SIMD optimization of linear expressions for programmable graphics hardware

초록

The increased programmability of graphics hardware allows efficient graphical processing units (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern, graphics processors. Linear expressions in the form of (y) over bar = A (x) over bar + (b) over bar, where A is a matrix, and (x) over bar, (y) over bar and (b) over bar are vectors, constitute one of the most basic operations in many scientific computations. In this paper we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods.

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