initial commit; version 22.5.12042

libs/Brick/Math/Internal/Calculator.php

@@ -0,0 +1,756 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Brick\Math\Internal;
+
+use Brick\Math\Exception\RoundingNecessaryException;
+use Brick\Math\RoundingMode;
+
+/**
+ * Performs basic operations on arbitrary size integers.
+ *
+ * Unless otherwise specified, all parameters must be validated as non-empty strings of digits,
+ * without leading zero, and with an optional leading minus sign if the number is not zero.
+ *
+ * Any other parameter format will lead to undefined behaviour.
+ * All methods must return strings respecting this format, unless specified otherwise.
+ *
+ * @internal
+ *
+ * @psalm-immutable
+ */
+abstract class Calculator
+{
+    /**
+     * The maximum exponent value allowed for the pow() method.
+     */
+    public const MAX_POWER = 1000000;
+
+    /**
+     * The alphabet for converting from and to base 2 to 36, lowercase.
+     */
+    public const ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
+
+    /**
+     * The Calculator instance in use.
+     *
+     * @var Calculator|null
+     */
+    private static $instance;
+
+    /**
+     * Sets the Calculator instance to use.
+     *
+     * An instance is typically set only in unit tests: the autodetect is usually the best option.
+     *
+     * @param Calculator|null $calculator The calculator instance, or NULL to revert to autodetect.
+     *
+     * @return void
+     */
+    final public static function set(?Calculator $calculator) : void
+    {
+        self::$instance = $calculator;
+    }
+
+    /**
+     * Returns the Calculator instance to use.
+     *
+     * If none has been explicitly set, the fastest available implementation will be returned.
+     *
+     * @return Calculator
+     *
+     * @psalm-pure
+     * @psalm-suppress ImpureStaticProperty
+     */
+    final public static function get() : Calculator
+    {
+        if (self::$instance === null) {
+            /** @psalm-suppress ImpureMethodCall */
+            self::$instance = self::detect();
+        }
+
+        return self::$instance;
+    }
+
+    /**
+     * Returns the fastest available Calculator implementation.
+     *
+     * @codeCoverageIgnore
+     *
+     * @return Calculator
+     */
+    private static function detect() : Calculator
+    {
+        if (\extension_loaded('gmp')) {
+            return new Calculator\GmpCalculator();
+        }
+
+        if (\extension_loaded('bcmath')) {
+            return new Calculator\BcMathCalculator();
+        }
+
+        return new Calculator\NativeCalculator();
+    }
+
+    /**
+     * Extracts the sign & digits of the operands.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return array{bool, bool, string, string} Whether $a and $b are negative, followed by their digits.
+     */
+    final protected function init(string $a, string $b) : array
+    {
+        return [
+            $aNeg = ($a[0] === '-'),
+            $bNeg = ($b[0] === '-'),
+
+            $aNeg ? \substr($a, 1) : $a,
+            $bNeg ? \substr($b, 1) : $b,
+        ];
+    }
+
+    /**
+     * Returns the absolute value of a number.
+     *
+     * @param string $n The number.
+     *
+     * @return string The absolute value.
+     */
+    final public function abs(string $n) : string
+    {
+        return ($n[0] === '-') ? \substr($n, 1) : $n;
+    }
+
+    /**
+     * Negates a number.
+     *
+     * @param string $n The number.
+     *
+     * @return string The negated value.
+     */
+    final public function neg(string $n) : string
+    {
+        if ($n === '0') {
+            return '0';
+        }
+
+        if ($n[0] === '-') {
+            return \substr($n, 1);
+        }
+
+        return '-' . $n;
+    }
+
+    /**
+     * Compares two numbers.
+     *
+     * @param string $a The first number.
+     * @param string $b The second number.
+     *
+     * @return int [-1, 0, 1] If the first number is less than, equal to, or greater than the second number.
+     */
+    final public function cmp(string $a, string $b) : int
+    {
+        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
+
+        if ($aNeg && ! $bNeg) {
+            return -1;
+        }
+
+        if ($bNeg && ! $aNeg) {
+            return 1;
+        }
+
+        $aLen = \strlen($aDig);
+        $bLen = \strlen($bDig);
+
+        if ($aLen < $bLen) {
+            $result = -1;
+        } elseif ($aLen > $bLen) {
+            $result = 1;
+        } else {
+            $result = $aDig <=> $bDig;
+        }
+
+        return $aNeg ? -$result : $result;
+    }
+
+    /**
+     * Adds two numbers.
+     *
+     * @param string $a The augend.
+     * @param string $b The addend.
+     *
+     * @return string The sum.
+     */
+    abstract public function add(string $a, string $b) : string;
+
+    /**
+     * Subtracts two numbers.
+     *
+     * @param string $a The minuend.
+     * @param string $b The subtrahend.
+     *
+     * @return string The difference.
+     */
+    abstract public function sub(string $a, string $b) : string;
+
+    /**
+     * Multiplies two numbers.
+     *
+     * @param string $a The multiplicand.
+     * @param string $b The multiplier.
+     *
+     * @return string The product.
+     */
+    abstract public function mul(string $a, string $b) : string;
+
+    /**
+     * Returns the quotient of the division of two numbers.
+     *
+     * @param string $a The dividend.
+     * @param string $b The divisor, must not be zero.
+     *
+     * @return string The quotient.
+     */
+    abstract public function divQ(string $a, string $b) : string;
+
+    /**
+     * Returns the remainder of the division of two numbers.
+     *
+     * @param string $a The dividend.
+     * @param string $b The divisor, must not be zero.
+     *
+     * @return string The remainder.
+     */
+    abstract public function divR(string $a, string $b) : string;
+
+    /**
+     * Returns the quotient and remainder of the division of two numbers.
+     *
+     * @param string $a The dividend.
+     * @param string $b The divisor, must not be zero.
+     *
+     * @return string[] An array containing the quotient and remainder.
+     */
+    abstract public function divQR(string $a, string $b) : array;
+
+    /**
+     * Exponentiates a number.
+     *
+     * @param string $a The base number.
+     * @param int    $e The exponent, validated as an integer between 0 and MAX_POWER.
+     *
+     * @return string The power.
+     */
+    abstract public function pow(string $a, int $e) : string;
+
+    /**
+     * @param string $a
+     * @param string $b The modulus; must not be zero.
+     *
+     * @return string
+     */
+    public function mod(string $a, string $b) : string
+    {
+        return $this->divR($this->add($this->divR($a, $b), $b), $b);
+    }
+
+    /**
+     * Returns the modular multiplicative inverse of $x modulo $m.
+     *
+     * If $x has no multiplicative inverse mod m, this method must return null.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library has built-in support.
+     *
+     * @param string $x
+     * @param string $m The modulus; must not be negative or zero.
+     *
+     * @return string|null
+     */
+    public function modInverse(string $x, string $m) : ?string
+    {
+        if ($m === '1') {
+            return '0';
+        }
+
+        $modVal = $x;
+
+        if ($x[0] === '-' || ($this->cmp($this->abs($x), $m) >= 0)) {
+            $modVal = $this->mod($x, $m);
+        }
+
+        $x = '0';
+        $y = '0';
+        $g = $this->gcdExtended($modVal, $m, $x, $y);
+
+        if ($g !== '1') {
+            return null;
+        }
+
+        return $this->mod($this->add($this->mod($x, $m), $m), $m);
+    }
+
+    /**
+     * Raises a number into power with modulo.
+     *
+     * @param string $base The base number; must be positive or zero.
+     * @param string $exp  The exponent; must be positive or zero.
+     * @param string $mod  The modulus; must be strictly positive.
+     *
+     * @return string The power.
+     */
+    abstract public function modPow(string $base, string $exp, string $mod) : string;
+
+    /**
+     * Returns the greatest common divisor of the two numbers.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library
+     * has built-in support for GCD calculations.
+     *
+     * @param string $a The first number.
+     * @param string $b The second number.
+     *
+     * @return string The GCD, always positive, or zero if both arguments are zero.
+     */
+    public function gcd(string $a, string $b) : string
+    {
+        if ($a === '0') {
+            return $this->abs($b);
+        }
+
+        if ($b === '0') {
+            return $this->abs($a);
+        }
+
+        return $this->gcd($b, $this->divR($a, $b));
+    }
+
+    private function gcdExtended(string $a, string $b, string &$x, string &$y) : string
+    {
+        if ($a === '0') {
+            $x = '0';
+            $y = '1';
+
+            return $b;
+        }
+
+        $x1 = '0';
+        $y1 = '0';
+
+        $gcd = $this->gcdExtended($this->mod($b, $a), $a, $x1, $y1);
+
+        $x = $this->sub($y1, $this->mul($this->divQ($b, $a), $x1));
+        $y = $x1;
+
+        return $gcd;
+    }
+
+    /**
+     * Returns the square root of the given number, rounded down.
+     *
+     * The result is the largest x such that x² ≤ n.
+     * The input MUST NOT be negative.
+     *
+     * @param string $n The number.
+     *
+     * @return string The square root.
+     */
+    abstract public function sqrt(string $n) : string;
+
+    /**
+     * Converts a number from an arbitrary base.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library
+     * has built-in support for base conversion.
+     *
+     * @param string $number The number, positive or zero, non-empty, case-insensitively validated for the given base.
+     * @param int    $base   The base of the number, validated from 2 to 36.
+     *
+     * @return string The converted number, following the Calculator conventions.
+     */
+    public function fromBase(string $number, int $base) : string
+    {
+        return $this->fromArbitraryBase(\strtolower($number), self::ALPHABET, $base);
+    }
+
+    /**
+     * Converts a number to an arbitrary base.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library
+     * has built-in support for base conversion.
+     *
+     * @param string $number The number to convert, following the Calculator conventions.
+     * @param int    $base   The base to convert to, validated from 2 to 36.
+     *
+     * @return string The converted number, lowercase.
+     */
+    public function toBase(string $number, int $base) : string
+    {
+        $negative = ($number[0] === '-');
+
+        if ($negative) {
+            $number = \substr($number, 1);
+        }
+
+        $number = $this->toArbitraryBase($number, self::ALPHABET, $base);
+
+        if ($negative) {
+            return '-' . $number;
+        }
+
+        return $number;
+    }
+
+    /**
+     * Converts a non-negative number in an arbitrary base using a custom alphabet, to base 10.
+     *
+     * @param string $number   The number to convert, validated as a non-empty string,
+     *                         containing only chars in the given alphabet/base.
+     * @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum.
+     * @param int    $base     The base of the number, validated from 2 to alphabet length.
+     *
+     * @return string The number in base 10, following the Calculator conventions.
+     */
+    final public function fromArbitraryBase(string $number, string $alphabet, int $base) : string
+    {
+        // remove leading "zeros"
+        $number = \ltrim($number, $alphabet[0]);
+
+        if ($number === '') {
+            return '0';
+        }
+
+        // optimize for "one"
+        if ($number === $alphabet[1]) {
+            return '1';
+        }
+
+        $result = '0';
+        $power = '1';
+
+        $base = (string) $base;
+
+        for ($i = \strlen($number) - 1; $i >= 0; $i--) {
+            $index = \strpos($alphabet, $number[$i]);
+
+            if ($index !== 0) {
+                $result = $this->add($result, ($index === 1)
+                    ? $power
+                    : $this->mul($power, (string) $index)
+                );
+            }
+
+            if ($i !== 0) {
+                $power = $this->mul($power, $base);
+            }
+        }
+
+        return $result;
+    }
+
+    /**
+     * Converts a non-negative number to an arbitrary base using a custom alphabet.
+     *
+     * @param string $number   The number to convert, positive or zero, following the Calculator conventions.
+     * @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum.
+     * @param int    $base     The base to convert to, validated from 2 to alphabet length.
+     *
+     * @return string The converted number in the given alphabet.
+     */
+    final public function toArbitraryBase(string $number, string $alphabet, int $base) : string
+    {
+        if ($number === '0') {
+            return $alphabet[0];
+        }
+
+        $base = (string) $base;
+        $result = '';
+
+        while ($number !== '0') {
+            [$number, $remainder] = $this->divQR($number, $base);
+            $remainder = (int) $remainder;
+
+            $result .= $alphabet[$remainder];
+        }
+
+        return \strrev($result);
+    }
+
+    /**
+     * Performs a rounded division.
+     *
+     * Rounding is performed when the remainder of the division is not zero.
+     *
+     * @param string $a            The dividend.
+     * @param string $b            The divisor, must not be zero.
+     * @param int    $roundingMode The rounding mode.
+     *
+     * @return string
+     *
+     * @throws \InvalidArgumentException  If the rounding mode is invalid.
+     * @throws RoundingNecessaryException If RoundingMode::UNNECESSARY is provided but rounding is necessary.
+     */
+    final public function divRound(string $a, string $b, int $roundingMode) : string
+    {
+        [$quotient, $remainder] = $this->divQR($a, $b);
+
+        $hasDiscardedFraction = ($remainder !== '0');
+        $isPositiveOrZero = ($a[0] === '-') === ($b[0] === '-');
+
+        $discardedFractionSign = function() use ($remainder, $b) : int {
+            $r = $this->abs($this->mul($remainder, '2'));
+            $b = $this->abs($b);
+
+            return $this->cmp($r, $b);
+        };
+
+        $increment = false;
+
+        switch ($roundingMode) {
+            case RoundingMode::UNNECESSARY:
+                if ($hasDiscardedFraction) {
+                    throw RoundingNecessaryException::roundingNecessary();
+                }
+                break;
+
+            case RoundingMode::UP:
+                $increment = $hasDiscardedFraction;
+                break;
+
+            case RoundingMode::DOWN:
+                break;
+
+            case RoundingMode::CEILING:
+                $increment = $hasDiscardedFraction && $isPositiveOrZero;
+                break;
+
+            case RoundingMode::FLOOR:
+                $increment = $hasDiscardedFraction && ! $isPositiveOrZero;
+                break;
+
+            case RoundingMode::HALF_UP:
+                $increment = $discardedFractionSign() >= 0;
+                break;
+
+            case RoundingMode::HALF_DOWN:
+                $increment = $discardedFractionSign() > 0;
+                break;
+
+            case RoundingMode::HALF_CEILING:
+                $increment = $isPositiveOrZero ? $discardedFractionSign() >= 0 : $discardedFractionSign() > 0;
+                break;
+
+            case RoundingMode::HALF_FLOOR:
+                $increment = $isPositiveOrZero ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0;
+                break;
+
+            case RoundingMode::HALF_EVEN:
+                $lastDigit = (int) $quotient[-1];
+                $lastDigitIsEven = ($lastDigit % 2 === 0);
+                $increment = $lastDigitIsEven ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0;
+                break;
+
+            default:
+                throw new \InvalidArgumentException('Invalid rounding mode.');
+        }
+
+        if ($increment) {
+            return $this->add($quotient, $isPositiveOrZero ? '1' : '-1');
+        }
+
+        return $quotient;
+    }
+
+    /**
+     * Calculates bitwise AND of two numbers.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library
+     * has built-in support for bitwise operations.
+     *
+     * @param string $a
+     * @param string $b
+     *
+     * @return string
+     */
+    public function and(string $a, string $b) : string
+    {
+        return $this->bitwise('and', $a, $b);
+    }
+
+    /**
+     * Calculates bitwise OR of two numbers.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library
+     * has built-in support for bitwise operations.
+     *
+     * @param string $a
+     * @param string $b
+     *
+     * @return string
+     */
+    public function or(string $a, string $b) : string
+    {
+        return $this->bitwise('or', $a, $b);
+    }
+
+    /**
+     * Calculates bitwise XOR of two numbers.
+     *
+     * This method can be overridden by the concrete implementation if the underlying library
+     * has built-in support for bitwise operations.
+     *
+     * @param string $a
+     * @param string $b
+     *
+     * @return string
+     */
+    public function xor(string $a, string $b) : string
+    {
+        return $this->bitwise('xor', $a, $b);
+    }
+
+    /**
+     * Performs a bitwise operation on a decimal number.
+     *
+     * @param string $operator The operator to use, must be "and", "or" or "xor".
+     * @param string $a        The left operand.
+     * @param string $b        The right operand.
+     *
+     * @return string
+     */
+    private function bitwise(string $operator, string $a, string $b) : string
+    {
+        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
+
+        $aBin = $this->toBinary($aDig);
+        $bBin = $this->toBinary($bDig);
+
+        $aLen = \strlen($aBin);
+        $bLen = \strlen($bBin);
+
+        if ($aLen > $bLen) {
+            $bBin = \str_repeat("\x00", $aLen - $bLen) . $bBin;
+        } elseif ($bLen > $aLen) {
+            $aBin = \str_repeat("\x00", $bLen - $aLen) . $aBin;
+        }
+
+        if ($aNeg) {
+            $aBin = $this->twosComplement($aBin);
+        }
+        if ($bNeg) {
+            $bBin = $this->twosComplement($bBin);
+        }
+
+        switch ($operator) {
+            case 'and':
+                $value = $aBin & $bBin;
+                $negative = ($aNeg and $bNeg);
+                break;
+
+            case 'or':
+                $value = $aBin | $bBin;
+                $negative = ($aNeg or $bNeg);
+                break;
+
+            case 'xor':
+                $value = $aBin ^ $bBin;
+                $negative = ($aNeg xor $bNeg);
+                break;
+
+            // @codeCoverageIgnoreStart
+            default:
+                throw new \InvalidArgumentException('Invalid bitwise operator.');
+            // @codeCoverageIgnoreEnd
+        }
+
+        if ($negative) {
+            $value = $this->twosComplement($value);
+        }
+
+        $result = $this->toDecimal($value);
+
+        return $negative ? $this->neg($result) : $result;
+    }
+
+    /**
+     * @param string $number A positive, binary number.
+     *
+     * @return string
+     */
+    private function twosComplement(string $number) : string
+    {
+        $xor = \str_repeat("\xff", \strlen($number));
+
+        $number ^= $xor;
+
+        for ($i = \strlen($number) - 1; $i >= 0; $i--) {
+            $byte = \ord($number[$i]);
+
+            if (++$byte !== 256) {
+                $number[$i] = \chr($byte);
+                break;
+            }
+
+            $number[$i] = "\x00";
+
+            if ($i === 0) {
+                $number = "\x01" . $number;
+            }
+        }
+
+        return $number;
+    }
+
+    /**
+     * Converts a decimal number to a binary string.
+     *
+     * @param string $number The number to convert, positive or zero, only digits.
+     *
+     * @return string
+     */
+    private function toBinary(string $number) : string
+    {
+        $result = '';
+
+        while ($number !== '0') {
+            [$number, $remainder] = $this->divQR($number, '256');
+            $result .= \chr((int) $remainder);
+        }
+
+        return \strrev($result);
+    }
+
+    /**
+     * Returns the positive decimal representation of a binary number.
+     *
+     * @param string $bytes The bytes representing the number.
+     *
+     * @return string
+     */
+    private function toDecimal(string $bytes) : string
+    {
+        $result = '0';
+        $power = '1';
+
+        for ($i = \strlen($bytes) - 1; $i >= 0; $i--) {
+            $index = \ord($bytes[$i]);
+
+            if ($index !== 0) {
+                $result = $this->add($result, ($index === 1)
+                    ? $power
+                    : $this->mul($power, (string) $index)
+                );
+            }
+
+            if ($i !== 0) {
+                $power = $this->mul($power, '256');
+            }
+        }
+
+        return $result;
+    }
+}

libs/Brick/Math/Internal/Calculator/BcMathCalculator.php

@@ -0,0 +1,116 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Brick\Math\Internal\Calculator;
+
+use Brick\Math\Internal\Calculator;
+
+/**
+ * Calculator implementation built around the bcmath library.
+ *
+ * @internal
+ *
+ * @psalm-immutable
+ */
+class BcMathCalculator extends Calculator
+{
+    /**
+     * {@inheritdoc}
+     */
+    public function add(string $a, string $b) : string
+    {
+        return \bcadd($a, $b, 0);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function sub(string $a, string $b) : string
+    {
+        return \bcsub($a, $b, 0);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function mul(string $a, string $b) : string
+    {
+        return \bcmul($a, $b, 0);
+    }
+
+    /**
+     * {@inheritdoc}
+     *
+     * @psalm-suppress InvalidNullableReturnType
+     * @psalm-suppress NullableReturnStatement
+     */
+    public function divQ(string $a, string $b) : string
+    {
+        return \bcdiv($a, $b, 0);
+    }
+
+    /**
+     * {@inheritdoc}
+     *
+     * @psalm-suppress InvalidNullableReturnType
+     * @psalm-suppress NullableReturnStatement
+     */
+    public function divR(string $a, string $b) : string
+    {
+        if (version_compare(PHP_VERSION, '7.2') >= 0) {
+            return \bcmod($a, $b, 0);
+        }
+
+        return \bcmod($a, $b);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divQR(string $a, string $b) : array
+    {
+        $q = \bcdiv($a, $b, 0);
+
+        if (version_compare(PHP_VERSION, '7.2') >= 0) {
+            $r = \bcmod($a, $b, 0);
+        } else {
+            $r = \bcmod($a, $b);
+        }
+
+        assert($q !== null);
+        assert($r !== null);
+
+        return [$q, $r];
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function pow(string $a, int $e) : string
+    {
+        return \bcpow($a, (string) $e, 0);
+    }
+
+    /**
+     * {@inheritdoc}
+     *
+     * @psalm-suppress InvalidNullableReturnType
+     * @psalm-suppress NullableReturnStatement
+     */
+    public function modPow(string $base, string $exp, string $mod) : string
+    {
+        return \bcpowmod($base, $exp, $mod, 0);
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * @psalm-suppress NullableReturnStatement
+     * @psalm-suppress InvalidNullableReturnType
+     */
+    public function sqrt(string $n) : string
+    {
+        return \bcsqrt($n, 0);
+    }
+}

libs/Brick/Math/Internal/Calculator/GmpCalculator.php

@@ -0,0 +1,156 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Brick\Math\Internal\Calculator;
+
+use Brick\Math\Internal\Calculator;
+
+/**
+ * Calculator implementation built around the GMP library.
+ *
+ * @internal
+ *
+ * @psalm-immutable
+ */
+class GmpCalculator extends Calculator
+{
+    /**
+     * {@inheritdoc}
+     */
+    public function add(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_add($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function sub(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_sub($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function mul(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_mul($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divQ(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_div_q($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divR(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_div_r($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divQR(string $a, string $b) : array
+    {
+        [$q, $r] = \gmp_div_qr($a, $b);
+
+        return [
+            \gmp_strval($q),
+            \gmp_strval($r)
+        ];
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function pow(string $a, int $e) : string
+    {
+        return \gmp_strval(\gmp_pow($a, $e));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function modInverse(string $x, string $m) : ?string
+    {
+        $result = \gmp_invert($x, $m);
+
+        if ($result === false) {
+            return null;
+        }
+
+        return \gmp_strval($result);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function modPow(string $base, string $exp, string $mod) : string
+    {
+        return \gmp_strval(\gmp_powm($base, $exp, $mod));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function gcd(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_gcd($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function fromBase(string $number, int $base) : string
+    {
+        return \gmp_strval(\gmp_init($number, $base));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function toBase(string $number, int $base) : string
+    {
+        return \gmp_strval($number, $base);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function and(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_and($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function or(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_or($a, $b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function xor(string $a, string $b) : string
+    {
+        return \gmp_strval(\gmp_xor($a, $b));
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function sqrt(string $n) : string
+    {
+        return \gmp_strval(\gmp_sqrt($n));
+    }
+}

libs/Brick/Math/Internal/Calculator/NativeCalculator.php

@@ -0,0 +1,634 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Brick\Math\Internal\Calculator;
+
+use Brick\Math\Internal\Calculator;
+
+/**
+ * Calculator implementation using only native PHP code.
+ *
+ * @internal
+ *
+ * @psalm-immutable
+ */
+class NativeCalculator extends Calculator
+{
+    /**
+     * The max number of digits the platform can natively add, subtract, multiply or divide without overflow.
+     * For multiplication, this represents the max sum of the lengths of both operands.
+     *
+     * For addition, it is assumed that an extra digit can hold a carry (1) without overflowing.
+     * Example: 32-bit: max number 1,999,999,999 (9 digits + carry)
+     *          64-bit: max number 1,999,999,999,999,999,999 (18 digits + carry)
+     *
+     * @var int
+     */
+    private $maxDigits;
+
+    /**
+     * Class constructor.
+     *
+     * @codeCoverageIgnore
+     */
+    public function __construct()
+    {
+        switch (PHP_INT_SIZE) {
+            case 4:
+                $this->maxDigits = 9;
+                break;
+
+            case 8:
+                $this->maxDigits = 18;
+                break;
+
+            default:
+                throw new \RuntimeException('The platform is not 32-bit or 64-bit as expected.');
+        }
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function add(string $a, string $b) : string
+    {
+        /**
+         * @psalm-var numeric-string $a
+         * @psalm-var numeric-string $b
+         */
+        $result = $a + $b;
+
+        if (is_int($result)) {
+            return (string) $result;
+        }
+
+        if ($a === '0') {
+            return $b;
+        }
+
+        if ($b === '0') {
+            return $a;
+        }
+
+        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
+
+        $result = $aNeg === $bNeg ? $this->doAdd($aDig, $bDig) : $this->doSub($aDig, $bDig);
+
+        if ($aNeg) {
+            $result = $this->neg($result);
+        }
+
+        return $result;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function sub(string $a, string $b) : string
+    {
+        return $this->add($a, $this->neg($b));
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function mul(string $a, string $b) : string
+    {
+        /**
+         * @psalm-var numeric-string $a
+         * @psalm-var numeric-string $b
+         */
+        $result = $a * $b;
+
+        if (is_int($result)) {
+            return (string) $result;
+        }
+
+        if ($a === '0' || $b === '0') {
+            return '0';
+        }
+
+        if ($a === '1') {
+            return $b;
+        }
+
+        if ($b === '1') {
+            return $a;
+        }
+
+        if ($a === '-1') {
+            return $this->neg($b);
+        }
+
+        if ($b === '-1') {
+            return $this->neg($a);
+        }
+
+        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
+
+        $result = $this->doMul($aDig, $bDig);
+
+        if ($aNeg !== $bNeg) {
+            $result = $this->neg($result);
+        }
+
+        return $result;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divQ(string $a, string $b) : string
+    {
+        return $this->divQR($a, $b)[0];
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divR(string $a, string $b): string
+    {
+        return $this->divQR($a, $b)[1];
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function divQR(string $a, string $b) : array
+    {
+        if ($a === '0') {
+            return ['0', '0'];
+        }
+
+        if ($a === $b) {
+            return ['1', '0'];
+        }
+
+        if ($b === '1') {
+            return [$a, '0'];
+        }
+
+        if ($b === '-1') {
+            return [$this->neg($a), '0'];
+        }
+
+        /** @psalm-var numeric-string $a */
+        $na = $a * 1; // cast to number
+
+        if (is_int($na)) {
+            /** @psalm-var numeric-string $b */
+            $nb = $b * 1;
+
+            if (is_int($nb)) {
+                // the only division that may overflow is PHP_INT_MIN / -1,
+                // which cannot happen here as we've already handled a divisor of -1 above.
+                $r = $na % $nb;
+                $q = ($na - $r) / $nb;
+
+                assert(is_int($q));
+
+                return [
+                    (string) $q,
+                    (string) $r
+                ];
+            }
+        }
+
+        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
+
+        [$q, $r] = $this->doDiv($aDig, $bDig);
+
+        if ($aNeg !== $bNeg) {
+            $q = $this->neg($q);
+        }
+
+        if ($aNeg) {
+            $r = $this->neg($r);
+        }
+
+        return [$q, $r];
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function pow(string $a, int $e) : string
+    {
+        if ($e === 0) {
+            return '1';
+        }
+
+        if ($e === 1) {
+            return $a;
+        }
+
+        $odd = $e % 2;
+        $e -= $odd;
+
+        $aa = $this->mul($a, $a);
+
+        /** @psalm-suppress PossiblyInvalidArgument We're sure that $e / 2 is an int now */
+        $result = $this->pow($aa, $e / 2);
+
+        if ($odd === 1) {
+            $result = $this->mul($result, $a);
+        }
+
+        return $result;
+    }
+
+    /**
+     * Algorithm from: https://www.geeksforgeeks.org/modular-exponentiation-power-in-modular-arithmetic/
+     *
+     * {@inheritdoc}
+     */
+    public function modPow(string $base, string $exp, string $mod) : string
+    {
+        // special case: the algorithm below fails with 0 power 0 mod 1 (returns 1 instead of 0)
+        if ($base === '0' && $exp === '0' && $mod === '1') {
+            return '0';
+        }
+
+        // special case: the algorithm below fails with power 0 mod 1 (returns 1 instead of 0)
+        if ($exp === '0' && $mod === '1') {
+            return '0';
+        }
+
+        $x = $base;
+
+        $res = '1';
+
+        // numbers are positive, so we can use remainder instead of modulo
+        $x = $this->divR($x, $mod);
+
+        while ($exp !== '0') {
+            if (in_array($exp[-1], ['1', '3', '5', '7', '9'])) { // odd
+                $res = $this->divR($this->mul($res, $x), $mod);
+            }
+
+            $exp = $this->divQ($exp, '2');
+            $x = $this->divR($this->mul($x, $x), $mod);
+        }
+
+        return $res;
+    }
+
+    /**
+     * Adapted from https://cp-algorithms.com/num_methods/roots_newton.html
+     *
+     * {@inheritDoc}
+     */
+    public function sqrt(string $n) : string
+    {
+        if ($n === '0') {
+            return '0';
+        }
+
+        // initial approximation
+        $x = \str_repeat('9', \intdiv(\strlen($n), 2) ?: 1);
+
+        $decreased = false;
+
+        for (;;) {
+            $nx = $this->divQ($this->add($x, $this->divQ($n, $x)), '2');
+
+            if ($x === $nx || $this->cmp($nx, $x) > 0 && $decreased) {
+                break;
+            }
+
+            $decreased = $this->cmp($nx, $x) < 0;
+            $x = $nx;
+        }
+
+        return $x;
+    }
+
+    /**
+     * Performs the addition of two non-signed large integers.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return string
+     */
+    private function doAdd(string $a, string $b) : string
+    {
+        [$a, $b, $length] = $this->pad($a, $b);
+
+        $carry = 0;
+        $result = '';
+
+        for ($i = $length - $this->maxDigits;; $i -= $this->maxDigits) {
+            $blockLength = $this->maxDigits;
+
+            if ($i < 0) {
+                $blockLength += $i;
+                /** @psalm-suppress LoopInvalidation */
+                $i = 0;
+            }
+
+            /** @psalm-var numeric-string $blockA */
+            $blockA = \substr($a, $i, $blockLength);
+
+            /** @psalm-var numeric-string $blockB */
+            $blockB = \substr($b, $i, $blockLength);
+
+            $sum = (string) ($blockA + $blockB + $carry);
+            $sumLength = \strlen($sum);
+
+            if ($sumLength > $blockLength) {
+                $sum = \substr($sum, 1);
+                $carry = 1;
+            } else {
+                if ($sumLength < $blockLength) {
+                    $sum = \str_repeat('0', $blockLength - $sumLength) . $sum;
+                }
+                $carry = 0;
+            }
+
+            $result = $sum . $result;
+
+            if ($i === 0) {
+                break;
+            }
+        }
+
+        if ($carry === 1) {
+            $result = '1' . $result;
+        }
+
+        return $result;
+    }
+
+    /**
+     * Performs the subtraction of two non-signed large integers.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return string
+     */
+    private function doSub(string $a, string $b) : string
+    {
+        if ($a === $b) {
+            return '0';
+        }
+
+        // Ensure that we always subtract to a positive result: biggest minus smallest.
+        $cmp = $this->doCmp($a, $b);
+
+        $invert = ($cmp === -1);
+
+        if ($invert) {
+            $c = $a;
+            $a = $b;
+            $b = $c;
+        }
+
+        [$a, $b, $length] = $this->pad($a, $b);
+
+        $carry = 0;
+        $result = '';
+
+        $complement = 10 ** $this->maxDigits;
+
+        for ($i = $length - $this->maxDigits;; $i -= $this->maxDigits) {
+            $blockLength = $this->maxDigits;
+
+            if ($i < 0) {
+                $blockLength += $i;
+                /** @psalm-suppress LoopInvalidation */
+                $i = 0;
+            }
+
+            /** @psalm-var numeric-string $blockA */
+            $blockA = \substr($a, $i, $blockLength);
+
+            /** @psalm-var numeric-string $blockB */
+            $blockB = \substr($b, $i, $blockLength);
+
+            $sum = $blockA - $blockB - $carry;
+
+            if ($sum < 0) {
+                $sum += $complement;
+                $carry = 1;
+            } else {
+                $carry = 0;
+            }
+
+            $sum = (string) $sum;
+            $sumLength = \strlen($sum);
+
+            if ($sumLength < $blockLength) {
+                $sum = \str_repeat('0', $blockLength - $sumLength) . $sum;
+            }
+
+            $result = $sum . $result;
+
+            if ($i === 0) {
+                break;
+            }
+        }
+
+        // Carry cannot be 1 when the loop ends, as a > b
+        assert($carry === 0);
+
+        $result = \ltrim($result, '0');
+
+        if ($invert) {
+            $result = $this->neg($result);
+        }
+
+        return $result;
+    }
+
+    /**
+     * Performs the multiplication of two non-signed large integers.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return string
+     */
+    private function doMul(string $a, string $b) : string
+    {
+        $x = \strlen($a);
+        $y = \strlen($b);
+
+        $maxDigits = \intdiv($this->maxDigits, 2);
+        $complement = 10 ** $maxDigits;
+
+        $result = '0';
+
+        for ($i = $x - $maxDigits;; $i -= $maxDigits) {
+            $blockALength = $maxDigits;
+
+            if ($i < 0) {
+                $blockALength += $i;
+                /** @psalm-suppress LoopInvalidation */
+                $i = 0;
+            }
+
+            $blockA = (int) \substr($a, $i, $blockALength);
+
+            $line = '';
+            $carry = 0;
+
+            for ($j = $y - $maxDigits;; $j -= $maxDigits) {
+                $blockBLength = $maxDigits;
+
+                if ($j < 0) {
+                    $blockBLength += $j;
+                    /** @psalm-suppress LoopInvalidation */
+                    $j = 0;
+                }
+
+                $blockB = (int) \substr($b, $j, $blockBLength);
+
+                $mul = $blockA * $blockB + $carry;
+                $value = $mul % $complement;
+                $carry = ($mul - $value) / $complement;
+
+                $value = (string) $value;
+                $value = \str_pad($value, $maxDigits, '0', STR_PAD_LEFT);
+
+                $line = $value . $line;
+
+                if ($j === 0) {
+                    break;
+                }
+            }
+
+            if ($carry !== 0) {
+                $line = $carry . $line;
+            }
+
+            $line = \ltrim($line, '0');
+
+            if ($line !== '') {
+                $line .= \str_repeat('0', $x - $blockALength - $i);
+                $result = $this->add($result, $line);
+            }
+
+            if ($i === 0) {
+                break;
+            }
+        }
+
+        return $result;
+    }
+
+    /**
+     * Performs the division of two non-signed large integers.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return string[] The quotient and remainder.
+     */
+    private function doDiv(string $a, string $b) : array
+    {
+        $cmp = $this->doCmp($a, $b);
+
+        if ($cmp === -1) {
+            return ['0', $a];
+        }
+
+        $x = \strlen($a);
+        $y = \strlen($b);
+
+        // we now know that a >= b && x >= y
+
+        $q = '0'; // quotient
+        $r = $a; // remainder
+        $z = $y; // focus length, always $y or $y+1
+
+        for (;;) {
+            $focus = \substr($a, 0, $z);
+
+            $cmp = $this->doCmp($focus, $b);
+
+            if ($cmp === -1) {
+                if ($z === $x) { // remainder < dividend
+                    break;
+                }
+
+                $z++;
+            }
+
+            $zeros = \str_repeat('0', $x - $z);
+
+            $q = $this->add($q, '1' . $zeros);
+            $a = $this->sub($a, $b . $zeros);
+
+            $r = $a;
+
+            if ($r === '0') { // remainder == 0
+                break;
+            }
+
+            $x = \strlen($a);
+
+            if ($x < $y) { // remainder < dividend
+                break;
+            }
+
+            $z = $y;
+        }
+
+        return [$q, $r];
+    }
+
+    /**
+     * Compares two non-signed large numbers.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return int [-1, 0, 1]
+     */
+    private function doCmp(string $a, string $b) : int
+    {
+        $x = \strlen($a);
+        $y = \strlen($b);
+
+        $cmp = $x <=> $y;
+
+        if ($cmp !== 0) {
+            return $cmp;
+        }
+
+        return \strcmp($a, $b) <=> 0; // enforce [-1, 0, 1]
+    }
+
+    /**
+     * Pads the left of one of the given numbers with zeros if necessary to make both numbers the same length.
+     *
+     * The numbers must only consist of digits, without leading minus sign.
+     *
+     * @param string $a The first operand.
+     * @param string $b The second operand.
+     *
+     * @return array{string, string, int}
+     */
+    private function pad(string $a, string $b) : array
+    {
+        $x = \strlen($a);
+        $y = \strlen($b);
+
+        if ($x > $y) {
+            $b = \str_repeat('0', $x - $y) . $b;
+
+            return [$a, $b, $x];
+        }
+
+        if ($x < $y) {
+            $a = \str_repeat('0', $y - $x) . $a;
+
+            return [$a, $b, $y];
+        }
+
+        return [$a, $b, $x];
+    }
+}