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IEEE Transactions on Computers

Issue 7 • July 1977

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Displaying Results 1 - 16 of 16
  • IEEE Transactions on Computers - Table of contents

    Publication Year: 1977, Page(s): c1
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    Freely Available from IEEE
  • IEEE Computer Society

    Publication Year: 1977, Page(s): c2
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  • Computer Arithmetic: Foreword and Survey

    Publication Year: 1977, Page(s): 609
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  • Mathematical Foundation of Computer Arithmetic

    Publication Year: 1977, Page(s):610 - 621
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3149 KB)

    During recent years a number of papers concerning a mathematical foundation of computer arithmetic have been written. Some of these papers are still unpublished. The papers consider the spaces which occur in numerical computations on computers depending on a properly defined computer arithmetic. The following treatment gives a summary of the main ideas of these papers. Many of the proofs had to be... View full abstract»

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  • Floating-Point Computation of Functions with Maximum Accuracy

    Publication Year: 1977, Page(s):621 - 632
    Cited by:  Papers (21)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3633 KB)

    Algorithms are given that compute multiple sums and products and arbitrary roots of floating-point numbers with maximum accuracy, The summation algorithm can be applied to compute scalar products, matrix products, etc. For all these functions, simple error formulas and the smallest floating-point intervals containing the exact result can be obtained. View full abstract»

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  • Matrix Processors Using p-adic Arithmetic for Exact Linear Computations

    Publication Year: 1977, Page(s):633 - 639
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2385 KB)

    A unique code (called Hensel's code) is derived for a rational number by truncating its infinite p-adic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure. View full abstract»

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  • Significance Arithmetic: Application to a Partial Differential Equation

    Publication Year: 1977, Page(s):639 - 642
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3168 KB)

    The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial-differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that repr... View full abstract»

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  • Analysis of Rounding Methods in Floating-Point Arithmetic

    Publication Year: 1977, Page(s):643 - 650
    Cited by:  Papers (10)  |  Patents (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2603 KB)

    The error properties of floating-point arithmetic using various rounding methods (including ROM rounding, a new scheme) are analyzed. Guard digits are explained, and the rounding schemes' effectiveness are evaluated and compared. View full abstract»

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  • A Unified Numeric Representation Arithmetic Unit and Its Language Support

    Publication Year: 1977, Page(s):651 - 659
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3029 KB)

    This paper describes a combined arithmetic unit and language support system which allows user specifications of the arithmetic. Limited extensions to a high-level language, in connection with a generalized underlying arithmetic unit, allow a single skeletal unified numeric operand type to be refined into a variety of data types. The interpretation of operands by the operators is based on type desc... View full abstract»

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  • Highlights of a Study of Floating-Point Instructions

    Publication Year: 1977, Page(s):660 - 666
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2400 KB)

    The research work that this paper is based on resulted in the development of tools for the theoretical definition, analysis and comparison of floating-point instructions as mathematical mappings. These tools can be used to study the properties of most floating-point instructions and their operands. View full abstract»

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  • A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer

    Publication Year: 1977, Page(s):667 - 680
    Cited by:  Papers (44)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3247 KB)

    A parallel computational method, amenable for efficient hardware-level implementation, is described. It provides a simple and fast algorithm for the evaluation of polynomials, certain rational functions and arithmetic expressions, solving a class of systems of linear equations, or performing the basic arithmetic operations in a fixed-point number representation system. The time required to perform... View full abstract»

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  • On-Line Algorithms for Division and Multiplication

    Publication Year: 1977, Page(s):681 - 687
    Cited by:  Papers (87)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2264 KB)

    In this paper, on-line algorithms for division and multiplication are developed. It is assumed that the operands as well as the result flow through the arithmetic unit in a digit-by-digit, most significant digit first fashion. The use of a redundant digit set, at least for the digits of the result, is required. View full abstract»

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  • Developing Large Binary to BCD Conversion Structures

    Publication Year: 1977, Page(s):688 - 700
    Cited by:  Papers (2)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1403 KB)

    Fast binary to BCD conversions consist of static implementation of a sequential algorithm and are limited to relatively small number of bits as the hardware increases rapidly with each added bit. View full abstract»

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  • On the Use of Continued Fractions for Digital Computer Arithmetic

    Publication Year: 1977, Page(s):700 - 704
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (741 KB)

    Recently, there has been some interest in the use of continued fractions for digital hardware calculations. We require that the coefficients of the continued fractions be integral powers of 2 and, therefore, well-known continued fraction expansions of functions cannot be used. Methods of expansion of a large number of functions are presented. We show that the problem of selection of coefficients o... View full abstract»

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  • IEEE Computer Society Publications

    Publication Year: 1977, Page(s): 704
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  • Papers to be Published in the Next Issue August 1977

    Publication Year: 1977, Page(s): 704
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Aims & Scope

The IEEE Transactions on Computers is a monthly publication with a wide distribution to researchers, developers, technical managers, and educators in the computer field.

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Paolo Montuschi
Politecnico di Torino
Dipartimento di Automatica e Informatica
Corso Duca degli Abruzzi 24 
10129 Torino - Italy
e-mail: pmo@computer.org