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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

Cited by 17 (2 self)
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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.
Enumeration of Primary, Secondary, and Tertiary Monosubstituted Alkanes
"... where the numbers of primary, secondary, and tertiary ones are calculated after deriving respective functional equations. The procedures of counting are programmed by means of the Maple programming language. They are executed and the results collected up to carbon content 100 in a tabular form. By o ..."
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where the numbers of primary, secondary, and tertiary ones are calculated after deriving respective functional equations. The procedures of counting are programmed by means of the Maple programming language. They are executed and the results collected up to carbon content 100 in a tabular form. By omitting the sphericities of the recursive functions a(x), c(x2), and b(x) so as to give a single dummy variable r(x), such functional equations with sphericity are transformed into Pólya’s functional equations without sphericity, which are applied to the enumeration of primary, secondary, and tertiary monosubstituted alkanes as graphs (chemically, constitutional isomers). The results of Fujita’s proligand method are compared with those based on Pólya’s theorem in connection with several cases of pseudoasymmetry.
Numbers of Monosubstituted Alkanes as Stereoisomers
"... Monosubstituted alkanes as stereoisomers, not as constitutional isomers, are regarded as planted threedimensional (3D) trees, which are defined as a 3D extension of planted trees (graphs). They are thus recognized as 3Dobjects (planted promolecules) and enumerated by Fujita’s proligand method (Fu ..."
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Monosubstituted alkanes as stereoisomers, not as constitutional isomers, are regarded as planted threedimensional (3D) trees, which are defined as a 3D extension of planted trees (graphs). They are thus recognized as 3Dobjects (planted promolecules) and enumerated by Fujita’s proligand method (Fujita S (2005)