@shriramk @racketlang
I am glad some big company, in this case Google, implemented in practice a phone calculator for exact real number computation.
My PhD thesis was, in fact, about this subject.
But I was more interested in theoretical questions, e.g. whether you could come up with a theoretical higher-order programming language including real numbers such that reals, functions, and functionals are definable in this language if and only if they are computable.
This I achieved. I called the language Real PCF. This is a Turing-universal higher-order programming language for exact real number computation.
And also, one of the papers I read regarding this was Boehm's 1987 one, on which the Android calculator is based on.
In any case, although my interests are mainly theoretical, by my nature, I also flirt with practical things, in particular regarding this subject.
Here is a 2011 Haskell file that computes exactly with real numbers:
https://martinescardo.github.io/papers/fun2011.lhs
In addition to all that Boehm computes, we compute integrals.
Also this literate file contains a lot of discussion of the history of the subject (although it doesn't aim to be comprehensive).
This was for Fun in the Afternoon (does this UK meeting series still exist)?