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<?php |
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namespace Samsara\Fermat\Provider; |
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use ReflectionException; |
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use Samsara\Exceptions\SystemError\PlatformError\MissingPackage; |
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use Samsara\Exceptions\UsageError\IntegrityConstraint; |
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use Samsara\Exceptions\UsageError\OptionalExit; |
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use Samsara\Fermat\Enums\NumberBase; |
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use Samsara\Fermat\Numbers; |
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use Samsara\Fermat\Types\Base\Interfaces\Callables\ContinuedFractionTermInterface; |
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use Samsara\Fermat\Types\Base\Interfaces\Numbers\SimpleNumberInterface; |
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use Samsara\Fermat\Values\ImmutableDecimal; |
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/** |
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* |
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*/ |
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class SeriesProvider |
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{ |
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public const SUM_MODE_ADD = 1; |
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public const SUM_MODE_SUB = 2; |
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public const SUM_MODE_ALT_ADD = 3; |
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public const SUM_MODE_ALT_SUB = 4; |
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public const SUM_MODE_ALT_FIRST_ADD = 5; |
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public const SUM_MODE_ALT_FIRST_SUB = 6; |
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/** |
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* Creates a series that evaluates the following: |
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* |
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* SUM[$startTerm -> infinity]( |
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* $numerator($n) × $input^$exponent($n) |
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* -------------------------------- |
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* $denominator($n) |
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* ) |
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* |
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* Where $n is the current term number, starting at $startTerm, and increasing by 1 each loop; where $numerator, |
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* $exponent, and $denominator are callables that take the term number (as an int) as their only input, and give the |
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* value of that section at that term number; and where $input is the x value being considered for the series. |
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* |
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* The function continues adding terms until a term has MORE leading zeros than the $scale setting. (That is, |
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* until it adds zero to the total when considering significant digits.) |
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* |
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* @param SimpleNumberInterface $input |
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* @param callable $numerator |
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* @param callable $exponent |
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* @param callable $denominator |
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* @param int $startTermAt |
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* @param int $scale |
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* @param int $consecutiveDivergeLimit |
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* @param int $totalDivergeLimit |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws OptionalExit |
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* @throws ReflectionException |
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*/ |
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public static function maclaurinSeries( |
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SimpleNumberInterface $input, // x value in series |
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callable $numerator, // a function determining what the sign (+/-) is at the nth term |
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callable $exponent, // a function determining the exponent of x at the nth term |
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callable $denominator, // a function determining the denominator at the nth term |
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int $startTermAt = 0, |
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int $scale = 10, |
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int $consecutiveDivergeLimit = 5, |
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int $totalDivergeLimit = 10): ImmutableDecimal |
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{ |
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++$scale; |
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37 |
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$sum = Numbers::makeZero($scale); |
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$value = Numbers::make(Numbers::IMMUTABLE, $input->getValue(NumberBase::Ten), $scale); |
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$continue = true; |
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$termNumber = $startTermAt; |
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$adjustmentOfZero = 0; |
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$prevDiff = Numbers::makeZero($scale); |
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$prevSum = $sum; |
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$divergeCount = -1; |
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$persistentDivergeCount = -1; |
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$currentScale = 0; |
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37 |
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while ($continue) { |
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$term = Numbers::makeOne($scale); |
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try { |
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$exTerm = $value->pow($exponent($termNumber)); |
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$term = $term->multiply($exTerm); |
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$term = $term->divide($denominator($termNumber), $scale); |
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$term = $term->multiply($numerator($termNumber)); |
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} catch (IntegrityConstraint $constraint) { |
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return $sum->truncateToScale($currentScale+1); |
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} |
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/** @var ImmutableDecimal $term */ |
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if ($term->numberOfLeadingZeros() >= $scale && !$term->isWhole()) { |
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$continue = false; |
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} |
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$currentScale = $term->numberOfLeadingZeros(); |
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if ($term->isEqual(0)) { |
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$adjustmentOfZero++; |
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} else { |
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$adjustmentOfZero = 0; |
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} |
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if ($adjustmentOfZero > 15) { |
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$continue = false; |
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} |
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/** @var ImmutableDecimal $sum */ |
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$sum = $sum->add($term); |
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$currDiff = $sum->subtract($prevSum)->abs(); |
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if ($prevDiff->isLessThan($currDiff)) { |
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$divergeCount++; |
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$persistentDivergeCount++; |
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} else { |
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$divergeCount = 0; |
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} |
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if ($divergeCount === $consecutiveDivergeLimit || $persistentDivergeCount === $totalDivergeLimit) { |
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throw new OptionalExit( |
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'Series appear to be diverging. Current diverge count: '.$divergeCount.' | Persistent diverge count: '.$persistentDivergeCount, |
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'A call was made to SeriesProvider::maclaurinSeries() that seems to be diverging. Exiting the loop.', |
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'The series being calculated appears to be diverging, and the process has been stopped in an attempt to avoid an infinite loop.' |
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); |
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} |
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$prevDiff = $currDiff; |
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$prevSum = $sum; |
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$termNumber++; |
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} |
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return $sum->roundToScale($scale); |
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} |
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/** |
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* This function processes a generalized continued fraction. In order to use this you must provide |
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* two callable classes that implement the ContinuedFractionTermInterface. This interface defines the |
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* expected inputs and outputs of the callable used by this function. |
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* |
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* This function evaluates continued fractions in the form: |
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* |
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* b0 + (a1 / (b1 + (a2 / (b2 + (a3 / b3 + ...))))) |
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* |
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* This is a continued fraction in the form used in complex analysis, referred to as a generalized continued fraction. |
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* |
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* For more information about this, please read the wikipedia article on the subject: |
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* |
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* [https://en.wikipedia.org/wiki/Generalized_continued_fraction](https://en.wikipedia.org/wiki/Generalized_continued_fraction) |
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* |
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* @param ContinuedFractionTermInterface $aPart |
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* @param ContinuedFractionTermInterface $bPart |
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* @param int $terms |
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* @param int $scale |
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* @param int $sumMode |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws MissingPackage |
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*/ |
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public static function generalizedContinuedFraction( |
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ContinuedFractionTermInterface $aPart, |
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ContinuedFractionTermInterface $bPart, |
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int $terms, |
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int $scale, |
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int $sumMode = self::SUM_MODE_ADD |
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): ImmutableDecimal |
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{ |
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$intScale = $scale; |
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$start = $bPart(0); |
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$prevDenominator = new ImmutableDecimal(0, $intScale); |
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$loop = 0; |
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for ($i = $terms;$i > 0;$i--) { |
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$loop++; |
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switch ($sumMode) { |
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case self::SUM_MODE_ADD: |
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case self::SUM_MODE_ALT_FIRST_SUB: |
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$prevDenominator = $bPart($i)->add($prevDenominator); |
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break; |
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case self::SUM_MODE_SUB: |
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case self::SUM_MODE_ALT_FIRST_ADD: |
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4 |
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$prevDenominator = $bPart($i)->subtract($prevDenominator); |
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4 |
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break; |
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} |
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if ($prevDenominator->isEqual(0)) { |
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throw new IntegrityConstraint( |
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'Cannot divide by zero', |
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'balh', |
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'Current $i: '.$i.' | Current terms: '.$terms.' | Loop: '.$loop |
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); |
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} else { |
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$prevDenominator = $aPart($i)->divide($prevDenominator, $intScale); |
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} |
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} |
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27 |
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switch ($sumMode) { |
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case self::SUM_MODE_SUB: |
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case self::SUM_MODE_ALT_FIRST_SUB: |
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1 |
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$result = $start->subtract($prevDenominator); |
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1 |
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break; |
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case self::SUM_MODE_ALT_FIRST_ADD: |
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case self::SUM_MODE_ADD: |
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$result = $start->add($prevDenominator); |
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break; |
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} |
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27 |
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return $result; |
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} |
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} |
JordanRL /
Fermat
Loading history...
This check compares calls to functions or methods with their respective definitions. If the call has more arguments than are defined, it raises an issue.
If a function is defined several times with a different number of parameters, the check may pick up the wrong definition and report false positives. One codebase where this has been known to happen is Wordpress. Please note the @ignore annotation hint above.