A while ago I made myself a calculator. I don’t know if anyone else uses it, but for the particular way I like doing calculations, it’s been really good. You’d think that if a calculator does anything, it should perform calculations correctly. But all calculators get things wrong sometimes! This is the story of how I made my calculator a bit more correct, using constructive real arithmetic.
One thing you need to think about when making a calculator is precision. How precise do the answers need to be? Is it OK to do rounding? If you do round, then it’s possible that errors accumulate as you compose operations.
I’ve always wanted to make a calculator that gives exactly correct answers. This isn’t strictly possible: there are more real numbers than a finite number of bits of memory can represent, or a digital display can show, no matter how you encode them. But I’m not going to use every real number, so I’ll be happy with just being correct on the numbers I’m likely to encounter.
