Add ForwardDiff-specific methods of second-derivative functions

Author: gerlero

ext/AbstractDifferentiationForwardDiffExt.jl

@@ -61,20 +61,38 @@ function AD.hessian(ba::AD.ForwardDiffBackend, f, x::AbstractArray)
     return (ForwardDiff.hessian(f, x, cfg),)
 end
 
+function AD.value_and_derivative(::AD.ForwardDiffBackend, f, x::Real)
+    T = typeof(ForwardDiff.Tag(f, typeof(x)))
+    ydual = f(ForwardDiff.Dual{T}(x, one(x)))
+    return ForwardDiff.value(T, ydual), (ForwardDiff.extract_derivative(T, ydual),)
+end
+
 function AD.value_and_gradient(ba::AD.ForwardDiffBackend, f, x::AbstractArray)
     result = DiffResults.GradientResult(x)
     cfg = ForwardDiff.GradientConfig(f, x, chunk(ba, x))
     ForwardDiff.gradient!(result, f, x, cfg)
     return DiffResults.value(result), (DiffResults.derivative(result),)
 end
 
+function AD.value_and_second_derivative(ba::AD.ForwardDiffBackend, f, x::Real)
+    T = typeof(ForwardDiff.Tag(f, typeof(x)))
+    ydual, ddual = AD.value_and_derivative(ba, f, ForwardDiff.Dual{T}(x, one(x)))
+    return value(T, ydual), (extract_derivative(T, ddual[1]),)
+end
+
 function AD.value_and_hessian(ba::AD.ForwardDiffBackend, f, x)
     result = DiffResults.HessianResult(x)
     cfg = ForwardDiff.HessianConfig(f, result, x, chunk(ba, x))
     ForwardDiff.hessian!(result, f, x, cfg)
     return DiffResults.value(result), (DiffResults.hessian(result),)
 end
 
+function AD.value_and_derivatives(ba::AD.ForwardDiffBackend, f, x::Real)
+    T = typeof(ForwardDiff.Tag(f, typeof(x)))
+    ydual, ddual = AD.value_and_derivative(ba, f, ForwardDiff.Dual{T}(x, one(x)))
+    return ForwardDiff.value(T, ydual), (ForwardDiff.value(T, ddual[1]),), (ForwardDiff.extract_derivative(T, ddual[1]),)
+end
+
 @inline step_toward(x::Number, v::Number, h) = x + h * v
 # support arrays and tuples
 @noinline step_toward(x, v, h) = x .+ h .* v