[QUESTION] Can we remove the `isnan` check in the `complex<T>` multiplication operator?

[jrhemstad]

The operator*(cuda::std::complex<T>, cuda::std::complex<T>) does an isnan check on the resulting real and imaginary parts of the operation before returning the resulting complex<T>.

Is this required by the C++ Standard?

At first glance, it would seem this is not required:

If the result of a function is not mathematically defined or not in the range of representable values for its type, the behavior is undefined.

https://eel.is/c++draft/complex.numbers#general-3

If it is not required, can we remove these checks?

[jrhemstad]

@griwes @wmaxey @gonzalobg @brycelelbach

Can any of you shine some light on this?

[jrhemstad]

CC @cliffburdick @luitjens

[jrhemstad]

This implementation appears to be inherited from the C99 Standard Annex G

Given that the C++ Standard does not implicitly inherit everything from the C Standard and https://eel.is/c++draft/complex.numbers#general-3 makes no mention of any requirement about anything like this, I am convinced that we can remove this from our implementation and remain conforming to the C++ Standard.

[luitjens]

Ran a quick experiment where I modified 11.5 libcu++. Modifications were to fix double cast and comment out isnan checks. This data indicates the isnan checks are still very expensive on performance. 65us vs 110us.

The benchmark is found here: https://github.com/NVIDIA/MatX/blob/main/bench/00_transform/conv.cu

A100 isnan checks, double fix

T	Samples	CPU Time	Noise	GPU Time	Noise	Batch GPU	Batch
cuda::std::__4::complex	31079x	120.867 us	1.40%	112.339 us	0.53%	109.970 us	31080x

A100 NO isnan checks, double fix

T	Samples	CPU Time	Noise	GPU Time	Noise	Batch GPU	Batch
cuda::std::__4::complex	32944x	76.357 us	1.45%	67.539 us	1.59%	64.615 us	32945x