510 lines
16 KiB
PHP
510 lines
16 KiB
PHP
<?php
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declare(strict_types=1);
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namespace Brick\Math;
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use Brick\Math\Exception\DivisionByZeroException;
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use Brick\Math\Exception\MathException;
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use Brick\Math\Exception\NumberFormatException;
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use Brick\Math\Exception\RoundingNecessaryException;
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/**
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* Common interface for arbitrary-precision rational numbers.
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*
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* @psalm-immutable
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*/
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abstract class BigNumber implements \JsonSerializable
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{
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/**
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* The regular expression used to parse integer or decimal numbers.
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*/
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private const PARSE_REGEXP_NUMERICAL =
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'/^' .
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'(?<sign>[\-\+])?' .
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'(?<integral>[0-9]+)?' .
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'(?<point>\.)?' .
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'(?<fractional>[0-9]+)?' .
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'(?:[eE](?<exponent>[\-\+]?[0-9]+))?' .
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'$/';
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/**
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* The regular expression used to parse rational numbers.
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*/
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private const PARSE_REGEXP_RATIONAL =
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'/^' .
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'(?<sign>[\-\+])?' .
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'(?<numerator>[0-9]+)' .
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'\/?' .
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'(?<denominator>[0-9]+)' .
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'$/';
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/**
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* Creates a BigNumber of the given value.
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*
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* The concrete return type is dependent on the given value, with the following rules:
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*
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* - BigNumber instances are returned as is
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* - integer numbers are returned as BigInteger
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* - floating point numbers are converted to a string then parsed as such
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* - strings containing a `/` character are returned as BigRational
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* - strings containing a `.` character or using an exponential notation are returned as BigDecimal
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* - strings containing only digits with an optional leading `+` or `-` sign are returned as BigInteger
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*
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* @throws NumberFormatException If the format of the number is not valid.
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* @throws DivisionByZeroException If the value represents a rational number with a denominator of zero.
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*
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* @psalm-pure
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*/
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final public static function of(BigNumber|int|float|string $value) : static
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{
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$value = self::_of($value);
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if (static::class === BigNumber::class) {
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// https://github.com/vimeo/psalm/issues/10309
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assert($value instanceof static);
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return $value;
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}
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return static::from($value);
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}
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/**
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* @psalm-pure
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*/
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private static function _of(BigNumber|int|float|string $value) : BigNumber
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{
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if ($value instanceof BigNumber) {
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return $value;
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}
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if (\is_int($value)) {
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return new BigInteger((string) $value);
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}
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if (is_float($value)) {
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$value = (string) $value;
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}
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if (str_contains($value, '/')) {
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// Rational number
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if (\preg_match(self::PARSE_REGEXP_RATIONAL, $value, $matches, PREG_UNMATCHED_AS_NULL) !== 1) {
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throw NumberFormatException::invalidFormat($value);
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}
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$sign = $matches['sign'];
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$numerator = $matches['numerator'];
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$denominator = $matches['denominator'];
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assert($numerator !== null);
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assert($denominator !== null);
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$numerator = self::cleanUp($sign, $numerator);
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$denominator = self::cleanUp(null, $denominator);
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if ($denominator === '0') {
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throw DivisionByZeroException::denominatorMustNotBeZero();
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}
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return new BigRational(
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new BigInteger($numerator),
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new BigInteger($denominator),
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false
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);
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} else {
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// Integer or decimal number
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if (\preg_match(self::PARSE_REGEXP_NUMERICAL, $value, $matches, PREG_UNMATCHED_AS_NULL) !== 1) {
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throw NumberFormatException::invalidFormat($value);
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}
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$sign = $matches['sign'];
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$point = $matches['point'];
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$integral = $matches['integral'];
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$fractional = $matches['fractional'];
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$exponent = $matches['exponent'];
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if ($integral === null && $fractional === null) {
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throw NumberFormatException::invalidFormat($value);
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}
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if ($integral === null) {
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$integral = '0';
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}
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if ($point !== null || $exponent !== null) {
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$fractional = ($fractional ?? '');
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$exponent = ($exponent !== null) ? (int)$exponent : 0;
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if ($exponent === PHP_INT_MIN || $exponent === PHP_INT_MAX) {
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throw new NumberFormatException('Exponent too large.');
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}
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$unscaledValue = self::cleanUp($sign, $integral . $fractional);
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$scale = \strlen($fractional) - $exponent;
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if ($scale < 0) {
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if ($unscaledValue !== '0') {
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$unscaledValue .= \str_repeat('0', -$scale);
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}
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$scale = 0;
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}
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return new BigDecimal($unscaledValue, $scale);
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}
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$integral = self::cleanUp($sign, $integral);
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return new BigInteger($integral);
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}
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}
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/**
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* Overridden by subclasses to convert a BigNumber to an instance of the subclass.
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*
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* @throws MathException If the value cannot be converted.
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*
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* @psalm-pure
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*/
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abstract protected static function from(BigNumber $number): static;
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/**
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* Proxy method to access BigInteger's protected constructor from sibling classes.
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*
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* @internal
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* @psalm-pure
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*/
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final protected function newBigInteger(string $value) : BigInteger
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{
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return new BigInteger($value);
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}
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/**
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* Proxy method to access BigDecimal's protected constructor from sibling classes.
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*
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* @internal
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* @psalm-pure
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*/
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final protected function newBigDecimal(string $value, int $scale = 0) : BigDecimal
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{
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return new BigDecimal($value, $scale);
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}
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/**
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* Proxy method to access BigRational's protected constructor from sibling classes.
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*
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* @internal
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* @psalm-pure
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*/
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final protected function newBigRational(BigInteger $numerator, BigInteger $denominator, bool $checkDenominator) : BigRational
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{
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return new BigRational($numerator, $denominator, $checkDenominator);
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}
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/**
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* Returns the minimum of the given values.
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*
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* @param BigNumber|int|float|string ...$values The numbers to compare. All the numbers need to be convertible
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* to an instance of the class this method is called on.
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*
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* @throws \InvalidArgumentException If no values are given.
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* @throws MathException If an argument is not valid.
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*
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* @psalm-pure
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*/
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final public static function min(BigNumber|int|float|string ...$values) : static
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{
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$min = null;
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foreach ($values as $value) {
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$value = static::of($value);
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if ($min === null || $value->isLessThan($min)) {
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$min = $value;
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}
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}
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if ($min === null) {
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throw new \InvalidArgumentException(__METHOD__ . '() expects at least one value.');
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}
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return $min;
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}
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/**
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* Returns the maximum of the given values.
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*
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* @param BigNumber|int|float|string ...$values The numbers to compare. All the numbers need to be convertible
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* to an instance of the class this method is called on.
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*
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* @throws \InvalidArgumentException If no values are given.
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* @throws MathException If an argument is not valid.
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*
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* @psalm-pure
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*/
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final public static function max(BigNumber|int|float|string ...$values) : static
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{
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$max = null;
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foreach ($values as $value) {
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$value = static::of($value);
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if ($max === null || $value->isGreaterThan($max)) {
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$max = $value;
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}
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}
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if ($max === null) {
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throw new \InvalidArgumentException(__METHOD__ . '() expects at least one value.');
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}
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return $max;
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}
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/**
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* Returns the sum of the given values.
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*
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* @param BigNumber|int|float|string ...$values The numbers to add. All the numbers need to be convertible
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* to an instance of the class this method is called on.
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*
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* @throws \InvalidArgumentException If no values are given.
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* @throws MathException If an argument is not valid.
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*
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* @psalm-pure
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*/
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final public static function sum(BigNumber|int|float|string ...$values) : static
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{
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/** @var static|null $sum */
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$sum = null;
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foreach ($values as $value) {
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$value = static::of($value);
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$sum = $sum === null ? $value : self::add($sum, $value);
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}
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if ($sum === null) {
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throw new \InvalidArgumentException(__METHOD__ . '() expects at least one value.');
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}
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return $sum;
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}
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/**
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* Adds two BigNumber instances in the correct order to avoid a RoundingNecessaryException.
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*
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* @todo This could be better resolved by creating an abstract protected method in BigNumber, and leaving to
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* concrete classes the responsibility to perform the addition themselves or delegate it to the given number,
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* depending on their ability to perform the operation. This will also require a version bump because we're
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* potentially breaking custom BigNumber implementations (if any...)
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*
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* @psalm-pure
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*/
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private static function add(BigNumber $a, BigNumber $b) : BigNumber
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{
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if ($a instanceof BigRational) {
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return $a->plus($b);
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}
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if ($b instanceof BigRational) {
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return $b->plus($a);
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}
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if ($a instanceof BigDecimal) {
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return $a->plus($b);
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}
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if ($b instanceof BigDecimal) {
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return $b->plus($a);
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}
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/** @var BigInteger $a */
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return $a->plus($b);
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}
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/**
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* Removes optional leading zeros and applies sign.
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*
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* @param string|null $sign The sign, '+' or '-', optional. Null is allowed for convenience and treated as '+'.
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* @param string $number The number, validated as a non-empty string of digits.
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*
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* @psalm-pure
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*/
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private static function cleanUp(string|null $sign, string $number) : string
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{
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$number = \ltrim($number, '0');
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if ($number === '') {
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return '0';
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}
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return $sign === '-' ? '-' . $number : $number;
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}
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/**
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* Checks if this number is equal to the given one.
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*/
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final public function isEqualTo(BigNumber|int|float|string $that) : bool
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{
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return $this->compareTo($that) === 0;
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}
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/**
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* Checks if this number is strictly lower than the given one.
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*/
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final public function isLessThan(BigNumber|int|float|string $that) : bool
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{
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return $this->compareTo($that) < 0;
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}
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/**
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* Checks if this number is lower than or equal to the given one.
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*/
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final public function isLessThanOrEqualTo(BigNumber|int|float|string $that) : bool
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{
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return $this->compareTo($that) <= 0;
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}
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/**
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* Checks if this number is strictly greater than the given one.
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*/
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final public function isGreaterThan(BigNumber|int|float|string $that) : bool
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{
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return $this->compareTo($that) > 0;
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}
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/**
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* Checks if this number is greater than or equal to the given one.
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*/
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final public function isGreaterThanOrEqualTo(BigNumber|int|float|string $that) : bool
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{
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return $this->compareTo($that) >= 0;
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}
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/**
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* Checks if this number equals zero.
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*/
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final public function isZero() : bool
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{
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return $this->getSign() === 0;
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}
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/**
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* Checks if this number is strictly negative.
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*/
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final public function isNegative() : bool
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{
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return $this->getSign() < 0;
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}
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/**
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* Checks if this number is negative or zero.
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*/
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final public function isNegativeOrZero() : bool
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{
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return $this->getSign() <= 0;
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}
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/**
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* Checks if this number is strictly positive.
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*/
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final public function isPositive() : bool
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{
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return $this->getSign() > 0;
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}
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/**
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* Checks if this number is positive or zero.
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*/
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final public function isPositiveOrZero() : bool
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{
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return $this->getSign() >= 0;
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}
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/**
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* Returns the sign of this number.
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*
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* @psalm-return -1|0|1
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*
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* @return int -1 if the number is negative, 0 if zero, 1 if positive.
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*/
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abstract public function getSign() : int;
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/**
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* Compares this number to the given one.
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*
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* @psalm-return -1|0|1
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*
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* @return int -1 if `$this` is lower than, 0 if equal to, 1 if greater than `$that`.
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*
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* @throws MathException If the number is not valid.
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*/
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abstract public function compareTo(BigNumber|int|float|string $that) : int;
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/**
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* Converts this number to a BigInteger.
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*
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* @throws RoundingNecessaryException If this number cannot be converted to a BigInteger without rounding.
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*/
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abstract public function toBigInteger() : BigInteger;
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/**
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* Converts this number to a BigDecimal.
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*
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* @throws RoundingNecessaryException If this number cannot be converted to a BigDecimal without rounding.
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*/
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abstract public function toBigDecimal() : BigDecimal;
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/**
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* Converts this number to a BigRational.
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*/
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abstract public function toBigRational() : BigRational;
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/**
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* Converts this number to a BigDecimal with the given scale, using rounding if necessary.
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*
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* @param int $scale The scale of the resulting `BigDecimal`.
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* @param RoundingMode $roundingMode An optional rounding mode, defaults to UNNECESSARY.
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*
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* @throws RoundingNecessaryException If this number cannot be converted to the given scale without rounding.
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* This only applies when RoundingMode::UNNECESSARY is used.
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*/
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abstract public function toScale(int $scale, RoundingMode $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal;
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/**
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* Returns the exact value of this number as a native integer.
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*
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* If this number cannot be converted to a native integer without losing precision, an exception is thrown.
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* Note that the acceptable range for an integer depends on the platform and differs for 32-bit and 64-bit.
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*
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* @throws MathException If this number cannot be exactly converted to a native integer.
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*/
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abstract public function toInt() : int;
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/**
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* Returns an approximation of this number as a floating-point value.
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*
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* Note that this method can discard information as the precision of a floating-point value
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* is inherently limited.
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*
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* If the number is greater than the largest representable floating point number, positive infinity is returned.
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* If the number is less than the smallest representable floating point number, negative infinity is returned.
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*/
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abstract public function toFloat() : float;
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/**
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* Returns a string representation of this number.
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*
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* The output of this method can be parsed by the `of()` factory method;
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* this will yield an object equal to this one, without any information loss.
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*/
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abstract public function __toString() : string;
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final public function jsonSerialize() : string
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{
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return $this->__toString();
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}
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}
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