Geodesic
Extension of the C-XSC Library with Scalar Products with Selectable Accuracy
Serdica Journal of Computing, Tome 4 (2010) no. 3, pp. 349-370.

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The C++ class library C-XSC for scientific computing has been extended with the possibility to compute scalar products with selectable accuracy in version 2.3.0. In previous versions, scalar products have always been computed exactly with the help of the so-called long accumulator. Additionally, optimized floating point computation of matrix and vector operations using BLAS-routines are added in C-XSC version 2.4.0. In this article the algorithms used and their implementations, as well as some potential pitfalls in the compilation, are described in more detail. Additionally, the theoretical background of the employed DotK algorithm and the necessary modifications of the concrete implementation in C-XSC are briefly explained. Run-time tests and numerical examples are presented as well.
Keywords: DotK Algorithm, Error-Free Transformations, C-XSC, Scalar Products, Long Accumulator, K-Fold Accuracy 
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Zimmer, Michael; Krämer, Walter; Bohlender, Gerd; Hofschuster, Werner. Extension of the C-XSC Library with Scalar Products with Selectable Accuracy. Serdica Journal of Computing, Tome 4 (2010) no. 3, pp. 349-370. http://geodesic.mathdoc.fr/item/SJC_2010_4_3_a5/