I need some help. I'm trying to approximate the square roots of very large numbers. I wrote the code, but it isn't working right, so obviously I'm overlooking something. In brief, the method for approximating square roots works like this:

1. Guess at the square root
2. Divide the number you're trying to get the square root of by the number you just guessed.
3. Add the quotient to your original guess and divide by 2.
4. Treat this new number as your guess at the square root and go back to step #2.

Here's my original code:

use Math::BigFloat;

sub SqrRoot {
    my $num = Math::BigFloat->new( shift );
    my $iterations = shift || 50;
    my $guess = Math::BigFloat->new( $num / 2 );
    for ( 1..$iterations ) {
        $guess = (( $num / $guess ) + $guess ) / 2;
    }
    return $guess;
}
[download]

When I saw that this wasn't working, I broke the code down a little further to check the values during the whole process.

use Math::BigFloat;

sub SqrRoot {
    my $num        = Math::BigFloat->new( shift );
    my $iterations = shift || 50;
    my $guess      = Math::BigFloat->new( $num / 2 );
    my $temp       = Math::BigFloat->new();
    for ( 1..$iterations ) {
        $temp  = Math::BigFloat->new( $num / $guess );
        print ("$num / $guess = $temp\n");
        $temp += $guess;
        $guess = $temp / 2;
        print ("$guess\n----------\n");
    }
    return $guess;
}
[download]

In theory, this process should become more and more accurate, the more iterations it is run through. However, for reasons I don't know, the above code is dropping decimal places, and actually makes the result less accurate on each iteration. What am I missing?

Thanks in advance.
___________________
Kurt

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