> But one should expect a single function does not vary in the last 5 digits as one example did. Why not? The whole selling point of floats is that they're a f

> But one should expect a single function does not vary in the last 5 digits as one example did. Why not? The whole selling point of floats is that they're a fast approximation to real arithmetic in a bunch of useful cases. I'd personally be much more miffed by an excessively slow implementation of a transcendental than one which was off even by a large number of bits. If there's a fast solution with better precision then that's great, but low precision by itself doesn't strike me as particularly problematic. > Why should anyone use double precision if that's the kind of slop an implementation can have? Because by using float64 instead of float32 you can cheaply get a ton more precision even with sloppy algorithms. If there's only 16ish bits of slop you could probably get a full-precision float32 operation just by using an intermediate cast to float64 (proof needed for the algorithm in question of course).