[zokier]

That Zimmermann paper is far more useful than the article. Notably LLVM libm is correctly rounded for most single precision ops.

Notable omission are crlibm/rlibm/core-math etc libs which claim to be more correct, but I suppose we can already be pretty confident about them.

[lifthrasiir]

CORE-MATH is working directly with LLVM devs to get their routines to the LLVM libm, so no additional column is really required.

[AlotOfReading]

I've found that LLVM is slightly worse than GCC on reproducibility once you get past the basic issues in libm. For example, LLVM will incorrectly round sqrt on ppc64el in some unusual circumstances:

https://github.com/J-Montgomery/rfloat/blob/8a58367db32807c8...

[dzaima]

On the ppc64 thing, some ways to avoid it: https://godbolt.org/z/fx88rYz5v

[dzaima]

...on -ffast-math. Of course you'll have arbitrary behavior of (at least) a couple ULPs on -ffast-math, but it'll be faster (hopefully)! That's, like, the flag's whole idea.

[AlotOfReading]

I didn't say it was a bug for exactly that reason, but as the comment explains this doesn't affect any platform or compiler combination except ppc64 LLVM, or even most usages of sqrt for that target.

LLVM has lots of small reproducibility issues like this that GCC doesn't, but also much better documentation around its limitations. The point of this library is to eliminate as many of those as possible without performance costs.

[dzaima]

"doesn't affect other things" is in no way ever whatsoever a reason to do anything in any way related to thinking, believing, or hoping that it might, would, or should affect nothing, especially around compiler optimizations (fun sentence to write, and one I violate myself for some things, but trivially true regardless). I'd be curious to hear about actual issues though.

The ppc64 case looks like llvm very intentionally not using the existing square root instruction, instead emitting a sequence of manual operations that supposedly run faster. And it's entirely in its right to do so, and it should affect no correct code (not that it's even really possible to write "correct code" under -ffast-math).

[AlotOfReading]

Note that this isn't even a case where a single sqrt() call is non-reproducible, but only sequences of inlined sqrt calls within an unrolled loop and I agree with you.

Some broader context is probably warranted though. This originated out of a discussion with the authors of P3375 [0] about the actual performance costs of reproducibility. I suspected that existing compilers could already do it without a language change and no runtime cost using inline assembly magic. This library was the experiment to see if I was full of it.

There were only a few minor limitations it found. One was this issue, which happens "outside" what the library is attempting to do (though potentially still fixable as your godbolt link demonstrated). Another was that Clang and GCC have slightly different interpretations of "creative" register constraints. Clang's interpretation is closer to GCC's docs than GCC itself, but produces worse code.

Otherwise, this gives you reproducibility right up to the deeper compiler limitations like NaN propagation at essentially no performance cost. I wasn't able to find any "real" cases where it's not reproducible, only incredibly specific situations like this one across all 3 major compilers and even the minor ones I tried.

[0] https://isocpp.org/files/papers/P3375R2.html

[dzaima]

> but only sequences of inlined sqrt calls within an unrolled loop

Somewhat-relatedly, that's also a problem with vectorized math libraries, affecting both gcc and clang, where the vectorized function has a different result to the scalar standard-libm one (and indeed gcc wants at least "-fno-math-errno -funsafe-math-optimizations -ffinite-math-only" to even allow using vector math libraries, even though it takes explicit flags to enable one (clang's fine with just "-fno-math-errno")).

For what it's worth, clang has __arithmetic_fence for doing the exact thing you're using inline asm for I believe; and the clang/llvm instruction-level constrained arith I noted would be the sane way to achieve this.

The code sample shown in P3375 should be just consequences of fma contraction on gcc/clang I believe? i.e. -ffp-contract=off makes the results consistent for both gcc and clang. I do think it's somewhat funky that -ffp-contract=on is the default, but oh well the spec allows it and it is a perf boost (and a precision boost.. if one isn't expecting the less precise result) and one can easily opt out.

Outside of -ffast-math and -ffp-contract=on (and pre-SSE x86-32 (i.e. ≥26-year-old CPUs) where doing things properly is a massive slowdown) I don't think clang and gcc should ever be doing any optimizations that change numerical values (besides NaN bit patterns).

Just optimization-fencing everything, while a nice and easy proof-of-concept, isn't something compiler vendors would just accept as the solution to implement; that's a ~tripling of IR instructions for each fp operation, which'd probably turn into a quite good compilation speed slowdown, besides also breaking a good number of correct optimizations. (though, again, this shouldn't even be necessary)

And -ffast-math should be left alone, besides perhaps desiring support to disable it at a given scope/function; I can definitely imagine that, were some future architecture to add a division instruction that can have 1ULP of error and is faster than the regular division, that compilers would absolutely use it for all divisions on -ffast-math, and you couldn't work around that with just optimization fences.

[pclmulqdq]

The current correctly rounded libraries work well with 32-bit float, but only provably produce correct rounding with 64-bit float in some cases. It turns out it's rather difficult to prove that you will produce a correctly rounded result in all cases, even if you have an algorithm that works. That means that each of these libraries has only a sunset of operations.