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An interesting question, but the answer is that your basic assumption is wrong. It's neither cache nor main memory. It's scratchpad RAM, called "local memory" by OpenCL and other things. It exists as part of the GPU, and is a significant factor in total mm^2 size of the GPU cores. It's not cache because it's separately addressable by GPU kernels. It might mostly be a local faster copy of data from main memory, but it's not maintained and managed by the GPU hardware, it's controlled directly by user code (or libraries).
Interesting! Every day’s a school day!

What sort of size are we talking about?
 
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