Applications of Conformal Computing techniques to problems in computational physics: the Fast Fourier Transform |
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Authors: | James E Raynolds Lenore R Mullin |
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Affiliation: | a College of Nanoscale Science and Engineering, University at Albany, State University of New York, Albany, NY 12203, USA b Department of Computer Science, University at Albany, State University of New York, Albany, NY 12203, USA |
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Abstract: | The techniques of Conformal Computing are introduced with an application to the Fast Fourier Transform. Conformal Computing is a design methodology, based on a rigorous mathematical foundation, which provides a systematic approach to the most efficient organization of all levels of the software and hardware design hierarchy from high-level software constructs all the way down to the design of the integrated circuits. We show that using these general design principles, without any specialized optimization, leads to portable, scalable, code that is competitive with other well-tuned machine specific routines. Further improvements are straightforward within our formalism by taking into account specific hardware details (e.g., cache loops) in a portable parametric way. We also argue that the present theory constitutes a uniform way of reasoning about physics and the data structures that define physics on computers. |
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Keywords: | Conformal Computing ψ-calculus Fast Fourier Transform (FFT) Optimization |
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