{"title":"Using the reverse-carry approach for double datapath floating-point addition","authors":"J. Bruguera, T. Lang","doi":"10.1109/ARITH.2001.930120","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930120","url":null,"abstract":"The double-datapath organization of a floating-point adder results in reduced latency. One of the main characteristics of this organization is the combination of addition/subtraction with rounding into a single add/round module, which is implemented as one pipeline stage and might be responsible for the cycle time. We propose the utilization of the most-significant carry detector and the corresponding adder using the reverse-carry approach to reduce the latency of this add/round module. In addition, the particular organization of the reverse-carry adder is used to reduce the contribution on the delay of the row of half adders that is included in the FAR datapath to produce the sum plus two. Estimates for a 64 bit add/round module show a potential reduction of delay of about 15%.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115275168","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}
J. Bajard, Laurent-Stéphane Didier, Peter Kornerup
{"title":"Modular multiplication and base extensions in residue number systems","authors":"J. Bajard, Laurent-Stéphane Didier, Peter Kornerup","doi":"10.1109/ARITH.2001.930104","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930104","url":null,"abstract":"We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's (1985) method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an effect corresponding to a redundant high-radix implementation is achieved, due to the carry-free nature of residue arithmetic. The actual computation in the multiplication takes place in constant time, where the unit of time is a few simple residue operations. However, it is necessary twice to convert values from one residue system into another, operations which take O(n) time on O(n) processors, where n is the number of moduli in the RNS systems. Thus these conversions are the bottlenecks of the method, and any future improvements in RNS base conversions, or the use of particular residue systems, can immediately be applied.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"32 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124945450","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}
{"title":"Low-power properties of the logarithmic number system","authors":"Vassilis Paliouras, T. Stouraitis","doi":"10.1109/ARITH.2001.930124","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930124","url":null,"abstract":"The potential of reducing power dissipation in a digital system using the logarithmic number system (LNS) is investigated. To provide a quantitative measure of power savings, the equivalence of an LNS to a linear fixed-point system is initially explored. The bit assertion activity of an LNS encoded signal is studied for both uniform and correlated Gaussian inputs. It is shown that LNS reduces the average bit assertion probability by more than 50%, in certain cases, over an equivalent linear representation. Finally, the impact of LNS on the hardware architecture and, thus, to power dissipation, is discussed. It is found that the average number of logic transitions is reduced by several times, for certain arithmetic operations and word lengths, thus compensating the power-dissipation overhead due to the unavoidable linear-to-logarithmic and logarithmic-to-linear conversion.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"14 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116431858","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}
{"title":"Effective continued fractions","authors":"D. Lester","doi":"10.1109/ARITH.2001.930116","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930116","url":null,"abstract":"Only the leading seven terms of a continued fraction are needed to perform on-line arithmetic, provided the continued fractions are of the correct form. This forms the basis of a proof that there is an effective representation of the computable reals as continued fractions; we also demonstrate that the basic arithmetic operations are computable using this representation.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123989326","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}
V. Dimitrov, J. Eskritt, L. Imbert, G. Jullien, W. Miller
{"title":"The use of the multi-dimensional logarithmic number system in DSP applications","authors":"V. Dimitrov, J. Eskritt, L. Imbert, G. Jullien, W. Miller","doi":"10.1109/ARITH.2001.930126","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930126","url":null,"abstract":"A recently introduced double-base number representation has proved to be successful in improving the performance of several algorithms in cryptography and digital signal processing. The index-calculus version of this number system can be regarded as a two-dimensional extension of the classical logarithmic number system. This paper builds on previous special results by generalizing the number system both in multiple dimensions (multiple bases) and by the use of multiple digits. Adopting both generalizations the paper shows that large reductions in hardware complexity are achievable compared to an equivalent precision logarithmic number system.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116149722","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}
{"title":"Correctly rounded reciprocal square-root by digit recurrence and radix-4 implementation","authors":"T. Lang, E. Antelo","doi":"10.1109/ARITH.2001.930107","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930107","url":null,"abstract":"We present a reciprocal square-root algorithm by digit recurrence and selection by a staircase function, and the radix-4 implementation. As similar algorithms for division and square-root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square-root). Although apparently a single selection function can only be used for j/spl ges/2 (the selection constants are different for j=0, j=1 and j/spl ges/2), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, specially for exactly rounded results.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124340904","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}
{"title":"A design of radix-2 on-line division using LSA organization","authors":"A. Tenca, Safiullah Hussaini","doi":"10.1109/ARITH.2001.930128","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930128","url":null,"abstract":"This paper presents the application of the Linear Sequential Array (LSA) organization to on-line division. The LSA method was originally developed for conventional digit-recurrence algorithms, but we apply it to the on-line division algorithm. The resulting architecture is a modular and fast pipelined structure which, due to a constant fan-out, makes the critical path delay, and consequently the clock cycle time, less sensitive to operand's precision. Such approach is particularly suitable for FPGA implementation for its modularity and reduced fanout. The basics of on-line division is presented, followed by the derivation of data dependencies and architecture according to the LSA design methodology. Experimental data is provided for both the LSA on-line divider design and standard online design, using 0.5 /spl mu/m CMOS ASIC and FPGA technologies.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133773113","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}
{"title":"High speed parallel-prefix modulo 2/sup n/+1 adders for diminished-one operands","authors":"H. T. Vergos, D. Nikolos, C. Efstathiou","doi":"10.1109/ARITH.2001.930121","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930121","url":null,"abstract":"We present a new methodology for designing modulo 2/sup n/+1 adders with operands in the diminished-one number system. The proposed methodology leads to parallel-prefix adder implementations. Both an analytical model and VLSI implementations in a standard-cell technology are utilized for comparing the adders designed following the proposed methodology against the existing solutions. Our results indicate; that the proposed parallel-prefix adders are considerably faster than any other already known in the open literature and as fast as the corresponding modulo 2/sup n/ and modulo 2/sup n/-1 adders.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116465906","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}
A. Naini, Atul Dhablania, Warren James, Debjit Das Sarma
{"title":"1 GHz HAL SPARC64/sup R/ Dual Floating Point Unit with RAS features","authors":"A. Naini, Atul Dhablania, Warren James, Debjit Das Sarma","doi":"10.1109/ARITH.2001.930117","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930117","url":null,"abstract":"An IEEE compliant, 1 GHz Sparc64-V Floating-Point Unit (FPU) with reliability-accessibility-serviceability (RAS) features and partial support for denormal operands and results is presented. The FPU has two functional units, each with an adder (FADD) and a multiplier (FMUL). Additionally, one of the functional units contains a graphics unit (VIS). Two floating-point instructions can be scheduled out of order each cycle, one to each functional unit. A peak performance of 4 GFLOP is achieved by scheduling two floating-point multiply add (FMA) instructions each cycle. The FADD unit is fully pipelined and can execute an addition, subtraction, conversion, or compare instruction every cycle. The FMUL unit executes pipelined multiply instructions. Divide and square-root instructions are executed with multiple iterations through the multiplier pipeline. The VIS unit is also pipelined and executes SIMD fixed-point graphics instructions. The adder and multiplier have latencies of 3 and 4 cycles respectively. Novel techniques are presented in the adder and multiplier implementations to reduce area and cycle time. The FPU provides RAS support for enhanced server reliability by using selective parity error detection. The FPU has been implemented in 0.15 u, 6-layer metal CMOS technology.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121321675","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}
{"title":"Bit-parallel systolic modular multipliers for a class of GF(2/sup m/)","authors":"Chiou-Yng Lee, E. Lu, Jau-Yien Lee","doi":"10.1109/ARITH.2001.930103","DOIUrl":"https://doi.org/10.1109/ARITH.2001.930103","url":null,"abstract":"In this paper, an effective algorithm for computing multiplication over a class of GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) is presented. The structures are the use of two special operations, called the cyclic shifting and the inner product, to construct the low-latency bit-parallel systolic multipliers. The circuits are simple and modular which is important for hardware implementation. The AOP-based multiplier is composed of (m+1)/sup 2/ identical cells, each of which consisting of one 2-bit AND gate, one 2-bit XOR gate and three 1-bit latches. This multiplier has very low latency and propagation delay, which makes them very fast. Moreover, the AOP-based multiplier of small size can also be applied to construct ESP-based multiplier of large size, in which the elements are represented with the root of an irreducible equally spaced polynomial of degree nr. It is shown that if, for a certain degree, an irreducible ESP of a large degree can be obtained from a corresponding irreducible AOP of a very small degree, then from the complexity point view, the structure of the ESP-based multiplier is beneficial to construct a modular architecture.","PeriodicalId":356830,"journal":{"name":"Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121789969","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}