A fast parallel high-precision summation algorithm based on AccSumK
TLDR
In this paper , a new parallel accurate algorithm called PAccSumK for computing summation of floating-point numbers is presented, which is based on AccSumK algorithm and it is designed to compute a result as if computed internally in K-fold the working precision.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2022-05-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Parallel algorithm & Ramer–Douglas–Peucker algorithm.read more
Citations
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Book ChapterDOI
Parallel Vectorized Implementations of Compensated Summation Algorithms
TL;DR: In this paper , the authors proposed a vectorized version of the Gill-Møller algorithm for summing long sequences of floating-point numbers using Intel AVX-512 intrinsics together with OpenMP constructs.
Journal ArticleDOI
Improving accuracy of summation using parallel vectorized Kahan's and Gill‐Møller algorithms
TL;DR: In this article , the authors show that Kahan's and Gill-Møller compensated summation algorithms that allow to achieve high accuracy of summing long sequences of floating-point numbers can be efficiently vectorized and parallelized using Intel AVX-512 intrinsics together with OpenMP constructs.
References
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Journal ArticleDOI
MPFR: A multiple-precision binary floating-point library with correct rounding
TL;DR: This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library, to extend to arbitrary- Precision, ideas from the IEEE 754 standard, by providing correct rounding and exceptions.
Journal ArticleDOI
A floating-point technique for extending the available precision
TL;DR: A technique is described for expressing multilength floating-point arithmetic in terms of singlelength floating point arithmetic, i.e. the arithmetic for an availablefloating-point number system.
Journal ArticleDOI
Accurate Sum and Dot Product
TL;DR: Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time and it is shown that the computed results are as accurate as if computed in twice or K-fold working precision.
Journal ArticleDOI
Accurate Floating-Point Summation Part I: Faithful Rounding
TL;DR: This paper presents an algorithm for calculating a faithful rounding of a vector of floating-point numbers, which adapts to the condition number of the sum, and proves certain constants used in the algorithm to be optimal.
Journal ArticleDOI
Accurate Floating-Point Summation Part II: Sign, $K$-Fold Faithful and Rounding to Nearest
TL;DR: An algorithm for calculating the rounded-to-nearest result of $s:=\sum p_i$ for a given vector of floating-point numbers $p_i$, as well as algorithms for directed rounding, working for huge dimensions.