# Potential small inefficiency in \`triu!\` and \`tril!\`?

**URL:** https://discourse.julialang.org/t/potential-small-inefficiency-in-triu-and-tril/11725
**Category:** Performance
**Created:** [June 16, 2018, 9:20pm UTC](https://discourse.julialang.org/t/potential-small-inefficiency-in-triu-and-tril/11725 "2018-06-16T21:20:58Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![Seif\_Shebl](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Seif\_Shebl](https://discourse.julialang.org/u/Seif_Shebl)
#### Post date: [June 16, 2018, 9:20pm UTC](https://discourse.julialang.org/t/potential-small-inefficiency-in-triu-and-tril/11725/1 "2018-06-16T21:20:58Z")

</div>

The definition of `triu!` in `dense.jl` of LinearAlgebra is copy-pasted below. Observing [line 181](https://github.com/JuliaLang/julia/blob/d9b10f08fa0bd65cb49c02661e2784ffda9061f3/stdlib/LinearAlgebra/src/dense.jl#L181), we see that `zero(M[i])` is calculated at each iteration of the inner loop. Obviously, this can be moved out of the loop and re-written as `ZERO = zero(M[1])` just below `idx = 1`. Line 181 now should read `M[i] = ZERO`. The same thing happens again at [line 225](https://github.com/JuliaLang/julia/blob/d9b10f08fa0bd65cb49c02661e2784ffda9061f3/stdlib/LinearAlgebra/src/dense.jl#L225) in `tril!`.

```julia
function tril!(M::AbstractMatrix, k::Integer)
    m, n = size(M)
    if !(-m - 1 <= k <= n - 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-m - 1) and at most $(n - 1) in an $m-by-$n matrix")))
    end
    idx = 1
    for j = 0:n-1
        ii = min(max(0, j-k), m)
        for i = idx:(idx+ii-1)
            M[i] = zero(M[i])
        end
        idx += m
    end
    M
end

```

Benchmarking the original and modified versions shows a small performance improvement of about 8% .

```julia
using BenchmarkTools
a = rand(1000,1000);
julia> @btime triu!(a,0);
  187.311 μs (0 allocations: 0 bytes)
julia> @btime my_triu!(a,0);
  173.455 μs (0 allocations: 0 bytes)

```

Should I open an issue to modify both functions or did I miss something?

**EDIT:**

Oh, sorry, my fault. I modified `a` between the two calls. The compiler of 0.7-alpha seems too smart and likely, it optimized that away and constant-propagated that `ZERO`.

```julia
julia> a = rand(1000,1000);

julia> b = copy(a);

julia> @btime triu!(a,0);
  173.969 μs (0 allocations: 0 bytes)

julia> @btime my_triu!(b,0);
  173.456 μs (0 allocations: 0 bytes)

```