Abstract
A formal specification of an arithmetic unit for computable normalized rational numbers is proposed. This specification, developed under the scope of the paradigm known as algebraic models of processors, exploits the connection between the signed digit representation for rational numbers in Type-2 Theory of Effectivity and online arithmetic in Computer Arithmetic. The proposal aims for specification formalization and calculation reliability together with implementation feasibility.
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Andrews, D., Sass, R., Anderson, E., Agron, J., Peck, W., Stevens, J., Baijot, F., Komp, E.: The Case for High Level Programming Models for Reconfigurable Computers. In: Proc. of the 2006 International Conference on Engineering of Reconfigurable Systems & Algorithms, pp. 21–32 (2006)
Avizienis, A.: Signed-digit number representations for fast parallel arithmetic. IRE Trans. Electronic Computers 10, 389–400 (1961)
Blanck, J.: Exact real arithmetic systems: Results of competition, Computability and Complexity in Analysis. In: Blank, J., Brattka, V., Hertling, P. (eds.) CCA 2000. LNCS, vol. 2064, pp. 390–394. Springer, Heidelberg (2001)
Blanck, J.: Exact real arithmetic using centred intervals and bounded error terms. Journal of Logic and Algebraic Programming 66, 207–240 (2006)
Borkar, S.: Getting Gigascale Chips: Challenges and Opportunities in Continuing Moore’s Law. ACM Queue 1(7), 26–33 (2003)
de Miguel Casado, G., García Chamizo, J.M.: The Role of Algebraic Models and Type-2 Theory of Effectivity in Special Purpose Processor Design. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988, pp. 137–146. Springer, Heidelberg (2006)
Ercegovac, M.D., Lang, T.: Digital Arithmetic. M. Kaufmann, Seattle (2004)
Fox, A.C.J., Harman, N.A.: Algebraic Models of Correctness for Abstract Pipelines. The Journal of Algebraic and Logic Programming 57(1-2), 71–107 (2003)
Gowland, P., Lester, D.: A Survey of Exact Arithmetic Implementations. In: Blank, J., Brattka, V., Hertling, P. (eds.) CCA 2000. LNCS, vol. 2064, pp. 30–47. Springer, Heidelberg (2001)
Harman, N.A. and Tucker, J.V.: Algebraic models of microprocessors: the verification of a simple computer. In: V Stravridou (ed), Mathematics of Dependable Systems II. Oxford : Clarendon Press; New York, Oxford University Press, (1997) 135–170
Harman, N.A.: Models of Timing Abstraction in Simultaneous Multithreaded and Multi-Core Processors, Logical Approaches to Computational Barriers, Report Series, Vol. CSR 7-2006, (2006) 129–139
Hayes, B.: A Lucid Interval. American Scientist 91, 484–488 (2003)
ISSCC Roundtable: Embedded Memories for the Future, IEEE Design and Test of Computers, vol. 20, pp. 66–81 (2003)
Lynch, T., Schulte, M.: A High Radix On-line Arithmetic for Credible and Accurate Computing. Journal of UCS 1, 439–453 (1995)
Post, D.E., Votta, L.G.: Computational science demands a new paradigm. Physics today 58(1), 35–41 (2005)
Schröder, M.: Admissible Representations in Computable Analysis. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006. LNCS, vol. 3998, pp. 471–480. Springer, Heidelberg (2006)
Weihrauch, K.: Computable Analysis. Springer, Heidelberg (2000)
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de Miguel Casado, G., García Chamizo, J.M., Signes Pont, M.T. (2007). Algebraic Model of an Arithmetic Unit for TTE-Computable Normalized Rational Numbers. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_23
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DOI: https://doi.org/10.1007/978-3-540-73001-9_23
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