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Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm by Richard J. Hanson; Tim Hopkins is a Computer Science article available to read on EtoBox.

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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__ < __N__ ~__max__~ where __N__ ~__max__~ 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

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Author

Richard J. Hanson; Tim Hopkins

Publisher

ACM

Published

2017

Language

EN

Field

Computer Science (Physical Sciences)