REreikonomusha·Jun 14, 2019
The COMPUTABLE-REALS [0] package from the article is interesting because it lets you change the precision even after a computation is “performed”. It basically builds up lazy representations of computations that can (internally) recompute to any precision specified. You do all of your arithmetic as normal and only until you need to do something with an actual decimal representation do you “request” it. You grab the actual approximation as a decimal number with the APPROX-R function, which provides as many digits as you please. There is no need to re-run all of your code which produced the (computable) number in the first place to reapproximate at higher precision.
This all directly falls out of a mathematical formalism called “computable real numbers” [1] which are the (countable!) set of real numbers for which an algorithm exists to comp
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ute the digits to any desired precision. (Usually binary digits are the standard way to write out the definition of a computable number.)
[0] https://github.com/stylewarning/computable-reals
[1] https://en.m.wikipedia.org/wiki/Computable_number