square root algorithm C++

Question

I can not figure out why this algorithm enters an infinite loop if the number entered is over 12 digits. Can anyone see why it will never end? Thanks. I just updated the algorithm to use the fabs() function and still get an infinite loop.

double squareroot(double x)

{ /* computes the square root of x */

/* make sure x is not negative .. no math crimes allowed! */
assert( x >= 0 );
if (x==0) return 0;

/* the sqrt must be between xhi and xlo */
double xhi = x;
double xlo = 0;
double guess = x/2;

/* We stop when guess*guess-x is very small */

while (abs(guess*guess-x) > 0.00001 )
{
    if (guess*guess > x){
        xhi = guess;
    }

    else {
        xlo = guess;
    }

    guess = (xhi + xlo)/2;
}
return guess;
}

Answer 1

I believe you should use relative error for the termination, and not the absolute error.

while (abs((guess*guess-x) / guess) > 0.00001)

Otherwise it will take very long time (it's not an infinite loop) to compute square root of very long values.

http://en.wikipedia.org/wiki/Approximation_error

Cheers!

EDIT: moreover, as pointed below in the comments, it is worthy to check if the guess was already guessed in order to avoid infinite loop with some specific corner cases.