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Une méthodologie du calcul hardware des fonctions élémentaires. (French) Zbl 0609.65010
Efficient hardware algorithms for computing the most usual mathematical functions are described using the notion of discrete basis. The author presents a class of algorithms including some well-known methods and some new ones.
Reviewer: M.Gaspar
MSC:
65D20 Computation of special functions and constants, construction of tables
68W30 Symbolic computation and algebraic computation
26A09 Elementary functions
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References:
[1] M. ABRAMOWITZ and I. A. STEGUN, Handbook of Mathematical Functions withformulas, graphs, and mathematical tables, Nat. Bur. Standards, Appl. Math. Series, 55, Washington D.C., 1964. Zbl0643.33001 · Zbl 0643.33001
[2] H. M. AHMED, J. M. DELOSME, M. MORF, Highly concurrent Computing structures or matrix arithmetic and signal processing, Computer, Jan. 1982.
[3] F. ANCEAU, Architecture and design of Von Neumann microprocessors, Nato advanced summer institute, July 1980.
[4] M. ANDREWS and T. M R A Z, Unified elementary function generator, Microprocessors and Microsystems, Vol. 2 n^\circ 5, Oct. 1978, pp. 270-274.
[5] P. W. BAKER, More efficient radix-2 algorithms for some elementary functions, IEEE Trans, on computers, vol. c-24 n^\circ 11, Nov. 1975, pp. 1049-1054. Zbl0324.68040 MR386336 · Zbl 0324.68040 · doi:10.1109/T-C.1975.224132
[6] P. W. BAKER, Suggestion for a fast binary Sine/Cosine generator, IEEE Trans, on Computers, Nov. 1976, pp. 1134-1136.
[7] R. P. BRENT, Multiple-precision zero-finding methods and the complexity of elementary function evaluation, Analytic Computational Complexity (Ed. by J. F. Traub), Academic Press, New York, 1975, pp. 151-176. Zbl0342.65031 MR423869 · Zbl 0342.65031
[8] R. P. BRENT, Fast multiple-precision evaluation of elementary functions, J. ACM 23, 1976, pp. 242-251. Zbl0324.65018 MR395314 · Zbl 0324.65018 · doi:10.1145/321941.321944
[9] R. P. BRENT, Unrestricted algorithms for elementary and special functions, Information Processing 80, S. H. Lavington ed., North-Holland Publishing Comp., pp. 613-619. Zbl0442.65013 · Zbl 0442.65013
[10] T. H. CHAN and O. H. IBARRA, On the space and time complexity of functions computable by sample programs, Siam J. Comput, Vol. 12, n^\circ 4, Nov. 1983. Zbl0524.68030 MR721008 · Zbl 0524.68030 · doi:10.1137/0212048
[11] T. C. CHEN, Automatic computation of exponentials, logarithms, ratios and square roots. IBM J. Res. and Development, Vol. 16, July 1972, pp. 380-388. Zbl0257.68057 MR336965 · Zbl 0257.68057 · doi:10.1147/rd.164.0380
[12] C. W. CLENSHAW and F. W. J. OLVER, Bzyond floating point, J. of the ACM,Vol. 31, n^\circ 2, April 1984, pp. 319-328. Zbl0628.65037 MR819141 · Zbl 0628.65037 · doi:10.1145/62.322429
[13] W. CODY and W. WAITE, Software manual for the elementary functions, Prentice-Hall, inc, Englewood cliffs, New-Jersey, 1980. Zbl0468.68036 · Zbl 0468.68036
[14] W. CODY, Implementation and testing of function software, ibid.Ibid.
[15] W. CODY, Basic concepts for computational software, Ibid.Ibid. · Zbl 0605.33001
[16] W. CODY, Performance testing of function subroutines, AFIPS Conf. Proc , Vol. 34,1969 SJCC, AFIPS Press, Montvale, N.J., 1969, pp. 759-763.
[17] J. T. COONEN, An implementation guide to a proposed standard for floating-point arithmetic, IEEE Computer, Jan. 1980. Zbl0544.65029 · Zbl 0544.65029
[18] J M DELOSME, VLSI implementatwn of rotations in pseudo-euchdian space, proc 1983 IEEE Int Conf on ASSP, Boston, April 1983, pp 927-930
[19] J M DELOSME, The matrix exponential approach to elementary operations, Depart of Electrical Engineering, Yale Univ, NewHaven
[20] B DE LUGISH, A class of algorithms for automatic evaluation of certain elementar functions in a binary computer, Ph D dissertation, Dep Computer sci, Univ of Illinois, Urbana, June 1970
[21] [21] B DERRIDA, A GERVOIS, Y POMEAU, Iteration of endomorphisms on thereal axis and representation of numbers Commissariat à l’énergie Atomique, Service de physique théorique, CEN Saclay Zbl0416.28012 · Zbl 0416.28012 · numdam:AIHPA_1978__29_3_305_0 · eudml:76009
[22] A M DESPAIN, Fourier transform computers using CORDIC iterations, IEEE Trans on Computers, Vol c-23 n^\circ 10,Oct 1974 Zbl0287.65073 · Zbl 0287.65073 · doi:10.1109/T-C.1974.223800
[23] A M DESPAIN, Pipeline and parallel-pipeline FFT Processors for VLSI implementations, IEEE Trans on Computers, Vol c-33 n^\circ 5, May 1984 Zbl0528.68019 · Zbl 0528.68019 · doi:10.1109/TC.1984.1676458
[24] M D ERCEGOVAC, Radix-16 evaluation of certain elementary functions, IEEE Trans on Computers, Vol c-22 n^\circ 16, June 1973 Zbl0257.68052 · Zbl 0257.68052 · doi:10.1109/TC.1973.5009107
[25] M D ERCEGOVAC, A general method for évaluation of functions in a digital computer, Computer sci dep , School of Engineering & Applied science, Univ of California, Los Angeles, Cahfornia 90024 · Zbl 0406.68039
[26] C T FIKE, Computational evaluation of math functions, Prentice-Hall, Englewoodcliffs, New-Jersey, 1968 Zbl0205.19301 · Zbl 0205.19301
[27] W M GENTLEMAN, More on algorithms that reveal properties of floating-point arithmetics units, Comm of the ACM, Vol 17, n^\circ 5, May 1974
[28] G W GERRITY, Computer representation of real numbers, IEEE Trans Computers, Vol c-31 n^\circ 8, Aug 1982 Zbl0488.68039 · Zbl 0488.68039 · doi:10.1109/TC.1982.1676076
[29] G H HAVILAND and A TUSZYNSKY, A CORDIC arithmetic processor chip, IEEE Trans on Computers, Vol c-29 n^\circ 2, Feb 1980
[30] J F HART, E W CHENE, C L LAWSON, H J MAEHLY, C K MESZTENYI, J R RICE, H C TACHER Jr, and C WITZGALL, Computer Approximations, Wiley NY, 1968
[31] J P KAHONE and R SALEM, Ensembles parfaits et séries trigonométriques, Actualités scientifiques et industrielles 1301, Hermann Pans, 1963 Zbl0112.29304 MR160065 · Zbl 0112.29304
[32] A H KARP, Exponential and logarithm by sequential squaring, IEEE Trans on Computers, Vol c-33, n^\circ 5, May 1984, pp 462-464
[33] D E KNUTH, The art of computer programming, Vol 2, Addison Wesley, ReadingD E KNUTH, Mass , 1969 Zbl0191.18001 MR633878 · Zbl 0191.18001
[34] J KROPA, Calculator algorithms, Math Mag , Vol 51 n^\circ 2, March 1978, pp 106-109 Zbl0397.65082 MR1572257 · Zbl 0397.65082 · doi:10.2307/2690146
[35] J D MARASA and D W MATULA, A simulated study of correlated error propagation in various finite-precision arithmetic, IEEE Trans on Computers, Vol c-22, n^\circ 6, June 1973 Zbl0257.65043 · Zbl 0257.65043 · doi:10.1109/TC.1973.5009111
[36] C MASSE, L’itération de Newton convergence et chaos, these de troisième cycle Université Grenoble I, Oct 1984
[37] D W MATULA, Basic digit sets for radix representation, J of the ACM, Vol 29n^\circ 4,Oct 1982, pp 1131-1143 Zbl0509.10008 MR674260 · Zbl 0509.10008 · doi:10.1145/322344.322355
[38] J E MEGGITT, Pseudo Division and Pseudo Multiplication Processes, IBM of Res and Dev , Vol 6, April 1962, pp 210-227 Zbl0201.48709 · Zbl 0201.48709 · doi:10.1147/rd.62.0210
[39] J M MULLER, Discrete basis and computation of elementary functions, IEEE Trans on Computers, Sept 1985, pp 857-862 MR810091
[40] J. M. MULLER, Conditionnement de fonctions et représentation flottante des nombres réels, RR Math. App. n^\circ 453, Grenoble, 1984.
[41] J. M. MULLER, A hardware algorithm for Computing the complex exponential fonction, RMath. App. n^\circ 467, Grenoble, 1984
[42] A. NASEEM and P. D. FISHER, A modified CORDIC Algorithm, Preprint Dept. of Electrical Engineering and Systems Science, Michigan State Univ., East Lansing, Michigan 48824.
[43] F. W. J. OLVER, A new approach to error arithmetic, SIAM J. Numer. Analysis, Vol. 15 n^\circ 2, April 1978. Zbl0385.65019 MR483379 · Zbl 0385.65019 · doi:10.1137/0715024
[44] G. PAUL and W. WAYNE WILSON, Should the elementary function library be incorporated into computer instruction sets, ACM Trans, on Math. Software, Vol. 2 n^\circ 2, June 1976, pp. 132-142.
[45] W. PARRY, On the ß-expansion of real numbers, Acta math. acad. sci.Hung., 11, 1960, pp. 401-416. Zbl0099.28103 MR142719 · Zbl 0099.28103 · doi:10.1007/BF02020954
[46] M. PICHAT, Contribution à l’étude des erreurs d’arrondi en arithmétique à virgule flottante, thèse d’état, Grenoble, France, 1976.
[47] A. RENYI, Representations for real numbers and their ergodic functions, Acta. Math.Acad. Sci. Hungary, 1957, pp. 477-493. Zbl0079.08901 MR97374 · Zbl 0079.08901 · doi:10.1007/BF02020331
[48] A. RENYI, On the distribution of the digits in Cantor’s series, Mat. Lapok 7, 1956 pp. 77-100. Zbl0075.03703 MR99968 · Zbl 0075.03703
[49] F. ROBERT, Itération machine d’une fonction affine, RR Math. App.n^\circ 440, IMAG, Grenoble, France.
[50] B. P. SARKAR and E. V. KRISHNAMURTHY, Economic pseudodivision processes for obtaining square root, logarithm and arctan, IEEE Trans, onComputers, Dec. 1971, pp. 1589-1593. Zbl0229.68007 · Zbl 0229.68007 · doi:10.1109/T-C.1971.223178
[51] C. W. SCHELIN, Calculator function approximation, Amer. Math. Monthly 90,5, May 1983. Zbl0532.65012 MR701572 · Zbl 0532.65012 · doi:10.2307/2975781
[52] H. SCHMID and A. BOGOCKI, Use decimal CORDIC for generation of many transcendental functions, Electrical design mag., Feb. 1973, pp. 64-73.
[53] O. SPANIOL, Computer arithmetic and design, J. Wiley & Sons, 1981. Zbl0493.68007 MR611684 · Zbl 0493.68007
[54] W. H. SPECKER, A Class of algorithms for In (JC), exp(x), sin(x), cos(x), arctan(x) and arcot(x), IEEE Trans, on electronic computers, Vol. ec-14, 1965, pp. 85-86. Zbl0146.14805 · Zbl 0146.14805 · doi:10.1109/PGEC.1965.264064
[55] C. TRICOT, Mesures et dimensions, Thèse d’état, Université Paris-sud, centre d’Orsay, Paris, Dec. 1983.
[56] J. M. TRIO, Microprocesseurs 8086-8088 Architecture et programmation, Copro-cesseur de calcul 8087, Éditions Eyrolles, Paris, 1984.
[57] J. VOLDER, The CORDIC Computing technique, IRE Trans, on Computers,Vol. ec-8, Sept. 1959, pp. 330-334.
[58] J. WALTHER, A Unified algorithm for elementary functions, Joint Computer Conference Proceedings, Vol. 38, pp. 379-385. Zbl0279.68032 · Zbl 0279.68032
[59] E. H. WOLD, Pipeline and parallel-pipeline FFT processors for VLSI implementations, IEEE Trans. on Computers, Vol. c-33 n^\circ 5, May 1984. Zbl0528.68019 · Zbl 0528.68019 · doi:10.1109/TC.1984.1676458
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