Free Access
Issue
ESAIM: M2AN
Volume 20, Number 4, 1986
Page(s) 667 - 695
DOI https://doi.org/10.1051/m2an/1986200406671
Published online 31 January 2017
  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. [Zbl: 0643.33001] [Google Scholar]
  2. H. M. AHMED, J. M. DELOSME, M. MORF, Highly concurrent Computing structures or matrix arithmetic and signal processing, Computer, Jan. 1982. [Google Scholar]
  3. F. ANCEAU, Architecture and design of Von Neumann microprocessors, Nato advanced summer institute, July 1980. [Google Scholar]
  4. M. ANDREWS and T. M R A Z, Unified elementary function generator, Microprocessors and Microsystems, Vol. 2 n° 5, Oct. 1978, pp. 270-274. [Google Scholar]
  5. P. W. BAKER, More efficient radix-2 algorithms for some elementary functions, IEEE Trans, on computers, vol. c-24 n° 11, Nov. 1975, pp. 1049-1054. [MR: 386336] [Zbl: 0324.68040] [Google Scholar]
  6. P. W. BAKER, Suggestion for a fast binary Sine/Cosine generator, IEEE Trans, on Computers, Nov. 1976, pp. 1134-1136. [Google Scholar]
  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. [MR: 423869] [Zbl: 0342.65031] [Google Scholar]
  8. R. P. BRENT, Fast multiple-precision evaluation of elementary functions, J. ACM 23, 1976, pp. 242-251. [MR: 395314] [Zbl: 0324.65018] [Google Scholar]
  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. [Zbl: 0442.65013] [Google Scholar]
  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° 4, Nov. 1983. [MR: 721008] [Zbl: 0524.68030] [Google Scholar]
  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. [MR: 336965] [Zbl: 0257.68057] [Google Scholar]
  12. C. W. CLENSHAW and F. W. J. OLVER, Bzyond floating point, J. of the ACM,Vol. 31, n° 2, April 1984, pp. 319-328. [MR: 819141] [Zbl: 0628.65037] [Google Scholar]
  13. W. CODY and W. WAITE, Software manual for the elementary functions, Prentice-Hall, inc, Englewood cliffs, New-Jersey, 1980. [Zbl: 0468.68036] [Google Scholar]
  14. W. CODY, Implementation and testing of function software, ibid.Ibid. [Google Scholar]
  15. W. CODY, Basic concepts for computational software, Ibid.Ibid. [Google Scholar]
  16. W. CODY, Performance testing of function subroutines, AFIPS Conf. Proc , Vol. 34,1969 SJCC, AFIPS Press, Montvale, N.J., 1969, pp. 759-763. [Google Scholar]
  17. J. T. COONEN, An implementation guide to a proposed standard for floating-point arithmetic, IEEE Computer, Jan. 1980. [Google Scholar]
  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 [Google Scholar]
  19. J M DELOSME, The matrix exponential approach to elementary operations, Depart of Electrical Engineering, Yale Univ, NewHaven [Google Scholar]
  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 [Google Scholar]
  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 [EuDML: 76009] [Zbl: 0416.28012] [Google Scholar]
  22. A M DESPAIN, Fourier transform computers using CORDIC iterations, IEEE Trans on Computers, Vol c-23 n° 10,Oct 1974 [Zbl: 0287.65073] [Google Scholar]
  23. A M DESPAIN, Pipeline and parallel-pipeline FFT Processors for VLSI implementations, IEEE Trans on Computers, Vol c-33 n° 5, May 1984 [Zbl: 0528.68019] [Google Scholar]
  24. M D ERCEGOVAC, Radix-16 evaluation of certain elementary functions, IEEE Trans on Computers, Vol c-22 n° 16, June 1973 [Zbl: 0257.68052] [Google Scholar]
  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] [Google Scholar]
  26. C T FIKE, Computational evaluation of math functions, Prentice-Hall, Englewoodcliffs, New-Jersey, 1968 [Zbl: 0205.19301] [Google Scholar]
  27. W M GENTLEMAN, More on algorithms that reveal properties of floating-point arithmetics units, Comm of the ACM, Vol 17, n° 5, May 1974 [Google Scholar]
  28. G W GERRITY, Computer representation of real numbers, IEEE Trans Computers, Vol c-31 n° 8, Aug 1982 [Zbl: 0488.68039] [Google Scholar]
  29. G H HAVILAND and A TUSZYNSKY, A CORDIC arithmetic processor chip, IEEE Trans on Computers, Vol c-29 n° 2, Feb 1980 [Google Scholar]
  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 [Google Scholar]
  31. J P KAHONE and R SALEM, Ensembles parfaits et séries trigonométriques, Actualités scientifiques et industrielles 1301, Hermann Pans, 1963 [MR: 160065] [Zbl: 0112.29304] [Google Scholar]
  32. A H KARP, Exponential and logarithm by sequential squaring, IEEE Trans on Computers, Vol c-33, n° 5, May 1984, pp 462-464 [Google Scholar]
  33. D E KNUTH, The art of computer programming, Vol 2, Addison Wesley, ReadingD E KNUTH, Mass , 1969 [MR: 633878] [Zbl: 0191.18001] [Google Scholar]
  34. J KROPA, Calculator algorithms, Math Mag , Vol 51 n° 2, March 1978, pp 106-109 [MR: 1572257] [Zbl: 0397.65082] [Google Scholar]
  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° 6, June 1973 [Zbl: 0257.65043] [Google Scholar]
  36. C MASSE, L'itération de Newton convergence et chaos, these de troisième cycle Université Grenoble I, Oct 1984 [Google Scholar]
  37. D W MATULA, Basic digit sets for radix representation, J of the ACM, Vol 29n°4,Oct 1982, pp 1131-1143 [MR: 674260] [Zbl: 0509.10008] [Google Scholar]
  38. J E MEGGITT, Pseudo Division and Pseudo Multiplication Processes, IBM of Res and Dev , Vol 6, April 1962, pp 210-227 [Zbl: 0201.48709] [Google Scholar]
  39. J M MULLER, Discrete basis and computation of elementary functions, IEEE Trans on Computers, Sept 1985, pp 857-862 [MR: 810091] [Google Scholar]
  40. J. M. MULLER, Conditionnement de fonctions et représentation flottante des nombres réels, RR Math. App. n°453, Grenoble, 1984. [Google Scholar]
  41. J. M. MULLER, A hardware algorithm for Computing the complex exponential fonction, RMath. App. n° 467, Grenoble, 1984 [Google Scholar]
  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. [Google Scholar]
  43. F. W. J. OLVER, A new approach to error arithmetic, SIAM J. Numer. Analysis, Vol. 15 n° 2, April 1978. [MR: 483379] [Zbl: 0385.65019] [Google Scholar]
  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° 2, June 1976, pp. 132-142. [Google Scholar]
  45. W. PARRY, On the ß-expansion of real numbers, Acta math. acad. sci.Hung., 11, 1960, pp. 401-416. [MR: 142719] [Zbl: 0099.28103] [Google Scholar]
  46. M. PICHAT, Contribution à l'étude des erreurs d'arrondi en arithmétique à virgule flottante, thèse d'état, Grenoble, France, 1976. [Google Scholar]
  47. A. RENYI, Representations for real numbers and their ergodic functions, Acta. Math.Acad. Sci. Hungary, 1957, pp. 477-493. [MR: 97374] [Zbl: 0079.08901] [Google Scholar]
  48. A. RENYI, On the distribution of the digits in Cantor's series, Mat. Lapok 7, 1956 pp. 77-100. [MR: 99968] [Zbl: 0075.03703] [Google Scholar]
  49. F. ROBERT, Itération machine d'une fonction affine, RR Math. App.n°440, IMAG, Grenoble, France. [Google Scholar]
  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. [Zbl: 0229.68007] [Google Scholar]
  51. C. W. SCHELIN, Calculator function approximation, Amer. Math. Monthly 90,5, May 1983. [MR: 701572] [Zbl: 0532.65012] [Google Scholar]
  52. H. SCHMID and A. BOGOCKI, Use decimal CORDIC for generation of many transcendental functions, Electrical design mag., Feb. 1973, pp. 64-73. [Google Scholar]
  53. O. SPANIOL, Computer arithmetic and design, J. Wiley & Sons, 1981. [MR: 611684] [Zbl: 0493.68007] [Google Scholar]
  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. [Zbl: 0146.14805] [Google Scholar]
  55. C. TRICOT, Mesures et dimensions, Thèse d'état, Université Paris-sud, centre d'Orsay, Paris, Dec. 1983. [Google Scholar]
  56. J. M. TRIO, Microprocesseurs 8086-8088 Architecture et programmation, Copro-cesseur de calcul 8087, Éditions Eyrolles, Paris, 1984. [Google Scholar]
  57. J. VOLDER, The CORDIC Computing technique, IRE Trans, on Computers,Vol. ec-8, Sept. 1959, pp. 330-334. [Google Scholar]
  58. J. WALTHER, A Unified algorithm for elementary functions, Joint Computer Conference Proceedings, Vol. 38, pp. 379-385. [Zbl: 0279.68032] [Google Scholar]
  59. E. H. WOLD, Pipeline and parallel-pipeline FFT processors for VLSI implementations, IEEE Trans. on Computers, Vol. c-33 n°5, May 1984. [Zbl: 0528.68019] [Google Scholar]

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