What is the algorithm to determine optimal work group size and number of workgroup

You discover these values experimentally for your algorithm. Use a profiler to get hard numbers.

I like to use CL_DEVICE_MAX_COMPUTE_UNITS as the number of work groups, because I often rely on synchronizing work items. I usually run kernels with little branching, so the take the same time to execute in each compute unit.

Some multiple of CL_KERNEL_PREFERRED_WORK_GROUP_SIZE_MULTIPLE will be optimal for your device. What that multiple actually is depends on your memory access pattern and type of work you are doing with each work item. Use 1 as the multiple when you are running a heavy, compute-bound (ALU) kernel. Try a larger multiple to hide memory latency if you are bottlenecked by memory access. Use a profiler to determine when your access time and your ALU time are optimal.

Optimal ratio for ALU to fetch is 1:1 for any device. This is rarely achieved in practice, so you want to keep the ALU/SIMD banks saturated. This means ALU:fetch should be greater than 1 whenever possible. Less than 1 means you should try a larger work group size to better hide the memory latency.

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