Table Of ContentAPPLIED MATHEMATICS
AND MECHANICS
A Series of Monographs Prepared Under the
Auspices of the Applied Physics Laboratory,
The Johns Hopkins University
EDITOR-IN-CHIEF
F. N. FRENKIEL
Applied Physics Laboratory,
The Johns Hopkins University, Silver Spring, Maryland
ADVISORY EDITORIAL BOARD
RICHARD COURANT CARL ECKART
A. M. KUETHE W. R. SEARS
Volume 1. K. OSWATITSCH: GAS DYNAMICS. ENGLISH VERSION BY G. KUERTI
Volume 2. G. BIRKHOFF and Ε. H. ZARANTONELLO: JETS, WAKES, AND CAVITIES
Volume 3. R. von MISES: MATHEMATICAL THEORY OF COMPRESSIBLE FLUID FLOW.
COMPLETED BY HILDA GEIRINGER and G. S. S. LUDFORD
Volume 4. F. L. ALT: ELECTRONIC DIGITAL COMPUTERS—THEIR USE IN SCIENCE AND
ENGINEERING
IN PREPARATION
Volume 5. W. D. HAYES and R. F. PROBSTEIN: HYPERSONIC FLOW THEORY
ACADEMIC PRESS INC., NEW YORK AND LONDON
ELECTRONIC
DIGITAL COMPUTERS
Their Use in Science and Engineering
by
FRANZ L. ALT
Notional Bureau of Standards
1958
ACADEMIC PRESS INC., NEW YORK AND LONDON
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PRINTED IN THE UNITED STATES OF AMERICA
PREFACE
The extremely rapid growth in the production and use of electronic com
puters has created a wide need for information about these machines. The
present volume is intended to serve as an introduction to this field. It is
meant first of all for users of computing machines who wish to understand
the principles underlying their design and operation. It may also be useful
as a first survey for persons who plan to go on to further study of some
specialized aspect of computing machinery.
At least two such fields of specialization have come into prominence: com
puting machine engineers, concerned with the design, construction, and
maintenance of these machines, and programmers and numerical analysts,
who prepare problems for them. We have included in this volume as much
about machine hardware as is needed for the problem analyst and enough
about numerical analysis to satisfy the future design engineer. Above all,
however, we address ourselves to experts in fields in which computers are
applied; and especially to physicists, chemists, engineers, and others in
similar occupations who have occasion to require the solution of computa
tional problems by means of digital computing machines. They will as a
rule not do their own programming but will obtain help from professional
programmers, and they may consult numerical analysts if the problem re
quires their aid—as it probably will. We have aimed to give the readers as
much information as they need in order to talk intelligently to the com
puter specialists with whom they deal. Close cooperation between the
originator of a computing problem and the team around the machine is
necessary and this is possible only if the originator has some understanding
of the difficulties which beset the professional computer.
Consequently, our description of the machines does not presuppose any
knowledge of engineering and deals mostly with the functioning, rather
than the design, of machines, although some of the underlying physical
principles are mentioned because of their general interest. On programming
and coding we have mainly attempted to give an explanation of the terms
heard around computing machines and a few warning signals to avoid
common pitfalls. Above all, our discussion of problem analysis should not
be considered as, nor compared with, a text on numerical analysis. There are
no proofs and no rigorous formulations. There is only a listing of commonly
used methods, some with a brief description, as well as an attempt at
ν
vi PREFACE
evaluating advantages and drawbacks of different methods from the stand
point of automatic computation. The mathematical background required
of the reader in that part is not more—probably less—than what can be ex
pected of engineers, chemists, experimental physicists and many students
of the social sciences.
Finally, we give a representative sample of computer applications, in
cluding at least two or three problems from each of the major fields in which
these machines have been used. We indicate the machine characteristics
required for their solution, and in the end we state the criteria by which the
originator of a problem may judge the suitability of a particular machine
installation for his problem, and the requirements for establishing his own
computing laboratory.
In summary, this is not a treatise for computer specialists. Rather, it is
about these specialists—about the work they perform when using a modern
digital computing machine.
The author's thanks are due first of all to John Todd, who participated
in the planning of the volume, wrote first drafts of some sections, and criti
cally read the entire manuscript; to Robert D. Elbourn, George E. Forsythe,
and Ida I. Rhodes, who read large parts of the manuscript, corrected errors,
and gave helpful advice on numerous questions; to Edward W. Cannon,
Robert D. Richtmyer, Mrs. J. V. Holberton, and many other computer
experts and colleagues who helped with suggestions and criticism.
Recognition should be given to Joseph H. Levin, whose unpublished
"Programming and Coding Handbook for SEAC" forms the basis of Chap
ter 3.1; to the International Business Machines Corporation for permission
to use in Chapter 3.2, in altered form, some of the material in the "IBM
Electronic Data Processing Machines Type 704 Manual of Operation."
The author is grateful to the Applied Physics Laboratory of The Johns
Hopkins University and in particular to Mrs. Betty Grisamore for assist
ance in the preparation of the manuscript.
Finally, the excellent editorial and production work of the publishers is
gratefully acknowledged.
May, 1958 F. L. A.
1.1 OBJECTIVES
1.11 Applications
In the short time since electronic digital computers became widely avail
able, three broad areas of applications for these machines have come to be
generally recognized. These are: (1) scientific and engineering calculations;
(2) problems in business management, operations analysis, assembly of
statistical information, data processing, etc.; and (3) real-time automatic
control of production processes, traffic, or military operations. To these
three areas might be added a fourth, of which only the beginnings can be
discerned at present: logical operations, usually nonnumerical, which imi
tate human thinking in such tasks as playing games, proving mathematical
theorems, musical composition, language translation, and learning situa
tions. The widespread use of machines for assisting in the preparation of
their own programs lies closer to this area than to any other.
There is a tendency to overemphasize the distinctions among these areas.
Actually, their similarities are greater than their differences, and the few
real differences are in degree rather than in kind. In particular, both pro
ducers and users have come to stress to an unnecessary degree the distinc
tion between scientific and engineering calculations on the one hand and
business-type or data processing problems on the other. This has been
accompanied by specialized development of some computing machines for
scientific and engineering problems, and others for data processing prob
lems. Here again the similarities are fundamental and ubiquitous, the
differences only occasional and superficial. In many cases computing ma
chines intended for scientific computation have performed better than others
on so-called data processing problems, and vice versa. It is not only difficult
to draw a borderline between the two areas, it is probably unnecessary and
even undesirable. We propose to use the words "computation" and "com
puting machines" as applying to all areas of application.
We address ourselves primarily to readers interested in scientific and
engineering applications; but in view of the foregoing, a large part of our
discussions will be valid for other areas as well.
3
4 1. INTRODUCTION
1.12 Stages
A computing problem begins when it is decided to obtain some desired
result by means of computation. We shall refer to this decision as problem
selection, although this designation might convey the misleading idea that
the computer personnel selects problems to be done on the computer,
whereas in almost all cases, it is the problem originator who selects nu
merical computation as the appropriate method for his problem—in prefer
ence, say, to an analytical solution or to physical experimentation.
Sometimes the decision to compute is followed by a deliberate process of
selecting the particular kind of computing machine best suited for the given
problem. Instead, this process may be delayed and carried on in conjunc
tion with some of the later steps. More frequently, however, the choice of
a machine is either dictated by convenience or is felt to be relatively unim
portant. Indeed, on many problems a large number of the most frequently
used machines perform about equally well; on many others the differences
in the performance of different machines are caused by minor peculiarities
of both problem and machine, and these cannot be detected except by a
most detailed study. Unless the problem is extremely long or extremely
repetitive, such a study is not worthwhile.
In any case, once these decisions have been made, the problem moves
through several stages: problem formulation and problem analysis, followed
by programming and coding. These are not too well defined but are usually
characterized by some or all of these names.
The problem must be stated precisely, often in the form of mathematical
equations. Numerical values are assigned to all constants. If a mathematical
function is to be evaluated for a range of parameters, the values of the
parameters are agreed upon. Plans are made for the presentation of results,
notably for the arrangement of the printed answers and for the preserva
tion of certain intermediate results (or by-products) of computation. Also
at this stage it must be established that the problem has at least one solu
tion and it should be determined whether it has more than one.
A choice is next made between alternative methods of computation. At
this point the problem is broken down into major components, such as
evaluation of functions, solutions of algebraic or differential equations, etc.
Infinite sums are replaced by finite ones, derivatives and integrals by finite-
difference approximations. For infinite sums or iterative processes, the
number of terms is decided upon or criteria are chosen for terminating the
process. Truncation and rounding errors are analyzed and error tolerances
fixed. The entire analysis ends with a list of clearly defined computing steps
which should lead to the desired solution.
The next stage consists of decisions regarding the order in which the
computing steps will be performed, the utilization of the different kinds of
1.1 OBJECTIVES 5
storage in the machine, the incorporation of available general-purpose sub
routines, and similar technical matters. This stage frequently culminates
in a flow chart which maps the planned course of computation.
Finally it is necessary to write, in complete detail, the instructions re
quired by the machine, including definite storage locations assigned to each
number or instruction, precise formats for both input and output, pro
visions for malfunctions, and numerous other details. The result is the
"code" which enables the computing machine to solve the problem at
hand.
When all this is done, machine operation begins. There is usually a period
known as code checking, during which trial runs are made with frequent
interruptions and generous recording of intermediate results, to enable the
coder to locate and remove mistakes in the code. This is followed by the
production runs, in which the desired answers are obtained in the quickest
way possible.
For didactic reasons we shall take up these stages in more or less reverse
order. We shall first describe the machines themselves, then turn to coding
and programming, next discuss the analysis and formulation of problems,
and finally touch briefly on problem and machine selection.
We have attempted to make each of these major parts of our description
reasonably self-contained, so as to accommodate those readers who may
wish to read only one or the other. This entails a moderate amount of
duplication.
1.13 Limitations
Computing machines are divided into two broad classes, analog and
digital. We are concerned exclusively with the latter. All the machines
described in Part 2 are of the digital type. They are characterized by the
system of number representation (2.3) which uses discrete states of some
physical elements. By contrast, analog machines represent numbers by
some continuously variable physical magnitudes, such as lengths, angles of
rotation, and voltages. While the basic idea of analog machines is old, they
have been developed in recent years almost as spectacularly as digital
machines. The techniques used and difficulties encountered in their applica
tion are fundamentally different from those in digital machines. To include
them in our discussion would have introduced an entirely foreign element.
Digital computing machines are likewise old. What distinguishes modern
machines of this type from their predecessors are the twin features of high
speed, made possible by the use of electronic circuits, and of automatic
control. In limiting our discussion to electronic automatic computers, we
are including all modern developments; we are excluding manual computa
tion, desk-type machines, the many older punched-card machines, and the
6 1. INTRODUCTION
few fully automatic large computers which are electromechanically rather
than electronically controlled. These, however, differ from the modern
electronic machines in degree rather than in fundamentals. Many features
of their applications coincide, and in particular much of the discussion in
Part 4 is applicable to all these types.
Having broadly outlined the aims, arrangement, and limitations of this
volume, we now proceed to sketch the purposes and planning of its major
parts.
1.2 MACHINES
1.21 Arrangement
In trying to describe modern computing machines one is faced with the
difficulty that the subject has quite a few novel and advanced aspects which
are so interdependent that neither can be properly explained or understood
without reference to the others. Thus the exposition must either proceed on
many fronts simultaneously, which may be all right didactically but is
awkward for later reference, or it must take up each portion separately,
making it frequently necessary for the reader to postpone complete under
standing of one sector until he has seen another. We have mainly followed
the latter approach, but we have tried to mitigate its shortcomings by
preceding the systematic treatment of Chapters 2.3-2.7 by general surveys
of the whole field, once very briefly in this introduction and once a little
more specifically in 2.2. Thus, for example, the answer to some specific
question or the definition of some term concerning, say, machine memory
may have to be looked up either in 2.2 or 2.4, and this uncertainty is the
price paid for what we hope to be a better didactic arrangement.
The interdependence of subjects turns up more pointedly in reference to
specific machines. The systematic description of each machine component
loses much of its value if it does not frequently refer to specific machines
which exhibit the traits discussed in the abstract. For example, it is un
attractive to discuss built-in floating arithmetic (2.332) without naming
specific machines which possess this feature. This means that the reader
must know at least the names and some gross characterizations of the
more important existing machines before being exposed to the systematic
study of machine design. For this reason Part 2 of this volume starts with
a bird's-eye view of machines in existence, their names, age, location, and
character. This arrangement has the unavoidable drawback that the "char
acter" of a machine cannot be explained without reference to the later
portions of Part 2.
Within Chapter 2.1, the arrangement is partly chronological and partly
according to the memory system used, the latter being the most prominent
characteristic of a digital machine.
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