Interferometric radio telescopes often rely on computationally expensive O(N^2) correlation calculations; fortunately these computations map well to massively parallel accelerators such as low-cost GPUs. This paper describes the OpenCL kernels developed for the GPU based X-engine of a new hybrid FX correlator. Channelized data from the F-engine is supplied to the GPUs as 4-bit, offset-encoded real and imaginary integers. Because of the low bit width of the data, two values may be packed into a 32-bit register, allowing multiplication and addition of more than one value with a single fused multiply-add instruction. With this data and calculation packing scheme, as many as 5.6 effective tera-operations per second (TOPS) can be executed on a 4.3 TOPS GPU. The kernel design allows correlations to scale to large numbers of input elements, limited only by maximum buffer sizes on the GPU. This code is currently working on-sky with the CHIME Pathfinder Correlator in BC, Canada.
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