zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

MSC:
65D20Computation of special functions, construction of tables
26A09Elementary functions of one real variable
References:
[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.