The `pid_m` calculation in matrix-multiplication tutorial

[Pairshoe]

The code at line 216 defines pid_m as follows:

pid_m = first_pid_m + (pid % group_size_m)

This line seems to be incorrect? Why we do not need an additional modulo operation as follows:

pid_m = first_pid_m + (pid % num_pid_in_group) % group_size_m

[jlebar]

num_pid_in_group = GROUP_SIZE_M * num_pid_n

Because num_pid_in_group is a multiple of GROUP_SIZE_M`, we don't need to do the mod twice?

[Pairshoe]

Yes, but the group_size_m is not always equal to GROUP_SIZE_M in the last group?

[jlebar]

Hm, you do have a good point...

I'm not 100% sure how this is supposed to work. Does the code do the wrong thing when we hit that branch?

[Jokeren]

num_pid_in_group >= group_size_m

[Jokeren]

Maybe you are confused about pid_m's order in the last group? IIUC, it doesn't matter as long as they are unique

[xinji1]

Hi @Pairshoe , From code readability side, it should be (pid % **num_pid_in_group**) % group_size_m. From computation side, it doesn't matter. Here's a possible explanation (correct if there's something wrong). Considering A = first_pid_m * num_pid_n, B is a variable within the range of [0, (num_pid_m - first_pid_m) * num_pid_n], while we can see A as constant for the last group, then for the last group,

pid % group_size_m is equal to (A + B) % (num_pid_m - first_pid_m) , and it must be in the range of [0, (num_pid_m - first_pid_m) ], just not the right order.