Implement [ Variable ] Precision Floating Point [ Arithmetic ] in CAS Mode

[hugh]

Implementing range arithmetic as an "extra digit" is an opportunity not to be missed, given the small amount of additional overhead compared to the enormous gain of having an error bound for _every_ calculation.

There is virtually no performance hit using this method over a regular BCD implementation. For example, basic arithmetic calculates the error as it handles the end of the mantissa.

I searched for ages for the ideal way calculators should do their math. I did not want to store two numbers in place of one and I did not want the overhead of representing reals as continued fractions.

I also wanted a drop-in replacement for regular BCD that I've been using in the past, that protects me from unstable results and is compatible.

Today's calculators may be relatively powerful, but they still require an embedded solution. I develop apps for mobiles and, more recently, wearable devices. Today's smart phones have x-GHz processors and y-GBs of RAM, but you can't go wasting it because power consumption is your real enemy. If phones, or indeed calculators ran at their advertised speed for more than a short time, the battery would surely be drained quite rapidly.