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ARCHITECTUREAWARE CLASSICAL TAYLOR SHIFT BY 1
, 2005
"... We present algorithms that outperform straightforward implementations of classical Taylor shift by 1. For input polynomials of low degrees a method of the SACLIB library is faster than straightforward implementations by a factor of at least 2; for higher degrees we develop a method that is faster th ..."
Abstract

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We present algorithms that outperform straightforward implementations of classical Taylor shift by 1. For input polynomials of low degrees a method of the SACLIB library is faster than straightforward implementations by a factor of at least 2; for higher degrees we develop a method that is faster than straightforward implementations by a factor of up to 7. Our Taylor shift algorithm requires more word additions than straightforward implementations but it reduces the number of cycles per word addition by reducing memory tra c and the number of carry computations. The introduction of signed digits, suspended normalization, radix reduction, and delayed carry propagation enables our algorithm to take advantage of the technique of register tiling which is commonly used by optimizing compilers. While our algorithm is written in a highlevel language, it depends on several parameters that can be tuned to the underlying architecture.
cs580Lib _ a comprehensive library of Maple objects supporting instruction and research in formal languages and automata theory
"... students, teachers, and researchers interested in formal languages and automata theory, the sophisticated use of Maple as a programming language, and the management of a large collaborative learning project cs580Lib is a comprehensive coherent wellplanned collection of help pages, procedures, and o ..."
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students, teachers, and researchers interested in formal languages and automata theory, the sophisticated use of Maple as a programming language, and the management of a large collaborative learning project cs580Lib is a comprehensive coherent wellplanned collection of help pages, procedures, and other Maple objects, currently under creation at Western Michigan University, that supports research and instruction in formal languages and automata theory, in particular the upperlevel course: cs580 Theory of Computation which uses T.A. Sudkamp,