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    SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

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    Date
    2004
    Author
    Chandrajit Bajaj
    Insung Ihm
    Jungki Min
    Jinsang Oh
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    Abstract
    The increased programmability of graphics hardware allows efficient graphical processing unit (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 , where A is a matrix, and and 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.
    BibTeX
    @article {10.1111:j.1467-8659.2004.00803.x,
    journal = {Computer Graphics Forum},
    title = {{SIMD Optimization of Linear Expressions for Programmable Graphics Hardware}},
    author = {Chandrajit Bajaj and Insung Ihm and Jungki Min and Jinsang Oh},
    year = {2004},
    publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/j.1467-8659.2004.00803.x}
    }
    URI
    http://dx.doi.org/10.1111/j.1467-8659.2004.00803.x
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