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Improved performances of trialDivision algorithm in primality test

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I improved the performances of trialDivision by performing fewer checks, while still using the same overall idea of the algorithm.
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Arthur Guiot 2021-10-05 13:19:20 -04:00 committed by GitHub
parent 4548296aff
commit e156b8afd5
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1 changed files with 7 additions and 13 deletions
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src/algorithms/math/primality-test/trialDivision.js
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@ -8,25 +8,19 @@ export default function trialDivision(number) {
return false; return false;
} }
if (number <= 1) {
// If number is less than one then it isn't prime by definition.
return false;
}
if (number <= 3) { if (number <= 3) {
// All numbers from 2 to 3 are prime. // If number is less than one then it isn't prime by definition. But all numbers from 2 to 3 are prime.
return true; return number > 1;
} }
// If the number is not divided by 2 then we may eliminate all further even dividers. // If the number is not divided by 2 or 3 then we may eliminate all further even dividers.
if (number % 2 === 0) { if (number % 2 === 0 || number % 3 === 0) {
return false; return false;
} }
// If there is no dividers up to square root of n then there is no higher dividers as well. // If there is no dividers up to square root of divider then there is no higher dividers as well. To make the algorithm more efficient, we increment by 6 everytime, and make sure to check divider + 2 as well.
const dividerLimit = Math.sqrt(number); for (let divider = 5; number >= (divider * divider); divider += 6) {
for (let divider = 3; divider <= dividerLimit; divider += 2) { if (number % divider === 0 || number % (divider + 2) === 0) {
if (number % divider === 0) {
return false; return false;
} }
} }