[retrac]

Rounding transcendentals correctly has unknown time and space complexity. [1] Sort of brushes up against the halting problem. With limited precision, the upper limit becomes calculable but it's rather large - packages that offer correct rounding on 64-bit floating point use potentially hundreds of bytes to deal with a single floating point value. Dedicated circuitry to implement it fast would be big and complicated even by today's standards.

https://en.wikipedia.org/wiki/Rounding#Table-maker's_dilemma

[lifthrasiir]

True in general, almost false for binary64. Important univariate functions have been thoroughly mapped for known hard-to-round cases, which resulted in the fact that we only need at most triple-double format to do the correct rounding. (Bivariate functions like `pow` are much harder, and not yet fully mapped as of this writing.) As a result we now have a mathematical library that almost ensures correct rounding [1], and a further optimization is currently in progress.

[1] https://core-math.gitlabpages.inria.fr/

[throwawaymaths]

unknown time and space complexity

True in general but for the basic datatypes sent through hardware regusters your processor architecture has fixed precision. So the time and space complexity is O(1)

[ImHereToVote]

We should just use analog circuit for this sort of thing where the exact precision doesn't matter.