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math/src/BigRational.php 0000644 00000030373 14736103132 0011176 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math;
use Brick\Math\Exception\DivisionByZeroException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NumberFormatException;
use Brick\Math\Exception\RoundingNecessaryException;
/**
* An arbitrarily large rational number.
*
* This class is immutable.
*
* @psalm-immutable
*/
final class BigRational extends BigNumber
{
/**
* The numerator.
*
* @var BigInteger
*/
private $numerator;
/**
* The denominator. Always strictly positive.
*
* @var BigInteger
*/
private $denominator;
/**
* Protected constructor. Use a factory method to obtain an instance.
*
* @param BigInteger $numerator The numerator.
* @param BigInteger $denominator The denominator.
* @param bool $checkDenominator Whether to check the denominator for negative and zero.
*
* @throws DivisionByZeroException If the denominator is zero.
*/
protected function __construct(BigInteger $numerator, BigInteger $denominator, bool $checkDenominator)
{
if ($checkDenominator) {
if ($denominator->isZero()) {
throw DivisionByZeroException::denominatorMustNotBeZero();
}
if ($denominator->isNegative()) {
$numerator = $numerator->negated();
$denominator = $denominator->negated();
}
}
$this->numerator = $numerator;
$this->denominator = $denominator;
}
/**
* Creates a BigRational of the given value.
*
* @param BigNumber|int|float|string $value
*
* @return BigRational
*
* @throws MathException If the value cannot be converted to a BigRational.
*
* @psalm-pure
*/
public static function of($value) : BigNumber
{
return parent::of($value)->toBigRational();
}
/**
* Creates a BigRational out of a numerator and a denominator.
*
* If the denominator is negative, the signs of both the numerator and the denominator
* will be inverted to ensure that the denominator is always positive.
*
* @param BigNumber|int|float|string $numerator The numerator. Must be convertible to a BigInteger.
* @param BigNumber|int|float|string $denominator The denominator. Must be convertible to a BigInteger.
*
* @return BigRational
*
* @throws NumberFormatException If an argument does not represent a valid number.
* @throws RoundingNecessaryException If an argument represents a non-integer number.
* @throws DivisionByZeroException If the denominator is zero.
*
* @psalm-pure
*/
public static function nd($numerator, $denominator) : BigRational
{
$numerator = BigInteger::of($numerator);
$denominator = BigInteger::of($denominator);
return new BigRational($numerator, $denominator, true);
}
/**
* Returns a BigRational representing zero.
*
* @return BigRational
*
* @psalm-pure
*/
public static function zero() : BigRational
{
/** @psalm-suppress ImpureStaticVariable */
static $zero;
if ($zero === null) {
$zero = new BigRational(BigInteger::zero(), BigInteger::one(), false);
}
return $zero;
}
/**
* Returns a BigRational representing one.
*
* @return BigRational
*
* @psalm-pure
*/
public static function one() : BigRational
{
/** @psalm-suppress ImpureStaticVariable */
static $one;
if ($one === null) {
$one = new BigRational(BigInteger::one(), BigInteger::one(), false);
}
return $one;
}
/**
* Returns a BigRational representing ten.
*
* @return BigRational
*
* @psalm-pure
*/
public static function ten() : BigRational
{
/** @psalm-suppress ImpureStaticVariable */
static $ten;
if ($ten === null) {
$ten = new BigRational(BigInteger::ten(), BigInteger::one(), false);
}
return $ten;
}
/**
* @return BigInteger
*/
public function getNumerator() : BigInteger
{
return $this->numerator;
}
/**
* @return BigInteger
*/
public function getDenominator() : BigInteger
{
return $this->denominator;
}
/**
* Returns the quotient of the division of the numerator by the denominator.
*
* @return BigInteger
*/
public function quotient() : BigInteger
{
return $this->numerator->quotient($this->denominator);
}
/**
* Returns the remainder of the division of the numerator by the denominator.
*
* @return BigInteger
*/
public function remainder() : BigInteger
{
return $this->numerator->remainder($this->denominator);
}
/**
* Returns the quotient and remainder of the division of the numerator by the denominator.
*
* @return BigInteger[]
*/
public function quotientAndRemainder() : array
{
return $this->numerator->quotientAndRemainder($this->denominator);
}
/**
* Returns the sum of this number and the given one.
*
* @param BigNumber|int|float|string $that The number to add.
*
* @return BigRational The result.
*
* @throws MathException If the number is not valid.
*/
public function plus($that) : BigRational
{
$that = BigRational::of($that);
$numerator = $this->numerator->multipliedBy($that->denominator);
$numerator = $numerator->plus($that->numerator->multipliedBy($this->denominator));
$denominator = $this->denominator->multipliedBy($that->denominator);
return new BigRational($numerator, $denominator, false);
}
/**
* Returns the difference of this number and the given one.
*
* @param BigNumber|int|float|string $that The number to subtract.
*
* @return BigRational The result.
*
* @throws MathException If the number is not valid.
*/
public function minus($that) : BigRational
{
$that = BigRational::of($that);
$numerator = $this->numerator->multipliedBy($that->denominator);
$numerator = $numerator->minus($that->numerator->multipliedBy($this->denominator));
$denominator = $this->denominator->multipliedBy($that->denominator);
return new BigRational($numerator, $denominator, false);
}
/**
* Returns the product of this number and the given one.
*
* @param BigNumber|int|float|string $that The multiplier.
*
* @return BigRational The result.
*
* @throws MathException If the multiplier is not a valid number.
*/
public function multipliedBy($that) : BigRational
{
$that = BigRational::of($that);
$numerator = $this->numerator->multipliedBy($that->numerator);
$denominator = $this->denominator->multipliedBy($that->denominator);
return new BigRational($numerator, $denominator, false);
}
/**
* Returns the result of the division of this number by the given one.
*
* @param BigNumber|int|float|string $that The divisor.
*
* @return BigRational The result.
*
* @throws MathException If the divisor is not a valid number, or is zero.
*/
public function dividedBy($that) : BigRational
{
$that = BigRational::of($that);
$numerator = $this->numerator->multipliedBy($that->denominator);
$denominator = $this->denominator->multipliedBy($that->numerator);
return new BigRational($numerator, $denominator, true);
}
/**
* Returns this number exponentiated to the given value.
*
* @param int $exponent The exponent.
*
* @return BigRational The result.
*
* @throws \InvalidArgumentException If the exponent is not in the range 0 to 1,000,000.
*/
public function power(int $exponent) : BigRational
{
if ($exponent === 0) {
$one = BigInteger::one();
return new BigRational($one, $one, false);
}
if ($exponent === 1) {
return $this;
}
return new BigRational(
$this->numerator->power($exponent),
$this->denominator->power($exponent),
false
);
}
/**
* Returns the reciprocal of this BigRational.
*
* The reciprocal has the numerator and denominator swapped.
*
* @return BigRational
*
* @throws DivisionByZeroException If the numerator is zero.
*/
public function reciprocal() : BigRational
{
return new BigRational($this->denominator, $this->numerator, true);
}
/**
* Returns the absolute value of this BigRational.
*
* @return BigRational
*/
public function abs() : BigRational
{
return new BigRational($this->numerator->abs(), $this->denominator, false);
}
/**
* Returns the negated value of this BigRational.
*
* @return BigRational
*/
public function negated() : BigRational
{
return new BigRational($this->numerator->negated(), $this->denominator, false);
}
/**
* Returns the simplified value of this BigRational.
*
* @return BigRational
*/
public function simplified() : BigRational
{
$gcd = $this->numerator->gcd($this->denominator);
$numerator = $this->numerator->quotient($gcd);
$denominator = $this->denominator->quotient($gcd);
return new BigRational($numerator, $denominator, false);
}
/**
* {@inheritdoc}
*/
public function compareTo($that) : int
{
return $this->minus($that)->getSign();
}
/**
* {@inheritdoc}
*/
public function getSign() : int
{
return $this->numerator->getSign();
}
/**
* {@inheritdoc}
*/
public function toBigInteger() : BigInteger
{
$simplified = $this->simplified();
if (! $simplified->denominator->isEqualTo(1)) {
throw new RoundingNecessaryException('This rational number cannot be represented as an integer value without rounding.');
}
return $simplified->numerator;
}
/**
* {@inheritdoc}
*/
public function toBigDecimal() : BigDecimal
{
return $this->numerator->toBigDecimal()->exactlyDividedBy($this->denominator);
}
/**
* {@inheritdoc}
*/
public function toBigRational() : BigRational
{
return $this;
}
/**
* {@inheritdoc}
*/
public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
{
return $this->numerator->toBigDecimal()->dividedBy($this->denominator, $scale, $roundingMode);
}
/**
* {@inheritdoc}
*/
public function toInt() : int
{
return $this->toBigInteger()->toInt();
}
/**
* {@inheritdoc}
*/
public function toFloat() : float
{
return $this->numerator->toFloat() / $this->denominator->toFloat();
}
/**
* {@inheritdoc}
*/
public function __toString() : string
{
$numerator = (string) $this->numerator;
$denominator = (string) $this->denominator;
if ($denominator === '1') {
return $numerator;
}
return $this->numerator . '/' . $this->denominator;
}
/**
* This method is required by interface Serializable and SHOULD NOT be accessed directly.
*
* @internal
*
* @return string
*/
public function serialize() : string
{
return $this->numerator . '/' . $this->denominator;
}
/**
* This method is only here to implement interface Serializable and cannot be accessed directly.
*
* @internal
*
* @param string $value
*
* @return void
*
* @throws \LogicException
*/
public function unserialize($value) : void
{
if (isset($this->numerator)) {
throw new \LogicException('unserialize() is an internal function, it must not be called directly.');
}
[$numerator, $denominator] = \explode('/', $value);
$this->numerator = BigInteger::of($numerator);
$this->denominator = BigInteger::of($denominator);
}
}
math/src/RoundingMode.php 0000644 00000007423 14736103132 0011375 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math;
/**
* Specifies a rounding behavior for numerical operations capable of discarding precision.
*
* Each rounding mode indicates how the least significant returned digit of a rounded result
* is to be calculated. If fewer digits are returned than the digits needed to represent the
* exact numerical result, the discarded digits will be referred to as the discarded fraction
* regardless the digits' contribution to the value of the number. In other words, considered
* as a numerical value, the discarded fraction could have an absolute value greater than one.
*/
final class RoundingMode
{
/**
* Private constructor. This class is not instantiable.
*
* @codeCoverageIgnore
*/
private function __construct()
{
}
/**
* Asserts that the requested operation has an exact result, hence no rounding is necessary.
*
* If this rounding mode is specified on an operation that yields a result that
* cannot be represented at the requested scale, a RoundingNecessaryException is thrown.
*/
public const UNNECESSARY = 0;
/**
* Rounds away from zero.
*
* Always increments the digit prior to a nonzero discarded fraction.
* Note that this rounding mode never decreases the magnitude of the calculated value.
*/
public const UP = 1;
/**
* Rounds towards zero.
*
* Never increments the digit prior to a discarded fraction (i.e., truncates).
* Note that this rounding mode never increases the magnitude of the calculated value.
*/
public const DOWN = 2;
/**
* Rounds towards positive infinity.
*
* If the result is positive, behaves as for UP; if negative, behaves as for DOWN.
* Note that this rounding mode never decreases the calculated value.
*/
public const CEILING = 3;
/**
* Rounds towards negative infinity.
*
* If the result is positive, behave as for DOWN; if negative, behave as for UP.
* Note that this rounding mode never increases the calculated value.
*/
public const FLOOR = 4;
/**
* Rounds towards "nearest neighbor" unless both neighbors are equidistant, in which case round up.
*
* Behaves as for UP if the discarded fraction is >= 0.5; otherwise, behaves as for DOWN.
* Note that this is the rounding mode commonly taught at school.
*/
public const HALF_UP = 5;
/**
* Rounds towards "nearest neighbor" unless both neighbors are equidistant, in which case round down.
*
* Behaves as for UP if the discarded fraction is > 0.5; otherwise, behaves as for DOWN.
*/
public const HALF_DOWN = 6;
/**
* Rounds towards "nearest neighbor" unless both neighbors are equidistant, in which case round towards positive infinity.
*
* If the result is positive, behaves as for HALF_UP; if negative, behaves as for HALF_DOWN.
*/
public const HALF_CEILING = 7;
/**
* Rounds towards "nearest neighbor" unless both neighbors are equidistant, in which case round towards negative infinity.
*
* If the result is positive, behaves as for HALF_DOWN; if negative, behaves as for HALF_UP.
*/
public const HALF_FLOOR = 8;
/**
* Rounds towards the "nearest neighbor" unless both neighbors are equidistant, in which case rounds towards the even neighbor.
*
* Behaves as for HALF_UP if the digit to the left of the discarded fraction is odd;
* behaves as for HALF_DOWN if it's even.
*
* Note that this is the rounding mode that statistically minimizes
* cumulative error when applied repeatedly over a sequence of calculations.
* It is sometimes known as "Banker's rounding", and is chiefly used in the USA.
*/
public const HALF_EVEN = 9;
}
math/src/BigInteger.php 0000644 00000061024 14736103132 0011017 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math;
use Brick\Math\Exception\DivisionByZeroException;
use Brick\Math\Exception\IntegerOverflowException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NegativeNumberException;
use Brick\Math\Exception\NumberFormatException;
use Brick\Math\Internal\Calculator;
/**
* An arbitrary-size integer.
*
* All methods accepting a number as a parameter accept either a BigInteger instance,
* an integer, or a string representing an arbitrary size integer.
*
* @psalm-immutable
*/
final class BigInteger extends BigNumber
{
/**
* The value, as a string of digits with optional leading minus sign.
*
* No leading zeros must be present.
* No leading minus sign must be present if the number is zero.
*
* @var string
*/
private $value;
/**
* Protected constructor. Use a factory method to obtain an instance.
*
* @param string $value A string of digits, with optional leading minus sign.
*/
protected function __construct(string $value)
{
$this->value = $value;
}
/**
* Creates a BigInteger of the given value.
*
* @param BigNumber|int|float|string $value
*
* @return BigInteger
*
* @throws MathException If the value cannot be converted to a BigInteger.
*
* @psalm-pure
*/
public static function of($value) : BigNumber
{
return parent::of($value)->toBigInteger();
}
/**
* Creates a number from a string in a given base.
*
* The string can optionally be prefixed with the `+` or `-` sign.
*
* Bases greater than 36 are not supported by this method, as there is no clear consensus on which of the lowercase
* or uppercase characters should come first. Instead, this method accepts any base up to 36, and does not
* differentiate lowercase and uppercase characters, which are considered equal.
*
* For bases greater than 36, and/or custom alphabets, use the fromArbitraryBase() method.
*
* @param string $number The number to convert, in the given base.
* @param int $base The base of the number, between 2 and 36.
*
* @return BigInteger
*
* @throws NumberFormatException If the number is empty, or contains invalid chars for the given base.
* @throws \InvalidArgumentException If the base is out of range.
*
* @psalm-pure
*/
public static function fromBase(string $number, int $base) : BigInteger
{
if ($number === '') {
throw new NumberFormatException('The number cannot be empty.');
}
if ($base < 2 || $base > 36) {
throw new \InvalidArgumentException(\sprintf('Base %d is not in range 2 to 36.', $base));
}
if ($number[0] === '-') {
$sign = '-';
$number = \substr($number, 1);
} elseif ($number[0] === '+') {
$sign = '';
$number = \substr($number, 1);
} else {
$sign = '';
}
if ($number === '') {
throw new NumberFormatException('The number cannot be empty.');
}
$number = \ltrim($number, '0');
if ($number === '') {
// The result will be the same in any base, avoid further calculation.
return BigInteger::zero();
}
if ($number === '1') {
// The result will be the same in any base, avoid further calculation.
return new BigInteger($sign . '1');
}
$pattern = '/[^' . \substr(Calculator::ALPHABET, 0, $base) . ']/';
if (\preg_match($pattern, \strtolower($number), $matches) === 1) {
throw new NumberFormatException(\sprintf('"%s" is not a valid character in base %d.', $matches[0], $base));
}
if ($base === 10) {
// The number is usable as is, avoid further calculation.
return new BigInteger($sign . $number);
}
$result = Calculator::get()->fromBase($number, $base);
return new BigInteger($sign . $result);
}
/**
* Parses a string containing an integer in an arbitrary base, using a custom alphabet.
*
* Because this method accepts an alphabet with any character, including dash, it does not handle negative numbers.
*
* @param string $number The number to parse.
* @param string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8.
*
* @return BigInteger
*
* @throws NumberFormatException If the given number is empty or contains invalid chars for the given alphabet.
* @throws \InvalidArgumentException If the alphabet does not contain at least 2 chars.
*
* @psalm-pure
*/
public static function fromArbitraryBase(string $number, string $alphabet) : BigInteger
{
if ($number === '') {
throw new NumberFormatException('The number cannot be empty.');
}
$base = \strlen($alphabet);
if ($base < 2) {
throw new \InvalidArgumentException('The alphabet must contain at least 2 chars.');
}
$pattern = '/[^' . \preg_quote($alphabet, '/') . ']/';
if (\preg_match($pattern, $number, $matches) === 1) {
throw NumberFormatException::charNotInAlphabet($matches[0]);
}
$number = Calculator::get()->fromArbitraryBase($number, $alphabet, $base);
return new BigInteger($number);
}
/**
* Returns a BigInteger representing zero.
*
* @return BigInteger
*
* @psalm-pure
*/
public static function zero() : BigInteger
{
/** @psalm-suppress ImpureStaticVariable */
static $zero;
if ($zero === null) {
$zero = new BigInteger('0');
}
return $zero;
}
/**
* Returns a BigInteger representing one.
*
* @return BigInteger
*
* @psalm-pure
*/
public static function one() : BigInteger
{
/** @psalm-suppress ImpureStaticVariable */
static $one;
if ($one === null) {
$one = new BigInteger('1');
}
return $one;
}
/**
* Returns a BigInteger representing ten.
*
* @return BigInteger
*
* @psalm-pure
*/
public static function ten() : BigInteger
{
/** @psalm-suppress ImpureStaticVariable */
static $ten;
if ($ten === null) {
$ten = new BigInteger('10');
}
return $ten;
}
/**
* Returns the sum of this number and the given one.
*
* @param BigNumber|int|float|string $that The number to add. Must be convertible to a BigInteger.
*
* @return BigInteger The result.
*
* @throws MathException If the number is not valid, or is not convertible to a BigInteger.
*/
public function plus($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '0') {
return $this;
}
if ($this->value === '0') {
return $that;
}
$value = Calculator::get()->add($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the difference of this number and the given one.
*
* @param BigNumber|int|float|string $that The number to subtract. Must be convertible to a BigInteger.
*
* @return BigInteger The result.
*
* @throws MathException If the number is not valid, or is not convertible to a BigInteger.
*/
public function minus($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '0') {
return $this;
}
$value = Calculator::get()->sub($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the product of this number and the given one.
*
* @param BigNumber|int|float|string $that The multiplier. Must be convertible to a BigInteger.
*
* @return BigInteger The result.
*
* @throws MathException If the multiplier is not a valid number, or is not convertible to a BigInteger.
*/
public function multipliedBy($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '1') {
return $this;
}
if ($this->value === '1') {
return $that;
}
$value = Calculator::get()->mul($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the result of the division of this number by the given one.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
* @param int $roundingMode An optional rounding mode.
*
* @return BigInteger The result.
*
* @throws MathException If the divisor is not a valid number, is not convertible to a BigInteger, is zero,
* or RoundingMode::UNNECESSARY is used and the remainder is not zero.
*/
public function dividedBy($that, int $roundingMode = RoundingMode::UNNECESSARY) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '1') {
return $this;
}
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
$result = Calculator::get()->divRound($this->value, $that->value, $roundingMode);
return new BigInteger($result);
}
/**
* Returns this number exponentiated to the given value.
*
* @param int $exponent The exponent.
*
* @return BigInteger The result.
*
* @throws \InvalidArgumentException If the exponent is not in the range 0 to 1,000,000.
*/
public function power(int $exponent) : BigInteger
{
if ($exponent === 0) {
return BigInteger::one();
}
if ($exponent === 1) {
return $this;
}
if ($exponent < 0 || $exponent > Calculator::MAX_POWER) {
throw new \InvalidArgumentException(\sprintf(
'The exponent %d is not in the range 0 to %d.',
$exponent,
Calculator::MAX_POWER
));
}
return new BigInteger(Calculator::get()->pow($this->value, $exponent));
}
/**
* Returns the quotient of the division of this number by the given one.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @return BigInteger
*
* @throws DivisionByZeroException If the divisor is zero.
*/
public function quotient($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '1') {
return $this;
}
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
$quotient = Calculator::get()->divQ($this->value, $that->value);
return new BigInteger($quotient);
}
/**
* Returns the remainder of the division of this number by the given one.
*
* The remainder, when non-zero, has the same sign as the dividend.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @return BigInteger
*
* @throws DivisionByZeroException If the divisor is zero.
*/
public function remainder($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '1') {
return BigInteger::zero();
}
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
$remainder = Calculator::get()->divR($this->value, $that->value);
return new BigInteger($remainder);
}
/**
* Returns the quotient and remainder of the division of this number by the given one.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @return BigInteger[] An array containing the quotient and the remainder.
*
* @throws DivisionByZeroException If the divisor is zero.
*/
public function quotientAndRemainder($that) : array
{
$that = BigInteger::of($that);
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
[$quotient, $remainder] = Calculator::get()->divQR($this->value, $that->value);
return [
new BigInteger($quotient),
new BigInteger($remainder)
];
}
/**
* Returns the modulo of this number and the given one.
*
* The modulo operation yields the same result as the remainder operation when both operands are of the same sign,
* and may differ when signs are different.
*
* The result of the modulo operation, when non-zero, has the same sign as the divisor.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigInteger.
*
* @return BigInteger
*
* @throws DivisionByZeroException If the divisor is zero.
*/
public function mod($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
return $this->remainder($that)->plus($that)->remainder($that);
}
/**
* Returns this number raised into power with modulo.
*
* This operation only works on positive numbers.
*
* @param BigNumber|int|float|string $exp The positive exponent.
* @param BigNumber|int|float|string $mod The modulo. Must not be zero.
*
* @return BigInteger
*
* @throws NegativeNumberException If any of the operands is negative.
* @throws DivisionByZeroException If the modulo is zero.
*/
public function powerMod($exp, $mod) : BigInteger
{
$exp = BigInteger::of($exp);
$mod = BigInteger::of($mod);
if ($this->isNegative() || $exp->isNegative() || $mod->isNegative()) {
throw new NegativeNumberException('The operands cannot be negative.');
}
if ($mod->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$result = Calculator::get()->powmod($this->value, $exp->value, $mod->value);
return new BigInteger($result);
}
/**
* Returns the greatest common divisor of this number and the given one.
*
* The GCD is always positive, unless both operands are zero, in which case it is zero.
*
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
*
* @return BigInteger
*/
public function gcd($that) : BigInteger
{
$that = BigInteger::of($that);
if ($that->value === '0' && $this->value[0] !== '-') {
return $this;
}
if ($this->value === '0' && $that->value[0] !== '-') {
return $that;
}
$value = Calculator::get()->gcd($this->value, $that->value);
return new BigInteger($value);
}
/**
* Returns the integer square root number of this number, rounded down.
*
* The result is the largest x such that x² ≤ n.
*
* @return BigInteger
*
* @throws NegativeNumberException If this number is negative.
*/
public function sqrt() : BigInteger
{
if ($this->value[0] === '-') {
throw new NegativeNumberException('Cannot calculate the square root of a negative number.');
}
$value = Calculator::get()->sqrt($this->value);
return new BigInteger($value);
}
/**
* Returns the absolute value of this number.
*
* @return BigInteger
*/
public function abs() : BigInteger
{
return $this->isNegative() ? $this->negated() : $this;
}
/**
* Returns the inverse of this number.
*
* @return BigInteger
*/
public function negated() : BigInteger
{
return new BigInteger(Calculator::get()->neg($this->value));
}
/**
* Returns the integer bitwise-and combined with another integer.
*
* This method returns a negative BigInteger if and only if both operands are negative.
*
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
*
* @return BigInteger
*/
public function and($that) : BigInteger
{
$that = BigInteger::of($that);
return new BigInteger(Calculator::get()->and($this->value, $that->value));
}
/**
* Returns the integer bitwise-or combined with another integer.
*
* This method returns a negative BigInteger if and only if either of the operands is negative.
*
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
*
* @return BigInteger
*/
public function or($that) : BigInteger
{
$that = BigInteger::of($that);
return new BigInteger(Calculator::get()->or($this->value, $that->value));
}
/**
* Returns the integer bitwise-xor combined with another integer.
*
* This method returns a negative BigInteger if and only if exactly one of the operands is negative.
*
* @param BigNumber|int|float|string $that The operand. Must be convertible to an integer number.
*
* @return BigInteger
*/
public function xor($that) : BigInteger
{
$that = BigInteger::of($that);
return new BigInteger(Calculator::get()->xor($this->value, $that->value));
}
/**
* Returns the integer left shifted by a given number of bits.
*
* @param int $distance The distance to shift.
*
* @return BigInteger
*/
public function shiftedLeft(int $distance) : BigInteger
{
if ($distance === 0) {
return $this;
}
if ($distance < 0) {
return $this->shiftedRight(- $distance);
}
return $this->multipliedBy(BigInteger::of(2)->power($distance));
}
/**
* Returns the integer right shifted by a given number of bits.
*
* @param int $distance The distance to shift.
*
* @return BigInteger
*/
public function shiftedRight(int $distance) : BigInteger
{
if ($distance === 0) {
return $this;
}
if ($distance < 0) {
return $this->shiftedLeft(- $distance);
}
$operand = BigInteger::of(2)->power($distance);
if ($this->isPositiveOrZero()) {
return $this->quotient($operand);
}
return $this->dividedBy($operand, RoundingMode::UP);
}
/**
* Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.
*
* For positive BigIntegers, this is equivalent to the number of bits in the ordinary binary representation.
* Computes (ceil(log2(this < 0 ? -this : this+1))).
*
* @return int
*/
public function getBitLength() : int
{
if ($this->value === '0') {
return 0;
}
if ($this->isNegative()) {
return $this->abs()->minus(1)->getBitLength();
}
return strlen($this->toBase(2));
}
/**
* Returns the index of the rightmost (lowest-order) one bit in this BigInteger.
*
* Returns -1 if this BigInteger contains no one bits.
*
* @return int
*/
public function getLowestSetBit() : int
{
$n = $this;
$bitLength = $this->getBitLength();
for ($i = 0; $i <= $bitLength; $i++) {
if ($n->isOdd()) {
return $i;
}
$n = $n->shiftedRight(1);
}
return -1;
}
/**
* Returns whether this number is even.
*
* @return bool
*/
public function isEven() : bool
{
return in_array($this->value[-1], ['0', '2', '4', '6', '8'], true);
}
/**
* Returns whether this number is odd.
*
* @return bool
*/
public function isOdd() : bool
{
return in_array($this->value[-1], ['1', '3', '5', '7', '9'], true);
}
/**
* Returns true if and only if the designated bit is set.
*
* Computes ((this & (1<<n)) != 0).
*
* @param int $n The bit to test, 0-based.
*
* @return bool
*/
public function testBit(int $n) : bool
{
if ($n < 0) {
throw new \InvalidArgumentException('The bit to test cannot be negative.');
}
return $this->shiftedRight($n)->isOdd();
}
/**
* {@inheritdoc}
*/
public function compareTo($that) : int
{
$that = BigNumber::of($that);
if ($that instanceof BigInteger) {
return Calculator::get()->cmp($this->value, $that->value);
}
return - $that->compareTo($this);
}
/**
* {@inheritdoc}
*/
public function getSign() : int
{
return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);
}
/**
* {@inheritdoc}
*/
public function toBigInteger() : BigInteger
{
return $this;
}
/**
* {@inheritdoc}
*/
public function toBigDecimal() : BigDecimal
{
return BigDecimal::create($this->value);
}
/**
* {@inheritdoc}
*/
public function toBigRational() : BigRational
{
return BigRational::create($this, BigInteger::one(), false);
}
/**
* {@inheritdoc}
*/
public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
{
return $this->toBigDecimal()->toScale($scale, $roundingMode);
}
/**
* {@inheritdoc}
*/
public function toInt() : int
{
$intValue = (int) $this->value;
if ($this->value !== (string) $intValue) {
throw IntegerOverflowException::toIntOverflow($this);
}
return $intValue;
}
/**
* {@inheritdoc}
*/
public function toFloat() : float
{
return (float) $this->value;
}
/**
* Returns a string representation of this number in the given base.
*
* The output will always be lowercase for bases greater than 10.
*
* @param int $base
*
* @return string
*
* @throws \InvalidArgumentException If the base is out of range.
*/
public function toBase(int $base) : string
{
if ($base === 10) {
return $this->value;
}
if ($base < 2 || $base > 36) {
throw new \InvalidArgumentException(\sprintf('Base %d is out of range [2, 36]', $base));
}
return Calculator::get()->toBase($this->value, $base);
}
/**
* Returns a string representation of this number in an arbitrary base with a custom alphabet.
*
* Because this method accepts an alphabet with any character, including dash, it does not handle negative numbers;
* a NegativeNumberException will be thrown when attempting to call this method on a negative number.
*
* @param string $alphabet The alphabet, for example '01' for base 2, or '01234567' for base 8.
*
* @return string
*
* @throws NegativeNumberException If this number is negative.
* @throws \InvalidArgumentException If the given alphabet does not contain at least 2 chars.
*/
public function toArbitraryBase(string $alphabet) : string
{
$base = \strlen($alphabet);
if ($base < 2) {
throw new \InvalidArgumentException('The alphabet must contain at least 2 chars.');
}
if ($this->value[0] === '-') {
throw new NegativeNumberException(__FUNCTION__ . '() does not support negative numbers.');
}
return Calculator::get()->toArbitraryBase($this->value, $alphabet, $base);
}
/**
* {@inheritdoc}
*/
public function __toString() : string
{
return $this->value;
}
/**
* This method is required by interface Serializable and SHOULD NOT be accessed directly.
*
* @internal
*
* @return string
*/
public function serialize() : string
{
return $this->value;
}
/**
* This method is only here to implement interface Serializable and cannot be accessed directly.
*
* @internal
*
* @param string $value
*
* @return void
*
* @throws \LogicException
*/
public function unserialize($value) : void
{
if (isset($this->value)) {
throw new \LogicException('unserialize() is an internal function, it must not be called directly.');
}
$this->value = $value;
}
}
math/src/BigDecimal.php 0000644 00000054303 14736103132 0010762 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math;
use Brick\Math\Exception\DivisionByZeroException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NegativeNumberException;
use Brick\Math\Internal\Calculator;
/**
* Immutable, arbitrary-precision signed decimal numbers.
*
* @psalm-immutable
*/
final class BigDecimal extends BigNumber
{
/**
* The unscaled value of this decimal number.
*
* This is a string of digits with an optional leading minus sign.
* No leading zero must be present.
* No leading minus sign must be present if the value is 0.
*
* @var string
*/
private $value;
/**
* The scale (number of digits after the decimal point) of this decimal number.
*
* This must be zero or more.
*
* @var int
*/
private $scale;
/**
* Protected constructor. Use a factory method to obtain an instance.
*
* @param string $value The unscaled value, validated.
* @param int $scale The scale, validated.
*/
protected function __construct(string $value, int $scale = 0)
{
$this->value = $value;
$this->scale = $scale;
}
/**
* Creates a BigDecimal of the given value.
*
* @param BigNumber|int|float|string $value
*
* @return BigDecimal
*
* @throws MathException If the value cannot be converted to a BigDecimal.
*
* @psalm-pure
*/
public static function of($value) : BigNumber
{
return parent::of($value)->toBigDecimal();
}
/**
* Creates a BigDecimal from an unscaled value and a scale.
*
* Example: `(12345, 3)` will result in the BigDecimal `12.345`.
*
* @param BigNumber|int|float|string $value The unscaled value. Must be convertible to a BigInteger.
* @param int $scale The scale of the number, positive or zero.
*
* @return BigDecimal
*
* @throws \InvalidArgumentException If the scale is negative.
*
* @psalm-pure
*/
public static function ofUnscaledValue($value, int $scale = 0) : BigDecimal
{
if ($scale < 0) {
throw new \InvalidArgumentException('The scale cannot be negative.');
}
return new BigDecimal((string) BigInteger::of($value), $scale);
}
/**
* Returns a BigDecimal representing zero, with a scale of zero.
*
* @return BigDecimal
*
* @psalm-pure
*/
public static function zero() : BigDecimal
{
/** @psalm-suppress ImpureStaticVariable */
static $zero;
if ($zero === null) {
$zero = new BigDecimal('0');
}
return $zero;
}
/**
* Returns a BigDecimal representing one, with a scale of zero.
*
* @return BigDecimal
*
* @psalm-pure
*/
public static function one() : BigDecimal
{
/** @psalm-suppress ImpureStaticVariable */
static $one;
if ($one === null) {
$one = new BigDecimal('1');
}
return $one;
}
/**
* Returns a BigDecimal representing ten, with a scale of zero.
*
* @return BigDecimal
*
* @psalm-pure
*/
public static function ten() : BigDecimal
{
/** @psalm-suppress ImpureStaticVariable */
static $ten;
if ($ten === null) {
$ten = new BigDecimal('10');
}
return $ten;
}
/**
* Returns the sum of this number and the given one.
*
* The result has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The number to add. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the number is not valid, or is not convertible to a BigDecimal.
*/
public function plus($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '0' && $that->scale <= $this->scale) {
return $this;
}
if ($this->value === '0' && $this->scale <= $that->scale) {
return $that;
}
[$a, $b] = $this->scaleValues($this, $that);
$value = Calculator::get()->add($a, $b);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
return new BigDecimal($value, $scale);
}
/**
* Returns the difference of this number and the given one.
*
* The result has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The number to subtract. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the number is not valid, or is not convertible to a BigDecimal.
*/
public function minus($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '0' && $that->scale <= $this->scale) {
return $this;
}
[$a, $b] = $this->scaleValues($this, $that);
$value = Calculator::get()->sub($a, $b);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
return new BigDecimal($value, $scale);
}
/**
* Returns the product of this number and the given one.
*
* The result has a scale of `$this->scale + $that->scale`.
*
* @param BigNumber|int|float|string $that The multiplier. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the multiplier is not a valid number, or is not convertible to a BigDecimal.
*/
public function multipliedBy($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '1' && $that->scale === 0) {
return $this;
}
if ($this->value === '1' && $this->scale === 0) {
return $that;
}
$value = Calculator::get()->mul($this->value, $that->value);
$scale = $this->scale + $that->scale;
return new BigDecimal($value, $scale);
}
/**
* Returns the result of the division of this number by the given one, at the given scale.
*
* @param BigNumber|int|float|string $that The divisor.
* @param int|null $scale The desired scale, or null to use the scale of this number.
* @param int $roundingMode An optional rounding mode.
*
* @return BigDecimal
*
* @throws \InvalidArgumentException If the scale or rounding mode is invalid.
* @throws MathException If the number is invalid, is zero, or rounding was necessary.
*/
public function dividedBy($that, ?int $scale = null, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
if ($scale === null) {
$scale = $this->scale;
} elseif ($scale < 0) {
throw new \InvalidArgumentException('Scale cannot be negative.');
}
if ($that->value === '1' && $that->scale === 0 && $scale === $this->scale) {
return $this;
}
$p = $this->valueWithMinScale($that->scale + $scale);
$q = $that->valueWithMinScale($this->scale - $scale);
$result = Calculator::get()->divRound($p, $q, $roundingMode);
return new BigDecimal($result, $scale);
}
/**
* Returns the exact result of the division of this number by the given one.
*
* The scale of the result is automatically calculated to fit all the fraction digits.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the divisor is not a valid number, is not convertible to a BigDecimal, is zero,
* or the result yields an infinite number of digits.
*/
public function exactlyDividedBy($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
[$a, $b] = $this->scaleValues($this, $that);
$d = \rtrim($b, '0');
$scale = \strlen($b) - \strlen($d);
$calculator = Calculator::get();
foreach ([5, 2] as $prime) {
for (;;) {
$lastDigit = (int) $d[-1];
if ($lastDigit % $prime !== 0) {
break;
}
$d = $calculator->divQ($d, (string) $prime);
$scale++;
}
}
return $this->dividedBy($that, $scale)->stripTrailingZeros();
}
/**
* Returns this number exponentiated to the given value.
*
* The result has a scale of `$this->scale * $exponent`.
*
* @param int $exponent The exponent.
*
* @return BigDecimal The result.
*
* @throws \InvalidArgumentException If the exponent is not in the range 0 to 1,000,000.
*/
public function power(int $exponent) : BigDecimal
{
if ($exponent === 0) {
return BigDecimal::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.',
$exponent,
Calculator::MAX_POWER
));
}
return new BigDecimal(Calculator::get()->pow($this->value, $exponent), $this->scale * $exponent);
}
/**
* Returns the quotient of the division of this number by this given one.
*
* The quotient has a scale of `0`.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal The quotient.
*
* @throws MathException If the divisor is not a valid decimal number, or is zero.
*/
public function quotient($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$p = $this->valueWithMinScale($that->scale);
$q = $that->valueWithMinScale($this->scale);
$quotient = Calculator::get()->divQ($p, $q);
return new BigDecimal($quotient, 0);
}
/**
* Returns the remainder of the division of this number by this given one.
*
* The remainder has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal The remainder.
*
* @throws MathException If the divisor is not a valid decimal number, or is zero.
*/
public function remainder($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$p = $this->valueWithMinScale($that->scale);
$q = $that->valueWithMinScale($this->scale);
$remainder = Calculator::get()->divR($p, $q);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
return new BigDecimal($remainder, $scale);
}
/**
* Returns the quotient and remainder of the division of this number by the given one.
*
* The quotient has a scale of `0`, and the remainder has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal[] An array containing the quotient and the remainder.
*
* @throws MathException If the divisor is not a valid decimal number, or is zero.
*/
public function quotientAndRemainder($that) : array
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$p = $this->valueWithMinScale($that->scale);
$q = $that->valueWithMinScale($this->scale);
[$quotient, $remainder] = Calculator::get()->divQR($p, $q);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
$quotient = new BigDecimal($quotient, 0);
$remainder = new BigDecimal($remainder, $scale);
return [$quotient, $remainder];
}
/**
* Returns the square root of this number, rounded down to the given number of decimals.
*
* @param int $scale
*
* @return BigDecimal
*
* @throws \InvalidArgumentException If the scale is negative.
* @throws NegativeNumberException If this number is negative.
*/
public function sqrt(int $scale) : BigDecimal
{
if ($scale < 0) {
throw new \InvalidArgumentException('Scale cannot be negative.');
}
if ($this->value === '0') {
return new BigDecimal('0', $scale);
}
if ($this->value[0] === '-') {
throw new NegativeNumberException('Cannot calculate the square root of a negative number.');
}
$value = $this->value;
$addDigits = 2 * $scale - $this->scale;
if ($addDigits > 0) {
// add zeros
$value .= \str_repeat('0', $addDigits);
} elseif ($addDigits < 0) {
// trim digits
if (-$addDigits >= \strlen($this->value)) {
// requesting a scale too low, will always yield a zero result
return new BigDecimal('0', $scale);
}
$value = \substr($value, 0, $addDigits);
}
$value = Calculator::get()->sqrt($value);
return new BigDecimal($value, $scale);
}
/**
* Returns a copy of this BigDecimal with the decimal point moved $n places to the left.
*
* @param int $n
*
* @return BigDecimal
*/
public function withPointMovedLeft(int $n) : BigDecimal
{
if ($n === 0) {
return $this;
}
if ($n < 0) {
return $this->withPointMovedRight(-$n);
}
return new BigDecimal($this->value, $this->scale + $n);
}
/**
* Returns a copy of this BigDecimal with the decimal point moved $n places to the right.
*
* @param int $n
*
* @return BigDecimal
*/
public function withPointMovedRight(int $n) : BigDecimal
{
if ($n === 0) {
return $this;
}
if ($n < 0) {
return $this->withPointMovedLeft(-$n);
}
$value = $this->value;
$scale = $this->scale - $n;
if ($scale < 0) {
if ($value !== '0') {
$value .= \str_repeat('0', -$scale);
}
$scale = 0;
}
return new BigDecimal($value, $scale);
}
/**
* Returns a copy of this BigDecimal with any trailing zeros removed from the fractional part.
*
* @return BigDecimal
*/
public function stripTrailingZeros() : BigDecimal
{
if ($this->scale === 0) {
return $this;
}
$trimmedValue = \rtrim($this->value, '0');
if ($trimmedValue === '') {
return BigDecimal::zero();
}
$trimmableZeros = \strlen($this->value) - \strlen($trimmedValue);
if ($trimmableZeros === 0) {
return $this;
}
if ($trimmableZeros > $this->scale) {
$trimmableZeros = $this->scale;
}
$value = \substr($this->value, 0, -$trimmableZeros);
$scale = $this->scale - $trimmableZeros;
return new BigDecimal($value, $scale);
}
/**
* Returns the absolute value of this number.
*
* @return BigDecimal
*/
public function abs() : BigDecimal
{
return $this->isNegative() ? $this->negated() : $this;
}
/**
* Returns the negated value of this number.
*
* @return BigDecimal
*/
public function negated() : BigDecimal
{
return new BigDecimal(Calculator::get()->neg($this->value), $this->scale);
}
/**
* {@inheritdoc}
*/
public function compareTo($that) : int
{
$that = BigNumber::of($that);
if ($that instanceof BigInteger) {
$that = $that->toBigDecimal();
}
if ($that instanceof BigDecimal) {
[$a, $b] = $this->scaleValues($this, $that);
return Calculator::get()->cmp($a, $b);
}
return - $that->compareTo($this);
}
/**
* {@inheritdoc}
*/
public function getSign() : int
{
return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);
}
/**
* @return BigInteger
*/
public function getUnscaledValue() : BigInteger
{
return BigInteger::create($this->value);
}
/**
* @return int
*/
public function getScale() : int
{
return $this->scale;
}
/**
* Returns a string representing the integral part of this decimal number.
*
* Example: `-123.456` => `-123`.
*
* @return string
*/
public function getIntegralPart() : string
{
if ($this->scale === 0) {
return $this->value;
}
$value = $this->getUnscaledValueWithLeadingZeros();
return \substr($value, 0, -$this->scale);
}
/**
* Returns a string representing the fractional part of this decimal number.
*
* If the scale is zero, an empty string is returned.
*
* Examples: `-123.456` => '456', `123` => ''.
*
* @return string
*/
public function getFractionalPart() : string
{
if ($this->scale === 0) {
return '';
}
$value = $this->getUnscaledValueWithLeadingZeros();
return \substr($value, -$this->scale);
}
/**
* Returns whether this decimal number has a non-zero fractional part.
*
* @return bool
*/
public function hasNonZeroFractionalPart() : bool
{
return $this->getFractionalPart() !== \str_repeat('0', $this->scale);
}
/**
* {@inheritdoc}
*/
public function toBigInteger() : BigInteger
{
if ($this->scale === 0) {
$zeroScaleDecimal = $this;
} else {
$zeroScaleDecimal = $this->dividedBy(1, 0);
}
return BigInteger::create($zeroScaleDecimal->value);
}
/**
* {@inheritdoc}
*/
public function toBigDecimal() : BigDecimal
{
return $this;
}
/**
* {@inheritdoc}
*/
public function toBigRational() : BigRational
{
$numerator = BigInteger::create($this->value);
$denominator = BigInteger::create('1' . \str_repeat('0', $this->scale));
return BigRational::create($numerator, $denominator, false);
}
/**
* {@inheritdoc}
*/
public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
{
if ($scale === $this->scale) {
return $this;
}
return $this->dividedBy(BigDecimal::one(), $scale, $roundingMode);
}
/**
* {@inheritdoc}
*/
public function toInt() : int
{
return $this->toBigInteger()->toInt();
}
/**
* {@inheritdoc}
*/
public function toFloat() : float
{
return (float) (string) $this;
}
/**
* {@inheritdoc}
*/
public function __toString() : string
{
if ($this->scale === 0) {
return $this->value;
}
$value = $this->getUnscaledValueWithLeadingZeros();
return \substr($value, 0, -$this->scale) . '.' . \substr($value, -$this->scale);
}
/**
* This method is required by interface Serializable and SHOULD NOT be accessed directly.
*
* @internal
*
* @return string
*/
public function serialize() : string
{
return $this->value . ':' . $this->scale;
}
/**
* This method is only here to implement interface Serializable and cannot be accessed directly.
*
* @internal
*
* @param string $value
*
* @return void
*
* @throws \LogicException
*/
public function unserialize($value) : void
{
if (isset($this->value)) {
throw new \LogicException('unserialize() is an internal function, it must not be called directly.');
}
[$value, $scale] = \explode(':', $value);
$this->value = $value;
$this->scale = (int) $scale;
}
/**
* Puts the internal values of the given decimal numbers on the same scale.
*
* @param BigDecimal $x The first decimal number.
* @param BigDecimal $y The second decimal number.
*
* @return array{0: string, 1: string} The scaled integer values of $x and $y.
*/
private function scaleValues(BigDecimal $x, BigDecimal $y) : array
{
$a = $x->value;
$b = $y->value;
if ($b !== '0' && $x->scale > $y->scale) {
$b .= \str_repeat('0', $x->scale - $y->scale);
} elseif ($a !== '0' && $x->scale < $y->scale) {
$a .= \str_repeat('0', $y->scale - $x->scale);
}
return [$a, $b];
}
/**
* @param int $scale
*
* @return string
*/
private function valueWithMinScale(int $scale) : string
{
$value = $this->value;
if ($this->value !== '0' && $scale > $this->scale) {
$value .= \str_repeat('0', $scale - $this->scale);
}
return $value;
}
/**
* Adds leading zeros if necessary to the unscaled value to represent the full decimal number.
*
* @return string
*/
private function getUnscaledValueWithLeadingZeros() : string
{
$value = $this->value;
$targetLength = $this->scale + 1;
$negative = ($value[0] === '-');
$length = \strlen($value);
if ($negative) {
$length--;
}
if ($length >= $targetLength) {
return $this->value;
}
if ($negative) {
$value = \substr($value, 1);
}
$value = \str_pad($value, $targetLength, '0', STR_PAD_LEFT);
if ($negative) {
$value = '-' . $value;
}
return $value;
}
}
math/src/Exception/DivisionByZeroException.php 0000644 00000001206 14736103132 0015530 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Exception;
/**
* Exception thrown when a division by zero occurs.
*/
class DivisionByZeroException extends MathException
{
/**
* @return DivisionByZeroException
*
* @psalm-pure
*/
public static function divisionByZero() : DivisionByZeroException
{
return new self('Division by zero.');
}
/**
* @return DivisionByZeroException
*
* @psalm-pure
*/
public static function denominatorMustNotBeZero() : DivisionByZeroException
{
return new self('The denominator of a rational number cannot be zero.');
}
}
math/src/Exception/IntegerOverflowException.php 0000644 00000001144 14736103132 0015733 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Exception;
use Brick\Math\BigInteger;
/**
* Exception thrown when an integer overflow occurs.
*/
class IntegerOverflowException extends MathException
{
/**
* @param BigInteger $value
*
* @return IntegerOverflowException
*
* @psalm-pure
*/
public static function toIntOverflow(BigInteger $value) : IntegerOverflowException
{
$message = '%s is out of range %d to %d and cannot be represented as an integer.';
return new self(\sprintf($message, (string) $value, PHP_INT_MIN, PHP_INT_MAX));
}
}
math/src/Exception/MathException.php 0000644 00000000425 14736103132 0013504 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Exception;
/**
* Base class for all math exceptions.
*
* This class is abstract to ensure that only fine-grained exceptions are thrown throughout the code.
*/
abstract class MathException extends \RuntimeException
{
}
math/src/Exception/NegativeNumberException.php 0000644 00000000370 14736103132 0015525 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Exception;
/**
* Exception thrown when attempting to perform an unsupported operation, such as a square root, on a negative number.
*/
class NegativeNumberException extends MathException
{
}
math/src/Exception/NumberFormatException.php 0000644 00000001437 14736103132 0015220 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Exception;
/**
* Exception thrown when attempting to create a number from a string with an invalid format.
*/
class NumberFormatException extends MathException
{
/**
* @param string $char The failing character.
*
* @return NumberFormatException
*
* @psalm-pure
*/
public static function charNotInAlphabet(string $char) : self
{
$ord = \ord($char);
if ($ord < 32 || $ord > 126) {
$char = \strtoupper(\dechex($ord));
if ($ord < 10) {
$char = '0' . $char;
}
} else {
$char = '"' . $char . '"';
}
return new self(sprintf('Char %s is not a valid character in the given alphabet.', $char));
}
}
math/src/Exception/RoundingNecessaryException.php 0000644 00000000774 14736103132 0016264 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Exception;
/**
* Exception thrown when a number cannot be represented at the requested scale without rounding.
*/
class RoundingNecessaryException extends MathException
{
/**
* @return RoundingNecessaryException
*
* @psalm-pure
*/
public static function roundingNecessary() : RoundingNecessaryException
{
return new self('Rounding is necessary to represent the result of the operation at this scale.');
}
}
math/src/Internal/Calculator.php 0000644 00000045460 14736103132 0012653 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Internal;
use Brick\Math\Exception\RoundingNecessaryException;
use Brick\Math\RoundingMode;
/**
* Performs basic operations on arbitrary size integers.
*
* Unless otherwise specified, all parameters must be validated as non-empty strings of digits,
* without leading zero, and with an optional leading minus sign if the number is not zero.
*
* Any other parameter format will lead to undefined behaviour.
* All methods must return strings respecting this format, unless specified otherwise.
*
* @internal
*
* @psalm-immutable
*/
abstract class Calculator
{
/**
* The maximum exponent value allowed for the pow() method.
*/
public const MAX_POWER = 1000000;
/**
* The alphabet for converting from and to base 2 to 36, lowercase.
*/
public const ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
/**
* The Calculator instance in use.
*
* @var Calculator|null
*/
private static $instance;
/**
* Sets the Calculator instance to use.
*
* An instance is typically set only in unit tests: the autodetect is usually the best option.
*
* @param Calculator|null $calculator The calculator instance, or NULL to revert to autodetect.
*
* @return void
*/
final public static function set(?Calculator $calculator) : void
{
self::$instance = $calculator;
}
/**
* Returns the Calculator instance to use.
*
* If none has been explicitly set, the fastest available implementation will be returned.
*
* @return Calculator
*
* @psalm-pure
* @psalm-suppress ImpureStaticProperty
*/
final public static function get() : Calculator
{
if (self::$instance === null) {
/** @psalm-suppress ImpureMethodCall */
self::$instance = self::detect();
}
return self::$instance;
}
/**
* Returns the fastest available Calculator implementation.
*
* @codeCoverageIgnore
*
* @return Calculator
*/
private static function detect() : Calculator
{
if (\extension_loaded('gmp')) {
return new Calculator\GmpCalculator();
}
if (\extension_loaded('bcmath')) {
return new Calculator\BcMathCalculator();
}
return new Calculator\NativeCalculator();
}
/**
* Extracts the sign & digits of the operands.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return array{0: bool, 1: bool, 2: string, 3: string} Whether $a and $b are negative, followed by their digits.
*/
final protected function init(string $a, string $b) : array
{
return [
$aNeg = ($a[0] === '-'),
$bNeg = ($b[0] === '-'),
$aNeg ? \substr($a, 1) : $a,
$bNeg ? \substr($b, 1) : $b,
];
}
/**
* Returns the absolute value of a number.
*
* @param string $n The number.
*
* @return string The absolute value.
*/
final public function abs(string $n) : string
{
return ($n[0] === '-') ? \substr($n, 1) : $n;
}
/**
* Negates a number.
*
* @param string $n The number.
*
* @return string The negated value.
*/
final public function neg(string $n) : string
{
if ($n === '0') {
return '0';
}
if ($n[0] === '-') {
return \substr($n, 1);
}
return '-' . $n;
}
/**
* Compares two numbers.
*
* @param string $a The first number.
* @param string $b The second number.
*
* @return int [-1, 0, 1] If the first number is less than, equal to, or greater than the second number.
*/
final public function cmp(string $a, string $b) : int
{
[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
if ($aNeg && ! $bNeg) {
return -1;
}
if ($bNeg && ! $aNeg) {
return 1;
}
$aLen = \strlen($aDig);
$bLen = \strlen($bDig);
if ($aLen < $bLen) {
$result = -1;
} elseif ($aLen > $bLen) {
$result = 1;
} else {
$result = $aDig <=> $bDig;
}
return $aNeg ? -$result : $result;
}
/**
* Adds two numbers.
*
* @param string $a The augend.
* @param string $b The addend.
*
* @return string The sum.
*/
abstract public function add(string $a, string $b) : string;
/**
* Subtracts two numbers.
*
* @param string $a The minuend.
* @param string $b The subtrahend.
*
* @return string The difference.
*/
abstract public function sub(string $a, string $b) : string;
/**
* Multiplies two numbers.
*
* @param string $a The multiplicand.
* @param string $b The multiplier.
*
* @return string The product.
*/
abstract public function mul(string $a, string $b) : string;
/**
* Returns the quotient of the division of two numbers.
*
* @param string $a The dividend.
* @param string $b The divisor, must not be zero.
*
* @return string The quotient.
*/
abstract public function divQ(string $a, string $b) : string;
/**
* Returns the remainder of the division of two numbers.
*
* @param string $a The dividend.
* @param string $b The divisor, must not be zero.
*
* @return string The remainder.
*/
abstract public function divR(string $a, string $b) : string;
/**
* Returns the quotient and remainder of the division of two numbers.
*
* @param string $a The dividend.
* @param string $b The divisor, must not be zero.
*
* @return string[] An array containing the quotient and remainder.
*/
abstract public function divQR(string $a, string $b) : array;
/**
* Exponentiates a number.
*
* @param string $a The base number.
* @param int $e The exponent, validated as an integer between 0 and MAX_POWER.
*
* @return string The power.
*/
abstract public function pow(string $a, int $e) : string;
/**
* Raises a number into power with modulo.
*
* @param string $base The base number; must be positive or zero.
* @param string $exp The exponent; must be positive or zero.
* @param string $mod The modulo; must be strictly positive.
*
* @return string The power.
*/
abstract function powmod(string $base, string $exp, string $mod) : string;
/**
* Returns the greatest common divisor of the two numbers.
*
* This method can be overridden by the concrete implementation if the underlying library
* has built-in support for GCD calculations.
*
* @param string $a The first number.
* @param string $b The second number.
*
* @return string The GCD, always positive, or zero if both arguments are zero.
*/
public function gcd(string $a, string $b) : string
{
if ($a === '0') {
return $this->abs($b);
}
if ($b === '0') {
return $this->abs($a);
}
return $this->gcd($b, $this->divR($a, $b));
}
/**
* Returns the square root of the given number, rounded down.
*
* The result is the largest x such that x² ≤ n.
* The input MUST NOT be negative.
*
* @param string $n The number.
*
* @return string The square root.
*/
abstract public function sqrt(string $n) : string;
/**
* Converts a number from an arbitrary base.
*
* This method can be overridden by the concrete implementation if the underlying library
* has built-in support for base conversion.
*
* @param string $number The number, positive or zero, non-empty, case-insensitively validated for the given base.
* @param int $base The base of the number, validated from 2 to 36.
*
* @return string The converted number, following the Calculator conventions.
*/
public function fromBase(string $number, int $base) : string
{
return $this->fromArbitraryBase(\strtolower($number), self::ALPHABET, $base);
}
/**
* Converts a number to an arbitrary base.
*
* This method can be overridden by the concrete implementation if the underlying library
* has built-in support for base conversion.
*
* @param string $number The number to convert, following the Calculator conventions.
* @param int $base The base to convert to, validated from 2 to 36.
*
* @return string The converted number, lowercase.
*/
public function toBase(string $number, int $base) : string
{
$negative = ($number[0] === '-');
if ($negative) {
$number = \substr($number, 1);
}
$number = $this->toArbitraryBase($number, self::ALPHABET, $base);
if ($negative) {
return '-' . $number;
}
return $number;
}
/**
* Converts a non-negative number in an arbitrary base using a custom alphabet, to base 10.
*
* @param string $number The number to convert, validated as a non-empty string,
* containing only chars in the given alphabet/base.
* @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum.
* @param int $base The base of the number, validated from 2 to alphabet length.
*
* @return string The number in base 10, following the Calculator conventions.
*/
final public function fromArbitraryBase(string $number, string $alphabet, int $base) : string
{
// remove leading "zeros"
$number = \ltrim($number, $alphabet[0]);
if ($number === '') {
return '0';
}
// optimize for "one"
if ($number === $alphabet[1]) {
return '1';
}
$result = '0';
$power = '1';
$base = (string) $base;
for ($i = \strlen($number) - 1; $i >= 0; $i--) {
$index = \strpos($alphabet, $number[$i]);
if ($index !== 0) {
$result = $this->add($result, ($index === 1)
? $power
: $this->mul($power, (string) $index)
);
}
if ($i !== 0) {
$power = $this->mul($power, $base);
}
}
return $result;
}
/**
* Converts a non-negative number to an arbitrary base using a custom alphabet.
*
* @param string $number The number to convert, positive or zero, following the Calculator conventions.
* @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum.
* @param int $base The base to convert to, validated from 2 to alphabet length.
*
* @return string The converted number in the given alphabet.
*/
final public function toArbitraryBase(string $number, string $alphabet, int $base) : string
{
if ($number === '0') {
return $alphabet[0];
}
$base = (string) $base;
$result = '';
while ($number !== '0') {
[$number, $remainder] = $this->divQR($number, $base);
$remainder = (int) $remainder;
$result .= $alphabet[$remainder];
}
return \strrev($result);
}
/**
* Performs a rounded division.
*
* Rounding is performed when the remainder of the division is not zero.
*
* @param string $a The dividend.
* @param string $b The divisor.
* @param int $roundingMode The rounding mode.
*
* @return string
*
* @throws \InvalidArgumentException If the rounding mode is invalid.
* @throws RoundingNecessaryException If RoundingMode::UNNECESSARY is provided but rounding is necessary.
*/
final public function divRound(string $a, string $b, int $roundingMode) : string
{
[$quotient, $remainder] = $this->divQR($a, $b);
$hasDiscardedFraction = ($remainder !== '0');
$isPositiveOrZero = ($a[0] === '-') === ($b[0] === '-');
$discardedFractionSign = function() use ($remainder, $b) : int {
$r = $this->abs($this->mul($remainder, '2'));
$b = $this->abs($b);
return $this->cmp($r, $b);
};
$increment = false;
switch ($roundingMode) {
case RoundingMode::UNNECESSARY:
if ($hasDiscardedFraction) {
throw RoundingNecessaryException::roundingNecessary();
}
break;
case RoundingMode::UP:
$increment = $hasDiscardedFraction;
break;
case RoundingMode::DOWN:
break;
case RoundingMode::CEILING:
$increment = $hasDiscardedFraction && $isPositiveOrZero;
break;
case RoundingMode::FLOOR:
$increment = $hasDiscardedFraction && ! $isPositiveOrZero;
break;
case RoundingMode::HALF_UP:
$increment = $discardedFractionSign() >= 0;
break;
case RoundingMode::HALF_DOWN:
$increment = $discardedFractionSign() > 0;
break;
case RoundingMode::HALF_CEILING:
$increment = $isPositiveOrZero ? $discardedFractionSign() >= 0 : $discardedFractionSign() > 0;
break;
case RoundingMode::HALF_FLOOR:
$increment = $isPositiveOrZero ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0;
break;
case RoundingMode::HALF_EVEN:
$lastDigit = (int) $quotient[-1];
$lastDigitIsEven = ($lastDigit % 2 === 0);
$increment = $lastDigitIsEven ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0;
break;
default:
throw new \InvalidArgumentException('Invalid rounding mode.');
}
if ($increment) {
return $this->add($quotient, $isPositiveOrZero ? '1' : '-1');
}
return $quotient;
}
/**
* Calculates bitwise AND of two numbers.
*
* This method can be overridden by the concrete implementation if the underlying library
* has built-in support for bitwise operations.
*
* @param string $a
* @param string $b
*
* @return string
*/
public function and(string $a, string $b) : string
{
return $this->bitwise('and', $a, $b);
}
/**
* Calculates bitwise OR of two numbers.
*
* This method can be overridden by the concrete implementation if the underlying library
* has built-in support for bitwise operations.
*
* @param string $a
* @param string $b
*
* @return string
*/
public function or(string $a, string $b) : string
{
return $this->bitwise('or', $a, $b);
}
/**
* Calculates bitwise XOR of two numbers.
*
* This method can be overridden by the concrete implementation if the underlying library
* has built-in support for bitwise operations.
*
* @param string $a
* @param string $b
*
* @return string
*/
public function xor(string $a, string $b) : string
{
return $this->bitwise('xor', $a, $b);
}
/**
* Performs a bitwise operation on a decimal number.
*
* @param string $operator The operator to use, must be "and", "or" or "xor".
* @param string $a The left operand.
* @param string $b The right operand.
*
* @return string
*/
private function bitwise(string $operator, string $a, string $b) : string
{
[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
$aBin = $this->toBinary($aDig);
$bBin = $this->toBinary($bDig);
$aLen = \strlen($aBin);
$bLen = \strlen($bBin);
if ($aLen > $bLen) {
$bBin = \str_repeat("\x00", $aLen - $bLen) . $bBin;
} elseif ($bLen > $aLen) {
$aBin = \str_repeat("\x00", $bLen - $aLen) . $aBin;
}
if ($aNeg) {
$aBin = $this->twosComplement($aBin);
}
if ($bNeg) {
$bBin = $this->twosComplement($bBin);
}
switch ($operator) {
case 'and':
$value = $aBin & $bBin;
$negative = ($aNeg and $bNeg);
break;
case 'or':
$value = $aBin | $bBin;
$negative = ($aNeg or $bNeg);
break;
case 'xor':
$value = $aBin ^ $bBin;
$negative = ($aNeg xor $bNeg);
break;
// @codeCoverageIgnoreStart
default:
throw new \InvalidArgumentException('Invalid bitwise operator.');
// @codeCoverageIgnoreEnd
}
if ($negative) {
$value = $this->twosComplement($value);
}
$result = $this->toDecimal($value);
return $negative ? $this->neg($result) : $result;
}
/**
* @param string $number A positive, binary number.
*
* @return string
*/
private function twosComplement(string $number) : string
{
$xor = \str_repeat("\xff", \strlen($number));
$number = $number ^ $xor;
for ($i = \strlen($number) - 1; $i >= 0; $i--) {
$byte = \ord($number[$i]);
if (++$byte !== 256) {
$number[$i] = \chr($byte);
break;
}
$number[$i] = \chr(0);
}
return $number;
}
/**
* Converts a decimal number to a binary string.
*
* @param string $number The number to convert, positive or zero, only digits.
*
* @return string
*/
private function toBinary(string $number) : string
{
$result = '';
while ($number !== '0') {
[$number, $remainder] = $this->divQR($number, '256');
$result .= \chr((int) $remainder);
}
return \strrev($result);
}
/**
* Returns the positive decimal representation of a binary number.
*
* @param string $bytes The bytes representing the number.
*
* @return string
*/
private function toDecimal(string $bytes) : string
{
$result = '0';
$power = '1';
for ($i = \strlen($bytes) - 1; $i >= 0; $i--) {
$index = \ord($bytes[$i]);
if ($index !== 0) {
$result = $this->add($result, ($index === 1)
? $power
: $this->mul($power, (string) $index)
);
}
if ($i !== 0) {
$power = $this->mul($power, '256');
}
}
return $result;
}
}
math/src/Internal/Calculator/NativeCalculator.php 0000644 00000033267 14736103132 0016115 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Internal\Calculator;
use Brick\Math\Internal\Calculator;
/**
* Calculator implementation using only native PHP code.
*
* @internal
*
* @psalm-immutable
*/
class NativeCalculator extends Calculator
{
/**
* The max number of digits the platform can natively add, subtract, multiply or divide without overflow.
* For multiplication, this represents the max sum of the lengths of both operands.
*
* For addition, it is assumed that an extra digit can hold a carry (1) without overflowing.
* Example: 32-bit: max number 1,999,999,999 (9 digits + carry)
* 64-bit: max number 1,999,999,999,999,999,999 (18 digits + carry)
*
* @var int
*/
private $maxDigits;
/**
* Class constructor.
*
* @codeCoverageIgnore
*/
public function __construct()
{
switch (PHP_INT_SIZE) {
case 4:
$this->maxDigits = 9;
break;
case 8:
$this->maxDigits = 18;
break;
default:
throw new \RuntimeException('The platform is not 32-bit or 64-bit as expected.');
}
}
/**
* {@inheritdoc}
*/
public function add(string $a, string $b) : string
{
$result = $a + $b;
if (is_int($result)) {
return (string) $result;
}
if ($a === '0') {
return $b;
}
if ($b === '0') {
return $a;
}
[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
if ($aNeg === $bNeg) {
$result = $this->doAdd($aDig, $bDig);
} else {
$result = $this->doSub($aDig, $bDig);
}
if ($aNeg) {
$result = $this->neg($result);
}
return $result;
}
/**
* {@inheritdoc}
*/
public function sub(string $a, string $b) : string
{
return $this->add($a, $this->neg($b));
}
/**
* {@inheritdoc}
*/
public function mul(string $a, string $b) : string
{
$result = $a * $b;
if (is_int($result)) {
return (string) $result;
}
if ($a === '0' || $b === '0') {
return '0';
}
if ($a === '1') {
return $b;
}
if ($b === '1') {
return $a;
}
if ($a === '-1') {
return $this->neg($b);
}
if ($b === '-1') {
return $this->neg($a);
}
[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
$result = $this->doMul($aDig, $bDig);
if ($aNeg !== $bNeg) {
$result = $this->neg($result);
}
return $result;
}
/**
* {@inheritdoc}
*/
public function divQ(string $a, string $b) : string
{
return $this->divQR($a, $b)[0];
}
/**
* {@inheritdoc}
*/
public function divR(string $a, string $b): string
{
return $this->divQR($a, $b)[1];
}
/**
* {@inheritdoc}
*/
public function divQR(string $a, string $b) : array
{
if ($a === '0') {
return ['0', '0'];
}
if ($a === $b) {
return ['1', '0'];
}
if ($b === '1') {
return [$a, '0'];
}
if ($b === '-1') {
return [$this->neg($a), '0'];
}
$na = $a * 1; // cast to number
if (is_int($na)) {
$nb = $b * 1;
if (is_int($nb)) {
// the only division that may overflow is PHP_INT_MIN / -1,
// which cannot happen here as we've already handled a divisor of -1 above.
$r = $na % $nb;
$q = ($na - $r) / $nb;
assert(is_int($q));
return [
(string) $q,
(string) $r
];
}
}
[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
[$q, $r] = $this->doDiv($aDig, $bDig);
if ($aNeg !== $bNeg) {
$q = $this->neg($q);
}
if ($aNeg) {
$r = $this->neg($r);
}
return [$q, $r];
}
/**
* {@inheritdoc}
*/
public function pow(string $a, int $e) : string
{
if ($e === 0) {
return '1';
}
if ($e === 1) {
return $a;
}
$odd = $e % 2;
$e -= $odd;
$aa = $this->mul($a, $a);
$result = $this->pow($aa, $e / 2);
if ($odd === 1) {
$result = $this->mul($result, $a);
}
return $result;
}
/**
* Algorithm from: https://www.geeksforgeeks.org/modular-exponentiation-power-in-modular-arithmetic/
*
* {@inheritdoc}
*/
public function powmod(string $base, string $exp, string $mod) : string
{
// special case: the algorithm below fails with 0 power 0 mod 1 (returns 1 instead of 0)
if ($base === '0' && $exp === '0' && $mod === '1') {
return '0';
}
// special case: the algorithm below fails with power 0 mod 1 (returns 1 instead of 0)
if ($exp === '0' && $mod === '1') {
return '0';
}
$x = $base;
$res = '1';
// numbers are positive, so we can use remainder instead of modulo
$x = $this->divR($x, $mod);
while ($exp !== '0') {
if (in_array($exp[-1], ['1', '3', '5', '7', '9'])) { // odd
$res = $this->divR($this->mul($res, $x), $mod);
}
$exp = $this->divQ($exp, '2');
$x = $this->divR($this->mul($x, $x), $mod);
}
return $res;
}
/**
* Adapted from https://cp-algorithms.com/num_methods/roots_newton.html
*
* {@inheritDoc}
*/
public function sqrt(string $n) : string
{
if ($n === '0') {
return '0';
}
// initial approximation
$x = \str_repeat('9', \intdiv(\strlen($n), 2) ?: 1);
$decreased = false;
for (;;) {
$nx = $this->divQ($this->add($x, $this->divQ($n, $x)), '2');
if ($x === $nx || $this->cmp($nx, $x) > 0 && $decreased) {
break;
}
$decreased = $this->cmp($nx, $x) < 0;
$x = $nx;
}
return $x;
}
/**
* Performs the addition of two non-signed large integers.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return string
*/
private function doAdd(string $a, string $b) : string
{
[$a, $b, $length] = $this->pad($a, $b);
$carry = 0;
$result = '';
for ($i = $length - $this->maxDigits;; $i -= $this->maxDigits) {
$blockLength = $this->maxDigits;
if ($i < 0) {
$blockLength += $i;
$i = 0;
}
$blockA = \substr($a, $i, $blockLength);
$blockB = \substr($b, $i, $blockLength);
$sum = (string) ($blockA + $blockB + $carry);
$sumLength = \strlen($sum);
if ($sumLength > $blockLength) {
$sum = \substr($sum, 1);
$carry = 1;
} else {
if ($sumLength < $blockLength) {
$sum = \str_repeat('0', $blockLength - $sumLength) . $sum;
}
$carry = 0;
}
$result = $sum . $result;
if ($i === 0) {
break;
}
}
if ($carry === 1) {
$result = '1' . $result;
}
return $result;
}
/**
* Performs the subtraction of two non-signed large integers.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return string
*/
private function doSub(string $a, string $b) : string
{
if ($a === $b) {
return '0';
}
// Ensure that we always subtract to a positive result: biggest minus smallest.
$cmp = $this->doCmp($a, $b);
$invert = ($cmp === -1);
if ($invert) {
$c = $a;
$a = $b;
$b = $c;
}
[$a, $b, $length] = $this->pad($a, $b);
$carry = 0;
$result = '';
$complement = 10 ** $this->maxDigits;
for ($i = $length - $this->maxDigits;; $i -= $this->maxDigits) {
$blockLength = $this->maxDigits;
if ($i < 0) {
$blockLength += $i;
$i = 0;
}
$blockA = \substr($a, $i, $blockLength);
$blockB = \substr($b, $i, $blockLength);
$sum = $blockA - $blockB - $carry;
if ($sum < 0) {
$sum += $complement;
$carry = 1;
} else {
$carry = 0;
}
$sum = (string) $sum;
$sumLength = \strlen($sum);
if ($sumLength < $blockLength) {
$sum = \str_repeat('0', $blockLength - $sumLength) . $sum;
}
$result = $sum . $result;
if ($i === 0) {
break;
}
}
// Carry cannot be 1 when the loop ends, as a > b
assert($carry === 0);
$result = \ltrim($result, '0');
if ($invert) {
$result = $this->neg($result);
}
return $result;
}
/**
* Performs the multiplication of two non-signed large integers.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return string
*/
private function doMul(string $a, string $b) : string
{
$x = \strlen($a);
$y = \strlen($b);
$maxDigits = \intdiv($this->maxDigits, 2);
$complement = 10 ** $maxDigits;
$result = '0';
for ($i = $x - $maxDigits;; $i -= $maxDigits) {
$blockALength = $maxDigits;
if ($i < 0) {
$blockALength += $i;
$i = 0;
}
$blockA = (int) \substr($a, $i, $blockALength);
$line = '';
$carry = 0;
for ($j = $y - $maxDigits;; $j -= $maxDigits) {
$blockBLength = $maxDigits;
if ($j < 0) {
$blockBLength += $j;
$j = 0;
}
$blockB = (int) \substr($b, $j, $blockBLength);
$mul = $blockA * $blockB + $carry;
$value = $mul % $complement;
$carry = ($mul - $value) / $complement;
$value = (string) $value;
$value = \str_pad($value, $maxDigits, '0', STR_PAD_LEFT);
$line = $value . $line;
if ($j === 0) {
break;
}
}
if ($carry !== 0) {
$line = $carry . $line;
}
$line = \ltrim($line, '0');
if ($line !== '') {
$line .= \str_repeat('0', $x - $blockALength - $i);
$result = $this->add($result, $line);
}
if ($i === 0) {
break;
}
}
return $result;
}
/**
* Performs the division of two non-signed large integers.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return string[] The quotient and remainder.
*/
private function doDiv(string $a, string $b) : array
{
$cmp = $this->doCmp($a, $b);
if ($cmp === -1) {
return ['0', $a];
}
$x = \strlen($a);
$y = \strlen($b);
// we now know that a >= b && x >= y
$q = '0'; // quotient
$r = $a; // remainder
$z = $y; // focus length, always $y or $y+1
for (;;) {
$focus = \substr($a, 0, $z);
$cmp = $this->doCmp($focus, $b);
if ($cmp === -1) {
if ($z === $x) { // remainder < dividend
break;
}
$z++;
}
$zeros = \str_repeat('0', $x - $z);
$q = $this->add($q, '1' . $zeros);
$a = $this->sub($a, $b . $zeros);
$r = $a;
if ($r === '0') { // remainder == 0
break;
}
$x = \strlen($a);
if ($x < $y) { // remainder < dividend
break;
}
$z = $y;
}
return [$q, $r];
}
/**
* Compares two non-signed large numbers.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return int [-1, 0, 1]
*/
private function doCmp(string $a, string $b) : int
{
$x = \strlen($a);
$y = \strlen($b);
$cmp = $x <=> $y;
if ($cmp !== 0) {
return $cmp;
}
return \strcmp($a, $b) <=> 0; // enforce [-1, 0, 1]
}
/**
* Pads the left of one of the given numbers with zeros if necessary to make both numbers the same length.
*
* The numbers must only consist of digits, without leading minus sign.
*
* @param string $a The first operand.
* @param string $b The second operand.
*
* @return array{0: string, 1: string, 2: int}
*/
private function pad(string $a, string $b) : array
{
$x = \strlen($a);
$y = \strlen($b);
if ($x > $y) {
$b = \str_repeat('0', $x - $y) . $b;
return [$a, $b, $x];
}
if ($x < $y) {
$a = \str_repeat('0', $y - $x) . $a;
return [$a, $b, $y];
}
return [$a, $b, $x];
}
}
math/src/Internal/Calculator/BcMathCalculator.php 0000644 00000003077 14736103132 0016021 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Internal\Calculator;
use Brick\Math\Internal\Calculator;
/**
* Calculator implementation built around the bcmath library.
*
* @internal
*
* @psalm-immutable
*/
class BcMathCalculator extends Calculator
{
/**
* {@inheritdoc}
*/
public function add(string $a, string $b) : string
{
return \bcadd($a, $b, 0);
}
/**
* {@inheritdoc}
*/
public function sub(string $a, string $b) : string
{
return \bcsub($a, $b, 0);
}
/**
* {@inheritdoc}
*/
public function mul(string $a, string $b) : string
{
return \bcmul($a, $b, 0);
}
/**
* {@inheritdoc}
*/
public function divQ(string $a, string $b) : string
{
return \bcdiv($a, $b, 0);
}
/**
* {@inheritdoc}
*/
public function divR(string $a, string $b) : string
{
return \bcmod($a, $b);
}
/**
* {@inheritdoc}
*/
public function divQR(string $a, string $b) : array
{
$q = \bcdiv($a, $b, 0);
$r = \bcmod($a, $b);
return [$q, $r];
}
/**
* {@inheritdoc}
*/
public function pow(string $a, int $e) : string
{
return \bcpow($a, (string) $e, 0);
}
/**
* {@inheritdoc}
*/
public function powmod(string $base, string $exp, string $mod) : string
{
return \bcpowmod($base, $exp, $mod, 0);
}
/**
* {@inheritDoc}
*/
public function sqrt(string $n) : string
{
return \bcsqrt($n, 0);
}
}
math/src/Internal/Calculator/GmpCalculator.php 0000644 00000005135 14736103132 0015403 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math\Internal\Calculator;
use Brick\Math\Internal\Calculator;
/**
* Calculator implementation built around the GMP library.
*
* @internal
*
* @psalm-immutable
*/
class GmpCalculator extends Calculator
{
/**
* {@inheritdoc}
*/
public function add(string $a, string $b) : string
{
return \gmp_strval(\gmp_add($a, $b));
}
/**
* {@inheritdoc}
*/
public function sub(string $a, string $b) : string
{
return \gmp_strval(\gmp_sub($a, $b));
}
/**
* {@inheritdoc}
*/
public function mul(string $a, string $b) : string
{
return \gmp_strval(\gmp_mul($a, $b));
}
/**
* {@inheritdoc}
*/
public function divQ(string $a, string $b) : string
{
return \gmp_strval(\gmp_div_q($a, $b));
}
/**
* {@inheritdoc}
*/
public function divR(string $a, string $b) : string
{
return \gmp_strval(\gmp_div_r($a, $b));
}
/**
* {@inheritdoc}
*/
public function divQR(string $a, string $b) : array
{
[$q, $r] = \gmp_div_qr($a, $b);
return [
\gmp_strval($q),
\gmp_strval($r)
];
}
/**
* {@inheritdoc}
*/
public function pow(string $a, int $e) : string
{
return \gmp_strval(\gmp_pow($a, $e));
}
/**
* {@inheritdoc}
*/
public function powmod(string $base, string $exp, string $mod) : string
{
return \gmp_strval(\gmp_powm($base, $exp, $mod));
}
/**
* {@inheritdoc}
*/
public function gcd(string $a, string $b) : string
{
return \gmp_strval(\gmp_gcd($a, $b));
}
/**
* {@inheritdoc}
*/
public function fromBase(string $number, int $base) : string
{
return \gmp_strval(\gmp_init($number, $base));
}
/**
* {@inheritdoc}
*/
public function toBase(string $number, int $base) : string
{
return \gmp_strval($number, $base);
}
/**
* {@inheritdoc}
*/
public function and(string $a, string $b) : string
{
return \gmp_strval(\gmp_and($a, $b));
}
/**
* {@inheritdoc}
*/
public function or(string $a, string $b) : string
{
return \gmp_strval(\gmp_or($a, $b));
}
/**
* {@inheritdoc}
*/
public function xor(string $a, string $b) : string
{
return \gmp_strval(\gmp_xor($a, $b));
}
/**
* {@inheritDoc}
*/
public function sqrt(string $n) : string
{
return \gmp_strval(\gmp_sqrt($n));
}
}
math/src/BigNumber.php 0000644 00000035234 14736103132 0010656 0 ustar 00 <?php
declare(strict_types=1);
namespace Brick\Math;
use Brick\Math\Exception\DivisionByZeroException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NumberFormatException;
use Brick\Math\Exception\RoundingNecessaryException;
/**
* Common interface for arbitrary-precision rational numbers.
*
* @psalm-immutable
*/
abstract class BigNumber implements \Serializable, \JsonSerializable
{
/**
* The regular expression used to parse integer, decimal and rational numbers.
*
* @var string
*/
private const PARSE_REGEXP =
'/^' .
'(?<integral>[\-\+]?[0-9]+)' .
'(?:' .
'(?:' .
'(?:\.(?<fractional>[0-9]+))?' .
'(?:[eE](?<exponent>[\-\+]?[0-9]+))?' .
')' . '|' . '(?:' .
'(?:\/(?<denominator>[0-9]+))?' .
')' .
')?' .
'$/';
/**
* Creates a BigNumber of the given value.
*
* The concrete return type is dependent on the given value, with the following rules:
*
* - BigNumber instances are returned as is
* - integer numbers are returned as BigInteger
* - floating point numbers are converted to a string then parsed as such
* - strings containing a `/` character are returned as BigRational
* - strings containing a `.` character or using an exponential notation are returned as BigDecimal
* - strings containing only digits with an optional leading `+` or `-` sign are returned as BigInteger
*
* @param BigNumber|int|float|string $value
*
* @return BigNumber
*
* @throws NumberFormatException If the format of the number is not valid.
* @throws DivisionByZeroException If the value represents a rational number with a denominator of zero.
*
* @psalm-pure
*/
public static function of($value) : BigNumber
{
if ($value instanceof BigNumber) {
return $value;
}
if (\is_int($value)) {
return new BigInteger((string) $value);
}
if (is_float($value)) {
$value = self::floatToString($value);
} else {
$value = (string) $value;
}
if (\preg_match(self::PARSE_REGEXP, $value, $matches) !== 1) {
throw new NumberFormatException(\sprintf('The given value "%s" does not represent a valid number.', $value));
}
if (isset($matches['denominator'])) {
$numerator = self::cleanUp($matches['integral']);
$denominator = \ltrim($matches['denominator'], '0');
if ($denominator === '') {
throw DivisionByZeroException::denominatorMustNotBeZero();
}
return new BigRational(new BigInteger($numerator), new BigInteger($denominator), false);
}
if (isset($matches['fractional']) || isset($matches['exponent'])) {
$fractional = isset($matches['fractional']) ? $matches['fractional'] : '';
$exponent = isset($matches['exponent']) ? (int) $matches['exponent'] : 0;
$unscaledValue = self::cleanUp($matches['integral'] . $fractional);
$scale = \strlen($fractional) - $exponent;
if ($scale < 0) {
if ($unscaledValue !== '0') {
$unscaledValue .= \str_repeat('0', - $scale);
}
$scale = 0;
}
return new BigDecimal($unscaledValue, $scale);
}
$integral = self::cleanUp($matches['integral']);
return new BigInteger($integral);
}
/**
* Safely converts float to string, avoiding locale-dependent issues.
*
* @see https://github.com/brick/math/pull/20
*
* @param float $float
*
* @return string
*
* @psalm-pure
* @psalm-suppress ImpureFunctionCall
*/
private static function floatToString(float $float) : string
{
$currentLocale = \setlocale(LC_NUMERIC, '0');
\setlocale(LC_NUMERIC, 'C');
$result = (string) $float;
\setlocale(LC_NUMERIC, $currentLocale);
return $result;
}
/**
* Proxy method to access protected constructors from sibling classes.
*
* @internal
*
* @param mixed ...$args The arguments to the constructor.
*
* @return static
*
* @psalm-pure
*/
protected static function create(... $args) : BigNumber
{
/** @psalm-suppress TooManyArguments */
return new static(... $args);
}
/**
* Returns the minimum of the given values.
*
* @param BigNumber|int|float|string ...$values The numbers to compare. All the numbers need to be convertible
* to an instance of the class this method is called on.
*
* @return static The minimum value.
*
* @throws \InvalidArgumentException If no values are given.
* @throws MathException If an argument is not valid.
*
* @psalm-pure
*/
public static function min(...$values) : BigNumber
{
$min = null;
foreach ($values as $value) {
$value = static::of($value);
if ($min === null || $value->isLessThan($min)) {
$min = $value;
}
}
if ($min === null) {
throw new \InvalidArgumentException(__METHOD__ . '() expects at least one value.');
}
return $min;
}
/**
* Returns the maximum of the given values.
*
* @param BigNumber|int|float|string ...$values The numbers to compare. All the numbers need to be convertible
* to an instance of the class this method is called on.
*
* @return static The maximum value.
*
* @throws \InvalidArgumentException If no values are given.
* @throws MathException If an argument is not valid.
*
* @psalm-pure
*/
public static function max(...$values) : BigNumber
{
$max = null;
foreach ($values as $value) {
$value = static::of($value);
if ($max === null || $value->isGreaterThan($max)) {
$max = $value;
}
}
if ($max === null) {
throw new \InvalidArgumentException(__METHOD__ . '() expects at least one value.');
}
return $max;
}
/**
* Returns the sum of the given values.
*
* @param BigNumber|int|float|string ...$values The numbers to add. All the numbers need to be convertible
* to an instance of the class this method is called on.
*
* @return static The sum.
*
* @throws \InvalidArgumentException If no values are given.
* @throws MathException If an argument is not valid.
*
* @psalm-pure
*/
public static function sum(...$values) : BigNumber
{
/** @var BigNumber|null $sum */
$sum = null;
foreach ($values as $value) {
$value = static::of($value);
if ($sum === null) {
$sum = $value;
} else {
$sum = self::add($sum, $value);
}
}
if ($sum === null) {
throw new \InvalidArgumentException(__METHOD__ . '() expects at least one value.');
}
return $sum;
}
/**
* Adds two BigNumber instances in the correct order to avoid a RoundingNecessaryException.
*
* @todo This could be better resolved by creating an abstract protected method in BigNumber, and leaving to
* concrete classes the responsibility to perform the addition themselves or delegate it to the given number,
* depending on their ability to perform the operation. This will also require a version bump because we're
* potentially breaking custom BigNumber implementations (if any...)
*
* @param BigNumber $a
* @param BigNumber $b
*
* @return BigNumber
*
* @psalm-pure
*/
private static function add(BigNumber $a, BigNumber $b) : BigNumber
{
if ($a instanceof BigRational) {
return $a->plus($b);
}
if ($b instanceof BigRational) {
return $b->plus($a);
}
if ($a instanceof BigDecimal) {
return $a->plus($b);
}
if ($b instanceof BigDecimal) {
return $b->plus($a);
}
/** @var BigInteger $a */
return $a->plus($b);
}
/**
* Removes optional leading zeros and + sign from the given number.
*
* @param string $number The number, validated as a non-empty string of digits with optional sign.
*
* @return string
*
* @psalm-pure
*/
private static function cleanUp(string $number) : string
{
$firstChar = $number[0];
if ($firstChar === '+' || $firstChar === '-') {
$number = \substr($number, 1);
}
$number = \ltrim($number, '0');
if ($number === '') {
return '0';
}
if ($firstChar === '-') {
return '-' . $number;
}
return $number;
}
/**
* Checks if this number is equal to the given one.
*
* @param BigNumber|int|float|string $that
*
* @return bool
*/
public function isEqualTo($that) : bool
{
return $this->compareTo($that) === 0;
}
/**
* Checks if this number is strictly lower than the given one.
*
* @param BigNumber|int|float|string $that
*
* @return bool
*/
public function isLessThan($that) : bool
{
return $this->compareTo($that) < 0;
}
/**
* Checks if this number is lower than or equal to the given one.
*
* @param BigNumber|int|float|string $that
*
* @return bool
*/
public function isLessThanOrEqualTo($that) : bool
{
return $this->compareTo($that) <= 0;
}
/**
* Checks if this number is strictly greater than the given one.
*
* @param BigNumber|int|float|string $that
*
* @return bool
*/
public function isGreaterThan($that) : bool
{
return $this->compareTo($that) > 0;
}
/**
* Checks if this number is greater than or equal to the given one.
*
* @param BigNumber|int|float|string $that
*
* @return bool
*/
public function isGreaterThanOrEqualTo($that) : bool
{
return $this->compareTo($that) >= 0;
}
/**
* Checks if this number equals zero.
*
* @return bool
*/
public function isZero() : bool
{
return $this->getSign() === 0;
}
/**
* Checks if this number is strictly negative.
*
* @return bool
*/
public function isNegative() : bool
{
return $this->getSign() < 0;
}
/**
* Checks if this number is negative or zero.
*
* @return bool
*/
public function isNegativeOrZero() : bool
{
return $this->getSign() <= 0;
}
/**
* Checks if this number is strictly positive.
*
* @return bool
*/
public function isPositive() : bool
{
return $this->getSign() > 0;
}
/**
* Checks if this number is positive or zero.
*
* @return bool
*/
public function isPositiveOrZero() : bool
{
return $this->getSign() >= 0;
}
/**
* Returns the sign of this number.
*
* @return int -1 if the number is negative, 0 if zero, 1 if positive.
*/
abstract public function getSign() : int;
/**
* Compares this number to the given one.
*
* @param BigNumber|int|float|string $that
*
* @return int [-1,0,1] If `$this` is lower than, equal to, or greater than `$that`.
*
* @throws MathException If the number is not valid.
*/
abstract public function compareTo($that) : int;
/**
* Converts this number to a BigInteger.
*
* @return BigInteger The converted number.
*
* @throws RoundingNecessaryException If this number cannot be converted to a BigInteger without rounding.
*/
abstract public function toBigInteger() : BigInteger;
/**
* Converts this number to a BigDecimal.
*
* @return BigDecimal The converted number.
*
* @throws RoundingNecessaryException If this number cannot be converted to a BigDecimal without rounding.
*/
abstract public function toBigDecimal() : BigDecimal;
/**
* Converts this number to a BigRational.
*
* @return BigRational The converted number.
*/
abstract public function toBigRational() : BigRational;
/**
* Converts this number to a BigDecimal with the given scale, using rounding if necessary.
*
* @param int $scale The scale of the resulting `BigDecimal`.
* @param int $roundingMode A `RoundingMode` constant.
*
* @return BigDecimal
*
* @throws RoundingNecessaryException If this number cannot be converted to the given scale without rounding.
* This only applies when RoundingMode::UNNECESSARY is used.
*/
abstract public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal;
/**
* Returns the exact value of this number as a native integer.
*
* If this number cannot be converted to a native integer without losing precision, an exception is thrown.
* Note that the acceptable range for an integer depends on the platform and differs for 32-bit and 64-bit.
*
* @return int The converted value.
*
* @throws MathException If this number cannot be exactly converted to a native integer.
*/
abstract public function toInt() : int;
/**
* Returns an approximation of this number as a floating-point value.
*
* Note that this method can discard information as the precision of a floating-point value
* is inherently limited.
*
* If the number is greater than the largest representable floating point number, positive infinity is returned.
* If the number is less than the smallest representable floating point number, negative infinity is returned.
*
* @return float The converted value.
*/
abstract public function toFloat() : float;
/**
* Returns a string representation of this number.
*
* The output of this method can be parsed by the `of()` factory method;
* this will yield an object equal to this one, without any information loss.
*
* @return string
*/
abstract public function __toString() : string;
/**
* {@inheritdoc}
*/
public function jsonSerialize() : string
{
return $this->__toString();
}
}
math/SECURITY.md 0000644 00000000633 14736103132 0007270 0 ustar 00 # Security Policy
## Supported Versions
Only the latest release stream is supported.
| Version | Supported |
| ------- | ------------------ |
| 0.8.x | :white_check_mark: |
| < 0.8 | :x: |
## Reporting a Vulnerability
To report a security vulnerability, please use the
[Tidelift security contact](https://tidelift.com/security).
Tidelift will coordinate the fix and disclosure.
math/psalm-baseline.xml 0000644 00000002361 14736103132 0011115 0 ustar 00 <?xml version="1.0" encoding="UTF-8"?>
<files psalm-version="3.8.5@e6ec5fa22a7b9e61670a24d07b3119aff80dcd89">
<file src="src/Internal/Calculator/BcMathCalculator.php">
<InvalidNullableReturnType occurrences="3">
<code>string</code>
<code>string</code>
<code>string</code>
</InvalidNullableReturnType>
<InvalidReturnStatement occurrences="1">
<code>[$q, $r]</code>
</InvalidReturnStatement>
<InvalidReturnType occurrences="1">
<code>array</code>
</InvalidReturnType>
<NullableReturnStatement occurrences="3">
<code>\bcdiv($a, $b, 0)</code>
<code>\bcmod($a, $b)</code>
<code>\bcpowmod($base, $exp, $mod, 0)</code>
</NullableReturnStatement>
</file>
<file src="src/Internal/Calculator/NativeCalculator.php">
<InvalidOperand occurrences="6">
<code>$a</code>
<code>$a</code>
<code>$a</code>
<code>$b</code>
<code>$blockA</code>
<code>$blockA</code>
</InvalidOperand>
<LoopInvalidation occurrences="4">
<code>$i</code>
<code>$i</code>
<code>$i</code>
<code>$j</code>
</LoopInvalidation>
<PossiblyInvalidArgument occurrences="1">
<code>$e / 2</code>
</PossiblyInvalidArgument>
</file>
</files>
math/LICENSE 0000644 00000002101 14736103132 0006474 0 ustar 00 The MIT License (MIT)
Copyright (c) 2013-present Benjamin Morel
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.