Commit version 24.12.13800
This commit is contained in:
676
libs/Brick/Math11/Internal/Calculator.php
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676
libs/Brick/Math11/Internal/Calculator.php
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@ -0,0 +1,676 @@
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<?php
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declare(strict_types=1);
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namespace Brick\Math\Internal;
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use Brick\Math\Exception\RoundingNecessaryException;
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use Brick\Math\RoundingMode;
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/**
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* Performs basic operations on arbitrary size integers.
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*
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* Unless otherwise specified, all parameters must be validated as non-empty strings of digits,
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* without leading zero, and with an optional leading minus sign if the number is not zero.
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*
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* Any other parameter format will lead to undefined behaviour.
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* All methods must return strings respecting this format, unless specified otherwise.
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*
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* @internal
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*
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* @psalm-immutable
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*/
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abstract class Calculator
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{
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/**
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* The maximum exponent value allowed for the pow() method.
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*/
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public const MAX_POWER = 1000000;
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/**
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* The alphabet for converting from and to base 2 to 36, lowercase.
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*/
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public const ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
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/**
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* The Calculator instance in use.
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*/
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private static ?Calculator $instance = null;
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/**
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* Sets the Calculator instance to use.
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*
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* An instance is typically set only in unit tests: the autodetect is usually the best option.
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*
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* @param Calculator|null $calculator The calculator instance, or NULL to revert to autodetect.
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*/
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final public static function set(?Calculator $calculator) : void
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{
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self::$instance = $calculator;
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}
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/**
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* Returns the Calculator instance to use.
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*
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* If none has been explicitly set, the fastest available implementation will be returned.
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*
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* @psalm-pure
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* @psalm-suppress ImpureStaticProperty
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*/
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final public static function get() : Calculator
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{
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if (self::$instance === null) {
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/** @psalm-suppress ImpureMethodCall */
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self::$instance = self::detect();
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}
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return self::$instance;
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}
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/**
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* Returns the fastest available Calculator implementation.
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*
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* @codeCoverageIgnore
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*/
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private static function detect() : Calculator
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{
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if (\extension_loaded('gmp')) {
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return new Calculator\GmpCalculator();
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}
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if (\extension_loaded('bcmath')) {
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return new Calculator\BcMathCalculator();
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}
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return new Calculator\NativeCalculator();
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}
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/**
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* Extracts the sign & digits of the operands.
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*
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* @return array{bool, bool, string, string} Whether $a and $b are negative, followed by their digits.
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*/
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final protected function init(string $a, string $b) : array
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{
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return [
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$aNeg = ($a[0] === '-'),
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$bNeg = ($b[0] === '-'),
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$aNeg ? \substr($a, 1) : $a,
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$bNeg ? \substr($b, 1) : $b,
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];
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}
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/**
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* Returns the absolute value of a number.
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*/
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final public function abs(string $n) : string
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{
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return ($n[0] === '-') ? \substr($n, 1) : $n;
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}
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/**
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* Negates a number.
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*/
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final public function neg(string $n) : string
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{
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if ($n === '0') {
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return '0';
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}
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if ($n[0] === '-') {
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return \substr($n, 1);
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}
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return '-' . $n;
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}
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/**
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* Compares two numbers.
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*
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* @return int [-1, 0, 1] If the first number is less than, equal to, or greater than the second number.
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*/
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final public function cmp(string $a, string $b) : int
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{
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[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);
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if ($aNeg && ! $bNeg) {
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return -1;
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}
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if ($bNeg && ! $aNeg) {
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return 1;
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}
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$aLen = \strlen($aDig);
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$bLen = \strlen($bDig);
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if ($aLen < $bLen) {
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$result = -1;
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} elseif ($aLen > $bLen) {
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$result = 1;
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} else {
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$result = $aDig <=> $bDig;
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}
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return $aNeg ? -$result : $result;
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}
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/**
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* Adds two numbers.
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*/
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abstract public function add(string $a, string $b) : string;
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/**
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* Subtracts two numbers.
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*/
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abstract public function sub(string $a, string $b) : string;
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/**
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* Multiplies two numbers.
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*/
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abstract public function mul(string $a, string $b) : string;
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/**
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* Returns the quotient of the division of two numbers.
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*
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* @param string $a The dividend.
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* @param string $b The divisor, must not be zero.
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*
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* @return string The quotient.
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*/
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abstract public function divQ(string $a, string $b) : string;
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/**
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* Returns the remainder of the division of two numbers.
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*
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* @param string $a The dividend.
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* @param string $b The divisor, must not be zero.
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*
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* @return string The remainder.
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*/
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abstract public function divR(string $a, string $b) : string;
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/**
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* Returns the quotient and remainder of the division of two numbers.
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*
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* @param string $a The dividend.
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* @param string $b The divisor, must not be zero.
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*
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* @return array{string, string} An array containing the quotient and remainder.
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*/
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abstract public function divQR(string $a, string $b) : array;
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/**
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* Exponentiates a number.
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*
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* @param string $a The base number.
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* @param int $e The exponent, validated as an integer between 0 and MAX_POWER.
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*
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* @return string The power.
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*/
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abstract public function pow(string $a, int $e) : string;
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/**
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* @param string $b The modulus; must not be zero.
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*/
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public function mod(string $a, string $b) : string
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{
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return $this->divR($this->add($this->divR($a, $b), $b), $b);
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}
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/**
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* Returns the modular multiplicative inverse of $x modulo $m.
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*
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* If $x has no multiplicative inverse mod m, this method must return null.
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*
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* This method can be overridden by the concrete implementation if the underlying library has built-in support.
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*
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* @param string $m The modulus; must not be negative or zero.
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*/
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public function modInverse(string $x, string $m) : ?string
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{
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if ($m === '1') {
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return '0';
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}
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$modVal = $x;
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if ($x[0] === '-' || ($this->cmp($this->abs($x), $m) >= 0)) {
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$modVal = $this->mod($x, $m);
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}
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[$g, $x] = $this->gcdExtended($modVal, $m);
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if ($g !== '1') {
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return null;
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}
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return $this->mod($this->add($this->mod($x, $m), $m), $m);
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}
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/**
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* Raises a number into power with modulo.
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*
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* @param string $base The base number; must be positive or zero.
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* @param string $exp The exponent; must be positive or zero.
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* @param string $mod The modulus; must be strictly positive.
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*/
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abstract public function modPow(string $base, string $exp, string $mod) : string;
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/**
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* Returns the greatest common divisor of the two numbers.
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*
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* This method can be overridden by the concrete implementation if the underlying library
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* has built-in support for GCD calculations.
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*
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* @return string The GCD, always positive, or zero if both arguments are zero.
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*/
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public function gcd(string $a, string $b) : string
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{
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if ($a === '0') {
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return $this->abs($b);
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}
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if ($b === '0') {
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return $this->abs($a);
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}
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return $this->gcd($b, $this->divR($a, $b));
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}
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/**
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* @return array{string, string, string} GCD, X, Y
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*/
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private function gcdExtended(string $a, string $b) : array
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{
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if ($a === '0') {
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return [$b, '0', '1'];
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}
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[$gcd, $x1, $y1] = $this->gcdExtended($this->mod($b, $a), $a);
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$x = $this->sub($y1, $this->mul($this->divQ($b, $a), $x1));
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$y = $x1;
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return [$gcd, $x, $y];
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}
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/**
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* Returns the square root of the given number, rounded down.
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*
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* The result is the largest x such that x² ≤ n.
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* The input MUST NOT be negative.
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*/
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abstract public function sqrt(string $n) : string;
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/**
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* Converts a number from an arbitrary base.
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*
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* This method can be overridden by the concrete implementation if the underlying library
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* has built-in support for base conversion.
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*
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* @param string $number The number, positive or zero, non-empty, case-insensitively validated for the given base.
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* @param int $base The base of the number, validated from 2 to 36.
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*
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* @return string The converted number, following the Calculator conventions.
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*/
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public function fromBase(string $number, int $base) : string
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{
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return $this->fromArbitraryBase(\strtolower($number), self::ALPHABET, $base);
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}
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|
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/**
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* Converts a number to an arbitrary base.
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*
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* This method can be overridden by the concrete implementation if the underlying library
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* has built-in support for base conversion.
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*
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* @param string $number The number to convert, following the Calculator conventions.
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* @param int $base The base to convert to, validated from 2 to 36.
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*
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* @return string The converted number, lowercase.
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*/
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public function toBase(string $number, int $base) : string
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{
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$negative = ($number[0] === '-');
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if ($negative) {
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$number = \substr($number, 1);
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}
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$number = $this->toArbitraryBase($number, self::ALPHABET, $base);
|
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|
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if ($negative) {
|
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return '-' . $number;
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||||
}
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|
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return $number;
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}
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/**
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||||
* Converts a non-negative number in an arbitrary base using a custom alphabet, to base 10.
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*
|
||||
* @param string $number The number to convert, validated as a non-empty string,
|
||||
* containing only chars in the given alphabet/base.
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* @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.
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||||
*/
|
||||
final public function fromArbitraryBase(string $number, string $alphabet, int $base) : string
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{
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// remove leading "zeros"
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$number = \ltrim($number, $alphabet[0]);
|
||||
|
||||
if ($number === '') {
|
||||
return '0';
|
||||
}
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||||
|
||||
// optimize for "one"
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||||
if ($number === $alphabet[1]) {
|
||||
return '1';
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||||
}
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||||
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||||
$result = '0';
|
||||
$power = '1';
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||||
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||||
$base = (string) $base;
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||||
|
||||
for ($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[$i]);
|
||||
|
||||
if ($index !== 0) {
|
||||
$result = $this->add($result, ($index === 1)
|
||||
? $power
|
||||
: $this->mul($power, (string) $index)
|
||||
);
|
||||
}
|
||||
|
||||
if ($i !== 0) {
|
||||
$power = $this->mul($power, '256');
|
||||
}
|
||||
}
|
||||
|
||||
return $result;
|
||||
}
|
||||
}
|
||||
75
libs/Brick/Math11/Internal/Calculator/BcMathCalculator.php
Normal file
75
libs/Brick/Math11/Internal/Calculator/BcMathCalculator.php
Normal file
@ -0,0 +1,75 @@
|
||||
<?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);
|
||||
}
|
||||
}
|
||||
108
libs/Brick/Math11/Internal/Calculator/GmpCalculator.php
Normal file
108
libs/Brick/Math11/Internal/Calculator/GmpCalculator.php
Normal file
@ -0,0 +1,108 @@
|
||||
<?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));
|
||||
}
|
||||
}
|
||||
581
libs/Brick/Math11/Internal/Calculator/NativeCalculator.php
Normal file
581
libs/Brick/Math11/Internal/Calculator/NativeCalculator.php
Normal file
@ -0,0 +1,581 @@
|
||||
<?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];
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user