Prototype for TBLIS contract for ForwardDiff.jl

contract_fwd_prototype.jl

# here idx has 3 entries corresponding to e.g. "ik,jk->ij".
contract!(A::Array{T},
          B::Array{T},
          C::Array{T},
          idx) where {T<:Dual} = contract!(T, sizeof(T)/sizeof(tovalue(T)), # tovalue unveils base type.
                                           A, 0, B, 0, C, 0, idx)

contract!(Type::Dual{Tg, T, ND}, topst, # top-level stride
          A::Array, sftA, # arrays here are all at their top-level (not dispatched)
          B::Array, sftB, 
          C::Array, sftC, 
          idx) = begin
    # direct dispatch for value types.
    contract!(T, topst, A, sftA, B, sftB, C, sftC, idx)

    # for all differentials
    # TODO: consider exchangability
    for id = 1:ND
        # unpacks one layer of dual. note that differentials are also in value's type.
        contract!(T, topst,
                  A, sftA + id*sizeof(T), 
                  B, sftB, 
                  C, sftC + id*sizeof(T),
                  idx)
        contract!(T, topst,
                  A, sftA,
                  B, sftB + id*sizeof(T), 
                  C, sftC + id*sizeof(T),
                  idx)
    end
end

contract!(Type::ValueType, # to be defined
          topst,
          A::Ptr{Cvoid}, sftA,
          B::Ptr{Cvoid}, sftB,
          C::Ptr{Cvoid}, sftC,
          idx) = begin
    # convert stride unit in top duals.
    stA = topst .* strides(A)
    stB = topst .* strides(B)
    stC = topst .* strides(C)
    # - build TBLIS-object for A, B and C from bare memory shifted by sft{A,B,C}.
    # - TLIBS-contract according to idx.
    return nothing
end