> Fast-math can cause hard range guarantees to fail. Maybe you’ve got code that you can prove that, even with rounding error, the result will still be >= 0.
Floats do this too, it’s pretty routine to bump into epsilon out-of-range issues without fast-math. Most people don’t prove things about their rounding error, and if they do, it’s easy for them to account for 3 ULPs of fast-math error compared to 1/2 ULP for the more accurate operations. Like, nobody who knows what they’re doing will call sqrt() on a number that is fresh out of a multiplier and might be anywhere near zero without testing for zero explicitly, right? I’m sure someone has done it, but I’ve never seen it, and it ranks high on the list of bad ideas even if you steer completely clear of fast-math, no?
I guess I just wanted to resist the unspecific parts of the FUD just a little bit. I like your list a lot because it’s specific. Fast-math does carry some additional risks for accuracy sensitive code, and clearly as you and others showed, can infect and impact your whole app, and it can sometimes lead to situations where things break that wouldn’t have happened otherwise. But I think in the grand scheme these situations are quite rare compared to how often people mess up regular floating point math. For a very wide swath of people doing casual arithmetic, fast-math is not likely to cause more problems than floats cause, but it’s fair to want to be careful and pay attention.
and yet, for audio processing, this is an option that most DAWs either implement silently, or offer users the choice, because denormals are inevitable in reverb tails and on most Intel processors they slow things by orders of magnitude.
My DAW uses both "denormals are zero" and "flush denormals to zero" to try to avoid them; it also offers a "DC Bias" option where extremely small values are added to samples to avoid denormals.
The slowing down on Intel platforms has always frustrated me because denorms provide nice smoothing around 0.
At the same time it was nice only having to consider normal floating point when trying to get more accuracy out of calculations, etc.