# Slower indexing on custom type for \`Complex{64}\`?

**URL:** <https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131>\
**Category:** General Usage\
**Created:** [July 29, 2017, 10:59pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131 "2017-07-29T22:59:37Z")\
**Posts on this page:** 13\
**Page:** 1

<div class="post-metadata">

**Author:** ![gasagna](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gasagna/32/1275_2.png) [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Post date:** [July 29, 2017, 10:59pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/1 "2017-07-29T22:59:38Z")

</div>

Hi,

I have a custom type, wrapping a matrix, for which I have defined the indexing behaviour.

The interesting fact is that indexing on the custom type is slower by 50% than indexing on the underlying matrix directly only when the `eltype` of the underlying array is `Complex{Float64}`. See the benchmark below.

```julia
using BenchmarkTools

struct Foo{T<:Number, A<:AbstractMatrix{T}}
    data::A
end

Foo(data::AbstractMatrix) = Foo{eltype(data), typeof(data)}(data)

@inline function Base.getindex(U::Foo, i::Int)
    @inbounds ret = U.data[i]
    ret
end

@inline function Base.setindex!(U::Foo, val::Number, i::Int)
    @inbounds U.data[i] = val
    val
end

Base.eachindex(U::Foo) = eachindex(U.data)

function test(a, b, c, d)
    @simd for i in eachindex(a)
        @inbounds a[i] = b[i] + c[i]*d[i]
    end
    a
end

# size
n = 128

for T in [Float16, Float32, Float64, 
          Complex{Float16}, Complex{Float32}, Complex{Float64}]
    a = Foo(zeros(T, n, n))
    b = Foo(zeros(T, n, n))
    c = Foo(zeros(T, n, n))
    d = Foo(zeros(T, n, n))

    t_foo = @belapsed test($a, $b, $c, $d)
    t_arr = @belapsed test($a.data, $b.data, $c.data, $d.data)

    @printf "%s %8.5f μs %8.5f μs\n" lpad(string(T), 16) 10^6*t_foo 10^6*t_arr
end

```

The output of this is

```julia
         Float16 296.075 μs 287.413 μs
         Float32 4.462 μs 4.455 μs
         Float64 12.278 μs 12.284 μs
Complex{Float16} 1205.071 μs 1192.119 μs
Complex{Float32} 26.366 μs 26.055 μs
Complex{Float64} 46.057 μs 29.107 μs

```

Has any of you encountered such behaviour for `Complex{Float64}` before, or is this known somehow?

Thanks.

Davide

P.S. This also shows that `Float16` is much slower then other floating point numbers. But this is not my problem!

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 29, 2017, 11:18pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/2 "2017-07-29T23:18:35Z")

</div>

As another data point, seems that `Complex{Float32}` has the same issue on 0.7-dev.

---

<div class="post-metadata">

**Author:** ![gasagna](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gasagna/32/1275_2.png) [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Post date:** [July 29, 2017, 11:21pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/3 "2017-07-29T23:21:44Z")

</div>

I do not have access to a v0.7 but here are better benchmarks for v0.5 and v0.6. These are run collecting the best out of 5.

```julia
# v0.5
          Float16 272.847 μs 250.319 μs
          Float32 3.970 μs 3.909 μs
          Float64 12.078 μs 12.315 μs
 Complex{Float16} 1084.366 μs 1063.182 μs
 Complex{Float32} 34.780 μs 29.384 μs
 Complex{Float64} 28.221 μs 28.357 μs

```

```julia
# v0.6
          Float16 294.426 μs 287.436 μs
          Float32 3.676 μs 3.865 μs
          Float64 12.290 μs 12.071 μs
 Complex{Float16} 1205.071 μs 1191.981 μs
 Complex{Float32} 26.366 μs 26.014 μs
 Complex{Float64} 46.057 μs 26.855 μs

```

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 29, 2017, 11:26pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/4 "2017-07-29T23:26:20Z")

</div>

Smaller example that gets rid of having to define all the indexing on the type:

```julia
function test2(a, b, c, d)
    for i in 1:length(a.data)
        @inbounds a.data[i] = b.data[i] + c.data[i]*d.data[i]
    end
    a
end

```

This is slower for `Foo` than `test` for `Array`s. So it seems the loads to the `data` field are not hoisted?

---

<div class="post-metadata">

**Author:** ![gasagna](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gasagna/32/1275_2.png) [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Post date:** [July 29, 2017, 11:32pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/5 "2017-07-29T23:32:11Z")

</div>

Yeah, I noticed that as well.

Indexing on the type is needed for using this type in generic code that does not know it can access the `.data` field.

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 29, 2017, 11:32pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/6 "2017-07-29T23:32:35Z")

</div>

I know, but I was trying to reduce the code to something smaller that still exhibit the performance problem…

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 30, 2017, 9:17am UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/7 "2017-07-30T09:17:39Z")

</div>

I created an issue for this: [https://github.com/JuliaLang/julia/issues/23042](https://github.com/JuliaLang/julia/issues/23042)

---

<div class="post-metadata">

**Author:** ![gasagna](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gasagna/32/1275_2.png) [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Post date:** [July 30, 2017, 10:32am UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/8 "2017-07-30T10:32:07Z")

</div>

Thanks. Could you please elaborate here on the difference in the code you have reported on the github issue? It seems to me from your example that the culprit is the `.data` field not being hoisted out of the loop.

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 30, 2017, 10:51am UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/9 "2017-07-30T10:51:02Z")

</div>

Yeah, it’s the same as manually inlining your getindex and setindex! for Foo.

---

<div class="post-metadata">

**Author:** ![Dan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dan/32/42581_2.png) [@Dan](https://discourse.julialang.org/u/Dan)\
**Post date:** [July 30, 2017, 8:28pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/10 "2017-07-30T20:28:16Z")

</div>

Did the same tests with a slightly modified `get/setindex`:

```julia
@inline function Base.getindex(U::Foo, i::Int)
        Udata = U.data
        @inbounds ret = Udata[i]
        ret
end
@inline function Base.setindex!(U::Foo, val::Number, i::Int)
        Udata = U.data
        @inbounds Udata[i] = val
        val
end

```

and it overcomes the 50% slowdown on Complex{Float64} (there was still a slowdown ~15% or perhaps less). It does not solve the LLVM issue, but might be worth using until then. The slowdown on Complex{Float32} remained substantial.

A similar change in the code in the issue, eliminated the slowdown in all types (but essentially the two benchmarks now tested the same operation).

The test was done on 0.7 (2017-07-22).

---

<div class="post-metadata">

**Author:** ![gasagna](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gasagna/32/1275_2.png) [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Post date:** [July 31, 2017, 9:19am UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/11 "2017-07-31T09:19:02Z")

</div>

Unfortunately, no big difference on my setup.

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 17, 2018, 9:29am UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/12 "2018-07-17T09:29:41Z")

</div>

Fixed on 0.7:

```julia
Float32 4.52129 μs 4.52586 μs
Float64 14.70700 μs 14.74500 μs
Complex{Float32} 18.98400 μs 19.00700 μs
Complex{Float64} 32.60400 μs 32.55700 μs

```

---

<div class="post-metadata">

**Author:** ![gasagna](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gasagna/32/1275_2.png) [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Post date:** [July 17, 2018, 1:15pm UTC](https://discourse.julialang.org/t/slower-indexing-on-custom-type-for-complex-64/5131/13 "2018-07-17T13:15:06Z")

</div>

Thanks for resurrecting this post with an update. I did similar tests few weeks back, and I remember somehow that there was a regression on Float16 from v0.6. Have you seen anything like that?