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Edit File: phph8llvi

Calculator/GmpCalculator.php������������������������������������������������������������������������0000644�����������������00000004420�15107326727�0012115 0����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������<?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
{
    public function add(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_add($a, $b));
    }

public function sub(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_sub($a, $b));
    }

public function mul(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_mul($a, $b));
    }

public function divQ(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_div_q($a, $b));
    }

public function divR(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_div_r($a, $b));
    }

public function divQR(string $a, string $b) : array
    {
        [$q, $r] = \gmp_div_qr($a, $b);

return [
            \gmp_strval($q),
            \gmp_strval($r)
        ];
    }

public function pow(string $a, int $e) : string
    {
        return \gmp_strval(\gmp_pow($a, $e));
    }

public function modInverse(string $x, string $m) : ?string
    {
        $result = \gmp_invert($x, $m);

if ($result === false) {
            return null;
        }

return \gmp_strval($result);
    }

public function modPow(string $base, string $exp, string $mod) : string
    {
        return \gmp_strval(\gmp_powm($base, $exp, $mod));
    }

public function gcd(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_gcd($a, $b));
    }

public function fromBase(string $number, int $base) : string
    {
        return \gmp_strval(\gmp_init($number, $base));
    }

public function toBase(string $number, int $base) : string
    {
        return \gmp_strval($number, $base);
    }

public function and(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_and($a, $b));
    }

public function or(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_or($a, $b));
    }

public function xor(string $a, string $b) : string
    {
        return \gmp_strval(\gmp_xor($a, $b));
    }

public function sqrt(string $n) : string
    {
        return \gmp_strval(\gmp_sqrt($n));
    }
}
������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Calculator/BcMathCalculator.php���������������������������������������������������������������������0000644�����������������00000002766�15107326727�0012543 0����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������<?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
{
    public function add(string $a, string $b) : string
    {
        return \bcadd($a, $b, 0);
    }

public function sub(string $a, string $b) : string
    {
        return \bcsub($a, $b, 0);
    }

public function mul(string $a, string $b) : string
    {
        return \bcmul($a, $b, 0);
    }

public function divQ(string $a, string $b) : string
    {
        return \bcdiv($a, $b, 0);
    }

/**
     * @psalm-suppress InvalidNullableReturnType
     * @psalm-suppress NullableReturnStatement
     */
    public function divR(string $a, string $b) : string
    {
        return \bcmod($a, $b, 0);
    }

public function divQR(string $a, string $b) : array
    {
        $q = \bcdiv($a, $b, 0);
        $r = \bcmod($a, $b, 0);

assert($r !== null);

return [$q, $r];
    }

public function pow(string $a, int $e) : string
    {
        return \bcpow($a, (string) $e, 0);
    }

public function modPow(string $base, string $exp, string $mod) : string
    {
        return \bcpowmod($base, $exp, $mod, 0);
    }

/**
     * @psalm-suppress InvalidNullableReturnType
     * @psalm-suppress NullableReturnStatement
     */
    public function sqrt(string $n) : string
    {
        return \bcsqrt($n, 0);
    }
}
����������Calculator/NativeCalculator.php���������������������������������������������������������������������0000644�����������������00000032665�15107326730�0012626 0����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������<?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.
     *
     * In 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)
     */
    private int $maxDigits;

/**
     * @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.');
        }
    }

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;
    }

public function sub(string $a, string $b) : string
    {
        return $this->add($a, $this->neg($b));
    }

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;
    }

public function divQ(string $a, string $b) : string
    {
        return $this->divQR($a, $b)[0];
    }

public function divR(string $a, string $b): string
    {
        return $this->divQR($a, $b)[1];
    }

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];
    }

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/
     */
    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
     */
    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.
     */
    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.
     */
    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.
     */
    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.
     *
     * @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.
     *
     * @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.
     *
     * @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];
    }
}
���������������������������������������������������������������������������Calculator.php��������������������������������������������������������������������������������������0000644�����������������00000045661�15107326730�0007366 0����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������<?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.
     */
    private static ?Calculator $instance = null;

/**
     * 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.
     */
    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.
     *
     * @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
     */
    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.
     *
     * @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.
     */
    final public function abs(string $n) : string
    {
        return ($n[0] === '-') ? \substr($n, 1) : $n;
    }

/**
     * Negates a number.
     */
    final public function neg(string $n) : string
    {
        if ($n === '0') {
            return '0';
        }

if ($n[0] === '-') {
            return \substr($n, 1);
        }

return '-' . $n;
    }

/**
     * Compares two numbers.
     *
     * @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.
     */
    abstract public function add(string $a, string $b) : string;

/**
     * Subtracts two numbers.
     */
    abstract public function sub(string $a, string $b) : string;

/**
     * Multiplies two numbers.
     */
    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 array{string, 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 $b The modulus; must not be zero.
     */
    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 $m The modulus; must not be negative or zero.
     */
    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);
        }

[$g, $x] = $this->gcdExtended($modVal, $m);

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.
     */
    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.
     *
     * @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));
    }

/**
     * @return array{string, string, string} GCD, X, Y
     */
    private function gcdExtended(string $a, string $b) : array
    {
        if ($a === '0') {
            return [$b, '0', '1'];
        }

[$gcd, $x1, $y1] = $this->gcdExtended($this->mod($b, $a), $a);

$x = $this->sub($y1, $this->mul($this->divQ($b, $a), $x1));
        $y = $x1;

return [$gcd, $x, $y];
    }

/**
     * 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.
     */
    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.
     *
     * @throws \InvalidArgumentException  If the rounding mode is invalid.
     * @throws RoundingNecessaryException If RoundingMode::UNNECESSARY is provided but rounding is necessary.
     *
     * @psalm-suppress ImpureFunctionCall
     */
    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.
     */
    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.
     */
    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.
     */
    public function xor(string $a, string $b) : string
    {
        return $this->bitwise('xor', $a, $b);
    }

/**
     * Performs a bitwise operation on a decimal number.
     *
     * @param 'and'|'or'|'xor' $operator The operator to use.
     * @param string           $a        The left operand.
     * @param string           $b        The right operand.
     */
    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.
     */
    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.
     */
    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.
     */
    private function toDecimal(string $bytes) : string
    {
        $result = '0';
        $power = '1';

for ($i = \strlen($bytes) - 1; $i >= 0; $i--) {
            $index = \ord($bytes[$i]);

if ($i !== 0) {
                $power = $this->mul($power, '256');
            }
        }

return $result;
    }
}
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