A Dynamic Storage Scheme For Conflict-free Vector Access

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Abstract
Previous investigations into data storage schemes have focused on finding a storage scheme that permits conflict-free access for a set of frequently encountered access patterns. This paper considers an alternative approach. Rather than forcing a single storage scheme to be used for all access patterns, conflict-free accesses of any constant stride can be made by selecting a storage scheme for each vector based on the accessing patterns used with that vector. By factoring the stride into two components, one a power of 2 and the other relatively prime to 2, a storage scheme can be synthesized which allows conflict-free access to the vector using the specified stride. All such schemes are based on a variation of the row rotation mechanism proposed by Budnik and Kuck[l]. Each storage scheme is based on two parameters, one describes the type of rotation to perform and the other describes the amount of memory to be rotated as a single block. Hardware required to implement this storage scheme is efficient. The performance of the memory under access strides other than th stride used to specify the storage scheme is also considered. This models a vector being accessed with multiple strides, in particular the row/column access of a matrix, and situations when the stride can not be determined prior to initializing the vector. Simulation results show that if a single buffer is added to each memory port then the average performance of the dynamic scheme surpasses that of the interleaved scheme for arbitrary stride accesses. For dynamic storage schemes to be effective, the compiler must be able to detect information about the stride of vector accesses. In general, this is within the capabilities of current vectorizing compilers. Dynamic storage schemes also may allow more flexibility in program transformations performed by vectorizing compilers during optimization.

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