Programming Massively Parallel Processors by David B. Kirk & Wen-mei W. Hwu

Author:David B. Kirk & Wen-mei W. Hwu
Language: eng
Format: epub
ISBN: 9780123914187
Publisher: Elsevier Inc.
Published: 2012-12-05T16:00:00+00:00

Figure 10.14 A sequential loop that implements SpMV/COO.

The loop is extremely simple. It iterates through all the data elements and performs the multiply and accumulate operations on the appropriate x and y elements using the accompanying col_index and row_index elements. We will not present a parallel SpMV/COO kernel. It can be easily constructed using each thread to process a portion of the data elements and use an atomic operation to accumulate the results into y elements. This is because the threads are no longer mapped to a particular row. In fact, many rows will likely be missing from the COO representation; only the rows that have an exceedingly large number of nonzero elements will have elements in the COO representation. Therefore, it is better just to have each thread to take a portion of the data element and use an atomic operation to make sure that none of the threads will trample the contribution of other threads.

The hybrid SpMV/ELL-COO method is a good illustration of productive use of both CPUs and GPUs in a heterogeneous computing system. The CPU can perform SpMV/COO fast using its large cache memory. The GPU can perform SpMV/ELL fast using its coalesced memory accesses and large number of hardware execution units. The removal of some elements from the ELL format is a form of regularization technique: it reduces the disparity between long and short rows and makes the workload of all threads more uniform. Such improved uniformity results in benefits such as less control divergence in a SpMV/CSR kernel or less padding in a SpMV/ELL kernel.

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