@article{M2AN_1986__20_4_667_0,
author = {Muller, Jean-Michel},
title = {Une m\'ethodologie du calcul hardware des fonctions \'el\'ementaires},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {667--695},
year = {1986},
publisher = {AFCET - Gauthier-Villars},
address = {Paris},
volume = {20},
number = {4},
mrnumber = {877060},
zbl = {0609.65010},
language = {fr},
url = {https://www.numdam.org/item/M2AN_1986__20_4_667_0/}
}
TY - JOUR AU - Muller, Jean-Michel TI - Une méthodologie du calcul hardware des fonctions élémentaires JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1986 SP - 667 EP - 695 VL - 20 IS - 4 PB - AFCET - Gauthier-Villars PP - Paris UR - https://www.numdam.org/item/M2AN_1986__20_4_667_0/ LA - fr ID - M2AN_1986__20_4_667_0 ER -
%0 Journal Article %A Muller, Jean-Michel %T Une méthodologie du calcul hardware des fonctions élémentaires %J ESAIM: Modélisation mathématique et analyse numérique %D 1986 %P 667-695 %V 20 %N 4 %I AFCET - Gauthier-Villars %C Paris %U https://www.numdam.org/item/M2AN_1986__20_4_667_0/ %G fr %F M2AN_1986__20_4_667_0
Muller, Jean-Michel. Une méthodologie du calcul hardware des fonctions élémentaires. ESAIM: Modélisation mathématique et analyse numérique, Tome 20 (1986) no. 4, pp. 667-695. https://www.numdam.org/item/M2AN_1986__20_4_667_0/
[1] and , Handbook of Mathematical Functions withformulas, graphs, and mathematical tables, Nat. Bur. Standards, Appl. Math. Series, 55, Washington D.C., 1964. | Zbl
[2] , , , Highly concurrent Computing structures or matrix arithmetic and signal processing, Computer, Jan. 1982.
[3] , Architecture and design of Von Neumann microprocessors, Nato advanced summer institute, July 1980.
[4] and , Unified elementary function generator, Microprocessors and Microsystems, Vol. 2 n° 5, Oct. 1978, pp. 270-274.
[5] , More efficient radix-2 algorithms for some elementary functions, IEEE Trans, on computers, vol. c-24 n° 11, Nov. 1975, pp. 1049-1054. | Zbl | MR
[6] , Suggestion for a fast binary Sine/Cosine generator, IEEE Trans, on Computers, Nov. 1976, pp. 1134-1136.
[7] , 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. | Zbl | MR
[8] , Fast multiple-precision evaluation of elementary functions, J. ACM 23, 1976, pp. 242-251. | Zbl | MR
[9] , Unrestricted algorithms for elementary and special functions, Information Processing 80, S. H. Lavington ed., North-Holland Publishing Comp., pp. 613-619. | Zbl
[10] and , On the space and time complexity of functions computable by sample programs, Siam J. Comput, Vol. 12, n° 4, Nov. 1983. | Zbl | MR
[11] , Automatic computation of exponentials, logarithms, ratios and square roots. IBM J. Res. and Development, Vol. 16, July 1972, pp. 380-388. | Zbl | MR
[12] and , Bzyond floating point, J. of the ACM,Vol. 31, n° 2, April 1984, pp. 319-328. | Zbl | MR
[13] and , Software manual for the elementary functions, Prentice-Hall, inc, Englewood cliffs, New-Jersey, 1980. | Zbl
[14] , Implementation and testing of function software, ibid.Ibid.
[15] , Basic concepts for computational software, Ibid.Ibid.
[16] , Performance testing of function subroutines, AFIPS Conf. Proc , Vol. 34,1969 SJCC, AFIPS Press, Montvale, N.J., 1969, pp. 759-763.
[17] , An implementation guide to a proposed standard for floating-point arithmetic, IEEE Computer, Jan. 1980.
[18] , VLSI implementatwn of rotations in pseudo-euchdian space, proc 1983 IEEE Int Conf on ASSP, Boston, April 1983, pp 927-930
[19] , The matrix exponential approach to elementary operations, Depart of Electrical Engineering, Yale Univ, NewHaven
[20] , 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] , , , Iteration of endomorphisms on thereal axis and representation of numbers Commissariat à l'énergie Atomique, Service de physique théorique, CEN Saclay | Zbl | Numdam
[22] , Fourier transform computers using CORDIC iterations, IEEE Trans on Computers, Vol c-23 n° 10,Oct 1974 | Zbl
[23] , Pipeline and parallel-pipeline FFT Processors for VLSI implementations, IEEE Trans on Computers, Vol c-33 n° 5, May 1984 | Zbl
[24] , Radix-16 evaluation of certain elementary functions, IEEE Trans on Computers, Vol c-22 n° 16, June 1973 | Zbl
[25] , 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
[26] , Computational evaluation of math functions, Prentice-Hall, Englewoodcliffs, New-Jersey, 1968 | Zbl
[27] , More on algorithms that reveal properties of floating-point arithmetics units, Comm of the ACM, Vol 17, n° 5, May 1974
[28] , Computer representation of real numbers, IEEE Trans Computers, Vol c-31 n° 8, Aug 1982 | Zbl
[29] and , A CORDIC arithmetic processor chip, IEEE Trans on Computers, Vol c-29 n° 2, Feb 1980
[30] , , , , , , , and , Computer Approximations, Wiley NY, 1968
[31] and , Ensembles parfaits et séries trigonométriques, Actualités scientifiques et industrielles 1301, Hermann Pans, 1963 | Zbl | MR
[32] , Exponential and logarithm by sequential squaring, IEEE Trans on Computers, Vol c-33, n° 5, May 1984, pp 462-464
[33] , The art of computer programming, Vol 2, Addison Wesley, ReadingD E KNUTH, Mass , 1969 | Zbl | MR
[34] , Calculator algorithms, Math Mag , Vol 51 n° 2, March 1978, pp 106-109 | Zbl | MR
[35] and , A simulated study of correlated error propagation in various finite-precision arithmetic, IEEE Trans on Computers, Vol c-22, n° 6, June 1973 | Zbl
[36] , L'itération de Newton convergence et chaos, these de troisième cycle Université Grenoble I, Oct 1984
[37] , Basic digit sets for radix representation, J of the ACM, Vol 29n°4,Oct 1982, pp 1131-1143 | Zbl | MR
[38] , Pseudo Division and Pseudo Multiplication Processes, IBM of Res and Dev , Vol 6, April 1962, pp 210-227 | Zbl
[39] , Discrete basis and computation of elementary functions, IEEE Trans on Computers, Sept 1985, pp 857-862 | MR
[40] , Conditionnement de fonctions et représentation flottante des nombres réels, RR Math. App. n°453, Grenoble, 1984.
[41] , A hardware algorithm for Computing the complex exponential fonction, RMath. App. n° 467, Grenoble, 1984
[42] and , A modified CORDIC Algorithm, Preprint Dept. of Electrical Engineering and Systems Science, Michigan State Univ., East Lansing, Michigan 48824.
[43] , A new approach to error arithmetic, SIAM J. Numer. Analysis, Vol. 15 n° 2, April 1978. | Zbl | MR
[44] and , Should the elementary function library be incorporated into computer instruction sets, ACM Trans, on Math. Software, Vol. 2 n° 2, June 1976, pp. 132-142.
[45] , On the ß-expansion of real numbers, Acta math. acad. sci.Hung., 11, 1960, pp. 401-416. | Zbl | MR
[46] , Contribution à l'étude des erreurs d'arrondi en arithmétique à virgule flottante, thèse d'état, Grenoble, France, 1976.
[47] , Representations for real numbers and their ergodic functions, Acta. Math.Acad. Sci. Hungary, 1957, pp. 477-493. | Zbl | MR
[48] , On the distribution of the digits in Cantor's series, Mat. Lapok 7, 1956 pp. 77-100. | Zbl | MR
[49] , Itération machine d'une fonction affine, RR Math. App.n°440, IMAG, Grenoble, France.
[50] and , Economic pseudodivision processes for obtaining square root, logarithm and arctan, IEEE Trans, onComputers, Dec. 1971, pp. 1589-1593. | Zbl
[51] , Calculator function approximation, Amer. Math. Monthly 90,5, May 1983. | Zbl | MR
[52] and , Use decimal CORDIC for generation of many transcendental functions, Electrical design mag., Feb. 1973, pp. 64-73.
[53] , Computer arithmetic and design, J. Wiley & Sons, 1981. | Zbl | MR
[54] , 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. | Zbl
[55] , Mesures et dimensions, Thèse d'état, Université Paris-sud, centre d'Orsay, Paris, Dec. 1983.
[56] , Microprocesseurs 8086-8088 Architecture et programmation, Copro-cesseur de calcul 8087, Éditions Eyrolles, Paris, 1984.
[57] , The CORDIC Computing technique, IRE Trans, on Computers,Vol. ec-8, Sept. 1959, pp. 330-334.
[58] , A Unified algorithm for elementary functions, Joint Computer Conference Proceedings, Vol. 38, pp. 379-385. | Zbl
[59] , Pipeline and parallel-pipeline FFT processors for VLSI implementations, IEEE Trans. on Computers, Vol. c-33 n°5, May 1984. | Zbl





