Basic building blocks for a triple-double intermediate format

Christoph Quirin Lauter 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : The implementation of correctly rounded elementary functions needs high intermediate accuracy before final rounding. This accuracy can be provided by (pseudo-) expansions of size three, i.e. a triple-double format. The report presents all basic operators for such a format. Triple-double numbers can be redundant. A renormalization procedure is presented and proven. Elementary functions' implementations need addition and multiplication sequences. These operators must take operands in double, double-double and triple-double format. The results must be accordingly in one of the formats. Several procedures are presented. Proofs are given for their accuracy bounds. Intermediate triple-double results must finally be correctly rounded to double precision. Two effective rounding sequences are presented, one for round-to-nearest mode, one for the directed rounding modes. Their complete proofs constitute half of the report.
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Submitted on : Friday, May 19, 2006 - 8:01:21 PM
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Christoph Quirin Lauter. Basic building blocks for a triple-double intermediate format. [Research Report] RR-5702, LIP RR-2005-38, INRIA, LIP. 2005, pp.67. ⟨inria-00070314⟩

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