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SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

Chandrajit Bajaj, Insung Ihm, Jungki Min, Jinsang Oh
Department of Computer Science, University of Texas at Austin, Texas, U.S.A.
Computer Graphics Forum, Volume 23, Issue 4, pages 697-714, December 2004

@conference{bajaj2004simd,

   title={SIMD optimization of linear expressions for programmable graphics hardware},

   author={Bajaj, C. and Ihm, I. and Min, J. and Oh, J.},

   booktitle={Computer Graphics Forum},

   volume={23},

   number={4},

   pages={697–714},

   issn={1467-8659},

   year={2004},

   organization={Wiley Online Library}

}

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The increased programmability of graphics hardware allows efficient 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 bar{y}= Abar{x}+ bar{b}, where A is a matrix, and bar{x}, bar{y}, and bar{b} 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 method.
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