Formula for optimal matrix block-size

[ParticularMiner]

Hi @Bergvca

I think that the optimal matrix block-size, or the maximum number of strings N_max for the master Series (beyond which cache-misses begin to dominate the computation and thus lead to computational slowdown) would be directly proportional to the CPU cache-size M_CPU and inversely proportional to the density ρ_right of the right operand-matrix encoding the strings in master. That is,
N_max  ∝  M_CPU / ρ_right .

Since for my computer, N_max = 8 × 10⁴, M_CPU = 6MB and ρ_right is a number I don't know yet but can easily find during runtime (that is, the number of nonzero matrix-elements divided by the total number of matrix-elements), we can then determine the constant of proportionality and use it to find N_max for any other computer whose CPU cache-size is known or can be queried (using python package psutil, for example).

What do you think?