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Numerical Accuracy Analysis Based on the Discrete Stochastic Arithmetic on Multiprocessor Platforms

Christian Motzing
Institute of Parallel and Distributed Systems, University of Stuttgart, Universitatsstrasse 38, D-70569 Stuttgart
University of Stuttgart, 2011

@article{motzing2011numerical,

   title={Numerical Accuracy Analysis Based on the Discrete Stochastic Arithmetic on Multiprocessor Platforms},

   author={M{"o}tzing, C.},

   year={2011}

}

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Simulating the real world has become one of the most widely used techniques in engineering today. Multiprocessor platforms play a key role in this development since bigger and bigger problems need more computing power to be solved. When the floating point standard was adopted in the early eighties of the 20th century, the amount of floating point operations executed in a simulation was very low compared to today. Nowadays, numerical errors accumulate to a noticeable amount, what is known as round-off error propagation and describes the problem that this error can grow over time, flnally making the result worthless in terms of informational content. Where lives, money or other critical aspects depend on computed results confidence about their correctness is of paramount importance. Therefore numerical analysis techniques were developed to make a statement about the accuracy of results computed with floating point arithmetic. They are well defined and understood in the theoretical world but rarely implemented or used in applications. This thesis will develop an approach to implement the accuracy analysis Discrete Stochastic Arithmetic in software aiming at integrating into an existing software package for simulating molecular dynamics. Discrete Stochastic Arithmetic is based on CESTAC, one of the first methods used for estimating round-off errors. An emphasis will be laid on easy applicability and improved performance of the developed methods. To review the effectiveness of the implementations a case study will be performed on a simple simulation example. General-Purpose computation on Graphics Processing Units (GPGPU) has recently established its reputation in scientific computing for accelerating parallelizable computations. Due to their completely different architecture, with hundreds of specialized cores, modern graphics cards achieve high ratings for floating-point operations per second (Flops). The difference to common CPU architectures also has a downside: developers need to rethink their usual implementation approaches and learn to handle the different tool and instruction set provided. This thesis will elaborate on the possibilities of implementing Discrete Stochastic Arithmetic on GPU as well as the merits compared to CPU.
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