Beware of Fast-Math

I helped design an API for "algebraic operations" in Rust: <https://github.com/rust-lang/rust/issues/136469>, which are coming along nicely. These operations are 1. Localized, not a function-wide or program-wide flag. 2. Completely safe, -ffast-math includes assumptions such that there are no NaNs, and violating that is undefined behavior. So what do these algebraic operations do? Well, one by itself doesn't do much of anything compared to a regular operation. But a sequence of them is allowed to be transformed…

Fun fact: when working on Herbie (http://herbie.uwplse.org), our automated tool for reducing floating-point error by rearranging your mathematical expressions, we found that fast-math often undid Herbie's improvements. In a sense, Herbie and fast-math are opposites: one makes code more accurate (sometimes slower, sometimes faster), while the other makes code faster (sometimes less accurate, sometimes more).

Previous discussion here: https://news.ycombinator.com/item?id=29201473 The injunction "Firstly, GCC should address the FTZ library issue: the bug has been open for 9 years, but is still marked NEW." is out of date, a fix is now in-place in the GCC master branch https://gcc.gnu.org/bugzilla/show_bug.cgi?id=55522#c45 (possibly prompted by this article). Well worth a read though.