Optimize dot(::Vector{Float64}, ::Vector{ForwardDiff.Dual})

General Usage
3

The 4 is for SIMD?

This is very neat:

using ForwardDiff, BenchmarkTools, LinearAlgebra

_dual(x) = ForwardDiff.Dual(x, x + 1, x + 2, x + 3, x + 4)

function dot4(a, b, len_trunc)
    z1 = z2 = z3 = z4 = zero(a[1] * b[1])
    i = 1
    @inbounds while i < len_trunc
        z1 += a[i] * b[i]
        z2 += a[i+1] * b[i+1]
        z3 += a[i+2] * b[i+2]
        z4 += a[i+3] * b[i+3]
        i += 4
    end
    z1 + z2 + z3 + z4
end

function dot_tail(z, a, b, i, len)
    @inbounds while i < len
        i += 1
        z += a[i] * b[i]
    end
    z
end

function mydot(a, b)
    @assert !Base.has_offset_axes(a, b)
    len = length(a)
    @assert len == length(b)
    len_trunc = len - len % 4
    z = dot4(a, b, len_trunc)
    dot_tail(z, a, b, len_trunc, len)
end

o = randn(69)
Do = _dual.(o)

@btime dot(o, Do)               # 97ns
@btime mydot(o, Do)             # 69ns