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The computation of elementary functions in radix 2 p . (English) Zbl 0809.65008

The author presents new algorithms computing the sine, the cosine, and the exponential functions.

The idea is to compute all this functions in radix 2 p in order to reduce the number of iterations. All these algorithms are based on the discrete bases decomposition algorithm. Each iteration is computed using the AXPY cell which is a small quick multiplier and the computation is between 2 and 3 times quicker than the standard algorithms.

A comparison between radix 2 and radix 2 p algorithms and between CORDIC and polynomial approximation is presented, too.

65D20Computation of special functions, construction of tables
26A09Elementary functions of one real variable
[1]Volder, J. A.: The cordic trigonometric computing technique. IRE Trans. Electron. Comput.8, 330–334 (1959). · doi:10.1109/TEC.1959.5222693
[2]Mazenc, C., Merrheim, X., Muller, J.-M.: Computing functions arccos and arcsin using cordic. Trans. Comput.42, 118–122 (1993). · Zbl 05103564 · doi:10.1109/12.192222
[3]Walther, J. S.: A unify algorithm for elementary functions. Proceedings of the Spring Joint Computer Conference, pp. 379–385, 1971.
[4]Bajard, J.-C., Kla, S., Muller, J.-M.: Bkm: A new harware algorithm for complex elementary functions. Proceedings of the 11th symposium on computer arithmetic, 1993.
[5]Schmid, H., Bogacki, A.: Use decimal cordic for generation of many transcendental functions. EDN, pp. 64–73, Feb. 1973.
[6]Kropa, J. C.: Calculator algorithms. Math. Mag.51, 106–109 (1978). · Zbl 0397.65082 · doi:10.2307/2690146
[7]Muller, J.-M.: Discrete basis and computation of elementary functions. IEEE Trans. Comput.34, 857–862 (1985). · Zbl 05338440 · doi:10.1109/TC.1985.1676643
[8]Ercegovac, M. D.: Radix-16 evaluation of certain elementary functions. IEEE Trans. Comput.22, 561–566 (1973). · Zbl 0257.68052 · doi:10.1109/TC.1973.5009107
[9]Wallace: A suggestion for parallel multipliers. IEEE Trans. Electron. Comput.,13, 14–17 (1964). · doi:10.1109/PGEC.1964.263830
[10]Briggs, W. S., Matula, D. W.: A 17×69 bit multiply and add unit with redundant binary feedback and single cycle latency. Proceedings of the 11th Symposium on Computer Arithmetic, 1993.
[11]Parikh, S. N., Matula, D. W.: A redundant binary euclidean gcd algorithm. Proceedings of the 10th Symposium on Computer Arithmetic, 1991.
[12]Merrheim, X.: Calcul des fonctions elementaires par material et bases discretes (in French). Ecole Normal Superieure de Lyon, 1994.
[13]Ferguson, W. E., Brightman, T.: Accurate and monotone approximations of some transcendental functions. Proceedings of the 10th Symposium on Computer Arithmetic, 1992.