Derivative issue with DiffResults and nested arrays

[Technici4n]

The following code works:

using ForwardDiff

g(x) = [[x^2, sqrt(x)]]
println(ForwardDiff.derivative(g, 2))

But this code:

using DiffResults
using ForwardDiff

g(x) = [[x^2, sqrt(x)]]
result = DiffResults.DiffResult(similar(g(2)), similar(g(2)))
result = ForwardDiff.derivative!(result, g, 2)
println(result)

Leads to a runtime error:

ERROR: LoadError: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(g), Int64}, Float64, 1})

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:207
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:792
  Float64(::IrrationalConstants.Fourπ)
   @ IrrationalConstants C:\Users\bruno\.julia\packages\IrrationalConstants\vp5v4\src\macro.jl:112
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(g), Int64}, Float64, 1})
    @ Base .\number.jl:7
  [2] setindex!(A::Vector{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(g), Int64}, Float64, 1}, i1::Int64)
    @ Base .\array.jl:1021
  [3] _unsafe_copyto!(dest::Vector{Float64}, doffs::Int64, src::Vector{ForwardDiff.Dual{…}}, soffs::Int64, n::Int64)
    @ Base .\array.jl:299
  [4] unsafe_copyto!
    @ .\array.jl:353 [inlined]
  [5] _copyto_impl!
    @ .\array.jl:376 [inlined]
  [6] copyto!
    @ .\array.jl:363 [inlined]
  [7] copyto!
    @ .\array.jl:385 [inlined]
  [8] copyto_axcheck!
    @ .\abstractarray.jl:1177 [inlined]
  [9] Vector{Float64}(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(g), Int64}, Float64, 1}})
    @ Base .\array.jl:673
 [10] convert
    @ .\array.jl:665 [inlined]
 [11] setindex!
    @ .\array.jl:1021 [inlined]
 [12] map!
    @ .\abstractarray.jl:3279 [inlined]
 [13] value!
    @ C:\Users\bruno\.julia\packages\DiffResults\YLo25\src\DiffResults.jl:167 [inlined]
 [14] extract_value!
    @ C:\Users\bruno\.julia\packages\ForwardDiff\UBbGT\src\apiutils.jl:5 [inlined]
 [15] derivative!(result::DiffResults.MutableDiffResult{1, Vector{Vector{…}}, Tuple{Vector{…}}}, f::typeof(g), x::Int64)
    @ ForwardDiff C:\Users\bruno\.julia\packages\ForwardDiff\UBbGT\src\derivative.jl:49

Adding the following line fixes this problem:

ForwardDiff.value(::Type{T}, x::AbstractArray) where T = map(d -> ForwardDiff.value(T, d), x)

[gdalle]

To me the issue is bigger than one missing method: you are trying to use ForwardDiff in a setting where it is not meant to work. As the docstring of ForwardDiff.derivative clearly states,

This method assumes that isa(f(x), Union{Real,AbstractArray}).

Thus, even if you add this method, calling derivative with non-array outputs will be outside of the public API. It won't necessarily be tested, and it will be vulnerable to breaking even between patch versions. That is, unless the API is extended, but I'm not sure it's worth it to open such a can of worms?