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<?php |
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namespace Riimu\Kit\BaseConversion; |
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/** |
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* Converts numbers using character replacement. |
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* |
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* ReplaceConverter converts numbers from base to another using a simple string |
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* replacement strategy. In other words. The digits from one base is simply |
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* replaced with digits from the other base. This strategy, however, is only |
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* possible if the two number bases share a common root or if the target number |
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* base is nth root of the source base. This is required, because it allows |
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* a sequence of digits to be simply replaced with an appropriate sequence of |
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* digits from the other number base. |
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* |
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* When possible, the replacement strategy offers considerable speed gains over |
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* strategies that employ arbitrary-precision arithmetic as there is no need |
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* to calculate anything. |
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* |
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* Note the replacement conversion strategy can always convert fractions |
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* accurately. Setting the precision for ReplaceConverter has no effect at all |
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* on the conversion results. |
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* |
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* @author Riikka Kalliomäki <[email protected]> |
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* @copyright Copyright (c) 2014-2017 Riikka Kalliomäki |
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* @license http://opensource.org/licenses/mit-license.php MIT License |
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*/ |
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class ReplaceConverter implements Converter |
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{ |
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/** @var NumberBase Number base used by provided numbers */ |
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private $source; |
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/** @var NumberBase Number base used by returned numbers */ |
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private $target; |
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/** @var ReplaceConverter Converter used to convert into common root base */ |
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private $sourceConverter; |
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/** @var ReplaceConverter Converter used to convert from common root base */ |
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private $targetConverter; |
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/** @var array<string,string> String replacement table for converting numbers */ |
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private $conversionTable; |
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/** |
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* Create new instance of ReplaceConverter. |
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* |
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* ReplaceConverter only supports number base combinations that have a |
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* common root or if the target base is nth root of the source base. In |
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* addition, due to using string replacement, any number base that has |
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* conflicting string digits are not supported. |
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* |
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* @param NumberBase $source Number base used by the provided numbers |
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* @param NumberBase $target Number base used by the returned numbers |
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* @throws InvalidNumberBaseException If the number bases are not supported |
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*/ |
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public function __construct(NumberBase $source, NumberBase $target) |
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{ |
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$root = $this->getRoot($source, $target); |
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if ($root !== $source->getRadix() && $root !== $target->getRadix()) { |
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$proxy = new NumberBase($root); |
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$this->sourceConverter = new self($source, $proxy); |
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$this->targetConverter = new self($proxy, $target); |
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} else { |
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$this->source = $source; |
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$this->target = $target; |
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$this->conversionTable = $this->buildConversionTable(); |
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} |
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} |
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/** |
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* Determines the common root for the number bases. |
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* @param NumberBase $source Number base used by the provided numbers |
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* @param NumberBase $target Number base used by the returned numbers |
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* @return int The common root for the number bases |
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* @throws InvalidNumberBaseException If the number bases are not supported |
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*/ |
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private function getRoot(NumberBase $source, NumberBase $target) |
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{ |
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if ($source->hasStringConflict() || $target->hasStringConflict()) { |
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throw new InvalidNumberBaseException('Number bases do not support string presentation'); |
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} |
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$root = $source->findCommonRadixRoot($target); |
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if ($root === false) { |
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throw new InvalidNumberBaseException('No common root exists between number bases'); |
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} |
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return $root; |
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} |
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/** |
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* Creates string replacement table between source base and target base. |
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* @return array<string,string> String replacement table for converting numbers |
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*/ |
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private function buildConversionTable() |
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{ |
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if ($this->source->getRadix() > $this->target->getRadix()) { |
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return $this->createTable($this->source->getDigitList(), $this->target->getDigitList()); |
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} |
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return array_flip($this->createTable($this->target->getDigitList(), $this->source->getDigitList())); |
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} |
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/** |
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* Creates a conversion table between two lists of digits. |
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* @param string[] $source Digits for the number base with larger number of digits |
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* @param string[] $target Digits for the number base with smaller number of digits |
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* @return array<string,string> String replacement table for converting numbers |
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*/ |
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private function createTable($source, $target) |
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{ |
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$last = count($target) - 1; |
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$size = (int) log(count($source), count($target)); |
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$number = array_fill(0, $size, $target[0]); |
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$next = array_fill(0, $size, 0); |
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$limit = count($source); |
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$table = [$source[0] => implode('', $number)]; |
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for ($i = 1; $i < $limit; $i++) { |
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for ($j = $size - 1; $next[$j] === $last; $j--) { |
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$number[$j] = $target[0]; |
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$next[$j] = 0; |
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} |
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$number[$j] = $target[++$next[$j]]; |
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$table[$source[$i]] = implode('', $number); |
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} |
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return $table; |
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} |
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public function setPrecision($precision) |
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{ |
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// Replace converter always converts accurately |
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} |
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public function convertInteger(array $number) |
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{ |
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return $this->convert($number, false); |
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} |
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public function convertFractions(array $number) |
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{ |
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return $this->convert($number, true); |
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} |
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/** |
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* Converts the digits from source base to target base. |
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* @param array $number The digits to convert |
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* @param bool $fractions True if converting fractions, false if not |
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* @return array The digits converted to target base |
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*/ |
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private function convert(array $number, $fractions = false) |
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{ |
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if (!isset($this->conversionTable)) { |
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return $this->targetConverter->replace( |
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$this->sourceConverter->replace($number, $fractions), |
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$fractions |
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); |
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} |
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return $this->replace($number, $fractions); |
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} |
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/** |
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* Replace digits using string replacement. |
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* @param array $number The digits to convert |
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* @param bool $fractions True if converting fractions, false if not |
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* @return array The digits converted to target base |
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*/ |
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private function replace(array $number, $fractions = false) |
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{ |
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return $this->zeroTrim($this->target->splitString(strtr(implode('', $this->zeroPad( |
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$this->source->canonizeDigits($number), |
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$fractions |
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)), $this->conversionTable)), $fractions); |
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} |
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/** |
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* Pads the digits to correct count for string replacement. |
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* @param array $number Array of digits to pad |
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* @param bool $right True to pad from right, false to pad from left |
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* @return array Padded array of digits |
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*/ |
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private function zeroPad(array $number, $right) |
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{ |
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$log = (int) log($this->target->getRadix(), $this->source->getRadix()); |
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if ($log > 1 && count($number) % $log) { |
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$pad = count($number) + ($log - count($number) % $log); |
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$number = array_pad($number, $right ? $pad : -$pad, $this->source->getDigit(0)); |
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} |
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return $number; |
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} |
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/** |
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* Trims extraneous zeroes from the digit list. |
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* @param array $number Array of digits to trim |
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* @param bool $right True to trim from right, false to trim from left |
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* @return array Trimmed array of digits |
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*/ |
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private function zeroTrim(array $number, $right) |
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{ |
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$zero = $this->target->getDigit(0); |
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while (($right ? end($number) : reset($number)) === $zero) { |
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unset($number[key($number)]); |
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} |
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return empty($number) ? [$zero] : array_values($number); |
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} |
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} |
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