Number of FLOPs for the inner and outer vector product?

Question

I'm trying to educate myself on the relative cost of the cross and dot products relative to the number of floating point operations (FLOPs) each one requires. My understanding based on this paper (see page 14) is that the inner product (dot product) has a FLOP count of O(n) and the outer product has a FLOP count of O(nm) is that correct? And with the kind of specialized graphics hardware that computers now have can we assume this is an accurate measure of relative speed performance?