I think it may be more efficient to have a single function find both the number of phases n_phases and the minimum phase min_phase and store both as member variables of info. This would reduce the amount of times we have to loop through all ranks and phases.

Getting the number of phases should be a constant time operation of just looking at the size of the phase_info for rank 0. The min_phase does cost more, but I agree that it should just happen once.

I have made min phase cached so it doesn't compute each time, which should improve performance.