Calculating the value of the Fibonacci number.

fibonacci.js

/**
 * +------------------------------------+ 
 * |           FIBONACCI TABLE          |
 * +------------------------------------+
 * | n   0 | 1 | 2 | 3 | 4 | 5 | 6 |  7 |
 * | xn  0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 |
 * +------------------------------------+
 *
 * @see https://en.wikipedia.org/wiki/Big_O_notation
 * @see https://en.wikipedia.org/wiki/Fibonacci_number#Sequence_properties
 */

/**
 * Calculates the value of the Fibonacci number using iterative solution.
 * @return {number} Returns the value of the Fibonacci number.
 * @see https://en.wikipedia.org/wiki/Fibonacci_number#Sequence_properties
 */
function fibonacci(n) {
  var list = [0, 1];
  
  for (var i = 2; i < n + 1; ++i) {
    // TODO: Add validation for `Number.MAX_SAFE_INTEGER`.
    list[i] = list[i - 1] + list[i - 2];
  }
  
  return list[n];
}

/**
 * Calculates the value of the Fibonacci number using recursive solution.
 * @return {number} Returns the value of the Fibonacci number.
 * @see https://en.wikipedia.org/wiki/Fibonacci_number#Sequence_properties
 */
function fibonacci(n) {
  // TODO: Add validation for `Number.MAX_SAFE_INTEGER`.
  return n < 2 ? n : fibonacci(n - 1) + fibonacci(n - 2);
}

/**
 * Calculates the value of the Fibonacci number using Golden ration.
 * @return {number} Returns the value of the Fibonacci number.
 * @see https://en.wikipedia.org/wiki/Fibonacci_number#Sequence_properties
 * @see https://en.wikipedia.org/wiki/Golden_ratio
 *
 * The golden ration `phi ^ n / sqrt(5)` is asymptotic to the fibonacci of n.
 * Rounding that value up, indeed get the fibonacci value.
 */
function fibonacci(n) {
  if (n > 1) {
    var phi = (1 + Math.sqrt(5)) / 2; // 1.6180339887...
    // `Math.pow` returns` Infinity` if the result is greater than `Number.MAX_VALUE`.
    var asymp = Math.pow(phi, n) / Math.sqrt(5);

    return Math.round(asymp);
  }
  return n;
}