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namespace Samsara\Fermat\Provider; |
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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\Fermat\Enums\CalcMode; |
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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\Numbers\DecimalInterface; |
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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 ConstantProvider |
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{ |
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private static DecimalInterface $pi; |
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private static DecimalInterface $e; |
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private static DecimalInterface $ln10; |
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private static DecimalInterface $ln2; |
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private static DecimalInterface $ln1p1; |
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/** |
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* @param int $digits |
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* @return string |
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* @throws IntegrityConstraint |
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* @throws MissingPackage |
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*/ |
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public static function makePi(int $digits): string |
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{ |
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if (isset(self::$pi) && self::$pi->numberOfDecimalDigits() >= $digits) { |
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return self::$pi->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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$internalScale = ($digits*2) + 10; |
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$C = Numbers::make(Numbers::IMMUTABLE, '10005', $internalScale)->setMode(CalcMode::Precision)->sqrt($internalScale)->multiply(426880); |
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$M = Numbers::make(Numbers::IMMUTABLE, '1', $internalScale)->setMode(CalcMode::Precision); |
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$L = Numbers::make(Numbers::IMMUTABLE, '13591409', $internalScale)->setMode(CalcMode::Precision); |
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$K = Numbers::make(Numbers::IMMUTABLE, '6', $internalScale)->setMode(CalcMode::Precision); |
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$X = Numbers::make(Numbers::IMMUTABLE, '1')->setMode(CalcMode::Precision); |
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$sum = Numbers::make(Numbers::MUTABLE,'0', $internalScale + 2)->setMode(CalcMode::Precision); |
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$termNum = 0; |
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$one = Numbers::makeOne($internalScale)->setMode(CalcMode::Precision); |
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$continue = true; |
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while ($continue) { |
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$term = $M->multiply($L)->divide($X, $internalScale); |
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if ($termNum > $internalScale) { |
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$continue = false; |
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} |
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$sum->add($term); |
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$M = $M->multiply($K->pow(3)->subtract($K->multiply(16))->divide($one->add($termNum)->pow(3), $internalScale)); |
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$L = $L->add(545140134); |
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$X = $X->multiply('-262537412640768000'); |
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$K = $K->add(12); |
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$termNum++; |
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} |
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$pi = $C->divide($sum, $internalScale); |
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self::$pi = $pi->truncateToScale($digits); |
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return $pi->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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/** |
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* Consider also: sum [0 -> INF] { (2n + 2) / (2n + 1)! } |
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* |
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* This converges faster (though it's unclear if the calculation is actually faster), and can be represented by this |
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* set of Fermat calls: |
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* |
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* SequenceProvider::nthEvenNumber($n + 1)->divide(SequenceProvider::nthOddNumber($n)->factorial()); |
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* |
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* Perhaps by substituting the nthOddNumber()->factorial() call with something tracked locally, the performance can |
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* be improved. Current performance is acceptable even out past 200 digits. |
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* |
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* @param int $digits |
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* @return string |
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* @throws IntegrityConstraint |
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*/ |
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public static function makeE(int $digits): string |
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{ |
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if (isset(self::$e) && self::$e->numberOfDecimalDigits() >= $digits) { |
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return self::$e->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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$internalScale = $digits + 3; |
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$one = Numbers::makeOne($internalScale+5)->setMode(CalcMode::Precision); |
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$denominator = Numbers::make(Numbers::MUTABLE, '1', $internalScale)->setMode(CalcMode::Precision); |
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$e = Numbers::make(NUmbers::MUTABLE, '2', $internalScale)->setMode(CalcMode::Precision); |
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$n = Numbers::make(Numbers::MUTABLE, '2', $internalScale)->setMode(CalcMode::Precision); |
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$continue = true; |
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while ($continue) { |
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$denominator->multiply($n); |
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$n->add($one); |
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$term = $one->divide($denominator); |
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if ($term->numberOfLeadingZeros() > $internalScale || $term->isEqual(0)) { |
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$continue = false; |
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} |
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$e->add($term); |
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} |
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self::$e = $e->truncateToScale($digits); |
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return $e->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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/** |
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* The lnScale() implementation is very efficient, so this is probably our best bet for computing more digits of |
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* ln(10) to provide. |
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* |
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* @param int $digits |
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* @return string |
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* @throws IntegrityConstraint |
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*/ |
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public static function makeLn10(int $digits): string |
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{ |
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if (isset(self::$ln10) && self::$ln10->numberOfDecimalDigits() >= $digits) { |
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return self::$ln10->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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$ln10 = Numbers::make(Numbers::IMMUTABLE, 10, $digits+2)->setMode(CalcMode::Precision); |
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$ln10 = $ln10->ln(); |
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self::$ln10 = $ln10; |
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return $ln10->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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/** |
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* This function is a special case of the ln() function where x can be represented by (n + 1)/n, where n is an |
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* integer. This particular special case converges extremely rapidly. For ln(2), n = 1. |
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* |
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* @param int $digits |
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* @return string |
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*/ |
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public static function makeLn2(int $digits): string |
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{ |
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if (isset(self::$ln2) && self::$ln2->numberOfDecimalDigits() >= $digits) { |
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return self::$ln2->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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$twoThirds = Numbers::make(Numbers::IMMUTABLE, str_pad('0.', $digits+3, '6')); |
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$nine = Numbers::make(Numbers::IMMUTABLE, 9, $digits+3); |
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$ln2 = self::_makeLnSpecial($digits, $nine, $twoThirds); |
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self::$ln2 = $ln2; |
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return $ln2->getValue(NumberBase::Ten); |
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} |
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/** |
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* This function is a special case of the ln() function where x can be represented by (n + 1)/n, where n is an |
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* integer. This particular special case converges extremely rapidly. For ln(1.1), n = 10. |
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* |
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* @param int $digits |
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* @return string |
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*/ |
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public static function makeLn1p1(int $digits): string |
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{ |
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if (isset(self::$ln1p1) && self::$ln1p1->numberOfDecimalDigits() >= $digits) { |
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return self::$ln1p1->truncateToScale($digits)->getValue(NumberBase::Ten); |
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} |
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$two = Numbers::make(Numbers::IMMUTABLE, 2, $digits+3); |
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$twentyOne = Numbers::make(Numbers::IMMUTABLE, 21, $digits+3); |
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$fourFortyOne = Numbers::make(Numbers::IMMUTABLE, 441, $digits+3); |
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$twoDivTwentyOne = $two->divide($twentyOne); |
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$ln1p1 = self::_makeLnSpecial($digits, $fourFortyOne, $twoDivTwentyOne); |
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self::$ln1p1 = $ln1p1; |
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return $ln1p1->getValue(NumberBase::Ten); |
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} |
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/** |
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* @param int $digits |
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* @param ImmutableDecimal $innerNum |
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* @param ImmutableDecimal $outerNum |
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* @return ImmutableDecimal |
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*/ |
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private static function _makeLnSpecial(int $digits, ImmutableDecimal $innerNum, ImmutableDecimal $outerNum): ImmutableDecimal |
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{ |
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$one = Numbers::makeOne($digits+3); |
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$two = Numbers::make(Numbers::IMMUTABLE, 2, $digits+3); |
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$sum = Numbers::makeZero($digits+3); |
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$k = 0; |
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do { |
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$diff = $one->divide($one->add($two->multiply($k))->multiply($innerNum->pow($k)), $digits+3)->truncate($digits+2); |
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$sum = $sum->add($diff); |
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$k++; |
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} while (!$diff->isEqual(0)); |
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$lnSpecial = $outerNum->multiply($sum); |
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return $lnSpecial->truncateToScale($digits); |
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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.