Reduce the allocation to zero

General Usage
1

I have a question about whether it’s possible to reduce the following simple case allocation to zero

a = rand(5)
b = rand(5)
c = rand(5)
d = rand(5)
N = rand(8)

@time acl = sum(a) * (N[1] - N[5]) + sum(b) * (N[2] - N[6]) + sum(c) * (N[3] - N[7]) + sum(d) * (N[4] - N[8])  #  in my computer, the allocation is 21 after compilation, which is unexpectedly high
2

Recommended profiling setup is something like

using BenchmarkTools

@btime acl = sum(a) * (N[1] - N[5]) + sum(b) * (N[2] - N[6]) + sum(c) * (N[3] - N[7]) + sum(d) * (N[4] - N[8]) setup=(
    a = rand(5);
    b = rand(5);
    c = rand(5);
    d = rand(5);
    N = rand(8);   
)

(you are measuring in global scope with non-consts: recipe for ‘disaster’).

3

So, you mean in reality the result from @time is not true or why it show so high outputs?

4

The results are true for what you are doing but not representative for what can be done with Julia.

Please see the first two sections in the Performance Tips.

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5

sum(rand(5)) is equivalent to sum(_ -> rand(), 1:5) so your code is equivalent to the following code which uses no arrays:

sumrand(n) = sum(_ -> rand(), 1:n)
acl = sumrand(5) * (rand() - rand()) + sumrand(5) * (rand() - rand()) + sumrand(5) * (rand() - rand()) + sumrand(5) * (rand() - rand())

which is allocation-free:

julia> using BenchmarkTools

julia> @btime acl = sumrand(5) * (rand() - rand()) + sumrand(5) * (rand() - rand()) + sumrand(5) * (rand() - rand()) + sumrand(5) * (rand() - rand());
  68.299 ns (0 allocations: 0 bytes)

You could even do

acl = sum(_ -> sumrand(5) * (rand() - rand()), 1:5)

This will show allocations, but only because it is in global scope; in a function it will be allocation-free a well:

julia> f(n, m) = sum(_ -> sumrand(m) * (rand() - rand()), 1:n)
f (generic function with 1 method)

julia> @btime f(5,5);
  102.041 ns (0 allocations: 0 bytes)
6

But maybe I misunderstood your question, and you are only asking about reducing the allocations in the acl = ... line. In that case, the problem is simply that you are benchmarking using global variables as noted above.

7

Thanks for your detailed explanation, so if I understand correct, it’s better to put all the formula within a function, right?

1 Like
8

Yes. Read the Performance Tips in the manual, especially the first two tips.

1 Like