Digital PDFs

DEC-9B-AFT0-D

2000

88 pages

Original

2.7MB

Document:	FORTRANII
Order Number:	DEC-9B-AFT0-D
Revision:
Pages:	88
Original Filename:	http://bitsavers.org/pdf/dec/pdp9/DEC-9B-AFT0-D_FORTRANII.pdf

OCR Text

FORTRAN II

BASI C SYSTEM

PDP-9

PROGRAMMING MANUAL

DIGITAL EQUIPMENT CORPORATION. MAYNARD. MASSACHUSET-rS

Page Missing From Original
Document

PDP-9 FORTRAN II

CONTENTS
Chapter

Page
INTRODUCTION TO THE FORTRAN II LANGUAGE •••.•

1.1

Introduction

1.2

FORTRAN II Language •••••

•••

•

•••• : •.••••••.•.••••.••..•••.•••••..•..••..••...•..•
0

••••••••••••••••••••••••••••••••••••••

2-1
2-1
2-1

1 .2. 1

Preparing the FORTRAN Program ••••.••.•..•.•.•.•..••••••••••..

2-2

1 .2.2

Requ ired Statements •••••...••••.•••••••.••••.•••.•••.••..••.•

2-3

1 .2.3

FORTRAN II Words ••••••..•••.••..••••••.•••••.••.•

2-4

2. 1

•••

•••••

ARITHMETIC AND DATA-SPECIFICATION STATEMENTS .•••...••..••••.• "
Arithmetic Expressions •••••..

o •••••• 0

••••••••••••

••••••••••••••••

2-9
2-9

2.1.1

Eval uat ion of an Expression .•••••.••••••.••••••.••.•••••••••.•.

2-11

2.1 .2

Use of Parent heses .•••••••••.•.••

2-11

2.1 .3

The Replacement (Equal) Sign

2.1.4-

Internal Arithmetic Statement ••••••••••.••••...•...••••.•.•...•

2-12

2.1 .5

Mode of Computation •••..•.••••.•..••••..••.•••••.•.•...•..•.

2-13

Date-Spec ification Statements .••••.••.•..••••.•••••....•••••.•.•••

2-14

2.2. 1

Dimension Statements ••••.•••••••••.••.••••.••...•••••••.••..•

2-14

2.2.2

Floating-Point Storage Specification .•••.••.•.•••..•.•...•••••..

2-15

PROGRAM CONTROL .••••••.•••.••••••••••.•.••.••.•.••••.••.•..••..

2-17

Bran c hes a nd Loops •••••.••••.•••••••••••.••.••••••••••.••••••••.•

2-17

3.1. 1

Unconditional GOTO Statements ..•••••.•.••••••..•.•..•......•

2-17

3.1.2

DO Loops .........•.........................................

2-19

3. 1 .3

The CONTINUE Statement ..••..••.••..••••....•..•.•.••.•••.•

2-22

3.1 .4

Computed GOTO .................."••.••••••.••..••••.••.•...•

2-22

3.1 .5

Assigned GOTO .•.••••••.••••••••.••••.•••••.•••.•..•.••••..

2-23

2.2

3. 1

3.2

••••••

•••••••••

•

••••

••••••••

•••••••••••••••••••••••

Program Termination •.••••••••.•.••••.•••..•.••

0.,

••••••••••••••••

3.2.1

The ST 0 P Statem ent •••..••••••••••.••••.••.••••.•.••.••••....

3.2.2

The PAU SE Statement o.

INPUT/OUTPUT STATEMENTS.

•

••••••

00.

•••••

0.,

•••

•

••

•

•••••••••

••••••

••

0.0

•

...

2-12

2-23
2-:2~_-1·J

2-24
2-25
2-25

4.1

Input/ Output Assignments .•••••••••••.••••••••••.•••

4.2

The I/O Data List ••••••••••••..••••••••••••••••••••••.••.•••... 0.

2-26

Ordering of Data Within an Array ..•••••••••..••••..•••.•.•.•.••

2-27

4.2.1

iii

•••••

• • • • • •,

•

PDP-9 FORTRAN II

CON TEN T S (continued)

4.3

I/O Spec ification Statements ••••••••••••••••••••••••••••••••••••.

2-27

4.3.1

Data Fields •••••••••••••••••••••••••••.••••••••.••••••••

2-27

4.3.2

Date Fi e Id Formats •.••

4.3.3

The Format Statement .••••••••••••••••••••.••.

4.3.4

Format Specifications o.

4.4

••••••••••••••••••••••••

••

00'

••••

••••••••••

••

••••••••••••••

••••••••••••••••••••••••••

2-28
2-28
2-29

Input/Output Devices •••••••••.•••••••••••••••••.•••••••.••••.•.

2-34

4.4.1

Data Organization •••••••••••.•••••••••••••••.••••••••••••••

2-34

4.4.2

I/O Operations with Paper Tape and Keyboard .•••••.•••••••.•••

2-38

SUBPROGRAMS: FUNCTIONS AND SUBROUTINES •••••••••••••••••••.•

2-39

.•••.••••••••...•.••••.•.••....•.•..••...•.•.•.......

2-39

5.1.1

The FUNCTION Definition Statement ..••••••••.••.•• ' 0 ' •• 0 ••••

2-39

5.1 .2

RETURN Statements •••••••••••••••••••••••••••••••...•••••..•

2-40

5.1 .3

Use of Functions ••••••••••••••.••

2-40

5.1 .4

Library Functions •••••••••••.•••

5. 1

5.2

Functions

Subroutines ••••••••••••

000

••••

•••

•

•••••••••

••

•••

....

o. o ••

••••••••••••••••••••••••••••••••••••••

2-41
2-42

5.2.1

The CAll Statement •••••••••••••.••••••.••.••.•.•••.•.•.••••

2-42

5.2.2

Common Storage ••.••••.•••••••••••••••.•••••••••••.•..••.•.

2-43

5.2.3

Array Names Used in Subroutines.

2-43

5.3

••••••••••

Machine language Coding in a FORTRAN Context

o ••••••

••••••

••••

o ••••

o ••

••

•••

••

2-45

5.3. 1

Handl ing of S Coding .

5.3.2

Compiler Generated Coding

5.3.3

Subprogram linking •••.•••••••

5.3.4

Construction of Dimensioned Variables .....•..•••..•

5.3.5

Allocation of Array Storage and the Subscript Calculator •.••.•...•

2-52

5.3.6

I/O Statements •••••.••••••.•..•...•••.•..

2-53

6.1
7

••••••

•••••••

•••

.0'

••••••••••••••

•••••••••••

••••••

•••

••••••••••

o •••••••••••

••••••••••••

o •••••

••••••••••

•••••••••••••••••

Procedure for Using FORTRAN with a PDP-9 Paper Tape System .

2-45
2-47
2-52

2-55

OPERATING PROCEDURES

DIAGNOSTICS

2-45

••••••• ••••••••••••••••••••••••••••••••••••

••••••

2-55
2-61

PDP-9 FORTRAN II

CON TEN T S (continued)

8.1

ERROR MESSAGES ..............•....•.....•.•.•..•..•........••.....

2-65

Error Messages (FORTRAN Assembler) ........................••...•.

2-65

8.1.1

Format A

2-65

8.1.2

Format B

2-65

8.1.3

Format C

2-66

8.1.4

Undefined Symbol Assignment .......................•....•.....

2-66

8.1 .5

Error Messages from the Linking Loader ......•.•..•...••.•••.....

2-67

8.1.6

Error Halts in the FORTRAN Object Time System ................ .

2-67

PDP-9 FORTRAN II OPERATING TEST ................•..•..••........•.

2-69

9
9. 1

Introduction

9.2

Preliminary Requirements ....

....................•....••..••.....................
0

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

2-69
2-69

9.2.1

Storage .......................•.•....••......•.........•....

2-69

9.2.2

Subprograms and/or Subroutines ....•.•..•......................

2-69

9.2.3

Equipment .........•...................•......•...•....•.....

2-69

Loading or Call ing Procedure ............•...............•......•..

2-69

9.3.1

Loading .........................••.••..•..•.•..•...••......

2-69

9.3.2

Switch Settings ........................................•.....

2-71

9.3

9.4

...............•............•••.••.•..•.•.....•

2-71

9.4.1

Errors in Usage ....................•...•...••..•.•.••••.•....

2-71

9.4.2

Recovery from Suc h Errors .•.•...••......•..•.•..•......••.....

2-72

Detai Is of Operation and Storage ...••...••.....•..•........••......

2-72

Examples and/or Applications ......••.• '.•••.••....••..••.•.....

2-72

CHARACTER CODE EQUIVALENCES. ... •.. .• ...• ••... .. .. .. .. .. .. ... . ..

2-75

USE OF EXTENDED MEMORY .......••....•••......•..••..••....•.•..•

2-79

FORTRAN SUMMARY DESCRIPTION

2-81

9.5
9.5. 1

Using the Program

Appendix

.......••...•••.•.•••.•••.••.•..•..

PDP-9 FORTRAN II

ILLUSTRATIONS

A FORTRAN Program ..••..••••..••.••

•

•••

•

••

•

••

•

••

2-2

Program Section with Comments

Example of the Continuation Character

Exampl e of a FORTRAN Program ..

Number Representation, Floating Point ..

Example of Subscripts

Arithmetic Statements

Examples of Arithmetic Expressions .•.•.••

Schematic Representation of Program Branches ...•..•..•..

Integer Summation ..•....•..

Use of IF Statement in Integer Summation Problem •..•.••...•..•

Fibanocci Series

2-19

Fibonacci Series Calculation Programmed as a DO Loop .................. .

2-20

Initialization of Array Storage ..•................•........•....•.•....

2-20

DO Loops

2-21

Program Branching in DO Loops .•.••.•..•.•••..•••

I/O Statement

FORMAT Statements

Funct ion Subprogram

Example of Factorial Calculator ..•..

Matrix Multiplication Subroutine ..•

••

•••

••

•

o ••

•

•••

.......

o ••••

•••••••••

•

•••

•••••••

•

o ••••••••••••

••••

o ••

••••

.•............•..••.•.•••

•

••••••••••

•

o ••••

••••••••••

2-3
2-3

2-4
2-6
2-8
2-9

•••••••

•••

••

o ••

••••••••••••••••••

o ••••••••••••••

••••••••••••••••••••••

••••••••

o ••••••••

••••••••••••••••••••••••••••••••••••••••••••••••••••••

...•.........

••••••••••••

••••••

•••••••••••••••••••••••••••••••••••••••

2-10
2-17
2-18
2-18

2-21
2-25
2-29

.....••.••..•

••••••

•••••••

••••••

••••••••••••

•••••••••••••••••••••••••••••••••

•••

••••••••••••••

•••••••••

•••••

•

2-40
2-42
2-44

TABLES
Table
Summary of Format Spec ifi cat ion Letters ....•••

••••

••••••••

•

••

••••

Definition of a Physical Record for I/O Devices

Input Format ...

Output Format ...••..

Core Representations of the ASCII Characters, A and H Formats .•...•..•.••

••••••••

••

•

•••

••••••••••••••••••••

•••••••••••••••

••••

•••

••••••

o •••••

••

•••••••••••••••••

••••••

••••••••••

2-28

2-35
2-36
2-38
2-75

PDP-9 FORTRAN II

CHAPTER 1
INTRODUCTION TO THE FORTRAN II LANGUAGE

1 .1

INTRODUCTION
FORTRAN II, like all compilers, relieves the programmer from exercising a detailed knowledge

of the computer language.

It is problem oriented and,"hus accepts input closely related to the problem

and converts this input into an executable machine language program.

For scientists and engineers, the

PDP-9@FORTRAN II system provides, in easily understood form, the means for writing PDP-9 FORTRAN II
programs. The compiler accepts input in the form of statements which resemble mathematical formulas,
and compiles the sequences of instructions needed to perform the procedures specified.

Using this system,

the programmer is able to concentrate on the problem rather than on detailed computer codes.
The PDP-9 FORTRAN II compiler can compile and run FORTRAN II programs written for other
computers, provided that reasonable restrictions (such as sufficient memory capacity, use of acceptable
terms and expressions; and availability of required peripheral equipment) are met. The PDp··9 FORTRAN
II system includes a compiler, assembler, operating system, and subroutine library. Each of these subsections is described in later chapters. The manual is intended as a reference manual and assumes that
the reader is familiar with the general principles of FORTRAN II programming.
1 .2

FORTRAN II LANGUAGE
PDP-9 FORTRAN II is composed of symbols which combine to form words or are used as

punctuation, and grouped into statements. These statements may be classified as follows:
a. Arithmetic Statements resemble algebraic formulas.

They specify the mathematical

.operations to be performed.
b.

Program Control Statements direct the sequence of operations of the program.

c. Specification Statements allocate data storage, determine variable and data types,
and specify input/output formats.
d.

Input/Output Statements control the transfer of information into and out of tlhe computer.

The rules of FORTRAN are somewhat stylized to permit ease in interpretation by the computer,
as shown in figure 1 •
Symbols which are meaningful to FORTRAN include letters, numbers, and various special
characters. The complete set is listed in appendix 3.

Since FORTRAN ignores spaces, they may be

used freely (except for two restrictions which will be noted in the text) to make a program more readable.

® PDP is a registered trademark of the Digital Equipment Corporation.
Order No. DEC-9B-AFTO-D

2-1

PDP-9 FORTRAN II

r--FACTORIAL PROGRAM
I C
THIS PROGRAM CALCULATES IX FACTORIAL FOR GIVEN IX
I
5
VVRITE 2, 100
10
READ 1, 200, IX
IFACT = IY = 1
IF (IX) 5, 32, 30
30
IF (lX-IY) 41, 32, 33
32
VVRITE 2, 300, IX, IFACT
33
41
100
200
300

GO TO 10
IFACT = IFACT * (IY = IY + 1)
GO TO 30
PAUSE 7777
GO TO 5
FORMAT (l30H PLEASE TYPE A POSITIVE NUMBER/)
FORMAT (14)
FORMAT (114, 13H FACTORIAL IS, 17/)
END
--- - -----"-""--"--------"-"-"--"--"-----,

Figure 1

1 .:2. 1

A FORTRAN Program

Prepari ng the FORTRA N Program
Each line of a FORTRAN program contains two fields (see figure 2): the first is an identifi-

cation field; the second, the statement proper.

1.2.1.1

The Identification Field - This field extends from the left-hand margin to the first tabulation,

and may be left blank. If not, it may contain in the leftmost position one of the following types of
identification:
a. The first digit of a statement number, which may be any integer from 1 to 99999, inclusive,
identifying the statement on that line, for reference by other parts of the program. Statement
numbers are used for program control or to assist the programmer in identifying segments of
his program.
b. The letter C which identifies the remainder of the I ine as a comment. Although a FORTRAN program, using Engl ish words and mathematical symbols, can be read and understood
more easily than a symbol ic language program, comments throughout the program explain the
procedures being used. Such comments, identified by a C in the first position of the identification field, are not interpreted by the compiler and have no effect on the executable
program. Figure 2 is a section of a program with comments.
c. The letter S, which identifies the remainder of the line as symbolic machine instructions.

2-2

PDP-9 FORTRAN II

C
C

CALCULATE PERCENTAGE OF CORRECT RESPONSES
PERCENTAGE = -1 IF THERE ARE NO ITEMS IN CATEGORY
DO 47 I = 1, 57
DO 48 J = 1, 6
IF (ITEMS (I,
46, 46, 49
PERCEN (I, J) = -1.0

J»

Figure 2

Program Section with Comments

d. The continuation c.haracter $, which identifies the statement as a continuqtion of the

preceding statement. Frequently a statement may be too long to fit on one line (th is is
especially true of format statements). If the character $ begins the identification field
of a line, the statement field of that line is treated as a continuation of the statement on
the I ine above. A statement may be continued on as many I ines as necessary to complete
it, but the maximum number of characters in the statement may not exceed 300 (approximately 4-1/2 lines). Figure 3 is an example of the continuation character.

Figure 3

1 .2.1.2

X=X+(ARG1+2.* ARG2+2. *ARG3+
ARG4)/6

Example of the Continuation Character

The Statement Field - This field begins immediately after the first tabulation and extends

through the next carriage return. Thus, no more than one statement can be written on one I ine, but
a single statement can extend over one I ine using the continuation character.

1 .2.2

Required Statements
Figure 4 is an example of a FORTRAN program, consisting of the title, the body of the

program, and the END statement.
The first line of the program is the title, which may be anything the programmer wishes to
write to identify his program. The title is not incorporated into the final executable program.

Note

that although a title is necessary, it need not be preceded by a C. A carriage return, I ine feed before
the title is optional.
The body of the program is a series of statements, each of which specifies a sequence of
mathematical operations, controls the flow of the program, or performs other tasks related to the
proper working of the program.
2-3

PDP-9 FORTRAN II

SUMMATION OF FIRST 50 INTEGERS
SET ITOTAL = 0 BEFORE SUMMING
ITOTAL = 0
DO 3 I = 1, 50
ITOTAL = ITOTAL +1
END

Figure 4

Example of a FORTRAN Program

The END statement is a required statement and must be the last statement of every FORTRAN
program. Its function is to indicate to the compiler that nothing more connected with the preceding
program is to follow. The END statement should be terminated by cgrriage return, line feed, carriage
return, line feed, form feed.

1 .2.3

FORTRAN II Words
Words faf! into three categories: numbers, variables, and commands.

Numbers and variables

are determined by the programmer and dealt with here, and commands are discussed in succeeding
chapters.
1.2.3.1

Number Representation -

In mathematics, there are many ways to categorize numbers. They

may be positive or negative, rational or imaginary, whole numbers or fractions.

In PDP-9 FORTRAN II,

the treatment of numbers is separated into integers and real numbers (single decimals or numbers in decimal
exponent form), distinguished as follows:
Integers are constants which are written without a decimal point. Typical integers are: 9,
17, -8192, 131071. The number 131071, (2 17 -1), is the largest magn itude that can be expressed as

---.....

a FORTRAN integer. Fractional quantities and numbers larger than ± 131071 require real numbers.
Real numbers* have two forms: either they are simple decimals such as 0.0025, .4, -57.,
2.71828; or they are numbers in decimal exponent form, a number multiplied by a power of 10. Examples:
Mathematical Form

FORTRAN Form

6.023 x 1023
16
- 1 .66 x 1012
72 x 10

6.023E23
-1.66E-16
72E12

In general, a real number in decimal exponent form is expressed as ±nE±K where n may be an
integer or simple decimal, and K is an integer exponent from 0 to 99, inclusive.

*This use of the term real should not be confused with the mathematical usage; in PDP-9 FORTRAN II
real applies only in the limited sense described above.

2-4

PDP-9 FORTRAN II

,Storage Modes - Another difference between PDP-9 FORTRAN II integers and real numbers
is the manner in which each is represented in core memory.
A FORTRAN integer is stored as a binary number in one 18-bit computer word. This representation, shown schematically in figure Sa is called fixed point, because the decimal point is always
considered to be to the right of the rightmost digit. Negative numbers are stored as the lis complement
of their magnitude, the leftmost bit being the sign bit.
A FORTRAN real number is stored as a binary number in floating-point representation.

this form, the number consists of two parts: an exponent and a mantissa. The mantissa is a decimal
fraction with the decimal point assumed to be to the left of the leftmost digit. The mantissa is always
normalized; that is, it is stored with leading Os eliminated in its binary form, so that the high order bit
is always 1. The exponent as stored represents the power of 2 by which the mantissa is multiplied to
obtain the value of the number for use in computation.
There are two versions of the floating-point representation: normal, or three-word, mode
and two-word mode. They differ in the number of words of core storage required, and, hence, in
prec ision of the number.
The normal mode requires three 18-bit words of memory for each number. The exponent, a
signed 17-bit integer (2 1 s complement if negative), is stored in the first word. The mantissa is a 35-bit
number stored in the second and third words. The sign of the mantissa is kept in the high-order bit of
the second word. A negative mantissa involves a change of sign. Figure 5b is a schematic representation of a three-word floating-point number.
The second floating-point mode requ ires only two words of memory and can be used where
space is at a premium and precision can be sacrificed. The exponent and its sign occupy the first nine
bits of the first word; the mantissa occupies the rest ofl-hatword and all of the second. The sign of the
mantissa is in the high-order bit of the second word. A negative mantissa involves a change of sign.
Figure 5c is a schematic representation of a two-word floating-point number.

2-5

PDP-9 FORTRAN II

Sign

I 1

Magnitude (lis complement if negative)

~
17

a. FORTRAN Integer

Sign

Exponent (2 1 5 complement if negative)

!
I

Sign

~ ,

I : high order Mantissa (sign change if negative)

0
3

low order Manti ssa

17
b. Normal Floating Point

Sign

.- ,

Exponent (2's compo
neQatlve

high order Mantissa

89
~2 complement if negative
1

Sign

I : low order Mantissa (sign change if negative)
0

Figure 5

1.2.3.2

c. Floating Point I Two-Word Format

Number Representation, Floating Point

Variable Representation - The term " var iable,1I as used in FORTRAN, means a quantity which

may assume different values during different executions of a program or at different stages of a program's
executionj hence, a variable name is a symbol ic representation of this quantity. A variable name is
composed of one or more characters according to three rules:
a. The only characters used in a variable name are A through Z and 0 through 9.
b. The first character must be alphabetic.
c. Only the first six characters of any variable name are meaningfulj the compiler ignores
all characters after the sixth.

2-6

PDP-9 FORTRAN II

Some examples of acceptable variables names are K, P51, ROB ROY, and EPSILON. The
name ROB ROY represents one variable, not two, because blank spaces are ignored by FORTRA.N. Thus,
ROB ROY, ROBROY, or even ROBR OY are identical names and reference the same variable. The
compiler interprets the name EPSILON as EPSILO, since only the first six characters are meaningful.
Care is necessary in selecting variable names. For example, the two names GEORGE 1 and
GEORGE 2 are considered identical because of the six-character restriction. Some incorrect variable
names are 9S0RT (first character not alphabetic) and GO#5 (illegal character included).
Since variables represent numeric quantities, the type of representation must be specified.
In normal programming, variable types are specified using the standard FORTRAN conventions, as
follows:
Integer variable names must begin with one of the letters I, J, K, L, M, or N.
Real variables are designated by names beg inn ing with any other letter.
Typical integer variable names are INDEX, KDATA, M359, LIST8. Typical real variable
names are XZERO, COUNT, FICA.
Subscripted Variables - An array is a grouping of data. A column of figures, the elements
of a vector, a list, and a matrix are all arrays.

In mathematics, an el ement of an array is referenced

by a symbol denoting the array and subscripts identifying the position of the element. For example,
the sixth element in a vector v is designated v 6' Likewise, the fourth element in the tenth column of
a matrix b is identified as b
m.

••

10' In general, an element of an n-dimensional array m is designated by

1 2,1 3 , • •• , In'

1 ,1

In PDP-9 FORTRAN II, array elements are similarly identified. The array is provided with
a name, subject to the same rules as the names of variables. The name determines the mode, integer
or real, of all the elements in the array. The subscripts which identify an element of the array are
enclos~d in parentheses and separated by commas.

The two elements, v 6 and b4 10' in FORTRAN

would have the following form:

V(6)

B(4, 10)

Subscripts may be quite diverse in form; in fact, a subscript may be any acceptable FORTRAN
arithmetic expression as long as it is integer-valued (i. e., floating-point quantities are not allowed).
Note that certain subscripts in figure 6 are themselves subscripted. Subscripting may be
carried to four levels, although it is unusual to do so to more than two levels. Each subscripted subscript in figure 6, i.e., 1(1), and K(2), is itself treated as a subscripted variable.

2-7

PDP-9 FORTRAN II

a. X (3,3)

b. C(I+l,J+1)
c. N (1(1), J(1), K(2»
d. Y (J/3 + (K-4»

Figure 6

Example of Subscripts

2-8

PDP-9 FORTRAN II

CHAPTER 2
ARITHMETIC AND DATA-SPECIFICATION STATEMENTS

The arithmetic statement relates a variable (V) to an arithmetic expression (E) by means of
the equal sign (=), thus:

V=E
Such a statement looks Iike a mathematical equation, but it is treated differently. The equal
sign does not merely represent a relation between left and right members, but specifies an operation to
be performed; namely, replace the value of V with the value of E. A few illustrations of the arithmetic
statement are given. in figure 7.

VMAX=VO+A* TO

T = 2*PI*SQRTF(L/G)

PI=3.14159

THETA = OMEGAD*T + ALPHA*Tt2/2

MIN=MINO

INDEX = INDEX +2
Figure 7

2.1

Arithmetic Statements

ARITHMETIC EXPRESSIONS
The elements of an arithmetic expression are of four types: constants, variables, functions,

and operators. An expression may consist of a single constant, a single variable, a function, or a
string of constants, variables, and functions connected by operators.
Constants are explicit numerical quantities. They may be integers, decimals, or numbers
in decimal exponent form.
Variables represent quantities whose values are not implicit; they may be redefined during
execution of the program.
Functions are special forms of variables consisting of a name immediately followed by an
argument enclosed in parentheses. The function name represents a mathematical operation
f'o be performed on the argument such as finding the square root of a number or determining
the sine or cosine of an angle. Certain basic functions are provided by the FORTRAN
system and are called I ibrary functions. A detai led discussion of functions is found iin
chapter 5. Of interest here, however, is their treatment within an arithmetic expression:
2-9

PDP-9 FORTRAN II

Whenever a function is encountered, it is evaluated and the result is treated
as a variable in the evaluation of the expression in which the function occurs.
Figures 8e and 8f ill ustrate the use of functions as variables in an arithmetic expression.
Included in these examples are SINF(THETA) and COSF(THETA-1 .5), corresponding to the trigonometric functions sine and cosine, and SQRTF(X), the square root operation.
Operators are symbols representing the common arithmetic operations:
Exponentiation
Multiplication
Division
Addition
Subtraction
Equivalence

+
=

Algebraic Expression
a.

az + bz + c

(a 2_b 2)
(a+b)

FORTRAN Expression

(A t2-B t2)/(A+B)t 2

41tr2
-32
3z -2 (z+y)

4.25

a sin Q + 2a cos (Q- 1 .5)

-3-

A* SI NF(THETA)+2*A*COSF(THE TA-1 .5)

217

2*SQRTF(Z)/3

---------Figure 8

Examples of Arithmetic Expressions

The important rule about operators in the FORTRAN arithmetic expression is that every
operation must be expl icitly represented by an operator symbol. In particular, the mul tipl ication
sign (*) must never be omitted. Likewise, since no superscript notation is avai lable, a symbol for
exponentiation (t) is provided.
Figure 8 demonstrates the properties of arithmetic expressions. Each expression is shown
with its corresponding algebraic form.

2-10

PDP-9 FORTRAN II

2. 1 • 1

Evaluation of an Expression
Normally, a FORTRAN expression is evaluated from left to right just as an algebraic formula.

As in algebra, however, there are exceptions. Certain operations are always performed before others,
regardless of order. This priority of evaluation is as follows:
a. Expressions within parentheses

()

b. Unary Minus*
c. Exponentiation
d. Mul tipl ication
Division

e. Addition
Subtraction

Equivalence

The term "binding strength II refers to an operator's relative position in a table such as the
one above. In it the operations are listed in the order of descending binding strength. Thus, exponentiation has a greater binding strength than addition, and multiplication and division have equal binding
strength.
The left-to-right rule can now be stated a little more precisely:
Operations are performed in order of decreasing binding strength. A sequence
of operations of equivalent binding strength is evaluated from left to right.

2.1.2

Use of Parentheses
To change the order of evaluation, parentheses are required. Thus, the FORTRAN expres-

sion, A-B+C is algebraically evaluated as (a-b}+c, whereas A-(B+C) is evaluated as a-(b+c}.
The expression

is eval uated as

A/B*C

-·C
B

A/B/C

A
A

--c
AtBtC

(AB}C

~ *The u.nary minus is the operator which precedes a quantity whose value is to be negated.

A unary minus
is recognized by the fact that it is preceded by another operator, not by an operand. Example:
A + B t - 2/C - D
The first minus (indicating a negative exponent) is unary; the second indicating a subtraction} is binary.

2-11

PDP-9 FORTRAN II

Figure ad illustrates the use of parentheses for grouping subexpressions within an expression.
In algebra, several devices, such as square brackets ([ J) and rococo brackets (1

p, are available for

distinguishing between levels when nesting subexpressions. In FORTRAN, only parentheses are available, so the programmer must be especially careful to make certain that parentheses are properly paired;
that it, in a given expression, the number of left parentheses must be equal to the number of right parentheses.

2.1.3

The Replacement (Equal) Sign
The equal sign has the lowest binding strength of all the operators; the whole of the expres-

sion on the right is evaluated before the replacement operation is performed. In an arithmetic statement, the value of the expression to the right of the equal sign replaces the value of the variable on
the left.
By this definition the statement in figure 7f would mean, IIAdd two to the current value of
INDEX. The result is the new value of INDEX.II
All variables occurring to the right of an equal sign must have been previously defined.

If the variable on the left of the equal sign was previously undefined, it will be defined by the arithmetic statement.

2.1.4

Internal Arithmetic Statement
The most important result of treating the equal sign as an operator is that it may be used

more than once in an arithmetic statement. Consider the following:
Q = A/(V=SQRTF(2*G* V))
Parentheses separate the internal arithmetic statement, V=SQRTF(2*G*Y), from the rest of
the statement. The complete statement in this illustration is a concise way of expressing the following
type of mathematical procedure:
Let

q = a/v

where

v :=

{2;;-

In the single FORTRAN statement, both of these equations are evaluated and val ues are assigned to
Q and V.

Another result of treating the equal sign as an operator is that there may be a series of
replacements, A=B=C=D, in a single FORTRAN statement.

Note that since the operand to the left

elf an equal sign must be a variable, only the rightmost operand, represented by D above, may be
Cin arithmetic expression.

2-12

PDP-9 FORTRAN II

The statement is interpreted as follows: "Let the value of expression D replace the value of
variable C, which then replaces the value of variable BII and so on*. In other words, the value of the
rightmost expression is given to each of the variables in the string to the left. A common use for this
construction is in setting up initial values:
VZERO=5ZERO=AZERO=O
T=Tl =T2=T3=60

P=PO=4* AT M- K
2.1 .5

Mode of Computation

PDP-9 FORTRAN II does not restrict the use of variable types within an arithmetic expression. Integer and real variables and constants may be freely mixed. The order in which the quantities
are encountered during the left-to-right evaluation determines the mode of computation; however, the
result is always stored in the mode of the left-hand variable of the arithmetic statement. In general,
the following rules apply:
a. For any expression, computations are carried out in fixed point until a floating-point
quantity appears; thereafter, all computations are carried out in floating point.
b. An expression in parentheses is considered separately from the main computation;
thus if a subexpression contains only integers, it is evaluated in fixed point. If necessary, the result is converted into floating point.
c. The value of an expression on the right of an equal sign is converted to the mode of
the Ieft-hand variabl e before storage, if necessary.
The following example illustrates the method of performing calculations in an arithmetic
statement.
In eval uating the statement
A = C*V*(J+2)
let

T1 = C*V floating point
T2 = J+2 fi xed

the resu It,

T2, is converted to floating point; then
A = Tl * T2 floating

*This may seem at first to violate the left-to-right rule. Whenever an equal sign is encountered in
scanning a statement, it cannot be executed unti I all operations of higher binding strength have been
performed. Thus, execution of each equal sign (replacement) is deferred unti I the expression on the
right has been evaluated. The replacements then occur in reverse order as the evaluation works back
to the leftmost variable.
2-13

PDP-9 FORTRAN II

2.2

DATA-SPECIFICATION STATEMENTS
Data-specification statements fall into two categories: those relating to data handl ing and

st1orage; and those dealing with input/output operations. This section discusses the first category (except
fOlr the COMMON statement which is directly related to subprograms and is described in chapter 5); the
I/O specification statements are discussed in chapter 4.

2 . 2.1

Dimension Statements
Array names must be identified as such to the FORTRAN compiler. Three items of information

must be provided in any program using arrays:
a. Which are the subscripted variables?
b. How many subscripts does each have?
c. What is the maximum dimension of each subscript? (When an array is used, a
certain amount of storage space must be set aside for its elements, hence, th is
requirement .)
All the above information is provided by the following specification statement type:
DIMENSION A(I,J,K,L), B(I,J,K,L)/;,C(I,J,K,L), •...
where A, B, and C are array names, and the integer constants I, J, K, L, are the maximum dimensions
of each subscri pt.
The rule governing the use of array names and the DIMENSION statement is as follows:
All array names must appear in a DIME NSIO N statement, and the DIME NSIO N s"tatement must precede
the first use of any of the nameS appearing in its list.
DIMENSION LIST2 (30), MAT3(10,20), RE GRES(2, 2, 5)
In the statement above (under normal FORTRAN variable naming conventions), the names
LIST2 and MAT3 designate integer arrays; that is, each element is an integer. The third name,
RE GRES, designates a real array. The first array is a I ist of 30 elements maxi mum, so that 30 words
of storage are set aside for its use. The second array is a matrix of 10 rows and 20 columns, making
a "total of 200 elements requiring 200 words of space. The third array is three-dimensional and real.
There are 2 x 2 x 5 == 20 elements, each requiring 3 words of storage for floating-point representation,
so that 60 words will be set aside for the array. A maximum of 4000 words is normally set aside for
storage of arrays.

If a subscript is subscripted, the name of the higher-level subscript must also appear in a
DIMENSION statement. For example, a program in which the following statement appears:
A (1 (1 ) , J (2) , K ( 10)) == B( 1(1 0) , J (2) , K( 1))

2-14

PDP-9 FORTRAN II

could contain a DIMENSION statement like the following:
DIMENSION A (5,5,10),8(10,5,5), 1(10),J(10),K(10)

If an array name is to be passed as an argument from one program to another (e.g", a subroutine provides values to a variable array in the calling program), both the call ing program and the
subroutine must agree in floating point storage mode (three-word or two-word). This restriction does
not apply when the argument is a specific array element rather than an array name.
When referencing dimensioned variables, use the correct number of subscripts. For example:
DIMENSION

A( 10, 10, 10)

A(3,4,6)

42 (correc t) .

A(705)

A =3.

2.2.2

42. (wi II cause haphazard
results at object time).
(wi II also cause undesired
results).

Floating-Point Storage Specification
Unless otherwise indicated, all real numbers in a given program are stored in three-word

form where 35 bits are reserved for the magnitude of each variable or constant. If the two-word form
is desired (26 bits reserved for magnitude), the following specification statement must appear as the
first statement of the program to which it applies:
2WORD
The two modes may not be mixed within anyone program or subprogram, and they may only
be mixed between programs when the level (depth) of call is at most one; e.g., a subprogram does not
call other subprograms. (Refer to section 1.2.3.1 for a discussion of storage modes.)

2-15

PDP-9 FORTRAN II

CHAPTER 3
PROGRAM CONTROL

Ordinarily, FORTRAN statements are executed in the order in which they are written unless
contrary instructions are given. The instructions provided by the program control statements allow the
programmer to alter the sequence, repeat sections, suspend operations, or halt the program.

3. 1

BRANCHES AND LOOPS

3. 1 • 1

Unconditional GOTO Statements
There are various ways in which program flow may be directed. As shown schematically in

figure 9 f a program may have a straight-I ine sequence (a), branch to an entirely different sequence (b),
return to an earl ier point (c), or skip to a later point (d).

b .....- - - f

Figure 9

Schematic Representation of Program Branches

All of the branches can be performed in several ways, but the simplest is by the statement
GOTO n
where n is a statement number used in the program. This statement is described in the following
example, which also illustrates the construction of a loop, the name given to program branches of
the type shown in figure 9c.

2-17

PDP-9 FORTRAN II

SUM OF FIRST N INTEGERS BY ITERATION
KSUM=O
INUM=l
KSUM=INUM+KSUM
IN,UM=INUM+l
GOT02
END
Figure 10

Integer Summation

In figure 10, the sum of successive integers is accumulated by repeated addition. The main
computation is provided by the three-instruction loop beginning with statement 2. The statements preceding this loop provide the starting conditions; this is called initial ization. The partial sum (KS UM)
is set to 0, and the first integer is given the value 1. The loop then proceeds to add the integer value
to the partial sum, increment the integer, and repeat the operation.

3.1 .1 • 1

The IF Statement - The program shown in figure 10 performs the required computation, but

thlere is one flaw: the loop is endless. To get out of the loop, iteration must be stopped and the next
step must be determined.
The IF statement ful fi lis both requirements. It has the following form:
IF (e) k, I, m
where e is any arithmetic expression, and k, I, and m are statement numbers. The IF statement is
interpreted in this way:

If the value of e is less than 0, go to statement k.
If the value of e is equal to 0, go to statement I.
If the value of e is greater than 0, go to statement m.
Thus, the IF statement makes the decision of when to stop by evaluating an expression, and also provides program branch choices which can depend on the results of the evaluation. Figure 11 illustrates
the use of the IF statement in the integer summation problem of figure 10.

2
3

Figure 11

SUM OF THE FIRST 50 INTEGERS
KSUM=O
INUM=l
KSUM=INUM+KSUM
INUM=INUM+l
IF (INUM-50) 2,2,3
STOP
END

Use of IF Statement in Integer Summation Problem

2-18

PDP-9 FORTRAN II

In this example, the initialization and main loop are the same as for figure 10, exceplr that
the GOTO statement of the earl ier program has been replaced by an IF statement. This statement says:

If the value of the variable INUM is less than or equal to 50 (which is the same as saying that the value
of the expression INUM-50 is less than or equal to 0), go to statement 2 and continue the computation.

If the val ue is greater than 50, stop.
A loop may also be used to compute a seri es of val ues. The following example is ':I program
to generate terms in the Fibonacci series of integers, in which each succeeding member of the series is
the sum of the two members preceding it: k =k 1 +k 2.
n nn-

FI BONACCI SERIES, 100 TERMS
DIME N SION FIB (1 00)
FI B (1)=1
FIB (2)=1
K=3
FIB(K)=FIB(K-1) + FIB(K-2)
K=K+1
I F (K - 100) 5, 5, 10
STOP
END
Figure 12

Fibonacci Series

In th is program, initial ization includes a DIMENSION statement to reserve space in memory
for the results, and two statements which provide the starting values necessary to generate the series.
Each time a term is computed, the subscript is indexed so that each succeeding term is stored in the
next location in the table. As soon as the subscript becomes greater than 100, the calculation stops.

3.1 .2

DO Loops
Iterative procedures such as the loop in figure 12 are so common that a more concise way of

implementing them !s warranted. In that example, three statements were required to initialize the subscript, increment it, and test for termination. The DO statement combines all these functions:
DO n i=kl,k2,k3
where n is a statement number, i is a simple integer variable, and kl, k2, and k3 are simple integer
variables or constants used as indexing parameters to provide, respectively, the initial values of i, the
final (terminating) value of i, and the indexing increment of i. The DO statement may be paraphrased
as: 1100 through statement n for i = kl; after statement n is completed, increment i by k3; if i is less
than or equal to k2, repeat the sequence; otherwise exit from the DO loop and continue on in the

2-19

PDP-9 FORTRAN II

program." Upon normal exit from a DO loop, the value of the DO variable (i) will be the one generated
at the final test, that is, greater than k2. If k3 is equal to 1, it may be omitted. Figure 13 shows the
Fibonacci series calculation programmed using a DO loop.

Figure 13

FI BONACCI SERIES, 100 TERMS
DIMENSION FI B(100)
FIB (1)=1
FIB (2)=1
DO 5 K=3, 100
FI B(K)=FI B(K-l )+FI B(K-2)
STOP
END

Fibonacci Series Calculation Programmed as a DO Loop

The DO statement is interpreted thus: Do the sequence of statements up to and including
statement 5, then index K by 1. If the new value of K is greater than 100, go to the statement following
statement 5.
DO loops are commonly used in computations with multiple-subscripted variables.

In these

cases, it is usually necessary to perform loops within loops. Such nesting of loops is permitted in
FORTRAN. A simple illustration is the initialization of array storage, shown in figure 14.
Initialize two 30 x 50 matrices and o~e 30-element vector, by setting the allotted storage
space to

o. Note that the PDP-9 FORTRAN II, the initial condition of variable storage is never impl ic-

itly cleared.

10
20

INITIALIZATION OF STORAGE
DIMENSION MATl (30,50), MAT2(30,50), VEC3(30)
DO 20 1=1, 30
DO 10 J=l, 50
MATl (I, J)=O
MAT2(1, J)=O
VE C3( 1)=0

Figure 14

Initialization of Array Storage

This sequence causes storage to be cleared in the inner loop column by column for each
matrix, while the outer loop advances the column index and clears the elements of the vector.

3.1 .2.1

General Rules for DO Loops - The following general rules about DO loops must be

observed:

2-20

PDP-9 FORTRAN II

a. DO loops may be nested, but they may not overlap. Nested loops may end on the same
statement, but an inner loop may not extend beyond the last statement of an outer loop.
Figure 15 schematicall y ill ustrates permitted and forbidden arrangements. Those in 15a are
permitted; loops 5, 6, and 7 end on the same statement. The arrangements in 15b are not
permitted; loop 2 ends on a DO statement, loop 3 extends beyond outer loop 1 •
1

,---- 2

1~--3

Figure 15

DO Loops

b. A program branch may not occur from a point outside a DO loop to a point inside, or
from an outer DO to within an inner DO.

Branches out of DO loops are permissible,

however. Figure 16 illustrates this rule. Branches 2, 5, 6, and 7 are permitted; branches
1, 3, and 4 are not.

Figure 16

Program Branching in DO Loops

2-21

PDP-9 FORTRAN II

c. A DO loop may not end on a program branching statement (GOTO, IF) or another
DO statement.

3.1 .3

The CO NTINUE Statement
Since a DO loop may contain alternate courses of action (such as branches to other parts of

the loop, or out of the loop entirely), programmers frequently wish to make the last executable statement of the loop a test to determine which of the alternatives is to be taken. However, rule c of the
above section forbids a DO loop to end on an IF or GOTO statement. To avoid this, the CO NTIN UE
statement is provided as a dummy statement. It performs no action or computation., but provides a
termination for any DO loop:
n

CONTINUE

where n is the statement number specified by the DO statement that initiated the loop.
A CONTINUE statement is not restricted to terminating DO loops; it may be used anywhere
in a program; e.g. ,. to provide points at which future program segments may be inserted.

3.1 .4

Computed GO TO
The GOTO statement described previously is unconditional and provides no alternatives.

The IF statement offers a maximum of three branch points. One way of providing a greater number of
alternatives is by using the computed GO TO , which has the following form:
GOTO (k1 ,k2,k3, ••• ,kn)' i
where the ks are statement numbers, and i is a simple integer variable which may take on values of 1,
2, 3, ••• n according to the results of some previous computation. For example,
GOTO (5,7,5,7,5,7,10), IVAR
causes a branch to statement 5 when IVAR=l, 3, or 5, to statement 7 when IVAR=2, 4, or 6, and to
statement 10 when IVAR=7. If IVAR is not one of the possible (legal) values, the GOTO is ignored
and control passes tc? the next statement.

If an argument of a subroutine is used as the argument of a computed GOTO statement in
the subroutine, the argument must be redefined (with a different name) in the subroutine; e.g.:
CALL SUB(JAY)
SUBROUTINE SUB{KAY)
MAY = KAY
GO TO (1, 2), MAY
Otherwise, the address of JAY will be used rather than the contents of JAY.

2-22

PDP-9 FORTRAN II

3.1 .5

Assigned GOTO
A sl ightly different way of providing a multibranched switch is by the assigned GOTD, which

has the following form:
GOTO i,(k ,k ,k ,·.·,k )
n
1 2 3
where i is a simple integer variable and the ks are statement numbers. In use, the variable i is assigned
a value of one of the numbers in the I ist by an ASSIGN statement of the form
ASSIGN k to i
where k is one of the statement numbers in the list. The ASSIGN statement must precede the GOTO in
order of execution. For example:

ASSIGN 30 TO IFORK
25 GOTO IFORK,(20,30,40,50)
30 ASSIGN 40 TO IFORK
GOTa 25
40 A=B+C

If the statement number assigned to i is not in the list, the computer halts. The AC contains a JMP to
the address of the statement number. Hitting CONTINUE transfers control to that address. The first
time statement number 25 is executed, and the program branches to statement 30 where IFORK is altered
so that the next execution of statement 25 initiates a branch to st"atement 40. An alternate form of the
ASSIGNED GOTO eliminates a list of statement numbers. It consists of the following:
GOTO i
where i is an integer variable whose value is established by an assign statement. This value must correspond to one of the statement numbers in the program.

3,.2

PROGRAM TERMINA nON

3.2.1

The STOP Statement
A program which is arranged so that the last written statement is the final and only stopping

place needs no special termination indicator. The END statement automatically produces the final halt.
Most programs, however, contain loops and branches so that the last executed statement is often somewhere in .the middle of the written program. Often, there may be more than one stopping point. Such
terminations are indicated by the statement:
STOP
2-23

PDP-9 FORTRAN II

This causes a final, complete halt; no further computation is possible. If more than one final halt is
possible, each can be identified by a number as follows:
STOP n
where n is an octal integer which is displayed in the console ACCUMULATOR lights when the program
stops.

This feature is very useful when several stops are possible, such as stops in error routines, and

it is desirable to know which one was reached.

3.2.2

The PAUSE Statement
The PAUSE statement allows suspension of operation for a time and then restarting the pro-

gram by manual control.

This is frequently necessary when the operator loads and unloads tapes in the

middle of a program. This kind of temporary halt is provided by the following statement:
PAUSE n
The octal integer n appears in the AC I ights when the pause is effected. Depressing the
CONTINUE switch on the console resumes opera'tion of the program.

2-24

PDP-9 FORTRAN II

CHAPTER 4
INPUT/OUTPUT STATEMENTS

In previous examples, all necessary information has been in the computer memory. Of course,
a special loader reads in these programs, but the programmer must provide for the input of data and the
output of results associated with his program.
For any input or output procedure, several items of information must be specified:
a. The direction of transfer (READ or WRITE).
b. The I/O device.
c. The amount, type, and location of the information to be. transferred.
d. The arrangement of the data. In FORTRAN terms, the order and format of the in'coming or outgoing data must be specified.
To provide all the information listed above, two statements are required for every data transfer
between core memory and an external device. The first three items are supplied by the input/output statement, an example of wh ich is shown in figure 17; the fourth is specified by the FORMAT statement.

device
number

data list
..

A._ __

READ 3, 100,tA, B(5),I,((C(J,K),J=M,N,I),K=M,N)\

op!ation

Format Statement
Number

Figure 17

4.1

I/O Statement

INPUT/OUTPUT ASSIGNMENTS
The first word in the I/O statement designates the direction of the data transfer. A READ state-

ment initiates all incoming transfers; a WRITE statement, a II outgoing transfers.
The use of a device number, which follows the first word and specifies the external device involved in the transfer, eliminates the need for additional commands such as PUNCH, PRINT, etc. These
device numbers are as follows:

2-25

PDP-9 FORTRAN II

INPUT
Device
Number

OUTPUT
Device
Number

Device

Keyboard

Teleprinter

Perforated Tape Reader

Perforated Tape Punch

PDP-7/9 line Printer

The format statement number is the third item in the I/O statement. It refers to a
FORMAT statement which determines the arrangement of the data being transferred. Commas
separate the format statement number from the device number and from succeeding items. The
remaining items in the I/O statement are components of the data list.

4.2

THE I/O DATA LIST
The last part of the I/O statement is a list, the elements of wh ich specify the locations in mem-

ory and the number of data elements being transferred. These elements, separated by commas, may be of
four types:
Variables (unsubscripted)
Array elements (subscripted variables)
Array transfer expression
Constants (output list on Iy)
The Iist in the statement in figure 17 contains four elements. These are, in order, a rea I variable I an array
element I an integer variable, and an array transfer expression enc losed in parentheses.
The array transfer expression transfers whole arrays or sections thereof, under control of a
single I/O statement. The expression consists of an array name with subscripts and a series of internal
arithmetic statements which specify the lower and upper limits of each subscript and the increment between elements. The upper limit must not exceed the maximum vlaue for that subscript given in the
DIMENSION statement in wh ich that array name appears. If the increment is 1, it may be omitted.
The function of the array transfer expression is shown in the I/O statement in figure 17. The
elements of array C are to be read into core. Every element in the K dimension between the limits M

2-26

PDP-9 FORTRAN II

and N I and every Ith element in the J dimension between the limits of M and N, are read into the computer.
When the loops are exhausted, the reading stops. The limit parameters, I, M, and N, must be defined before they can be used in the expression.
The array transfer expression is a sequence of nested DO loops; the operations described in the
preceding paragraph would have to be programmed as follows if the array transfer expressio1n were not
available:

DO 15 K=M,N
DO 15 J=M, N,I
READ '3,100', C(J, K)

The following forms produce the indicated results:
READ 3, 100, (C(I,I), 1=1, 10)
Result

C(l, 1) C(2,2) C(3,3)

C (4,4) ••• C ( 10, 10)
READ 3~iU~0~i~CC(I), B(I), 1=1, 10)
Result

4.2.1

FORTRAN diagnostic errors

Ordering of Data Within an Array
In the language of matrix algebra, the data ordering specified by the array transfer expression

in figure 17 is by columns. If M=l, N=5, and 1=2, the elements of C must be ordered:
c 1 l' c 31' c 51' c 12' c 32' c 5 2' c 13' • • • • • , c 35' c 55
Note that should one reverse the left-to-right arrangement of the arithmetic expressions defining K and J
in the array transfer expression of figure 17, the data must be ordered by rows:

That is, the ordering of the subscript defining expressions in an array transfer expression is independent of
the subscript ordering in the array variable. The subscript encountered in the first definiti()n expression,
proceeding from left to right, varies most.

4.3

I/O SPECIFICA nON STATEMENTS

4.3.1

Data Fields
The space allotted to an item of data is called the data field. The width of the data field is the

number of character positions occupied by the item. The width may be greater than that required to hold

2-27

PDP-9 FORTRAN II

all the characters of the item of data including the sign, but no more than one item may appear in a field.
For example, a five-digit integer may appear in a field seven positions wide (empty positions are denoted
by the letter b, for blank):
bb34729
An item of data may be numeric (numbers), non-numeric (alphanumeric test or coded characters), or blank.

4.3.2

Data Field Formats
Information may be read in or written out in one of six data field formats: three numeric and

three non-numeric. Each format is designated by a single letter contained in the format specification.
The format specification indicates the type of data field (numeric or alphanumeric), the length of the data
field, the form of the item it contains, and the storage mode of the item in the computer. The properties
of tlhe six format specification letters are summarized in table 1; each specification type is described in
detcli I in th is chapter.

TABLE 1 SUMMARY OF FORMAT SPECIFICATION LETTERS
Format
Spec. Letter

Type of
Field

Storage
Mode

Input

Output

numeric

decima I,
decimal exponent

floating point
number

decimal exponent

numeric

decimal,
decima I exponent

floating point
number

decimal,
decimal exponent

numeric

integer

fixed point
number

integer

non-numeri c

any characters
and/or blanks

none

blank space

non-numeri c

text

packed Flexowriter
FIODEC

text

non-numeric

text

packed Line Printer
FIODEC

text

The Format Statement
Each format specification provides information about one data field. To determine the arrangement of these fields, for both input and output, the format specifications must be combined in a FORMAT
stat'ement, as shown in figure 18.

2-28

PDP-9 FORTRAN II

100 FORMAT (2E12.2,3X,F5.2) - numeric fields

200 FORMAT (8HRAW DATA,5A3) - alphanumeric fields
Figure 18

FORMAT Statements

Following th~ word FORMAT is a statement list made up of format specifications, separated from
each other by commas, and the whole enclosed in parentheses. Formats of all six types may be freely combined; however, the format specification, the item of data, and (H, X excepted) the variable type in the
I/O statement list must all correspond.

If successive data fields have identical formats, it is not necessary to write out each specification in full; instead, the format specification may be preceded by a repetition count, equal to the number
of identica I data fields. The repetition count may not be larger than 15. For example, the first member
of the list in figure 18a is:
2E12.2
This indicates that the next two data fields have identical E-formats. Likewise, 3X indicates three successive characters of X-format.

However, groups of more than one data field may not be repeated by

preceding the group with a repetition number. For example 6(F5.2,3X) is illegal.
Every FORMAT statement must be identified by a statement number so that it can be referenced
by an I/O statement. When an I/O statement is executed, its data list and the list of format specifications
in the corresponding FORMAT statement are scanned from left to right. Each item of data is matched with
a format specification and transferred according to the format specified. This procedure continues until
"the I/O data list is exhausted. If the format list runs out before the I/O operation is completed, the
format scan returns to the last previous left parenthesis and continues from that point.

If there are no interna I parentheses in a format list, the scan wou Id return to the beginning and
repeat the format list. If the I/O list is exhausted before the format list, the remainder of the format list
is simply ignored.

4.3.4

Format Specifications
The following paragraphs discuss the properties of each data field format, and the form of data

permitted in each. The three numeric formats are described first, followed by the three non-numeric formats. The letter r in all cases symbolizes the optional repetition count which can precede the format
specific.otion.

2-29

PDP-9 FORTRAN II

4.:L4.1

Integers: I-Format - Integer fields are specified by the letter I. The general form of the

specification is

rlw
whlere r is the number of times the specification is to be used and w denotes the field width including one
position for the sign, whether or not it appears; that is, w-l digits are allowed. The field width must be
les!s than 7, or it wi II be set to 7. On input, the field must contain a FORTRAN integer not exceeding
a magnitude of 131071. The integer may be signed or unsigned and may be placed anywhere within the
field as long as there are no blanks embedded in the number. Input is converted to fixed point for storage.
ThE~ following are examples of I-format input.

Specification

Acceptable Input

Unacceptable Input

32
+5012
-317

34729 (too many characters)
50b31 (embedded blank)
3.57b (not an integer)

On output, integers are right justified within the field. Positive integers are unsigned. If an
int,eger is too large to fit in the fie Id, w x's wi II appear in the output; w digits are a I lowed if the sign
is positive. The storage mode for I-format output must be fixed-point.

4.:3.4.2

Real Numbers: F- and E-Formats - Real number fields are specified by the letters F and E.

The genera I forms are
rFw.d

rEw.d

where w denotes the total field width including the decimal point, exponent, and sign, and d specifies
the number of digits to the right of the decimal point. While w is limited to a maximum of 31 characters,
d c:an be as large as 15. If an exponent is to be spec ified in input data, the character E must be present.
Both format specifications permit the same type of input. An incoming number may be in one
of three forms:
a. A simple decimal: 95.34729; -7. 132
b. A decimal exponent: 1.66E-16; -6.032E+23; 1.66-16; -6.032B23 (-6.032+23)
c. A string of digits with no indication of magnitude: 9534729; -6032E-23
Incoming numbers may be signed or unsigned and placed anywhere within the field. As with integers,
thE~re may be no embedded blanks, though a blank preceding an exponent is allowed; thus,

1.32E 36.

If the incoming number contains an explicit decimal point, the fraction delimiter (d) of the
format specification is ignored. If there is no explicit decimal point, the number must be followed by

2-30

PDP-9 FORTRAN II

either an exponent or the end of the field, but not by blanks. A decimal point is inserted in the number,
independently of the exponent value according to the d specif~cation only if there are at least d digits in
the number. If there are fewer than d digits, the decimal point is placed to the right of the number, regardless of d. The following illustrates the effect of the fraction delimiter.

If the specification is

And the incoming
field appears as

E12.2

bbbbb9534729

95347.29

F10.5

bb953.4729

953.4729 (explicit
decimal point overrides)

E10.2

b+l.66E-16

1.66E-16

E10.2

bbb166E-16

1.66E-16

F10.5

bbbbbbb222

222.0 (less than 5 digits
input)

The magnitude of
the number is

Both E- and F-format causes the incoming data to be converted to Hoating-point for storage.
The two formats differ on Iy in the form of output each produces. E-format output a Iways appears as a
decimal exponent with the exponent signed and the E omitted. The number is right justified in the field.
Positive numbers are not signed. The following illustrates E-format output.

If the specification is

And the magn itude
of the stored number is

E10.3

1 .66 x 10-

E12.5
E12.2

16
23

- 1 .324 x 10
23
- 1 . 324 x 10

The output appears as

bbb.166-15
bb-. 13240 24
bbbbb-. 13 24

The important points to observe in these examples are:
a. The printed number is normalized; that is, scaled so that it is less than 1.0 and no Os
appear immediately to the ri~ht of the decimal point.
b. The E representing the exponent is missing, and the exponent itself is signed whether
it is positive (blank) or negative (-).
c. If the fractiona I part is too large to fit in the space reserved for it, the least significant digits are truncated.
2-31

PDP-9 FORTRAN II

F-format output is in the form of a simple decimal. The number is right justified in the field,
and the decimal point is placed according to the format specification. Positive numbers are unsigned.
Fractional parts are truncated if they would overflow the space reserved.

If the specification is

And the magnitude of
the stored number is

The output appears as

F9.4

953.4729

b953.4729

F12.5

4
- .007315 x 10

bbb-73.15000

F10.2

55.9328

bbbbb55.93

If F-format is specified, and the number to be printed is so large that the integral part would
not fit in the available space, the number is automatically printed under E-format. For example,

If the format specification is
and the stored number has a value of
the format is interpreted as
and the number wi II appear as

F10.5
57329.46
E10.5
.57329 05

For both formats, the stored data must be in floating-point form for output. The field width w must include
one position each for the sign and the decimal point; and in the case of E-format f three positions for the
signed exponent.

4.3.4.3

Non-numeric Fields: X-Format - One way to separate items of data for readability is to provide

wide enough fields in the format specifications so that there witt be some leading blanks. Another way
tel separate items is by using the X-format specification, whose only function is to indicate the presence

of a blank position. A string of blank spaces is indicated by a repetition count before the X:
rX
On input, an X-format specification causes the input scan to skip ahead the number of spaces
specified by the repetition count and continue reading input from that point using the succeeding format
specifications in the list.
On output, the X-format causes the number of spaces indicated by the repetition count to be
inserted between the preceding and fol lowing items of data. For example, the specification

F5 • 2, 3X, F5 •2
cCluses the output of two items of decima I data to be separated by three blank spaces.
When reading FORTRAN produced paper tape input, a lX format specification may be used
wherever a slash (/) appears in the output format statement which produced the tape. The slash causes
2-32

PDP-9 FORTRAN II

a carriage return to be punched following the last field. This is read as a blank item (0) unless the X
specification skips the carriage return character. A more detailed description of field del imiters appears
in section 4.4.1.2. The lX specification is not required if the input format is identical to the output
format.

4.3.4.4

Non-numeric Fields: H-Format (Hollerith) - The output of text such as table headings, captions,

instructions to the computer operator, and descriptive information is done by inc luding the text expl icitly
within the FORMAT statement, using the H-format, which specifies that the characters immediately following the H are to be taken as an item of textual data. To handle a string of text, the total number of characters, including blanks, is counted and substituted for the repetition count. An error results if the number of characters is counted incorrectly. Figure 18b shows a FORMAT statement which contains an H-format
specification.

Note that the field count 8 corresponds exactly to the number of characters and blanks in

the field.
The programmer may mix H-format with other specifications in a format list. On output, the
I/O data list scan is suspended when an H-format specification is encountered, the text in the Hollerith
field is printed, and the data I ist scan resumes. If an output statement is to transfer H-format information
only, the data lists may be omitted.

Hollerith text is packed three characters to a word and stored in

Flexowriter FIODEC code. Alphanumeric (A-format) information is stored 1, 2, or 3 characters per word,
right justified, in line printer FIODEC code.
The information in the following format statement
50

FORMAT (41 HSATELLITE TRACKING DATA, CAMBRIDGE, MASS./
23HTELOS I, SEPTEMBER 1964)

would be printed on the teleprinter by the statement
WRITE 2, 50
and would appear as follows:
SATELLITE TRACKING DATA, CAMBRIDGE, MASS
TELOS I, SEPTEMBER 1964

4.3.4.5

Non-numeric Fields: A-Format - Frequently, it is desirable to vary text analogous to data.

For example, a billing program may process a larger number of accounts in the same mannelr with identical
output format for each, except for the name of the person associated with the account. It would be burdensome to write a long sequence of FORMAT statements with Hollerith fields and make frequent corrections simply to store a II the account names.

2-33

PDP-9 FORTRAN II

The A-format specification allows the user to both READ and WRITE textual information. Its
general form is
rAn
where r designates the number of 18-bit words required to store the characters of text in the data field.
On input, characters are read and packed 1, 2, or 3 to a word depending on the count n. On output,
the stored words contain packed text, and 1, 2, or 3 characters are printed from each according to the
count n. (The number of characters is r x n.) In the I/O statement, the packed text is designated by an
in1'eger variable name. If a repetition count accommodates a long string of text, the variable name is
subscripted; the value of the subscript, r, is the number of words of packed text. Such an array name
must appear in a DIMENSION statement. Since r ~15, n'::;3, the format specification cannot be greater
them 15A3. To read a large number of characters, FORMAT (A3) is sufficient since the specification may
be indefinitely repeated.
To illustrate "the use of A-format, take a hypothetical billing program. Assume that input is
from paper tape and output is on the teleprinter. The first item on paper tape for each account is the
name of the account in the first 36 character positions and no other information. To read this information,
the following two statements would suffice (here r x n=36, the number of characters):
READ 3, 300, (NAMACC(I), 1=1, 12)
300

FORMAT (12A3)

The information in the 36 character positions is read into the 12 locations designated by the array name,
NAMACC; the text is packed 3 characters to a word.
To print out A-format, the following statement is necessary:
WRITE 2, ·300, (NAMACC(I), 1=1,12)
The A-format is a Iso usefu I when the same program runs over a long period of time and the date of each
run is recorded. A date can be provided with the input, a location reserved for it, and the information
trcmsferred using an A-format specification.

4.4

INPUT/OUTPUT DEVICES

4.4.1

Data Organization

4.4.1.1

Records - In every I/O device, data is organized into records. Because of the dissimilarity of

devices, the definition of a record varies. Table 2 lists the I/O devices and the definition of a record
for each.

2-34

PDP-9 FORTRAN II

TABLE 2

DEFINITION OF A PHYSICAL RECORD FOR I/o DEVICES

Device

Physical Record Definition

Keyboard and Teleprinter

The information typed on a single line (maximum 72
characters) •

Perforated Tape Reader I Punch

The information punched between two carriage returns
(practical maximum 72 characters, for compatibility
with other devices) •

Line Printer

120 characters (one line).

Norma Ily, one FORMAT statement corresponds to one record and the programmer must be careful that the total number of characters in the format specifications, including repetitions, does not exceed
the maximum for one record on the respective devi ce.

4.4.1.2

Multirecord Formats - To make the arrangement of output data as flexible as possible, a single

FORMAT statement can specify more than one record. The method can best be illustrated by an example.
The following FORMAT statement,
50

FORMAT (F12.2, 5X 316, 2E15.5, 17)

causes the associated output to be printed on a single line. If the statement is changed to read
50

FORMAT (F12.2, 5X, 316/2E15.5, 17)

the insertion of a slash (/) in place of the comma after the third specification causes the remaining data
to be written as a new record on the next line.
In general, whenever a slash appears in a FORMAT (other than an H-format) statement, it
terminates the record. If two slashes appear in succession with no intervening specifications, the effect
is the same as if an empty record were transferred. For example, if two slashes were inserted instead of
one in the i Hustration:
50

FORMAT (F12.2, 5X, 316//2E15.5, 17)

and the data were written on the teleprinter, the result would be a line of data, a blank line, then another
line of data. Use of multirecord formats greatly increases the flexibility with which the programmer may
arrange tabular data for output. Table 3 and 4, respectively indicate the effects and limitations of multirecord formatting for input and output operations.

2-35

PDP-9 FORTRAN II

TABLE 3

INPUT FORMAT

Paper Tape

Teletype

Tab

Effect of
Field Del imiter

Terminates
current fie Id
if reached
before the
count in the
format statement runs out.

Record
2
Delimiter

Carriage
return

Carriage return-line
feed

Effec t of Record Delimiter

Terminates
the current
field if
reached before the
count in the
format statement runs out.

Field Delimiters

-- --

Other
Delimiters

None

!
1Field delimiters are never required on input but will have the indicated effect if present. They are
a Iways ignored when the first character of any fie Id (except in A-format where they should never be used;
the only legal characters for A-format are the Anelex character set).
2Record delimiters are never required on input except where needed for the correct operation of the
slash function as when using paper tape.

2-36

PDP-9 FORTRAN II

TABLE 3

INPUT FORMAT (continued)

Paper Tape
Effect of Slash
in Format
Statement 3

Teletype

Causes the
None
next field requested to be
taken from information after
the next carriage return on
the paper tape.

3Successive slashes are ignored in all cases. This can be visualized logically since the slash merely signifies that the current buffer is empty and does not cause the next record to be read. No implicit slashes
are assumed at the end of an input format statement; i • e., a II characters appear as one long string, irrespective of the input device, except where the slash is used explicitly.
In all cases the unit record consists of the characters requested between slashes in the output
format statement or by the entire statement if no slashes are used. As noted above, the end of an output
format statement is taken as an implicit slash. The maximum record which can be requested in any case
is 256-(N+1) characters where N equals the number of fields desired. All requested characters above
that figure are lost. The following additional limitations apply:
a. For the Iine printer, a request of more than 120 characters per unit record destroys
the program.
b. For the paper tape punch, a request of more than 72 characters per un it record pro-duces a tape wh ich cannot be read off-I ine. If that restriction is not appl i cable, the
maximum size record (256-(N+l) characters) can be used.
c. For the Teletype, a II characters requested after the 72nd character per un it record
type over the 72nd character.

2-37

PDP-9 FORTRAN II

TABLE 4

OUTPUT FORMAT

Line Printer

4.4.2

Paper Tape

Teletype

Field Delimiters
Generated

None

Cause of
Generated
Field Delimiter

None

Record
Delimiters
Generated

Space line
printer 1 line

Carriage
return (plus
line feed in
ASCII mode)

Carriage
return-line
feed

Effect of Slash
in Format
Statement

Output the
present contents of the
buffer, if any,
and always
genera te the
end-of-record
indicator.

Output the
present contents of the
buffer, if any,
and always
generate the
end-of-record
indicator.

Output the
present contents of the
buffer, if any,
and always
generate the
end'-of-record
indicator.

Effect of
End of Format
Statement

Implicit slash

Impl ic it slash

Implicit slash

I/O Operations with Paper Tape and Keyboard
Use of FORTRAN with paper tape and a keyboard permits a relaxation of some of the constraints

on input formats for numbers. With paper tape or keyboard, an item of data being read can be delimited
by a tabulation or a carriage return-line feed combination (for keyboard), or a carriage return (for paper
tape), which overrides the field width allotted in the format specification. The limits on maximum field
widths still apply; however, 7 for integer fields and 31 for real number fields. The number of characters
in a field must be less than or equal to the width specified or the overflow will be considered another field.
60

FORMAT (214, E9.2)

wi II accept input from a keyboard thus:
176

-20

+16742E 13 ~~ (line feed-carriage return)

or analogous paper tape input.
Also when using the keyboard for input, incorrect characters can be erased by striking the
rubout key. The rubout key erases the last character; successive rubouts erase the next previous
character. Thus to erase the last three characters, strike the rubout key three times. However, no
changes in data may be made after typing a tab or carriage return since this processes the data.

:2-38

PDP-9 FORTRAN II

CHAPTER 5
SUBPROGRAMS:

FUNCTIONS AND SUBROUTINES

The programmer may employ separate subprograms to perform a sequence of operations required
in the solution ofa problem or to evaluate functions. For example, whenever a function occurs in an
arithmetic expression, a subprogram is called into operation to evaluate the function, using as data the
qrguments provided. The resulting single value is then returned for use in the computation of the expression in which the f~nction appears. A second type of subprogram, the subroutine, is used when a
sequence of statements is used repeatedly or when it is necessary to generate more than one result (a matrix
operation, for example).
Since a subprogram is a separate program, communication with the main program must be established; that is, an entry to the subprogram from the main program and an exit from the subprogram back
to the main program must be provided. In the case of a function, entry is effected by the use of the
function name in an arithmetic expression. In the case of a subroutine, entry i6 effected by the CALL
statem'ent. The RETURN statement provides an exit from both types of subprograms. A subprogrcJm cannot come to a full stop (though subroutines may include pa.uses) but must always return control to, the
co II ing program.

5. 1

FUNCTIONS
In addition to the Iibrary functions suppl ied with FORTRAN, the user can write h is own as

needed. The writing of a function subprogram follows the rules for writing any sort of program in that
there must be a title, a body, and an END statement. In addition, two special statements are required:
FUNCTION definition and RETURN.

5. 1 • 1

The FUNCTION Definition Statement
The FUNCTION definition statement identifies the subprogram and has the fol rowing form:
FUNCTION f (d , d , d ,· .• ,d )
1 2
3
n

where f is the name of the function and d is a dummy name which represents a main program argument of
the function. The function and dummy names follow the ru les given for variables in section 1 .2.3.2: they
are restricted to the same character set, the first character must be alphabetic, and only the first six
characters are significant. A main program argument can be a constant, a variable, or any legitimate
arithmetic expression. It may itse If include functions. At least one argument is required with a function
su bprogram •

2-39

PDP-9 FORTRAN II

Because a function is an element of an arithmetic expression, it must always return a value to
the main computation. To do this, in the function subprogram there must be at least one arithmetic statement in which the function name appears as the left-hand variable. This also defines the mode of the return value. A function returns an integer-value if its name is defined as an integer variable, or a realvalue if its name is defined as a real variable. Exceptions to this rule are: 1) a function whose name
begins with the letter X is integer-valued; 2} if a function name does not begin with X but ends with F,
the function returns a rea I-va lue. A function name cannot represent an array. STOP or PAUSE cannot
be used in a function.

5.1.2

RETURN Statements
The statement
RETURN

terminates the subprogram {function or subroutine} and transfers control to the calling program. There may
be more than one RETURN statement in a subprogram, corresponding to alternative exits. Figure 19 illustrates the writing of a function subprogram which calculates the factorial of an integer ~:
n! = 2 ·3·4· •.• {n-2} (n-l) {n}

FACTORIAL CALCULATOR
FUNCTION NFACT (N)
NFACT = 1
DO 10J=1,N
10
NFACT = NFACT * J
RETURN
END
Figure 19

Function Subprogram

In figure 19, the name NFACT specifies an integer-valued function. The dummy name N denotes an integer argument. The body of the subprogram is a loop which calculates the factorial. Statement 10 provides for the va lue to be returned, since the function name appears as a lefthand variable.
Finally, the RETURN statement transfers control to the calling program.

5.1.3

Use of Functions
Dummy names need not agree in mode with the function name or with each other. They must

agree, however, with the mode (integer, floating two- or three-word) of corresponding arguments in the
calling program. For example, the factorial function above may be called this way (the dots represent
parts of an arithmetic statement):

2-40

PDP-9 FORTRAN II

.•.• + NFACT(15)/ ••••
but not this way:

•••. + NFACT(l5. 0)/ ....
because the argument is not an integer.
Library functions which require real arguments, such as SQRTF, COSF, are treated ClS floating-

--.

-......::.....

point variables in arithmetic expressions. No diagnostic check occurs during compilation to insure that
the arguments specified by the programmer are in fact real. For example:
A=SQRTF(I*K 2.2)
compiles correctly since the real nature of the exponent forces the entire parenthetic expression to be
real.

However,
A=SQRTF(I* K!2)

must be written as
A=SQRTF(T=I* K/2)
or some equiva lent form if correct compi lation is expected.

5.1.4

Library Functions
Severa I common functions are provided with the FORTRAN system to save the programmer the

necessity of writing them. These library functions are named according to the following conventions:
a. Every library function name ends with the letter F.

b. A function whose name begins with the letter X is integer-valued; otherwise

it is real-valued.
Library functions may be used by the programmer without any special preparationi;they are placed in
memory from a library tape which is read prior to run time. The library functions are:

Function Name

Operation Performed

SQRTF(A)
SINF(A)
COSF(A)
ATANF(A)
LOGF(A)
CLOGF(A)
EXPF(A)
ABSF(A)
XABSF(N)

square root:
sin a (argument in radians)
cos a (argument in radians)
arc tan a
loge a
10910 a
ea
absolute value: la
absolute value (integer): n

XABSF is the only integer-valued library function.

2-41

I I

PDP-9 FORTRAN II

5.2

SUBROUTINES
It is often desirable to write whole procedures, not as functions (which can return only a single

quantity) but as complete subprograms which compu'te multiple quantities for use by the main program.
Such a subprogram is ca lied a subroutine. Its definition statement is:
SUBROUTINE s (d , d , d ,··· ,d )
1 2
3
n
where s is the subroutine name, and d. are dummy arguments.
I

Like a function subprogram, a subroutine must have at least one RETURN statement. Unlike a
function, however, a subroutine does not directly return a value to the calling program; instead results
are stored in locations designated by the main program I where they are avai lable to the main program.
A subroutine name differs from a function name in that it may not appear as the left-hand variable in an
arithmetic statement of the subprogram. A subroutine differs further from a function in that it requires no
arguments. When arguments are present, they obey the same ru les as functions wi th regard to mode.

5.2.1

The CALL Statement
To call a subroutine into operation, the following statement is used:
CALL s (a , a , a ,··· ,an)
1 2
3

where s is the subroutine name, and a. are arguments, if any. The argument list of the CALL statement
I

must be simi lar to the argument list in the subroutine.
The factoria I ca Icu lator written as a function in figure 19 may be written as a subroutine as
shown in figure 20. In this example the main calculation is the same as before, but to make the result
C:lvailable to the calling program, another argument has been provided. If a program were to use this subroutine to calculate, for instance, the factorial of an integer variable K, the following statement might
be used:
CALL FACT (K, KPROD)
FACTORIAL CALCULATOR
SUBROUTINE FACT (N, NPROD)
NPROD=l
DO 10J=1,N
10
NPROD = NPROD * J
RETURN
END

Figure 20

Example of Factorial Calculator

The value of the resulting product, assigned the dummy name NPROD in the subroutine, is given to the
variable KPROD in the calling program.

2-42

PDP-9 FORTRAN II

5.2.2

Common Storage
As figure 20 shows, information can be transmitted between a calling program and a subprogram

via the argument list. Information can also be passed between programs through a special section of memory, set aside as common data storage. Space in this area is assigned by the following spec:ification
statement:
COMMON vl, v2, v3, •.• ,vn
where each v represents a variable name, either s,imple or subscripted. Each simple variable is assigned
a location (or group of locations, depending on the storage mode) beginning at the end of clvailable memory and working backward. Arrays are assigned enough locations to store the maximum number of elements,
as indicated by the DIMENSION statement. For example, if an integer array which appears in a DIMENSION statement
DIME NSION MATRIX (20, 40)
also appears in a COMMON statement
COMMON MATRIX
20 x 40 = 800 locations wi II be set aside in common storage.
Programs which have common data must each have a COMMON statement in which the variables
are assigned in correct order and storage mode, although the names do not have to be identical from program to program. For example, two programs could share three variables if one program contained the
statement
COMMON VARL, INDEX, AVAL
and the second program contained the statement
COMMON VARX, ITEST, ARGL
The first program uses the name VARL, and the second VARX, but both names refer to the same
quantity. Likewise, INDEX and ITEST are corresponding names, and so on down the line of variables.

5.2.3

Array Names Used jn Subroutines
Array names may be transmitted between a calling program and a subroutine either as arguments

or as variables in common storage. The two methods require different treatments.
a. If an array is placed in common, it must be dimensioned in both programs and must
appear in a COMMON statement in both programs. The names need not be the same
but they must correspond in mode, number, and order in the COMMON statements.
For example, if an array appears in the calling program as follows:

2-43

PDP-9 FORTRAN II

DIMENSION ARRAY (10, 10, 30)
COMMON VAR1, VAR2, ARRAY, IVAR
and is referred to in a subroutine by the name ARR2, this name must appear in the
subroutine in statements such as these:
DIMENSION ARR2 (10, 10, 30)
COMMON Xl, X2, ARR2
Here, the array name appears in the common list, following two rea I variables just
as the corresponding name does in the ca !ling program.

MATRIX MULTIPLICATION SUBROUTINE
SUBROUTINE MATMUL (lD, JD, KD)
DIMENSION DA(10, 10), DB(10,10), DC(10, 10)
COMMON DC, DA, DB
DO 101=1,10
DO 10 J=l, 10
10
DC(I,J)=O
DO 20 J=l, JD
DO 20 1=1, ID
DO 20 K=l, KD
20
DC(I, J)=DC(I, J) + DA(I, K) * DB(K, J)
RETURN
END
Figure 21

Matrix Multiplication Subroutine

In figure 21, the three arrays necessary for the calculation are placed in common. A
main program using this subroutine to multiply matrices of dimensions 5 x 10 and lOx 7,
respectively I must contain statements such as the following:
DIMENSION AMTX(10, 10), BMTX(lO, 10), CMTX(10, 10)
COMMON CMTX, AMTX, BMTX
CALL MATMUL (5,7,10)

b. If array names are to be transmitted as arguments, they must appear, unsubscripted,
in a DIMENSION statement in the subroutine. For example, the names of the matrices
required by the subroutine of figure 21 could be used as arguments in this manner:

2-44

PDP-9 FORTRAN II

MATRIX MULTIPLICATION SUBROUTINE
SUBROUTINEMATMUL(ID, JD, KD, DA, DB, DC)
DIMENSION DA, DB, DC

END
The ca II ing program cou Id then have statements as follows:
DIMENSION AMTX (10, 10), BMTX (10, 10), CMTX (10, 10)

CALL MATMUL (5,7, 10,AMTX, BMTX,CMTX)
Note that the array names appear without subscripts in the subroutine call a Iso.
Elements of an array may be transferred via the argument list when the subroutine
considers the argument as an undimensioned variable, e. g. ,
CALL SUB (C(l))

SUBROUTINE SUB (A)

5.3

MACHINE LANGUAGE CODING IN A FORTRAN CONTEXT
Since the symbolic output of the compiler is in the language of the assembler, familiarity with

that language is basic to a thorough understanding of the topics discussed. Information on the assembler
language can be obtained from the PDP-9 Symbolic Assembler and the PDP-9 User Handbook.

5.3.1

Handl ing of S Coding
As mentioned in chapter 1, whenever the letter S (for symbolic) appears in the identification

field, the remainder of the line is transferred to the object program exactly as written.
is made for an S-coded line.

No error diagnosis

Unless the programmer is absolutely certain that he can omit them in safety,

all S coding should be bracketed (preceded and followed) by CONTINUE statements, where the terminating CONTINUE has a statement number attached. An LFM should precede the other S coding. Example:

S
S
S
S
10

'5.3.2

READ 402
CONTINUE
LFM
LAS
AND (7
DAC J.
CONTINUE

Compiler Generated Coding
The FORTRAN compiler generates an object program of symbolic machine instructions and

pseudo instructions from the FORTRAN statements it reads.

2-45

In general, each statement is processed

PDP-9 FORTRAN II

individually without reference to previous or subsequent statements; as a consequence, errors such as the
duplication of statement numbers are not detected by the diagnostic routines of the compi ler. Coding to
test the iteration variable of a DO loop is not generated unti I after the last statement in the DO loop.

5.:3.2.1

Symbolic Conventions - To avoid conflicts with symbols which appear in the FORTRAN source

program and symbols which appear in the assembler permanent symbol table {machine language instructions
and assembly pseudo instructions}, or symbols which reference permanent locations in the FORTRAN object
time system, spec ia I conventions are established:
1. Symbols which appear in the FORTRAN source program and which are five characters or less are modified by appending the period (.) character.

2. Statement numbers are transformed into symbols by prefixing the per'iod (.) character to the statement numbers.

3. All symbols generated internally by FORTRAN are four character symbols: the
period (.) character followed by three letters.
The period (.) character is not a permissible character for symbols which appear in FORTRAN source programs. It is a permissible character for symbols
in the object program as input to the assembler. A consequence is that
FORTRAN source program symbols (names) and the symbols which are part of
the compi led object program ordinari Iy differ. For example:

1=2
generates the code
LAC (2
DAC I.
hence the variables name I must be referenced as I. if it occurs in a line of S
coding.
The conventions established for symbols insure that all symbols which appear in the FORTRAN
object program contain a period except those which are machine language instructions, mnemonics, assembler pseudo instructions, FORTRAN object-time system references or six-character symbols from the
source program. To avoid conflicts, the following six-character symbols should not appear in the FORTRAN source program:
DECIMA
ANALEX
NOSYMB
EXTERN
EXPUNG
FIODEC
NOINPU
NINDIG

VARIAB
LIBFRM
PUNDEF
TELETY
SYMBOL
INTERN
NARITH
LOGCOM

2-46

SECPRG
MODSET
MODRES
EFMTEM
EXTADD
EARITH
SARITH
SIXDIG

PDP-9 FORTRAN II

5.3.2.2

Floating-Point Commands - Instructions generated by the FORTRAN compi ler may use fixed-

or floating-point operands. Standard machine instructions, i.e., directly executable instructions, are
generated when the operands are fixed point. When the operands are floating point (rea I), the instructions
generated must be interpreted since the PDP-9 does not have such instructions in its instruction set.
The floating-point interpreting program is an integral part of the FORTRAN object-time system.
It is entered by the pseudo instruction EFM (enter floating mode) which initializes the interpretive program
counter. Instructions are interpreted and executed sequentia IIy unti I a transfer of program control (subprogram call) or the pseudo instruction LFM (leave floating mode) is encountered. The compiler generates
an EFM or LFM for each executable statement number to insure that a" internal program trolnsfers are in
the proper arithmetic mode. EFM1s or LFM1s are also generated whenever they are needed; example:

I =1
A= 1.
When the instruction sequence is in floating mode, the following mnemonics, which are the same as the
standard PDP-9 machine instruction mnemonics, are interpreted as floating-mode commands:
LAC
ADD
DAC
JMP
JMS

load floating accumulator
floating add
deposit floating accumu lator
floating jmp
floating jms

In addition, the following mnemonics are used only in the floating interpretive system:
FCS
FSB
FMP
FDV
CAS

floating c lear and subtract
floating subtract
floating multiply
floating divide
floating compare accumu lator to storage

Two instructions which may be generated are:
FXA
FLO

fix the floating accumulator and leave floating mode
float the fixed accumulator and enter floating mode

Notice that FXA carries an implicit LFM and that FLO carries an implicit EFM.
CAL instructions are handled by a program in the object-time system ca lied the CAL Handler.
The CAL Handler saves all relevant information in a push-down stack, and the CAL executes in fixedpoint mode.

5.3.3

Subprogram Linking

5.3.3.1

Implicit Subprogram Calls - An implicit subprogram call occurs when implementoltion of a feature

included in the source language requires an internal subsection of the object time system or use of the
FORTRAN library exponentia I function. An example of the latter case is the generation of a JMS XPN
fixed-point operand or JMS EXP floating-point operand in response to the appearance of the exponentia I
operator (t).

2-47

PDP-9 FORTRAN II

The appearance of an array name in a DIMENSION statement generates an implicit subprogram
call,::>f ,the following form:
NAME,

JMS CALSB
LAW TWO
LAW THREE
LAW INTDIM
.GS

The example above supposes a three-dimensional array. CALSB is the name of the subscript
calclJlating section of the object-time system. TWO and THREE stand for the actual values of the second
'::Jnd third bounds. The initial bound is not needed for subscript calculation but generates storage allocation for the array. INTDIM wi II be 1, 2, or 3 for, respectively, fixed point, 2-word or 3-word floating
poinj". It specifies the number of memory locations required for each array element. The symbol • GS
stands for the generated symbol which actually defines the address of the array. NAME is the actual array
name:. (Refer to Construction of Dimensioned Variables, section 2.2.1). Four additional implicit subprograms which may be called in a FORTRAN object program are:
GOTO
CALST
GTARG
SET2W

5.3.3.2

computed go to
to initia lize the CAL Handler
to get arguments of a subroutine or function
to initia Iize 2-word floating-point data storage

Explicit Subprogram Calls - Explicit subprogram calls are generated by the following features

of the FORTRAN language:
1. A library function reference
2. A CALL statement (subroutine)
3. Reference to a subscripted variable
4. An I/O control statement
The code generated by items 1, 2, and 3 conforms to a general form; the code generated by item 4 is
slightly different and is discussed under I/O statements.
A norma I subprogram ca II generates
CAL A
where A is the name of the subprogram. If the subprogram has arguments (a function must have arguments;
a subroutine mayor may not have arguments; the arguments of a subscripted variable reference are its
subscripts), the CAL instruction is followed by code of the following form:
ARz .GS
where ARz is ARX for fixed-point mode or ARF for floating mode. The argument name of • GS is the
memory location (if floating point, the first of two or three words) .

2-48

PDP-9 FORTRAN II

When passing an array name to a subroutine, subscripts are omitted and the array name appears
as an argument:
ARz NAME.
When the CAL is processed, the CAL Handler saves the mode (fixed- or floating-point), the
corresponding accumu lator, and the return address. It then transfers control to the address indicated in
the CAL instruction. Control is returned to the calling program by means of the return portion of the CAL
Handler which restores the accumulator and mode and transfers control back to the instruction following
the calling sequence.

5.3.3.3

Function Linkage - A function is always used in an arithmetic expression. It acts like a variable

which is equal to the value of the function with the given arguments. When the function nClme occurs to
the left of the equal sign (in the body of the function) the value of the arithmetic expression to the right
of the equal sign is intepreted by the compiler to be the value of the function.
This value is placed in an internal location named RES, and when the return statement is encountered, the address RES returns to the return portion of the CAL Handler. This address is placed in a
location ca lied TEMAD (temporary address storage) interna I to the object-time system I and the va lue of
the function is then accessed indirectly through this location. Shou Id another function ca II occur before
this address is referenced by the calling 'Program, the compiler generates a code to retrieve the previously
ca Icu luted function va lue. Dimensioned variable references are effected through location TEMAD as
though they were functions.
For example, the statement

100

A=SIN (B)+C

generates the following object code:

. 100,

EXTERNAL SIN.
CAL SIN.
ARF B.
LAC I TEMAD
ADD C.
DAC A.

A function definition statement:
FUNCTION FNAME (A, B,I)
generates the following code:
FNAME. ,

A. ,
B"
I.,

INTERNAL FNAME.
JMS GTARG
JMP .GS

o
o
o

.GS,

2-49

PDP-9 FORTRAN II

where .GS is a symbol generated by the FORTRAN compiler. The GTARG routine, when executed, would
plcJce the addresses of the dummy arguments A., B., and I. in the locations reserved for them.
Note the use of pseudo instructions EXTERNAL and INTERNAL. When EXTERNAL is encountered by the assembler, it generates information to the loader, requiring that all references to the accompanying symbol (or symbols since more than one may occur with EXTERNAL) be saved by linking until the
occurrence of a definition of that symbol; this is signaled by the occurrence of INTERNAL and one accompanying symbol (only one symbol may occur with INTERNAL).
For example, consider a factorial calculator function which returns a floating-point value.
FACTORIAL CALCULATOR
FUNCTION FACT(N)
FACT=l
DO 10J=1,N
10
FACT=FACT* J
RETURN
END
The compi ler generates the following code:
FACTORIAL CALCULATOR
DECIMA*
FIODECt
INTERNAL FACT.
JMS GTARG
FACT. ,
JMP .AAA
N.,
0

/GTARG PICKS UP ARZ ADDRESS
/ AND PLACES IT IN N •

. AAA
LAC (1
FLO
DAC RES
LFM
LAC (1
DAC J •
•AAB,
• 10,

LFM
LAC J.
FLO
FMP RES
DAC RES
LFM
LAC J.
ADD (1
DAC J.
CMA
ADD IN.
ADD (l
SMA

/FLOA TING POINT RESULT STORED IN RES

* DECIMA indicates that all subsequent numbers will be interpreted in decimal radix rather than in octal
radix.
tFIODEC indicates that all character translations are to FIODEC code; i.e., H-format in format statements •
....

2-50

PDP-9 FORTRAN II

JMP .AAB
LAW RES
RETUR
HLT

/ ADDRESS OF RES IS RETURNED

TEM,
TEM+O/
START
5.3.3.4

Subroutine Linkage - The code generated by the control word ·SUBROUTINE is very simi lar.

Since a subroutine need not return a value, the user must establish storage for results either by passing the
argument(s) to the subroutine in the ca II statement or by establ ishing them in a common statement.
The following is a possible version of the factorial calculator written as a subroutine:
FACTORIAL CALCULATOR
SU BROUTINE FACT (N, R)
R=l
DO 10 J=l, N
10
R=R*J
RETURN
END
where R contains factorial N in floating point.
The compi ler generates the following code:
FACTORIAL CALCULATOR
DECIMA
FIODEC
INTERNAL FACT.
FACT. ,
JMS GTARG
JMP .AAA
o
N. ,
o
R. ,
.AAA
LAC (1
FLO
DAC I R.
LFM
LAC (1
DAC J •
. AAB,
.10

LFM
LAC J.
FLO
FMP I R.
DAC I R.
LFM
LAC J.
ADD (1
DAC J.

2-51

PDP-9 FORTRAN II

CMA
ADD I N.
ADD (1
SMA
JMP .AAB
RETUR
HLT
TEM
TEM+O/
START

5.3.4

Construction of Dimensioned Variables
When dimensioned variable references occur in the FORTRAN source language, the code gen-

erated is very similar to that generated by a function call. A DIMENSION statement generates an internal
function which has "the name of the variable. When the function is called, its value is the address of the
element of the array specified by the vlaues of the subscripts at the time of the call, and that address is
placed in location TEMAD. For example, the statement

Z=A(I)
generates the objec·t code
CALA.
ARX I.
EFM
LAC I TEMAD
DAC Z.
On the other hand, the statement

A{I)=Z
generates the object code
CALA.
ARX I.
EFM
LAC Z.
DAC I TEMAD

5.3.5

Allocation of Array Storage and the Subscript Calculator
A simple example of array storage allocation is the two-dimensional array A(2,2). A two-

dimensional array is stored sequentially by rows indexed by columns (in this case):

A(l,l)
A(l,2)
A{2,1)
A{2,2)

2-52

PDP-9 FORTRAN II

or in general, an n-dimensional array is stored with the first dimension varying least. The standard objecttime system subscript calculation program accommodates up to four dimensions.

Higher dimensions may be

provided for upon request.

5.3.6

I/O Statements
An VO statement of the general form
RW n,m,a,b,i

generates the following code
RW
JMS .IOX

N
FOR .M
ARF A.
ARF B.
ARX I.
ENDIO
where RW is READ or WRITE, . lOX designates the corresponding I/O device processor. X may be 1-9,
.101 is keyboard input, .107 corresponds to ASCII line printer output etc.; devices 5,6,8, and 9 are
presently unassigned.

(N is the device number (n)), and the next location designates the address (.M)

of the accompanying format statement. Succeeding entries contain the addresses (A., B., I.) of' the
referenced variables (a, b, i). Code generated by an array transfer expression is fairly complicated
but sim ilar to the code generated by an expl ic it DO loop. EN 010 is the address of that section of the
object-time system which terminates I/O operations.

Note that Hollerith text is stored with the object

program code sequence generated by the corresponding FORMAT statement.

2-53

PDP-9 FORTRAN II

CHAPTER 6
OPERATING PROCEDURES

This chapter details standard operating procedures for the PDP-9 FORTRAN II system. PDP-9
FORTRAN II is written for a machine having at least 8K of memory and an exclusively paper-tape conlocations are available f~r program and data.
10
The principal subsections of the FORTRAN system for paper tape are:

figuration. In an 8Ksystem approximately 460°

Compiler
Assembler
Operat i ng System
I/O Library
Six Decimal Digit Arithmetic Library
Nine Decimal Digit Arithmetic Library
The compiler accepts input in the FORTRAN language and produces an object program output
in computer source language acceptable to the assembler. The assembler accepts the compiler output
and produces a binary relocatable version of the program and a binary version of the Linking Loader.
When the user is ready to run the program, he loads the main program and any subprograms followed by
any built-in functions called from the library. Once the total program is in memory, he loads the operating system and executes the program. The operating system contains an interpreter for floating-point
arithmetic, an interpreter for FORMAT statements, red tape routines such as fix a floating number and
vice versa, and the I/O routines. The operating system must be in memory when a FORTRAN program
is executed.

6.1

PROCEDURE FOR USING FORTRAN WITH A PDP-9 PAPER TAPE SYSTEM
The Bootstrap Loader with starting address 177708 (for 8K machines) is called the readin mode,

or RIM, Loader. Pressing the START switch on the console with 177708 in the ADDRESS switche.s is
referred to as RIM start.
Step 1

Prepare programs to be compiled in accordance with the conventions described
in the preceding section. Each program or subprogram on paper tape must be
followed by "the three-character sequence
carriage return-I ine feed
carriage return-I ine feed
form feed

2-55

PDP-9 FORTRAN II

Step 2

Place the paper tape labeled FORTRAN Compiler in the reader, set ADDRESS
switches to 17770 , and press START.
8

Step 3

Position ACCUMULATOR switches 9 and 10 as follows to indicate tape formats
for, respectivel y, the intermediate object program (assembler source) tape and
the compiler source tape: AC9 (intermediate object tape) - up for ASCII, down
for FIODEC. AC10 (compiler source) - up for ASCII, down for FIODEC. Turn
on the tape punch. Place the program tape to be compiled in the reader and
press CONTINUE. FORTRAN punches out the intermediate object program tape.

Step 4

If other programs are to be compiled, repeat step 3. However, if more than one
program is on a single tape, the tape must be pull ed back before restarting, since
it will have read past the END statement into the next program. If an accidental
error occurs at any ti me, the compi lation procedure may be restarted by replac ing
the source tape in the reader, placing 228 in the ADDRESS switches, and depressing START. If the punch runs out of paper tape, the machine halts with all 1s in
the AC. Refill the punch and press CONTINUE to proceed with the compilation;
then t he two tapes can be sp Ii ced together.

Step 5

If an error occurs in the source language, the compiler types a three-letter plus
two-digit code on the teleprinter followed by the current (last encountered) statement number. The compiler also prints the offending line with the errant character flagged by a line feed. See chapter 8 for the associated error conditions.
As a rule, a source language error prevents proper execution of the compiled
program. The error must be corrected and the program compiled again. However,
compilation should be completed to uncover all errors in the same program.

Step 6

When all necessary compilations have been successfully completed, remove the
output tape(s} from the punch.

Step 7

Place the pap.er tape labeled FORTRAN Assembler in the reader, set ADDRESS
switches to 177708' and depress START. Set ACCUMULATOR switch 10 as
follows: up if the assembler source tape is ASC IIi down if it is FIODEC.

NOTE: The setting of AC1 0 should be identical to the setting of AC9 in
step 3, above.

Step 8

Place the first program to be assembled in the reader. If several programs were
compiled together, they will be separated from each other by a short length of

2-56

PDP-9 FORTRAN II

blank tape. The punch must be on. Depress CONTINUE. The assembler punches
a partial binary output, displaying all ACCUMULATOR lights on when it is finished. Should an error occur during the assembly procedure, the assembler prints
a message on the teleprinter. For a summary see chapter 8.
Step 9

Depress CONTINUE to finish punching the binary output. Undefined symbols in
the source program (symbols which never appear on the left-hand side of an arithmetic statement, in an input statement or as the argument of a subroutine call, or
in a COMMON statement) are printed with a relative location automatically
assigned by the assembler.· Any statement number which is referred to but never
used as a statement label will be printed also. When finished, all ACCUMULATOR

I ights wi II again be on.
Step 10

If a printout of the relative locations of program symbols (ordered alphanumerically
by symbols) is desired, put the rightmost switch of the ACCUMULATOR switches
(bits 17) to the up position and press CONTINUE. With AC switch 16 up, pressing
CONTINUE produces a listing ordered numerically by location counter. If the
printout is not desired, leave the switch in the down position and press CONTINUE
to restore the assembler for the next assembly. The ACCUMULATOR lights wi" a"
be off at this stage. If AC switch 11 is in the up position (on), listing wi II be done
at the line printer.

Step 11

If more programs are to be assembled, place the next tape in the reader (lnd return
to step 8. If several programs were compiled together, be sure that the blank tape
area separating them is under the reader I ight before continuing. Since the assembler uses a buffered loader, the end of one program and the beginning of the next
program are likely to be read into the same buffer. It is usually necessary to withdraw a portion of tape which has already been read in order to start reading at the
beginning of the second and succeeding programs on the same paper tape.

Step 12

Remove the assembled programs from the punch. Each program will have its title
punched in readable format at the beginn ing. Since the FORTRAN Assembler is a
one-pass assembler, the title will be the last item punched on the tape.

NOTE: The following steps describe the loading process. After each tape is
loaded into memory the ACCUMULATOR I ights display the first memory address not used.
Step 13

Load the main program through RIM start. It is important that the main program
be loaded first since the Linking Loader is punched on the main program tape

2-57

PDP-9 FORTRAN II

only. The loader is a lengthy strip of tape immediately following the title with
the eighth hole punched in every line. The RIM Loader, through use of a Bootstrap Routine, loads the Linking Loader which, in turn, loads the main program.
Step 14

Place any subprograms in the reader (readable title is always in the leader)' and
load through RIM start. The Linking Loader handles the problems of I inking
between programs. The first instruction executed by the RIM Loader is a jump
to an entry in the Linking Loader.

Step 15

To obtain a printout of the absol ute locations in memory of subprogram symbols
and/or to determine if I ibrary subroutines are required, place 58 in the ADDRESS
switches and depress START. If a subroutine or library function has been called
but not yet loaded, its symbol will be preceded on the I ine by a minus sign
followed by the address of the first reference to th is symbol. If further subprograms are needed, they should be loaded as in step 14.

Step 16

Load the Library I/O tape; i.e., place the I ibrary tape in the reader, place
58 in the ADDRESS switches and depress START. If any subroutine names are
preceded by II -

,II

load the 6DD or 9DD Library tape Ii. e., set ADDRESS

switches to 6 and depress START. When all called functions have been loaded,

the loader halts, perhaps part way through the I ibrary tape.
Step 17

Load the tape labeled "FORTRAN Operating System ll through RIM start. If
paper tape input to the FORTRAN program is used, th is should be ready in the
reader. AC switches 9 and 10 must be set (up position) to indicate ASCII objecttime output and input, respectively-.

Step 18

Place 228 in the ADDRESS switches and depress START to execute the program.

NOTE: The Linking Loader does not detect when the user has loaded a program over common storage (assigned backward from the last address in memory).
To guarantee that an overlay has not occurred, the first program address not
used as indicated in the AC I ights after loading should always be equal to or
smaller than the lowest address in common st9rage necessary to store the arrays
and common variables used in the program.

General Notes:
a. The first word of every FORTRAN program (main or subroutine) has a relative address
of 1 •
8
b. The initial relocation constant is 21 8 •
2-58

PDP-9 FORTRAN II

c. After each program is loaded, the AC Iights display the address of the next free location.
This address is also the relocation of the next program to be loaded. (One location is unused
between programs.)

2-59

PDP-9 FORTRAN II

CHAPTER 7
DIAGNOSTICS

The following diagnostics may be printed during compilations followed by the offending statement with a I ine feed after the last character processed. Each diagnostic is identified by a three-letter
name, and a two-digit number. For all errors except those which indicate storage capacity exceeded,
processing continues. The diagnostic error print (below) is followed by the current statement number.
As previously noted the occurrence of an error necessitates correction of the error and recompilation.

Error
Name

Error
Number

CON

Reason for Error

CONTROL STATEMENT
Illegal control statement.

2
COM

Upper case charac ter in contro I statement.
COMMON STATEMENT
Illegal entry in list.

2
ASG

Symbol appears twice in COMMON.
ASSIGN

N not a fixed-point number.

Number not followed by litO. II

No fixed-point variable.

Illegal format - variable.

SUB

SUBROUTINE AND FUNCTION

Name not a variable.

Dummy symbol not a variable.

Dummy symbol used twice.

DIM

DIMENSION
Array name not a variable.

Array dimensioned twice.

Dimension not a fixed-point number.

2-61

PDP-9 FORTRAN II

Error
Name

Error
Number

Reason for Error
:;

DO STATEMENT

First two letters not DO.

No statement number.

No end test value specified.

Too many characters.

ILF

ILLE GAL FORMAT
Nonstatement number at left margin.

Missing left parenthesis.

Missing right parenthesis.

Missing left parenthesis.

Missing right parenthesis.

Comma missing in GOTO.

Variable missing in arithmetic statements.

Illegal device number in input or output statement.

Illegal format in accept statement.

Extra right parenthesis.

Extra characters in statement.

Comma missing in repetitive element in I/O list.

Illegal format in I/O I ist element.

Illegal format statement number in an I/O statement.

ICH

ILLEGAL CHARACTER
Illegal character.

Illegal upper-case character.

No more characters after an illegal one.

DIT

Miscellaneous errors. Cannot proceed.
Logi c error.

Wrong place in table.

Dispatch number too big.

Too many CALS.

Illegal CAL.

Too many exits.

If any of the errors labeled DIT occurs, correct all other errors and recompile; if DIT
errors sti II occur, note any pertinent data and send to DEC Programm ing Group.

2-62

PDP-9 FORTRAN II

Error
Name

Error
Number

Reason for Error

UNSEEN FIXED POINT

UFX

Fixed-point number expected; punctuation
character or no character appeared.
2

Floating-point quantity appeared where fixed-pqint number expected.

Fixed-point number expected; decimal number
appeared.
FORMAT STATEMENT

FOR

Character missing.
2

III ega I format.

Characters missing.

Illegal control character.

Illegal punctuation.

Spec ification letter other than I, F, E, X, H .

N too large in H format.
ILLEGAL FUNCTION USAGE

IFU

Function name on left side outside function
definition.
STORAGE CAPACITY EXCEEDED

SCE

Processing may not proceed.
Pol ish stack exhausted.
2

Table exceeded.

Symbol generator exhausted.

Table exceeded.

Statement too long.

Push down stack exceeded (too many nested DOS).

2-63

PDP-9 FORTRAN II

CHAPTER 8
ERROR MESSAGES

8. 1

ERROR MESSAGES (FORTRAN ASSEMBLER)
The following error messages refer to the object program code generated by the compi ler.

Famil iarity with this code is necessary for an understanding of this chapter. See the PDP-9 Symbol ic
Assembler program description for details.
With the exception of SCE (storage capacity exceeded) and ILP (illegal parity), assembly
continues after the error message has been printed unless assembling a library tape. An error message
may occur in one of three formats.

8.1.1

Format A
ERROR

PREVIOUS VALUE

SYMBOL

NEW VALUE

Format A indicates errors in the redefinition of symbols. ERROR represents a three-letter code for the
particular error. Whether the symbol was redefined depends upon the particular error.

8.1.2

Error

Meaning

MDT

The symbol was redefined with a comma.

RPS

A permanent symbol was redefined ..

RDA

An attempt to redefine a symbol was made.
The symbol was not redefined.

Format B
ERROR

OCTAL ADDRESS

SYMBOLIC ADDRESS

The general error message is printed in format B. It includes both the octal address and the! symbolic
address at which the error occurred.
Error

Meaning

IFP

Illegal format in parameter assignment.

IFC

Illegal format in a symbolic address tag.

IFQ

Illegal format in library list.

IFY

Illegal format in internal declaration.

IFZ

More than one symbol in internal declaration.

Illegal term punctuation in I ibrary list.

2-65

PDP-9 FORTRAN II

Mean ing

Error

8.,1.3

MDT

The location counter and address disagree in an
address assignment.

TUA

Too many undefined symbols in a symbol ic address
tag.

ILF

Illegal format in a pseudo instruction

LIT

Illegal terminator in a PUNDEF or EXTERNAL list.

IFL

Illegal format in a PUNDEF or EXTERNAL list.

IFS

Illegal format in a START.

IFI

Illegal format in an input pseudo instruction.

SCE

Storage capacity exceeded.

INS

A nonsymbol appeared in a PUNDEF list.

IFX

External symbol preceeded external declaration.

Format C
ERROR

OCTAL ADDRESS

SYMBOLIC ADDRESS

CAUSE

Fe>rmat C is an expanded version of Format B. CAUSE is additional information to help the programmer
ascertain the cause of the error. For example, in the case of an error caused by an undefined symbol,
the symbol will be printed.

8.1 .4

Error

Cause

Meaning

ILP

character

Illegal parity (place correct character in ACS and press
CONTINUE). May also be caused by reading tape in
backward order.

UST

symbol

Undefined symbol in a START or PAUSE.

UAA

symbol

Undefined symbol in an absolute address assignment.

.UPA

symbol

Undefined symbol in a parameter assignment.

ICH

character

III ega I character.

SYS

symbol

Previously defined symbol in internal declaration.

UPN

symbol

Undefined symbol in a punch pseudo instruction.

Undefined Symbol Assignment
At the end of assembly before the loader is punched, the undefined symbols and their defini··

tions are printed. Each undefined symbol used in a storage word will be defined as the address of a
rE~gister at the end of the program, and the definition printed.

If the symbol was not used in a storage

word, the symbol is printed and not defined. An example of the latter is a symbol which appears to the
right in a parameter assignment only.

2-66

PDP-9 FORTRAN II

8.1.5

Error Messages from the Linking loader
Error

8.1 .6

Mean ing

CSE

Data Block had checksum error.

SCE

Storage capacity exceeded. Program will load into the
loader's symbol table if allowed.

ASE

Assembly error. Tape is in error or failed to read properly.

lMR

Assemb Iy error in library format. Tape is in error or fa i led
to read properly.

Error Halts in the FORTRAN Object Time System
The following entries refer to the OTS itself which is always in core at run time.
PC

Symbolic

Meaning

12725

CHECK-1

Illegal device number in I/O call.

14423

EFMEND

An illegal interpretive.

15553

TOOCAl

Too many CAlS. Program error, implies
CAL entry but no exit.

NOTE: If the computer appears to hand up in a loop in either of the
following areas:

14324 H. , 13753 ff
an arithmetic error is the probable cause. (Division by zero, log
(-0 etc .). The apparent hang-up is not real. The program will
eventually resume.

2-67

PDP-9 FORTRAN II

CHAPTER 9
PDP-9 FORTRAN II OPERATING TEST

9. 1

INTRODUCTION
This program, while not an exhaustive test of the DEC FORTRAN II System, uses most of the

algebraic and control features of the language. If a user can compile, assemble, load, and then run
this test successfully, it indicates that both the FORTRAN System and the PDP-9 are operating satisfactorily.

9.2

PRELIMINARY REQUIREMENTS

9.2. 1

Storage
The program uses locations 22-5420 for itself and its two subroutines, plus space for the

following FORTRAN requirements: SARITH, NARITH, or EARITHi 102; all of the FORTRAN arithmetic
library (SQRTF, SINF, COSF, ATANF, LOGF .• CLOGF, EXPF, ABSF, and SABSF)i and finally, the
Object Time System.

9.2.2

Subprograms and/or Subroutines
The program consists of the Main Test, a Test Subroutine, and a Test Function, meant to be

run with the FORTRAN Object Time System.

9.2.3

Equipment
8K PDP-9
Paper Tape Reader

A Type 33, or 35 Teletype

9.3

LOADING OR CALLING PROCEDURE

9.3.1

Loading
The original FORTRAN symbolic tapes should be used for the test. In the procedure that

follows, the RIM Loader is assumed in core, and all FORTRAN tapes are part of the FORTRAN System.

Order No: DEC-9B-QFl A-D
2-69

PDP-9 FORTRAN II

a. Place the FORTRAN compi ler in the reader, 17770 in the ADDRESS switches, and
press START.
b. When the compiler has been read in, place FORTRAN symbolic tape 1 of 3 (the first subroutine)
in the reader, set ACCUMULATORswitches9and 10toa 1 (ASCII input),andpressCONTINUE.
c. When the compiler stops with all AC I ights on, it has finished punching the assembly
version of the first subroutine. There is no typeout in an error-free compilation. Manually
punch out one fanfold of tape leader, place FORTRAN symbol ic tape 2 of 3 in the reader,
and press CONTINUE to compile the second subroutine. When the computer stops, place
FORTRAN symbol ic tape 3 of 3 in the reader, manually punch one fanfold of tape leader,
and press CONTINUE.
d. When punching stops, remove the three programs from the punch, place the FORTRAN
assembler in the reader, and press START.
e. When the assembler has read in, insert the tape just punched in the reader, and press
CONTINUE.
f. When the assembler stops with all AC lights on, press CONTINUE to finish assembly of
the first subroutine. The only typeout should consist of the title of the tape and a few
carriage returns. The same applies to the additional assemblies to be done below. When
the assembler stops a second time with all AC lights on, press CONTINUE to reinitialize:
the assembler.
g. When the assembler stops with all AC I ights off, it has finished punching the binary
version of the first subroutine. Since the paper tape may be positioned past the beginning
of the second subroutine (the assembler reads until a buffer is filled or a stop code is
reached without reference to the end of each subprogram), move it back to the leader
preceding the second subroutine and press CONTINUE.
h. When the assembler halts with all AC lights on, press CONTINUE to finish assembly of
the second subroutine. When the assembler stops a second time with al I AC lights on, press
CONTINUE to reinitialize the assembler.
i. When the assembler halts with all AC lights off, it has finished punching the binary
version of the second subroutine. Position the paper tape at the beginning of the main
program, and press CONTINUE to assemble the main program.

i. When the assembler stops with all AC lights on, press CONTINUE to finish assembly of
the main program. When the assembler stops a second time with all AC lights on, remove the
binary tape from the paper tape punch.
2-70

PDP-9 FORTRAN II

k. The front of the binary tape is the last item punched. A title is punched on the tape
at the end which should say TEST. Place the binary tape in the reader and press START.

I. The tape stops after the main program has loaded. Press START to read, in the first
subroutine and start again for the second subroutine.
m. The tape stops after the second subroutine has loaded. Place the FORTRAN I/O library
in the reader, 00006 in the ADDRESS switches, and press START.
n. When the tape runs out of the reader, press STOP and then EXAMIN E to c Iear a read
select; place the FORTRAN arithmetic library (6- or 9-digit accuracy) in the reader, and
press START.
o. When the tape stops, place 00005 in the ADDRESS switches, and press START to get a
memory map on the Teletype. If no names are preceded by a minus sign, loading was
successfu I.
p. Place the FORTRAN Object Time System (OTS) in the reader, 17770 in the ADDRESS
switches, and press START.

q. When the OTS has loaded, the program is ready to begin. Place 00022 in the ADDRESS
switches, clear the ACCUMULATOR switches, and press START.

9.3.2

Switch Settings
During run time, if the program detects an error, it types out a message and re-executes

the bad code. Setting AC switch bit 0 to a 1 suppresses re-execution of bad code and causes the
program to proceed. All switches should be set to 0 when starting.

9.4

USING THE PROGRAM
The program is started or restarted by placing 00022 in the ADDRESS switches and pressing

START. The program types out a set of tautologies (truth statements), calculates, and types out END
OF TEST. Any departure from this procedure is an error.

9.4.1

Errors in Usage
Although the user cannot initiate any errors himself, the program attempts to detec:t any

irregularities in its own execution. If it finds any, it writes an error message and (unless AC switch

o is set) re-executes the faulty code. An error is indicated if one of the tautologies is false 4Jr if one
of the following messages is typed.

2-71

PDP-9 FORTRAN II

BAD GOTO, DRAGON FLY = nnnn
BAD ARRAY, INDXS = nnnn
BAD DO LOOP, NUM = nnnn
BAD FUNCTION VALUE = nnnn
BAD SUBROUTINE RETURN, VALUE = nnnn
where:
The first message means that in a series of different kinds of IF statements and GOTO statements, one failed, and the variable DRAGONFLY was the wrong value in the wrong place.
The second message means that a number placed in the IN DXS"';th position in an array was
not there when it was requested later.
The third message means that a series of nested DO LOOPS was not executed in the predeterm i ned number of times.
The last two messages indicate that the test function and/or the test subroutine returned
unexpected values.

9.4.2

Recovery from Such Errors
Any error indicates that either the computer is not functioning correctly or that an incorrect

or obsolete version of the compiler or assembler has been used.

9. S

DETAILS OF OPERATION AN D STORAGE
The usefulness of the test I ies in the fact that the program has been compiled, assembled,

run previously, and, therefore, should run again without errors. It uses the five basic operations in
fixed and floating point, the nine I ibrary functions, the IF statement, nested and non-nested DO loops,
four different formats of GOTO statements, the ASSIGN statement, comments, CONTINUE, CALL,
RETURN, SUBROUTINE, FUNCTION, and STOP.

9.S.1

Examples and/or Applications
The test should be used when there is doubt of the reliability of the hardware or software

systems. If the test compiles, assembles, loads, and runs without an error, the computer and compiler
can be presumed to be in correct working condition. The output from a successful run should appear
as follows:

2··72

PDP-9 FORTRAN II

SQRTF
SINF

( 4.00000) =
( 1.57079)

2.00000
.99999

COSF

( 3. 14159)

-.99999

4.0*ATANF
LOGF
CLOGF
EXPF
ABSF
4.00000
4.00000
4.00000
4.00000
4.00000

( 1 .00000)
( 1.00000)
( 1 .00000)
( .00000)
(-1 .00000)
+2.00000
-2.00000
*2.00000
/2.00000
t2.00000

3. 14159
.16138-09
.70089-10
1.00000
1 .00000
6.00000
2.00000
8.00000
2.00000
16.00000

XABSF
4+
44*
4/
4t

-1 )
2
2
2
2
2

1
6
2
8
2
16

END OF TEST.

2-73

(1 .00000 if using 9-digit
subroutines
(-1 .00000 if using 9-digit
subroutines

(15.99999 if using 9-digit
subroutines)

PDP-9 FORTRAN II

APPENDIX 1
CHARACTER CODE EQUIVALENCES

The two test handling modes (A, H) use character code sets for which the octal E~quivalents
differ in some respects for the two formats. Under A format, characters are stored in a 6-bit, 64character code called "line printer FIODEC. II Under H format, characters are stored in a code called
flexowriter FIODEC, which includes a case shift, indicated by u in the table. The upper-case escape
code is 74; the return code, 72.
When providing a dummy string of text for a READ Hollerith operation, the user must remember
that the code is compiled directly into the format control I ist. This requires that the number of core
locations occupied by the dummy text correspond exactly to the test read in at run time. Since this
may vary in content, the following rules are necessary:
1. The dummy string and the input string must be the same length.
2. Corresponding characters in each string must agree in case; i. e., both the characters
in the dummy string and the character in the input string must be from the set which is
flagged by a u or both be from the set which is not flagged.

NOTE: If a character equivalence is indicated by NA in the table, the
character is not available for use in the indicated format. On the model
33, a shift with the letters M, L, K produces the characters 1, \, [
respectively.

TABLE 5 CORE REPRESENTATIONS OF
THE ASCII CHARACTERS, A AND H FORMATSt
IAI

Format

IHI

Character

ASCII

Space

240

241

242

243

244

0/0

245

Format
0

56
u

40
NA

tThis table applies when typing a FORTRAN program either off-line or using the Symbolic Tape Editor.

2-75

PDP-9 FORTRAN II

TABLE 5 CORE REPRESENTATIONS OF
THE ASCII CHARACTERS, A AND H FORMATSt (continued)
IAI

IHI

Character

ASCII

246

247

250

251

252

253

254

255

256

54.
73

257

260

261

262

263

264

265

266

267

270

271

272

273

274

275

276

277

300

301

302

303

304

*
+

Format

Format
NA

tThis table applies when typing a FORTRAN program either off-I ine or using the Symbol ic Tape Editor.

2-76

PDP-9 FORTRAN II

TABLE 5 CORE REPRESENTATIONS OF
THE ASCII CHARACTERS, A AND H FORMATSt (continued)
IAI

IHI

Character

ASCII

305

306

307

Format

?S--

310

311

312

313

314

315

316

317

320

321

322

323

324

325

326

327

330

331

332

333

-T7,

334

.76··

carr iage return

~~tu.:(

.K"" , . . . ",.

~ .. P

336

~
'-3~ .

337

211

215

tThis table appl ies when typing a FORTRAN program either off-I ine or using the Symbol ic Tape Editor.

2-77

.....

335

tab

Page Missing From Original
Document

DIGITAL EQUIPMENT CORPORATION. MAYNARD. MASSACHUSETTS
Printed in U.S.A.