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<?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.
*/
private BigInteger $numerator;
/**
* The denominator. Always strictly positive.
*/
private BigInteger $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
* @var BigRational|null $zero
*/
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
* @var BigRational|null $one
*/
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
* @var BigRational|null $ten
*/
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
{
$simplified = $this->simplified();
return $simplified->numerator->toFloat() / $simplified->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 for serializing the object and SHOULD NOT be accessed directly.
*
* @internal
*
* @return array{numerator: BigInteger, denominator: BigInteger}
*/
public function __serialize(): array
{
return ['numerator' => $this->numerator, 'denominator' => $this->denominator];
}
/**
* This method is only here to allow unserializing the object and cannot be accessed directly.
*
* @internal
* @psalm-suppress RedundantPropertyInitializationCheck
*
* @param array{numerator: BigInteger, denominator: BigInteger} $data
*
* @return void
*
* @throws \LogicException
*/
public function __unserialize(array $data): void
{
if (isset($this->numerator)) {
throw new \LogicException('__unserialize() is an internal function, it must not be called directly.');
}
$this->numerator = $data['numerator'];
$this->denominator = $data['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
* @psalm-suppress RedundantPropertyInitializationCheck
*
* @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);
}
}
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