Research and Advances

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 and were constructed by a recurrence procedure. They are of interest in molecular quantum chemistry. Trivial coding techniques were used to write the relevant programs in FORTRAN. The results were photocomposed on a Photon S-560 system, that was controlled by tapes which were punched directly from the computer output, so avoiding manual keyboarding, transcription errors and keyboarded correction.

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 large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.

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 the determination of these effects from hardware usage measurements.

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-generating device but also as a method for expressing a meaning, then the grammar of ALGOL is open to some criticism.

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 affecting other sections stored on the same tape.