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<?php |
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namespace Samsara\Fermat\Provider; |
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use Samsara\Exceptions\UsageError\IntegrityConstraint; |
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use Samsara\Fermat\Numbers; |
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use Samsara\Fermat\Types\Base\Selectable; |
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class ConstantProvider |
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{ |
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public static function makePi(int $digits): string |
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{ |
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$internalPrecision = $digits + 10; |
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$C = Numbers::make(Numbers::IMMUTABLE, '10005', $internalPrecision)->sqrt($internalPrecision)->multiply(426880); |
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$M = Numbers::make(Numbers::IMMUTABLE, '1', $internalPrecision); |
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$L = Numbers::make(Numbers::IMMUTABLE, '13591409', $internalPrecision); |
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$K = Numbers::make(Numbers::IMMUTABLE, '6', $internalPrecision); |
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$X = Numbers::make(Numbers::IMMUTABLE, '1'); |
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$sum = Numbers::make(Numbers::MUTABLE,'0', $internalPrecision + 2); |
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$termNum = 0; |
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$one = Numbers::makeOne($internalPrecision); |
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$continue = true; |
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while ($continue) { |
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$term = $M->multiply($L)->divide($X); |
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if ($term->numberOfLeadingZeros() > $internalPrecision || $term->isEqual(0)) { |
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$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), $internalPrecision)); |
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$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, $internalPrecision); |
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return $pi->truncateToPrecision($digits)->getValue(); |
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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 $digits): string |
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{ |
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$internalPrecision = $digits + 3; |
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$one = Numbers::makeOne($internalPrecision+5)->setMode(Selectable::CALC_MODE_PRECISION); |
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$denominator = Numbers::make(Numbers::MUTABLE, '1', $internalPrecision)->setMode(Selectable::CALC_MODE_PRECISION); |
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$e = Numbers::make(NUmbers::MUTABLE, '2', $internalPrecision)->setMode(Selectable::CALC_MODE_PRECISION); |
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$n = Numbers::make(Numbers::MUTABLE, '2', $internalPrecision)->setMode(Selectable::CALC_MODE_PRECISION); |
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$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() > $internalPrecision || $term->isEqual(0)) { |
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$continue = false; |
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} |
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$e->add($term); |
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} |
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return $e->truncateToPrecision($digits)->getValue(); |
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} |
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} |
JordanRL /
Fermat
