ada - bernoulli / joelondon

Published

Edited

Feb 24, 2021

{

const output = [];

let state = {

n: 3,

results: []

};

for (var i = 0; i < 4; ++i) {

nativeJavaScript(state);

output.push(state.results[i + 2]);

}

// Change state structure

function nativeJavaScript(state) {

const n = state.n;

state.results[0] = 1 / 6; // B1

state.results[1] = -1 / 30; // B3

let k = n - 2;

let denom = 2;

let accumulatingFraction = (2 * n) / denom; // i.e. 2n / 2, to keep it authentic

let accumulatingTotal = 0;

// Manually process the first 2 terms

accumulatingTotal += -(2 * n - 1) / (2 * n + 1) / 2; // '#4 and #5' - A0

accumulatingTotal += accumulatingFraction * state.results[0]; // A1

let numerator = 2 * n;

let indexToResult = 1;

do {

accumulatingFraction *= (numerator - 1) / (denom + 1); // first terms of A : (2n-1)/3

accumulatingFraction *= (numerator - 2) / (denom + 2); // #19 second 2n+1/4

accumulatingTotal += accumulatingFraction * state.results[indexToResult]; // #21 A3 * B3

numerator -= 2;

denom += 2;

++indexToResult;

} while (--k > 0);

state.results[indexToResult] = -accumulatingTotal;

state.n++;

}

return output;

}

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