Product of Inf terms leading to NaNs

[Uroc327]

ForwardDiff (v1.0.1 as well as v0.10.38) fails to compute the gradient when the inputs are too large for the following function.

julia> using ForwardDiff

julia> foo(a) = a[1] * exp(-a[2])
foo (generic function with 1 method)

julia> ForwardDiff.gradient(foo, [1., -1e3])
2-element Vector{Float64}:
 NaN
 NaN

The correct gradient should be [Inf, -Inf]. This works for values a2 small enough such that exp(a2) is finite.

[devmotion]

The more general issue is #774. As mentioned in #774, until the problem is fixed you can work around this problem by enabling NaN-safe mode AND restricting the chunksize to 1:

julia> ForwardDiff.gradient(foo, [1., -1e3], ForwardDiff.GradientConfig(foo, [1., -1e3], ForwardDiff.Chunk{1}()))
2-element Vector{Float64}:
  Inf
 -Inf