square root approximation in C

sqrt-approx.c

// Note: sqrt -- approximate method for calculating the square root of a number.
double sqrt (double num)
{
    double start = 0.0;
    double epsilon = 0.1;       // Accuracy granularity.

    // Find nearest perfect square.
    while ((num - start * start) > 0)
        start += 1;

    // Calculate the avg of the difference between successive estimates until
    // the value is less than epsilon.

    // Method relies on the fact that if ab=n and a < sqrt(n), then b has to be
    // greater than sqrt(n).

    // Since 'start' is a guess that is less than sqrt(n), it must be that  
    // (n / start) > sqrt(n) -- b/c (n / start) * start = n
    // (that is, n = ab and a = start, and b = n / start).
    double approx, estimate = start;
    while (approx = ((estimate + (num / estimate)) / 2), approx - estimate > epsilon)
        estimate = approx;

    return approx;
}