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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();
+ }
+
+ [, $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;
+ }
+}