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 ȳ = A + , where A is a matrix, and , ȳ 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.
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机译：图形硬件的可编程性增强，可在商用PC上对各种常规计算进行有效的图形处理单元（GPU）实现。这种实现方式中的一个重要因素是如何充分利用现代图形处理器提供的SIMD计算能力。 ȳ= A 展开▼
