Memory Coalescing and Matmul | Dataford Interview Questions

How does memory coalescing work on a GPU, and how would you design a matrix multiplication kernel to maximize global memory bandwidth?

Implement choose_matmul_tile(m, n, k) to select a tile configuration for multiplying an m x k matrix by a k x n matrix. Evaluate the candidate tiles listed in the function contract, count 32-element coalesced global-memory transactions for all required tiles, and return the configuration with the fewest transactions. Break ties by larger output-tile area, then larger tile_k.

Signature: def choose_matmul_tile(m, n, k):

Return a dictionary containing tile, global_transactions, and shared_bytes.

Constraints

1 <= m, n, k <= 10^9
Matrix elements are four-byte values
A transaction covers at most 32 contiguous elements
Candidate tiles are exactly the seven configurations listed in the solution
Partial tiles count only valid matrix elements

Function Signature

def choose_matmul_tile(m, n, k):

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