Performance regression in version 1.8 for `exp` of complex argument

[simonp0420]

I noticed a slowdown when switching from 1.7.3 to 1.8-rc4 in a function that performs millions of complex exponentials. Benchmarking shows a small but significant slowdown in 1.8. The first two benchmarks below are for 1.7.3 and show that the complex exponential is just as fast as using exp on the real part of the argument and cis on the imaginary part. But for 1.8, the last two benchmarks show that exp is slower by about 2 nsec.

~ >>> julia -t8                                                                
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.7.3 (2022-05-06)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> versioninfo()
Julia Version 1.7.3
Commit 742b9abb4d (2022-05-06 12:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i7-9700 CPU @ 3.00GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, skylake)
Environment:
  JULIA_NUM_THREADS = 8

julia> using BenchmarkTools

julia> z = complex(-0.8, 22.34*pi)
-0.8 + 70.18317988119598im

julia> @benchmark exp($z)
BenchmarkTools.Trial: 10000 samples with 998 evaluations.
 Range (min … max):  13.525 ns … 36.088 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     14.751 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   14.825 ns ±  1.036 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

                                 █                             
  ▂▁▁▂▂▂▁▂▂▂▂▁▂▂▂▂▂▂▂▄█▂▂▂▁▃▃▂▂▂▇█▃▁▂▂▇▄▁▂▂▃▃▁▂▂▂▃▂▂▁▂▃▃▁▂▂▂▂ ▂
  13.5 ns         Histogram: frequency by time        15.8 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark exp(real($z)) * cis(imag($z))
BenchmarkTools.Trial: 10000 samples with 998 evaluations.
 Range (min … max):  14.411 ns … 60.727 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     14.696 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   14.851 ns ±  1.520 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

          ▂█▃                                                  
  ▂▁▂▂▂▂▂▃███▇▅▄▅▇▅▃▃▃▂▂▂▂▂▂▁▂▁▁▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▁▁▁▁▂▁▂▂▁▂▂ ▃
  14.4 ns         Histogram: frequency by time          16 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.


julia> 
~ >>> julia +rc -t8                                                            
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.8.0-rc4 (2022-08-08)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> versioninfo()
Julia Version 1.8.0-rc4
Commit 7853436ccd7 (2022-08-08 07:55 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × Intel(R) Core(TM) i7-9700 CPU @ 3.00GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, skylake)
  Threads: 8 on 8 virtual cores
Environment:
  JULIA_NUM_THREADS = 8

julia> using BenchmarkTools

julia> z = complex(-0.8, 22.34*pi)
-0.8 + 70.18317988119598im

julia> @benchmark exp($z)
BenchmarkTools.Trial: 10000 samples with 998 evaluations.
 Range (min … max):  16.669 ns … 57.521 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     16.786 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   16.841 ns ±  1.144 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

                      ▂▃▃▄▃▄▂▆▆▇██▄▇▆▆▅▄▂ ▂▁                   
  ▁▁▁▁▁▁▁▁▂▃▃▄▄▄▆▆▆█████████████████████████▇▅▅▃▃▂▂▂▂▂▂▂▂▂▁▁▁ ▄
  16.7 ns         Histogram: frequency by time        16.9 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark exp(real($z)) * cis(imag($z))
BenchmarkTools.Trial: 10000 samples with 998 evaluations.
 Range (min … max):  14.835 ns … 52.246 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     14.891 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   14.994 ns ±  1.412 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

      ▁▆▅▆▆▇▇█▃                                                
  ▂▂▃▆██████████▆▄▄▃▂▂▂▂▁▂▂▂▂▂▁▁▁▂▂▂▁▁▂▂▂▂▁▁▁▁▁▁▁▁▂▁▁▁▁▁▁▁▁▂▂ ▃
  14.8 ns         Histogram: frequency by time        15.2 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

[gbaraldi]

@oscardssmith

[N5N3]

Looks like exp(::Float64) would be inlined automately by our compiler after 1.8.
Add @noinline at callsite fix the regression.
exp(x::Float64) was not inlined on 1.7 and rc3 only because 2.0^-53 was not const-foldable there.

[oscardssmith]

wait, exp is getting inlined? it includes a ton of code. that's wild

[simonp0420]

@noinline does not fix the regression for me:

julia> @benchmark @noinline exp($z)
BenchmarkTools.Trial: 10000 samples with 998 evaluations.
 Range (min … max):  16.679 ns … 54.252 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     16.792 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   16.876 ns ±  1.339 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

              ▁ ▁▄▂▄▆▄▄█▆▅█▄▃▃                                 
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  16.7 ns         Histogram: frequency by time          17 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> f(z) = @noinline exp(z)
f (generic function with 1 method)

julia> @benchmark f($z)
BenchmarkTools.Trial: 10000 samples with 998 evaluations.
 Range (min … max):  16.674 ns … 51.611 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     16.755 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   16.834 ns ±  1.145 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

            ▁ ▂▂▇▆█▅▇▃▅▃▄▁                                     
  ▂▂▂▂▂▂▃▄▇▆███████████████▆▅▅▄▃▄▃▃▃▃▃▃▂▃▂▂▃▃▂▂▂▂▂▂▂▂▂▂▂▁▂▁▁▂ ▄
  16.7 ns         Histogram: frequency by time        16.9 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

[N5N3]

I mean

function exp2(z::Complex)
    zr, zi = reim(z)
    if isnan(zr)
        Complex(zr, zi==0 ? zi : zr)
    elseif !isfinite(zi)
        if zr == Inf
            Complex(-zr, oftype(zr,NaN))
        elseif zr == -Inf
            Complex(-zero(zr), copysign(zero(zi), zi))
        else
            Complex(oftype(zr,NaN), oftype(zi,NaN))
        end
    else
        @noinline er = exp(zr) # here
        if iszero(zi)
            Complex(er, zi)
        else
            s, c = sincos(zi)
            Complex(er * c, er * s)
        end
    end
end

[oscardssmith]

if exp is getting inlined, that's a bigger issue.

[simonp0420]

Sorry if this is a stupid question, but how does inlining make it slower? I would have thought that inlining would be at least as fast as a function call.