2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH)最新文献_第2页

Correctly Rounded Arbitrary-Precision Floating-Point Summation 正确舍入任意精度浮点和

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.9

V. Lefèvre

引用次数: 6

Quad Precision Floating Point on the IBM z13 IBM z13上的四精度浮点

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.26

C. Lichtenau, S. Carlough, S. M. Müller

引用次数: 20

Automated Design of Floating-Point Logarithm Functions on Integer Processors 整数处理器上浮点对数函数的自动化设计

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.28

G. Revy

引用次数: 4

Accuracy and Performance Trade-Offs of Logarithmic Number Units in Multi-Core Clusters 多核集群中对数单位的精度和性能权衡

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.10

Michael Schaffner, Michael Gautschi, Frank K. Gürkaynak, L. Benini

{"title":"Accuracy and Performance Trade-Offs of Logarithmic Number Units in Multi-Core Clusters","authors":"Michael Schaffner, Michael Gautschi, Frank K. Gürkaynak, L. Benini","doi":"10.1109/ARITH.2016.10","DOIUrl":"https://doi.org/10.1109/ARITH.2016.10","url":null,"abstract":"When compared to traditional floating point (FP) number representation, logarithmic number systems (LNS) have superior performance when evaluating complex functions, since multiplications and divisions can be calculated with ease in the logarithmic domain. However, additions and subtractions become costly nonlinear operations. Efficient LNS units (LNUs) implementing ADD/SUB operations in hardware rely on interpolation techniques to save area. Even the most advanced LNUs are still larger than standard single-precision FPUs -- which renders them impractical for most general purpose processors. In this paper, we show that in a multi-core setting, when shared among several processor cores, LNUs become a very attractive solution. We present a methodology to generate LNUs with various error bounds and perform a design space exploration with different parameterizations. We show that already small precision relaxations in the order of a few units in the last place (ulp) reduce the LNU area significantly. Using examples from several signal processing domains, we demonstrate that shared approximate LNUs can outperform their standard FP counterpart on average by 2.14x in speed and 1.92x in energy-efficiency, with insignificant degradation of the output quality.","PeriodicalId":145448,"journal":{"name":"2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114144545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Multi-fault Attack Detection for RNS Cryptographic Architecture 基于RNS密码体系结构的多故障攻击检测

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.16

J. Bajard, J. Eynard, Nabil Merkiche

引用次数: 15

An Iterative Logarithmic Multiplier with Improved Precision 改进精度的迭代对数乘法器

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.25

Syed Ershad Ahmed, Sanket V. Kadam, M. Srinivas

引用次数: 17

A Formulation of Fast Carry Chains Suitable for Efficient Implementation with Majority Elements 适合多数元素高效实施的快速进位链公式

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-10 DOI: 10.1109/ARITH.2016.14

G. Jaberipur, B. Parhami, Dariush Abedi

引用次数: 8

Evaluating Straight-Line Programs over Balls 评估球上的直线规划

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-01 DOI: 10.1109/ARITH.2016.12

J. Hoeven, Grégoire Lecerf

引用次数: 4

Computing floating-point logarithms with fixed-point operations 用定点运算计算浮点对数

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-01 DOI: 10.1109/ARITH.2016.24

Julien Le Maire, Nicolas Brunie, F. D. Dinechin, J. Muller

{"title":"Computing floating-point logarithms with fixed-point operations","authors":"Julien Le Maire, Nicolas Brunie, F. D. Dinechin, J. Muller","doi":"10.1109/ARITH.2016.24","DOIUrl":"https://doi.org/10.1109/ARITH.2016.24","url":null,"abstract":"Elementary functions from the mathematical library input and output floating-point numbers. However it is possible to implement them purely using integer/fixed-point arithmetic. This option was not attractive between 1985 and 2005, because mainstream processor hardware supported 64-bit floating-point, but only 32-bit integers. This has changed in recent years, in particular with the generalization of native 64-bit integer support. The purpose of this article is therefore to reevaluate the relevance of computing floating-point functions in fixed-point. For this, several variants of the double-precision logarithm function are implemented and evaluated. Formulating the problem as a fixed-point one is easy after the range has been (classically) reduced. Then, 64-bit integers provide slightly more accuracy than 53-bit mantissa, which helps speed up the evaluation. Finally, multi-word arithmetic, critical for accurate implementations, is much faster in fixed-point, and natively supported by recent compilers. Thanks to all this, a purely integer implementation of the correctly rounded double-precision logarithm outperforms the previous state of the art, with the worst-case execution time reduced by a factor 5. This work also introduces variants of the logarithm that input a floating-point number and output the result in fixed-point. These are shown to be both more accurate and more efficient than the traditional floating-point functions for some applications.","PeriodicalId":145448,"journal":{"name":"2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH)","volume":"32 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114118645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 15

On-line Multiplication and Division in Real and Complex Bases 实数和复数基的在线乘法和除法

2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH) Pub Date : 2016-07-01 DOI: 10.1109/ARITH.2016.13

Marta Brzicova, Christiane Frougny, E. Pelantová, Milena Svobodová

{"title":"On-line Multiplication and Division in Real and Complex Bases","authors":"Marta Brzicova, Christiane Frougny, E. Pelantová, Milena Svobodová","doi":"10.1109/ARITH.2016.13","DOIUrl":"https://doi.org/10.1109/ARITH.2016.13","url":null,"abstract":"A positional numeration system is given by a base and by a set of digits. The base is a real or complex number β such that |β| > 1, and the digit set A is a finite set of real or complex digits (including 0). In this paper, we first formulate a generalized version of the on-line algorithms for multiplication and division of Trivedi and Ercegovac for the cases that β is any real or complex number, and digits are real or complex. We show that if (β, A) satisfies the so-called (OL) Property, then on-line multiplication and division are feasible by the Trivedi-Ercegovac algorithms. For a real base β and alphabet A of contiguous integers, the system (β, A) has the (OL) Property if #A > |β| . Provided that addition and subtraction are realizable in parallel in the system (β, A), our on-line algorithms for multiplication and division have linear time complexity. Three examples are presented in detail: base β = 3+√5/2 with alphabet A = {-1, 0, 1}; base β = 2i with alphabet A = {-2, -1, 0, 1, 2} (redundant Knuth numeration system); and base β = -3/2 + z√3/2 = -1 + ω, where ω = exp 2iπ/3 , with alphabet A = {0, ±1, ±ω, ±ω<sup>2</sup>} (redundant Eisenstein numeration system).","PeriodicalId":145448,"journal":{"name":"2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126355931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9