Sort three numbers

Question

So, I wrote this function to sort three numbers in Julia. Any feedback on readability, performance, and Julian-ness would be appreciated.

function sort_asc(a, b, c)
 # defined in function so as not to overwrite Base.minmax
 minmax(x, y) = ifelse(x < y, (x, y), (y, x))
 l1, h1 = minmax(a, b)
 lo, h2 = minmax(l1, c)
 md, hi = minmax(h1, h2)
 return lo, md, hi
end

• CiaPan: There's no need to swap x and y if they're equal, so I'd prefer less-or-equal instead of less-than.
• phipsgabler: Have a look at the code in SortingNetworks.jl. They seem to be using your approach, but with a branching minmax. Probably for good reason.

Answer 1

As it turns out

function sort_asc(a, b, c)
 l1, h1 = minmax(a, b)
 lo, h2 = minmax(l1, c)
 md, hi = minmax(h1, h2)
 return lo, md, hi
end

results in the exact same native assembly instructions on my machine (compared to the branchless version). So, given its greater simplicity, I think this is the best version so far.

Here are comparisons to other implementations

function sort3(a, b, c)
 l1, h1 = minmax(a, b)
 lo, h2 = minmax(l1, c)
 md, hi = minmax(h1, h2)
 return lo, md, hi
end
@inline minmax_nb(x, y) = ifelse(isless(x, y), (x, y), (y, x))
function sort3_nb(a, b, c)
 l1, h1 = minmax_nb(a, b)
 lo, h2 = minmax_nb(l1, c)
 md, hi = minmax_nb(h1, h2)
 return lo, md, hi
end
function sort3_koen(a, b, c)
 lo, md = minmax(a, b)
 if md > c
 hi = md
 lo, md = minmax(lo, c)
 else
 hi = c
 end
 return lo, md, hi
end

Here is the benchmark code

using BenchmarkTools
function map_sort3!(f::F, out, data) where F
 @inbounds for i in eachindex(out, data)
 a, b, c = data[i]
 out[i] = f(a, b, c)
 end
end
for f in [sort3, sort3_nb, sort3_koen]
 print(rpad(f, 12), ":")
 @btime map_sort3!($f, out, data) setup=begin
 data = [ntuple(i -> rand(Int), 3) for _ in 1:10_000]
 out = similar(data)
 end evals=1
end

And here are the results on my machine:

sort3 : 17.286 μs (0 allocations: 0 bytes)
sort3_nb : 17.624 μs (0 allocations: 0 bytes)
sort3_koen : 21.776 μs (0 allocations: 0 bytes)

Answer 2

I'd expect this to be marginally faster:

(lo,md) = minmax(a,b)
if md > c
 hi = md
 (lo,md) = minmax(lo,c)
else
 hi = c

I don't know where this sits in the scale of Julianesquinness since I'm not familiar with Julia (not even sure if my "if-else" adheres to its syntax, but the intention should be clear).