Make complex sin and cos type stable

[malmaud]

cf #11839

[yuyichao]

Would it be too much to add an specialization for Complex{T<:Integer} that bypass the check for infinity and nan?

[tkelman]

Could use a few @inferred tests

[malmaud]

@tkelman Done
@yuyichao What's the advantage? I'm just following @andreasnoack 's suggestion in the linked issue.

[yuyichao]

Performance? (This is why I didn't go ahead and implement that).

See my benchmark result here

Depending on the machine I use, I can see on average 1%-20% performance improvement for Int and ~1-2% performance improvement (as well as 1% reduction in allocation) for BigInt.

[malmaud]

@yuyichao What do you think of this solution?

[yuyichao]

LGTM as long as there AbstractFloat is the only type that can have infinity / nan....

I've also noticed that the speed up I've seen for the Int version might be related to #13551 (The results are very different with #13553 and the version that has special treatment for integers can be ~10% slower in some cases).

It's probably better to benchmark different versions and pick the best one.

[malmaud]

Hmm, maybe it would be more generic to reverse things and have the generic version check for infinity and nan and an int-specialized version bypass those checks.

[malmaud]

Alright, this is g2g.