Abstract
A method and an algorithms are proposed for residue number scaling, using arbitrary positive, including fractional, scales.
Keywords
Operating System Artificial Intelligence System Theory Number System Residue Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Literature Cited
- 1.W. K. Jenkins and B. J. Leon, “The use of residue number systems in the design of finite impulse response digital filters,” IEEE Trans. Circuits Systems,CAS-24, No. 4, 191–200 (1977).Google Scholar
- 2.G. A. Jullien, “Residue number scaling and other operations using ROM arrays,” IEEE Trans. Comput.,C-27, No. 4, 325–336 (1978).Google Scholar
- 3.W. K. Jenkins, “Recent advances in residue number techniques for recursive digital filtering,” IEEE Trans. Acoust., Speech, and Signal Process.,ASSP-27, No. 1, 19–30 (1979).Google Scholar
- 4.B. D. Tseng, G. A. Jullien, and W. C. Miller, “Implementation of FFT structures using the residue number system,” IEEE Trans. Comput.,C-28, No. 11, 831–845 (1979).Google Scholar
- 5.D. D. Miller and J. N. Polky, “An implementation of the LMS algorithm in the residue number system,” IEEE Trans. Circuits Systems,CAS-31, No. 5, 452–461 (1985).Google Scholar
- 6.A. A. Kolyada, “A device for evaluation of functions in residue number system,” USSR Patent 1322268, Otkrytiya, Izobret., No. 25, 193–194 (1987).Google Scholar
- 7.F. J. Taylor and C. H. Huang, “A floating-point residue arithmetic unit,” J. Franklin Inst.,311, No. 1, 33–53 (1981).Google Scholar
- 8.V. G. Evstigneev, V. V. Gorskaya, and L. V. Filippova, “Some issues of scaling for the solution of problems in RCS in irredundant arithmetic range,” Trans. on Microelectronics, Moscow Inst. Electronic Engineering [in Russian], No. 9 (1972), pp. 200–212.Google Scholar
- 9.V. G. Evstigneev, A. N. Kosharovskii, A. V. Markin, and A. S. Novozhilov, “A device for multiplication in residue class system,” USSR Patent 1236472, Otkrytiya, Izobret., No. 21, 204 (1986).Google Scholar
- 10.A. A. Kolyada and M. Yu. Selyaninov, “Multiplication of fractions in residue number system using the interval index, ” Vestn. Beloruss. Univ., Ser. 1, Fiz., Mat. Mekh., No. 3, 33 (1986).Google Scholar
- 11.A. A. Kolyada and M. Yu. Selyaninov, “An arithmetic unit in residue number system,” USSR Patent 1244665, Otkrytiya, Izobret., No. 26, 217–218 (1986).Google Scholar
- 12.I. Ya. Akushskii, V. M. Burtsev, and I. T. Pak, “Division algorithms using a core characteristic,” in: Coding Theory and Optimization of Complex Systems [in Russian], Nauka KazSSR, Alma-Ata (1977), pp. 26–33.Google Scholar
- 13.F. J. Taylor and C. H. Huang, “An autoscale residue multiplier,” IEEE Trans. Comput.,C-31, No. 4, 321–324 (1982).Google Scholar
- 14.A. A. Kolyada, “A device for division in residue class system,” USSR Patent 1287152, Otkrytiya, Izobret., No. 4, 227 (1987).Google Scholar
- 15.V. A. Torgashev, Residue Class System and Digital Computer Reliability [in Russian], Sovet-skoe Radio, Moscow (1973).Google Scholar
- 16.V. M. Amerbaev, Theoretical Principles of Machine Arithmetic [in Russian], Nauka KazSSR, Alma-Ata (1976).Google Scholar
- 17.K. J. Clemens, “A modified definition of symmetric RNS improving scaling and overflow detection,” IEEE Trans. Circuits Systems,CAS-32, No. 4, 412–413 (1985).Google Scholar
- 18.V. V. Klyaznik and S. K. Laskeev, “Application of residue class system to digital filter design,” Vychislitel. Sredstva Tekh. Sistemakh Svyazi, No. 3, 69–73 (1978).Google Scholar
- 19.A. M. Popov, “A device for scaling in residue class systems,” USSR Patent 1330632, Otkrytiya, Izobret., No. 30, 222 (1987).Google Scholar
- 20.A. A. Kolyada, “A device for scaling in interval-residue code,” USSR Patent 1305678, Otkrytiya, Izobret., No. 15, 204 (1987).Google Scholar
- 21.V. N. Akhremenko, A. P. Byk, A. A. Kolyada, and V. V. Revinskii, “A device for scaling in residue number system,” USSR Patent 1140114, Otkrytiya, Izobret., No. 6, 156 (1985).Google Scholar
- 22.I. M. Vinogradov, Fundamentals of Number Theory [in Russian], Nauka, Moscow (1981).Google Scholar
- 23.A. A. Kolyada, “Algorithms for generalized RCS arithmetic,” Vestn. Beloruss. Univ., Ser. 1, Fiz., Mat. Mekh., No. 1, 6–12 (1980).Google Scholar
- 24.V. N. Akhremenko, A. A. Kolyada, M. Yu. Selyaninov, and A. F. Chernyavskii, “A device for rounding in residue number system,” USSR Patent 1190381, Otkrytiya, Izobret., No. 41, 217–218 (1985).Google Scholar
Copyright information
© Plenum Publishing Corporation 1990