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ekmett / compensated

Compensated floating-point arithmetic
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deadlinks for reference papers #12

Open cartazio opened 1 year ago

cartazio commented 1 year ago

OgRuOi05.pdf is a dead link and i cant reconstruct what it actually refers to, though its definitely true that this stuff is related to shewchuk's work on robust geometric predicates

claudeha commented 3 months ago

I found a PDF at http://web.archive.org/web/20180713135754/http://www.ti3.tuhh.de/paper/rump/OgRuOi05.pdf

published in SIAM Journal on Scientific Computing (SISC), 26(6):1955-1988, 2005.

ACCURATE SUM AND DOT PRODUCT∗

TAKESHI OGITA † , SIEGFRIED M. RUMP ‡ , AND SHIN’ICHI OISHI §

Abstract. Algorithms for summation and dot product of floating point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or K-fold working precision, K ≥ 3. For twice the working precision our algorithms for summation and dot product are some 40 % faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction and multiplication of floating point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.

Key words. accurate summation, accurate dot product, fast algorithms, verified error bounds, high precision

AMS subject classifications. 15-04, 65G99, 65-04

RyanGlScott commented 3 months ago

Thanks!

Unless I'm missing something, https://www.tuhh.de/ti3/paper/rump/OgRuOi05.pdf is a modern link to the same paper that we could use.