[jacobolus]

Floats follow a clear specification which determines precisely how basic arithmetic should work. They should work the same on all popular modern platforms. (Whether specific software libraries are the same is a separate question.)

[zokier]

But transcendentals like sine are not part of the strictly defined basic arithmetic; they are intentionally defined with relaxed behavior.

[jacobolus]

If you implement sine in software using the same sequence of basic arithmetic instructions, the result should be the same across platforms. If you make two different implementations using different arithmetic, then of course you can't rely on them being the same.

[zokier]

Point being that IEEE 754 defines two sets of operations, the required operations (section 5) that should be produce correctly rounded results to the last digit, and recommend operations (section 9) with relaxed requirements. And sine belongs to the latter section, so IEEE 754 does not mandate reproducible results for sine.

[jacobolus]

My understanding is that most software always uses some software implementation of sine, rather than calling a hardware instruction. Which is definitely what you should do if you care about getting the exact same results across platforms.

[dzaima]

Software implementations can and do differ (even dynamically) based on the hardware though - e.g. glibc's sin(x) function, what C code will end up using (if not other languages relying on the C stdlib), uses FMA instructions on my CPU, and thus the exact same binary on the exact same OS with the exact same glibc should behave differently on a very old CPU without FMA where it should have a different implementation (as generally things using FMA cannot be exactly ported to hardware without it without a gigantic drop in performance which'd be extremely unacceptable).

[jacobolus]

Yeah, the lack of FMA in some contexts is a serious bummer. It would be great if every popular CPU platform would figure out a way to get FMA implemented, and if programming languages would figure out better ways to help programmers use it explicitly without making their code too ugly.

[gpderetta]

Even there many standard libraries provide very good precision at least within sane domain.

[TylerE]

Yeah, that’s kind of my point. 99% consistent isn’t.