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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\NegativeNumberException;
use Brick\Math\Internal\Calculator;
/**
* Immutable, arbitrary-precision signed decimal numbers.
*
* @psalm-immutable
*/
final class BigDecimal extends BigNumber
{
/**
* The unscaled value of this decimal number.
*
* This is a string of digits with an optional leading minus sign.
* No leading zero must be present.
* No leading minus sign must be present if the value is 0.
*
* @var string
*/
private $value;
/**
* The scale (number of digits after the decimal point) of this decimal number.
*
* This must be zero or more.
*
* @var int
*/
private $scale;
/**
* Protected constructor. Use a factory method to obtain an instance.
*
* @param string $value The unscaled value, validated.
* @param int $scale The scale, validated.
*/
protected function __construct(string $value, int $scale = 0)
{
$this->value = $value;
$this->scale = $scale;
}
/**
* Creates a BigDecimal of the given value.
*
* @param BigNumber|int|float|string $value
*
* @return BigDecimal
*
* @throws MathException If the value cannot be converted to a BigDecimal.
*
* @psalm-pure
*/
public static function of($value) : BigNumber
{
return parent::of($value)->toBigDecimal();
}
/**
* Creates a BigDecimal from an unscaled value and a scale.
*
* Example: `(12345, 3)` will result in the BigDecimal `12.345`.
*
* @param BigNumber|int|float|string $value The unscaled value. Must be convertible to a BigInteger.
* @param int $scale The scale of the number, positive or zero.
*
* @return BigDecimal
*
* @throws \InvalidArgumentException If the scale is negative.
*
* @psalm-pure
*/
public static function ofUnscaledValue($value, int $scale = 0) : BigDecimal
{
if ($scale < 0) {
throw new \InvalidArgumentException('The scale cannot be negative.');
}
return new BigDecimal((string) BigInteger::of($value), $scale);
}
/**
* Returns a BigDecimal representing zero, with a scale of zero.
*
* @return BigDecimal
*
* @psalm-pure
*/
public static function zero() : BigDecimal
{
/** @psalm-suppress ImpureStaticVariable */
static $zero;
if ($zero === null) {
$zero = new BigDecimal('0');
}
return $zero;
}
/**
* Returns a BigDecimal representing one, with a scale of zero.
*
* @return BigDecimal
*
* @psalm-pure
*/
public static function one() : BigDecimal
{
/** @psalm-suppress ImpureStaticVariable */
static $one;
if ($one === null) {
$one = new BigDecimal('1');
}
return $one;
}
/**
* Returns a BigDecimal representing ten, with a scale of zero.
*
* @return BigDecimal
*
* @psalm-pure
*/
public static function ten() : BigDecimal
{
/** @psalm-suppress ImpureStaticVariable */
static $ten;
if ($ten === null) {
$ten = new BigDecimal('10');
}
return $ten;
}
/**
* Returns the sum of this number and the given one.
*
* The result has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The number to add. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the number is not valid, or is not convertible to a BigDecimal.
*/
public function plus($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '0' && $that->scale <= $this->scale) {
return $this;
}
if ($this->value === '0' && $this->scale <= $that->scale) {
return $that;
}
[$a, $b] = $this->scaleValues($this, $that);
$value = Calculator::get()->add($a, $b);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
return new BigDecimal($value, $scale);
}
/**
* Returns the difference of this number and the given one.
*
* The result has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The number to subtract. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the number is not valid, or is not convertible to a BigDecimal.
*/
public function minus($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '0' && $that->scale <= $this->scale) {
return $this;
}
[$a, $b] = $this->scaleValues($this, $that);
$value = Calculator::get()->sub($a, $b);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
return new BigDecimal($value, $scale);
}
/**
* Returns the product of this number and the given one.
*
* The result has a scale of `$this->scale + $that->scale`.
*
* @param BigNumber|int|float|string $that The multiplier. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the multiplier is not a valid number, or is not convertible to a BigDecimal.
*/
public function multipliedBy($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '1' && $that->scale === 0) {
return $this;
}
if ($this->value === '1' && $this->scale === 0) {
return $that;
}
$value = Calculator::get()->mul($this->value, $that->value);
$scale = $this->scale + $that->scale;
return new BigDecimal($value, $scale);
}
/**
* Returns the result of the division of this number by the given one, at the given scale.
*
* @param BigNumber|int|float|string $that The divisor.
* @param int|null $scale The desired scale, or null to use the scale of this number.
* @param int $roundingMode An optional rounding mode.
*
* @return BigDecimal
*
* @throws \InvalidArgumentException If the scale or rounding mode is invalid.
* @throws MathException If the number is invalid, is zero, or rounding was necessary.
*/
public function dividedBy($that, ?int $scale = null, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
if ($scale === null) {
$scale = $this->scale;
} elseif ($scale < 0) {
throw new \InvalidArgumentException('Scale cannot be negative.');
}
if ($that->value === '1' && $that->scale === 0 && $scale === $this->scale) {
return $this;
}
$p = $this->valueWithMinScale($that->scale + $scale);
$q = $that->valueWithMinScale($this->scale - $scale);
$result = Calculator::get()->divRound($p, $q, $roundingMode);
return new BigDecimal($result, $scale);
}
/**
* Returns the exact result of the division of this number by the given one.
*
* The scale of the result is automatically calculated to fit all the fraction digits.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal The result.
*
* @throws MathException If the divisor is not a valid number, is not convertible to a BigDecimal, is zero,
* or the result yields an infinite number of digits.
*/
public function exactlyDividedBy($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->value === '0') {
throw DivisionByZeroException::divisionByZero();
}
[$a, $b] = $this->scaleValues($this, $that);
$d = \rtrim($b, '0');
$scale = \strlen($b) - \strlen($d);
$calculator = Calculator::get();
foreach ([5, 2] as $prime) {
for (;;) {
$lastDigit = (int) $d[-1];
if ($lastDigit % $prime !== 0) {
break;
}
$d = $calculator->divQ($d, (string) $prime);
$scale++;
}
}
return $this->dividedBy($that, $scale)->stripTrailingZeros();
}
/**
* Returns this number exponentiated to the given value.
*
* The result has a scale of `$this->scale * $exponent`.
*
* @param int $exponent The exponent.
*
* @return BigDecimal The result.
*
* @throws \InvalidArgumentException If the exponent is not in the range 0 to 1,000,000.
*/
public function power(int $exponent) : BigDecimal
{
if ($exponent === 0) {
return BigDecimal::one();
}
if ($exponent === 1) {
return $this;
}
if ($exponent < 0 || $exponent > Calculator::MAX_POWER) {
throw new \InvalidArgumentException(\sprintf(
'The exponent %d is not in the range 0 to %d.',
$exponent,
Calculator::MAX_POWER
));
}
return new BigDecimal(Calculator::get()->pow($this->value, $exponent), $this->scale * $exponent);
}
/**
* Returns the quotient of the division of this number by this given one.
*
* The quotient has a scale of `0`.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal The quotient.
*
* @throws MathException If the divisor is not a valid decimal number, or is zero.
*/
public function quotient($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$p = $this->valueWithMinScale($that->scale);
$q = $that->valueWithMinScale($this->scale);
$quotient = Calculator::get()->divQ($p, $q);
return new BigDecimal($quotient, 0);
}
/**
* Returns the remainder of the division of this number by this given one.
*
* The remainder has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal The remainder.
*
* @throws MathException If the divisor is not a valid decimal number, or is zero.
*/
public function remainder($that) : BigDecimal
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$p = $this->valueWithMinScale($that->scale);
$q = $that->valueWithMinScale($this->scale);
$remainder = Calculator::get()->divR($p, $q);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
return new BigDecimal($remainder, $scale);
}
/**
* Returns the quotient and remainder of the division of this number by the given one.
*
* The quotient has a scale of `0`, and the remainder has a scale of `max($this->scale, $that->scale)`.
*
* @param BigNumber|int|float|string $that The divisor. Must be convertible to a BigDecimal.
*
* @return BigDecimal[] An array containing the quotient and the remainder.
*
* @throws MathException If the divisor is not a valid decimal number, or is zero.
*/
public function quotientAndRemainder($that) : array
{
$that = BigDecimal::of($that);
if ($that->isZero()) {
throw DivisionByZeroException::divisionByZero();
}
$p = $this->valueWithMinScale($that->scale);
$q = $that->valueWithMinScale($this->scale);
[$quotient, $remainder] = Calculator::get()->divQR($p, $q);
$scale = $this->scale > $that->scale ? $this->scale : $that->scale;
$quotient = new BigDecimal($quotient, 0);
$remainder = new BigDecimal($remainder, $scale);
return [$quotient, $remainder];
}
/**
* Returns the square root of this number, rounded down to the given number of decimals.
*
* @param int $scale
*
* @return BigDecimal
*
* @throws \InvalidArgumentException If the scale is negative.
* @throws NegativeNumberException If this number is negative.
*/
public function sqrt(int $scale) : BigDecimal
{
if ($scale < 0) {
throw new \InvalidArgumentException('Scale cannot be negative.');
}
if ($this->value === '0') {
return new BigDecimal('0', $scale);
}
if ($this->value[0] === '-') {
throw new NegativeNumberException('Cannot calculate the square root of a negative number.');
}
$value = $this->value;
$addDigits = 2 * $scale - $this->scale;
if ($addDigits > 0) {
// add zeros
$value .= \str_repeat('0', $addDigits);
} elseif ($addDigits < 0) {
// trim digits
if (-$addDigits >= \strlen($this->value)) {
// requesting a scale too low, will always yield a zero result
return new BigDecimal('0', $scale);
}
$value = \substr($value, 0, $addDigits);
}
$value = Calculator::get()->sqrt($value);
return new BigDecimal($value, $scale);
}
/**
* Returns a copy of this BigDecimal with the decimal point moved $n places to the left.
*
* @param int $n
*
* @return BigDecimal
*/
public function withPointMovedLeft(int $n) : BigDecimal
{
if ($n === 0) {
return $this;
}
if ($n < 0) {
return $this->withPointMovedRight(-$n);
}
return new BigDecimal($this->value, $this->scale + $n);
}
/**
* Returns a copy of this BigDecimal with the decimal point moved $n places to the right.
*
* @param int $n
*
* @return BigDecimal
*/
public function withPointMovedRight(int $n) : BigDecimal
{
if ($n === 0) {
return $this;
}
if ($n < 0) {
return $this->withPointMovedLeft(-$n);
}
$value = $this->value;
$scale = $this->scale - $n;
if ($scale < 0) {
if ($value !== '0') {
$value .= \str_repeat('0', -$scale);
}
$scale = 0;
}
return new BigDecimal($value, $scale);
}
/**
* Returns a copy of this BigDecimal with any trailing zeros removed from the fractional part.
*
* @return BigDecimal
*/
public function stripTrailingZeros() : BigDecimal
{
if ($this->scale === 0) {
return $this;
}
$trimmedValue = \rtrim($this->value, '0');
if ($trimmedValue === '') {
return BigDecimal::zero();
}
$trimmableZeros = \strlen($this->value) - \strlen($trimmedValue);
if ($trimmableZeros === 0) {
return $this;
}
if ($trimmableZeros > $this->scale) {
$trimmableZeros = $this->scale;
}
$value = \substr($this->value, 0, -$trimmableZeros);
$scale = $this->scale - $trimmableZeros;
return new BigDecimal($value, $scale);
}
/**
* Returns the absolute value of this number.
*
* @return BigDecimal
*/
public function abs() : BigDecimal
{
return $this->isNegative() ? $this->negated() : $this;
}
/**
* Returns the negated value of this number.
*
* @return BigDecimal
*/
public function negated() : BigDecimal
{
return new BigDecimal(Calculator::get()->neg($this->value), $this->scale);
}
/**
* {@inheritdoc}
*/
public function compareTo($that) : int
{
$that = BigNumber::of($that);
if ($that instanceof BigInteger) {
$that = $that->toBigDecimal();
}
if ($that instanceof BigDecimal) {
[$a, $b] = $this->scaleValues($this, $that);
return Calculator::get()->cmp($a, $b);
}
return - $that->compareTo($this);
}
/**
* {@inheritdoc}
*/
public function getSign() : int
{
return ($this->value === '0') ? 0 : (($this->value[0] === '-') ? -1 : 1);
}
/**
* @return BigInteger
*/
public function getUnscaledValue() : BigInteger
{
return BigInteger::create($this->value);
}
/**
* @return int
*/
public function getScale() : int
{
return $this->scale;
}
/**
* Returns a string representing the integral part of this decimal number.
*
* Example: `-123.456` => `-123`.
*
* @return string
*/
public function getIntegralPart() : string
{
if ($this->scale === 0) {
return $this->value;
}
$value = $this->getUnscaledValueWithLeadingZeros();
return \substr($value, 0, -$this->scale);
}
/**
* Returns a string representing the fractional part of this decimal number.
*
* If the scale is zero, an empty string is returned.
*
* Examples: `-123.456` => '456', `123` => ''.
*
* @return string
*/
public function getFractionalPart() : string
{
if ($this->scale === 0) {
return '';
}
$value = $this->getUnscaledValueWithLeadingZeros();
return \substr($value, -$this->scale);
}
/**
* Returns whether this decimal number has a non-zero fractional part.
*
* @return bool
*/
public function hasNonZeroFractionalPart() : bool
{
return $this->getFractionalPart() !== \str_repeat('0', $this->scale);
}
/**
* {@inheritdoc}
*/
public function toBigInteger() : BigInteger
{
if ($this->scale === 0) {
$zeroScaleDecimal = $this;
} else {
$zeroScaleDecimal = $this->dividedBy(1, 0);
}
return BigInteger::create($zeroScaleDecimal->value);
}
/**
* {@inheritdoc}
*/
public function toBigDecimal() : BigDecimal
{
return $this;
}
/**
* {@inheritdoc}
*/
public function toBigRational() : BigRational
{
$numerator = BigInteger::create($this->value);
$denominator = BigInteger::create('1' . \str_repeat('0', $this->scale));
return BigRational::create($numerator, $denominator, false);
}
/**
* {@inheritdoc}
*/
public function toScale(int $scale, int $roundingMode = RoundingMode::UNNECESSARY) : BigDecimal
{
if ($scale === $this->scale) {
return $this;
}
return $this->dividedBy(BigDecimal::one(), $scale, $roundingMode);
}
/**
* {@inheritdoc}
*/
public function toInt() : int
{
return $this->toBigInteger()->toInt();
}
/**
* {@inheritdoc}
*/
public function toFloat() : float
{
return (float) (string) $this;
}
/**
* {@inheritdoc}
*/
public function __toString() : string
{
if ($this->scale === 0) {
return $this->value;
}
$value = $this->getUnscaledValueWithLeadingZeros();
return \substr($value, 0, -$this->scale) . '.' . \substr($value, -$this->scale);
}
/**
* This method is required by interface Serializable and SHOULD NOT be accessed directly.
*
* @internal
*
* @return string
*/
public function serialize() : string
{
return $this->value . ':' . $this->scale;
}
/**
* 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($this->value)) {
throw new \LogicException('unserialize() is an internal function, it must not be called directly.');
}
[$value, $scale] = \explode(':', $value);
$this->value = $value;
$this->scale = (int) $scale;
}
/**
* Puts the internal values of the given decimal numbers on the same scale.
*
* @param BigDecimal $x The first decimal number.
* @param BigDecimal $y The second decimal number.
*
* @return array{0: string, 1: string} The scaled integer values of $x and $y.
*/
private function scaleValues(BigDecimal $x, BigDecimal $y) : array
{
$a = $x->value;
$b = $y->value;
if ($b !== '0' && $x->scale > $y->scale) {
$b .= \str_repeat('0', $x->scale - $y->scale);
} elseif ($a !== '0' && $x->scale < $y->scale) {
$a .= \str_repeat('0', $y->scale - $x->scale);
}
return [$a, $b];
}
/**
* @param int $scale
*
* @return string
*/
private function valueWithMinScale(int $scale) : string
{
$value = $this->value;
if ($this->value !== '0' && $scale > $this->scale) {
$value .= \str_repeat('0', $scale - $this->scale);
}
return $value;
}
/**
* Adds leading zeros if necessary to the unscaled value to represent the full decimal number.
*
* @return string
*/
private function getUnscaledValueWithLeadingZeros() : string
{
$value = $this->value;
$targetLength = $this->scale + 1;
$negative = ($value[0] === '-');
$length = \strlen($value);
if ($negative) {
$length--;
}
if ($length >= $targetLength) {
return $this->value;
}
if ($negative) {
$value = \substr($value, 1);
}
$value = \str_pad($value, $targetLength, '0', STR_PAD_LEFT);
if ($negative) {
$value = '-' . $value;
}
return $value;
}
}