Free Access
Volume 20, Number 4, 1986
Page(s) 667 - 695
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]
  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° 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° 11, Nov. 1975, pp. 1049-1054. [MR: 386336] [Zbl: 0324.68040]
  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. [MR: 423869] [Zbl: 0342.65031]
  8. R. P. BRENT, Fast multiple-precision evaluation of elementary functions, J. ACM 23, 1976, pp. 242-251. [MR: 395314] [Zbl: 0324.65018]
  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]
  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]
  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]
  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]
  13. W. CODY and W. WAITE, Software manual for the elementary functions, Prentice-Hall, inc, Englewood cliffs, New-Jersey, 1980. [Zbl: 0468.68036]
  14. W. CODY, Implementation and testing of function software, ibid.Ibid.
  15. W. CODY, Basic concepts for computational software, Ibid.Ibid.
  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.
  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. 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]
  22. A M DESPAIN, Fourier transform computers using CORDIC iterations, IEEE Trans on Computers, Vol c-23 n° 10,Oct 1974 [Zbl: 0287.65073]
  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]
  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]
  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 [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° 5, May 1974
  28. G W GERRITY, Computer representation of real numbers, IEEE Trans Computers, Vol c-31 n° 8, Aug 1982 [Zbl: 0488.68039]
  29. G H HAVILAND and A TUSZYNSKY, A CORDIC arithmetic processor chip, IEEE Trans on Computers, Vol c-29 n° 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 [MR: 160065] [Zbl: 0112.29304]
  32. A H KARP, Exponential and logarithm by sequential squaring, IEEE Trans on Computers, Vol c-33, n° 5, May 1984, pp 462-464
  33. D E KNUTH, The art of computer programming, Vol 2, Addison Wesley, ReadingD E KNUTH, Mass , 1969 [MR: 633878] [Zbl: 0191.18001]
  34. J KROPA, Calculator algorithms, Math Mag , Vol 51 n° 2, March 1978, pp 106-109 [MR: 1572257] [Zbl: 0397.65082]
  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]
  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°4,Oct 1982, pp 1131-1143 [MR: 674260] [Zbl: 0509.10008]
  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]
  39. J M MULLER, Discrete basis and computation of elementary functions, IEEE Trans on Computers, Sept 1985, pp 857-862 [MR: 810091]
  40. J. M. MULLER, Conditionnement de fonctions et représentation flottante des nombres réels, RR Math. App. n°453, Grenoble, 1984.
  41. J. M. MULLER, A hardware algorithm for Computing the complex exponential fonction, RMath. App. n° 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° 2, April 1978. [MR: 483379] [Zbl: 0385.65019]
  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.
  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]
  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. [MR: 97374] [Zbl: 0079.08901]
  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]
  49. F. ROBERT, Itération machine d'une fonction affine, RR Math. App.n°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. [Zbl: 0229.68007]
  51. C. W. SCHELIN, Calculator function approximation, Amer. Math. Monthly 90,5, May 1983. [MR: 701572] [Zbl: 0532.65012]
  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. [MR: 611684] [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. [Zbl: 0146.14805]
  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. [Zbl: 0279.68032]
  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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you