We have set up a vectorized Monte Carlo code to simulate the two- and three-dimensional spin-exchange kinetic Ising model with particular reference to the diamond lattice. We have extended the checkerboard ordering scheme used in the spin-flip dynamics to our case achieving a high degree of vectorization. The gain in computational speed lying between 14 and 20 has allowed to run the code for stimulating precipitation phenomena in binary alloys, for a number of MCS/atom ten times higher than in a previous work, with less execution time. The time of formation of a single giant cluster depends on the lattice structure. For the simple cubic lattice this is observed after 62 500 MCS/atom, a time previously not attained. An error in the previous scalar code for the diamond lattice has been eliminated, shifting the time of formation of the giant cluster to much larger values, i.e. 125 000 MCS/atom. For the square lattice …