JavaScript – Cube Root & Beyond

Lately, I have been in a math oriented mood.  Yesterday, I was thinking about how the fact that you can take the square root of a number in JavaScript, but not the cube root, 4^th root, etc..  Naturally, I looked to Wikipedia to find the algorithm to find the n^th root of a number.  I developed the following unnecessary function:

function bad_nthroot(x, n) {
  // If an error occurs, don't return anything.
  try {
    // If an error occurs
    // Loop through the nth root algorithm until no difference is found.
    var x2, A = x, n1 = n - 1, itersLeft = 99;
    do {
      x2 = x;
      x = (n1 * x2 + A / Math.pow(x2, n1)) / n;
    } while(x != x2 && itersLeft--);
    
    // If less than 100 iterations were done or if the difference between the
    // previous approximation and the current one is acceptable, return the
    // current one.
    if((itersLeft || (Math.abs(x - x2) < 1 && (x < 0) == (x2 < 0))) && isFinite(x))
      return x;
  } catch(e){}
}

After testing out the function a bit and taking a look at an online example, I realized that I could have done it with the Math.pow(). After all, the cube root of a number is the same thing as that number to the power of ¹/₃. With this in mind, I redeveloped the function and came up with the following, more accurate function:

function nthroot(x, n) {
  try {
    var negate = n % 2 == 1 && x < 0;
    if(negate)
      x = -x;
    var possible = Math.pow(x, 1 / n);
    n = Math.pow(possible, n);
    if(Math.abs(x - n) < 1 && (x > 0 == n > 0))
      return negate ? -possible : possible;
  } catch(e){}
}

One notable difference is the fact that calling bad_nthroot(8, 1/2) results in 63.99999999999999. On the other hand, nthroot(8, 1/2) results in 64. There are many other differences as well.

The reason I created this function instead of using Math.pow(x, 1 / n) is because of examples such as Math.pow(-8, 1 / 3). Even though the cube root of -8 is -2, Math.pow(-8, 1 / 3) results in NaN. On the other hand, nthroot(-8, 3) results in the expected value of -2.

If you find something wrong with my nthroot function, please let me know.