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<?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;
}
}