Remove type restriction on Dual

Author: Keno

docs/src/dev/how_it_works.md

@@ -11,7 +11,7 @@ Partial derivatives are stored in the `Partials` type:
 
 ```julia
 struct Partials{N,V} <: AbstractVector{V}
-    values::NTuple{N,V}
+    values::TT
 end
 ```
 

src/partials.jl

@@ -2,6 +2,9 @@ struct Partials{N,V} <: AbstractVector{V}
     values::NTuple{N,V}
 end
 
+Partials(values::NTuple{N, Any}) where {N} =
+    Partials{N, mapreduce(typeof, typejoin, values)}(values)
+
 ##############################
 # Utility/Accessor Functions #
 ##############################
@@ -197,27 +200,27 @@ end
     return tupexpr(i -> :(rand(V)), N)
 end
 
-@generated function scale_tuple(tup::NTuple{N}, x) where N
+@generated function scale_tuple(tup::NTuple{N, Any}, x) where N
     return tupexpr(i -> :(tup[$i] * x), N)
 end
 
-@generated function div_tuple_by_scalar(tup::NTuple{N}, x) where N
+@generated function div_tuple_by_scalar(tup::NTuple{N, Any}, x) where N
     return tupexpr(i -> :(tup[$i] / x), N)
 end
 
-@generated function add_tuples(a::NTuple{N}, b::NTuple{N})  where N
+@generated function add_tuples(a::NTuple{N, Any}, b::NTuple{N, Any})  where N
     return tupexpr(i -> :(a[$i] + b[$i]), N)
 end
 
-@generated function sub_tuples(a::NTuple{N}, b::NTuple{N})  where N
+@generated function sub_tuples(a::NTuple{N, Any}, b::NTuple{N, Any})  where N
     return tupexpr(i -> :(a[$i] - b[$i]), N)
 end
 
-@generated function minus_tuple(tup::NTuple{N}) where N
+@generated function minus_tuple(tup::NTuple{N, Any}) where N
     return tupexpr(i -> :(-tup[$i]), N)
 end
 
-@generated function mul_tuples(a::NTuple{N}, b::NTuple{N}, afactor, bfactor) where N
+@generated function mul_tuples(a::NTuple{N, Any}, b::NTuple{N, Any}, afactor, bfactor) where N
     return tupexpr(i -> :((afactor * a[$i]) + (bfactor * b[$i])), N)
 end