misc.jl

## Pushforward
DI.overloaded_input_type(prep::ForwardDiffOneArgPushforwardPrep) = typeof(prep.xdual_tmp)
DI.overloaded_input_type(prep::ForwardDiffTwoArgPushforwardPrep) = typeof(prep.xdual_tmp)

function DI.overloaded_input(
        ::typeof(DI.pushforward), f::F, backend::AutoForwardDiff, x, tx::NTuple{B}
    ) where {F, B}
    T = tag_type(f, backend, x)
    xdual = make_dual(T, x, tx)
    return xdual
end

function DI.overloaded_input(
        ::typeof(DI.pushforward), f!::F, y, backend::AutoForwardDiff, x, tx::NTuple{B}
    ) where {F, B}
    T = tag_type(f!, backend, x)
    xdual = make_dual(T, x, tx)
    return xdual
end

## Derivative
function DI.overloaded_input_type(prep::ForwardDiffOneArgDerivativePrep)
    return DI.overloaded_input_type(prep.pushforward_prep)
end
function DI.overloaded_input_type(
        prep::ForwardDiffTwoArgDerivativePrep{SIG, X, <:DerivativeConfig{T}}
    ) where {SIG, X, T}
    return typeof(Dual{T}(one(X), one(X)))
end

## Gradient
DI.overloaded_input_type(prep::ForwardDiffGradientPrep) = typeof(prep.config.duals)

## Jacobian
DI.overloaded_input_type(prep::ForwardDiffOneArgJacobianPrep) = typeof(prep.config.duals)
DI.overloaded_input_type(prep::ForwardDiffTwoArgJacobianPrep) = typeof(prep.config.duals[2])