# Redefining an integer makes computing time blow up

#1

This topic is a follow-up of this one: Improve performance of matrix computation where @foobar_lv2 proposed an improved version for the computation of a matrix given some three other matrices x, \mu and \sigma of respective sizes D \times N, D \times K and D \times K.

By trying to integrate this function to my project, I found out a very strange behaviour when the number D was defined two times by looking at the size of the matrices. The following MWE shows what’s wrong, the only change between f1 and f2 is that _, N = size(x) is replaced with D, N = size(x) so that D is defined two times. This results in a multiplication of several 1,000s of the overall computing time, regardless of the number of threads used.

N = 100
D = 1000
K = 5
x = rand(D, N)
μ = rand(D, K)
σ = rand(D, K)
x0 = x[1:2,1:2]
μ0 = μ[1:2,1:2]
σ0 = σ[1:2,1:2]

function f1(x::Matrix, μ::Matrix, σ::Matrix)
D, K = size(μ)
_, N = size(x)
p = zeros(N, K)
@inbounds for n = 1:N
pnk = 0.0
@simd for d = 1:D
pnk -= (x[d,n] - μ[d,k]) * (x[d,n] - μ[d,k])
end
p[n,k] = pnk
end
end
return p
end

function f2(x::Matrix, μ::Matrix, σ::Matrix)
D, K = size(μ)
D, N = size(x)
p = zeros(N, K)
@inbounds for n = 1:N
pnk = 0.0
@simd for d = 1:D
pnk -= (x[d,n] - μ[d,k]) * (x[d,n] - μ[d,k])
end
p[n,k] = pnk
end
end
return p
end

p10 = f1(x0, μ0, σ0)
p20 = f2(x0, μ0, σ0)

function print_name(name, space = 3)
print(name)
for i = 1:space-length(name) print(" ") end
end

print_name("f1"); @time p1 = f1(x, μ, σ)
print_name("f2"); @time p2 = f2(x, μ, σ)


On my computer, with JULIA_NUM_THREADS=1 the previous code gives:

f1 0.000192 seconds (87 allocations: 10.607 KiB)
f2 0.356826 seconds (4.49 M allocations: 68.570 MiB, 53.96% gc time)


and with JULIA_NUM_THREADS=4:

f1 0.000124 seconds (87 allocations: 10.607 KiB)
f2 0.203320 seconds (2.25 M allocations: 34.356 MiB, 28.90% gc time)


Does anyone know why this happens? Many thanks.

#2

#3

Thank you very much for the quick reply, I’ve skimmed through the issue, several things are still obscure to me, I’ll read it more carefully when I have more time.

#4

That’s pretty much that issue… There are many seemingly unrelated things that you can do to trigger it and cause a huge performance hit…

#5

This issue comment provides a good overview, and it explains two workarounds: https://github.com/JuliaLang/julia/issues/15276#issuecomment-318598339.

#6

Yes, thanks, I’ve reread the whole topic, in particular this comment, and I understand more clearly what the problem is. And in my case, this indeed fixes the issue:

function f2(x::Matrix, μ::Matrix, σ::Matrix)
D, K = size(μ)
D, N = size(x)
p = zeros(N, K)
let D = D