# Rolling Sum

**URL:** <https://discourse.julialang.org/t/rolling-sum/30793>\
**Category:** Statistics\
**Tags:** question\
**Created:** [November 6, 2019, 2:01pm UTC](https://discourse.julialang.org/t/rolling-sum/30793 "2019-11-06T14:01:50Z")\
**Posts on this page:** 1\
**Showing post:** 4

<div class="post-metadata">

**Author:** ![klaff](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/klaff/32/7637_2.png) [@klaff](https://discourse.julialang.org/u/klaff)\
**Post date:** [November 6, 2019, 2:32pm UTC](https://discourse.julialang.org/t/rolling-sum/30793/4 "2019-11-06T14:32:05Z")

</div>

Not too hard to roll a simple one (for simple situations) which might be faster than the more generic approach.

```julia
function rolling_sum(a, n::Int)
    @assert 1<=n<=length(a)
    out = similar(a, length(a)-n+1)
    out[1] = sum(a[1:n])
    for i in eachindex(out)[2:end]
        out[i] = out[i-1]-a[i-1]+a[i+n-1]
    end
    return out
end

```

This seems to work but no warranty implied, etc.

P.S. Just for fun, here’s a threaded version, which with four threads gives me about 2x performance.

```julia
function trolling_sum(a, n::Int)
    @assert 1<=n<=length(a)
    nseg=4
    if nseg*n >= length(a)
        return rolling_sum(a,n)
    else
        out = similar(a, length(a)-n+1)
        lseg = (length(out)-1)÷nseg+1
        segments = [(i*lseg+1, min(length(out),(i+1)*lseg)) for i in 0:nseg-1]
        Threads.@threads for (start, stop) in segments
            out[start] = sum(a[start:start+n-1])
            for i in start+1:stop
                out[i] = out[i-1]-a[i-1]+a[i+n-1]
            end
        end
        return out
    end
end

```

I’m not completely sure about thread safety here. All threads write to `out`, but never to the same location in `out`.

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