Sure I agree completely and didn’t mean to suggest otherwise. Most languages have implementations of all the above - attempts at certain types of exact real, arbitrary precision, and big integers. It’s worth noting that this library is made out of big nums and rationals, so it tries to be exact when it can, but it can’t always, so it may not be accurate to call it exact real arithmetic. That’s why the title is “toward” real numbers and didn’t claim to be exact.

And I’m curious whether you meant that exact real arithmetic is different in such a way that it would change either of the points that I made? Does it mean that performance is good enough that all languages should have it built in? Does it mean that approximation errors should then be considered the same as execution errors?