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node_modules/fraction.js/examples/rational-pow.js

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+/*
+Fraction.js v5.0.0 10/1/2024
+https://raw.org/article/rational-numbers-in-javascript/
+
+Copyright (c) 2024, Robert Eisele (https://raw.org/)
+Licensed under the MIT license.
+*/
+const Fraction = require('fraction.js');
+ 
+// Calculates (a/b)^(c/d) if result is rational
+// Derivation: https://raw.org/book/analysis/rational-numbers/
+function root(a, b, c, d) {
+
+  // Initial estimate
+  let x = Fraction(100 * (Math.floor(Math.pow(a / b, c / d)) || 1), 100);
+  const abc = Fraction(a, b).pow(c);
+
+  for (let i = 0; i < 30; i++) {
+    const n = abc.mul(x.pow(1 - d)).sub(x).div(d).add(x)
+
+    if (x.n === n.n && x.d === n.d) {
+      return n;
+    }
+    x = n;
+  }
+  return null;
+}
+
+root(18, 2, 1, 2); // 3/1