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Arbitrary-Precision Arithmetics on the GPU

Bernhard Langer
Vienna University of Technology
Spring Conference on Computer Graphics (SCCG), 2015

@article{langer2015arbitrary,

   title={Arbitrary-Precision Arithmetics on the GPU},

   author={Langer, Bernhard},

   year={2015}

}

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The majority of computer applications employ numerical data types with a fixed amount of precision for their computations. Their limited numerical range and precision are sufficient for most use cases. However, for some purposes, such as cryptography or geometrical computations, the required range and precision can become arbitrarily large. Numerical types that can handle such demands have higher memory requirements and are not natively supported by common hardware, which leads to increased computational complexity. In this paper, we examine how basic arithmetic operations on arbitrary-precision integers can be adapted to many-core architectures in the form of graphics processing units, which are widely available as commodity hardware. Apart from a detailed description of our method, we show superior performance characteristics of our implementation in comparison to state-of-the-art CPU libraries for high computational loads.
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