Wrong answers for `Tropical{Float32}`

[chriselrod]

e.g.

julia> using TropicalNumbers, Octavian, TropicalGEMM, BenchmarkTools, Tullio

julia> v2!(r, d) = @tullio (max) r[j, i] = d[k, j] + d[i, k]
v2! (generic function with 1 method)

julia> d = rand(Float32, 4000, 4000); r = similar(d); td = Tropical.(d); tr = similar(td);

julia> typeof(tr)
Matrix{TropicalF32} (alias for Array{Tropical{Float32}, 2})

julia> typeof(td)
Matrix{TropicalF32} (alias for Array{Tropical{Float32}, 2})

julia> @time(Octavian.matmul!(tr, td', td'));
 11.552436 seconds (28.39 M allocations: 1.414 GiB, 7.06% gc time, 198.04% compilation time)

julia> @time(v2!(r,d));
  2.761347 seconds (439.87 k allocations: 27.319 MiB, 20.82% compilation time)

julia> r[1:10,1:10]
10×10 Matrix{Float32}:
 1.98815  1.98032  1.96756  1.97688  1.98138  1.99293  1.99121  1.99046  1.98951  1.99046
 1.98347  1.97355  1.98345  1.96617  1.98862  1.97611  1.98876  1.98316  1.98376  1.98263
 1.98005  1.98607  1.94482  1.99388  1.97896  1.98763  1.97235  1.95483  1.98607  1.97469
 1.97811  1.96782  1.96914  1.99468  1.9638   1.96488  1.99281  1.96719  1.99046  1.99007
 1.97995  1.99206  1.96033  1.99925  1.97888  1.99531  1.98424  1.97277  1.96929  1.99149
 1.98175  1.97349  1.98187  1.96846  1.97438  1.99013  1.98184  1.96848  1.97482  1.99134
 1.97559  1.99141  1.97511  1.98494  1.98186  1.97386  1.95691  1.95286  1.97816  1.98359
 1.96895  1.95868  1.96969  1.98323  1.98321  1.96809  1.96434  1.9723   1.97961  1.9598
 1.97215  1.98366  1.97773  1.98742  1.98507  1.95414  1.96615  1.98585  1.97801  1.97805
 1.98135  1.98764  1.98053  1.96926  1.97798  1.988    1.94989  1.97951  1.98827  1.99674

julia> tr[1:10,1:10]
10×10 Matrix{TropicalF32}:
 1.9881469ₜ  1.9545851ₜ  1.9813809ₜ  1.9596899ₜ  1.9895067ₜ  1.9505024ₜ  1.9669962ₜ  1.9318342ₜ  1.9598813ₜ  1.9938858ₜ
 1.9601333ₜ  1.9426515ₜ  1.9789603ₜ  1.9723496ₜ   1.972192ₜ  1.9418759ₜ  1.9936779ₜ  1.9892867ₜ  1.9816258ₜ  1.9438664ₜ
 1.9267545ₜ  1.9517486ₜ  1.9759095ₜ  1.9842439ₜ   1.969292ₜ  1.9947274ₜ   1.967751ₜ  1.9854705ₜ  1.9549026ₜ  1.9786203ₜ
 1.9466515ₜ  1.9751123ₜ  1.9818645ₜ  1.9569125ₜ  1.9781556ₜ  1.9860659ₜ  1.9599998ₜ  1.9799122ₜ  1.9720198ₜ  1.9701405ₜ
  1.972152ₜ  1.9777286ₜ  1.9671929ₜ  1.9584064ₜ  1.9780083ₜ  1.9773908ₜ   1.958333ₜ  1.9829702ₜ  1.9757335ₜ  1.9570483ₜ
 1.9852564ₜ   1.976543ₜ  1.9943745ₜ   1.965773ₜ  1.9823151ₜ  1.9887956ₜ  1.9841229ₜ  1.9784414ₜ  1.9614553ₜ  1.9801428ₜ
 1.9767675ₜ  1.9753637ₜ  1.9792922ₜ  1.9716537ₜ  1.9809005ₜ  1.9872162ₜ  1.9794067ₜ  1.9565374ₜ  1.9802582ₜ   1.963557ₜ
 1.9824476ₜ  1.9638793ₜ  1.9712152ₜ  1.9819689ₜ  1.9859302ₜ  1.9882684ₜ  1.9788489ₜ  1.9857358ₜ   1.979456ₜ  1.9608781ₜ
 1.9712175ₜ  1.9773014ₜ  1.9713657ₜ   1.985241ₜ  1.9794915ₜ  1.9511222ₜ   1.959055ₜ  1.9835603ₜ  1.9517698ₜ  1.9724486ₜ
 1.9561397ₜ  1.9714637ₜ  1.9776536ₜ  1.9738066ₜ  1.9854319ₜ  1.9693574ₜ  1.9678532ₜ  1.9894817ₜ  1.9719748ₜ  1.9628868ₜ

while it works for Float64:

julia> d = rand(4000, 4000); r = similar(d); td = Tropical.(d); tr = similar(td);

julia> @time(v2!(r,d));
  2.539927 seconds (261.82 k allocations: 16.076 MiB, 16.36% compilation time)

julia> @time(Octavian.matmul!(tr, td', td'));
  9.220967 seconds (25.62 M allocations: 1.240 GiB, 3.42% gc time, 192.78% compilation time)

julia> tr == Tropical.(r)
true

[chriselrod]

Note this is on the following custom branches:
JuliaLinearAlgebra/Octavian.jl#157
JuliaArrays/ArrayInterface.jl#369
as it threw errors before.

[GiggleLiu]

Hey, @chriselrod . Thanks for the issue. The adjoint of Tropical numbers are not well defined.

julia> (Matrix(td') * Matrix(td'))[1:10, 1:10]
ERROR: MethodError: no method matching conj(::TropicalF32)
Closest candidates are:
  conj(::Union{LinearAlgebra.Hermitian{T, S}, LinearAlgebra.Symmetric{T, S}} where {T, S}) at ~/.julia/juliaup/julia-1.8.3+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/symmetric.jl:368
  conj(::LinearAlgebra.UniformScaling) at ~/.julia/juliaup/julia-1.8.3+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/uniformscaling.jl:123
  conj(::LinearAlgebra.Adjoint) at ~/.julia/juliaup/julia-1.8.3+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/adjtrans.jl:345
  ...
Stacktrace:
  [1] adjoint(x::TropicalF32)
    @ Base ./number.jl:213

So I am confused why matmul! can produce a result. If you use the following statement instead,

julia> @time(Octavian.matmul!(tr, transpose(td), transpose(td)));

The result is correct.

My package versions

(jl_QKsjQL) pkg> st
Status `/tmp/jl_QKsjQL/Project.toml`
  [6fd5a793] Octavian v0.3.18
  [a4ad3063] TropicalGEMM v0.1.8 `~/.julia/dev/TropicalGEMM`   # master branch is the same as the registered  version
  [bc48ee85] Tullio v0.3.5

[chriselrod]

If you're curious, the motivation was this slack discussion: https://julialang.slack.com/archives/C67TK21LJ/p1670593631969889

I can confirm that tranpose works. I was using adjoints because ' is faster to type.