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Edit File : BigDecimal.php \| Size : 22.19 KB
<?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(); } [, $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; } } Back

Edit File : BigDecimal.php | Size : 22.19 KB

<?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();
        }

[, $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;
    }
}

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