dist-javascript-algorithms-and-data-structures/dist/algorithms/math/fibonacci/fibonacciNthClosedForm.js

Algorithms and data-structures implemented on JavaScript

"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.default = fibonacciClosedForm;

/**
 * Calculate fibonacci number at specific position using closed form function (Binet's formula).
 * @see: https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression
 *
 * @param {number} position - Position number of fibonacci sequence (must be number from 1 to 75).
 * @return {number}
 */
function fibonacciClosedForm(position) {
  const topMaxValidPosition = 75; // Check that position is valid.

  if (position < 1 || position > topMaxValidPosition) {
    throw new Error(`Can't handle position smaller than 1 or greater than ${topMaxValidPosition}`);
  } // Calculate √5 to re-use it in further formulas.


  const sqrt5 = Math.sqrt(5); // Calculate φ constant (≈ 1.61803).

  const phi = (1 + sqrt5) / 2; // Calculate fibonacci number using Binet's formula.

  return Math.floor(phi ** position / sqrt5 + 0.5);
}