Add hash for FusionTreeBlock to fix cacheing behind AdjointTensorMap permutes

[leburgel]

Potential first step to addressing #516.

The cache underlying permutes of AdjointTensorMaps ( GLOBAL_FSBRAID_CACHE) never gets a single hit, making it effectively useless. This cache uses keys generated from a FusionTreeBlock, but Base.hash wasn't defined for this type causing literally all keys to miss. Adding the hash improves the performance of permuting AdjointTensorMaps with non-Abelian sector types.

Running the reproduction script from #516 gives:

Reproduction script

using TensorKit, BenchmarkTools
using TensorKit.VectorInterface: One, Zero

p = ((2, 3), (4, 1))

function compare(name, V)
    t   = randn(ComplexF64, V ⊗ V ← V ⊗ V)
    adj = t'         # AdjointTensorMap
    mat = copy(t')   # identical space and contents, but a genuine TensorMap

    Vdst    = TensorKit.permute(space(mat), p)
    dst_adj = similar(mat, Vdst)
    dst_mat = similar(mat, Vdst)

    # NB: permute(::AdjointTensorMap, p) unwraps the adjoint and is therefore NOT affected.
    # The slow path is the in-place one, which is what `tensoradd!`/`blas_contract!` use.
    f_adj() = permute!(dst_adj, adj, p, One(), Zero())
    f_mat() = permute!(dst_mat, mat, p, One(), Zero())
    f_adj(); f_mat()
    @assert convert(Array, dst_adj) ≈ convert(Array, dst_mat)

    b_adj = @benchmark $f_adj() samples = 500 seconds = 10
    b_mat = @benchmark $f_mat() samples = 500 seconds = 10
    println(rpad(name, 14),
            " adjoint ", round(minimum(b_adj).time / 1e6; digits = 4), " ms (", b_adj.allocs, " allocs)",
            "  tensormap ", round(minimum(b_mat).time / 1e6; digits = 4), " ms (", b_mat.allocs, " allocs)",
            "  ratio ", round(minimum(b_adj).time / minimum(b_mat).time; digits = 2), "x")
end

compare("fZ2",    Vect[FermionParity](0 => 8, 1 => 8))
compare("fZ2xU1", Vect[FermionParity ⊠ U1Irrep]((0,0) => 4, (1,1) => 4, (0,2) => 3, (1,-1) => 3))
compare("SU2",    Vect[SU2Irrep](0 => 4, 1//2 => 4, 1 => 3, 3//2 => 2))

# needs SUNRepresentations
using SUNRepresentations
compare("fZ2xU1xSU3", Vect[FermionParity ⊠ U1Irrep ⊠ SU3Irrep](
    (0, 0, SU3Irrep(0,0,0)) => 2, (1, 1, SU3Irrep(1,0,0)) => 1,
    (0, 2, SU3Irrep(1,1,0)) => 1, (1, 3, SU3Irrep(1,1,1)) => 1))

After

sector type	adjoint	TensorMap	ratio	allocs (adjoint / TensorMap)
fℤ₂	0.0784 ms	0.0580 ms	1.35×	129 / 65
fℤ₂ ⊠ U(1)	0.1302 ms	0.0360 ms	3.62×	669 / 317
SU(2)	1.1759 ms	0.4083 ms	2.88×	7 864 / 2 847
fℤ₂ ⊠ U(1) ⊠ SU(3)	0.6915 ms	0.0527 ms	13.12×	8 011 / 652

Before

sector type	adjoint	TensorMap	ratio	allocs (adjoint / TensorMap)
fℤ₂	0.0717 ms	0.0539 ms	1.33×	122 / 58
fℤ₂ ⊠ U(1)	0.1232 ms	0.0319 ms	3.86×	794 / 310
SU(2)	2.4282 ms	0.3382 ms	7.18×	27 094 / 2 840
fℤ₂ ⊠ U(1) ⊠ SU(3)	3.8169 ms	0.0465 ms	82.08×	43 529 / 645

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

Files with missing lines	Coverage Δ
src/fusiontrees/fusiontrees.jl	96.66% <100.00%> (+0.01%)	⬆️

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[lkdvos]

I think you only want to hash the uncoupled and isdual on these, which is probably a lot faster than hashing the actual array