You have to go back to basics here. The map reduce paradigm was introduced by Iverson in 1962 with APl.. When applying maps to arrays this can be very efficient and it is incorporated in a number of modern languages Matlab, Single Assignment C, ZPL, Vector Pascal. Most of these have now been targeted to multi-core machines very effectively.

Dear Prof. Cockshott

Yes, modern computing adopts Map Reduced strategy in many computation problems. Currently, I do some experiments and compare between the two approaches. In general, Map reduced gives better performance in GPU. On the other hand the two approaches I mentioned by the question still comparative in Multicore CPUs.

I tend to perform mapping along dimension 0 using SIMD and map over dimension 1 using multicore, but that may not give the best locality. It works well on the Sandybridge, but not so well on the Xeon Phi.