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Systematic Alias Sampling

In this article, we combine the Alias method with the concept of systematic sampling, a method commonly used in particle filters for efficient low-variance resampling. The proposed method allows very fast sampling from a discrete distribution: drawing k samples is up to an order of magnitude faster than binary search from the cumulative... (more)

Parallel Memory-Efficient Adaptive Mesh Refinement on Structured Triangular Meshes with Billions of Grid Cells

We present sam(oa)2, a software package for a dynamically adaptive, parallel solution of 2D partial... (more)

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New ACM TOMS Editor-in-Chief

Call for Nominations

Mike Heroux's term as EiC of ACM TOMS is coming to an end and nominations, including self-nominations, are invited for a three-year term as TOMS EiC to begin on March 1, 2017.

The nomination procedure is now available. The closing date for applications is September 15, 2016.

The ACM TOMS Replicated Computational Results (RCR) Initiative.

ACM TOMS has introduced a new initiative to optionally review the computationals results of a TOMS submission. This new effort is intended to assist in improving the quality of scientific publication for TOMS and for the computational science community as a whole. Manuscripts that successfully complete the RCR Review process receive the RCR designation when published. If you are interested in participating in this initiative, either as an author or reviewer, please contact the TOMS Editor-in-Chief. Details of the TOMS RCR Initiative are available here.


New options for ACM authors to manage rights and permissions for their work

ACM introduces a new publishing license agreement, an updated copyright transfer agreement, and a new author-pays option which allows for perpetual open access through the ACM Digital Library. For more information, visit the ACM Author Rights webpage.

 

Forthcoming Articles
Optimizing the NIST Statistical Test Suite and the Berlekamp-Massey algorithm

The NIST Statistical Test Suite is one of the most popular tools for randomness analysis. This test battery is widely used but its implementation is quite inefficient. Complete randomness analysis using the NIST STS can take hours on a standard computer when the tested data volume is in the order of GBs. We improved the most time consuming tests (Spectral, Linear complexity) of the previous most efficient implementation of the NIST STS. We also optimised other tests and achieved minimal overall speed-up 38.5x compared to the NIST STS reference implementation. This means that 20 MB of data can be tested within a minute using our new optimised version of the NIST STS. To speed up the Linear complexity test, we proposed a new version of the Berlekamp-Massey algorithm computing just the linear complexity of a sequence. This new variant does not construct a linear feedback shift register and it is about 1.5 times faster than the standard version of the Berlekamp-Massey algorithm.

IEEE754 precision-$k$ base-$\beta$ arithmetic inherited by precision-$m$ base-$\beta$ arithmetic for $k<m$

Suppose an $m$-digit floating-point arithmetic in base $\beta\ge 2$ following the IEEE754 arithmetic standard is available. We show how a $k$-digit arithmetic with $k<m$ can be inherited solely using $m$-digit operations. This includes the rounding into $k$ digits, the four basic operations and the square root, all for even or odd base $\beta$. In particular, we characterize the relation between $k$ and $m$ so that no double rounding occurs when computing in $m$ digits and rounding the result into $k$ digits. We discuss rounding to nearest as well as directed rounding, and our approach covers exceptional values including signed zero. For binary arithmetic, a Matlab toolbox based on binary64 including $k$-bit scalar, vector and matrix operations as well as $k$-bit interval arithmetic is part of Version 8 of INTLAB, the Matlab toolbox for reliable computing.

Chopping a Chebyshev series

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function $f(x)$ defined on an interval $[a,b]$ is ``rounded'' to a prescribed precision by constructing a Chebyshev series and chopping it at an appropriate point. Designing a chopping algorithm with the right properties proves to be a surprisingly complex and interesting problem. We describe the chopping algorithm introduced in Chebfun Version 5.3 in 2015 after many years of discussion and the considerations that led to this design.

Algorithm xxx: DISODE45: A Matlab Runge-Kutta solver for Piecewise Smooth IVPs of Filippov type

In this paper an adaptive Runge-Kutta code, based on the DOPRI5(4) pair, for solving Initial Value Problems for differential systems with Piecewise Smooth solutions (PWS) is presented and the algorithms used in the code are described. The code automatically detects and locate accurately the switching points of the PWS, restarting the integration after each discontinuity. Further, in the case of Filippov systems, algorithms to handle properly sliding mode regimes in an automatic way are included. The code requires from the user a description of the IVP and the functions defining the hypersurfaces where the switching points are located, and it gives the discrete approximated solution together with the switching points. Several numerical experiments are presented to illustrate the reliability and efficiency of the code.

An efficient representation format for fuzzy intervals based on symmetric membership functions

This paper proposes a novel implementation of fuzzy arithmetics that exploits both fuzzy intervals and hardware specificities. First, we propose and evaluate the benefit of an alternative representation format to the traditional lower-upper and midpoint-radius representation formats for intervals. Thanks to the proposed formats, we show that it is possible to halve the number of operations and memory requirements compared to conventional methods. Then, we show that operations on fuzzy intervals are sensitive to hardware specificities of accelerators such as GPU. These include static rounding, memory usage, instruction level parallelism (ILP) and thread-level parallelism (TLP). We develop a library of fuzzy arithmetic operations in CUDA and C++ over several formats. The proposed library is evaluated using compute-bound and memory-bound benchmarks on Nvidia GPUs, and shows a performance gain of 2 to 20 over traditional approaches.

\texttt{PSelInv}--A Distributed Memory Parallel Algorithm for Selected Inversion : the Symmetric Case

We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix $A$ that can be decomposed as $A = LU$, where $L$ is lower triangular and $U$ is upper triangular. The implementation described in this paper focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization \texttt{SuperLU\_DIST}. However, the underlying data structure and design of \texttt{PSelInv} allows it to be easily combined with other factorization routines such as \texttt{PARDISO}. We discuss general parallelization strategies such as data and task distribution schemes. In particular, we describe how to exploit the concurrency exposed by the elimination tree associated with the $LU$ factorization of $A$. We demonstrate the efficiency and accuracy of \texttt{PSelInv} by presenting a number of numerical experiments. In particular, we show that \texttt{PSelInv} can run efficiently on more than $4,000$ cores for a modestly sized matrix. We also demonstrate how \texttt{PSelInv} can be used to accelerate large-scale electronic structure calculations.

GPU-accelerated generation of correctly-rounded elementary functions

The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Makers Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such computations, namely Lefèvre algorithm on Graphics Processing Units (GPUs) which are massively parallel architectures with a partial SIMD execution (Single Instruction Multiple Data). We first propose an analysis of the Lefèvre hard-to-round argument search using the concept of continued fractions. We then propose a new parallel search algorithm much more efficient on GPU thanks to its more regular control flow. We also present an efficient hybrid CPU-GPU deployment of the generation of the polynomial approximations required in Lefèvre algorithm. In the end, we manage to obtain overall speedups up to 53.4x on one GPU over a sequential CPU execution, and up to 7.1x over a multi-core CPU, which enable a much faster solving of the Table Makers Dilemma for the double precision format.

Algorithm xxx: Computation of the incomplete gamma function for negative values of the argument

An algorithm for computing the incomplete gamma function $\gamma^*(a,z)$ for real values of the parameter a and negative real values of the argument z is presented. The algorithm combines the use of series expansions, Poincare-type expansions, uniform asymptotic expansions and recurrence relations, depending on the parameter region. A relative accuracy $10^{-13}$ in the parameter region $(a,z) \in [-500,\,500] \times [-500,\,0)$ can be obtained when computing the function $\gamma^*(a,z)$ with the Fortran 90 module IncgamNEG implementing the algorithm.

Firedrake: automating the finite element method by composing abstractions

Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only implementation centred on the composition of several existing and new abstractions for particular aspects of scientific computing. The result is a more complete separation of concerns which eases the incorporation of separate contributions from computer scientists, numerical analysts and application specialists. These contributions may add functionality, or improve performance. Firedrake benefits from automatically applying new optimisations. This includes factorising mixed function spaces, transforming and vectorising inner loops, and intrinsically supporting block matrix operations. Importantly, Firedrake presents a simple public API for escaping the UFL abstraction. This allows users to implement non--finite-element operations such as flux-limiters.

About TOMS

The purpose of the ACM Transactions on Mathematical Software (TOMS) is to communicate important research results addressing the development, evaluation and use of mathematical software...

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Bibliometrics

Publication Years 1975-2016
Publication Count 1473
Citation Count 13433
Available for Download 1473
Downloads (6 weeks) 5212
Downloads (12 Months) 44258
Downloads (cumulative) 983765
Average downloads per article 668
Average citations per article 9
First Name Last Name Award
Vernon Austel ACM Gordon Bell Prize (2006)
David H Bailey ACM Gordon Bell Prize (2008)
George Biros ACM Gordon Bell Prize
Performance (2010) ACM Gordon Bell Prize
Performance (2010)
Ronald Boisvert ACM Distinguished Member (2006)
Bruno Buchberger ACM Paris Kanellakis Theory and Practice Award (2007)
Edmond Chow ACM Gordon Bell Prize
Special Category (2009) ACM Gordon Bell Prize
Special Category (2009)
James Demmel ACM Paris Kanellakis Theory and Practice Award (2014)
Jack Dongarra ACM-IEEE CS Ken Kennedy Award (2013)
Stuart Feldman ACM Software System Award (2003)
John Gunnels ACM Gordon Bell Prize (2007)
John A. Gunnels ACM Gordon Bell Prize (2006)
Michael A Heroux ACM Distinguished Member (2009)
William Kahan ACM A. M. Turing Award (1989)
Matthew Knepley SIAM/ACM Prize in Computational Science and Engineering (2014)
David J Kuck ACM-IEEE CS Ken Kennedy Award (2010)
ACM-IEEE CS Eckert-Mauchly Award (1993)
Byounghak Lee ACM Gordon Bell Prize (2008)
Dhairya Malhotra ACM-IEEE CS George Michael Memorial HPC Fellowships (2015)
ACM Gordon Bell Prize
Performance (2010)
Lois C McInnes SIAM/ACM Prize in Computational Science and Engineering (2014)
Cleve Moler SIAM/ACM Prize in Computational Science and Engineering (2009)
Dianne P O'Leary ACM Distinguished Member (2006)
Naren Ramakrishnan ACM Distinguished Member (2009)
Sartaj K Sahni ACM Karl V. Karlstrom Outstanding Educator Award (2003)
Robert Schreiber ACM Distinguished Member (2006)
Horst D Simon ACM Gordon Bell Prize
Special Category (2009) ACM Gordon Bell Prize
Special Category (2009)
Barry Smith SIAM/ACM Prize in Computational Science and Engineering (2014)
James E. Smith ACM-IEEE CS Eckert-Mauchly Award (1999)
Kris Stewart ACM Senior Member (2015)
Nathan Tallent ACM-IEEE CS George Michael Memorial HPC Fellowships (2009)
Robert E Tarjan ACM Paris Kanellakis Theory and Practice Award (1999)
ACM A. M. Turing Award (1986)
Jeffrey S Vetter ACM Distinguished Member (2012)
ACM Gordon Bell Prize
Performance (2010)
Robert A. Walker Outstanding Contribution to ACM Award (2007)
ACM Distinguished Member (2006)
Bruce W Weide ACM Senior Member (2009)
Kesheng Wu ACM Distinguished Member (2010)
ACM Senior Member (2007)
Andrew C Yao ACM A. M. Turing Award (2000)
Hong Zhang SIAM/ACM Prize in Computational Science and Engineering (2014)
Benjamin G Zorn ACM Distinguished Member (2011)

First Name Last Name Paper Counts
Iain Duff 28
Robert Renka 22
Robert Van De Geijn 20
Fred Krogh 20
Jennifer Scott 19
John Reid 17
Jack Dongarra 17
Bo Kågström 15
Timothy Davis 15
Donald Amos 14
Lawrence Shampine 14
Wayne Enright 14
Richard Hanson 13
Jorge Moré 12
John Rice 12
Layne Watson 12
Burton Garbow 12
James Demmel 12
Joseph Liu 11
Fred Gustavson 11
William Cody 10
Timothy Hopkins 9
Walter Gautschi 9
Elias Houstis 9
Jeff Cash 9
Linda Kaufman 9
Xiaoyesherry Li 9
Nicholas Higham 8
Field Van Zee 8
Nico Temme 8
Ping Tang 8
Amparo Gil 8
Enrique Quintana-Ortí 8
Javier Segura 8
Patrick Keast 8
John Pryce 8
Terje Espelid 7
Michael Heroux 7
Ronald Boisvert 7
Gregorio Quintana-Ortí 7
Nicholas Gould 7
Ralph Kearfott 7
Hiroshi Akima 7
John Lewis 7
A Buckley 7
Almerico Murli 7
Thomas Hull 6
Albrecht Preusser 6
James Lyness 6
Roger Grimes 6
Richard Bartels 6
Robert Kirby 6
David Gay 6
Sven Hammarling 6
Anders Logg 6
Robert Ward 6
Pierre L'Ecuyer 6
Ian Gladwell 6
Ronald Cools 6
Panos Pardalos 6
Annie Cuyt 6
Gilbert Stewart 6
Geoffrey Hill 5
Robert Schnabel 5
Tamar Schlick 5
Patrick Gaffney 5
Thomas Coleman 5
Jerzy Waśniewski 5
Philippe Toint 5
Paul Muir 5
Kendall Atkinson 5
Graeme Fairweather 5
Tony Chan 5
Van Van Snyder 5
Jarle Berntsen 5
Sivan Toledo 5
Richard Sincovec 5
Zhaojun Bai 5
Alexander Morgan 5
Krzysztof Sikorski 5
Anil Rao 5
William Mitchell 5
Yu Kuznetsov 5
Paolo Bientinesi 5
Mauricio Resende 5
Jeremy Du Croz 5
Paolo Toth 4
Tzemeng Low 4
Ian Robinson 4
Wayne Dyksen 4
David Dodson 4
Daniel Kressner 4
Alan George 4
Valerio Parisi 4
Francesco Zirilli 4
William Hager 4
Richard Lehoucq 4
Christof Vömel 4
Wolfgang Bangerth 4
Paul Bailey 4
Jean Muller 4
Norman Schryer 4
Naren Ramakrishnan 4
Uwe Naumann 4
Christian Bischof 4
Werner Rheinboldt 4
Jan Verwer 4
Calvin Ribbens 4
John Monahan 4
Daniel Lozier 4
Lothar Reichel 4
Charles Fulton 4
Osni Marques 4
David Kahaner 4
Jorge Nocedal 4
Ahmed Sameh 4
Joke Blom 4
Michael Saunders 4
Filippo Aluffi-Pentini 4
Carl De Boor 4
Beresford Parlett 4
Michael Patterson 4
David Smith 4
Tamara Kolda 4
Richard Brent 4
Sanjiva Weerawarana 3
David Kincaid 3
Thomas Aird 3
Yifan Hu 3
Ron Dembo 3
Francesco Romani 3
Alfred Morris 3
Armido DiDonato 3
Alan Jennings 3
Jonathan Hogg 3
William Brown 3
R Brankin 3
Philip Sharp 3
Joachim Ahrens 3
Paola Favati 3
Juan Meza 3
William Kahan 3
Marzio Sala 3
David Bailey 3
Desmond Higham 3
Maria Sosonkina 3
Bennett Fox 3
Aaron Fogelson 3
Webb Miller 3
Mariarosaria Rizzardi 3
David Shanno 3
Martin Berzins 3
Peter Benner 3
Yozo Hida 3
Anton Zettl 3
Kenneth Neves 3
Stan Cabay 3
Richard Fateman 3
Anshul Gupta 3
Ian Barrodale 3
Ulrich Dieter 3
Alan Laub 3
William Symes 3
Giorgio Carpaneto 3
Steven Pruess 3
Julien Langou 3
Francisco Igual 3
Roscoe Bartlett 3
Salvatore Filippone 3
Arnold Neumaier 3
Grazia Lotti 3
Bruce Schmeiser 3
Chao Yang 3
Danny Sorensen 3
Lars Karlsson 3
Andrew Sommese 3
Christoph Lauter 3
John Rice 3
Ron Brown 3
Alfredo Buttari 3
Kristján Jónasson 3
Bruno Lang 3
Niel Madsen 3
Toyat Cheung 3
Stavros Zenios 3
Giulio Giunta 3
Masao Kodama 3
Kanghoh Phua 3
J Diaz 3
Robert Granat 3
Garth Wells 3
Michael Berry 3
Eric Grosse 3
David Stoutemyer 3
Luisa D'amore 3
Frank Stenger 3
Granville Sewell 3
Phyllis Fox 3
Fayez Alhargan 3
Andrew Conn 3
Kenneth Hillstrom 3
Steven Benson 3
John Gunnels 3
Margaret Wright 3
Charles Gear 3
Silvano Martello 3
Richard Simard 3
Luís Vicente 3
Wolfgang Hörmann 3
Willy Govaerts 3
Hatem Ltaief 3
Shaun Forth 3
Norman Gibbs 3
Alan Genz 3
Jon Bentley 3
Tobin Driscoll 3
Ali Bouaricha 2
Cleve Moler 2
Robert Russell 2
J Christiansen 2
Charles Dunkl 2
Donald Ramirez 2
Greg Henry 2
Jeffrey Vitter 2
Per Hansen 2
S Barry 2
Sunyoung Kim 2
Leslie Foster 2
Piotr Luszczek 2
Jan Olszewski 2
Mauro Dell'Amico 2
Nikos Chrisochoides 2
Yves Nievergelt 2
Richard Weiss 2
Michael Giles 2
Rida Farouki 2
Mohamed Kamel 2
Bengt Fornberg 2
Theodore Papatheodorou 2
J Smith 2
Vincent Lefèvre 2
Daniel Kressner 2
Catherine Houstis 2
James Willenbring 2
Zvi Drezner 2
Robert Skeel 2
Lois McInnes 2
Jian He 2
Sebastian Ferrando 2
Jean Utke 2
Michael Mascagni 2
Tapio Schneider 2
Roy Welsch 2
Arunachalam Ravindran 2
Kenneth Jackson 2
Malcolm Pike 2
Mofreh Zaghloul 2
Alexandru Nicolau 2
Wilfried Gansterer 2
Mark Gockenbach 2
Michael Jenkins 2
Frederick Fritsch 2
Paul Bratley 2
Peter Hanson 2
Karla Hoffman 2
Francisco Sayas 2
Benjamin Burton 2
Joaquim Martins 2
Kazushige Goto 2
George Miminis 2
Michele Goano 2
Bart Waanders 2
I Hill 2
Thomas Foley 2
J Weideman 2
Michel Cosnard 2
H Knoble 2
José Morales 2
Nelson Beebe 2
James Ball 2
George Davis 2
Duncan, Lawrie 2
Christopher Darby 2
Ilyssa Sanders 2
Geoffrey Huntington 2
Voratas Kachitvichyanukul 2
Jean L'excellent 2
Christopher Paige 2
P Culligan-Hensley 2
David Jeffrey 2
Joaquim Júdice 2
L Stoltz 2
Charles Duris 2
Charles Van Loan 2
Spencer Shellman 2
Per Thomsen 2
Dennis Snow 2
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Stanimire Tomov 2
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Kevin Broughan 2
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Nathan Bell 2
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Richard Wang 2
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V Kane 1
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Mukkai Krishnamoorthy 1
Andy Froncioni 1
Yong Li 1
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L Nikolenko 1
Pierluigi Amodio 1

Affiliation Paper Counts
Edinboro University of Pennsylvania 1
NVIDIA 1
The MathWorks, Inc. 1
Ariel University Center of Samaria 1
StatoilHydro 1
Computer Sciences Corporation, Australia 1
Airbus Deutschland GmbH 1
Camosun College 1
Barcelona Supercomputing Center 1
Research Institute for Advanced Computer Science 1
Institute of Mathematical Problems of Biology, Russian Academy of Sciences 1
Universite de Bordeaux 1
University of Houston-Downtown 1
Avago Technologies Manufacturing (Singapore) Pte. Ltd. 1
Universite Grenoble Alpes 1
Waseda University 1
Universite Claude Bernard Lyon 1 1
Institute of Marine Research 1
Brooklyn College 1
AT&T Information Systems 1
Ecole Centrale Paris 1
Southern Illinois University 1
Open University of the Netherlands 1
Universite Paris-Sud XI 1
University of California, Santa Cruz 1
University of Alabama 1
Harris Corporation 1
Indian Institute of Technology, Madras 1
Korea Institute of Science and Technology 1
Alcatel-Lucent 1
Mathematical Research Institute, Utrecht University 1
Defence Science and Technology Laboratory 1
Winthrop University 1
University of Nebraska - Lincoln 1
Stony Brook University 1
Universite Hassan 1er 1
Universidad Autonoma de Madrid 1
Clark University 1
Polytechnic University, Gdansk 1
Oracle Corporation 1
University of Hamburg 1
Palo Alto Research Center 1
St. Louis University 1
Siemens AG 1
Sunnybrook Health Sciences Centre 1
California State University Long Beach 1
Institute of Chemical Methodologies, Rome 1
University of California, Riverside 1
University of Aarhus 1
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ACM Transactions on Mathematical Software (TOMS)
Archive


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2003
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2001
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2000
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1999
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1990
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1989
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1988
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1987
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1986
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1985
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1984
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1983
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1982
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1981
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1980
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1979
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1978
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1977
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1976
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1975
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