in reply to
adding numbers and floating point errors
Computers don't handle fractional floating point values very well. Anything other than powers of 1/2 (or their multiples) results in a form that repeats endlessly. This results in truncation or rounding errors, and these will tend to accumulate when you iterate.
You might want to consider keeping your data in rational form (e.g., bigrat) while you are performing your calculations. Doing this can save you lots of problems with rounding or truncation errors. Once you've finished your calculations you can convert your rationals into floating point format, if you wish, for display.