Heron's method JavaScript

Question

The following code is supposed to return the square root using Heron's method. I am trying to find a "bug" in it, but to be honest, I haven't been able to spot it. I have a question about the "var prevGuess = n" statement. How does "n" work the first time? Is that the bug, and what's the "fix?"

Thanks, I am a bit confused at the moment......

function heronSqrt(n)
{
    var DELTA = 1.0E-10;
    var nextGuess;
    var prevGuess = n;
    do
    {
        nextGuess = (prevGuess + (n/prevGuess))/2;
        prevGuess = nextGuess;
    } while (nextGuess-prevGuess > DELTA)
    return nextGuess;
}

Answer 1

Here is a working version:

function heronSqrt(n)
{
    var DELTA = 1.0E-10;
    var nextGuess  = n;
    var prevGuess;
    do
    {
        prevGuess = nextGuess;
        nextGuess = (prevGuess + (n/prevGuess))/2;
    } while (Math.abs(nextGuess-prevGuess) > DELTA)
    return nextGuess;
}

There were two problems. First, you were updating "prevGuess" before doing the limit check. Second, you need to check the absolute value of the difference between the guesses. I altered the initialization so that it's "nextGuess" that's initialized to the input value, moved the update to "prevGuess" to the first line of the loop, and I added the call to Math.abs().

To make this work for a greater range of values, I think you need to have the value of "DELTA" be proportional to the magnitude of "n". If you try this with huge numbers, it probably won't converge.