generated_partials.jl

function tupexpr(f, N)
    ex = Expr(:tuple, [f(i) for i=1:N]...)
    return quote
        @inbounds return $(ex)
    end
end

@inline iszero_tuple(::Tuple{}) = true
@inline zero_tuple(::Type{Tuple{}}) = tuple()
@inline one_tuple(::Type{Tuple{}}) = tuple()
@inline rand_tuple(::AbstractRNG, ::Type{Tuple{}}) = tuple()
@inline rand_tuple(::Type{Tuple{}}) = tuple()

@generated iszero_tuple{N,T}(tup::NTuple{N,T}) = :(Base.@_inline_meta(); z = zero(T); @inbounds return $(Expr(:&&, [:(z == tup[$i]) for i=1:N]...)))
@generated zero_tuple{N,T}(::Type{NTuple{N,T}}) = :(Base.@_inline_meta(); z = zero(T); $(tupexpr(i -> :(z), N)))
@generated one_tuple{N,T}(::Type{NTuple{N,T}}) = :(Base.@_inline_meta(); z = one(T); $(tupexpr(i -> :(z), N)))
@generated rand_tuple{N,T}(rng::AbstractRNG, ::Type{NTuple{N,T}}) = :(Base.@_inline_meta(); $(tupexpr(i -> :(rand(rng, T)), N)))
@generated rand_tuple{N,T}(::Type{NTuple{N,T}}) = :(Base.@_inline_meta(); $(tupexpr(i -> :(rand(T)), N)))
@generated scale_tuple{N}(tup::NTuple{N}, x) = :(Base.@_inline_meta(); $(tupexpr(i -> :(tup[$i] * x), N)))
@generated div_tuple_by_scalar{N}(tup::NTuple{N}, x) = :(Base.@_inline_meta(); $(tupexpr(i -> :(tup[$i] / x), N)))
@generated add_tuples{N}(a::NTuple{N}, b::NTuple{N}) = :(Base.@_inline_meta(); $(tupexpr(i -> :(a[$i] + b[$i]), N)))
@generated sub_tuples{N}(a::NTuple{N}, b::NTuple{N}) = :(Base.@_inline_meta(); $(tupexpr(i -> :(a[$i] - b[$i]), N)))
@generated minus_tuple{N}(tup::NTuple{N}) = :(Base.@_inline_meta(); $(tupexpr(i -> :(-tup[$i]), N)))
@generated mul_tuples{N}(a::NTuple{N}, b::NTuple{N}, afactor, bfactor) = :(Base.@_inline_meta(); $(tupexpr(i -> :((afactor * a[$i]) + (bfactor * b[$i])), N)))