Файл: vendor/brick/math/src/BigRational.php
Строк: 954
<?php
declare(strict_types=1);
namespace BrickMath;
use BrickMathExceptionDivisionByZeroException;
use BrickMathExceptionInvalidArgumentException;
use BrickMathExceptionMathException;
use BrickMathExceptionRoundingNecessaryException;
use BrickMathInternalDecimalHelper;
use BrickMathInternalSafe;
use LogicException;
use Override;
use function max;
use function min;
use function strlen;
use function substr;
/**
* An arbitrarily large rational number.
*
* This class is immutable.
*
* Fractions are automatically simplified to lowest terms. For example, `2/4` becomes `1/2`.
* The denominator is always strictly positive; the sign is carried by the numerator.
*/
final readonly 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.
* @param bool $simplify Whether to simplify the fraction to lowest terms.
*
* @throws DivisionByZeroException If the denominator is zero.
*
* @pure
*/
protected function __construct(BigInteger $numerator, BigInteger $denominator, bool $checkDenominator, bool $simplify)
{
if ($checkDenominator) {
if ($denominator->isZero()) {
throw DivisionByZeroException::zeroDenominator();
}
if ($denominator->isNegative()) {
$numerator = $numerator->negated();
$denominator = $denominator->negated();
}
}
if ($simplify) {
$gcd = $numerator->gcd($denominator);
$numerator = $numerator->quotient($gcd);
$denominator = $denominator->quotient($gcd);
}
$this->numerator = $numerator;
$this->denominator = $denominator;
}
/**
* 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|string $numerator The numerator. Must be convertible to a BigInteger.
* @param BigNumber|int|string $denominator The denominator. Must be convertible to a BigInteger.
*
* @throws MathException If an argument is not valid, or is not convertible to a BigInteger.
* @throws DivisionByZeroException If the denominator is zero.
*
* @pure
*/
public static function ofFraction(
BigNumber|int|string $numerator,
BigNumber|int|string $denominator,
): BigRational {
$numerator = BigInteger::of($numerator);
$denominator = BigInteger::of($denominator);
return new BigRational($numerator, $denominator, true, true);
}
/**
* Returns a BigRational representing zero.
*
* @pure
*/
public static function zero(): BigRational
{
/** @var BigRational|null $zero */
static $zero;
if ($zero === null) {
$zero = new BigRational(BigInteger::zero(), BigInteger::one(), false, false);
}
return $zero;
}
/**
* Returns a BigRational representing one.
*
* @pure
*/
public static function one(): BigRational
{
/** @var BigRational|null $one */
static $one;
if ($one === null) {
$one = new BigRational(BigInteger::one(), BigInteger::one(), false, false);
}
return $one;
}
/**
* Returns a BigRational representing ten.
*
* @pure
*/
public static function ten(): BigRational
{
/** @var BigRational|null $ten */
static $ten;
if ($ten === null) {
$ten = new BigRational(BigInteger::ten(), BigInteger::one(), false, false);
}
return $ten;
}
/**
* Returns the numerator of this rational number.
*
* @pure
*/
public function getNumerator(): BigInteger
{
return $this->numerator;
}
/**
* Returns the denominator of this rational number.
*
* The denominator is always strictly positive.
*
* @pure
*/
public function getDenominator(): BigInteger
{
return $this->denominator;
}
/**
* Returns the integral part of this rational number.
*
* Examples:
*
* - `7/3` returns `2` (since 7/3 = 2 + 1/3)
* - `-7/3` returns `-2` (since -7/3 = -2 + (-1/3))
*
* The following identity holds: `$r->isEqualTo($r->getFractionalPart()->plus($r->getIntegralPart()))`. Note that in
* this identity, the operand order is significant: the reversed form throws when the fractional part is non-zero.
*
* @pure
*/
public function getIntegralPart(): BigInteger
{
return $this->numerator->quotient($this->denominator);
}
/**
* Returns the fractional part of this rational number.
*
* Examples:
*
* - `7/3` returns `1/3` (since 7/3 = 2 + 1/3)
* - `-7/3` returns `-1/3` (since -7/3 = -2 + (-1/3))
*
* The following identity holds: `$r->isEqualTo($r->getFractionalPart()->plus($r->getIntegralPart()))`. Note that in
* this identity, the operand order is significant: the reversed form throws when the fractional part is non-zero.
*
* @pure
*/
public function getFractionalPart(): BigRational
{
return new BigRational($this->numerator->remainder($this->denominator), $this->denominator, false, false);
}
/**
* Returns the sum of this number and the given one.
*
* @param BigNumber|int|string $that The number to add.
*
* @throws MathException If the number is not valid.
*
* @pure
*/
public function plus(BigNumber|int|string $that): BigRational
{
$that = BigRational::of($that);
if ($that->isZero()) {
return $this;
}
if ($this->isZero()) {
return $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, true);
}
/**
* Returns the difference of this number and the given one.
*
* @param BigNumber|int|string $that The number to subtract.
*
* @throws MathException If the number is not valid.
*
* @pure
*/
public function minus(BigNumber|int|string $that): BigRational
{
$that = BigRational::of($that);
if ($that->isZero()) {
return $this;
}
if ($this->isZero()) {
return $that->negated();
}
$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, true);
}
/**
* Returns the product of this number and the given one.
*
* @param BigNumber|int|string $that The multiplier.
*
* @throws MathException If the multiplier is not valid.
*
* @pure
*/
public function multipliedBy(BigNumber|int|string $that): BigRational
{
$that = BigRational::of($that);
if ($that->isZero() || $this->isZero()) {
return BigRational::zero();
}
$numerator = $this->numerator->multipliedBy($that->numerator);
$denominator = $this->denominator->multipliedBy($that->denominator);
return new BigRational($numerator, $denominator, false, true);
}
/**
* Returns the result of the division of this number by the given one.
*
* @param BigNumber|int|string $that The divisor.
*
* @throws MathException If the divisor is not valid.
* @throws DivisionByZeroException If the divisor is zero.
*
* @pure
*/
public function dividedBy(BigNumber|int|string $that): BigRational
{
$that = BigRational::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$numerator = $this->numerator->multipliedBy($that->denominator);
$denominator = $this->denominator->multipliedBy($that->numerator);
return new BigRational($numerator, $denominator, true, true);
}
/**
* Returns this number exponentiated to the given value.
*
* Unlike BigInteger and BigDecimal, BigRational supports negative exponents:
* the result is the reciprocal raised to the absolute value of the exponent.
*
* @throws DivisionByZeroException If the exponent is negative and this number is zero.
*
* @pure
*/
public function power(int $exponent): BigRational
{
if ($exponent === 0) {
return BigRational::one();
}
if ($exponent === 1) {
return $this;
}
if ($exponent < 0) {
if ($this->isZero()) {
throw DivisionByZeroException::zeroToNegativePower();
}
return $this->reciprocal()->power(Safe::neg($exponent));
}
return new BigRational(
$this->numerator->power($exponent),
$this->denominator->power($exponent),
false,
false,
);
}
/**
* Returns the reciprocal of this BigRational.
*
* The reciprocal has the numerator and denominator swapped.
*
* @throws DivisionByZeroException If this number is zero.
*
* @pure
*/
public function reciprocal(): BigRational
{
if ($this->isZero()) {
throw DivisionByZeroException::reciprocalOfZero();
}
return new BigRational($this->denominator, $this->numerator, true, false);
}
#[Override]
public function negated(): static
{
return new BigRational($this->numerator->negated(), $this->denominator, false, false);
}
#[Override]
public function compareTo(BigNumber|int|string $that): int
{
$that = BigRational::of($that);
if ($this->denominator->isEqualTo($that->denominator)) {
return $this->numerator->compareTo($that->numerator);
}
return $this->numerator
->multipliedBy($that->denominator)
->compareTo($that->numerator->multipliedBy($this->denominator));
}
#[Override]
public function getSign(): int
{
return $this->numerator->getSign();
}
#[Override]
public function toBigInteger(): BigInteger
{
if ($this->denominator->isEqualTo(1)) {
return $this->numerator;
}
throw RoundingNecessaryException::rationalNotConvertibleToInteger();
}
#[Override]
public function toBigDecimal(): BigDecimal
{
$scale = DecimalHelper::computeScaleFromReducedFractionDenominator($this->denominator->toString());
if ($scale === null) {
throw RoundingNecessaryException::rationalNotConvertibleToDecimal();
}
return $this->numerator->toBigDecimal()->dividedBy($this->denominator, $scale)->strippedOfTrailingZeros();
}
#[Override]
public function toBigRational(): BigRational
{
return $this;
}
#[Override]
public function toScale(int $scale, RoundingMode $roundingMode = RoundingMode::Unnecessary): BigDecimal
{
if ($scale < 0) { // @phpstan-ignore smaller.alwaysFalse
throw InvalidArgumentException::negativeScale();
}
if ($roundingMode === RoundingMode::Unnecessary) {
$requiredScale = DecimalHelper::computeScaleFromReducedFractionDenominator($this->denominator->toString());
if ($requiredScale === null) {
throw RoundingNecessaryException::rationalNotConvertibleToDecimal();
}
if ($requiredScale > $scale) {
throw RoundingNecessaryException::rationalScaleTooSmall();
}
}
return $this->numerator->toBigDecimal()->dividedBy($this->denominator, $scale, $roundingMode);
}
#[Override]
public function toInt(): int
{
return $this->toBigInteger()->toInt();
}
#[Override]
public function toFloat(): float
{
if ($this->denominator->isEqualTo(1)) {
return $this->numerator->toFloat();
}
// Avoid $this->numerator->toFloat() / $this->denominator->toFloat(): converting both operands to float first
// adds an extra rounding step before the division and can change the final float. Instead, divide in decimal
// first and convert the resulting decimal approximation to float once.
// We need ~17 significant digits for double precision (we use 20 for some margin). Since $scale controls
// decimal places (not significant digits), we subtract the estimated order of magnitude so that large results
// use fewer decimal places and small results use more (to look past leading zeros). Clamped to [0, 350] as
// doubles range from e-324 to e308 (350 ≈ 324 + 20 significant digits + margin).
$magnitude = strlen($this->numerator->abs()->toString()) - strlen($this->denominator->toString());
$scale = min(350, max(0, 20 - $magnitude));
$result = $this->numerator
->toBigDecimal()
->dividedBy($this->denominator, $scale, RoundingMode::HalfEven)
->toFloat();
// Preserve the sign when the decimal approximation underflows to zero.
if ($result === 0.0 && $this->numerator->isNegative()) {
return -0.0;
}
return $result;
}
#[Override]
public function toString(): string
{
$numerator = $this->numerator->toString();
$denominator = $this->denominator->toString();
if ($denominator === '1') {
return $numerator;
}
return $numerator . '/' . $denominator;
}
/**
* Returns the decimal representation of this rational number, with repeating decimals in parentheses.
*
* WARNING: This method is unbounded.
* The length of the repeating decimal period can be as large as `denominator - 1`.
* For fractions with large denominators, this method can use excessive memory and CPU time.
* For example, `1/100019` has a repeating period of 100,018 digits.
*
* Examples:
*
* - `10/3` returns `3.(3)`
* - `171/70` returns `2.4(428571)`
* - `1/2` returns `0.5`
*
* @return non-empty-string
*
* @pure
*/
public function toRepeatingDecimalString(): string
{
if ($this->isZero()) {
return '0';
}
$sign = $this->numerator->isNegative() ? '-' : '';
$numerator = $this->numerator->abs();
$denominator = $this->denominator;
$integral = $numerator->quotient($denominator);
$remainder = $numerator->remainder($denominator);
$integralString = $integral->toString();
if ($remainder->isZero()) {
return $sign . $integralString;
}
$digits = '';
$remainderPositions = [];
$index = 0;
while (! $remainder->isZero()) {
$remainderString = $remainder->toString();
if (isset($remainderPositions[$remainderString])) {
$repeatIndex = $remainderPositions[$remainderString];
$nonRepeating = substr($digits, 0, $repeatIndex);
$repeating = substr($digits, $repeatIndex);
return $sign . $integralString . '.' . $nonRepeating . '(' . $repeating . ')';
}
$remainderPositions[$remainderString] = $index;
$remainder = $remainder->multipliedBy(10);
$digits .= $remainder->quotient($denominator)->toString();
$remainder = $remainder->remainder($denominator);
$index++;
}
return $sign . $integralString . '.' . $digits;
}
/**
* 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
*
* @param array{numerator: BigInteger, denominator: BigInteger} $data
*
* @throws LogicException
*/
public function __unserialize(array $data): void
{
/** @phpstan-ignore isset.initializedProperty */
if (isset($this->numerator)) {
throw new LogicException('__unserialize() is an internal function, it must not be called directly.');
}
/** @phpstan-ignore deadCode.unreachable */
$this->numerator = $data['numerator'];
$this->denominator = $data['denominator'];
}
#[Override]
protected static function from(BigNumber $number): static
{
return $number->toBigRational();
}
}