* Richard Biener: >> > > GCC contraction behavior is rather inconsistent. It does not contract x >> > > + x - x without -ffast-math, for example, although I believe it would be >> > > permissible under the rules that enable FMA contraction. This whole > > Is that really just x + x - x? We currently gate simplifying x - x to zero > on no-signed-zeros and round-to-nearest and have no special > handling for x + x - x.
It's just an example I made up, and checked that GCC wouldn't optimize it by default (without -ffast-math et al.). I believe the rule that GCC invokes to introduce FMA under -ffp-contract=standard (and -ffp-contract=fast) would apply to these contractions as well. Or put differently, -ffp-contract= seems to be exclusively about FMA, while the option name and description is more generic. x - x is different because replacing it with 0 doesn't seem to be a valid contraction because it's incorrect for NaNs. x + x - x seems to be different in this regard, but in our implementation, there might be a quirk about sNaNs and qNaNs. >> The "correctness trumps performance" principle still applies, and >> -ffp-contract=fast (the current default outside of -std=cNN) is >> known to cause correctness issues and violates the C language standard. >> And -ffast[-and-loose]-math for is not going away. > > I think that changing the default to =standard without -ffast-math is > reasonable. IIRC the standard allows such default if it's indicated, > so it doesn't require =off anywhere. How much numerical code is compatible with that? For example, David Goldberg's What Every Computer Scientist Should Know About Floating-Point Arithmetic (revised) contains this sentence: | A language definition that does not require parentheses to be honored | is useless for floating-point calculations. <https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html> Few people have access to the IEEE 754 standard, and Goldberg's article is therefore widely quoted as gospel. If I understand this correctly, according to Goldberg, contractions make C “useless”. But I'm not a floating point person, and I nowadays regret that I looked down upon the numerical methods people at university. Thanks, Florian
