Journal ArticleDOI
Parallel algorithms for the rounding exact summation of floating point numbers
H. Leuprecht,Wilhelm Oberaigner +1 more
TLDR
Three parallel versions of this algorithm for the rounding exact summation of floating point numbers are proposed, namely a pipeline version, an algorithm similar to the exchange methods for sorting and a tree-like algorithm, associating a tree to the sum.Abstract:
Pichat and Bohlender studied an algorithm for the rounding exact summation of floating point numbers which can be executed on any floating point arithmetic unit. We propose parallel versions of this algorithm, namely a pipeline version, an algorithm similar to the exchange methods for sorting and a tree-like algorithm, associating a tree to the sum. For all these algorithms we discuss the properties, a multiprocessor architecture should have for an efficient implementation of an algorithm without restricting us to a special architecture.read more
Citations
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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.
Proceedings ArticleDOI
Algorithms for arbitrary precision floating point arithmetic
TL;DR: The author presents techniques for performing computations of very high accuracy using only straightforward floating-point arithmetic operations of limited precision, and an algorithm is presented which computes the intersection of a line and a line segment.
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 and Efficient Floating Point Summation
James Demmel,Yozo Hida +1 more
TL;DR: Several simple algorithms for accurately computing the sum of n floating point numbers using a wider accumulator are presented and how the cost of sorting can be reduced or eliminated while retaining accuracy is investigated.
Accurate Floating Point Summation
James Demmel,Yozo Hida +1 more
TL;DR: In this article, the authors present and analyze several simple algorithms for accurately summing n floating point numbers, independent of how much cancellation occurs in the sum, and assume a register is available with F = 33.
References
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Journal ArticleDOI
Correction d'une somme en arithmetique a virgule flottante
TL;DR: In this paper, a rounding-off law with a guard digit was proposed to obtain all the digits of the sum of given numbers as significant digits, and an algorithm to correct the rounding off law in one step.
Book ChapterDOI
Genaue Summation von Gleitkommazahlen
TL;DR: In this paper, angegebene Algorithmus liefert die genauestmogliche Naherung und das kleinest Einschliesungsintervall fur die Summe von n Gleitkommazahlen.
Book ChapterDOI
Roundings and Approximations in Ordered Sets
TL;DR: In this paper, the authors introduced the notions of adherence, co-adherence, and limit of a rounding, and a uniform topologization of the Space of Filter and Ideal Basis on an ordered set with a rounding.
Journal ArticleDOI
Concept of a multi-processor parallel processing unit
TL;DR: The logical concept of a processing system withm, 1