About: Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm

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type	http://eprints.org/ontology/ArticleEPrint http://eprints.org/ontology/EPrint Article Academic Article
seeAlso	HTML Summary of #67205 Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm
sameAs	Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm
http://eprints.org/ontology/hasDocument	Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (PDF) Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (Other) Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (Other) Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (Other) Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (Other) Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (Other)
http://eprints.org/ontology/hasSubmitted	Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (PDF)
dc:hasVersion	Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (PDF)
Title	Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm
described by	https://demo.openlinksw.com/about/id/entity/https/raw.githubusercontent.com/annajordanous/CO644Files/main/export_kar_RDFN3.n3
Date	2018-04-26
Creator	Richard J. Hanson Tim Hopkins
status	peer reviewed published
Publisher	ACM
abstract	We propose a set of new Fortran reference implementations, based on an algorithm proposed by Kahan, for the Level 1 BLAS routines *NRM2 that compute the Euclidean norm of a real or complex input vector. The principal advantage of these routines over the current offerings is that, rather than losing accuracy as the length of the vector increases, they generate results that are accurate to almost machine precision for vectors of length N < Nmax where Nmax depends upon the precision of the floating point arithmetic being used. In addition we make use of intrinsic modules, introduced in the latest Fortran standards, to detect occurrences of non-finite numbers in the input data and return suitable values as well as setting IEEE floating point status flags as appropriate. A set of C interface routines is also provided to allow simple, portable access to the new routines. To improve execution speed, we advocate a hybrid algorithm; a simple loop is used first and, only if IEEE floating point exception flags signal, do we fall back on Kahan’s algorithm. Since most input vectors are ‘easy’, i.e., they do not require the sophistication of Kahan’s algorithm, the simple loop improves performance while the use of compensated summation ensures high accuracy. We also report on a comprehensive suite of test problems that has been developed to test both our new implementation and existing codes for both accuracy and the appropriate settings of the IEEE arithmetic status flags.
Is Part Of	ACM Transactions on Mathematical Software https://kar.kent.ac.uk/id/repository
list of authors	https://kar.kent.ac.uk/id/eprint/67205#authors
issue	3
volume	44
is topic of	https://raw.githubusercontent.com/annajordanous/CO644Files/main/export_kar_RDFN3.n3
is primary topic of	HTML Summary of #67205 Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm

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