How does the TileMMA thread layout in cute work?

[mutou-wl]

I have read all the documents of CuTe, and I have always been puzzled about the TileMMA thread layout setting ThrLayoutVMNK (_32,_2,_2,_1):(_1,_32,_64,_0). When I use print_latex to print, I see that the data of matrix A is distributed among threads 0-31 and 32-63. Does this mean that the two warps of thread idx 64~127 do not hold any data of matrix A? Similarly, matrix B is also distributed among the threads of 2 warps (0-31, 64-95), but the data of matrix C is distributed within the full 4 warps (0-127). My current understanding is that all threads hold parts of the data of matrices A, B, and C, it's just that print_latex cannot print them out. I would be very grateful if someone could answer this!

sing mma_op = SM80_16x8x16_F16F16F16F16_TN;
 using mma_traits = MMA_Traits<mma_op>;
 using mma_atom = MMA_Atom<mma_traits>;

 using MMA = decltype(make_tiled_mma(mma_atom{}, 
                                        make_layout(Shape<_2, _2, _1>{}), // ThrLayoutVMNK (_32,_2,_2,_1):(_1,_32,_64,_0)
                                        Tile<_32, _32, _16>{}// PermutationMNK
    )); 
print(MMA{});print("\n");

And the output latex as follow:

[ccecka]

The A and B layouts have projections in the threads which are difficult to depict in these diagrams.

T64 is "missing" from the A Layout. T64 will read the same values that T0 reads in A.
T65 is "missing" from the A Layout. T65 will read the same values that T1 reads in A.

T32 is "missing" from the B Layout. T32 will read the same values that T0 reads in B.
T33 is "missing" from the B Layout. T33 will read the same values that T1 reads in B.

Your understanding is correct -- all threads hold parts of the data of matrices A, B, and C, but that data may actually be reproduced across multiple threads.

[mutou-wl]

Thank you for your wonderful reply, which helped me solve the problem that has been bothering me for a long time.