/*
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* newton-method-sqrt.js
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*
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*/
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import {terminal} from "./dfhi.js";
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window.main = function(...argv) {
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const testData = [0, 1.25, 3.758, 4.229, 6.735, 123456.789, (1<<30) + 1];
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for(const c of testData) {
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const cquad = c*c;
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const csqrt = sqrt(cquad);
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const msqrt = Math.sqrt(cquad);
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terminal.printl({"quadrat": cquad, "sqrt":csqrt, "Math.sqrt":msqrt, "expected": c})
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}
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};
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function sqrt(c) {
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const EPSILON = 1E-16;
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let xn = c;
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let q = c/xn; // auxiliary variable to avoid multiple division c/xn
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// !\left| \frac{x^2 - c}{c} \right| > \varepsilon!
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while(Math.abs(xn - q) > EPSILON*q ) { // same as |xn - c/xn| > EPSILON * c/xn
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xn = (q + xn) / 2;
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q = c/xn;
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}
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return xn;
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}
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