#18 Improved roman numerals conversions and validation

mathematicator-core · Jun 6, 2020 · d440971 · d440971
2 parents 7ee22e5 + 6ff6707
commit d440971
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Showing 14 changed files with 810 additions and 154 deletions.
diff --git a/src/Converter/IntToRoman.php b/src/Converter/IntToRoman.php
@@ -7,133 +7,50 @@
 
 use Brick\Math\BigInteger;
 use Brick\Math\BigNumber;
-use Brick\Math\BigRational;
 use Brick\Math\Exception\RoundingNecessaryException;
 use Brick\Math\RoundingMode;
-use Mathematicator\Numbers\Exception\NumberFormatException;
-use Mathematicator\Numbers\Exception\OutOfRomanNumberSetException;
-use Nette\StaticClass;
+use Mathematicator\Numbers\Exception\OutOfSetException;
 use Stringable;
 
 /**
- * Convert integer to roman numerals
+ * Convert an integer to roman numerals
+ *
+ * Tip: Use validators if you want to do custom checks (e.g. not zero, or in original ancient set)
  *
  * @see https://en.wikipedia.org/wiki/Roman_numerals
+ * @see https://www.wolframalpha.com/input/?i=1000000+to+roman
+ * @see https://www.calculatorsoup.com/calculators/conversions/roman-numeral-converter.php
  */
-final class IntToRoman
+final class IntToRoman extends IntToRomanBasic
 {
-	use StaticClass;
-
-	/** @var int[] */
-	private static $conversionTable = [
-		'M' => 1000,
-		'CM' => 900,
-		'D' => 500,
-		'CD' => 400,
-		'C' => 100,
-		'XC' => 90,
-		'L' => 50,
-		'XL' => 40,
-		'X' => 10,
-		'IX' => 9,
-		'V' => 5,
-		'IV' => 4,
-		'I' => 1,
-	];
-
-	/** @var string[] */
-	private static $fractionConversionTable = [
-		'1/12' => '·',
-		'2/12' => '··',
-		'3/12' => '···',
-		'4/12' => '····',
-		'5/12' => '·····',
-		'6/12' => 'S',
-		'7/12' => 'S·',
-		'8/12' => 'S··',
-		'9/12' => 'S···',
-		'10/12' => 'S····',
-		'11/12' => 'S·····',
-	];
-
 
 	/**
 	 * @param BigNumber|int|string|Stringable $input
 	 * @return string
-	 * @throws OutOfRomanNumberSetException
+	 * @throws OutOfSetException
 	 */
 	public static function convert($input): string
 	{
-		try {
-			$integer = BigInteger::of((string) $input);
-		} catch (RoundingNecessaryException $e) {
-			return self::convertRationalNumber($input);
-		}
-
-		return self::convertInteger($integer);
-	}
-
-
-	/**
-	 * @param BigNumber|int|string|Stringable $input
-	 * @return string
-	 * @throws OutOfRomanNumberSetException
-	 * @see https://en.wikipedia.org/wiki/Roman_numerals (Fractions)
-	 */
-	public static function convertRationalNumber($input): string
-	{
-		$rationalNumber = BigRational::of((string) $input)->simplified();
-
-		if ($rationalNumber->isLessThan('1/12')) {
-			throw new OutOfRomanNumberSetException((string) $input);
-		}
-
-		$denominatorOriginal = $rationalNumber->getDenominator();
-
-		if (in_array((string) $denominatorOriginal, ['2', '3', '4', '6', '12'], true) && $denominatorOriginal->isLessThanOrEqualTo(12)) {
-			$toFinalMultiplier = BigInteger::of(12)->dividedBy($denominatorOriginal)->toInt();
-			$numeratorMultiplied = $rationalNumber->getNumerator()->multipliedBy($toFinalMultiplier);
+		$allowedSetDescription = 'integers >= 0';
 
-			$intFinal = $numeratorMultiplied->quotient(12);
-			$numeratorFinal = $numeratorMultiplied->mod(12)->toInt();
-
-			$out = '';
-
-			// Integer part
-			if ($intFinal->isGreaterThan(0)) {
-				$out .= self::convertInteger($intFinal);
-			}
-
-			// + fraction part
-			return $out . self::$fractionConversionTable["$numeratorFinal/12"];
-		} else {
-			throw new OutOfRomanNumberSetException((string) $input);
-		}
-	}
-
-
-	/**
-	 * @param BigInteger|int|string|Stringable $input
-	 * @return string
-	 * @throws OutOfRomanNumberSetException
-	 */
-	public static function convertInteger($input): string
-	{
 		try {
 			$int = BigInteger::of((string) $input);
 		} catch (RoundingNecessaryException $e) {
-			throw new OutOfRomanNumberSetException((string) $input);
+			throw new OutOfSetException($input . ' (not integer)', $allowedSetDescription);
 		}
 
-		// According to Wikipedia, largest valid roman number is 3999: https://en.wikipedia.org/wiki/Roman_numerals
-		if ($int->isLessThan(1) || $int->isGreaterThan(3999)) {
-			throw new OutOfRomanNumberSetException((string) $input);
+		if ($int->isLessThan(0)) {
+			throw new OutOfSetException($input . ' (negative)', $allowedSetDescription);
 		}
 
 		$out = '';
 
-		$conversionTable = self::$conversionTable;
+		// Prepare a conversion table
+		$numberLength = strlen((string) $int);
+		$numberThousands = ($numberLength - $numberLength % 3) / 3;
+		$conversionTable = RomanToInt::getConversionTable($numberThousands);
 
+		// Process each roman numeral
 		foreach ($conversionTable as $roman => $value) {
 			$matches = $int->dividedBy($value, RoundingMode::DOWN)->toInt();
 			$out .= str_repeat($roman, $matches);
@@ -145,12 +62,23 @@ public static function convertInteger($input): string
 
 
 	/**
-	 * @param string $romanNumber
-	 * @return BigInteger
-	 * @throws NumberFormatException
+	 * @param BigNumber|int|string|Stringable $input
+	 * @return string
+	 * @throws OutOfSetException
 	 */
-	public static function reverse($romanNumber): BigInteger
+	public static function convertToLatex($input): string
 	{
-		return RomanToInt::convert($romanNumber);
+		$out = self::convert($input);
+
+		// Get count of leading underscores (e.g. 2 for __M)
+		preg_match('/^_*/', $out, $leadingUnderscoresMatches);
+		$leadingUnderscoresCount = isset($leadingUnderscoresMatches[0]) ? strlen($leadingUnderscoresMatches[0]) : 0;
+
+		// Convert underscores to latex overline
+		for ($i = $leadingUnderscoresCount; $i > 0; $i--) {
+			$out = (string) preg_replace('/_([IVXLCDM]|(\\\overline\{[\w{}]*\}))/', '\\overline{$1}', $out);
+		}
+
+		return $out;
 	}
 }
diff --git a/src/Converter/IntToRomanBasic.php b/src/Converter/IntToRomanBasic.php
@@ -0,0 +1,66 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Mathematicator\Numbers\Converter;
+
+
+use Brick\Math\BigInteger;
+use Brick\Math\BigNumber;
+use Brick\Math\Exception\RoundingNecessaryException;
+use Brick\Math\RoundingMode;
+use Mathematicator\Numbers\Exception\NumberFormatException;
+use Mathematicator\Numbers\Exception\OutOfSetException;
+use Nette\StaticClass;
+use Stringable;
+
+/**
+ * Convert integer to basic roman numerals (original ancient set)
+ *
+ * @see https://en.wikipedia.org/wiki/Roman_numerals
+ */
+class IntToRomanBasic
+{
+	use StaticClass;
+
+	/**
+	 * @param BigNumber|int|string|Stringable $input
+	 * @return string
+	 * @throws OutOfSetException
+	 */
+	public static function convert($input): string
+	{
+		try {
+			$int = BigInteger::of((string) $input);
+		} catch (RoundingNecessaryException $e) {
+			throw new OutOfSetException($input . ' (not integer)');
+		}
+
+		if ($int->isLessThan(0)) {
+			throw new OutOfSetException((string) $input, 'integers >= 0');
+		}
+
+		$out = '';
+
+		$conversionTable = RomanToInt::getConversionTable(0);
+
+		foreach ($conversionTable as $roman => $value) {
+			$matches = $int->dividedBy($value, RoundingMode::DOWN)->toInt();
+			$out .= str_repeat($roman, $matches);
+			$int = $int->mod($value);
+		}
+
+		return $out;
+	}
+
+
+	/**
+	 * @param string $romanNumber
+	 * @return BigInteger
+	 * @throws NumberFormatException
+	 */
+	public static function reverse($romanNumber): BigInteger
+	{
+		return RomanToInt::convert($romanNumber);
+	}
+}
diff --git a/src/Converter/RationalToRoman.php b/src/Converter/RationalToRoman.php
@@ -0,0 +1,81 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Mathematicator\Numbers\Converter;
+
+
+use Brick\Math\BigInteger;
+use Brick\Math\BigNumber;
+use Brick\Math\BigRational;
+use Mathematicator\Numbers\Exception\OutOfSetException;
+use Nette\StaticClass;
+use Stringable;
+
+/**
+ * Convert rational number to basic roman fractions (original ancient set)
+ *
+ * @see https://en.wikipedia.org/wiki/Roman_numerals
+ */
+final class RationalToRoman
+{
+	use StaticClass;
+
+	/** @var string[] */
+	protected static $fractionConversionTable = [
+		'1/12' => '·',
+		'2/12' => '··',
+		'3/12' => '···',
+		'4/12' => '····',
+		'5/12' => '·····',
+		'6/12' => 'S',
+		'7/12' => 'S·',
+		'8/12' => 'S··',
+		'9/12' => 'S···',
+		'10/12' => 'S····',
+		'11/12' => 'S·····',
+	];
+
+
+	/**
+	 * @param BigNumber|int|string|Stringable $input
+	 * @return string
+	 * @throws OutOfSetException
+	 * @see https://en.wikipedia.org/wiki/Roman_numerals (Fractions)
+	 */
+	public static function convert($input): string
+	{
+		$rationalNumber = BigRational::of((string) $input)->simplified();
+
+		if ($rationalNumber->isLessThan('1/12')) {
+			throw new OutOfSetException((string) $input . ' (less than 1/12)', 'integers >= 0, fractions /12');
+		}
+
+		$denominatorOriginal = $rationalNumber->getDenominator();
+
+		if (in_array((string) $denominatorOriginal, ['1', '2', '3', '4', '6', '12'], true) && $denominatorOriginal->isLessThanOrEqualTo(12)) {
+			$toFinalMultiplier = BigInteger::of(12)->dividedBy($denominatorOriginal)->toInt();
+			$numeratorMultiplied = $rationalNumber->getNumerator()->multipliedBy($toFinalMultiplier);
+
+			$intFinal = $numeratorMultiplied->quotient(12);
+			$numeratorFinal = $numeratorMultiplied->mod(12)->toInt();
+
+			$out = '';
+
+			// Integer part
+			if ($intFinal->isGreaterThan(0)) {
+				$out .= IntToRoman::convert($intFinal);
+			}
+
+
+			// Fraction part
+			if ($numeratorFinal > 0) {
+				$out .= self::$fractionConversionTable["$numeratorFinal/12"];
+			}
+
+			return $out;
+		} else {
+			throw new OutOfSetException((string) $input);
+		}
+	}
+}