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/*
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* Reference: https://en.wikipedia.org/wiki/Farey_sequence
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* Inspiration: https://www.youtube.com/watch?v=7LKy3lrkTRA
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*
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* Farey Approximation algorithm is an algorithm to
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* approximate a reduced fraction value for a certain
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* decimal number x where 0 < x < 1.
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*
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* The algorithm works by keeping two fractional upper and
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* lower bounds which start at 0 / 1 and 1 / 1. These values
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* are then used to find the "mediate" which is a value between
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* the two fractions.
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*
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* For any two fractions a / b and c / d,
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* mediate = a + c / b + d
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*
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* Then it is checked if the decimal is greater than or less
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* than the mediate and then the lower or the upper value is
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* set to be the mediate respectively.
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*
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* This is repeated for n times and then the mediate is
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* returned.
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*
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* This is explained in a greater detail in the "Inspiration"
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* link.
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*/
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2021-07-19 13:04:44 +05:30
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2023-10-03 23:08:19 +02:00
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function fareyApproximation(decimal, repeat = 20) {
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let a = 0
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let b = 1
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let c = 1
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let d = 1
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let numerator
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let denominator
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for (let i = 0; i < repeat; i++) {
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numerator = a + c
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denominator = b + d
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if (decimal > numerator / denominator) {
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;[a, b] = [numerator, denominator]
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} else {
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;[c, d] = [numerator, denominator]
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}
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}
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return { numerator, denominator }
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}
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export { fareyApproximation }
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