(); } $remainder = Calculator::get()->divR($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(BigNumber|int|float|string $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. * * @throws DivisionByZeroException If the divisor is zero. */ public function mod(BigNumber|int|float|string $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. * * @throws DivisionByZeroException If $m is zero. * @throws NegativeNumberException If $m is negative. * @throws MathException If this BigInteger has no multiplicative inverse mod m (that is, this BigInteger * is not relatively prime to m). */ public function modInverse(BigInteger $m) : BigInteger { if ($m->value === '0') { throw DivisionByZeroException::modulusMustNotBeZero(); } if ($m->isNegative()) { throw new NegativeNumberException('Modulus must not be negative.'); } if ($m->value === '1') { return BigInteger::zero(); } $value = Calculator::get()->modInverse($this->value, $m->value); if ($value === null) { throw new MathException('Unable to compute the modInverse for the given modulus.'); } return new BigInteger($value); } /** * Returns this number raised into power with modulo. * * This operation only works on positive numbers. * * @param BigNumber|int|float|string $exp The exponent. Must be positive or zero. * @param BigNumber|int|float|string $mod The modulus. Must be strictly positive. * * @throws NegativeNumberException If any of the operands is negative. * @throws DivisionByZeroException If the modulus is zero. */ public function modPow(BigNumber|int|float|string $exp, BigNumber|int|float|string $mod) : BigInteger { $exp = BigInteger::of($exp); $mod = BigInteger::of($mod); if ($this->isNegative() || $exp->isNegative() || $mod->isNegative()) { throw new NegativeNumberException('The operands cannot be negative.'); } if ($mod->isZero()) { throw DivisionByZeroException::modulusMustNotBeZero(); } $result = Calculator::get()->modPow($this->value, $exp->value, $mod->value); return new BigInteger($result); } /** * Returns the greatest common divisor of this number and the given one. * * The GCD is always positive, unless both operands are zero, in which case it is zero. * * @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number. */ 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; } $value = Calculator::get()->gcd($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. * * @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. */ public function abs() : BigInteger { return $this->isNegative() ? $this->negated() : $this; } /** * Returns the inverse of this number. */ public function negated() : BigInteger { return new BigInteger(Calculator::get()->neg($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. */ public function and(BigNumber|int|float|string $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. */ public function or(BigNumber|int|float|string $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. */ public function xor(BigNumber|int|float|string $that) : BigInteger { $that = BigInteger::of($that); return new BigInteger(Calculator::get()->xor($this->value, $that->value)); } /** * Returns the bitwise-not of this BigInteger. */ public function not() : BigInteger { return $this->negated()->minus(1); } /** * Returns the integer left shifted by a given number of bits. */ 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. */ 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))). */ 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. */ public function getLowestSetBit() : int { $n = $this; $bitLength = $this->getBitLength(); for ($i = 0; $i <= $bitLength; $i++) { if ($n->isOdd()) { return $i; } $n = $n->shiftedRight(1); } return -1; } /** * Returns whether this number is even. */ public function isEven() : bool { return \in_array($this->value[-1], ['0', '2', '4', '6', '8'], true); } /** * Returns whether this number is odd. */ 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. * * @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(); } public function compareTo(BigNumber|int|float|string $that) : int { $that = BigNumber::of($that); if ($that instanceof BigInteger) { return Calculator::get()->cmp($this->value, $that->value); } return - $that->compareTo($this); } public function getSign() : int { return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1); } public function toBigInteger() : BigInteger { return $this; } public function toBigDecimal() : BigDecimal { return self::newBigDecimal($this->value); } public function toBigRational() : BigRational { return self::newBigRational($this, BigInteger::one(), false); } public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal { return $this->toBigDecimal()->toScale($scale, $roundingMode); } public function toInt() : int { $intValue = (int) $this->value; if ($this->value !== (string) $intValue) { throw IntegerOverflowException::toIntOverflow($this); } return $intValue; } 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. */ 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. * * @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. * * @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()) { $bin = \hex2bin($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' . $hex; } } } return \hex2bin($hex); } public function __toString() : 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 * @psalm-suppress RedundantPropertyInitializationCheck * * @param array{value: string} $data * * @throws \LogicException */ public function __unserialize(array $data): void { if (isset($this->value)) { throw new \LogicException('__unserialize() is an internal function, it must not be called directly.'); } $this->value = $data['value']; } /** * This method is required by interface Serializable and SHOULD NOT be accessed directly. * * @internal */ public function serialize() : string { return $this->value; } /** * This method is only here to implement interface Serializable and cannot be accessed directly. * * @internal * @psalm-suppress RedundantPropertyInitializationCheck * * @throws \LogicException */ public function unserialize($value) : void { if (isset($this->value)) { throw new \LogicException('unserialize() is an internal function, it must not be called directly.'); } $this->value = $value; } }