Extremely slow compilation time

[fredrikekre]

On julia 0.6:

julia> @time gausslobatto(2);
  7.649899 seconds (9.86 M allocations: 451.546 MiB, 4.05% gc time)

On 0.5 it is about 3.5 seconds. Some quick debugging with @code_warntype suggests the problem is in this method with the following return type as a result: Tuple{Union{Array{Complex{Float64},1}, Array{Float64,1}},Union{Array{Complex{Float64},1}, Array{Float64,1}}}

[dlfivefifty]

I'm guessing the issue is that `eig` called on a `Matrix` is not type stable. This should be calling `eig` on a `SymTridiagonal`

…

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On 5 Apr 2017, at 09:24, Fredrik Ekre ***@***.***> wrote: On julia 0.6: julia> @time gausslobatto(2); 7.649899 seconds (9.86 M allocations: 451.546 MiB, 4.05% gc time) On 0.5 it is about 3.5 seconds. Some quick debugging with @code_warntype suggests the problem is in this method with the following return type as a result: Tuple{Union{Array{Complex{Float64},1}, Array{Float64,1}},Union{Array{Complex{Float64},1}, Array{Float64,1}}} — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub, or mute the thread.

[ajt60gaibb]

Yes, I agree. See #31.

[dlfivefifty]

I fixed the type stability, though it didn't improve the compilation time by much. But slow compilation is a known bug in the 0.6 betas.

[fredrikekre]

Nice! Was about to push an update but you were faster :)
Yea, the compilation time is still a problem. Digging a bit further:

julia> @time FastGaussQuadrature.JacobiAsy(101,1., 1.)
  6.638096 seconds (5.96 M allocations: 270.349 MiB, 1.98% gc time)

[dlfivefifty]

Ah, given the other issue had been here for almost a year, I wasn't expecting it to be a race 😉

You’ll see in my code I needed to type assert ::Vector{Float64}, as cat wasn't type inferring correctly (in 0.5). There is also an unnecessary allocation, so a better solution may be

aa = Array{Float64}(n)
aa[1]                  = (b - a)/(2 + ab)
view(aa,2:n-1)    .=  (b^2 - a^2)./((abi - 2).*abi)
aa[end]             = (b^2 - a^2)./((2*n - 2+ab).*(2*n+ab))

If you are looking into it further, I'll leave it to you to try that change.

[fredrikekre]

Yea, I did it with a for-loop instead. I will try to fix some more later and make a PR if I can improve the compilation time

[KristofferC]

On 0.7.

julia> @time FastGaussQuadrature.JacobiAsy(101,1., 1.)
 28.552633 seconds (61.87 M allocations: 2.746 GiB, 4.82% gc time)

Going deeper

julia> @time FastGaussQuadrature.asy1(101, 1.0, 1.0, 10)
 26.084398 seconds (55.88 M allocations: 2.453 GiB, 4.57% gc time)

[dlfivefifty]

This is compile time right? Is it really an issue with this package, or with Julia’s compiler?

[KristofferC]

Yes, compile time; just posting an update. Seems the code here is written in a way that interacts badly with the compiler but yeah, indeed an issue with the compiler.

[KristofferC]

I think the large dotted expressions is a problem for the compiler. A workaround might be to not use the @. macro so much and use normal operators between scalars and only dot operators between arrays.

[timueh]

I also noticed a big increase in compilation time going from Julia 0.6 to Julia 0.7. Is there any remedy ahead?

[hyrodium]

Current master branch on Julia 1.5:

julia> using FastGaussQuadrature

julia> t = time(); gausslobatto(2); time() - t
7.010434865951538

julia> using FastGaussQuadrature

julia> t=time(); FastGaussQuadrature.jacobi_asy(101,1., 1.); time() - t
5.734845161437988

Not as much compilation time as on Julia 0.7, but there may be still a problem.

[dlfivefifty]

Note KristofferC seemed to think the issue is the large broadcasted line

FastGaussQuadrature.jl/src/gaussjacobi.jl

Line 205 in 5506f5f

tt = K .+ (1/(2n+α+β+1)^2).*((0.25-α^2).*cot.(K/2).-(0.25-β^2).*tan.(K/2))

probably this whole function should be de-MATLABed so it doesn't allocate so much