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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;
/**
* Common interface for arbitrary-precision rational numbers.
*
* @psalm-immutable
*/
abstract class BigNumber implements \JsonSerializable
{
/**
* The regular expression used to parse integer or decimal numbers.
*/
private const PARSE_REGEXP_NUMERICAL =
'/^' .
'(?<sign>[\-\+])?' .
'(?<integral>[0-9]+)?' .
'(?<point>\.)?' .
'(?<fractional>[0-9]+)?' .
'(?:[eE](?<exponent>[\-\+]?[0-9]+))?' .
'$/';
/**
* The regular expression used to parse rational numbers.
*/
private const PARSE_REGEXP_RATIONAL =
'/^' .
'(?<sign>[\-\+])?' .
'(?<numerator>[0-9]+)' .
'\/?' .
'(?<denominator>[0-9]+)' .
'$/';
/**
* 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
*
* @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
*/
final public static function of(BigNumber|int|float|string $value) : static
{
$value = self::_of($value);
if (static::class === BigNumber::class) {
// https://github.com/vimeo/psalm/issues/10309
assert($value instanceof static);
return $value;
}
return static::from($value);
}
/**
* @psalm-pure
*/
private static function _of(BigNumber|int|float|string $value) : BigNumber
{
if ($value instanceof BigNumber) {
return $value;
}
if (\is_int($value)) {
return new BigInteger((string) $value);
}
if (is_float($value)) {
$value = (string) $value;
}
if (str_contains($value, '/')) {
// Rational number
if (\preg_match(self::PARSE_REGEXP_RATIONAL, $value, $matches, PREG_UNMATCHED_AS_NULL) !== 1) {
throw NumberFormatException::invalidFormat($value);
}
$sign = $matches['sign'];
$numerator = $matches['numerator'];
$denominator = $matches['denominator'];
assert($numerator !== null);
assert($denominator !== null);
$numerator = self::cleanUp($sign, $numerator);
$denominator = self::cleanUp(null, $denominator);
if ($denominator === '0') {
throw DivisionByZeroException::denominatorMustNotBeZero();
}
return new BigRational(
new BigInteger($numerator),
new BigInteger($denominator),
false
);
} else {
// Integer or decimal number
if (\preg_match(self::PARSE_REGEXP_NUMERICAL, $value, $matches, PREG_UNMATCHED_AS_NULL) !== 1) {
throw NumberFormatException::invalidFormat($value);
}
$sign = $matches['sign'];
$point = $matches['point'];
$integral = $matches['integral'];
$fractional = $matches['fractional'];
$exponent = $matches['exponent'];
if ($integral === null && $fractional === null) {
throw NumberFormatException::invalidFormat($value);
}
if ($integral === null) {
$integral = '0';
}
if ($point !== null || $exponent !== null) {
$fractional = ($fractional ?? '');
$exponent = ($exponent !== null) ? (int)$exponent : 0;
if ($exponent === PHP_INT_MIN || $exponent === PHP_INT_MAX) {
throw new NumberFormatException('Exponent too large.');
}
$unscaledValue = self::cleanUp($sign, $integral . $fractional);
$scale = \strlen($fractional) - $exponent;
if ($scale < 0) {
if ($unscaledValue !== '0') {
$unscaledValue .= \str_repeat('0', -$scale);
}
$scale = 0;
}
return new BigDecimal($unscaledValue, $scale);
}
$integral = self::cleanUp($sign, $integral);
return new BigInteger($integral);
}
}
/**
* Overridden by subclasses to convert a BigNumber to an instance of the subclass.
*
* @throws MathException If the value cannot be converted.
*
* @psalm-pure
*/
abstract protected static function from(BigNumber $number): static;
/**
* Proxy method to access BigInteger's protected constructor from sibling classes.
*
* @internal
* @psalm-pure
*/
final protected function newBigInteger(string $value) : BigInteger
{
return new BigInteger($value);
}
/**
* Proxy method to access BigDecimal's protected constructor from sibling classes.
*
* @internal
* @psalm-pure
*/
final protected function newBigDecimal(string $value, int $scale = 0) : BigDecimal
{
return new BigDecimal($value, $scale);
}
/**
* Proxy method to access BigRational's protected constructor from sibling classes.
*
* @internal
* @psalm-pure
*/
final protected function newBigRational(BigInteger $numerator, BigInteger $denominator, bool $checkDenominator) : BigRational
{
return new BigRational($numerator, $denominator, $checkDenominator);
}
/**
* Returns the minimum of the given values.
*
* @param BigNumber|int|float|string ...$values The numbers to compare. All the numbers need to be convertible
* to an instance of the class this method is called on.
*
* @throws \InvalidArgumentException If no values are given.
* @throws MathException If an argument is not valid.
*
* @psalm-pure
*/
final public static function min(BigNumber|int|float|string ...$values) : static
{
$min = null;
foreach ($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.
*
* @throws \InvalidArgumentException If no values are given.
* @throws MathException If an argument is not valid.
*
* @psalm-pure
*/
final public static function max(BigNumber|int|float|string ...$values) : static
{
$max = null;
foreach ($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.
*
* @throws \InvalidArgumentException If no values are given.
* @throws MathException If an argument is not valid.
*
* @psalm-pure
*/
final public static function sum(BigNumber|int|float|string ...$values) : static
{
/** @var static|null $sum */
$sum = null;
foreach ($values as $value) {
$value = static::of($value);
$sum = $sum === null ? $value : self::add($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...)
*
* @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 applies sign.
*
* @param string|null $sign The sign, '+' or '-', optional. Null is allowed for convenience and treated as '+'.
* @param string $number The number, validated as a non-empty string of digits.
*
* @psalm-pure
*/
private static function cleanUp(string|null $sign, string $number) : string
{
$number = \ltrim($number, '0');
if ($number === '') {
return '0';
}
return $sign === '-' ? '-' . $number : $number;
}
/**
* Checks if this number is equal to the given one.
*/
final public function isEqualTo(BigNumber|int|float|string $that) : bool
{
return $this->compareTo($that) === 0;
}
/**
* Checks if this number is strictly lower than the given one.
*/
final public function isLessThan(BigNumber|int|float|string $that) : bool
{
return $this->compareTo($that) < 0;
}
/**
* Checks if this number is lower than or equal to the given one.
*/
final public function isLessThanOrEqualTo(BigNumber|int|float|string $that) : bool
{
return $this->compareTo($that) <= 0;
}
/**
* Checks if this number is strictly greater than the given one.
*/
final public function isGreaterThan(BigNumber|int|float|string $that) : bool
{
return $this->compareTo($that) > 0;
}
/**
* Checks if this number is greater than or equal to the given one.
*/
final public function isGreaterThanOrEqualTo(BigNumber|int|float|string $that) : bool
{
return $this->compareTo($that) >= 0;
}
/**
* Checks if this number equals zero.
*/
final public function isZero() : bool
{
return $this->getSign() === 0;
}
/**
* Checks if this number is strictly negative.
*/
final public function isNegative() : bool
{
return $this->getSign() < 0;
}
/**
* Checks if this number is negative or zero.
*/
final public function isNegativeOrZero() : bool
{
return $this->getSign() <= 0;
}
/**
* Checks if this number is strictly positive.
*/
final public function isPositive() : bool
{
return $this->getSign() > 0;
}
/**
* Checks if this number is positive or zero.
*/
final public function isPositiveOrZero() : bool
{
return $this->getSign() >= 0;
}
/**
* Returns the sign of this number.
*
* @psalm-return -1|0|1
*
* @return int -1 if the number is negative, 0 if zero, 1 if positive.
*/
abstract public function getSign() : int;
/**
* Compares this number to the given one.
*
* @psalm-return -1|0|1
*
* @return int -1 if `$this` is lower than, 0 if equal to, 1 if greater than `$that`.
*
* @throws MathException If the number is not valid.
*/
abstract public function compareTo(BigNumber|int|float|string $that) : int;
/**
* Converts this number to a BigInteger.
*
* @throws RoundingNecessaryException If this number cannot be converted to a BigInteger without rounding.
*/
abstract public function toBigInteger() : BigInteger;
/**
* Converts this number to a BigDecimal.
*
* @throws RoundingNecessaryException If this number cannot be converted to a BigDecimal without rounding.
*/
abstract public function toBigDecimal() : BigDecimal;
/**
* Converts this number to a BigRational.
*/
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 RoundingMode $roundingMode An optional rounding mode, defaults to UNNECESSARY.
*
* @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, RoundingMode $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.
*
* @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.
*/
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.
*/
abstract public function __toString() : string;
final public function jsonSerialize() : string
{
return $this->__toString();
}
}
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