On-Line Arithmetic: An Overview

We discuss in a tutorial manner the principles and techniques of on-line arithmetic. Several examples of on-line algorithms for the basic operations, the evaluation of vector and matrix expressions, solving linear systems and evaluating polynomials, are used to illustrate the characteristics of on-line arithmetic.

[1]  Milos D. Ercegovac,et al.  An On-Line Square Root Algorithm , 1982, IEEE Transactions on Computers.

[2]  Mary Jane Irwin An arithmetic unit for on-line computation. , 1977 .

[3]  Adriano Valenzano,et al.  FAST AND ACCURATE MATRIX TRIANGULARIZATION USING AN ITERATIVE STRUCTURE. , 1981 .

[4]  Daniel Ewell Atkins,et al.  A study of methods for selection of quotient digits during digital division , 1970 .

[5]  Milos D. Ercegovac A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer , 1977, IEEE Transactions on Computers.

[6]  David L. Kuck,et al.  The Structure of Computers and Computations , 1978 .

[7]  Milos D. Ercegovac,et al.  Floating-point on-line arithmetic: Error analysis , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[8]  James E. Robertson,et al.  A New Class of Digital Division Methods , 1958, IRE Trans. Electron. Comput..

[9]  Fredrich Adam Rohatsch A Study of Transformations Applicable to the Development of Limited Carry-Borrow Propagation Adders , 1967 .

[10]  Kishor S. Trivedi,et al.  On-line algorithms for division and multiplication , 1975, 1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH).

[11]  Milos D. Ercegovac,et al.  An on-line square rooting algorithm , 1978, 1978 IEEE 4th Symposium onomputer Arithmetic (ARITH).

[12]  H. T. Kung New Algorithms and Lower Bounds for the Parallel Evaluation of Certain Rational Expressions and Recurrences , 1976, JACM.

[13]  Milos D. Ercegovac,et al.  Design of a digit-slice on-line arithmetic unit , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[14]  Daniel E. Atkins,et al.  Introduction to the Role of Redundancy in Computer Arithmetic , 1975, Computer.

[15]  Milos D. Ercegovac A general method for evaluation of functions and computations in a digital computing , 1975, 1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH).

[16]  Milos D. Ercegovac,et al.  Floating-point on-line arithmetic: Algorithms , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[17]  Milos D. Ercegovac,et al.  A simulator for on-line arithmetic , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[18]  Algirdas Avizienis,et al.  Signed-Digit Numbe Representations for Fast Parallel Arithmetic , 1961, IRE Trans. Electron. Comput..

[19]  Mary Jane Irwin Reconfigurable Pipeline Systems , 1978, ACM Annual Conference.

[20]  Algirdas Avizienis,et al.  On a Flexible Implementation of Digital Computer Arithmetic , 1962, IFIP Congress.

[21]  Robert Michael Owens Digit on-line algorithms for pipeline architectures , 1980 .

[22]  Milos D. Ercegovac,et al.  On-line multiplicative normalization , 1983, 1983 IEEE 6th Symposium on Computer Arithmetic (ARITH).

[23]  Osaaki Watanuki Floating-point on-line arithmetic for highly concurrent digit-serial computation: application to mesh problems , 1981 .