# \`\`mod1\`\` based Periodic Indexing on GPUs

**URL:** <https://discourse.julialang.org/t/mod1-based-periodic-indexing-on-gpus/128657>\
**Category:** Performance\
**Tags:** gpu, indexing\
**Created:** [May 3, 2025, 1:25pm UTC](https://discourse.julialang.org/t/mod1-based-periodic-indexing-on-gpus/128657 "2025-05-03T13:25:49Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![bpsomu](https://avatars.discourse-cdn.com/v4/letter/b/ee7513/32.png) [@bpsomu](https://discourse.julialang.org/u/bpsomu)\
**Post date:** [May 3, 2025, 1:25pm UTC](https://discourse.julialang.org/t/mod1-based-periodic-indexing-on-gpus/128657/1 "2025-05-03T13:25:49Z")

</div>

I am using the following approach to apply boundary conditions using `mod1` for my Simulation code, that I want to be performant on GPUs:

```julia
struct DirichletArray{arr<:AbstractArray, T}
    data::arr
    core_boundary_value::T
    edge_boundary_value::T
end

function Base.getindex(arr::DirichletArray, i::Integer, j::Integer)
    nₓ, nᵧ = size(arr.data)
    if i < 1
        # Left/Upper Dirichlet boundary (i < 1)
        return arr.core_boundary_value
    elseif i > nₓ
        # Right/Lower Dirichlet boundary (i > nₓ)
        return arr.edge_boundary_value
    else
        # Periodic in y
        return @inbounds arr.data[i, mod1(j, nᵧ)]
    end
end

Base.size(arr::DirichletArray) = size(arr.data)

Base.length(arr::DirichletArray) = length(arr.data)

```

I am using the following function to create the array:

```julia
function array_with_bounds(gpuArrayType, nx, ny, boundary)
    array = gpuArrayType{Float64}(undef, nx, ny)
    if boundary == "dirichlet"
        n_core = 1.5
        n_edge = 0.5
        return DirichletArray(array, n_core, n_edge)
    else
        error("Unknown boundary type: $(boundary)")
    end
end

```

I am concerned about performance on GPUs since doing it this way seems like using scalar indexing. When I run it, it doesn’t return a scalar indexing error though.

How much performance am I losing by doing it this way? Is there a better way to do this apart from using Ghost cells?

---

<div class="post-metadata">

**Author:** ![eldee](https://avatars.discourse-cdn.com/v4/letter/e/b5a626/32.png) [@eldee](https://discourse.julialang.org/u/eldee)\
**Post date:** [May 3, 2025, 5:27pm UTC](https://discourse.julialang.org/t/mod1-based-periodic-indexing-on-gpus/128657/2 "2025-05-03T17:27:42Z")

</div>

> [@bpsomu](#):
>
> I am concerned about performance on GPUs since doing it this way seems like using scalar indexing.

I imagine you’re only going to use your `getindex` within kernels (possibly implicitly)? Then I don’t think there are going to be any big performance issues (though the `mod1`s will add some overhead of course). You can always just perform a quick benchmark to be certain.