`Base.two_mul` is constant folding incorrectly on 1.10 (but not 1.9 or 1.11)

[Moelf]

It's useful for something: https://cds.cern.ch/record/2866130/files/ANA-EXOT-2022-18-PAPER.pdf#page=9

(this is a fitting, so you want this exponential to be very fast)

julia> @benchmark x^y setup=begin x=rand(); y=rand()end
BenchmarkTools.Trial: 10000 samples with 988 evaluations.
 Range (min … max):  47.248 ns … 440.931 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     47.567 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   49.616 ns ±   4.787 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▅█▇▁     ▂▁       ▁▁▁                ▆▇▄       ▁             ▂
  ████▁▃▄▁▇██▇▇▆▆▆▆▇███▇▇▆▆▆▆▆▅▇▆▆▆▆▆▆█████▇▇▇▇▇███▆▆▆▅▅▆▅▇▇█▇ █
  47.2 ns       Histogram: log(frequency) by time      55.5 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark x^y setup=begin x=rand(); y=rand(3:9)end
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
 Range (min … max):  2.408 ns … 20.031 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     9.003 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   8.631 ns ±  2.849 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▇                           ▇       █     █   ▂
  █▃▂▂▂▂▂▁▂▂▂▂▁▂▁▁▁▁▁▁▁▁▁▁▁▁▁▂█▂▂▁▃▂▇▄█▇▂▂▂▃█▆▂▂█▃▃▇▂▇▆▂▂▂▂▂ ▃
  2.41 ns        Histogram: frequency by time        12.7 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

Maybe we're hitting the physical limit of how fast this can go?

In [2]: a=np.random.rand(100);

In [3]: b=np.random.rand(100);

In [5]: %timeit np.power(a,b)
514 ns ± 3.64 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)

[oscardssmith]

What CPU is that? I see timings of around 20ns on my laptop (11th gen Intel). I think there's probably a few ns that could be shaved (roughly 1-2 on my laptop), primarily in our exp implementation which isn't quite optimal. That said, this is largely expected. Floating point exponentiation is somewhat inherently slow, primarily because the "only" workable formula is x^y = exp(log(x)*y) which puts a pretty strict upper bound on speed (and it's even worse because it turns out you need roughly 12 extra bits of accuracy in the log computation because exp magnifies errors for larger inputs.

It's also possibly worth noting that Float32 exponentiation is a lot faster since it can use Float64 for extended precision rather than needing to rely on double-doubles.

[Richard-Sti]

There is another working example related to this to consider which higlights this issue:

using BenchmarkTools

function test()
    x = 1.
    for i in 1:100_000_000
        x += x^2.
    end
    return x
end

@btime test()

Thir runs in ~220 ms on Julia 1.7.3, ~900 ms on Julia 1.9.x and ~2000 ms on Julia 1.10.x so there is a factor of few slow-down compared to the older version.

[Moelf]

I see timings of around 20ns on my laptop (11th gen Intel).

damn am I using fake Intel?

Vendor ID:               GenuineIntel
  Model name:            11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz
    CPU family:          6
    Model:               140

[oscardssmith]

What Julia version are you testing on?

[Moelf]

Version 1.10.0-rc1 (2023-11-03)

[oscardssmith]

Ok something is actually very wrong here. 1.10 is 2x slower than 1.9 or nightly and I have no idea why.

[Moelf]

well, at least 1.7 was equally slow (do we have benchmark tests we can add to?)

[stevengj]

On my computer (Apple M1 Max), I find that 1.9 is faster than 1.8 or nightly. Note also that there is a special-case optimization for x^y if y is an integer-valued float, which is worth benchmarking separately.

On Julia 1.8:

julia> @btime x^y setup=begin x=rand(); y=rand(); end;
  15.698 ns (0 allocations: 0 bytes)

julia> @btime $(Ref(1.2))[]^$(Ref(3.4))[];
  15.782 ns (0 allocations: 0 bytes)

julia> @btime $(Ref(1.2))[]^$(Ref(3.0))[];
  3.958 ns (0 allocations: 0 bytes)

On Julia 1.9 (fastest):

julia> @btime $(Ref(1.2))[]^$(Ref(3.4))[];
  11.637 ns (0 allocations: 0 bytes)

julia> @btime $(Ref(1.2))[]^$(Ref(3.0))[];
  3.916 ns (0 allocations: 0 bytes)

On nightly (1.11.0-DEV.860):

julia> @btime $(Ref(1.2))[]^$(Ref(3.4))[];
  14.863 ns (0 allocations: 0 bytes)

julia> @btime $(Ref(1.2))[]^$(Ref(3.0))[];
  5.167 ns (0 allocations: 0 bytes)

[Zentrik]

Some discussion here as well https://discourse.julialang.org/t/exponentiation-of-floats/105951/22, seems to be some sort of weird bug.