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1968

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Document:	FORTRAN IV Part \|. Language Part II. Object Time System Part Ill. Science Library ADVANCED SOFTWARE SYSTEM Programmer’'s Reference Manual Direct comments concerning this manual to Software Quality Control, Maynarc, Mass. }>
Order Number:	DEC-9A-AF4B-D
Revision:
Pages:	100
Original Filename:	http://bitsavers.org/pdf/dec/pdp9/DEC-9A-AF4B-D_FORTRANIV_1968.pdf

OCR Text

FORTRAN IV
Part I.

Language

Part II.

Object Time System

Part III. Science Library
ADVANCED SOFTWARE SYSTEM
Programmer's Reference Manual

I o r d e r No. DEC-9A-AF4B-D from Program Library, Maynard, Mass. Price: $2.50

~ct comments concerning this manual to Software Quality Control, Maynard, Mass.
DIGITAL EQUIPMENT CORPORATION. MAYNARD. MASSACHUSETTS

PREFACE

This manual describes the FORTRAN IV language and compiler system for the PDP-9 computer.

It provides the user with the necessary information for writing FORTRAN programs for compila-

tion and execution with the PDP-9 Advanced Software System. The manual is divided into three parts:
Basic FORTRAN Language (Part I), FORTRAN Object Time System (Part II), and the FORTRAN Science
Library (Part I II) .
Part I, Basic FORTRAN IV Language, is divided into chapters as follows:
Chapter 1 .

Introduction

Chapter 2.

Elements of the FORTRAN Language

Chapter 3.

Arithmetic Statements

Chapter 4.

Control Statements

Chapter 5.

Input/Output Statements

Chapter 6.

Specification Statements

Chapter 7.

Subprograms

Part I is intendeq to familiarize the user with specific PDP-9 FORTRAN coding procedures.
Several excellent texts are available for a more elementary approach to FORTRAN programming.

Guide to FORTRAN IV Programming, II by Daniel D. McCracken (published by John Wiley and Sons,
Inc.) is recommended.
Part I I, FORTRAN IV Object Time System, describes the group of subprograms that process
compi led FORTRAN statements, parti cu larly I/O statements, at execution time.
Part ",, PDP-9 Science Library, provides deta iled descriptions of the intrinsi c functions,
external functions, subfunctions, and arithmetic routines in the PDP-9 Science Library.
PDP-9 FORTRAN IV is essentially the language specified by the United States of America
Standards Institute (X3.9 - 1966) with the exceptions noted in Appendix 2 at the end of Pari' I of this
manual.

PDP-9 FORTRAN IV

CONTENTS

PART I
CHAPTER 1
INTRODUCTION
1.1

FORTRAN

1-1

1.2

Source Program Format

1-1

1 .2. 1

Card Format (I BM Model 029 Keypunch Codes)

1-2

1 .2.2

Paper Tape Format

1-2CHAPTER 2
ELEMENTS OF THE FORTRAN LANGUAGE

2. 1

Constants

1-5

2. 1 . 1

Integer Constants

1-5

2.1.2

Rea I Constants

1-5

2.1 .3

Double-Precision Constants

1-6

2.1.4

Log i ca I Consta nts

1-6

2.1.5

Hollerith Constants

1-7

2.2

Variables

1-7

2.2. 1

Variable Types

1-7

2.2.2

Integer Variables

1-7

2.2.3

Real Variables

1-8

2.2.4

Double-Precision and Logical Variables

1-8

2.3

Arrays and Subscripts

1-8

2.3.1

Arrangement of Arrays in Storage

1-8

2.3.2

Subscript Expressions

1-9

2.3.3

Subscripted Variables

1-9

2.4

Express ions

1-9

2.4.1

Arithmetic Expressions

1-9

2.4.2

Relational Expressions

1-11

2.4.3

Log i ca I Expressions

1-12

2.5

Statements

1-13
CHAPTER 3
ARITHMETIC STATEMENTS

iii

1-14

PDP-9 FORTRAN IV

CONTENTS (Cont)

~~
CHAPTER 4
CONTROL STATEMENTS
4.1

Unconditional GO TO Statements

1-17

4.2

ASSIGN Statement

1-17

4.3

Assigned GO TO Statement

1-17

4.4

Computed GO TO Statement

1-18

4.5

Arithmetic IF Statement

1-18

4.6

Logical IF Statement

1-18

4.7

DO Statement

1-19

4.8

CONTI NUE Statement

1-21

4.9

PAUSE Statement

1-21

4.10

STOP Statement

1-21

4.11

END Statement

1-21
CHAPTER 5
INPUT/OUTPUT STATEMENTS

Genera I I/O Statements

1-24

Input/Output Argument Lists

1-24

5.1.2

READ Statement

1-24

5. 1 .3

WRITE Statement

1-25

5.2

FORMA T Statements

1-26

5.2.1

Specifying FORMAT

1-26

5.2.2

Conversion of Numeric Data

1-28

5.2.3

P-Scale Factor

1-30

5.2.4

Conversion of Alphanumeric Data

1-31

5.2.5

Logical Fields, L Conversion

1-31

5.2.6

Blank Fields, X Conversion

1-31

5.2.7

FORTRAN Statements Read in at Object Time

1-32

5.2.8

Printing of a Formatted Record

1-32

5.3

Auxi I iary I/O Statements

1-33

5.3.1

BACKSPACE Statement

1-33

5.3.2

REWI ND Statement

1-33

5.3.3

EN DF ILE Statement

1-33

5. 1
.. 5. 1 . 1

PDP-9 FORTRAN IV

CONTENTS (Cont)

CHAPTER 6
SPECIFICATION STATEMENTS
6.1

TYPE Statements

1-35

6.2

DIMENSION Statement

1-35

6.3

COMMON Statement

1-36

6.4

EQUIVALENCE Statement

1-37

6.5

EXTERNAL Statement

1-37

6.6

DATA Statement

1-38

CHAPTER 7
SUBPROGRAMS
7. 1

Statement Functions

1-39

7.2

Intrinsic or Library Functions

1-40

7.3

External Functions

1-42

7.4

Subroutines

1-44

7.5

Block Data Subprogram

1-45

7.5.1

Example of BLOCK DATA Subprogram

1-45

APPENDIX 1
SUMMARY OF PDP-9 FORTRAN IV STATEMENTS

1-47

APPENDIX 2
A NOTE ON PDP-9 FORTRAN IV

1-49

APPENDIX 3
FORTRAN IV AND MACRO-9 LIN KAGE

I-51

APPENDIX 4
CHAINING FORTRAN IV PROGRAMS

I-53

APPENDIX 5
FORTRAN IV ERROR LIST

I-55

ILLUSTRATION
1-1

1-3

TABLES
1-1

Intrinsic Functions

1-41

1-2

External Functions

1-43

PDP-9 FORTRAN IV

CONTENTS
Page _
PART II
FORTRAN IV OBJECT - TIME SYSTEM
11-1

Introduction
OTS Binary Coded Input/Output

11-3

OTS Binary Input/Output

11-6

OTS Auxi Iiary Input/Output

11-8

OTS lOPS Communication

11-10

OTS Calculate Array Element Address

11-12

OTS Computed GOTO

11-14

OTS Stop

11-15

OTS Pause

11-16

OTS Octal Print

11-17

OTS Errors

11-18

File Commands

11-19

TABLE
Page
II-1

ors Errors

111-1

PDP-9 Science Library

II-2
111-5

PART III
PDP-9 SCIENCE LIBRARY

111-1

Introduction
Intrinsic Functions

111-1

Externa I Functions

111-1

External Functions

111-1

Sub-Functions

111-1

The Arithmeti c Package

111-1

Accumulators

111-2

A-Register

111-2

Floa'ting Accumulator

111-2

Held Accumulator

111-3

Co II ing Sequences

111-3
111-15

PDP-9 Science Library Algorithm Descriptions

PDP-9 FORTRAN IV

CHAPTER 1
INTRODUCTION

1.1

FORTRAN
Each type of digital computer is designed to respond to certain machine language codes.

The codes are different for each type of computer. FORTRAN makes it unnecessary for the scientist or
eng ineer to learn the machine language for specifi c computers. Using FORTRAN, he can write programs in a simple language that adapts easily to scientific usage. The FORTRAN language is composed
of mathematical-like statements, constructed in accordance with precisely formulated rules. A
FORTRAN program consists of meaningful sequences of FORTRAN statements that direct the computer to
perform specific operations and calculations. A program written using FORTRAN statements is called a
source program.

It must be translated by the FORTRAN compiler program before execution. The trans-

lated version of the program is referred to as an object program.

It is in a binary-coded form that the

machine can understand.

1 .2

SOURCE PROGRAM FORMAT
The FORTRAN character set consists of the 26 letters:

A, B, C, D, E, F, G, H, I, J, K, L, M,
N, 0, P, Q, R, S, T, U, V, W, X, Y, Z.
the 10 digits:
0, 1,2,3,4,5,6,7,8,9
and 11 specia I characters:
Blank
Equals
Plus
Minus
Asterisk
Slash
Left Parent~es is
Right Parenthesis
Comma
Decimal Point
Dollar Sign

*
/
(
)

1-1

PDP-9 FORTRAN IV

1 .2. 1

Card Format (IBM Model 029 Keypunch Codes)
The FORTRAN source program is written on a standard FORTRAN coding sheet (Figure 1-1)

whi ch consists of the following fields: statement number field, I ine continuation field, statement field,
and identification field.
The FORTRAN statement is written in columns 7-72.

If the statement is too long for one

I ine, it can be continued in the statement field of as many lines as necessary if column 6 of each continuation line contains any character other than blank or zero. There are two exceptions to this rule:

(1) the DO statement must be on one line; and (2) the equal sign (=) of an assignment statement must
appear on the first line.
For one statement to be referenced by another, a statement number is placed in col umns 1
through 5 of the first line of that statement. This number is made up of digits only, and may contain
from one to five digits.

Leading zeros and all blanks in this field are ignored. The statement numbers

are used for identification only, and may be assigned in any order.
The FORTRAN compiler ignores the last eight columns (columns 73 through 80) which may be
used for program identifi cation, sequencing, or any other purpose desired by the user. Comments may
be included in the program by putting a IIC II in column 1 of each line containing a comment (or continuation of a comment). The compi ler ignores these comments except for printing them.
Blanks may be used to aid readability of a FORTRAN statement, except where indicated in
this manual.

1 .2.2

Paper Tape Format
When FORTRAN source program statements are prapared on paper tape, the sequence of

c:haracters is exactly the same as for card input, and each I ine is terminated with a carriage return,
I ine feed sequence.
A statement number (all digits) may be written as the first five characters, or a IIC
the first character to indi cate a comment Iine or a continuation of a comment line.

may be

For statement con-

tinuation lines, any numeric character other than blank or zero is written as the sixth character. The
seventh character begins the statement and must be alphabetic.

Each line is terminated with a carriage

return, line feed.
The TAB key can increase the speed of writing FORTRAN statements on paper tape. A TAB
followed by an alphabetic character begins the statement in column 7. A TAB followed by a digit
places the digit in column 6, indicating a statement continuation line.

A statement number less than

five digits, followed by a TAB, places the next character in column 6 if it is a digit, or in column 7 if
it is a letter.

1-2

PAGE

DATE

CODER

FORTRAN

PROBLEM

CODING FORM
C-COnll"lent g
S-Symbolic "-g
B - Boolean c:
STATEMENT "~
NUMBER 8

FORTRAN STATEMENT

IDENTIf ICATION

123456 7 8 9 1011 12131415161718192021222324252627282930 313233 343536373839404142434445464748495051525354555657585960616263646566676869707172 737475767778798C

.
,
;

-0

-0
I
~

i'
w

:;:0

--I

:;:0

»
z
:(

.
I
I

.
I

--'

..
I

•

;

1 2 3 4 5 6 7 8 9 10 11 12131"151617181920212223242526272829303132-3334353637383940"142"3"""546474U9S051 S2S3s.l5S56S7S8S960616263U6,S666768bP 70 71 72 7374757677717980

PG-3

DIGITAL EQUIPMENT CORPORATION

•

MAYNARD, MASSACHUSETTS

Figure 1-1 FORTRAN Coding Form

100 -12f64

PDP-9 FORTRAN IV

If it is desired to have a title at the beginning of the tape for Iisting purposes, it must be
entered as a comment line.

1-4

PDP-9 FORTRAN IV

CHAPTER 2
ELEMENTS OF THE FORTRAN LANGUAGE

2.1

CONSTANTS
There are five types of constants allowed in the FORTRAN source program: integer, rea I,

double-precision, logi cal, and Hollerith.

2. 1 . 1

Integer Constants
An integer constant is a number written without a decimal po int, consisting of one to six

decimal digits. A + or - sign preceding the number is optional. The magnitude of the constant must
17
be less than or equal to 131071 (2 -1).
Example:
+97

-2176
576
If the magn itude> 217_1, an error message will be output.

Negative numbers are repre-

sented in 2 s complement notation.

2.1.2

Real Constants (6-decimal-digit accuracy)
A real constant is an integer, fraction, or mixed format number and may be written in the

following forms:
a. A number consisting of one to six significant decimal digits with a decimal point included
someplace within the constant. A + or .;, sign preceding the number is optional.
b. A number followed by the letter E, indicating a decimal exponent, and a 1-· or 2-digit
constant with magnitude less than 76* indicating the appropriate power of 10.

A + or - sign may pre-

cede the scale factor. The decimal point is not necessary in real constants having a decimal exponent.
Example:
352.
+12.03
-.0054
5.E-3
+5E7
*If the adjusted magnitude exceeds 75, an error results.
illegal.

1-5

.999999E75 is legal, but 999.99'9E73 is

PDP-9 FORTRAN IV

Real constants are stored in two words in the following format:

LOW ORDER
MANTISSA

EXPONENT
(2'S COMP.)

L . . - - - ._ _- - - I _ _ _

SIGN OF
MANTISSA

HIGH ORDER MANTISSA

-IL-----.JL-_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

~
----.J

Negative mantissae are indicated with a change of sign.

2.1 .3

Double-Precision Constants {9-decimal-digit accuracy}
A double-precision constant is written as a real number followed by a decimal exponent,

indicated by the letter D and a 1- or 2-digit constant with magnitude not greater than 76. A + or sign may precede the constant and may also precede the scale factor. A decimal point within the
constant is optional. A double-precision constant is interpreted identically to a real constant, the
,only difference being that the degree of accuracy is greater.
Example:
-3.0DO
987.6542D15
32.1230+7
Double-precision constants are stored in three PDP-9 words:

L. _ - -~XPONENT
- - - - - -]
(2'S COMP.)

SIGN OF
MANTISSA

L . . _ L . . -_ _ _ _ _ _ _ _ _ _
H_IGH_O_R_DE_R_M._AN_T_IS_SA_ _ _ _ __

[

LOW ORDER MANTISSA

2.1.4

]

NEGATIVE
MANTISSAE
ARE
INDICATED
WITH A
CHANGE
OF
SIGN

]
17

Log i ca I Constants
The two logical constants are the words TRUE and FALSE, each both preceded and followed

by a decimal point .
. TRUE.
.FALSE.

777777

o
1-6

PDP-9 FORTRAN IV

2.1.5

Hollerith Constants
A Hollerith constant is written as an unsigned integer constant, whose value, n, must be

equal to or greater than one and less than or equal to five, followed by the letter H, followed by
exactly n characters, which are the Hollerith data. Any FORTRAN character, including blank, is
acceptable. The Hollerith constants are used only in CALL and DATA statements and must be associated with real variable names. The Hollerith constants are packed in 7-bit ASCII, five, per two words
of storage with the rightmost bit always zero.
Examples:
lHA
4HA$C

2.2

VARIABLES
A variable is a symbolic representation of a numeric quantity whose values may change

during the execution of a program either by assignment or by computation. The symbol's representation,
or name of the FORTRAN variable consists of from one to six alphanumeric {alphabetic and numeric}
characters, the first of which must be alphabetic.
Example:
X=Y+l0.

Both X and Yare variables; X by computation, and Y by
assignment in some previous statement.

TEST
GAMMA
X12345
NOTE
If three or less characters are used for each symbol, considerable core space can be saved.

2.2. 1

Variable Types
Variables in FORTRAN may represent one of the following types of quantities: integer, real,

double-precision, or logical. This corresponds to the type of constant the variable is supposed to
represent.

2.2.2

Integer Variables
Variable names beginning with the letters I, J, K, L, M, or N are considered to be integer

variables.

If the first letter is not one of the above letters, it is an integer variable only if it was named

in a previous integer type specification statement.

/-7

PDP-9 FORTRAN IV

2.2.3

Real Variables
Variable names beginning 'with letters other than I, J, K, L, M, or N are considered to be

real variables.

If the first character is one of the above letters, it is a real variable only if it was

named in a previous real type specification statement.

2.2.4

Double-Precision and Logi cal Variables
A type specification statement is the only way to assign a variable value to one of these two

types. This is done with either a double precision statement or a logical statement.

2.3

ARRAYS AND SUBSCRIPTS
An array is an ordered set of data identified by a symbol i c name.

Each individual quantity

in this set of data is referred to in terms of its position within the array. This identifier is called a subscript. For example,

A (3)
represents the third element in a one-dimensional array named A. To generalize further, in an array A
with n elements, A (I) represents the Ith element of the array A where 1= 1, 2, ... , n.
FORTRAN allows for one, two, and three-dimensional arrays, so there can be up to three
subscripts for the array, each subscript separated from the next by a comma. For example,

B (1, 3)
represents the value located in the first row and the third column of a two-dimensional array named B.
A dimension statement defining the size of the array (i. e., the maximum values each of its subscripts
can attain) must precede the array in the source program.

2.3. 1

Arrangement of Arrays in Storage
Arrays are stored in column order in ascending absolute storage locations. The array is stored

with the first of its subscripts varying most rapidly and the last varying least rapidly. For example, a
three-dimensional array A, defined in a DIMENSION statement as A (2,2,2) will be stored sequentially
in this order:
A(l,l,l)
A(2,1 , 1)
A(l,2,1)
A(2,2,1)
A(l, 1 ,2)
A(2, 1,2)
A(l,2,2)
A(2,2,2)

ascending absolute
storage locations

1-8

PDP-9 FORTRAN IV

2.3.2

Subscript Expressions
Subscripts may be written in any of the following forms:

V
C
V+k
V- k
C*V
C*V+k
C*V-k
where C and k represent unsigned integer constants and V represents an unsigned integer variable.
Example:

I
13
IMOST + 3
ILAST - 1
5 * IFIRST
2*J+9
4 * Ml - 7
2.3.3

Subscripted Variables
A subscripted variable is a variable name followed by a pair of parentheses which contain

one to three subscripts separated by commas.
Example:
A (I)
B (I, J - 3)
BETA (5 * J + 9, K + 7, 6 * JOB)

2.4

EXPRESSIO NS
An expression is a combination of elements (constants, subscripted or nonsubscripted varia-

bles, and functions) each of which is related to another by operators and parentheses. An expression
represents one single value which is the result of the calculations specified by the values and operators
that make up the expression. The FORTRAN language provides two kinds of expressions: arithmetic
and logical.

2.4.1

Arithmetic Expressions
An arithmetic expression consists of arithmetic elements joined by the arithmetic operators +,

*, I, and **, whi ch denote addition, subtraction, multipl ication, division, and exponentiation,

respectively. An expression may consist of a single element (meaning a constant, a variable, or a

1-9

PDP-9 FORTRAN IV

function name}. An expression enclosed in parentheses is considered a single e~ement. Compound
expressions use arithmetic operators to combine single elements.

2.4. 1 . 1

Mode of an Expression - The type of quantities making up an expression determines its mode;

i.e., a simple expression consisting of an integer constant or an integer variable is said to be in the
integer mode. Simi larly, real constants or variables produce a real mode of expression, and doubleprecision constants or variables produce a double-precision mode. The mode of an arithmeti c expression
is important because Kt determines the accuracy of the expression.
In general, variables or constants of one mode cannot be combined with variables or constants
of another mode in the same expression. There are, however, except ions to th is ru Ie.
a. The following examples show the modes of the val id arithmetic expressions involving the
use of the arithmetic operators +, -, *, and I.

I, R, and D indicate integer, real, and double-

precision variables or constants. A + is used to indicate anyone of the four operators:

I+ I
R+R

Integer result
Real result

R+ D }
D+R
D+D

Double-precision result

b. When raising a value to a power, the mode of the power may be different than that of
the value being raised. The following examples show the modes of the valid arithmetic expressions
using the arithmetic operator**. As above, I, R, and D indicate integer, real, and double-precision.
1**1
R**I
R**R
R**D
D**I
D**R
D**D

Integer result

Real result

Double-precision result

The subscript of a subscripted variable, which is always an integer quantity, does not affect
the mode of the expression.

2.4. 1 .2

Hierarchy of Operations - The order in whi ch the operations of an arithmetic expression are

to be computed is based on a priority rating. The operator with the highest priority takes precedence
over other operators in the expression. Parentheses may be used to determine the order of computation.
If no parentheses are used, the order is understood to be as follows:

1-10

PDP-9 FORTRAN IV

a.
b.
c.
d.
e.

Function reference
**(Exponentiation)
Unary minus evaluation
* and/(multipl ication and division)
+ and -(addition and subtraction)

Within the same priority, operations are computed from left to right.
Example:
FUNC + A*B/C-D(I,J) + E**F*G-H
interpreted as,
F
FUNC + ((A*B)/C) - D(I,J) + (E * G) - H
2.4.1.3

Rules for Constructing Arithmetic Expressions a. Any expression may be enclosed in parentheses.
b. Expressions may be preceded by a + or - sign.
c. Simple expressions may be connected to other simple expressions to form a compound

expression, provided that:
(1)

No two operators appear together.

(2)

No operator is assumed to be present.

d. Only val id mode combinations may be used in an expression (described under Mode of an
Expression, Section 2.4. 1 .1).

e. The expression must be constructed so that the priority scheme determines the order of
operation desired (described in Section 2.4. 1 .2, Hierarchy of Operations).
Examples of arithmetic expressions follow:

3
A(I)
B + 7.3

C*D
A + (B*C) - D**2 + EjF
2.4.2

Relational Expressions
A relational expression is formed with the arithmetic expressions separated by al relational

operator. The result value is either true or false depending upon whether the condition e!xpressed by
the relational operator is met or not met. The arithmetic expressions may both be of the integer mode
or they may be a combination of real and/or double-precision. No other mode combinations are legal.
The relational operators must be preceded by and followed by a decimal point. They are:

1-11

PDP-9 FORTRAN IV

· LT.
· LE.
· EQ.
· NE.
· GT .
· GE.

Less than (<)
Less than or equal to ~
Equal to (=)
4
Not equal to (r)
Greater than (»
Greater than or equa I to (»

Examples:
N .LT.5
DELTA + 7. 3 . LE. B/3E7
(KAPPA + 7/5 .NE.IOTA
1 • 736D-4. GT. BETA
X.GE. Y*Z**2
2.4.3

Logical Expressions
A logical expression consists of logical elements joined by logical operators. The value is

€!ither true or false. The logical operator symbols must be preceded by and followed by a decimal point.
They are:
.NOT.

Logical negation. Reverses the state of the logical quantity that
follows.

.AND.

Logical AND generates a logical result (TRUE or FALSE) determined by two logical elements as follows:
T .AND. T generates T
T .AND. F generates F
F .AND. T generates F
F .AND. F generates F

.OR.

Logical OR generates a logical result determined by two logical
elements as follows:
T . OR. T generates T
T .OR. F generates T
F . OR. , T generates T
F . OR.F generates F

2.4.3.1

Rules for Construction Logical Expression a. A logical expression may consistofa logical constant, a logical variable, a reference

tC) a logical function, a relational expression, or a complex logical expression enclosed in parentheses.
b. The logical operator. NOT. need only be followed by a logical expression, while the
Ic)gical operators .AND. and .OR. must be both preceded by and followed by a logical expression for
more complex logical expressions.
c. Any logical expression may be enclosed in parentheses. The logical expression following
the logical operator. NOT. must be enclosed in parentheses if it contains more than one ,quantity.

1-12

PDP-9 FORTRAN IV

No two logical operators may appear in sequence, not separated by a comma or paren-

thesis unless the second operator is . NOT.

',..··ciddition, no two decimal points may appear. together,
...,.,.
not separated by a comma or parenthesis, unless one belongs to a constant and the other to a relational
.

operator.
2.4.3.2

Hierarchy of Operations - Parentheses may be used as in normal mathematical notation to

specify the order of operations. Within the parentheses, or where there are no parentheses, the order
in which the operations are performed is as follows:
a. Evaluation of functions
b. **(Exponentiation)
c. Evaluation of unary minus quantities
d. * and/ (multiplication and division)
e. + and - (addition and subtraction)
f.

. LT., . LE ., . EQ ., . N E., . G T ., . G E.

g . . NOT.
h.

.AND. and .OR.

= Replacement operator

Unlike an arithmetic expression where sequence of elements of the same priority (i .e., operations being performed from left to right) is important for the end result of the expression, the order of
operation within the same priority in logical and relational expressions is unimportant.
2.5

STATEMENTS
Statements specify the computations required to carry out the processes of the FORTRAN pro-

gram. There are four categories of statements provided for by the FORTRAN language:
a. Arithmetic statements define a numerical calculation.
b. Control statements determine the sequence of operation in the program.
c.

Input/output statements are used to transmit information between the computer and

related input/output devi ces.
d. Specification statements define the properties of variables, functions, and arrays appear ..
ing in the source program. They also enable the user to control the allocation of storage.

1-13

PDP-9 FORTRAN IV

CHAPTER 3
ARITHMETIC STATEMENTS

An arithmetic statement is a mathematical equation written' in the FORTRAN language which
defines a numerical or logical calculation.

It directs the assignment of a calculated quantity to a given

variable. An arithmetic statement has the form
V=E
where V is a variable (integer, real, double-precision, or logical, subscripted or nonsubscripted) or any
array element name; = means replacement rather than equivalence, as opposed to the conventional
mathematical notation; and E is an expression.
In some cases, the mode of the variable may be different from that of the expression.

In such

cases an automati c conversion takes place. The rules for the assignment of an expression E to a variable
V are as follows:
V Mode

E Mode

Assianment Rule

Integer

Assign

Integer

Real

Fix and assign

Integer

Double-precision

Fix and assign

Real

Integer

Float and assign

Real

Assign

Real

Double-precision

Double-precision evaluate and real assign

Double-precision

Integer

Double-precision float
and assign

Double-precision

Real

Double-precision evaluate and assign

Double-precision

Assign

Logical

Assign

Mode conversions involving logical quantities are illegal unless the mode of both V and E is
logical. Examples of an assignment statement:
ITEM = ITEM + 1
A(I) = B(I) = ASSIN (C (I) )
V = .FALSE.
X = A. GT . B. AND. C . LE. G
A=B

I-15

PDP-9 FORTRAN IV

CHAPTER 4
CONTROL STATEMENTS

The statements of a FORTRAN program normally are executed as written. However, it is
frequently desirable to alter the normal order of execution. Control statements give the FORTRAN user
this capability. This section discusses the reasons for control statements and the ways in which they
may be used.
4.1

UNCONDITIONAL GO TO STATEMENTS
The form of the unconditional GO TO statement is
GO TO n

where n is a statement number. Upon the execution of this statement, control is transferred to the statement identified by the statement number, n, which is the next statement to be executed.
Example:
GO TO 17
4.2

ASSIGN STATEMENT
The general form of an ASSIGN statement is
ASSIGN n TO i

where n is a statement number and i is a nonsubscripted integer variable name which appears in a subsequently executed assigned GO TO statement. The statement number, n, is the statement' to which
control will be transferred after the execution of the assigned 'GO TO statement.
Example:
ASSIGN 27 TO ITEST
4.3

ASSIGNED GO TO STATEMENT
Assigned GO TO statements have the form
GO TO i, (n , n , .... , n )
1 2
m

where i is a nonsubscripted integer variable reference appearing in a previously executed ASSIGN
statement, and n , n , .... , nm are the statement numbers which the ASSIGN statement may legally
1 2
assign to i. Examples:
ASSIGN 13 TO KAPPA
GO TO KAPPA, (1, 13, 72, 1DO, 35)
There is no object time checking to ensure that the assignment is one of the legal statement
numbers.
1-17

PDP-9 FORTRAN IV

4.4

COMPUTED GO TO STATEMENT
The format of a computed GO TO statement is
GO TO (n l' n , .... , nm)' i
2

where n , n , .... , nm are statement numbers and i is an integer variable reference whose value is
1 2
greater than or equal to 1 and less than or equal to the number of statement numbers enclosed in parentheses.

If the value of i is out of this range, the statement is effectively a CONTINUE statement.

Example:
GO TO (3, 17,25,50,66), ITEM
If the value of ITEM is 2 at the time this GO TO statement is executed, the statement to which control
i:s transferred is the statement whose number is second in the series, i. e., statement number 17.
4.5

ARITHMETIC IF STATEMENT
The form of the arithmetic IF statement is
IF (e) n f n , n3
1 2

where e is an arithmetic expression and n , n , n3 are statement numbers. The IF statement evaluates
1 2
the expression in parentheses and transfers control to one of the referenced statements. If the value of
the expression (e) is less than, equal to, or greater than zero, control is transferred to n , n , or n3
1 2
r,espectively.
Example:
IF (AUB (I) - B*D) 10, 7, 23
4.6

LOGICAL IF STATEMENT
The general format of a logical IF statement is
IF (e) s

where e is a logical expression and s is any executable statement other than a DO statement or another
logical IF statement. The logical expression is evaluated, and different statements are executed
depending upon whether the expression is true or false.

If the logical expression e is true, statement s

is executed and control is then transferred to the following statement (unless the statement is a GO TO
statement or an arithmetic IF statement, in which cases control is transferred as indicated; or the statement s is a CALL statement, in which case control is transferred to the next statement after return from
the subprogram).

If the logical expression e is false, statement s is ignored and control is transferred to

the statement fo Ilow i ng the IF statement.

1-18

PDP-9 FORTRAN IV

Example:
IF (L 1) I = I + 1
IF (L. LE. k) GO TO 17
IF (LOG.AND. (. NOT. LOG1) ) IF (X) 3,5,5

4.7

DO STATEMENT
The DO statement is a command used to execute repeated Iy a specified series of statements.

The general format of the DO statement is
DO n i = m l' m2 , m3
or
DO n i = m , m
1
2
where n is a statement number representing the terminal statement or the end of the II range II,; i is a nonsubscripted integer. variable known as the II index" i and m , m , and m3 are unsigned nonzero integer
1
2
constants or nonsubscripted integer variables, which represent the "initial, II "final, II and "increment"
values of the index.

If m3 is omitted, as in the second form of the DO statement, its value is assumed

to be 1 .
The DO statement is a command used to execute repeatedly a group of statements; following it,
up to and including statement n. The initial value of i is m (m must be less than or equal to m ).
1
2
1
Each succeeding time the statements are operated, i is increased by the value of m . When is is greater
3
than m , control passes to the statement follow ing statement number n.
2
The range of a DO statement is a series of statements to be executed repeatedly. It consists
of all statements immediately following the DO, up to and including statement n. Any number of statements may appear between the DO and statement n. The terminal statement (statement n) may not be a
GO TO (of any form), an arithmetic IF, a RETURN, a STOP, a PAUSE, or a DO statement, or a logical
IF statement containing any of these forms.
The index of a DO is the integer variable i which is controlled by the DO statement in such
a way that its initial value is set to m , and is increased each time the range of statements is executed
1
by m3' until a further incrementation would cause the value of m to be exceeded. Throughout the
2
range of' the DO, the index is avai lable for computation either as an ordinary integer variable or as the
variable of a subscript.

However, the index may not be changed by any statement within the DO range.

The in itia I va Iue is the va Iue of the index at the time the range is executed for the first time.
The final value is the value which the index must not exceed. When the condition is satisfied the DO is completed and control passes to the first executable statement following statement n.
The increment is the amount by which the index is to be increased after each execution of
the range.

If the increment is omitted, a value of 1 is implied.

1-19

PDP-9 FORTRAN IV

Example:
DO 72 I = 1, 10, 2
DO 15K = 1, 5
DO 23 I = 1, 1 1, 4
Any FORTRAN statement may appear within the range of a DO statement, including another
DO statement. When such is the case, the range of the second DO must be contained entirely within
the range of the first; i. e., it is not permissible for the ranges of DOs to overlap. A set of DOs satisfying this rule is called a nest of DOs.

It is possible for a terminal statement to be the terminal state,-

ment for more than one DO statemen't. The following configuration, where brackets are used to represent the range of the DOs, indicates the permissible and illegal nesting procedures.

PERMISSIBLE , . . . - - - - - - - DO

ILLEGAL ~----- DO

~DO

, . . . - - - - - DO

!r=DO

Transfer of control from within the range of a DO statement to outside its range is permitted
at any time. However, the reverse is not true; i. e., control cannot be transferred from outside the
range of a DO statement to inside its range. The following examples show both valid and invalid
transfers.

VALID

INVALID

-:?)

1-20

3
3

PDP-9 FORTRAN IV

4.8

CONTINUE STATEMENT
The CONTINUE statement causes no action and generates no machine coding.

It is a dummy

statement which is used for terminating DO loops when the last statement would otherwise be an illegal
terminal statement (i. e., GO TO, arithmetic IF, RETURN, STOP, PAUSE, or DO, or a logical I F containing any of these forms). The form consists of the single word
CONTINUE
4.9

PAUSE STATEMENT
A PAUSE statement is a temporary halt of the program at run time. The PAUSE statement has

one of the two forms
PAUSE
or
PAUSE n
where n is an octal integer whose value is less than 777777 . ,The integer n is typed out on the console
8
Teletype for the purpose of determining which of several PAUSE statements was encountered. Program
execution is resumed, by typing control P (f'P), starting with the first statement following the PAUSE
statement.
4.10

STOP STATEMENT
The STOP statement is of one of the forms
STOP

or
STOP n
where n is an octal integer whose value, is less than 7777777 . The STOP statement is placed at the
8
logical end of a program and causes the computer to type out on the console Teletype, the integer n
and then to exit back to the Monitor. There must be at least one STOP statement per main program,
but none are allowed in subprograms.
4.11

END STATEMENT
The END statement is placed at the physical end of a program or subprogram. The form con-

sists of the sing Ie word
END
The END statement is used by the compiler and generates no code.
that the processing of the source program is complete.

1-21

It signals the compiler

P DP-9 FORTRAN IV

A control transfer type statement, a STOP statement, or a RETURN statement must immediately precede END. This will be checked by the compiler.

1-22

PDP-9 FORTRAN IV

CHAPTER 5
INPUT/OUTPUT STATEMENTS

The input/output (I/O) statements direct the exchange of data between the computer and I/O
devices. The information thus transmitted by an I/O statement is defined as a logical record, which
may be formatted or unformatted. A logical record, or records, may be written on a device as one or
more physical records. This is a function of the size of the logical record{s) and the physical device
used.
The definition of the data which comprises a user's optimum physical record varies for each
I/O device, as follows:
Unit
or
Device
Typewriter
(input and output)

Formatted Physi ca I
Record Definition

Unformatted
(Binary) Physical
Record Defi'nition

One Iine of type is term inated by a carriage
return. Maximum of 72 printing characters
per line

Undefined

Line printer

One line of printing. Maximum of 120
chara cters per line

Undefined

Cards
(input and output)

One card. Maximum of 80 characters

50 words

Paper tape
(input and output)

One Iine image of 72 printing characters

50 words

Magneti c tape

One Iine image of 630 characters

252 words

Disc/drum/
DECtape

One Iine image of 630 characters

252 words

Each I/O device is identified by an integer constant which is associated with a device
assignment table in the PDP-9 Monitor. This table may be modified at system generation time, or just
before run time. For example, the statement
READ (u, f) list
requests one logical record from the device associated with slot u in the device assignment table.
The statement descriptions in this section use u to identify a specific I/O unit, f as the statement number of the FORMAT statement describing the type of data conversion, and Iist as a Iist of
arguments to be input or output.

1-23

PDP-9 FORTRAN IV

5.1

GENERAL I/O STATEMENTS
These statements cause the transfer of data between the computer and I/O devices.

5. 1 .1

Input/Output Argument Lists
An I/O statement which calls for the transmission of information includes a I ist of quantities

to be transmitted.

In an input statement this list consists of the variables to which the incoming data is

'to be assigned; in an output statement the list consists of the variables whose values are to be transmitted
'to the given I/O device. The list is ordered, and the order must be that in which the data words exist
(input) or are -to exist (output) in the I/O device. Any number of items may appear in a single list. The same statement may transmit integer and real quantities.

If the data to be transmitted exceeds the

items in the list, only the number of quantities equal to the number of items in the list are transmitted.
The remaining data is ignored.

Conversely, if the items in the list exceed th~ data to be transmitted,

:succeeding superfluous records are transmitted unti I a II items specified in the list have been transmitted.
Simple List~ - The Iist uses the form

5. 1 . 1 . 1

C , C , .... , C
1
2
n
where each C. is a variable, a subscripted variable, or an array identifier. Constants are not allowed
I

•

(lS Iist items. The Iist reads from left to right. When an array identifier appears in the list, the entire
(lrray is to be transmitted before the next item in the list.

Examples of Simple Lists:

Y,Y,Z
A, B (3), C, D (I + 1, 4)
5.1 .1 .2

DO-Implied Lists - Indexing similar to that of the DO statement may be used to control the

number of times a group of simple I ists is to be repeated. The I ist elements thus controlled, and the
index control itself, are enclosed in parentheses, and the contents of the parentheses are regarded as
IJ sing Ie

item of the I/O list.

Example:

w, X (3), (Y (I), Z (I, K), I = 1, 10)
5. 1 .2

REA D Statement
The READ statement is used to transfer data from any input device to the computer. The

!~eneral READ statement can be used to read either BCD or binary information.

ment determines what kind of input will be performed.

1-24

The form of the state-

PDP-9 FORTRAN IV

5. 1 .2. 1

Formatted READ - The formatted READ statements have the general form
REA D (u, f) list

or
READ (u, f)
Execution of this statement causes input from device u to be converted as specified by format statement
f, the resulting values to be assigned to the items specified by list, if any.
Examples:
READ (3, 13) A, B, C
READ (2, 10) A, (B (I), I = 1,5)
READ (1,3)
5. 1 .2.2

Unformatted READ - An unformatted READ statement has the genera I form
READ (u) list

or
READ (u)
Execution of this statement causes input from device u, in binary format, to be assigned to the items
specified by list.

If no list is given, one record will be read, but ignored.

information words than the Iist requires, that part of the record is lost.

If the record contains more

If more elements are in the list

than are in one record, additional records are read unti I the list is satisfied.
Example:
READ (5) I,J, K
READ (8)
5.1 .3

WR ITE Statement
The WR ITE statement is used to transmit information from the computer to any I/O dev ice.

The WRITE statement closely parallels the READ statement in both format and operation.

5.1 .3. 1

Formatted WRITE - The formatted WRITE statement has the general form
WRITE (u,f) list

or
WRITE (u,f)
Execution of this statement causes the list elements, if any, to be converted according to format statement f, and output into device u.

1-25

PDP-9 FORTRAN IV

5. 1 .3.2

Unformatted WR ITE - The unformatted WR ITE statement has the genera I form
WRITE (u) list

Execution of this statement causes output onto dev i ce u, in binary format, of a II words specified by the
list.

If the list elements do not filII the record, the remaining part of the record is filled with blanks.

If the list elements more than fi II one record, success ive records are written unti I a II elements of the
I ist are satisfied, the last record padded with blanks if necessary.

Examples of WR ITE:

W RIT E (1 , 10) A, (B (I), (C (I, J), J =2, 10, 2), 1=1, 5)
WRITE (2,7) A, B, C
WRITE (5) W,X(3), Y(I + l,4),Z
5.2

FORMAT STATEMENTS
These statements are used in conjunction with the general I/O statements.

They specify the

type of conversion which is to be performed between the internal machine language and the external
notation.

FORMAT statements are not executed.

Their function is to supply information to the object

program.
5.2.1

specJiring FORMAT
The general form of the FORMAT statement is
FORMAT (51' 52' .... , Sn)

where 51'" . sn are data field descriptions.

Breaking this format down further, the basic data field

descriptor is written in the form
nkw.d
where n is a positive unsigned integer indicating the number of sllccessive fields for which the data conversion will be performed according to the same specification.
If n is equal to 1, it may be omitted.
be performed.

This is also known as the repeat count.

The control character k indicates which type of conversion will

This character may be I, E,F, D,P, L,A,H, or X.

f:ies the width of the field.

The nonzero integer constant w speci-

The integer constant d indicates the number of digits to the right of the

decimal point.
Six of the nine control characters I isted above provide for data conversion between internal
machine language and external notation.
Internal

Externa I

Integer variable

Decima I integer

Rea I variable

Float i ng-po i nt, sca led

Rea I variable

Floating-point, mixed

1-26

PDP-9 FORTRAN IV

Internal

Real variable

Floating-point, mixed/scaled

Double-precision
variable

Floating-point, scaled

Logical variable

Letter T or F

Alphanumeric

Alphanumeric (BCD) characters

External

The other three control types are special purpose control characters:
~

Purpose

Used to set a scale factor for use with E, F, and D conversions.

Provides for skipping characters in input or specifying blank characters
in output.

Designates Hollerith fields.

FORMAT statements are not executed and therefore may be placed anywhere in the source
program.

Because they are referenced by READ or WRITE statements, each FORMAT statement must be

given a statement number.
Commas (,) and slashes (,I) are used as field separators. The comma is used to separate field
descriptors, with the exception that a comma need not follow a field specified by an H or X control
character. The slash is used to specify the termination of formatted records. A series of slashes is also
a field separator. Multiple slashes are the equiva lent of blank records between output records, or
records skipped for input records.

If the series of n slashes occurs at the beginning or the end of the

FORMAT specifications, the number of input records skipped or blank lines inserted in output is n.

the series of n slashes occurs in the middle of the FORMAT specifications, this number is n-l. A comma
may precede and/or follow a slash, but is not necessary. An integer va lue cannot precede a slash.
For all field descriptors (with the exception of H and X), the field width must be specified.
For those descriptors of the w. d type (see next page), the d must be specified even if it is zero. The
field width should be large enough to provide for all characters (including decimal point and sign) necessary to constitute the data value as well as blank characters needed to separate it from other data values.
Since the data value within a field is right justified, if the field specified is too small, the most significant characters of the value will be lost.
Successive items in the I/O Iist are transmitted according to successive descriptors in the
FORMAT statement, until the entire I/O Iist is satisfied.

If the list conta ins more items than descriptors

in the FORMAT statement, a new record must be begun. Control is transferred to the preceding left
parenthesis where the same specifications are used again until the list is complete.

I-27

PDP-9 FORTRAN IV

Field descriptors (except H and X) are repeated by preceding the descriptor with an unsigned
integer constant (the repeat count). A group repeat count is used to enable the repetition of a group of
Held descriptors or' field separators enclosed in parentheses. The group count is placed to the left of
the parenthesis. Two levels of parentheses (not including those enclosing the FORMAT specification)
are permitted.
The field descriptors in the FORMAT must be the same type as the corresponding item in the
I/O list; i.e., integer quantities require integer (I) conversion; real quantities require real (E or F)
conversion, etc.
Example:
FORMAT (17, FlO. 3)
FORMAT (13, 17/E10.4, E10.4)
FORMAT (214,3(15,010.3)
5.2.2

Conversion of Numeric Data

5.2.2.1

I-Type Conversion - Field descriptor: Iw or nlw
The number of characters specified by w is converted as a decimal integer.
On input, the number in the input field by w is converted to a binary integer. A minus sign

indicates a negative number. A plus sign, indicating a positive number, is optional. The decimal
pc:>int is illegal.

If there are blanks, they must precede the sign or first digit. All imbedded blanks are

interpreted as zero digits.
On output, 'the converted number is right justified.
aillows, the leftmost spaces are filled with blanks.
are truncated and lost.

If the number is small.er than the field w

If an integer is too large, the most significant digits

Negative numbers have a minus sign just preceding their most significant digit

if suffi cient spaces have been reserved.

No sign indi cates a positive number.

Examples (b indi cates blank):
Format Descriptor
15
13
18

5.2.2.2

bbbbb
-b5
bbb12345

Internal

Output

+00000
-05
+12345

bbbbO
b-5
bbb12345

E-Type Conversion - Field descriptor: Ew.d or nEw.d
The number of characters specified by w is converted to a floating-point number with d

spaces reserved for the digits to the right of the decimal point. The w includes field d, spaces for a
si~gn, the decimal point, plus four spaces for the exponent (written E

optional sign and one dig it preceding the decimal point.

1-28

± XX) in addition to space for

PDP-9 FORTRAN IV

The input format of an E-type number consists of an optional sign, followed by a string of
digits containing an optional decimal point, followed by an exponent.

Input data can be qny number

of digi'ts in length,' although it must fall within the range of 0 to ± 10±39.
E output consists of a minus sign if negative (blank if positive), the digit 0, a decimal point,
a string of digits rounded to d signifi cant digits, followed by an exponent of the form E ± XX.
Examples:
Format Descriptor
E10.4
E9.4
E10.3
5.2.2.3

00.2134E03
0.2134E02
bb-23.0321

Internal

Output

213.4
21 .34
-23.0321

0.2134E+03
.2134E+02
-0.230E+02

F-Type Conversion - Fie Id descriptor: Fw. d or nFw. d
The number of characters specified by w is converted as a floating-point mixed number with

d spaces reserved for the digits to the right of the decimal point.
Input for F-type conversion is basically the same as that for E-type conversion, described
above.
The output consists of a minus sign if the number is negative (blank if positive), the integer
portion of the number, a decimal point, and the fractional part of the number rounded to d significant
digits.
Examples:
Format Descriptor
F6.3
F6.3
F9.2
F7.2
5.2.2.4

bl3457
313457
-21367.
-21367.

Internal

Output

13.457
313.457
-21367.
-21367-

13.457
13.457
-21367.00
1367.00

G-Type Conversion - Field descriptor: Gw.d or nGw.d
The external field occupies w positions with d significant digits. The value of' the list item

appears, or is to appear, internally as a rep I number.
Input for G-type conversion is basically the same as that for E-type conversion, described
in paragraph 5.2.2.2.
The form of the G-type output depends upon the magnitude of the internal floating-point
number. Comparison is made between the exponent (e) of the internal value and the number of significant dig its (d) specified by the format descriptor.

If e is greater than d, the E-type conversion is used.

If e is less than or equal to d, the F-type conversion is used, but modified by the following formula:
F (w-4). (d-e) ,4X

1-29

PDP-9 FORTRAN IV

T.he 4X represents four blank spaces that are always appended to the value.

If the value to be repre-

semted is less than . 1 ,the E-type conversion is always used.
Examples:

5.2.2.5

Format Descri ptor

Int'ernal

G14.6
G14.6
G14.6
G14.6

· 12345678 x 10· 12345678 x 100
· 12345678 x 104
· 12345678 x 108

Output
1

0.12345678E-01
bbO. 123456bbbb
bbb 1234 . 56bbbb
bbO. 123456E+08

D-Type Conversion - Field descriptor: Dw.d or nDw.d
The number of characters specified by w is converted as a double-precision floating-point

number with the number of digits specified by d to the right of the decimal point.
The input and output are ,the same as those for E-type conversion except that a D is used in
pllace of the E in the exponent.
Examples:
Format Descriptor
D12.6
D12.6
D12.6
5,,2.3

bb+21345D 03
b+3456789012
.,.12345.6D-02

Internal

Output

21.345
3456.789012
-123.456

0.213450D+02
0.345678D+04
O. 123456D+03

P-Scale Factor - Field descriptor: nP or -nP
This scale factor n is an integer constant. The scale factor has effect only on E, F, G, and

D-type conversions.

Initially, a scale factor of zero is implied. Once a P field descriptor has been

processed, the sca Ie factor establ ished by n rema ins in effect for a II subsequent E, F, and D descriptors
within the same FORMAT statement unti'l another scale factor is encountered.
For E, F, G, and D input conversions {when no exponent exists in the external field} the
scale factor is defined as external quantity = internal quantity x 1On .
The sca Ie factor has no effect if there is an exponent in the externa I field.
The definition of scale factor for F output conversion is the same as it is for F input. For E
n
and D output, the fractional part is multiplied by 10 and the exponent is reduced by n.
Examples:
Format Descriptor

Sca Ie Fa ctor

Interna I

Output

-3PF6.3
,-3PE12.4
1PD10.4

123456
123456
12.3456

-3
-3
+1

+123456.
+12345.6
+1 .23456

23.456
bbO.0001E+08
1.2345D+00

1-30

PDP-9 FORTRAN IV

5.2.4

Conversion of Alphanumeric Data

5.2.4.1

A-Type Conversion (7-Bit ASCII, Handled As REAL Variables) - Field descriptor: Aw or nAw
The number of alphanumeric characters specified by w is transmitted according to list specifi-

cations.
If the field width specified for A input is greater than or equal to five (the number of characters representable in two machine words), the rightmost five characters are stored interna II)'.

If w is

less than five, 5-w trailing blanks are added.
For A output, if w is greater than five, w-5 leading blanks are output followed by five
alphanumeric characters.
5.2.4.2

If w is less than or equal to five, the leftmost w characters are output.

H-Field Descriptor (7-Bit ASCII) - Field descriptor: nHa

a a ... a
1 2 3
n

The number of characters specifieq by n immediately following the H descriptor are transmitted
to or from the external device.

Blanks may be included in the alphanumeric string. The value of n must

be greater than o.
On Hollerith input, n characters read from the external device replace the n characters following the letter H.
In output mode, the n characters following the letter H, including blanks, are output.
Examples:
3HABC
17H THIS IS AN ERROR
16H JANUARY 1, 1966
5.2.5

Logical Fields, L Conversion - Field descriptor: Lw or nLw
The external format of a logical quantity is T or F. The internal format of a logical quantity

is T or F. The interna I format is 7777778 for T or 0 for F.
On L input, the first nonblank character must be a T or F.

Leading blanks are ignored. A

nonblank character is illegal.
For L output, if the internal value is 0, an F is output. Otherwise a T is output'. The F or T
is preceded by w-l leading blanks.
5.2.6

Blank Fields, X Conversion - Field descriptor: nX
The value of n is an integer number greater than O. On X input, n characters are read but

ignored. On X output, n spaces are output.

1-31

PDP-9 FORTRAN IV

5.2.7

FORTRAN Statements Read in at Object Time
FORTRAN provides the faci I ity of including the formatting data along with the input data.

This is done by using an array name in place of the reference to a FORMAT statement label in any of
the formatted I/O statements. For an array to be referenced in such a manner, the name of the variable
FORMA T specifi cation must appear in a DIMENSION statement, even if the size of the array is 1. The
statements have the genera I for-m:
READ (u, name)
READ (u, name) list
WRITE (u, name)
WRITE (u, name) list
The form of the FORMAT specifi cation whi ch is to be inserted into the array is the same as the source
program FORMAT statement, except that the word FORMAT is omitted and the nH field descriptor may
not be used. The FORMAT specification may be inserted into the array by using a data initialization
statement, or by using a READ statement together with an A format.
For example, this facility can be used to specify at object time, the format of a deck of
cards to be read. The first card of the deck wou Id conta in the format statement!

1
10
( ( 17 , FlO. 3)
the subsequent cards would contain data in the general form,

(

7
xx

17
xxxx

DIMENSION AA (10)
13 FORMAT (10A5)
READ (3, 13) (AA(I) , 1=1, 10)
READ (3,AA) JJ, BOB
With the card reader assigned to device number 3, the first READ places the format statement
from the first card into the array AA, and the second READ statement causes data from the subsequent
cards to be read into JJ and BO B with format specifi cations 17 and FlO. 3, respectively.

5.2.8

Printing of a Formatted Record
When formatted records are prepared for printing, the first character of the record is not

printed. The first character is used instead to determine vertical spacing as follows:

1-32

PDP-9 FORTRAN IV

Character

Vertical Spacing Before Printing

Blank

One line
Two lines
Skip to first Iine of next page
No advance

o
1
+

Output of formatted records to other devices considers the first character as an ordinary character in the
record.
5.3

AUXILIARY I/O STATEMENTS
These statements manipulate the I/O file oriented devices. The u is an unsigned integer

constant or integer variable specifying the device.
5.3. 1

BACKSPACE Statement
The BACKSPACE statement has-the general form
BACKSPACE u

Execution of this statement causes the I/O device identified by u, to be positioned so that the record
which had been the preceding record becomes the next record.

If the unit u is positioned at its initial

point, execution of this statement has no effect.

5.3.2

REWIND Statement
The REWIND statement has the general form
REWIND u

Execution of this statement causes the I/O device identified by u to be positioned at its initial point.

5.3.3

EN OF ILE Statement
The EN DF ILE statement has the genera I form
ENDFILE u

Execution of this statement causes an endfile record to be written on the I/O device identified by u.

1-33

PDP-9 FORTRAN IV

and another program which is called later contains the statement,
COMMON/N/XX, YY,ZZ
the latter program will find the values 3, 4, and 5 in its variables XX, YY, and ZZ, respectively,
since variables in the same relative positions in COMMON statements share the same registers in memory.

6.4

EQUI VALENCE STATEMENT
The EQUIVALENCE statement is used to permit two or more entities of the same size and type

to share the same storage location. The general format of the EQUIVALENCE statement is:

where each k represents a I ist of two or more variables or subscripted variables separated by commas.
EOich element in the I ist is assigned the same memory storage location.
An EQUIVALENCE statement may lengthen the size of a COMMON block.

The size can

only be increased by extending the COMMON block beyond the last assignment for that block made
directly by a COMMON statement. A variable cannot be made equivalent to an element of an array
if it causes the array to extend past the beginning of the COMMON block.
When two variables or array elements share the same storage location because of the use of
an EQUI VALENCE statement, they may not both appear in COMMON statements within the same program.
Example:
EQUIVALENCE (A,B), (C(10), D(lO), E(15) )

6.5

EXTERNAL STATEMENT
An EXTERNAL statement is used to pass a subprogram name on to another subprogram.

general form of an EXTERNAL statement is:
EXTERNAL y, z, •••
Example:
EXTERNAL I SUM, 1 SUB
CALL DEBUG (I SUM, A, B)
CALL DEBUG (I SUB, A, B)

END

1-34

The

PDP-9 FORTRAN IV

CHAPTER 6
SPECIFICATION STATEMENTS

Specification statements are nonexecutable because they do not generate instructions in the
object program. They provide the compiler with information about the nature of the constants and variables used in the program. They also supply the information required to allocate locations in storage
for certain variables and/or arrays. All SPECIFICATION statements must appear before any executable
code generating statement. They must appear in this order: type statements, DIMENSION statements,
-.....~

COMMON statements, and EQU IVALENCE statements.

-- ..

EXTERNAL and DATA statements may appear

anywhere after all type statementsand before the executable code generating statements.
6.1

TYPE STATEMENTS
The type statements are of the forms
INTEGER a, b, c
REAL a, b, c
DOUBLE PRECISION a,b,c
LOGICAL a,b, c

where a, b, and c are variable names which may be dimensional or function names. A type statement
is used to inform the compiler that the identifiers listed are variables or functions of a specified type,
i.e., INTEGER, REAL, etc.

It overrides any implicit typing; i.e., identifiers which begin with the

letters I, J, K, L, M, or N are implicitly of the INTEGER mode; those beginning with any other letter
are implicitly of the REAL mode. The type statement may be used to supply dimension information. The
variable or function names in each type statement are defined to be of that specific type throughout the
program; the type may not change.
Examples:
INTEGER ABC, JJ K,XYZ
REAL A (2,4), I,J, K
DOUBLE PRECISION ITEM, GROUP
LOGICAL TRUE, FALSE
6.2

DIMENSION STATEMENT
The DIMENSION statement is used to declare arrays and to provide the necessary information

to allocate storage for them in the object program.
The general form of the DIMENSION statement is:

1-35

PDP-9 FORTRAN IV

where each V is the name of an array and each i is composed of one, two, or three unsigned integer
constants separated by commas. The number of constants represents the number of dimensions the array
contains; the value of each constant represents the maximum size of each dimension.

If the dimension

information for the variable is given in a type statement or a COMMON statement, it must not be
included in a DIMENSION statement.
Example:
DIMENSION ITEM (150), ARRAY (50,50)
vVhen arrays are passed to subprograms, they must be redeclared in the subprogram. ihe mode, number
of dimensions, and size of each dimension must be the same as that declared by the call ing program.
6.3

COMMON STATEMENT
The COMMON statement provides a means of sharing memory storage between a program and

ilrs subprograms. The genera I form of the COMMON statement is:

where each x is a variable whi ch is a COMMON block name, or it can be blank.
Hrst two slashes are optional.

If xl is blank, the

Each a represents a Iist of variables and arrays separated by commas.

The list of elements pertaining to a block name ends with a new block name, with a blank COMMON
block designation (two slashes), or the end of the statement.
The elements of a COMMON block, which are listed following the COMMON block name
(c)r the blank name), are located sequentially in order of their appearance in the COMMON statement.
An entire array is assigned in sequence.

Block names may be used more than once in a COMMON

slratement, or may be used in more than one COMMON statement within the program. The entries so
assigned are strung together in the given COMMON block in order of their appearance.

Labeled

COMMON blocks with the same name appearing in several programs or subprograms executed together
must contain the same number of total words. The elements within the blocks, howeve.r, need not agree
in name, mode, or order. A blank COMMON may be any length.
Examples:
COMMON A, B, C/XX/X, Y, Z
COMMON/A/X(3,3), Y(2,5)//Z(5, 10, 15)
The COMMON statement is a means of transferring data between programs.
contains the statements,
COMMON/N/AA, SB, CC
AA=3
BS=4
CC=5

1-36

If one program

PDP-9 FORTRAN IV

and another program which is called later contains the statement,
COMMON/N/XX, YY, ZZ
the latter program will find the values 3, 4, and 5 in its variables XX, YY, and ZZ, respectively,
since variables in the same relative positions in COMMON statements share the same registers in memory.
6.4

EQUIVALENCE STATEMENT
The EQU IVALENCE statement is used to permit two or more entities of the same size and type

to share the same storage location. The genera I format of the EQU IVALENCE statement is:

where each k represents a I ist of two or more variables or subscripted variables separated by commas.
Each element in the I ist is assigned the same memory storage location.
An EQUIVALENCE statement may lengthen the size of a COMMON block. The size can
only be increased by extending the COMMON block beyond the last assignment for that block made
directly by a COMMON statement. A variable cannot be made equivalent to an element of an array
if it causes the array to extend past the beginning of the COMMON block.
When two variables or array elements share the same storage location because of the use of
an EQUIVALENCE statement, they may not both appear in COMMON statements within the same program.
Example:
EQUIVALENCE (A,B), (C(10), D(10), E(15))
6.5

EXTERNAL STATEMENT
An EXTERNAL statement is us,ed to pass a subprogram name on to another subprogram. The

general form of an EXTERNAL statement is:
EXTERNAL y,z, ...
Example:
EXTERNAL ISUM, ISUB

CALL DEBUG (ISUM, A, B)

CALL DEBUG (ISUB, A, B)

END

1-37

PDP-9 FORTRAN IV

SUBROUTINE DEBUG (X,Y,Z)

RETURN
END
6.6

DATA STATEMENT
The DATA statement is used to set variables or array elements to initial values at the time

the object program is loaded. The general form of the DATA initialization statement is:

where each k is a list of variables or array elements (with constant subscripts) separated by commas, and
each d is a corresponding list of constants with optional signs. The k list may not contain dummy arguments. There must be a one-to-one correspondence between the name Iist and the data list, except
where the data list consists of a sequence of identical constants.

In such a case, the constant need be

written only once, preceded by an integer constant indicating the number of repeats and an asterisk.
A Hollerith constant may appear in the data list.
Variable or array elements appearing in a DATA statement may not be in blank COMMON.
Thley may be in a labeled COMMON block and initially defined only in a BLOCK DATA subprogram.
EX'Jmple:

DATA A,B,C/3*2.0/
DATA X(l), X(2), X(3), X(4)/0.0, 0.1, 0.2, 0.3/,Y(l)' Y(2)'
DATA Y(3), Y(4)/1. OE2, 1. OE-2, 1. OE4, 1. OE-4/

1-38

PDP-9 FORTRAN IV

CHAPTER 7
SUBPROGRAMS

A subprogram i's a series of instructions which another program uses to perform complex or
frequently used operations. Subprograms are stored only once in the computer, regardless how many
times they are referred to by another program.
There are five categories of subprograms:
a. Statement Functions
b. Intrinsi c or Library Functions
c. External Functions
d. Externa I Subroutines
e. Block Data Subprograms
The first three categories of subprograms are referred to as functions. The fourth category is
referred to as subroutines. Functions and subroutines differ in the following two respects. Functions
can return only a sing Ie value to the call ing program; subroutines can return more than one va lue.
Functions are called by writing the name of the function and an argument Iist in a standard arithmetic
expression; subroutines are called by using a CALL statement. The last category is a special purpose
subprogram used for data initia Iization purposes.
7.1

STATEMENT FUNCTIONS
A statement function is defined by a single statement similar in form to that of an arithmetic

assignment statement.

It is defined internally to the program unit by which it is referenced.

Statement

functions must follow all specification statements and precede any executable statements of the program
unit of which they are a part. The general format of a statement function is:

where f is a function name; the als are nonsubscripted variables, known as dummy arguments, which are
to be used in evaluating the function; and e is an expression.
The value of a function is a real quantity unless the name of the function begins with I, J,
K, L, M, or N; in whi ch case it is an integer quantity, or the function type may be defined by using
the appropriate specifi cation statement.
Since the arguments are dummy variables, their names are unimportant, except to indi cate
mode, and may be used elsewhere in the program, including within the expression on the right side of
the statement function.
The expression of a statement funct·ion, in addition to containing nonsubscripted dummy
arguments, may only contain:

1-39

PDP-9 FORTRAN IV

a. Non-Hollerith constants
b. Variable references
c. Intrinsi c function references
d. References to previously defined statement functions
e. Externa I function references
A statement function is called any time the name of the function appears in any FORTRAN arithmetic
expression. The actual arguments must agree in order, number, and type with the corresponding dummy
arguments.
Execution of the statement function reference results in the computations indicated by the
function definition. The resulting quantity is used in the expression whi ch conta ins the function reference.
Examples:
A(X) = 3.2+SQRT (5.7* X**2)
SUM (A, B,C) = A+B+C
FUNC (A, B) = 2. *A/B**2.+Z
7.2

INTRINSIC OR LIBRARY FUNCTIONS
Intrinsic or library fu,":,ctions are predefined subprograms that are a part of the FORTRAN

s;{stem library. The type of each intrinsi c function and its arguments are predefined and cannot be
changed.
An intrinsi c function is referenced by using its function name with the appropriate arguments
in an arithmetic statement. The arguments may be arithmetic expressions, subscripted or simple variables, constants, or other intrinsi c functions (see table 1-1).
Examples:

x = ABS (A)
1= INT (X)

J = IFIX (R)

1-40

PDP-9 FORTRAN IV

Table 1-1 .
Intrinsi c Functions

Intrinsi c Functions

Definition

Absolute value

No. of
Arguments

Symbolic
Name

Ar~ument

Type of

Type of
Function

ABS
lABS
DABS

Real
Integer
Double

AINT
INT
IDINT

Real
Real
Double

Real
Integer
Integer

Truncation

Sign of a times largest
integer ~ I a I

Remaindering*

a 1 (mod O )
2

AMOD
MOD

Real
Integer

Choosing largest
value

Max (a 1 ,02' ... )

AMAXO
AMAX1
MAXO
MAX1
DMAX1

Integer
Real
Integer
Real
Double

Real
Real
Integer
Integer
Double

Choosing smallest
value

Min (a, ,0 ",,)
2

AMINO
AMIN1
MINO
MIN1
DMIN1

Integer
Real
Integer
Real
Double

Real
Real
Integer
Integer
Double

Float

Conversion from
integer to real

FLOAT

Integer

Real

Fix

Conversion from rea I
to integer

IFIX

Real

Integer

Transfer of sign

Sign of O times
2

SIGN
ISIGN
DSIGN

Real
Integer
Double

DIM
IDIM

Real
Integer

Obtain most signifi cant part of double
precision argument

SNGL

Double

Real

Express sing Ie precision argument in
double precision
form

DBLE

Real

Double

I01 I
Positive difference

- Min (a, ,0 )
2

*The function MOD or AMOD (a, ,0 ) is. defined as a - [0,/0 ] O , where [x] is the integer whose
2
2
2
magnitude does not exceed the magnitude of x and whose sign is the same as x.

1-41

PDP-9 FORTRAN IV

7.3

EXTERNAL FUNCTIONS
An external function is an independently written program which is executed whenever its

name appears in another program. The general form in which an external function is written is:
t

FUNCTION NAME (a ,a ,·· .,a )
1 2
n
(FORTRAN statements)

NAME = final calculation
RETURN
END
where t is either INTEGER, REAL, DOUBLE PRECISION, LOGICAL, or is blank; NAME is the symbol ic name of the function to be defined; and the als are dummy arguments which are nonsubscripted
variable names, array names, or other externa I function names.
The first letter of the function name impl i citly determines the type of function.
letter is I, J, K, L, M, or N, the value of the function is INTEGER.

If that

If it is any other letter, the

value is REAL. This can be overridden by preceding the word FUNCTION with the specific type name.
The symbolic name of a function is one to six alphanumeric characters, the first of which
must be the alphabetic name and must not appear in any nonexecutable statement of the function subprogram except in the FUNCTION statement where it is named. The function name must also appear
at least once as a variable name within the subprogram.

During every execution of the subprogram, the

variable must be defined before leaving the function subprogram. Once defined, it may be referenced
or redefined. The value of this variable at the time any RETURN statement in the subprogram is
encountered is called the value of the function.
There must be at least one argument in the FUNCTION statement. There must be nonsubscripted variable names.

If a dummy argument is an array name, an appropriate DIMENSION statement

is necessary. The dummy argument names may not appear in an EQUIVALENCE, COMMON, or DATA
statement in the function subprogram.
The function subprogram may contain any FORTRAN statements with the exception of a
BLOCK DATA, SUBROUTINE, or another FUNCTION statement.

It, of course, cannot contain any

statement which references itself, either directly or indirectly.
A function subroutine must contain at least one RETURN statement. The general form is:
RETURN
This signifies the logical end of the subprogram and returns control and the computed value to the calling
program.
An END statement, described in section 4.11, signals the compiler that the physical end of
the subprogram has been reached.

1-42

PDP-9 FORTRAN IV

An external function is called by using its function name, followed by an actual argument
list enclosed in parentheses, in an arithmetic or logical expression. The actual arguments must correspond in number,' order, and type to the dummy arguments. An actua I argument may be one of the
following:
a.
b.
c.
d.
e.

A variable name
An array element name
An array name
Any other expression
The name of an external function or subroutine

Example:
DIMENSION A(100), B(100)
RSLT = SUM (A, B)**2

Main Program

END
FUNCTION SUM (X, Y)
DIMENSION X (100), Y(100)
SUM = X(l) + Y(l)
DO 10K = 2, 100
SUM = SUM + X(K) + Y (K)
RETURN
END

Function Subprogram

Table 1-2.
External Functions
Basic
External Function

Definition

No. of
Arguments

Symbolic
Name

Type of
Argument

Type of
Function

EXP
DEXP

Real
Double

Exponent ia I

Natura I logarithm

log (a)
e

1
1

ALOG
DLOG

Real
Double

Common logarithm

10910 (a)

1
2

ALOG10
DLOG10

Real
Double

Trigonometric sine

sin (a)

SIN
DSIN

Real
Double

Trigonometric cosine

cos (a)

COS
DCOS

Real
Double

Hyperbol i c tangent

tanh (a)

TANH

Real

Square root

(a) 1/2

SQRT
DSQRT

Real
Double

1-43

PDP-9 FORTRAN IV

Table 1-2. (Cont)
Externa I Functions
Basic
External Function

Definition

Arctangent

arctan (a)

No. of
Arguments

Symbolic
Name

Type of
Argument

Type of
Function

1
1
2
2

ATAN
DATAN
ATAN2
DATAN2

Real
Double
Real
Double

DMOD

Double

arctan (a /a )
l 2
Remaindering*

a 1 (mod 02)

*The function DMOD (a ,a ) is defined as a - [a /a ] a , where [ x ] is the integer whose
1 2
2
1 2
1
magn itude does not exceed the magn itude of x and whose sign is the same as the sign of x.

7.4

SUBROUTINES
A subroutine is defined externally to the program un it whi ch references it.

It is simi lar to

an external function in that both contain the same sort of dummy arguments, and both require at least
one RETURN statement and an END statement. A subroutine, however, may have multiple outputs.
The general form of a subroutine is:
SUBROUTINE NAME (a ,a , ... ,an)
1 2
or
SUBROUTINE NAME
where NAME is the symbol ic name of the subroutine subprogram to be defined; and the a's are dummy
arguments (there need not be any) whi ch are nonsubscripted variable names, array names, or the dummy
name of another subroutine or external function.
The name of a subroutine consists of one to six alphanumeric characters, the first of which is
a Iphabeti c. The symbol i c names of the subroutines cannot appear in any statement of the. subroutine
except the SUBROUTINE statement itself.
The dummy variables represent input and output variables. Any arguments used as output
variables must appear on the left side of an arithmetic statement or an input list within the subprogram.
If an argument is the name of an array, it must appear in a DIMENSION statement within the subrou,tine.
The dummy argument names may not appear in an EQUIVALENCE, COMMON, or DATA statement in
the subprogram.
The subroutine subprogram may contain any FORTRAN subprograms with the exception of
FUNCTION, BLOCK DATA, or another SUBROUTINE statement.

1-44

P DP-9 FORTRAN IV

The logical termination of a subroutine is a RETURN statement. The physical end of the subroutine is an EN D statement.
A subroutine is referenced by a CALL statement, which has the general form

or
CALL NAME
where NAME is the symbol i c name of the subroutine subprogram being referenced, and the a's are the
actual arguments that are being supplied to the subroutine. The actual arguments in the CALL statement
must agree in number, order, and type with the corresponding arguments in the SUBROUTINE subprogram. The array sizes must be the same. An actual argument in the CALL statement may be one of the
following:
a.
b.
c.
d.
e.
f.
7.5

A Hollerith constant
A variable name
An array element name
An array
Any other expression
The name of an external function or subroutine

BLOCK DATA SUBPROGRAM
The BLOCK DATA subprogram is a special subprcg"om used to enter data into a COMMON

block during compilation.

A BLOCK DATA statement takes the form

BLOCK DATA
This special subprogram contains only DATA, COMMON, EQUIVALENCE, DIMENSION, and TYPE
statements.

It cannot contain any executable statements.

It can be used to initialize data ()nly in a

labeled COMMON block area; not in a blank COMMON block area.
All elements of a given COMMON block must be listed in the COMMON statement, even
if they do not a II appear in a DATA statement.

Data may be entered in more than one COMMON block

in a single BLOCK DATA subprogram.
An END statement signifies the termination of a BLOC K DATA subprogram.
7.5. 1

Example of BLOC K DATA Subprogram
BLOCK DATA
DIMENSION X(4), Y(4)
COMMON/NAME/A, B, C, I,J ,X, Y
DATA A,B,C/3*2.0/
2

DATA X(l), X(2), X(3), X(4)/0.0, 0.1, 0.2, 0.3;Y(l), Y(2)
DATA Y(3), Y(4)/1 .OE2, 1. OE-2, 1. OE4, I. OE-4/
END
1-45

PDP-9 FORTRAN IV

APPENDIX 1
SUMMARY OF PDP-9 FORTRAN IV STATEMENTS
CONTROL STATEMENTS
ASSIGN n to i

1-15

CALL name (0 ,0 , ••• )
1 2
CONTINUE • • • • • • •

1-42

DOn i=m 1' m2 ' m3 • • • • • • •
GO TO n • • • • • • •

1-17

1-19

GO TO i, (n ,n , ••• )

1 2
GO TO (n ,n , ••• },i • • • • •
1 2
IF (e ) n1'n ,n • • • • • • • •
1
2 3

IF (e) s •

•

1-15
• • • • • • • •

••••••••••••
• • • • • • •

1-15
1-16
1-16
1-16

•

PAUSE •

1-19

PAUSE n

1-19

STOP

1-19

STOP n

1-19

END

1-19

RETURN

1-39

SUBROUT INE NAME (0 ,0 , ••• a )
1 2
n
FUNCTION NAME (0 ,0 , ••• a )
n
1 2

1-41

1-39

INPUT/OUTPUT STATEMENTS
BACKSPACE u ••

1-31

END FILE u

1-31

FORMAT (sl' s2' • •• ,sn)
READ (u,f)

1-24

READ (u,f) list

1-23

READ (u) • • •

1-23

READ (u) list

1-23

•

READ (u, name)

1-30

READ (u,name) list

1-30

REWIND u

1-31

••

1-23

WR IT E (u, f) list • • •

1-47

PDP-9 FORTRAN IV

WR ITE (u, f)

1-23

WR IT E (u) list

1-24

WRITE (u, name) •

1-30

WRITE (u, name) list

1-30

SPECIF ICATION STATEMENTS
COMMON /x 1/a 1/xia2/·· ./xn/a n • ••• • • •

1-33

DATA k1/d 1/,k2/d /,·· .kn/d n/ ,. • '.
2
DIMENSION V (il)' V (i2), ••• V (in)
1
n
2
DOUBLE PRECISION a,b,c ••

1-35

EQU IVALENCE (k ) ,(k )·· .(k ) • • •••
1
n
2
EXTERNAL y ,z, ••• ,

1-34

INTEGER a,b,c •

1-32

LOGICAL a,b,c ••

1-32

REAL a,b, c

1-32

BLOCK DATA ••

1-42

1-48

1-32
1-32

1-34

PDP-9 FORTRAN IV

APPENDIX 2
A NOTE ON PDP-9 FORTRAN IV

The FORTRAN language used in this manual is essentially the language of USASI Standard
FORTRAN (X3. 9-1966) with the exception of the following features which are modified to allow the
compi ler to operate in 8192 words of core storage:
a.

All references to complex arithmetic are illegal.

The size of arrays in subprograms is not adjustable to the size specified by the calling

Blank COMMON is treated as name COMMON.

The implied DO feature is not legal in a DATA statement.

program.

There are two versions of the FORTRAN IV compi ler: F4 and F4A. F4 is the basic compi ler,
and F4A is an abbreviated version of the compiler that allows DECtape input and output in an 8K system.
F4A operates under control of the Keyboard Monitor only, and is called by typing F4A rather than F4
on the Teletype. The F4A version does not provide for the following options available in the F4 version:

o
S
L

Object code listing
Symbol table printout
Source listing

In paper tape systems, the FORTRAN compiler along with necessary I/O device handlers and
an appropriate version of the I/O Monitor are punched on a tape in absolute format, referred to as a
"system tape. II At the beginning of the system tape is a Bootstrap Loader. The system tape can be loaded
by setting the starting address of the Loader (17720 for 8K systems, 37720 for 16K) on the' console address
switches, pressing I/O RESET, and then pressing the READIN switch. (Refer to the I/O Monitor Guide
for Paper Tape Systems, DEC-9A-NGAA-D.)
In larger systems with a bulk storage device such as DECtape, the Keyboard Monitor accepts
direct keyboard commands to load the compiler in a device-independent environment. (Refer to Keyboard
Monitor Guide, DEC-9U-NGAA-D.) This feature enables use of READ (I,f) or READ (I) statements where
the value of I is undefined at compile and load times. If such statements are used, it is important to
clear unused positive .DAT slots before loading to avoid loading device handlers that are not required.
Either DDT -9 or the Linking Loader must be used to load user object programs for execution.
Refer to the appropriate Monitor Guide (I/O Monitor of Keyboard Monitor) for operating procedures.

1-49

PDP-9 FORTRAN IV

Since A is a single-precision, floating-point number, two machine words are required and
rnust be accounted for in the subprogram. Thus MINl and MIN2 (which contain the addresses of A and

B) must be incremented to get to the second word of each number. FORTRAN expands the CALL state'rnent as follows:
CALL MIN (A, B)
00013
JMS*
00014
JMP
.DSA
00015
00016
.DSA
$00014=00017

MIN
$00014

(Exit to MACRO-9 subprogram)
(Entry from MACRO subprogram)

A
B

When the program is loaded, the address (plus relocation factor) of A is stored in location
00015 (plus relocation factor) and the address of B in 00016 (plus relocation factor). When .DA is
c:alled from the MACRO-9 subprogram, it stores these addresses in MIN1 and MIN2 (plus relocation
factor). Thus MIN 1 must be referenced indirectly to get the value of A (a direct reference would get
the address of A).

Linking MACRO-9 Programs With FORTRAN IV Subprograms:
There are two forms of FORTRAN IV subprograms: subroutines and external functions. The

main difference between the two is the method of returning arguments to the calling program: subroutines
return the argument directly to the calling program, while functions return arguments through accumulators.
The MACRO-9 program set-up for a FORTRAN IV subroutine is basically that described in
Part III of this manual for FORTRAN IV Science Library routines. The name of the subroutine to be
c:alled must be declared as a global, there must be a jump around the argument addresses, and the number and type (integer, real, double precision) of arguments must agree from the calling program to the
subroutine.
An example of a calling routine:
TITLE
.GLOBL
JMS*
JMP
.DSA
.DSA

SUBROT
SUBROT
.+N+l
ADDR OF ARG1
ADDR OF ARG2

/+400000 if indirect
/+400000 if indirect

.DSA

ADDR OF ARGN

/+400000 if indirect

I-50

PDP-9 FORTRAN IV

APPENDIX 3
FORTRAN IV AND MACRO-9 LIN KAGE
Linking FORTRAN IV Programs With MACRO-9 Subprograms

1•

There are two essential elements of a MACRO subprogram that is linked to FORTRAN IV.
One is the dec laration of the name of the subprogram (as used in the F4 program) in a • Gl.OBL statement
with in the subprogram. The second is leaving open registers in the subprogram for the transfer vectors of
the arguments used in the FORTRAN calling sequence. The number of open registers must agree with the
number of arguments given in the calling sequence.
As an illustrative example, consider a FORTRAN program and a MACRO-9 subprogram wh ich
read negate, and write a number. One positive, sing le-prec ision floating-point number is read by the
I

FORTRAN program, negated in the MACRO-9 subprogram, and written out from the FORTRAN program.
FORTRAN IV PROGRAM:
C
C
1

100
C
C

TEST MACRO SUBPROGRAM
READ A NUMBER (A)
READ (l, 100) (A)
FORMAT (E12.4)
NEGATE THE NUMBER AND PUT IT IN B
CALL MIN (A, B)
WRITE OUT THE NUMBER (B)
WRITE (2, 100) B
STOP
END

MACRO-9 SUBPROGRAM:
•TITLE MIN
.GLOBL MIN, .DA

MIN

MINl
MIN2

JMS*

.DA

JMP

.+3

.DSA
.DSA
LAC*
DAC*
ISZ
ISZ
LAC*
TAD
DAC*
JMP*
.END

0
0
MINl
MIN2
MINl
MIN2
MINl
(400000
MIN2
MIN

/ENTRY/EXIT
fUSE THE F4 GENERAL GET ARGUMEI\JT
/SUBPROGRAM TO LOAD THE ARGUMENTS
/JUMP AROUND REGISTERS LEFT FOR
/ ARGUMENT ADDRESSES
/ARG 1
/ARG2
/PICK UP FIRST WORD OF A
/STORE IN FIRST WORD OF B
/BuMp THE POINTER TO SECOND WORD
/OF A AND B
/PICK UP SECOND WORD OF A
/SIGN BIT = 1
/STORE IN SECOND WORD OF B
/EXIT

I-51

PDP-9 FORTRAN IV

When the FORTRAN IV subroutine is compiled, the compiler will generate code for .DA,
the General Get Argument Routine, which will transfer the arguments from the MACRO-9 calling program to the FORTRAN IV subroutine.

• DA expects to find the calling sequence just described for the

c(]11 ing program. The following is an example of an expansion of the beginning of a FORTRAN IV
subroutine.

TITLE SUBROT
SUBROUTINE SUBROT (A, B)
CAL
0
JMS*
.DA
JMP
$000002
.DSA
A
.DSA
B

000000
000001
000002
000003
00004
$000002=000005

The simplest method of passing arguments be"tween the main program and the subroutine is to
use one of the calling clrguments as output.

For example, if the value of D is to be calculated in the

subroutine, use D as one of the calling arguments.

IID=II will generate a IIDAC* D", which will store

the value calculated for D by the subroutine in location D in the calling program.
The MACRO-9 program set-up for a FORTRAN IV External Function is identical to that for
liinkage with subroutines, except that some provision must be made for storage of the values calculated
and stored in the accumulator.

In the case of integers, the value is returned in the A-register, and in

the floating accumu lator for rea I and double prec ision numbers. The simplest method of storing the
values is to use the FORTRAN IV routines furnished in the library for this purpose • . AH store real values, and .AP stores double precision values.

Since the A-register is the standard hardware accumulator,

a DAC instruction will store integer values.

3,.

Linking MACRO-9 Programs With FORTRAN IV Library Routines
Refer to Part III of this manual, PDP-9 Science Library, for a complete description of the

linkage to library routines.

I-52

PDP-9 FORTRAN IV

APPENDIX 4
CHAINING FORTRAN IV PROGRAMS

Chaining is a method of program segmentation that allows for multiple core overlap of
executable code and certain types of data areas. FORTRAN programs can thus be divided into segments
and executed separately, with intersegment commun ication of data accomplished through c.ommon storage. Common areas of core are reserved by means of the blank COMMON statement.
Transfer of control from one chain segment to another can be specified in a FORTRAN source
program with the statement
CALL CHAIN (N)
where N is the segment number to be called. The chain number (N) is established at chain-build time
(refer to the CHAIN section of the Keyboard Monitor Guide, DEC-9U-NGAA-D). N can be greater
than or less than but not equal to the current chain number. A STOP statement must immediately precede the END statement in the main program for each chain. Only variables and arrays named in blank
COMMON statements are retained from one chain segment to another. Blank common size should be
the same for all chain segments.
C
C
C

TEST CHAIN PROGRAM
CHAIN JOB SEGMENT 1
COMMON A,B,C
DIMENSION ARRAY (10, 10)
READ (4,5) ARRAY

CALL CHAIN (2)
STOP
END

CHAIN JOB SEGMENT 2
COMMON A,B,C
DIMENSION TABLE (30)

CALL CHAIN (3)

STOP
END
C

CHAIN JOB SEGMENT 3
COMMON A,B,C
DIMENSION A LIST (5,5)

I-53

PDP-9 FORTRAN IV

WRITE (4,6) ALIST

6 FORMAT (E10.3)
STOP
END

I-54

PDP-9 FORTRAN IV

APPENDIX 5
FORTRAN IV ERROR LIST

These letter-coded error messages apply to F4 V2A and all versions of F4 thereafter and all
versions of F4A. Refer to page II-2 of this manual for a list of object-time errors.

Error Code

Cause

Syntax error

Statement cannot be recognized as a properly
constructed FORTRAN IV statement.

Variable/constant
mode error

Illegal mode mixing. Missing constant, variable or
exponent, or illegal matching of constants or variables in a DATA statement.

Statemen t number error

Phase error, number more than 5 digits, no statement
number where one is required, statement shouldn It
be labeled or doubly defined statement numbers.

Argument/subscript error

Missing argument or subscript, illegal use of subscripts, illegal construction of subscripted variable,
more than 3 subscripts or stated number of subscripts
does not agree with declared number.

FORMAT statement error

Illegal FORMAT specification or illegal construction
of FORMAT statement.

Charac ter/ statemen t/
term error

Illegal character, unrecognizable statement, illegal
statement for program type, statement out of order
or improper statement preceding END statement.

DO loop error

Illegal DO construction or illegal statement terminating DO LOOP.

Table overflow

Symbol/constant/arg (I)/OP(I) table limits exceeded.

Nesting error

Illegal nesting or DO nesting too deep.

Magn itude error

Program exceeds 8190 words, maximum number of
dummy arguments or EQUIVALE NCE c lasses exceeded,
or constant/variable exceeds specified limits.

COMMON/EQUIVALENCE/
DIMENSION/DATA statement
error

Illegal construction of statement, illegal EQUIVALENCE relationships, illegal COMMON declaration
or non-common storage declared in BLOCK DATA
subprogram.

FUNCTION/SUBROUTIN E/
EXTERNAL/CALL statement
error

Illegal use of FUNCTION/SUBROUTINE name, out
of order I or illegal variable for EXTERNAL dec laration.

Ho Ilerith error

Hollerith data illegal in this statement or illegal of
Hollerith constant.

I-55

PDP-9 FORTRAN IV

APPENDIX 5A
FORTRAN IV ERROR LIST

Th is I ist of error messages appl ies of all versions of F4 prior of V2A.
Error Code

Cause

001

Improper statement preceding END statement.

002

FUNCTION/SUBROUTINE name not used or used improperly in a subprogram.

003

Variable required.

004

Positive non-zero constant required.

005

Symbol-constant table limits exceeded.

006

Statement number has more than 5 digits.

007
008

Unsigned simple integer argument required.
17
Integer va lue greater than (2
-1).

009

Magnitude of number (ignoring decimal point and/or exponent) greater than (2

010

Array element (function reference) and next argument not separated by comma.

012

Exponent missing from numeric field.

014

Open parenthesi s in subscript.

015

Binary operator used in unary sense or missing argument.

016

Additional grouping parenthesis not allowed.

017

Subscri pt I ist terminated before last argument obtained.

018

Too many right parenthesis.

019

Argument follows converted argument (no operator separating them).

021

E or D in numeric field after exponent has been processed.

023

Format descriptor character used in non-format statement.

024

Holleri th data illegal this statement.

025

Non-integer constant precedes Hollerith constant.

026

Length of Hollerith constant exceeds range (0<x<6).

027

Hollerith constant contains statement termination character.

030

Symbolic name exceeds 6 characters.

031

Limit on number of nested functions exceeded.

032

Simple variable delineated by left parenthesis.

033

Subscripted variable used as subscript.

034

Unrecognizable logic term.

036

Logical • NOT. used as binary operator or logical constant used as a binary operator.

037

I1lega I character.

I-57

- 1).

PDP-9 FORTRAN IV

Cause

Error Code
040

Adjusted floating point exponent exceeds 76.

045

Subscri pt expression not de I imited by ", II or ")" •

050

Arg (I), op (I) table overflow.

051

Unsubscripted array reference used as a variable.

052

Function name used as a variable.

053

Comma used other than as parameter separator.

054

Function or array name used in an expression representing a function parameter.

055

Expression used as an assignment variable.

056

Expression contains uneven number of parenthesis.

060

Illegal mode mixing.

063

Signed assignment variable.

069

Doubly defined statement numbers or phase error.

070

Illegal statement for BLOCK DATA program.

071

Statement not a DO or DO illegal as True statement for logical IF.

072

Illegal logical IF true statement.

074

Unrecognizable statement (first 3 characters).

075

Unrecognizable statement (4-n characters).

076

Statement out of order.

077

Statement shouldn It be labeled.

078

First character following READ or WRITE not a left parenthesis.

079

Illegal format specification in READ or WRITE.

080

Binary WRITE has no list.

081

Illegal list element separator.

082

Illegal implied DO construction.

086

DO nesting too deep.

087

Missing DO parameter.

088

Illegal DO parameter construction.

089

Illegal statement type terminated DO.

090

Improper DO nesting.

091

Illegal character following I/o unit specification.

092

Illegal character following FORMAT specification.

095

Name previously appeared in a specification statement.

096

Statement improperly del imited.

097

Illegal array declaration - DIMENSION statement.

I-58

PDP-9 FORTRAN IV

Error Code

Cause

098

Array size greater than 78192 - DATA specification statement.

100

Improper subscript list delimiter in a DIMENSION statement.

101

More than 3 subscripts (dimensions).

102

Integer argument not a constant.

103

Integer constant not less than 8192.

104

Integer constant negative.

105

FORMAT statement has no statement number.

106

Illegal FORMAT specification.

114

COMMON block name has illegal delimiter (not /).

115

Name dec lared as COMMON Block name previously dec lared otherwise.

116

COMMON block size exceeds 8190 words.

117

Declared COMMON variable is a dummy I fu.nction I or already in COMMON.

118

ASSIGN statement missing liTO".

120

Computed GOTO statement number list members not delimited.

121

Computed GOTO statement number list not delimited.

123

Assigned GOTO statement number list no preceded by left parenthesis.

124

Assigned GOTO statement number list not delimited.

126

DATA/EQUIVALENCE variable is a dummy variable.

127

DATA/EQUIVALENCE variable is a function name.

128

DAT A/EQUIVALENCE simple variable subscripted by more than one number.

129

DATA/EQUIVALENCE array element greater than 8192.

130

Missing right or redundant left parenthesis in FORMAT statement.

131

Stated number of subscripts does not agree with declared number.

132

EQUIVALENCE class not started with left parenthesis.

136

EQUIVALENCE class improperly delimited (no right parenthesis).

137

Maximum number of EQUIVALENCE classes exceeded.

138

Illegal EQUIVALENCE relationships.

139

Illegal extension of common block caused by EQUIVALE NCE relationsh ip.

140

Illegal variable for EXTERNAL declaration.

142

Program size exceeds 8190 words.

143

Non-common storage dec lared in BLOCK DATA subroutine.

144

IF expression not terminated by closing parenthesis.

145

No comma separating statement numbers - IF statement.

147

No statement number where one is required.

I-59

PDP-9 FORTRAN IV

Enror Code

Cause

148

Referenced statement number does not appear as a statement label.

149

Illegal statement function name (used twice or is external).

150

Del imiter following statement function dummy argument list not "=" .

151

Function statement out of order {or more than one}.

152

FUNCTION name not followed by argument list.

153

Dummy variable previously dec Iqred as something else.

154

Dummy argument list not enclosed in parenthesis.

155

Maximum number of dummy arguments exceeded.

156

STOP/PAUSE statement constant contains a non-octal digit.

157

STOP/PAUSE statement constant contains too many digits.

158

DATA statement variable is "common" but data not "block data".

159

DATA statement is "block data" but variable is not "common".

160

DAT A statement variables not delimited by a slash.

161

DAT A statement argument not a constant.

162

Mode of variable and corresponding constant disagree in a DATA statement.

163

DAT A statement constants not separated by a comma (may indicate more variables
than constants).

164

Two SlJccessive asterisks used as operators in a DATA statement.

165

Constant preceding asterisk is not integer in a DATA statement.

167

More constants than variables in a DATA statement.

168

RETURN statement in main-body program un it (not subroutine).

169

CALL statement - name is not a function name.

1-60

PDP-9 FORTRAN IV

FORTRAN IV OBJ ECT - TIME SYSTEM

INTRODUCTION
Part II describes the subprograms included in the PDP-9 FORTRAN IV Object Time System.
The Object Time System is a group of subprograms that process compiled FORTRAN IV statements,
particularly I/O statements, at execution time. The compiler outputs calls in the form of globals to
various subprograms, depending upon the content of the FORTRAN program. When the compi led program is loaded via the Linking Loader, the Loader attempts to satisfy these globals by searching the
FORTRAN library. As it finds the required object time subprograms, it brings them into core and sets
up the necessary linkages.
Included in the package are programs for processing formatted and unformatted READ and
WRITE statements, BACKSPACE, REWI ND and ENDFI LE statements, the index of computed GO TO
statements, STOP and PAUSE statements, and File commands. There are eight error messages output by
the object time system which are described in Table 11-1 .
The following information is given for each program:
a.
b.
c.
d.
e.
f.

Class
Purpose
Calling sequence
External calls
Size
Error conditions

11-1

PDP-9 FORTRAN IV

Table 11-1.
OTS Errors
Error Description

Error Number

Library Routines*
That May Cause Error

Not used
Negative REAL Square Root Argument

SQRT

Negative DOUBLE PRECISION Square
Root Argument

DSQRT

¢7

Illegal Index in Computed GO TO

.GO

1;0

Illegal I/O Device Number

.FR, .FW, .FS, .FX,
.FR, .FA, .FE, .FF, .FS,

Bad input data - lOPS Mode Incorrect

.FR,.FA,.FE,.FF,.FS,

Bad FORMAT

.FA, .FE, .FF

Negative or Zero REAL Logarithmic
Argument

. BC,. BE,ALOG

Negative or Zero DOUBLE PRECISION
Logarithmic Argument

. BD, . BF , . BG, . BH,
DLOG, DLOG 1¢

~~Only those routines whose calls are generated by the compiler are listed.

1/-2

PDP-9 FORTRAN IV

OTS Binary Coded Input/Output
BCDIO
1. Cla!ss:

Object - Time System

2. Purpose:

The BCD input/output ohject-time package is designed to process the fOl'matted
READ and WRITE statements in FORTRAN IV programs and subprograms. The
FORTRAN IV compiler generates all the necessary object-time subroutine calls to
perform input and output operations on a character-to-character basis under the
control of a FORMAT statement. To permit FORMAT statements to be a~tered or
read at execution time, the FORMAT statements are interpreted~ by BCDIO at
execution time rather than at compile-time. This has two advantages:
1)

It provides a greater flexibil ity to the FORTRAN programmer,

It provides the ability to utilize fully the capabilities of BCDIO in
machine-language programs.

In demonstrating this capabi Iity, an illustrative MACRO-9 language program is
given below, which reads 8 floating point numbers into memory with F-conversion
and writes them on an output device using the E-conversion.
Example:

ENTRY

. TITLE
.GLOBL
.IODEV
JMS*
JMS*
.DSA
.DSA
LAW
DAC
LAC
DAC

LOOP1
ARG1

.FP,.FR,.FE,.EE,.FW
3,4
.FP
/Initialize I/O device status table.
.FR
/Initial ize device 3 for input
(3)
/under control of FORMAT statement
FRMT1
/FRMT1 and read first record into line
/buffer.
-1¢
/Set loop counter to 8.
COUNT
(ARRAY) /Set element address to first word
ARG1
lin the array.

JMS*
¢

.FE

ISZ
ISZ
ISZ
JMP
JMS*

ARG1
ARG1
COUNT
LOOP1
.FF

JMS*
.DSA
. DSA
LAW
DAC

.FW
(4)
FRMT2
-1¢
COUNT

11-3

/Convert next I ine buffer field from
/BCD to floating point binary and
/store in ARRAY.
/Increment ARRAY address by two.
/Check the counter and
/if not done, repeat loop.
/Otherwise, terminates reading.
/Initia Iize devi ce 4 for output
/under control of FORMAT
/statement FRMT2 .
/Set loop counter to 8.

PDP-9 FORTRAN IV

OTS Binary Coded Input/Output'

LAC
LOOP2
ARG2

DAC
JMS*

/Set element address to first
/word in the array.
/Convert floating-point binary word
/pcir to BCD and store in line-buffer.

ARG2
ARG2
COUNT
LOOP2
.FE

/Increment ARRAY address by 2.

fJ
ISZ
ISZ
ISZ
JMP
JMS*

ARRAY
FRMTl
FRMT2
COUNT

(ARRAY)
ARG2
.FE

HLT
.BLOCK
.ASCII
.ASCII

/
/Check count.
/If not done, go to LOOP 2.
/if done, output last line-buffer
land terminates writing.

2fJ
'{8Fl O. 5} I
'{8E12.5}'

¢
.END

3. Calling Sequences:
a. To initialize a device for BCD input {output}:
JMS*
· DSA
· DSA

.FR (.FW)
address of slot number.
address of first word of FORMAT statement or array.

b. To input (output) a data element:
JMS*
• DSA

.FE
address of element (first word)

c. To input (output) an entire FORTRAN array:
JMS*
• DSA

.FA
address of last word in the Array Descriptor Block.

d. To terminate the current logical record:
JMS*

.FF

All BCDIO routines utilize the F lOPS object-time package to perform all
I/O data transfers between devices and the FlOPS line buffer. Device level
communication is never employed.
e. External Calls:
FlOPS, OTSER, REAL ARITHMETIC

Size:

2773 octal locations

11-4

PDP-9 FORTRAN IV

OTS Binary Coded Input/Output
g. Error Conditions:
OTS ERROR 1.0' - Illegal I/O Device Number
OTS ERROR 11 - Bad Input Data (lOPS Mode Incorrect)
OTSERROR 12 - Illegal FORMAT

11-5

PDP-9 FORTRAN IV

OTS Binary Input/Output
BINIO
1. Class:

Object - Time System

2. Purpose:

The Binary Input/Output .Object-Time package is designed to process the unformatted
READ and WRITE statements in FORTRAN IV programs and subprograms. A FORMAT
statement is not required and the data transfer is on a word-to-word basis instead of
on character-to-character basis, regardless of data type.
The size of the physical data record is always the standard line buffer size provided
by lOPS.
Logical data records are comprised of one or more physical records, the number of
which is determined by the length of the I/O list associated with the WRITE statements that generates the log i ca I record.
Each WRITE statement generates one logical record.
Each READ statement reads one logical record, regardless of the length of its I/O
Iist. For this reason, it is the responsibil ity of the FORTRAN programmer to ensure
that I/O Iists for WR ITE and READ statemerits are compatible.

3. Call ing Sequences:
a. To initialize a device for binary input (output):
JMS*
.DSA

.FS (.FW)
DEVICE

b. To input (or output) an integer data element:
JMS*
.DSA

.FI
address of the element

c. To input (or output) an integer data element:
JMS*
.DSA

.FJ
address of the element (first word)

d. To input (or output) a double precision data element:
JMS*
.DSA

.FK
address of the element (first word)

e. To input (or output) a logical data element:
JMS*
.DSA

.FL
address of the element

f. To input (or output) an entire FORTRAN array:
JMS*
. DSA

.FB
address of the last word in the Array Descriptor Block •

11-6

PDP-9 FORTRAN IV

OTS Binary Input/Output
g. To terminate the current logical record:
JMS*

.FG

The third word of each physical record contains a record of ID numbers starting with
ZERO for the first record. Then ID is incremented by one as each physical record
is generated until the last record in the logical record has bit fI set.
A typical WRITE statement may generate the following record for ID:

LOGICAL
RECORD

PHYSICAL RECORD
FOR ID (OCTAL)

4. External Calls:
F lOPS I OTSER
5. Size:
6.

244 octal locations

Error Conditions:
OTS ERROR 1f1- Illegal I/O Device Number
OTS ERROR 11 - Illegal Input Data (lOPS Mode Incorrect)

11-7

PDP-9 FORTRAN IV

OTS Auxi Iiary Input/Output
AUXIO
1. Class:

Object - Time System

2. Purpose:

Auxil iary Input/Output consists of the processors for the three auxiliary I/O statements in FORTRAN IV: BACKSPACE, REWIND, and ENDFILE.
These statements are normally used to control Magnetic Tape Transports which are
being used by unformatted READ and WRITE statements (BIN 10).

BACKSPACE (.FT):
Repositions the tape at a point just prior to the first physical record
associated with the current logical record.
Example:
WR ITE (7) A, B, C
BACKSPACE (7)
READ (7) D, E,F
These three instructions as shown in the above order cause the data of
A, B, and C to be transferred to D, E, and F.

REWIND (.FU)
Causes the specified device to be positioned at its initial (load) point.

ENDF ILE (. FV)
Issues an lOPS command to close the current file on the specified device.
In the case of Magnetic Tape, this writes a file mark.

Calling Sequences:
a. To backspace one logical record:
JMS*
. DSA

.FT
DEVICE

b. To position a device at its initial point:
JMS*
.DSA

.FU
DEVICE

c. To end (close) a file:
JMS*
. DSA

.FV
DEVICE

4. External Calls:
FlOPS

11-8

PDP-9 FORTRAN IV

OTS Auxil iory Input/Output
5. Size:

64 octal locations

6. Error Conditions:
OTS ERROR l~ - Illegal. I/O Device Number

11-9

PDP-9 FORTRAN IV

OTS lOPS Communi cation
FlOPS
1. Class:

Object - Time System

2. Purpose:

F lOPS provides the nece,ssary calls to lOPS required by all FORTRAN input and
output statements.
Slot numbers are initialized by the .FC routine {Initialize I/O Device}. Initialization of all slots is maintained in the device status table. The first time that .FC is
called for any device, the appropriate .INIT call is made to lOPS. The buffer size
and input/output flag are'stored in the status word table. Then all subsequent calls
to . FC for the same device suppress another .IN IT unless the input/output flag has
changed.
One life buffer is used by all FORTRAN programs. Data transfersbetween the line
buffer and I/O devices are performed by the .FQ routine, which performs a .READ
if the input/output flag {.FH} is "ZERO" or a .WRITE if .FH is "ONE." A .WAIT
is a Iways performed.
The .FP routine is called at the beginning of all FORTRAN main programs. This
routine sets all words in the device status table to zero, indicating that all devices
are uninitialized.

3. Calling Sequences:
a. To initialize the I/O device status table:

JMS*

.FP

b. To specify input:

DZM*

.FH

c. To specify output:

(1)
.FH

LAC

DAC*

d. To select device:
LAC

DEV ICE {address of slot number}
.FC

JMS*

e. 'To input or output the I ine buffer:
LAC

address of . DAT slot number {bits 9-17} and lOPS mode {bits 6-8}
.FQ

JMS*
f.

Notes:
1}
2}

DEVICE is a cell containing the slot number.
The line buffer is in locations .FN to .FN+377 •
8

1/-10

PDP-9 FORTRAN IV

OTS lOPS Communication
3)
4)

The standard line buffer size (for the device currently selected) is in
location .FM.
On output, lOPS header words (.FN and .FN + 1) must be prepared by
the user.

4. External Calls:
OTSER
5. Size:

530 octal locations

6. Error Conditions:
OTS ERROR 1¢ - Illegal I/O Device Number

"-11

PDP-9 FORTRAN IV
OTS Calculate Array Element Address
· SS
1. Class:

Object - Time System

To calculate the array element address. The Array Descriptor Block is constructed
as follows:

Purpose:

wd 1

I 000 I M I Size
0

2 345

wd 2

In * Imax

wd 3

In * Imax * J max

wd 4

I Address of Array I

M: data type - translates to number of words per array element (n)

Type

00
01
10
11

01
02
03
01

integer
real
double precision
logical

Subscript calculation formula (for declared A (I/J , K) and specified A (i/j/k) )
Addr of A (i I j I k) =
A + (i - 1) * n + (j - 1) * 1 * n + (k+ 1) * 1 * J * n
~

wd 4

wd 2

wd 3

1-dimension array
\

2-dimension array

•
3-dimension array
3. Calling Sequence;
JMS*
.DSA

.SS
ARRAY

LAC
LAC
LAC
DAC

Sl
S2
S3

/Address (indirect) of array
/Descriptor Block
/Subscript 1 (I)
/Subscript 2 (J)
/Subscript 3 (K)
/Store array element address

11-12

PDP-9 FORTRAN IV

OTS Calculate Array Element Address
4. External Calls:
INTEGER and REAL ARITHMETIC
5. Size:

57 octa I locations

6. Error Conditions:
None.

11-13

PDP-9 FORTRAN IV

OTS Computed GOTO
GOTO (.GO)
1. Class:

Object - Time System

2. Purpose:

To compute the index of. a computed GO TO

3. Ca II ing Sequence:
LAC
V
JMS*
.GO
-N
STMT ADDR (1)
STMT ADDR (2)

/Index value in A-register
/Number of statement addresses

STMT ADDR (N)

4. External Calls:
OTSER

5. Size:

26 octa I locations

6. Error Conditions:
OTS ERROR 7 if the index is illegal (equal to or less than zero).

11-14

PDP-9 FORTRAN IV

OTS Stop
STOP (. ST)
1. Class:

Object - Time System

2. Purpose:

To process the STOP stat·ement and return control to the monitor.

3. Call ing Sequence:
LAC
JMS*
4.

(Octal number to be printed)
. ST

External Calls:
SPMSG (. SP)

5. Size:
6.

13 octo I locations

Error Conditions:
None

11-15

PDP-9 FORTRAN IV

OTS Pause
PAUSE (.PA)

1. Class:

Object - Time System

2. Purpose:

To process the PAUSE statement. After receiving a t P (Control P) from the keyboard, control is returned to the program.

3. Calling Sequence:
LAC
JMS*

(Octal number to be printed)
.PA

4. Externa I Co lis:
SPMSG (. SP)

5. Size:

14 octo I locations

6. Error Conditions:
None

11-16

PDP-9 FORTRAN IV

OTS Octa I Print
SPMSG (. SP)
1. Class:

Object - Time System

2. Purpose:

To print the octal number coded with STOP and PAUSE.
zero (J1) is assumed.

3. Calling Sequence:
LAC
JMS*
. DSA
LAC
LAC
LAC
LAC
LAC
LAC
4.

(Octal integer to be printed)
.SP
{Control return} /pause only
1st Character
2nd Character
3rd Character
4th Character
5th Character
6th Character

Externa I Ca lis:
None

5. Size:
6.

74 octal locations

Error Conditions:
None

11-17

If no number is given,

PDP-9 FORTRAN IV

OTS Errors
OTSER (. ER)
1. Class:

Object - Time System

2. Purpose:
a.

To announce an error on the teletype:

JMS*
.DSA

.ER
Error number

If bit ¢ of the error number is a 1, the error is recoverable and program controi
is returned to the calling program at the first location following the error number.

If bit ¢ of the error number is a ¢, the error is unrecoverable and program co~trol
is transferred to the monitor by means of the. EXIT function.

In the case of recoverable errors, the AC and link are restored to their original
contents prior to returning control to the caller.

If the error is a bad format statement (unrecoverable), the current 5/7 ASCII
word pair of the erroneous format statement is printed in clddition to the error
number.

Calling Sequence:

JMS*
.DSA
ERROR #12
only

LAC
LAC

.ER
Error number, octa I
Note word 1
Note word 2

Words 1 and 2 are the current 5 characters (in 5/7 ASCII of the bad
format statement (ERROR #12)
4.

External Calls:
None

5. Size:
6.

117 octal locations

Error Conditions:
None

11-18

PDP-9 FORTRAN IV

File Commands
FILE
1. Class:

External Subroutine

2. Purpose:

To provide the device-independent .IOPS commands SEEK, ENTER, and CLOSE.
These commands are used to allow the FORTRAN IV Object Time System to communicate with .IOPS file-oriented devices.
a.

SEE K finds and opens a named input fi Ie.

ENTER initiates and opens a named output file.

CLOSE terminates an input or an output file and must be used if SEEK or ENTER
has been used.
NOTE
BACKSPACE, REWIND, and ENDFILE commands should never
be used with a device that is operating in the fi Ie-oriented
mode using the above subroutines.

3. Call ing Sequences:
a.

To seek a named file:
CALL SEEK (N,A)
where N = device number
A = array name containing the- 9-character 5/7 ASC 1/
file name and extension.

To enter a named file:
CALL ENTER (N,A)
where N and A are the same as for SEEK.

To close a named file:
CALL CLOSE (N)
where N is the same as for SEEK.

External Calls:
FlOPS, . DA, . SSe

5. Size:
6.

174 octal locations

Error Conditions:
OTS Error 10 if I/O device number is illegal.

1/-19

PDP-9 FORTRAN IV

PDP-9 SCIENCE LIBRARY

INTRODUCTION
All mathematica I routines in the PDP-9 Sc ience Library are descri bed in Part III. Most of the
descriptive material is listed in Table 111-1; in cases where detailed calculations or algorithms are involved, a reference (~) is made in column 1 to detailed descriptions following the table. Information
given in Table 111-1 for each routine includes the routine name, mnemonic, calling sequence, function,
mode, errors, accuracy and timing (where ava i lable), storage requirements, and external ca lis. Routines are categorized by Intrinsic Functions, External Functions, Sub-Functions, or part of the Arithmetic Package and are listed in the table accordingly.

Intrinsi c Functions
Intrinsi c Functions are predefined subprograms that are part of the FORTRAN library. The
type of each Intrinsic Function and its arguments is predefined and cannot be changed.

Intrinsic

Functions are referenced in a FORTRAN program by writing the function name along with the desired
arguments in an appropriate FORTRAN statement.
Example:

x = ABS (A)
External Functions
External Functions are independently written programs that are executed each time their
name appears in a FORTRAN program.
and computes a single result.

Each External Function accepts one or more numerical arguments

SIN, COS, and ALOG are examples of external functions. All basic

External Functions suppl ied with the FORTRAN system are described in Table 111-1 •
Sub-F unct ions
Sub-Functions are called by Intrinsic and External Functions, but are not directly accessible
to the user via FORTRAN. For example, the Sub-Function . EB is called by the External Function SIN,
and performs the actual computation of the sine.
The Arithmeti c Package
The Arithmetic Package contains all arithmetic routines required for integer, real, and
double precision arithmetic.

Both EAE and non-EAE versions are available, depending upon the hardware.

111-1

P DP-9 FORTRAN IV

Accumulators
There are three accumulators referred to in the CALLING SEQUENCE column of the table.
These include the A-register, the floating accumulator, and the held accumulator.
A·-Reg ister
The A-register is the standard hardware accumulator and is used in some of the computations
thlJt involve integer values.
Fk>ating Accumulator
The floating accumulator is a software accumulator that is included in the REAL ARITHMETIC
package.

It is a 3-word accumulator, .AA being the label of the first word, .AS the second, and .AC

the third.

Numbers are stored in this accumulator in the following format:

EXPONENT (2 1s COMP.)

.AA

17
SIGN OF MANTISSA

.AS

HIGH ORDER MANTISSA

012

.AC

LOW ORDER MANTISSA

Negative mantissae are indicated with a change of sign.
Used by both the single and double precision routines, this format is also that of double preci~don numbers.

Sing Ie precision numbers have a different format and must be converted before and

after use in the floating accumulator. The format of sing Ie precision numbers is:
EXPONENT
(2 1s COMP.)

LOW ORDER
MANTISSA

o
SIGN OF
MANTISSA

I> I
o

HIGH ORDER MANTISSA

111-2

PDP-9 FORTRAN IV

Held Accumulator
The held accumulator has the same format as the floating accumulator and is used as temporal'y storage by some routines. The labels of the three words are CE01, CE02, and CE03.
,'AII ~..
~ F.I'\ ,a. \c 'iQ,o.. \

.~()r :=. .c.t£ -I : .. CE ~/, .c_'Eo -3':

Calling Sequences

The MACRO-9 call ing sequences, given in the third column of Table 3-1, assume in some
cases where there are two arguments, that the appropriate accumulator has been loaded with the first
argument.

If the first argument is an integer value, it can be loaded into the A-register wHh a LAC

instruction.

If the first argument is a real or double precision value, the routines .AG and .AO,

respectively, should be used to load the floating accumulator. The DAC instruction may be used to
store the result of routines that return with an integer value in the A-register. The routines .AH and
.AP should be used to store the result of routines that return with real or double precision values in the
floating accumulator.
In calling sequences that use the. DSA pseudo operation to define the symbolic address of
arguments, 400000 must be added to the address field if indirect addressing is involved.
FORTRAN I ibrary routines that are used in MACRO-9 programs must be declared with a
. GLOBL pseudo operation in the MACRO-9 program. There must be agreement in the number and type
of arguments between the calling program and the FORTRAN libra~y routine.
The following example shows a section of a MACRO-9 main program that uses the FORTRAN
External Function SIN .
. TITLE
.GLOBL

SIN, .AH

JMS*
JMP
.DSA
JMS*
.DSA

.DSA
.DSA

o
o

SIN
.+2
.AH
X

/JUMP AROUND ARGUMENT
/+400000 IF INDIRECT
/STORE IN REAL FORMAT AT X

When the above MACRO-9 program is loaded, the Linking Loader will attempt to sat isfy the
globals by searching the Science Library. The External Function SIN and the REAL ARITHMETIC package wi II be loaded.

The references to these routines in the MACRO-9 program must be indirect (as

indicated in the example) since only the transfer vectors are given in the main program.

" 1-3

Table III-l
PDP-9 Science Library

ROUT! NE NAME

Mnemonic

Calling Sequence

Errors

Accur.
Bits

1=1**1

None

N.A.
26

Mode

Function

Timing
NonEAE
EAE

Storage
(Octal)

Externa I Co lis

INTRINSIC FUNCTIONS
Exponentiation:

I .BB
Integer Base, Integer Exponent

I~~.
LAC

ARGI

(oo"')}

. SS
ARG2 (exp)

I**K
-..,

Note 1

I
45

INTEGER

23.2 ms

· EE, . EF, REAL

Real Base, Integer Exponent

.BC

A**K

R=R**I

#13, if base .:sO

DP Base, Integer Exponent

.BD

A**K

D=D**I

#14, if base

27.8 ms

· DE, . DF , DOUBL~

Rea I Base, Rea I Exponent

. BE

A**B

R=R**R

#13, if base <0

23.0 ms

.EE, .EFrREAl

Real Base, DP Exponent

.BF

A**B

D=R**D

#13, if base .::5,0 26

27.6 ms

· EE, ~ DF, DOUBLE

DP Base, Real Exponent

.BG

A**B

D=D**R

#14, if base.5!J

27.6 ms

· DE, . DF, DOUBLE

DP Base, DP Exponent

.BH

A**B

D=D**D

#14, if base

.:so 32

26.6 ms

· DEr . DF, DOUBLE

R=ABS(R)

None

N.A.

120 f.lS

· DA,REAL

II I

I=IABS(I)

None

N.A.

64 f.ls

.DA

IA I

D=DABS{D)

None

N.A.

120 f.lS

.DA, DOUBLE

of A H_}
~lest integer

R=AINT(R)
I=INT(R)
I=IDINT{D)

I None

N.A.
N.A.
N.A.

365 f.lS
180 f.lS
180 f.ls

15
13
13

· DA,REAL
.DA,REAL
.DA,REAL/DOUBLE

JMS*
.DSA

SUBR
ADDR of ARG2
(exp.)

......

Absolute Value:
Real Absolute Value

ABS

Integer Absolute Value

lABS

DP Absolute Value

DABS

IA
JMS*
1-< JMP
.DSA

SUBR
.+2
~
ADDR of ARG

Truncation:
Real to Real Truncation
Real to Integer Truncation
DP to Integer Truncation

:s.0 32

AINT
INT
IDINT

-,.

.....

Remo indering:

None
None

Real Remaindering

AMOD

Note 2

R=AMOD(R,R)

None

N.A.

3015 f.lS

.DA,REAL

Integer Remaindering

MOD

Note 2

I=MOD(I, I)

None

N.A.

477 f.lS

· DA, INTEGER

DP Remaindering

DMOD

Note 2

D=DMOD(D, D)

None

N.A.

3335 flS

.DA,DOUBLE

R=SIGN(R,R)
I=SIGN(I,I)
D=SIGN(D,D)

None
None
None

N.A.
N.A.
N.A.

198 f.lS
81 f.lS
192 f.lS

26
20
26

· DA,REAL
.DA
.DA,DOUBLE

Tronsfer of Sign:
Real Transfer of Sign

SIGN

Integer Transfer of Sign

ISIGN

DP Transfer of Sign

DSIGN

JMS*
JMP
1-< .DSA
.DSA

SUBR
.+3
ADDR of ARGI )0ADDR of ARG2

gnr

Sign of A2

Positive Difference:
Real Positive Difference

DIM

Al-MIN(Al,A2)

R=DIM(R,R)

None

N.A.

794 f.ls

· DA,REAL

Integer Positive Difference

IDIM

Il-MIN(ll,12)

I=IDIM(I,I)

None

N.A.

85 f.1S

• DA, INTEGER

Conversion:
Integer to Real Conversion

FLOAT

A-I

R=FLOAT(I)

None

N.A.

246 f.1S

· DA,REAL

Reo I to Integer Conversion

IFIX

I A

I=IFIX{R)

None

N.A.

180 f.lS

· DA,REAL

A-B

R=SNGL(D)

None

N.A.

144 f.ls

.DA,DOUBLE

A-B

D=DBLE(R)

None

, N.A.,

115 flS

,. DA,REAL

DP to Real Conversion

SNGL

Re~1 to DP Conversion

DBLE

NOTES:
1.
2.

fMS'
JMP

SUBR

}

.+2
.DSA ADDR of ARG

Timing indicated in this column is estimated unless indicated to be otherwise with a dagger (t). The dagger indicates actual, average-to-worst'-case times based on arbitrarily chosen values.
Timing is dependent upon the size of the exponent, but is appraximately equal to 335 f.lS times n, where n is the largest powe' of 2 in the exponent.
Remaindering is defined as Al - [Al/A2] A2, where [Al/A2] is the integer whose magnitude does not exceed the magnitude of Al/A2 and whose sign is the some as Al/A2.

111-5

Table III-l (cont)
PDP ... 9 Science Library

IFunction

Calling Sequence

Mnemonic

ROUTINE NAME

Mode

Errors

INTRINSIC FUNCTIONS (Coot)

, ,
I,
Max.mum/Mlnlmum
Va.ue.

Integer Maximum/Minimum

IMNMxl

GMS* MAXO,MINO,
AMAXO, or AMINO
.+n+l
ADDR of ARGI
ADDR of ARG2

Integer to Integer Max.

MAXO

Integer to Integer Min.

MIND

Integer to Real Max.

AMAXOI

Integer to Real Min.

AMINO

Real Maximum/Minimum

RMNMX

Real to Real Max

AMAXI

ADDR of ARGn

•• t
TImina
NonEAE
EAE

Accur.
Bits.

106 IINTEGER, REAL

I=MAXO(II r ••• fin)

None

N.A.

Note 3

1=MINO(1l

In)

None

N.A.

Note 3

Max. Value

R=AMAXO( 11 , ... In)

None

N.A.

Note 4

Min. Value

R=AMINO(ll, ••• ln}

None

N.A.

Note 4

Max. Value

I Min. Value

JMS* AMAX1,AMIN1,
MAXI, or MIN2
.+n+1
JMP
.DSA ADDR of ARGI
.DSA ADDR of ARG2

, .,

N.A.

R=AMAX1(RI, ...Rn)

None

Real to Real Min.

Min. Value

R=AMiNl (R 1, •••Rn)

None

N.A.

Note 5

Real to Integer Max.

MAXl

Max. Value

I=MAXI (Rl, ... Rn)

None

N.A.

Note 6

Real to Integer Min.

MINI

Min. Value

I=MiNJ(Rl, ... Rn)

None

N.A.

Note 6

. DSA ADDR of ARGn

::Xlltq~·E

DP Maximum

DMAXI or DMINI
.+n+l
ADDR of ARGI

DN\INI

DP Minimum

External Calls

Max. Value

DP Maximum;Minimum

Stol"Clge
(Octal)

117

INTEGER, REAL

105

DOUBLE

Note 5

Max. Value

I ":DMAX 1,(01, ••• ""I None

N.A.

Note 7

Min. Value

D-DMIN1\Dl, ... Dn} None

N.A.

Note 7

.DSA ADDR of ARGn
EXTERNAL FUNCTIONS
Square Root:
Real Square Root

SQRT

DP Square Root

DSQRT

Exponential:

&
DP Exponentia I &

EXP

Real Exponential

DEXP

I
I

Natul"Cll Logarithm:

ill
&

Real Natural Logarithm
DP Natural Logarithm

Real Common Logarithm
DP Common Logarithm

Sine:

DP Sine
Cosine:
Real Cosine
DP Cosine
NOTES:

3.
4.
5.

&
&
&
~

JMS*

SUBR

JMP

.+2

.DSA ADDR of ARG

AlOG
DLOG

R=SQRT(R)

#S,ARG < 0

t6.657ms

t 3.584 ms

· DA t • ER,REAl

D=DSQRT(D)

#6,ARG < 0

tS.191ms t 4.094 ms

· DA t • ER, DOUBLE

R=EXP(R)

#13, ARG ~O

t 15.489 ms t 4.672 ms

.DA, .EF, .ER,REAL

#14, ARG ::=:0 I 34

D=DEXP(D)

T 17.664 ms. ·7.223 ms

.DA,DF, .ER/
DOUBLE

R=ALOG(R)

#13, ARG <0

· DA, . EE, . ER,REAL

D=DLOG(D)

#14, ARG <0

t 8.197 ms t 4 . 092 ms
t 15.489 ms t 4.095 ms

· DA f • DE, . ER,

DOUBLE

Common Logarithm:

Real Sine

I
ALOGlq

R=ALOG10(R)

#13, ARG <0

t S. 197 ms t 4.094 ms

DLOGlq

D=DLOG 1O(D)

#14, ARG <0

t ll . 7ms

Sin (X)

R=SIN(R)

None

I t 10.368 msl t 4 . 094 ms

D=SIN(D)

None

I t 16.383

=1 t 5.632 =

I·DA/.EB,REAL

Sin (X)

Cos (X)
Cos (X)

R=COS(R)
D=COS(D)

None
None

26
34

I '11.025 ""I t 4.901 ""
I t 16.383 msl t 6.145 ms

20
21

~~N
COS
OCOS

57,",5 + 40 ps for each argument.
242 VS + 40..,s for each argument.
168..,s + 624 ps for each argument.

J
6.
7.

233 ~ + 624 ps for each argument.
163 tis + 607 fS for each argument.

II 1-7

· DA t . EE,. ERtREAL

I'
I'

DA,. DE, .,ER,
DOUBLE

DA, DB, DOUBLE

DA,. EB,REAL
· DA, . DB, DOUBLE

Table 111-1 (cont)
PDP=9 Science Library

ROUTINE NAME

Mnemonic

Ca II ing Sequence

Function

Mode

Errors

EXTERNAL FUNCTIONS (Cont)

ill
DP Arctangent
&
Real Arctangent (x/y) &

tan -1 (a)

R=ATAN(2)

tan -1 (a)
-1
tan (x/y)

D=DATAN(D)
R=ATAN2(R,R)
D=DATAN2(D, D)

tanh (a)

.EB

ill
ill

Real Arctangent

DP Arctangent (x/y)
Hyperbolic Tangent

ATAN

ATAN or DATAN
JMP
.DSA ADDR or ARG

Storage
(Octo I) External Calls

tMS'

Arctangent:

Timing
NonEAE
EAE

Accur.
(Bit.s)

None

16.352 ms

None

14.6 ms

• DA, . DD I DOUBLE

None

12.4 ms

.DA,.ED,REAL

None

16.2 ms

· DA,. DD, DOUBLE

R=TANH(R)

None

16.383 ms

• DAr. EF, REAL

Sin (a)

R=. EB(R)

None

9.3 ms

100

· EC, .REAL

.DB

Sin (a)

D=. DB(D)

None

10.8 ms

116

· OC / • DOUBLE

.ED

tan -I (a)

R=.ED(R)

None

11.0 ms

· EC , .REAL

tan -1 (a)

D=.DD{D)

None

14.5 ms

144

· DC / . DOUBLE

109 a
2
1092 a

R=.EE(R)
D=.DE(D)

#13, ARG ~ 0 26
#14, ARG ~ 0 32

9.0 ms
10.7 ms

71
101

.ER/.REAL
· ER, . DOUBLE

R=. EF(R)

None

12.2 ms

116

REAL

D=. DF(D)

None

15.0 ms

137

DOUBLE

R=.EC(R ,R 11
2
... R )
n

None

N.A.

Note 8

REAL

D=. DC(D2, Dll

None

N.A.

Note 8

DOUBLE

DATAN

t~S'

ATAN2 or DATAN2
JMP
.+3
.DSA ADDR of ARGI
.DSA ADDR of ARG2

ATAN2

DATAN2

TANH

~S'

TANH
.+2
JMP
.DSA ADDR OF ARG

}

-1

(x/y)

7.233 ms

.DA, .ED,REAL

......

SUB-FUNOIONS

tan

5.632 ms

Sine Computation:
Real Sine
DP Sine

ill

Arctangent Computation:
Real Arctangent
DP Arctangent

.DD

1-< JMS* SUBR

Logarithm (Base 2) Computation:
Real Log
DPL09

NOTE

ill

.EE

Enter with argument in
floating accumulator.
Returns with result in
floating accumulator.

Exponential Computation:
Real Exponential
DP Exponential

.EF

.DF

Real Polynomial Evaluation

DP. Polynomial Evaluation

......,

Polynomial Evaluation:

JMS*
CAL

.EC

.EC or .DC
PLiST

X
X

n
~

i=O
2i+l
CZi+1 Z

ill

.DC

PLiST

1-<

-N

/-No. of
terms +1
/last term

;>
C
i=O
n
2i+l
C
/next to last
C2i+1 Z
n-l

... Dr!

NOTES:

/2nd term

/Ist term

2.0 ms + I .3 ms for each coeffi cient.

111-9

Table III-l (cont)
PDP-9 Science Library

ROUTINE NAME

IMre=J

Calling Sequence

Function

SUB-FUNCTIONS (Cont)
~

Routine that calls
Calling Routine

.DA

General Get Argument

JMS*
JMP
.DSA
.DSA

SUBR
.+n+l
ARGI
ARG2

Calli",

JMP
._,
(address of ARG1)
(addre~s of ARG2)

DSA

ARGn

ARITHMETIC PACKAGE

Multipl ication
Division
Reverse Division
Subtraction
Reverse Subtraction
Double Precision Arithmetic:

INTEGE

ARGI
A-Register

.AD
.AE
.AF
.AY
.AZ

Multiplicand
Dividend
Divisor
Minuend
Subtrahend

DOUBLE

Load
Store
Add
Subtract

.AO
.AP
.AQ
.AR

Reverse Subtract
Multiply
Divide
Reverse Divide

.AU
.AS
.AT
.AV

Real Arithmetic {Includes
Floating}:
Load
Store
Add
Subtract
Reverse Subtract
Multiply
Divide
Reverse Divide

REAL

I
I
I

ARGI
FL.ACC.
Value
Augend
Minuend
Subtrahend
Multiplicand
Dividend
Divisor
ARGI
FL.ACC.

I Errors
None

N.A.

Note 9

I N.A.
I

I
II
I

Multiplier
Divisor
Dividend
Subtrahend
Minuend

I I*J
JMS*
LAC

SUBR
ARG2

None

J-J

1=1*1
1=1/1
1=1/1
1=1-1
1=1-1

N.A.
N.A.
A+B
A-B

D=.AO(D) None
D=.AP{D) None
D=D-D
None
D=D-D
None

I/J
J/I
!-J

None
None
None
None
None

Note 11

>81 fJS
352 fJs

t 48 fJS
t 55 fJS

ARG2
-

REAL

142

Address
Address
Addend
Subtrahend )..-JMS* SUBR
.DSA ARG2
Minuend
Multiplier
Divisor
Dividend
ARG2
-

.AG
.AH
.AI
.AJ

Value
Augend
Minuend

Address
Address
Addend
Subtrahend

.AM
.AK
.AL
.AN

Subtrahend
Multiplicand
Dividend
Divisor

Minuend
Multiplier
Divisor
Dividend

I B-A

D=D-D
O=D*D
D=D/D
D=D/D

A*B
A/B
B/A

None
None
None
None

t 70 flS
t72 f.is
t 255 J.lS
t 324 fJS
t 1. 937 rns ~ 264 f..IS
tl.327 rns T 324 f..!S

Note 12

I N.A.

JMS* SUBR
.DSA ARG2

N.A.
N.A.

Ii A+B
A-B

R=.AG{R)
R=.AH(R)
R=R+R
R=R-R

None
None
None
None

R=R-R
R=R*R
R=RjR
R=R;R

None
None
None
None

N.A.
N.A.

t 67 f..!S

t 70 fls
t280 fJS
t 385 fJS
!

8-A
I A*B

I A/B

I B/A

37 fJS + 15 fls for each argument.

10.

The sign of the resul t (the exc! usive OR of the sign bits of .AB and CE02) is stared in .C E. The sign of .AB is saved in CE05.

11.

130 for EAE, 164 for non EAE.

12.

Stomg·1
(Octal)
External Calls

I EAE

ARG2
-

NOTES:

N.A.

--.,

Integer Arithmetic:

Mode

NonEAE

(addre~ of ARGnJ

Accur.
Bits

Routin~

CAL
.DA

SUBR
JMS*

Timing t

t
t2.047 ms

+
;.272 }-is

1.537 ms

\ 352 fJS

II
I

8
8
764 for EAE I 733 for 110n EAE.
8

III-ll

Table III-l (cont)
PDP-9 Science Library
Timing
Mode

Errors

A~-A

R=.AW(I)
1=. AX(R)
R=. eA(R)

None
None
None

N.A.
N.A .
N.A.

Function

Colling Sequence

Mnemonic

Accur.
Bits

NonEAE

185 ~
65 J.lS
10 J.IS

EAE

Storage
(Octal)

External Calls

ARITHMETIC PACKAGE (Cont)
A-R~ister

Floating Arithmetic

'l.ACC. }
F.P. No •
F.P. No.

A~I

Float
Fix
Negate

. AW
•AX
.BA

Integer

FL.ACC.

HELD ACC;

Multiply

.CA

Multiplicand

Multiplier

A*B

R=R*R

None

Divide

.CI

Divisor

Dividend

A/B

R=R/R

None

Add

.CC

Augend

Addend

A+B

R=R+R

None

Normalize

. CD

Value

N.A .

R=.CD(R)

None

N.A.

Hold
Round & Sign
Sign Control

.CF
. CH
.CG

Value
Value
Value

N.A.
N.A .
Note 10

R=.CF(R)
R=.CH(R)
R=.CG(R)

None
None
None

N.A.
N.A.
N.A.

(avg)
1124 J.IS
(real)
1444 J.lS
(DP)
300 ~
(avg)
160 J.IS
(avg)
16 J.IS
30 J.ls
3OJ.IS

Short Get Argument

.CB

R=. CB(R)

None

N.A.

28 J.IS

JMS*

fl 0 }
JMS* .CB
CAL a
.DSA 0

Value

JMS*

SUBR

I+-A

774 J.lS

N.A.

III-13

PDP-9 SCIENCE LIBRARY ALGORITHM DESCRIPTIONS
1.

SQUARE ROOT (SQRT, DSQRT)
A first-guess approximation of the square root of the argument is obtained as follows.
If the exponent (EXP) of the argument is odd:
f. EXP - 1\
'-2-)

Po = .5

(EXP-l )
+ ARG

If the exponent (EXP) of the argument is even:
(EXP -1)
+ ARG 2
Newton's iterative approximation is then applied three times.

-r-'
(.if'+: AR,Q ,,)
i+l
2
=

b" tt'C-~ <:JL. ~.-\.U ~

1'r'.".~

?; ?-l ~-r

)

EXPONENTIAL (EXP, DEXP, .EF, .DF)

eX is ca Icu lated as

and will have an integral portion (I) and a fractional portion (F). Then

and n = 6.

where

The values of Care:

Co
C

1.0

f 0.34657359

0.06005663

0.00693801

0.00060113

0.00004167

4
5

0.00000241

111-15

PDP-9 FORTRAN IV

NATURAL AND COMMON LOGARITHMS (ALOG, ALOG10, DLOG, DLOG10)
The exponent of the argument is saved as one greater than the integral por'tion of the
result. The fractiona I portion of the argument is considered to be a number between

1 and 2. Z is computed as fo I lows .

x - t.J2

Z=---

X + tJ"2
Then

log X = -1 +

i=O

C
2i + 1

Z2i+i\
)

where n = 2 for ALOG, and n = 3 for DLOG. The values of C are as follows.
ALOG & ALOG10
C
C
C

1
3
5

DLOG & DLOG10

= 2.8853913

= 0.96147063

= 0.59897865

C
C

Finally,

1
3
5
7

2.8853900
0.96180076
= 0.57658434

0.43425975

2
log X = (I092 X) (log ), for ALOG & DLOG
e
e

and

2
10910 X = (I092 X) (I0910 ), for ALOG10 & DLOG10.

SINE AND COSINE (SIN, COS, DSIN, DCOS, . EB, . DB)
The argument is converted to quarter circles by multiplying by 2/1'1'. The low two bits
of the integral portion determine the quadrant of the argument and produce a modified
value of the fractional portion (Z) as follows.
Low 2 Bits

Quadrant

Modified Value (Z)

00
01
10
11

F
1-F
-F
-(l-F)

"
III
IV

Z is then applied to the following polynomial expression.
sin X

=(~

i=O

Z 2i + 1,\
C
2i + 1
)

where n=4 for REAL routines and n=6 for DP routines. The values of C are as follows.

III-16

PDP-9 FORTRAN IV

REAL ROUTINES

DP ROUTINES

= 1.570796318

=-0.6459637111
3
C5 = 0.7968967928

1
3

= 1.5707932680
=-0.6459640975

C :;:: 0.06969262601
5
C :;:: -0.004681752998
7
C = O. 00016043839964
9
C :;::-0.000003595184353
11
C 1 3 = 0.00000005446285

C =-0.00467376557
7
C = 0.00015148419
9

The argument for COS and DCOS routines is adjusted by adding 'h' /2. The sin subfunction is then used to compute the cosine according to the following relationship:
cos x = sin (~ + x)
5.

ARCTANGENT (ATAN, DATAN, ATAN2, DATAN2, . ED, . DD)
For X less than or equal to 1, Z = X, and:
C
Z2i+l\
2i+l

arctangent X = ( ;
i:;::O

where n = 8 for REAL routines and n = 3 for DP routines. For X greater than 1,
Z = l/X, and:

arctangent X:;::

¥-(.~1:;::0 C2i+l Z2i+l\)

where n :;:: 8 for REAL routines and n :;:: 3 for DP routines. The va lues of C are as
follows.
REAL ROUTINES
C
C
C

1
3
5

DP ROUTINES

1.570796327

0.9999993329

:;:: -0.3332985605

C = O. 1994653599
7
C :;:: -0. 1390853351
9
C = 0.0964200441
l1
C = -0.0559098861
13
C :;:: 0.0218612288
15
C :;:: -0.0040540580
17
111-17

= 0.9992150

= -0.3211819
3
C :;:: 0.1462766
5
C = -0.0389929
7

PDP-9 FORTRAN IV

HYPERBOLIC TANGENT (TANH)

tanh

IX I=G
- l+e 21 X I "\-;
\:

e , cal culated as

X lo92 e

X I092e)

will have an integral portion (I) and a

fra cHona I port ion (F), then:

where

2F =

and n = 6

i=O
The values of C are as follows.

C = 1.0
1
C
0.34657359
2
C = 0.06005663
3
C
0.00693801
4
C
0.00060113
5

C = 0.00004167
6
C = 0.00000241
7

LOGARITHM, BASE 2 (. EE,. DE)
The exponent of the argument is saved as one greater than the integer portion of the
result. The fractional portion of the argument is considered to be a number between
1 and 2. Z is computed as follows.

X - ~2

Z=--Then
log X = -1 +

i=O

C2i +1 Z

2i+i\
)

where n = 2 for. EE and n = 3 for. DE. The values of C are as follows.

1II-18

PDP-9 FORTRAN IV

.EE

.DE
C = 2.8853900
1
C = 0.96180076
3
C = 0.57658434
5
C = 0.43425975
7

C = 2.8853913
1
C = 0.96147063
3
C
0.59897865
5

POLYNOMIAL EVALUATOR (. EC , . DC)
The polynomial is evaluated as follows.

111-19