faster hypot(::IEEEFloat...)

[mikmoore]

hypot(::IEEEFloat...) can be made faster for 3+ arguments.

using BenchmarkTools

t3 = ntuple(_->randn(), 3)
t4 = ntuple(_->randn(), 4)
t8 = ntuple(_->randn(), 8)
t16 = ntuple(_->randn(), 16)

@btime hypot($t3...)
@btime hypot($t4...)
@btime hypot($t8...)
@btime hypot($t16...)

# master
  9.810 ns (0 allocations: 0 bytes)
  10.110 ns (0 allocations: 0 bytes)
  19.759 ns (0 allocations: 0 bytes)
  50.203 ns (0 allocations: 0 bytes)

# SHA 1a0340c
  7.808 ns (0 allocations: 0 bytes)
  8.008 ns (0 allocations: 0 bytes)
  10.010 ns (0 allocations: 0 bytes)
  14.529 ns (0 allocations: 0 bytes)

The notable savings here come from casting to integers before computing maximum(abs,...) (same result but faster comparisons) and re-associating the final sum (see #48129).

[giordano]

Does this help with #47917?

[mikmoore]

Does this help with #47917?

It appears that issue should be closed on the current master -- probably by #44357. You can see from the timings presented above that 3 not slower than 4 (although it's only marginally faster) on both master and this PR.

[giordano]

It appears that issue should be closed on the current master -- probably by #44357.

#44357 is already in v1.9, where #47917 was reported on.

[KristofferC]

I don't see the issue having been reprod on beta2.

[sethaxen]

I don't see the issue having been reprod on beta2.

Yes, I still see the specific issues in #47917 (comment) and #47917 (comment) on v1.9.0-beta2

[mikmoore]

In any case, the issue was fixed before any efforts from this PR (or otherwise never existed on my architecture). If someone's ambitious, they can try to find the responsible PR and see if it'll be accepted as a backport to 1.9.

[ViralBShah]

Merge?

[mikmoore]

There isn't anything else I was planning to do with this unless someone had additional comments. It's good to merge on my end.

[IanButterworth]

I think this broke build. Was CI green on it?

math.jl
error during bootstrap:
LoadError("sysimg.jl", 3, LoadError("Base.jl", 328, LoadError("math.jl", 844, LoadError("math.jl", 851, UndefVarError(Symbol("@fastmath"))))))
ijl_undefined_var_error at /home/ian/Documents/GitHub/julia/src/rtutils.c:132

[oscardssmith]

CI was green but possibly got rebase broken

[mikmoore]

So I'm guessing the issue here is that @fastmath is not defined at the point this code is loaded. It's significant to the performance here, due to #48129. Does someone have a suggestion for how to resolve this?

[giordano]

Move hypot to another file which is included in Base after fastmath?

Edit: ah, but this is inside the Math module....