In article 9...@elna.ethz.ch, e...@ife.ee.ethz.ch (Edi Hiltebrand) writes:

>I visited Edinburgh University some years ago (19850 and I

>was told that they intend to do bit serial computing with

>the idea to speed up things. I'm still interested in the

>results of this project. Maybe someone from Edinburgh

>(Scotland) could give you some references and inform us

>about the things they found out.

>Greetings Edi

Maybe you wanted to talk about on-line arithmetic, which is a digit-serial

most significant digit first arithmetic that requires the use of a redundant number system. The advantage of on-line arithmetic over classical bit-serial arithmetic is 1) the ability to compute quotients, square roots, trancendental functions in serial mode, and 2) the fact that the most interesting digits are generated first. Such an arithmetic makes it possible to accelerate intrinsecally sequential calculations by allowing a digit-level pipe-line. On-line arithmetic was introduced in 1977 by Ercegovac and Trivedi. Please find below some references (I do not claim that the following list is exhaustive). Hope this helps. Jean-Michel.

@INPROCEEDINGS{BEW89,

AUTHOR = "R.H. Brackert and M.D. Ercegovac and A.N. Willson",

TITLE = "Design of an On-line Multiply-Add Module for Recursive Digital Filters.",

YEAR = "1989",

PAGES = "34-41",

EDITOR = {M. D. Ercegovac and E. Swartzlander},

BOOKTITLE = {9th Symposium on Computer Arithmetic, Santa Monica, USA},

MONTH = {sep},

PUBLISHER = {IEEE Computer Society Press}

@INPROCEEDINGS{EG83,

AUTHOR = "M.D. Ercegovac and A.L. Grnarov",

TITLE = "On-Line Multiplicative Normalization",

YEAR = "1983",

PAGES = "151-155",

BOOKTITLE = {6th Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

@ARTICLE{EL87,

AUTHOR = "M.D. Ercegovac and T. Lang",

TITLE = "On-the-fly conversion of redundant into conventional representations",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1987",

VOLUME = "C-36",

NUMBER = "7",

MONTH = Jul,

NOTE = "Reprinted in E.E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, 1990" }

@ARTICLE{EL88,

AUTHOR = "M.D. Ercegovac and T. Lang",

TITLE = "On-Line Sheme for Computing Rotation Factors",

JOURNAL = "Journal of Parallel and Distributed Computing",

YEAR = "1988",

VOLUME = "Special Issue on Parallelism in Computer Arithmetic",

NUMBER = "5",

NOTE = "Reprinted in E.E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, 1990" }

@INPROCEEDINGS{EL88a,

AUTHOR = "M.D. Ercegovac and T. lang",

TITLE = "On-line arithmetic: a design methodology and applications in digital signal processing",

YEAR = "1988",

PAGES = "252-263",

NOTE = "Reprinted in E.E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, 1990",

EDITOR = "",

BOOKTITLE = "VLSI Signal Processing III",

EDITION = "",

VOLUME = "",

NUMBER = "",

SERIES = "",

MONTH = "",

ADDRESS = "",

PUBLISHER = "",

ORGANIZATION = "",

ISBN = "" }

@ARTICLE{EL92,

AUTHOR = "M.D. Ercegovac and T. Lang",

TITLE = "On-the-fly rounding",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1992",

VOLUME = "41",

NUMBER = "12",

MONTH = Dec,

PAGES = "1497-1503" }

@ARTICLE{EO82,

AUTHOR = "V.G. Oklobdzija and M.D. Ercegovac",

TITLE = "An on-line square root algorithm",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1982",

VOLUME = "C-31",

PAGES = "70-75" }

@ARTICLE{Erc77,

AUTHOR = "M.D. Ercegovac",

TITLE = "A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer",

JOURNAL = "IEEE Trans. Comp.",

YEAR = "1977",

VOLUME = "C-26",

NUMBER = "7",

PAGES = "667-680" }

@INPROCEEDINGS{Erc78,

AUTHOR = "M.D. Ercegovac",

TITLE = "An on-line square rooting algorithm",

YEAR = "1978",

BOOKTITLE = {fourth Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

@INPROCEEDINGS{Erc84,

AUTHOR = "M.D. Ercegovac",

TITLE = "On-line Arithmetic: an Overview.",

YEAR = "1984",

PAGES = "pp 86-93",

EDITOR = "SPIE",

BOOKTITLE = {SPIE, Real Time Signal Processing VII} }

@INPROCEEDINGS{Erc91,

AUTHOR = "M.D. Ercegovac",

TITLE = "On-Line Arithmetic For Recurrence Problems",

YEAR = "1991",

BOOKTITLE = {Advanced Signal Processing Algorithms, Architectures, and implementations II},

PUBLISHER = {SPIE-The International Society for Optical Engeneering} }

@INPROCEEDINGS{ET75,

AUTHOR = "K.S. Trivedi and M.D. Ercegovac",

TITLE = "On-line algorithms for division and multiplication",

YEAR = "1975",

PAGES = "161-167",

EDITOR = "",

BOOKTITLE = "3rd Symposium on Computer Arithmetic",

EDITION = "",

VOLUME = "",

NUMBER = "",

SERIES = "",

MONTH = "",

ADDRESS = "",

PUBLISHER = "",

ORGANIZATION = "",

ISBN = "" }

@ARTICLE{ET77,

AUTHOR = "M.D. Ercegovac and K.S. Trivedi",

TITLE = "On-line algorithms for division and multiplication",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1977",

VOLUME = "C-26",

NUMBER = "7",

PAGES = "681-687",

NOTE = "Reprinted in E.E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, 1990" }

@INPROCEEDINGS{ET87,

AUTHOR = "M. D. Ercegovac and P. K. G. Tu",

TITLE = "A radix-4 on-line division algorithm.",

YEAR = "1987",

BOOKTITLE = {8th Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

@INPROCEEDINGS{ET89,

AUTHOR = "M. D. Ercegovac and P. K. G. Tu",

TITLE = "Design of On-line Division Unit.",

YEAR = "1989",

PAGES = "42-49",

EDITOR = {Milos D. Ercegovac and Earl Swartzlander},

BOOKTITLE = {proceedings of the 9th Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

@INPROCEEDINGS{ET91,

AUTHOR = "M.D. Ercegovac and P.K.G. Tu",

TITLE = "Application of on-line arithmetic algorithms to the SVD computation: preliminary results",

YEAR = "1991",

PAGES = "246-255",

EDITOR = {P. Kornerup and D. Matula},

BOOKTITLE = {proceedings of the 10th IEEE Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press},

MONTH = {June} }

@ARTICLE{EW83,

AUTHOR = "O. Watanuki and M.D. Ercegovac",

TITLE = "Error analysis of certain floating-point on-line algorithms",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1983",

VOLUME = "C-32",

PAGES = "352-358",

NOTE = "Reprinted in E.E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, 1990" }

@INPROCEEDINGS{GHM89,

AUTHOR = "A. Guyot and Y. Herreros and J. M. Muller",

TITLE = "JANUS, an On-line Multiplier/divider for manipulating large numbers.",

YEAR = "1989",

PAGES = "106-111",

BOOKTITLE = {proceedings of the 9th Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

@INPROCEEDINGS{IO79,

AUTHOR = "M.J. Irwin and R.M. Owens",

TITLE = "On-line algorithms for the design of pipeline architectures",

YEAR = "1979",

BOOKTITLE = {4th Symposium on Computer Architecture},

PUBLISHER = {IEEE Computer Society Press} }

@ARTICLE{IO83a,

AUTHOR = "M.J. Irwin and R.M. Owens",

TITLE = "Fully Digit On-Line Networks",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1983",

NOTE = "Reprinted in E.E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, 1990" }

@ARTICLE{IO87,

AUTHOR = "M.J. Irwin and R.M. Owens",

TITLE = "Digit-pipelined arithmetic as illustrated by the paste-up system: a tutorial",

JOURNAL = "IEEE Computer",

YEAR = "1987",

PAGES = "61-73" }

@PHDTHESIS{Irw77,

AUTHOR = "M.J. Irwin",

TITLE = "An arithmetic unit for on-line computation",

YEAR = "1977",

SCHOOL = "Dept. of Computer Science, university of Illinois, Champaign-urbana, IL 61801" }

@INPROCEEDINGS{Irw78,

AUTHOR = "M.J. Irwin",

TITLE = "A pipelined processing unit for on-line division",

YEAR = "1978",

PAGES = "24-30",

EDITOR = "",

BOOKTITLE = "5th Symposium on Computer Architecture",

EDITION = "",

VOLUME = "",

NUMBER = "",

SERIES = "",

MONTH = "",

ADDRESS = "",

PUBLISHER = "IEEE Computer Society Press",

ORGANIZATION = "",

ISBN = "" }

@ARTICLE{KM88,

AUTHOR = "P. Kornerup and D.W. Matula",

TITLE = "An On-Line Arithmetic Unit for Bit-Pipelined Rational Arithmetic",

JOURNAL = "Journal of Parallel and distributed Computing",

YEAR = "1988",

VOLUME = "Special Issue on Parallelism in Computer Arithmetic",

NUMBER = "5" }

@INPROCEEDINGS{LS87,

AUTHOR = "H. Lin and H.J. Sips",

TITLE = "A novel floating-point on-line division algorithm",

YEAR = "1987",

EDITOR = "M.J. Irwin and R. Stefanelli",

BOOKTITLE = "8th IEEE Symposium on Computer Arithmetic (ARITH8)",

EDITION = "",

VOLUME = "",

NUMBER = "",

SERIES = "",

MONTH = "May",

ADDRESS = "",

PUBLISHER = "IEEE Computer Society Press",

ORGANIZATION = "",

ISBN = "" }

@INPROCEEDINGS{LS89,

AUTHOR = "H. Lin and H. J. Sips",

TITLE = "On-Line CORDIC algorithms.",

YEAR = "1989",

PAGES = "26-33",

EDITOR = {M. D. Ercegovac and E. Swartzlander},

BOOKTITLE = {proceedings of the 9th Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

@PHDTHESIS{Owe80,

AUTHOR = "R.M. Owens",

TITLE = "An arithmetic unit for on-line computation",

YEAR = "1980",

SCHOOL = "Dept. of Computer Science, The Pennsylvania State University, University Park" }

@ARTICLE{Owe83,

AUTHOR = "R.M. Owens",

TITLE = "Techniques to Reduce the Inherent Limitation of Fully Digit On-Line Arithmetic",

JOURNAL = "IEEE Transactions on Computers",

YEAR = "1983" }

@ARTICLE{BDKM93,

AUTHOR = "J.C. Bajard and J. Duprat and S. Kla and J.M. Muller",

TITLE = "Some operators for on-line radix 2 computations",

JOURNAL = "Journal of Parallel and Distributed Computing",

YEAR = "1994",

VOLUME = "22",

NUMBER = "2",

PAGES = "336-345",}

@INPROCEEDINGS{RT78,

AUTHOR = "J.G. Rusnak and K.S. Trivedi",

TITLE = "Higher radix on-line division",

YEAR = "1978",

BOOKTITLE = {fourth Symposium on Computer Arithmetic},

PUBLISHER = {IEEE Computer Society Press} }

----------------------------------------------------------------------

Jean-Michel Muller, CNRS, Lab. LIP, Ecole Normale Superieure de Lyon

46 Allee d'Italie, 69364 Lyon Cedex 07, FRANCE

Tel. +33 72 72 82 29 Fax. +33 72 72 80 80 jmmul...@lip.ens-lyon.fr