Allreduce
Expand our tree into a butterfly … log_2(P) cycles
stage 0: process 0 sends/recvs to/from 1
process 2 sends/recvs to/from 3
process 4 sends/recvs to/from 5
process 6 sends/recvs to/from 7
stage 1: process 0 sends/recvs to/from 2
process 1 sends/recvs to/from 3
process 4 sends/recvs to/from 6
process 5 sends/recvs to/from 7
stage 2: process 0 sends/recvs to/from 4
process 1 sends/recvs to/from 5
process 2 sends/recvs to/from 6
process 3 sends/recvs to/from 7