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Communications of the ACM

Table of Contents


President's letter to the ACM membership


On ACM's role and its welfare


Algorithm 245: Treesort


Algorithm 247: Radical-inverse quasi-random point sequence


Algorithm 246: Graycode


Certification of algorithm 237: Greatest common divisor


Certification of algorithm 224: Evaluation of determinant


Certification of algorithm 181: Complementary error function—large X


Mechanization of tedious algebra—the e coefficients of theoretical chemistry

A table of formulas for certain integrals involving Legendre functions has been constructed mechanically by a program which performed algebraic operations. The formulas are all rational algebraic expressions in a single variable …

Relative effects of central processor and input-output speeds upon throughput on the large computer

Presented in this paper is a technique for determining the relative effects of the internal speed of the computer and the speed of the input-output units upon the overall speed of the system. Equations are derived which permit …

Double-precision square root for the CDC-3600

In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second …

Limited bit manipulation using FORTRAN II

Techniques are developed for manipulating bits using only FORTRAN II. These techniques allow individual bits to be tested, certain fields to be shifted, and numbers coded in BCD to be converted to Binary.

Curve fitting with format FORTRAN


Mark sense and port-a-punch programming inputs

The United States Military Academy is faced with the situation whereby 700 cadets may in a single subject prepare computer programs in class one day and get their solutions in the form of a computer runoff at their next class …

A case of too much precision

I was so impressed and pleased by RDNUM, A. Hassitt's General-Purpose Input Routine [Comm. ACM 7, 6 (June 1964), 350-355], that I have transliterated it into FORTRAN II for the IBM 7094. In doing this I stumbled across solutions …

Method for partial rewriting of magnetic tape

In simulating the operation of a large storage computer on the IBM 7094, a technique was developed whereby sections of the computer memory which were stored on magnetic tape (IBM 729 Mod II tape drive) could be rewritten without …

A family of test matrices

A family of test matrices with the following properties is described here: (a) an explicit inverse is given; (b) the characteristic polynomial is easily obtained; (c) a large measure of control over the eigenvalues is possible …

A class of matrices to test inversion procedures

The test matrices given by M. L. Pei [Comm. ACM 5, 10 (Oct. 1962), 508] and R. D. Rodman [Comm. ACM 6, 9 (Sept. 1963, 515] are special cases of a general class of matrices with complex elements for which an explicit form of the …

A note on the calculation of probabilities in an F-distribution

Tests of significance based on analysis of variance calculations often require the determination of the probabilities of obtaining values of F greater than those arising from the analysis. These probabilities are customarilyF …

Another use of FORTRAN II chaining

The letter by Ackermann appearing in the Communications of the ACM of May 1964, presented one of a number of the very interesting uses of the FORTRAN II CHAIN procedure. Another unusual application of this procedure has been  …

Scanning text with a 1401

Scanning text on a computer, as in forming word lists or editing, usually involves isolating and identifying certain characters or classes of characters. For example, if we scan text to form a list of words, the definition of …

Rational Chebyshev approximations to the Bessel function integrals Kis(x)

The second Remes algorithm is used to approximate the integrals Kis by rational functions. The related coefficients for the approximations of Ki1, Ki2, Ki3 are given for different precisions.

Parallel methods for integrating ordinary differential equations

This paper is dedicated to the proposition that, in order to take full advantage for real-time computations of highly parallel computers as can be expected to be available in the near future, much of numerical analysis will have …

Integer and signed constants in ALGOL

A few remarks are given on the relations between syntax and semantics in the programming languages. The aim is to point out that, it is true that the grammar of a contex-free language should be conceived not only as a strings …

backus normal form vs. Backus Naur form


Note on the use of procedures

The very generality of a language like ALGOL renders it inefficient when a number of programs have to be written all dealing with a fairly narrow range of problems. This can be largely overcome by the construction of a package …

Futher comment on the MIRFAC controversy


More on reducing truncation errors