Communication Control Program for DBCSR Matrix Multiplication

The patent transitions from a conventional one-dimensional or two-dimensional process grid to a multidimensional torus structure (3D, 4D, or higher dimensions). This dimensional expansion allows processes to be organized in multiple spatial dimensions, enabling more efficient communication patterns when the number of processes exceeds the matrix size. The torus topology provides wraparound connections in each dimension, reducing communication distance and overhead in high-process configurations.

The patent segments the matrix multiplication algorithm into distinct communication phases (forward communication, backward communication, and local computation) that can be executed in an optimized sequence. By dividing the computation into blocks and processes across multiple dimensions, the system can manage communication more efficiently, reducing the total communication overhead even when using many processes.

The patent implements bidirectional communication in a periodic, structured manner using the torus topology. Communication occurs in alternating phases (forward and backward) along different dimensions, with each phase following a predetermined pattern. This periodic structure allows the system to achieve high network utilization while maintaining manageable complexity through regular, repeating communication templates rather than arbitrary communication patterns.

The patent performs preliminary setup of communication patterns and buffer allocations before the actual matrix multiplication begins. Communication routes, buffer sizes, and phase timing are predetermined based on the torus topology and process configuration, allowing the system to execute bidirectional communication efficiently during runtime without dynamically determining complex communication patterns on-the-fly.