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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); } }