Computer Programming. A Mixed Language Approach

465 Pages·1964·20.616 MB·

by  Marvin L. Stein and William D. Munro (Auth.)

COMPUTER
PROGRAMMING:
Λ Λ/Ι/xed Language Approach
by
Marvin L. Stein and
William D. Munro
Division of Mathematics, Numerical Analysis Center
University of Minnesota, Minneapolis, Minnesota
ACADEMIC PRESS, New York and London
COPYRIGHT © 1964, BY ACADEMIC PRESS INC.
ALL RIGHTS RESERVED.
NO PART OP THIS BOOK MAY BE REPRODUCED IN ANY FORM,
BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT
WRITTEN PERMISSION FROM THE PUBLISHERS.
ACADEMIC PRESS INC.
Ill Fifth Avenue, New York, New York 10003
United Kingdom Edition published by
ACADEMIC PRESS INC. (LONDON) LTD.
Berkeley Square House, London W.l
LIBRARY OF CONGRESS CATALOG CARD NUMBER: 64-20324
First Printing, 1964
Second Printing, 1965
Third Printing, 1966
PRINTED IN THE UNITED STATES OF AMERICA.
For Ruth and Anne
Preface
The purpose of this book is to help in providing the training of two
classes of computer users. For the professional programmer-to-be, it aims
to furnish a solid foundation for the more complex and subtle programs
with which he will ultimately deal. For the nonprofessional, who neverthe-
less is required to make consistent use of the computer, it represents an
attempt to give him an adequate training with which the additional
practice of use will suffice. For this reason we treat three kinds of pro-
gramming languages, the absolute machine language required by the com-
puter "hardware," the symbolic machine language, and the problem-
oriented language provided by the "software" of symbolic assembly
programs and compilers. For the occasional user of a computer with perhaps
a differential equation to solve, a minimum of one of the problem-oriented
languages and the help of a professional will be adequate. It is our belief,
however, that a consistent user of a computer must delve deeper. An in-
telligent and efficient use of the convenience furnished by the software
languages can only be attained with a thorough understanding of how the
computer itself functions and of machine language. A thorough mastery of
the subject of programming includes the versatility to make effective use
of the hardware and software aspects of the total system provided. In
particular, this can be achieved through the utilization of the mixed
languages which are neither the absolute machine languages nor the more
facile problem-oriented languages alone, but a composite of both. In this
book we attempt the task of drawing together this material into a unified
whole to illustrate the basic way in which the computer operates and how
this is related to a convenient mixed language in current use.
In the earlier days of digital computers the transition from the original
problem to an acceptable version for the computer was usually accomplished
vii
viii PREFACE
by a staff of trained personnel who could do the necessary programming
and coding. The increased speeds and capacities of modern computers and
the increased demand for their use, however, have made it impossible to
maintain a sufficiently large body of professional programmers to meet
all needs. For this reason, an ever growing numbefr of persons who are not
primarily interested in digital computers as such have, nevertheless, found
it necessary to learn enough to do the major part of the programming for
their own problems. This raises the two questions which this book attempts
to answer. How are these people to be trained to use a computer with a
minimum of help, and how are additional professional programmers to be
educated at the same time?
The fact that the ordering of the topics follows a historical pattern is
incidental. We believe that this is both the logical order and the order which
is pedagogically most sound. It is easy for a person well grounded in
absolute machine language who has written at least a few programs in this
form to make the transition to the more convenient symbolic languages
of the assemblers, and from these to the problem-oriented language.
Furthermore, he will better understand what is involved in the translation
from the symbolic language to the objective program, and can make a
more intelligent and efficient use of the software. It is our experience that
the inversion of this order makes it much more difficult to attain the same
level of programming proficiency. Some people, however, will disagree
with this point of view and will prefer to start with a symbolic language.
This objective can still be achieved by reordering the chapters of the book.
For those who wish to start with a compiler, Chapters 7 and 9 give a
reasonably complete and self-contained version of Fortran, after which
the other chapters can be considered in any desired order. We recommend,
however, that early attention be given to Chapter 2, at least to the extent
that the student becomes sufficiently familiar with machine organization to
understand why we can identify symbolic addresses and variable names.
For those who wish to start with a symbolic form of machine language,
Chapter 8 can be treated earlier. Whatever the order of its use, the book
tries to give a complete fundamental description of each of the three
languages, alone and intermixed, and presents numerous examples for
illustration. We have also provided a variety of exercises for each of the
topics covered, together with answers to selected ones of these where a
single answer is meaningful.
We have chosen Fortran as the compiler language of this book because
it is a widely used language available in some form at most installations, and
serves, with the Fortran Symbolic Assembly Program, to give a good
illustration of mixed language programming.
PREFACE ix
In the basic description of the organization of a computer and the use of
machine language, we have attempted to present the topics with as great
a generality as possible. For purposes of explicit illustration, however, it is
necessary to introduce a specific machine, real or hypothetical. We feel
that the use of a real machine which is widely employed has advantages
over the use of a hypothetical one, provided that the salient generalities
are not obscured by the painful detail of a manufacturer's manual. At the
same time, the direct introduction of some of the typical hardware and
software idiosyncrasies associated with any real computing system will
guard against a complete idealization and give the student a feel for the
actualities he will encounter in practice. We have chosen for illustration
the Control Data Corporation Model 1604 (which we will hereafter refer
to as the CDC 1604). In terms of instruction repertoire this is representa-
tive of most large scale modern computers. It is also completely compatible
with a subset of the instruction repertoires of the Control Data 3400* and
3600* systems, and all discussions in the book are directly applicable to
these. Furthermore, the format of its instruction words is such as to teach
something of a feel for both single address and double address computers.
It is true that once machine language is learned for a particular machine,
the transition to another machine is relatively simple. This is so to the ex-
tent that many of our students have done the laboratory problems on
other kinds of computers available to them, even though the text illustrates
programming concepts with the CDC 1604. Except for Chapter 3 in which
the specific programs all relate to it, those sections which deal specifically
with the CDC 1604 are so labeled.
Although the practice of external scaling is much less prevalent in current
usage than it was formerly, we have treated the topic in considerable detail.
This was done with a twofold purpose in mind. First, to understand floating
point operation, which is merely scaling handled by the computer, a
programmer needs to know what scaling is all about. Moreover, in some
oroblems he will have to use it. Second, we felt that the literature lacked a
detailed exposition of the topic which could be used as a reference. This
aspect is of more interest if we note that an increase in the use of external
scaling is likely to result from the development of the modern hybrid
digital and analog systems.
The material in the complete book is suitable for a course of three quarters
or two semesters, although in a course of such length we usually include
some additional material on topics such as circuit logic and Algol. For a
one-quarter or one-semester course, the book can be used in various ways.
It can be used for training in Fortran alone. Alternatively, as we use it,
* Registered.
χ PREFACE
it is suitable for a brief introduction to machine language, floating point
operation, and elementary Fortran. The material is designed for the junior,
senior, and early graduate level. No specific background of mathematical
knowledge is required, although the maturity acquired by, say, a first
course in differential equations is valuable. Students in almost all fields
including physical sciences, behavioral sciences, biological sciences, educa-
tion, and agriculture have successfully mastered the material.
The book should be used, if possible, in conjunction with a laboratory
program which permits the students at the earliest possible moment to
write and run programs on a computer. In starting with machine language
we have found that students can write successful programs of the sort sug-
gested in the exercises within a week of starting Chapter 3. The writing of
programs of increasing complexity and diversity should run concurrently
with the material covered in class during the entire course. We have found
it useful for students to write simple assembly programs before using the
more sophisticated ones.
The joint experience of the authors in the use and teaching of a variety
of computers and a variety of topics in the computing field totals more than
twenty-five years. This book reflects our judgment of the topics and
presentation which will best guide the novice along the road to becoming a
well-rounded programmer. We find it impossible to mention all of the
associates or authors who have contributed invaluably to our present
way of thinking, nevertheless, we thank them all. We also thank James
Carlson, Richard Hotchkiss, and Lawrence Liddiard for invaluable criti-
cisms and contributions, and Mrs. Janet Schuffenhauer for care and pa-
tience in typing the manuscript. We also express our appreciation to
Control Data Corporation for their permission to use the CDC 1604 as the
illustrative model of a computer. Finally, we would like to express our
appreciation to Academic Press for their competence and skill in producing
the book.
Minneapolis, Minnesota MARVIN L. STEIN
WILLIAM D. MUNRO
Introduction
0-0. General Description of a Modem Digital Computer
We will use the terminology modem digital computer to describe a high-
speed, internally programmed, general-purpose, automatic, digital com-
puting machine. In what follows we will deal with three basic questions
regarding the modern digital computer: What is it? What does it do? How
do we get it to do whatever it is that it does do? As a specific model for
illustration we shall use the CDC 1604; however, the general ideas carry-
over to other modern computing systems since they are all similar in their
main operating features, although they differ somewhat in the design of
these features.
To say that a computer is digital is to say that it operates on numbers
represented by sequences of digits. This is in contrast to the class of com-
puting machines called analog computers that operate on continuous input
data represented in terms of some physical quantity (such as voltage or an-
gular displacement of a wheel) which varies in proportion to the actual data
which it represents. The digital computer, on the other hand, deals with
discrete sets of digits in much the same way as a human being in carrying
out the operations of addition, subtraction, multiplication, and division It
can also distinguish between a sequence of digits representing a number
greater than or equal to zero and one representing a number less than zero;
however, this is about as far as its ability in arithmetic will ordinarily
extend. Very few modern digital calculators come from the assembly line
with the builtin ability to evaluate such functions as the logarithm to the
base e or the Bessel function of order zero. Any one of these machines can
be used to turn out a table of logarithms or Bessel functions, but it must be
1
2 INTRODUCTION
made to carry out such complex operations by a proper sequence of the
elementary operations which are built into it.
The fact that the digital computer performs only very simple operations
upon digits is compensated for by the extremely high speeds at which it
performs them. It carries out literally thousands of operations each second.
Speed alone, however, is not enough. The ingenuity and skill displayed by
the human operator in expressing his problems in terms of mathematical
models that lend themselves to solution by means of sequences of the simple
operations available, and in actually creating the correct sequences of such
operations, is also of prime importance.
The modern high-speed digital calculator is automatic only in the sense
that, after being presented with its input, it can operate upon that input to
produce the desired output without further intervention by any human
operator. It operates in this manner by means of its program. By the pro-
gram of a machine we mean its way of selecting the sequence in which the
operations will actually be carried out in order to solve a specific problem.
A special-purpose computer will have a fixed program built in to solve its
specific problem. Such a computer is a useful and economical device if we
wish only to solve the same problem for different input values a large
number of times. The modern digital calculator, however, is a general-
purpose type of machine. It aims at versatility. With it the user can attempt
any particular problem he has in mind; and once his programs are prepared,
he can switch from one program to another in a few seconds.
If its repertoire of operations is suitably versatile, a machine may be
judged to be general-purpose by the degree of ease with which its program
can be changed. There are a variety of ways in which a change of program
can be facilitated. A common technique is to provide easily accessible
external switches or an external plugboard. This technique can be made
more effective by making the plugboards removable, thus enabling one to
set up any number of programs in advance. Another common method for
changing the program is to feed into the machine a sequence of punched
cards or, what is logically the same, a punched paper tape. The holes in the
tape are used to change internal switch settings. Even greater flexibility in
the changing of programs can be provided by a combination of removable
plugboards and punched paper tape. Automatic computing machines
which employ any of the above or similar means for changing their programs
are referred to as externally programmed machines. The programs of these
machines are external in the sense that the machines must accept them as
given by their operators and can do little, if anything at all, to change or
modify them by means of their own operations. In the modern digital
calculator, however, this is not the case. The program of a modern digital
0-1. FUNCTIONAL DESCRIPTION 3
calculator is stored within the calculator in the same form as its data. As
a consequence, the modern digital calculator can operate upon its program
just as it can operate upon its data and can change and modify the program
during the course of the operation. For this reason the modern digital
calculating machine is referred to as an internally programmed machine.
Internal programming and high speed of operation are what make a
general-purpose, automatic, digital calculator truly versatile. It is clear
that these two features must go hand-in-hand. In order for a machine that
can perform thousands of operations each second to be economically in
balance, it must receive its instruction as to which of its operations it is to
perform next just as quickly as it can perform that operation. The machine
cannot afford to wait for a relatively slow moving tape; no plugboard would
contain enough hubs to set up the thousands of operations necessary to
keep it going even a few seconds unless a small set of operations is used
repetitively. Similarly, unless a small set of operations is used repetitively,
the machine's internal storage capacity would have to be unaffordably
large before a sequence of internally stored operations could be set up
which was long enough to keep the machine going for a length of time
sufficient for the operator even to remove his finger from the start button.
The solution is for the machine to have the ability to manufacture its
instructions internally on the basis of a set of initial instructions to be
loaded in with the data. Thus, to solve a problem we do not write a complete
sequence which includes one operation for each computation that is to be
made. Rather, we prepare a relatively small set of instructions (small in
relation to the eventual number of operations that are to be executed)
which will cause the computing machine to create internally, as it needs
it, the program that is necessary to the solution of the given problem. It is
obvious that a departure from older methods of problem preparation is
called for if such a machine is to be put into effective use.
0-1. Functional Description of a Modern Digital Computer
In solving a given problem a modern digital computer performs the
functions of input of information, storage of information, control, arithmetic,
logic, and, finally, output of information. These are all indicated in the
figure below, the traditional block diagram of a calculator. The parallel
with a human being who is doing hand computation on a desk calculator
is straightforward. The human being is replaced by the control; his desk
calculator is replaced by the arithmetic-logic unit; and his pencil and paper,
books of tables, and human memory are replaced by the input-output and
storage units.