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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
Order Number:	DEC-9A-KFZA-D
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Pages:	118
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FORTRAN IV
Language
Object Time System
Science Library

ADVANCED
SOFTVVARE SYSTEM

DIGITAL EQUIPMENT CORPORATION. MAYNARD, MASSACHUSETTS

FORTRAN IV
Part I. Language
Part II . Object Time System
Part III. Science Library
ADVANCED SOFTWARE SYSTEM
Programmer's Reference Manual

Order No.DEC-9A-KFZA-D from Program Library, Maynard, Mass. Price: $2.50
Direct comments concerning this manual to Software Quality Control, Maynard, Mass.
DIGITAL EQUIPMENT CORPORATION. MAYNARD. MASSACHUSETTS

1st Edition
2nd Edition (Revised)

The following are registered trademarks of Digital
Equi pment Corporati on, Maynard, Massachusetts:
PDP
FOCAL
COMPUTER LAB

DEC
FLIP CHIP
DIGITAL

April 1968
October 1968

CONTENTS

Part I: Language

CHAPTER 1
INTRODUCTION

1.1

Fortran

1-1

1.2

Source Program Format

1-1

1 .2.1

Card Format (IBM Model 029 Keypunch Codes)

1-2

1 .2.2

Paper Tape Format

1-2

CHAPTER 2
ELEMENTS OF THE FORTRAN LANGUAGE

2.1

1-5

Constants

2.1.1

Integer Constants

1-5

2.1.2

Real Constants (6-decimal-digit accuracy)

1-5

2.1 .3

Double-Precision Constants (9-decimal-digit accuracy)

1-6

2.1.4

Logical Constants

1-6

2.1.5

Hollerith Constants

1-7

2.2

1-7

Variables

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

1-8

Arrays and Subscripts

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

1-9

Expressions

2.4.1

Arithmetic Expressions

1-9

2.4.2

Relational Expressions

1-11

2.4.3

Logical Expressions

1-12

2.5

1-13

Statements
CHAPTER 3
ARITHMETIC STATEMENTS

iii

CONTENTS (Cont)
Page
CHAPTER 4
CONTROL STATEMENTS
4.1

Unconditional Go To Statements

1-17

4.2

Ass ign 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

CONTINUE 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

5.1

General I/O Statements

1-24

5.1.1

Input/Output Argument Lists

1-24

5.1 .2

READ Statement

1-24

5.1 .3

WRITE Statement

1-25

FORMAT Statements

1-26

5.2
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

Auxiliary I/o Statements

1-33

5.3.1

BACKSPACE Statement

1-33

5.3.2

REWIN D Statement

1-33

5.3.3

ENDFILE Statement

1-33

CONTENTS (Cont)
Page
CHAPTER 6
SPECIFICATION STATEMENTS
6.1

Type Statements

1-35

6.2

DIMENSION Statement

1-36

6.3

COMMON Statement

1-36

6.4

EQUIVALENCE Statement

1-37

6.5

EXTERNAL Statement

1-38

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 LINKAGE

I-51

APPENDIX 4
CHAINING FORTRAN IV PROGRAMS

I-55

APPENDIX 5
FORTRAN IV ERROR LIST

I-57

APPENDIX 6
SYMBOL TABLE SIZES (F4 V3A)

I-59

ILLUSTRATIONS
1-1

FORTRAN Coding Form

1-3

TABLES
Page
1-1

Intrinsic Functions

1-41

1-2

External Functions

1-43

Part II: FORTRAN IV OBJECT - TIME SYSTEM
Introduction

11-1

OTS Binary Coded Input/Output

11-3

OTS Binary Input/Output

11-6

OTS Auxiliary 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

Fi Ie Commands

11-19

Clock Handling

11-21

Adjustable Dimensioning

11-23
TABLES

11-1

OTS Errors

11-2

Part III: PDP-9 SCIENCE LIBRARY
Introducti on

III-1

Intri nsi c Functi ons

III-1

Externa I Functi ons

111-1

Sub-Functions

111-1

The Arithmetic Package

111-1

Accumulators

III-2

A-Register

III-2

Floating Accumulator

III-2

Held Accumulator

III-3

Calling Sequences

III-3

Algorithm Descriptions

III-l0

TABLES

Page
III-l

III-5

PDP-9 Science Library

vii

HOW TO OBTAIN REVISIONS AND CORRECTIONS

Notification of changes and revisions to currently available Digital software and
of new software manuals is available from the DEC Program Library for the PDP-5,
8,8/S, 8/1, L1NC-8, the PDP-4, 7, and 9 is currently published in DECUSCOPE,
the magazine of the Digital Equipment Computer User's Society (DEC US). This
information appears in a section of DECUSCOPE called "Digital Small Computer
News".
Revised software products and documents are shipped only after the Program Library
receives a specific request from a user.
DECUSCOPE is distributed periodically to both DEC US members and to non-members
who request it. If you are not now receiving this information, you are urged to
return the request form below so that your name will be placed on the mailing list.

To: DECUS Office,
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Maynard, Mass. 01754
Please send DECUS installation membership information.
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Please add my name to the DECUSCOPE non-member mailing list.
Name
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PREFACE

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

rt 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 III).
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 intended 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," by Daniel D. McCracken (published by John Wiley and Sons,
Inc.) is recommended.
Part II, FORTRAN IV Object Time System, describes the group of subprograms that process
compiled FORTRAN statements, particularly I/O statements, at execution time.
Part III, PDP-9 Science Library, provides detailed descriptions of the intrinsic 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 Part I of this
manual.

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

engineer to learn the machine language for specific computers.

Using FORTRAN, he can write pro-

grams 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 FORTRA N compi ler program before execution.

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

It is in a binary-coded form that the

ma chi ne 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 special characters:
Blank
Equals
Plus
Minus
Asterisk
Slash
Left Parent~es is
Right Parenthesis
Comma
Decimal Point
Dollar Sign

/
(
)

1-1

The trans-

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)

which consists of the following fields: statement number field, line continuation field, statement field,
and identification field.
The FORTRAN statement is written in columns 7-72.

If the statement is too long for one

Iine, it can be continued in the statement field of as many Iines 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 columns 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 identification, sequencing, or any other purpose desired by the user. Comments may
be included in the program by putting a "C" in column 1 of each line containing a comment (or continuation of a comment). The compiler ignores these comments except for printing them.
Blanks may be used to aid readabi lity of a FORTRAN statement, except where otherwise
indicated in this manual.

1.2.2

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

characters is exactly the same as for card input, and each line is terminated with a carriage return,
Iine feed sequence.
A statement number (all digits) may be written as the first five characters, or a "C" may be
the first character to indicate a comment line or a continuation of a comment line. For statement continuation 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, Iine 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 fivedigits,
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.

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

1-2

CODER

FORTRAN

DATE

FORTRAN STATEMENT

+ +-+---+-+-+-+--+-+ I I I

I I

~-1

PAGE

PROBLEM

CODING FO~M

I I I

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DIGITAL EQUIPMENT CORPORATION

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..... AYNARD. MASSACHUSETTS

Figure 1-1 FORTRAN Coding Form

ii"

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737475 71777179

100 -12(04

CHAPTER 2
ELEMENTS OF THE FORTRAN LANGUAGE

2.1

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

double-precision, logical, and Hollerith.

2.1.1

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

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

-2176
576
If the magnitude>2 17-1, 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. 999E73 is

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

EXPONENT
12'S COM~)

LOW ORDER
MANTISSA

SIGN OF
MANTISSA

HIGH ORDER MANTISSA
L _ . L -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _- '

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 identi cally to a rea I cons.tant, the
only difference be ing that the degree of accuracy is greater.
Example:
-3.0DO
987. 6542D15
32. 123D+7
Double-precision constants are stored in three PDP-9 words:

EXPONENT 12'S COMP.)

SIGN OF
MANTISSA

HIGH ORDER MANTISSA

NEGATIVE
MANTISSAE
ARE
INDICATED
WITH A
CHANGE
OF
SIGN

LOW ORDER MANTISSA

2.1.4

Lo~ical Constants

The two logical constants are the words TRUE and FALSE, each both preceded and followed
by a decimal point.
. TRUE.
.FALSE.

777777

1-6

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 reai 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$CD

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+10.

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

TEST
GAMMA
Xl 2345
NOTE
If three or less characters are used for each symbol, considerable core space can be saved during compi lation.

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.

1-7

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 Logical 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 symbolic 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 (l, 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(1,2,1)
A(2,2,1)
A(1,1,2)
A(2,1,2)
A(l,2,2)
A(2,2,2)

ascending absolute
storage locations

1-8

2.3.2

Subscri pt Express ions
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

EXPRESSIONS
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 **, which denote addition, subtraction, multiplication, division, and exponentiation,
respectively. An expression may consist of a single element (meaning a constant, a variable, or a

1-9

function name). An expression enclosed in parentheses· is considered a single element. 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. Similarly, real constants or variables produce a real mode of expression, and doubleprecision constants or variables produce a double-precision mode. The mode of an arithmetic expression
is important because it 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, exceptions to this rule.
a. The following examples show the modes of the valid arithmetic expressions involving the
use of the arithmetic operators +, -, *, and /.

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 which 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

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-O(I,J) + E**F*G-H
interpreted as,
FUNC + ((A*B)/C) - O(I,J) + (E F * G) - H
2.4. 1 .3

Rules for Constructing Arithmeti c 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 valid 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*O
A + (B*C) - 0**2 + E/F
2.4.2

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

operator. The result value is either true or false depending upon whether the condition expressed 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

· LT.
· LE.
.EQ.
· NE.
· GT .
· GE.

Less than «)
~
Less than or equal to
Equalto(=)
Not equal to (1)
Greater than (»
Greater than or equal 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

either 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 consist of a logical constant, a logical variable, a reference

to 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
logical 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

d. No two logical operators may appear in sequence, not separated by a comma or parenthesis unless the second operator is . NOT.

In addition, 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. Eva Iuation of functions
b. **(Exponentiation)
c. Evaluation of unary minus quantities
d. * and/ (multiplication and division)
e. + and - (addition and subtraction)

. LT., . LE. , .EQ., .NE., .GT., .GE .
~4V £.
p/teCIJ ,1-I£SiS /jte.QIJPO
g . . NOT.- MU ~
f.

.AND. and .OR.

= Replacement operator

fi!..£.f!.£O£O

4";)(

i-C C;; I <!-/J J-

Olf/&£

U AJ , , .

syt-?8c,-

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 devices.
d. Specification statements define the properties of variables, functions, and arrays appearing in the source program. They also enable the user to control the allocation of storage.

1-13

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

V 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

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

1-15

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 1, n2 , .... , nm)

where i is a nonsubscripted integer variable reference appearing in a previously executed ASSIGN
statement, and n 1 , n2 , .... , nm are the statement numbers which the ASSIGN statement may legally
assign to i.

Examples:
ASSIGN 13 TO KAPPA
GO TO KAPPA, (1, 13, 72, 100, 35)
There is no object time checking to ensure that the assignment is one of the legal statement

numbers.

1-17

4.4

COMPUTED GO TO STATEMENT
The format of a computed GO TO statement is
GO TO (n 1 , n2 , .... , nm), i

where n 1 , n2 , .... , nm are statement numbers and i is an integer variable reference whose value is
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
is 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 1 , n2 , n3

where e is an arithmetic expression and n 1, n2 , n3 are statement numbers. The IF statement evaluates
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 1 , n2 , or n3
respective Iy.
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 following the IF statement.

I3c

elJ Al

PINAL

efJl.JTIIlJ vEO

Ct-fJ 81AJt:

(

~• .12.,

1-18

p/Ht£Al TJ.le6IS

IF ()(, AJ£.,
I

ON1-'!

(JOrD

iJe,PIJIe,E

Example:
IF (Ll) I = 1+ 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 repeatedly a specified series of statements.

The general format of the DO statement is
DO n i = m1 , m2 , m3
or

where n is a statement number representing the terminal statement or the end of the "range"; i is a nonsubscripted integer variable known as the" index"; and m1 , m2 , and m~.are unsigned nonzero integer
<-II\JI-\'<!.H

MuS,T O/.jUY

8£ As.~/C'1UCO

FbS/ililC'

V4?U£"~

constants or nonsubscripted integer variables, which represent the "initial," "final," 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 m1 (m 1 must be less than or equal to m2).
Each succeeding time the statements are operated, i is increased by the value of m3 . When is is greater
than m2 , control passes to the statement following statement number n.
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 m1 , and is increased each time the range of statements is executed
by m3 , until a further incrementation would cause the value of m2 to be exceeded. Throughout the
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 initial value is the value 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

Example:
D072I=l, 10,2
DO 15 K= 1, 5
DO 23 I = 1, 11, 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 statement. The following configuration, where brackets are used to represent the range of the DOs, indicates the permissible and illegal nesting procedures.

PERMISSIBLE , - - - - - - - DO

ILLEGAL , - - - - - - 00

Ir=DO

~oo

,-----00

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

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., GOTO, arithmetic IF, RETURN, STOP, PAUSE, or DO, ora logical IF 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 8 . The integer n is typed out on the console
Teletype for the purpose of determining which of several PAUSE statements was encountered.

Program

execution is resumed, by typing control P (fP), 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 8 . The STOP statement is placed at the
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 single word
END
The END statement is used by the compiler and generates no code.
that the processing of t he source program is comp Iete.

1-21

A/OW
,~

It signals the compiler

ASSt.JtI'-t£O

IUD ~
,

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

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 Physical
Record Definition

Unformatted
(Binary) Physical
Record Definition

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

Undefined

Line printer

One line of printing. Maximum of 120
characters per line

Undefined

Cards
(input and output)

One card. Maximum of 80 characters

50 words

Paper tape
(input and output)

One line image of 72 printing characters

50 words

Magneti c tape

One line 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 list as a I ist of
arguments to be input or output.

1-23

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 the data to be transmitted,
succeeding superfluous records are transmitted until all items specified in the Iist have been transmitted.
5. 1 . 1 . 1

Simple Lists - The Iist uses the form

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

as Iist items. The Iist reads from left to right. When an array identifier appears in the list, the entire
array 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 Iists 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
a single item of the I/O list.
Example:

W, X (3), (Y (I), Z (I, K), I = 1, 10)

5.1.2

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

general READ statement can be used to read either BCD or binary information. The form of the statement determines what kind of input will be performed.

1-24

5.1.2.1

Formatted READ - The formatted READ statements have the general form
READ (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), 1=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 I ist 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 I ist is satisfied.
Example:
READ (5) I,J, K
READ (8)
5.1.3

WRITE Statement
The WRITE statement is used to transmit information from the computer to any I/O device.

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 dev i ce u.

1-25

5.1 .3.2

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

Execution of this statement causes output onto device u, in binary format, of all words specified by the
list.

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

If the Iist elements more than fill one record, successive records are written until all elements of the
Iist are satisfied, the last record padded with blanks if necessary.

Examples of WR ITE:

WRITE (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 + 1,4),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

Specifying FORMAT
The genera I form of the FORMAT statement is
FORMAT (Sl' S2' .... , Sn)

where Sl .... 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 successive fields for which the data conversion will be performed according to the same specification. This is also known as the repeat count.
If n is equal to 1, it may be omitted. The control character k indicates which type of conversion will
be performed. Thi s character may be I, E, F , G, D, P, L,A, H, or X. The nonzero integer constant w specifies the width of the field. The integer constant d indicates the number of digits to the right of the
decimal point.
Six of the nine control characters listed above provide for data conversion between internal
machine language and external notation.
Internal

External

Integer variable

Decimal integer

Real variable

Floating-point, scaled

Rea I variable

Floating-point, mixed

1-26

Internal

Type

Real variable

Floating-point, mixed/scaled

Double-precision
variable

Floating-point, scaled

Logical variable

Letter Tor F

Alphanumeric

Alphanumeric (BCD) characters

External

The other three control types are special purpose cantrol 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.

FORMA T 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 (j) 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 equivalent 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 not precede and/or follow a slash. An integer value 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 list is satisfied. If the list contains 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.

1-27

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
field 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
point 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. If the number is smaller than the field w
allows, the leftmost spaces are filled with blanks. If an integer is too large, the most significant digits
are truncated and lost. Negative numbers have a minus sign just preceding their most significant digit
if sufficient spaces have been reserved.

No sign indicates a positive number.

Examples (b indicates blank):
Format Descriptor
15
13
18
-r-

I £MpoiAtt1

5.2.2.2

teGSTt,.I(!.T/ON - MUST

bbbbb
-b5
bbb12345
Us£

Internal

Output

+00000
-05
+12345

bbbbO
b-5
bbb12345

O£CIHIII- POI tv

I!J

IN oOtH

Of-.r

r::.

p(JRHAT,s

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
sign, the decimal point, plus four spaces for the exponent (written E ± XX) in addition to space for
optional sign and one digit preceding the decimal point.

1-28

The input format of an E-type number consists of an optional sign, followed by a string of
.1igits containing an optional decimal point, followed by an exponent. Input data can be any number
±39
0f digits in length, although it must fall within the range of 0 to ± 10
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 significant 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 - Field 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

b13457
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 real 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 digits (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

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

If the value to be repre-

sented is less than .1 ,the E-type conversion is always used.
Examples:
Format Descriptor

Internal

Output

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

.12345678 x 10- 1
· 12345678 x 100
· 12345678 x 104
· 12345678 x 108

0.12345678E-01
bbO.123456bbbb
bbb1234.56bbbb
bbO.123456E+08

Tcf1,tJOCAl! y /t66TltltTIOAf - H()5 T us& pce /I:?/li- fJo/A.-IT /AJ 080//-1
5.2.2.5 D-Type Conversion - Field descriptor: Dw.d or nDw.d
Or-£ FORHifTS
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
place 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
0.123456D+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 scale factor established by n remains in effect for all subsequent E,F, and D descriptors
within the same FORMAT statement until 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 10n.
The scale factor has no effect if there is an exponent in the external field.
The definition of scale factor for F output conversion is the same as it is for F input. For E
and D output, the fractional part is multiplied by 10 n and the exponent is reduced by n.
Examples:
Format Descriptor

Input

Scale Factor

Internal

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

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 internally.

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 1 a 2a 3 ... a n
The number of characters specified 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
(See Paragraph 5.2.8 for an exception to this rule when printing a formatted record.)
5.2.5

Logical Fields, L Conversion - Field descriptor: Lw or nLw
The external format of a logi cal 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 interna I va Iue is 0, an F is output. Otherw ise a T is output. The F or T
is preceded by w-1 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

5.2.7

FORTRAN Statements Read in at Object Time
FORTRAN provides the facility 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
FORMAT specification must appear in a DIMENSION statement, even if the size of the array is 1. The
statements have the general form:
READ (u, name)
READ (u, name) list
WRITE (u, name)
WRITE (u, name) list
The form of the FORMAT specification which 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 would contain the format statement,
1
10
( (I 7 , FlO. 3)

the subsequent cards would contain data in the general form,

(

7
xx

17
xxxx

DIMENSION AA (10)
13 FORMAT (lOA5)
READ (3,13) (AA( 1),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 BOB with format specifications 17 and F10.3, respectively.
5.2.8

Printing of a Formatted Record
When formatted records are prepared for output on a hard-copy devi ce, the first character of

the record is not printed. The first character is used instead to determine vertical spacing as follows:

1-32

Character

Vertical Spacing Before Printing

Blank

One line
Two lines
Skip to first I ine 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

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

Execution of this statement causes an endfi Ie record to be written on the I/O dev i ce identified by u.

1-33

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 SPECIFICA nON statements must appear before any executable code
generating statement. They must appear in this order: type statements, DIMENSION statements,
COMMON statements, and EQUIVALENCE statements. EXTERNAL and DATA statements must appear
a fter a II other speci fi cati on statements and before executab le-code-generati ng statements and FORMAT
statements.
6.1

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

where a, b, andcarevariable names which may be dimensional or function names. A type statement is
used to inform the compi ler 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,IJK,XYZ
REAL A (2,4), I,J,K
DOUBLE PRECISION ITEM, GROUP
LOGICAL TRUE, FALSE
Any functi on references (statement functi ons, i ntri nsi c functi ons, or externa I functi ons) whi ch
are not implicitly REAL or INTEGER must appear in the appropriate TYPE statement.
Example:
DOUBLE PRECISION B,X,DABS,DATAN

B = DATAN (DABS (X))
In this example, if DABS and DATAN were not declared double precision, improper code
would be generated by the compi ler and no error diagnostic wi II occur.

1-35

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 formof the DIMENSION statement is:

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. The dimension information for the variable can be given in a type statement, a COMMON statement I or a DIMENSION
statement; however, di mensi oni ng i nformati on should on Iy be given once.
Example:
DIMENSION ITEM (150), ARRAY (50,50)
When arrays are passed to subprograms, they must be redeclared in the subprogram. The 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

its subprograms. The general form of the COMMON statement is:

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

If Xl is blank, the

Each a represents a list 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
(or 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

statement, 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, however, need not agree
in name, mode, or order. A blank COMMON may be any length.

1-36

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.

If one program

contains the statements,
COMMON/N/AA, BB,CC
AA=3
BB=4
CC=5
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 general format of the EQUIVALENCE statement is:

where each k represents a list of two or more variables or subscripted variables separated by commas.
Each element in the list is assigned the same memory storage location.
An EQU IVALENCE 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), 0(10), E(l5))
An EQUIVALENCE statement which refers to an array which also appears in a COMMON
statement must refer to the first element of that array.
Example:
DIMENSION A(100),B(50)
COMMON A
EQUIVALENCE (A(1), B(1) )

1-37

The above example shows a legal EQUIVALENCE statement. If, however, the statement
were changed to read
EQUIVALENCE (A (50) , B(1}}
the statement would cause an error diagnostic.
6.5

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

genera I form of an EXTERNAL statement is:
EXTERNA L Y,z, •••
Example:
EXTERNAL ISUM, ISUB

CALL DEBUG «SUM,A,B}

CALL DEBUG (ISUB,A,B)
END
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.

~ {)ocJ8~£ IR£~<>I()IJ . (l.cA.lSil1,.!T /-liI~{r.,
BE.. wll.,..-reiJ' £:;ILPJ,(C,-rl,... Y IN 0() pc.

"",..,4-

O-r «)1)
Variable or array elements appearing in a DATA statement mat not be in blank COMMON.
(lbf/' I. c

They may be in a labeled COMMON block and initially defined only in a BLOCK DATA subprogram.
Example:
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)
2Y(3), Y(4)/1.0E2, 1.0E-2, 1.0E4, 1.0E-4/

1-38

CHAPTER 7
SUBPROGRAMS

A subprogram is 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.
b.
c.
d.
e.

Statement Functions
Intrinsic or Library Functions
External Functions
External Subroutines
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 single value to the calling program; subroutines can return more than one value.
Functions are called by writing the name of the function and an argument list in a standard arithmetic
expression; subroutines are called by using a CALL statement. The last category is a special purpose
subprogram used for data initialization 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 a's 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 which case it is an integer quantity, or the function type may be defined by using
_
'TZl rl-J£. 1l ,Co N 7
.
s 1Z£~rL
Ie. T£ P
~I'-l- F vp.)<'! n >;J,v ,
t he appropriate specl'f"Icatlon st atement.
-'-1/1£//" US t : '
t£..
s;r/rrl£ r l AI rlns tJ,J /L-L
~
Since the arguments are dummy variables,'
mode, aeel me) hi

lJ,ed dseyvLe ... it

tL;,1Oi£.eex .,Ig : n . t,,:;' e:~e;ft~'ifc,fc~~;'~F~E.v)
\/41Z..11I-131-£

I :ogluiiI, including within the expression on the right side ofw ,TH
S'/Jr"7C

the statement function.

#: 0 F

a£:

f}IJ~1"1 Y Vrl/(..I/I ICd/oJ,..,....
IJI-c.-

The expression of a statement function, in addition to containing nonsubscripted dummy
arguments, may only contain:

1-39

THe
IfAJO A);tlMC
"
_

/ 0 ,

a. Non-Hollerith constants
b. Variable references
c. Intrinsic 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 which contains 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 functions are predefined subprograms that are a part of the FORTRAN

system library. The type of each intrinsic 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 intrinsic functions (see table 1-1).
Examples:

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

J = IF IX (R)

1-40

Table 1-1.
Intrinsic Functions

Definition

Intrinsi c Functions
Absolute value

No. of
Arguments

Symbolic
Name

Type of
Argument

Type of
Function

ABS
lABS
DABS

Real
Integer
Double

AINT
INT
IDINT

Real
Real
Double

Real
Integer
Integer

AMOD
MOD

Real
Integer

10 I

Truncation

Sign of a times largest
integer::; I a I

Rema indering*

0 1 (mod O 2)

Choosing largest
value

Max (0 1 ,0 2 ,

... )

AMAXO
AMAX1
MAXO
MAX1
DMAX1

Integer
Real
Integer
Real
Double

Real
Real
Integer
Integer
Double

Choosi ng sma "est
value

Min (0 1,0 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 real
to integer

IFIX

Real

Integer

Transfer of sign

Sign of O 2 times

SIGN
ISIGN
DSIGN

Real
Integer
Double

DIM
101M

Real
Integer

Obtain most significant part of double
precision argument

SNGL

Double

Real

Express single precision argument in
double precision
form

DBLE

Real

Double

I 1I
0

Positive difference

0 1 -

Min (0 1 ,0 2 )

*The function MOD or AMOD (0 1 ,0 2) is defined as a - [a/a 2 J O 2 , where[xJ is the integer whose
magnitude does not exceed the magnitude of x and whose sign is the same as x.

1-41

7.3

EXTERNAL FU NCT ION S
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 1 ,a 2 , .•. ,an)
(FORTRAN statements)

NAME = final calculation
RETURN
END
where t is either INTEGER, REAL, DOUBLE PRECISION, LOGICAL, or is blank; NAME is the symbolic name of the function to be defined; and the als are dummy arguments which are nonsubscripted
variable names, array names, or other external function names.
The first letter of the function name impl icitly 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. These 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
.
.
~-rIU.. AhlrllJ£rt.- () F ()Ih.,,,,, Y ,QIZC ()M ~ -rs ~ /1)
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. At least one RETURN statement must appear between the last executable statement and the
END statement.
An END statement, described in Section 4.11, signals the compiler that the physical end of
the subprogram has been reached.

1-42

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 actual 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:
DIMENS ION A(l 00), 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
10 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

Exponential

Natura I logarithm

log (a)
e

ALOG
DLOG

Real
Double

Common logarithm

10910 (a)

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

Table 1-2". (Cont)
External 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 2)
Remaindering*

a 1 (mod a 2)

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

7.4

SUBROUTINES
A subroutine is defined externally to the program unit which references it.

It is similar 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 1 ,a2 , ... ,an)
or
SUBROUTINE NAME
where NAME is the symbolic 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
alphabetic. The symbolic 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 subroutine.
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

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

1t...5.IO
US C

I!Ol'l/"1IJIU

r:-

-x.. >1 0

CALL NAME
where NAME is the symbolic name of the subroutine subprogram being referenced, and the als 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 SUBROUT INE subprogram. The array sizes must be the same.
following:
a.
b.
c.
d.
e.
f.

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

M411V

p,ed(!,.

PIM&JV;;,Q"'; 4t~

(iOMMol(,J

BLOCK DATA SUBPROGRAM

7.5

{t;'JLL :5&J8 (AlI~

The BLOCK DATA subprogram is a special subprogram used to enter data into a COMMON
block during compilation.

A BLOCK DATA statement takes the form

:SW!Jte4 .JT/AJ€ SV$
~

P'I'1EIJ~;>lDt..J 14(1)

BLOCK DATA

t!. DM,..,/J.u
<!4J.L 4t:q" I

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 only 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 all 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 BLOCK DATA subprogram.

7.5.1

Example of BLOCK 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/
DATA X(l), X(2), X(3), X(4)/0.O, 0.1, 0.2, 0.3;Y(l), Y(2)
2Y(3) , Y(4)/1 .OE2, 1.0E-2, 1 .OE4, 1.0E-4/
END
1-45

If\

( :;JIil~

APPENDIX 1
SUMMARY OF PDP-9 FORTRAN IV STATEMENTS

CONTROL STATEMENTS
1-15

1'-ASS IG N n to i
CALL name (a 1,a 2, ••• )

1-42

CONTINUE • • • • • • •

1-19

DO n i=m 1,m2 ,m 3 ••

1-17

GO TO n • • • • • • •

1-15

~GO TO i, (n 1,n2 , ••• )

1-15

GO TO (n 1,n 2 , ••. ), i

1-16

IF (e 1) n1,n2 ,n 3 ••

1-16

IF (e) 5 •

1-16

•

PAUSE •

1-19

PAUSE n

1-19

STOP

1-19

STOP n

1-19

END

1-19

RETURN

1-39

SUBROUTINE NAME (a 1,a 2,·· • an)

1-41

FUNCTION NAME (a 1,a2, •.. an)

'.\< O£1-6T~D

•• • • •

1-39

Flo,"", F0l...,e,HJ 1Sl:.

INPUT/OUTPUT STATEMENTS
BACKSPACE u. •

1-31

END FILE u

1-31

FORMAT (5 1,52 , ••• ,sn)

1-24

READ (u,f)

1-23

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

WRITE (u,f) list

1-23

1-47

WRITE (u, f)

1-23

WRITE (u) list

1-24

WR ITE (u, name)

1-30

WR ITE (u, name) list

1-30

SPECIF ICATION STATEMENTS
COMMON /x/a/x 2/a 2/ ••• /x/a n •

1-33

DATA k/d/,k2/d 2/, ... kn/d/ ••

1-35

DIMENSION V1(il)' V2(i2), ... Vn(in)

1-32

DOUBLE PRECISION a,b,c ••

1-32

l'EQU IVALENCE (k 1) ,(k2) ... (k n)

1-34

*'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

t-ofl..ET£O

FeoN r=otlfAAi JI!

1-48

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 com pi ler 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 EQUIVALENCE, EXTERNAL, ASSIGN, and
Assigned GOTO statments, or the following options available in the F4 version:

Objeet GOde IisI! "g

Source Ii sti ng

f'flIAlToUTS
~

oPTlolJ

Hils 10 eGIJ

DEJ.,{;;.T£D

~~FI/-

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." 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-91\-NGAA-D.)
In larger systems with a bulk storage device such as DECtape, the Keyboard Monitor accepts
direct keyboard commands to load the com pi ler 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

APPENDIX 3
FORTRAN IV AND MACRO-9 LIN KAGE

1•

Linking FORTRAN IV Programs With MACRO-9 Subprograms
There are two essential elements of a MACRO subprogram that is linked to FORTRAN IV.

One is the declaration of the name of the subprogram (as used in the F4 program) in a .GLOBL 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, single-precision floating-point number is read by the
FORTRAN' program, negated in the MACRO-9 subprogram, and written out from the FORTRAN program.

FORTRAN IV PROGRAM:
C
C
1

100
C

TEST MACRO SUBPROGRAM
READ A NUMBER (A)
READ (1,100) 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

MIN1
MIN2

o
JMS*

.DA

JMP

.+3

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

0
0
MIN1
MIN2
MIN1
MIN2
MIN1
(400000
MIN2
MIN

/ENTRY/EXfT
fUSE THE F4 GENERAL GET ARGUMENT
/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

Since A is a single-precision, floating-point number, two machine words are required and
must be accounted for in the subprogram. Thus MIN1 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-

ment as follows:
CALL MIN (A, B)
00013
JMS*
00014
JMP
00015
.DSA
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 Bin 00016 (plus relocation factor). When .DA is
called 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 va lue of A (a direct reference wou Id 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
called 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 ARGl
ADDR OF ARG2

/+400000 if indirect
/+400000 if indirect

.DSA

ADDR OF ARGN

/+400000 if indirect

I-52

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

calling 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 between the main program and the subroutine is to
use one of the calling arguments as output. For example, if the value of D is to be calculated in the
subroutine, use D as one of the calling arguments. "D=" will generate a "DAC* 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
linkage 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 accumulator for real and double precision 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 val-

ues, and .AP stores double precision values. Since the A-register is the standard hardware accumulator,
a DAC instruction wi II store integer values.

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.

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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 communication of data accomplished through common
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 ~egment 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-NGBA-D).
than or less than but not equal to the current chain number.

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.

NOTE
Use of a CALL CHAI N (N) statement rather than a STOP
statement immediately preceding the END statement wi II
cause an I error during compilation (illegal statement preceding the END statement). This error should be ignored
since it is a warning only. The CHAIN subroutine will
never return control to the statement followi ng the CALL
CHAIN (N) statement (control is transferred to the beginning of the chain which is called).

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)
END
C

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

CALL CHAIN (3)
END
I-55

N can be greater

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

WRITE (4,6) AUST
6 FORMAT (E10.3)
STOP
END

I-56

APPENDIX 5
FORTRAN IV ERROR LIST

These Ietter-coded error messages app Iy to a II versi ons of F4 and F4A. Refer to page II-2
of this manua I 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.

Statement number 'error

Phase error, number more than 5 digits, no statement
number where one is required, statement shouldn't
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 dec lared number.

FORMAT statement error

Illegal FORMAT specification or illegal construction
of FORMAT statement.

Character/ statemen t/
term error

Illega I character, unrecogn izable statement, i lIega I
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 i tude error

Program exceeds 8190 words, maximum number of
dummy arguments or EQUIVALENCE classes exceeded,
or constant/variable exceeds specified limits.

COMMON/EQUIVALENCE/
DIMENSION/DATA statement
error

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

-Jo'E

FUNCTION/SUBROUTINE/
EXTERNAL/CALL statement
error

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

Hollerith error

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

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I-57

FUIUc...n{)~ OO£S-

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vJ I'-L Ot!. e. () Ie

APPENDIX 6
SYMBOL TABLE SIZES (F4 V3A)

The following symbol table sizes are for 8K systems with the full complement of skip lOTs
in the skip chain.

NOTE
Handlers listed are for DAT slots -11, -12, and -13, respecti ve Iy.

F4
a.

PRB, TTA, PPC -

189 symbo Is (deci ma I)

DTC, TTA, PPC -

62 symbols (decimal)

PRB, HA, PPC-

407 symbols (decimal)

DTC, TTA, PPC -

278 symbols (decimal)

DTB, TTA, DTB -

54 symbols (decimal)

F4A

I-59

FORTRAN IV OBJECT - TIME SYSTEM

INTRO DUCT 10 N
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 globels to
various subprograms, depending upon the content of the FORTRAN program. When the compiled program is loaded via the Linking Loader, the Loader attempts to satisfy these globels 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, REWIND and ENDFILE 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

Table 11-1.
OTS Errors

Error Number

Error Description

Library Routines*
That May Cause Error

Not used
Negative REAL Square Root Argument

SQRT

Negative DOUBLE PRECISION Square
Root Argument

DSQRT

!D7

"'ega' 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!D

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

1/-2

OTS Binary Coded Input/Output
BCDIO
l.

Class:

Object - Time System

Purpose:

The BCD input/output object-time package is designed to process the formatted
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 altered or
read at execution time, the FORMAT statements are interpreted by BCDIO at
execution time rather than at compile-time. This has two advantages:

It provides a greater flexibility to the FORTRAN programmer,

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

In demonstrating this capability, 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 devi ce using the E-conversion.
Example:

ENTRY

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

LOOPl
ARGl

.FP, .FR, .FE, .FF, .FW
3,4
.FP
/Initialize I/O device status table.
.FR
/Initialize device 3 for input
(3)
/under control of FORMAT statement
FRMTl
/FRMTl and read first record into line
/buffer.
- l,0'
/Set loop counter to 8.
COUNT
(ARRAY) /Set element address to first word
ARGl
lin the array.

JMS*
,0'

. FE

ISZ
ISZ
ISZ
JMP
JMS*

ARGl
ARGl
COUNT
LOOPl
.FF

JMS*
.DSA
. DSA
LAW
DAC

.FW
(4)
FRMT2
- l,0'
COUNT

/1-3

/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.
/Initialize device 4 for output
/under control of FORMAT
/statement FRMT2.
/Set loop counter to 8.

OTS Binary Coded Input/Output

LAC
LOOP2
ARG2

DAC
JMS*

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

ARG2
ARG2
COUNT
LOOP2
.FF

/Increment ARRAY address by 2.

¢
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.

2¢
'(8F10.5)'
'(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 Blo ck.

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
f.

Size:

2773 octal locations

11-4

OTS Binary Coded Input/Output
g. Error Conditions:
OTS ERROR 1¢ - Illegal I/O Device Number
OTS ERROR 11 - Bad Input Data (lOPS Mode Incorrect)
OTS ERROR 12 - Illegal FORMAT

11-5

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 logical record.
Each WRITE statement generates one logical record.
Each READ statement reads one logical record, regardless of the length of its I/O
I ist. For this reason, it is the responsibil ity of the FORTRAN programmer to ensure
that I/O Iists for WR ITE and READ statements are compatible.

3. Call ing Sequences:
a. To initialize a device for binary input (output):
FX
JMS*
.FS (.EW)
DEVICE
.DSA
b. To input (or output) an integer data element:
JMS*
.DSA

.FI
address of the element

c. To input(or output) a real 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

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 st set.
A typical WRITE statement may generate the following record for ID:

LOGICAL
RECORD

PHYSICAL RECORD
FOR ID (OCTAL)

External Calfs:
FlOPS, OTSER

5. Size:
I

244 octal locations

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

1/-7

OTS Auxi I iary Input/Output
AUXIO
1. Class:

Object - Time System

2. Purpose:

Auxi I iary Input/Output consists of the processors for the three aux i Iiary 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 (BINIO).

BACKSPACE (.FT):
Repositions the tape at a point just prior to the first physical record
associated with the current logical record.
Example:
WRITE (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.

EN DF 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.

3. 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

OTS Auxil iary Input/Output
5. Size:

64 octa I locations

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

/1-9

OTS lOPS Communication
FlOPS
1. Class:

Object - Time System

2. Purpose:

F lOPS provides the necessary 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 .INIT unless the input/output flag has
changed.
One life buffer is used by all FORTRAN programs. Data transfers between 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:
.FH

DZM*

c . To specify output:

(1)

LAC
DAC*

.FH

d. To select device:
LAC
JMS*

DEV ICE (address of slot number)
.FC

e . To input or output the line buffer:
address of . DAT slot number (bits 9-17) and lOPS mode (bits 6-8)
.FQ

LAC
JMS*
f.

Notes:

1)
2)

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

11-10

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 1.0'- Illegal I/O Device Number

11-11

OTS Calculate Array Element Address
. SS
1. Class:

Object - Time System

2. Purpose:

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

wd 1

.-z?r&l\ f

wd 2

wd 4

IN* Imax

wd 3

1j/lf.AY

M
Size
1000
2 345
0

IN* I
*J
max:
:
max

Generated by
F4

I Address of Array

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

Type

00
01
10

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, j, k) =
A + (i-1) * n + (j-1) * 1* n + (k-1) * 1* J 'k n

'--y-J

'---v---"

•

wd 4

wd 2

wd 3

1-dimension array
2-dimension array
3-dimension array

3. Calling Sequence;
.GLOBL
JMS*
.DSA

ARRAY
.SS
ARRAY

LAC
LAC
LAC
DAC

Sl
S2
S3

/Address (indirect) of array
/Descri ptor Block
/S ubscri pt 1 (l)
/Subscript 2 (J)
/Subscript 3 (K)
/Store array element address here

11-12

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

57 octo I locations

6. Error Conditions:
None.

11-13

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

Object - Time System

2. Purpose:

To compute the index of a computed GO TO

3. Calling 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. Externa I Co lis:
OTSER

5. Size:
6.

26 octal locations

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

1/-14

OTS Stop
STOP (. ST)
1. Class:

Object - Time System

2. Purpose:

To process the STOP statement and return control to the monitor.

3. Calling Sequence:
LAC
JMS*
4.

(Octal number to be printed)
.ST

External Calls:
SPMSG (. SP)

5. Size:

13 octal locations

6. Error Conditions:
None

11-15

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 octal locations

6. Error Conditions:
None

1/-16

OTS Octal Print
SPMSG (. SP)
1. Class:

Object - Time System

2. Purpose:

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

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

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

4. Externa I Co lis:
None
5. Size:
6.

74 octal locations

Error Conditions:
None

/1-17

If no number is given,

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 fJ of the error number is a 1, the error is recoverable and program control
is returned to the calling program at the first location following the error number.

If bit fJ of the error number is a fJ, the error is unrecoverable and program control
is transferred to the monitor by means of the . EX IT 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 pa ir of the erroneous format statement is printed in addition to the error
number.

3. Ca II ing Sequence:

ERROR #12
only

JMS*
.DSA
LAC
LAC

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

Words 1 and 2 are the current 5 chara cters (i n 5/7 ASC II of the bad
format statement (ERROR #12)
4.

External Calls:
None

5. Size:
6.

117 octal locations

Error Conditions:
None

11-18

Additions to the PDP-9 FORTRAN IV Subroutine Library
Fi Ie Commands
FILE
Externa I Subrouti ne

1. Class
2. Purpose:

To provide the device-independent .IOPS commands SEEK, ENTER, CLOSE, FSTAT,
RENAM, and DLETE. These commands are used to allow the FORTRAN IV Object Time
System to communi cate wi th .IOPS fi le-ori ented devi ces.
a.

SEEK finds and opens a named input fi Ie.

ENTER initiates and opens a named output fi Ie.

CLOSE terminates an input or an output fi Ie and must be used if SEEK or ENTER
has been used.

FSTAT checks for the presence of a named fi Ie.

RENAM checks for the presence of a fi Ie and renames it if found.

DLETE checks for the presence of a file and deletes it if found.

NOTE
BACKSPACE, REWIND, and ENDFILE commands should
never be used with a device that is operating in the fi leori en ted mode usi ng the above subrouti nes •
3. Ca Iling Sequences:
a.

To seek a named file:
CALL SEEK (N ,A)
where N = device number
A = array name containing the 9-character 5/7
ASCII fi Ie name and extension.
The fi Ie array has the following format for the named fi Ie FILNAM EXT:
DIMENSION FILEN (2)
DATA FILEN(l), FILEN(2)/5HFILNA,4HMEXT/
To use this named file for input on .DAT slot 1:
CALL SEEK (l,FILEN)

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

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

11-19

d•

To check for the presence of a named fi Ie
CALL FSTAT (N, A, I)
where N and A are the same as for SEEK and I = -1
(.FALSE.) if fj Ie not found and I = 0 (. TRUE.) if fj Ie found and action complete.

To rename a fjle A and call it B
CALL RENAM (N, A, B, I)
where N, A (B is the same as A), and I are the same as for FSTAT.

f. To delete a named fi Ie
CALL DLETE (N, A, I)
where N, A, and I are the same as for FSTAT •

4. Externa I Ca lis
FlOPS, .DA, .SS, .SEEK, .ENTER, .CLOSE, • FSTAT , .RENAM, .DLETE

5. Si ze
322 octa I locations
6. Error Conditi ons
.OTS Error 10 if I/o device number is illegal
.IOPS Error 13 if fj Ie not found on SEEK
.IOPS Error 14 if directory full on ENTER

11-20

Clock Handling
TIME
1. Class:

Externa I Subroutine

2. Purpose:

To provide the ability to record elapsed time in minutes and seconds

3. Calling Sequence:
CALL TIME (IMIN, ISEC, IOFF)
This ca II causes the c lock to be started and the elapsed time recorded as minutes
and seconds in IMIN and ISEC. To stop the clock, set IOFF to non-zero.
Only one call to TIME or TIME10 can be active at any point in the user program.
Example:

CALL TIME (1M, IS, IOF)
A

IOF = 1
WRITE (4,100) 1M, IS
This sequence wi" cause the time taken to execute the code at A to be output.
4 • Externa I Ca lis:
.DA, •TIMER
5. Size:
53 octal locations
6. Error Conditions:
None

11-21

Clock Handling
TIME10
1. Class:

Externa I S ubrouti ne

2. Purpose:

To provide the ability to record elapsed time in minutes, seconds, and tenths of
seconds.

3. Ca Iii ng Sequence:
CALL TIME10 (IMIN, ISEC, ISEC10, IOFF)
This call causes the clock to be started and the elapsed time to be recorded as
minutes, seconds, and tenths of seconds in IMIN, ISEC, and ISEC10 respectively.
To stop the clock, set IOFF to non-zero. Only one call at TIME10 or TIME can
be active at any point in the user program.
Example:

See TIME

4. Externa I ca lis:
.DA, • TIMER
5. Size:
66 octa I locati ons
6. Error conditions:
None

11-22

Adjustable Dimensioning
ADJ1
1. Class:

Externa I S ubrouti ne

2. Purpose:

To provi de di mensi on adj ustment on a one di mensi ona I array

3. Calling Sequence:
DIMEN SIaN B(l)
CALL ADJ1

(B,A)

Where B is the array whose storage begins at A. A must be an array element (such
as C (200)) wi th suffi ci ent storage beyond A to a IIow for a II the entri es of array B.
The di mensi ons or type of array A do not have to agree with array B.
B cannot be a dummy argument in a subroutine but A can be a dummy argument.
Example:
DIMENSION A(300), B(I), C(I)
CALL ADJ1 (B, A(l 01))
CALL ADJ1 (C,A(201))
After the ca lis to ADJ 1, the arrays Band C may be referenced as if they had been
dimensioned as (100) each. No further calls to ADJ1 have to be made.

4. External calls:
.DA
5. Size:
17 octa I Iocati ons
6. Error Condi ti ons:
None

II-23

Adjustable Di mensioning
ADJ2
1. Class:

Externa I Subroutine

2. Purpose:

To provide dimension adjustment for a two dimension array.

3. Calling Sequence:
DIMENSION B(l,l)
CALL ADJ2 (B ,A, NR)
where NR is the number of rows to appear in array B.
See ADJl for comments on B and A.
Example:
DIMENSION A(300), B(l,l), C(l,l)
CALL ADJ2 (B ,A (1), 10)
CALL ADJ2 (C,A (101), 20)
After the ca lis to ADJ2, the arrays Band C may be referenced as if they had been
dimensioned (10,10) and (20,10) respectively. No further calls to ADJ2 have to
be made.
4. Externa I Ca lis:
DA, .AD
5. Size:
36 octal locations
6. Error Conditions:
None

II-24

Adjustable Dimensioning
ADJ3
1. Class:

Externa I S ubrouti ne

2. Purpose:

To provide dimension adjustment for a three dimension array

3. Calling Sequence:
DIMENSION B (1,1,1)
CALL ADJ3 (B,A, NR, NC)
where NR and NC are the number of rows and columns respectively to appear in array
B. See ADJI for comments on Band A.
Example:
See ADJI and ADJ2
4. Externa I Ca lis:
.DA, .AD
5. Size:
41 octal locations
6. Error Conditions:
None

11-25

PDP-9 SCIENCE LIBRARY

INTRODUCTION
All mathematical routines in the PDP-9 Science Library are described 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 (6.) is made in column 1 to detailed descriptions following the table.

Information

given in Table III-1 for each routine includes the routine name, mnemonic, calling sequence, function,
mode, errors, accuracy and timing (where available), storage requirements, and external calls.

Rou-

tines are categorized by Intrinsic Functions, External Functions, Sub-Functions, or part of the Arithmetic Package and are listed in the table accordingly.

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

The

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)
Externa I Fun ctions
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 supplied with the FORTRAN system are described in Table III-l.
Sub-F unctions
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 actua I computation of the sine.
The Arithmetic 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

A ccumu lators
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
that involve integer values.
F loati ng Accumu lator
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, .AB the second, and .AC

the third.

Numbers are stored in this accumulator in the following format:

.AA

EXPONENT (2's COMP.)

17
SIGN OF MANTISSA

.AB

HIGH ORDER MANTISSA

o
.AC

17
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 precision numbers.

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

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

LOW ORDER
MANTISSA '

HIGH ORDER MANTISSA

SIGN OF
MANTISSA

•

111-2

Held Accumulator
The held accumulator has the same format as the floating accumulator and is used as temporary storage by some routines.

The labels of the three words are CE01, CE02, and CE03.

Calling Sequences
The MACRO-9 calling 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 with 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 library 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

SIN
.+2
A
.AH
X

· DSA
· DSA

o
o

/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 satisfy the
globals by searching the Science Library. The External Function SIN and the REAL ARITHMETIC package will be loaded.

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

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

111-3

Table III-l
PDP-9 Science Library
t

Mode

Errors

Bits

Timing
NonEAE
EAE

I**'K

1=1**1

None

N.A.

Note 1

A**K

R=R**I

#13, if base '::::0 26

23.2 ms

.EE, .EF, REAL

A**K

D=D**I

#14, if base .sO

27.8 ms

· DE, . DF, DOUBLE

A**B

R=R**R

#13, if base .s9

23.0 ms

· EE,. EF ,REAL

A**B

D=R**D

#13, if base "::::'0 26

27.6 ms

· EE, . DF, DOUBLE

Accur.

ROUTINE NAME

Mnemonic

Calling Sequence

Function

Storage
(Octal)

Externa I Ca lis

INTRINSIC FUNCTIONS
Exponentiation:
.BB

JMS*
{fC
LAC

Real Base, Integer Exponent

.BC

DP Base, Integer Exponent

.BD

Real Base, Real Exponent

. BE

Integer Base, Integer Exponent

Real Base, DP Exponent

. BF

ARGl (base)}
.BB
ARG2 (exp)

....

-< JMS* SUBR
.DSA ADDR of ARG2
(exp.)

OP Base, Rea I Exponent
OP Base, DP Exponent

......
......
......

INTEGER

.BG

A**B

D=O**R

#14, if base .:::p

27.6 ms

· DE, . DF, DOUBLE

.BH

A-'B

D=D**O

#14, if base .5fJ

26.6 ms

· DE, . DF, DOUBLE

IAI

R=ABS(R)

None

N.A.

120 ~s

.OA,REAL

II I

I=IABS(I)

None

N.A.

64 ~s

.DA

IA I

D=OABS(O)

None

N.A.

120 ~s

· DA, DOUBLE

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

None
None
None

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

365 ~s
180 ~s
180 ~s

15
13
13

.DA,REAL
· DA,REAL
· DA, REAL, DOUBLE

Absolute Value:
Real Absolute Value

....

ABS

Integer Absolute Value

lABS

DP Absolute Value

DABS

I
LIl

JMS* SUBR
1-< JMP .+2
;>.DSA ADDR of ARG

Truncation:

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

AINT
INT
IDINT

Remoindering:

rgnOfA time'}
~1est integer

.....

Real Remaindering

AMOD

Note 2

R=AMOD(R,R)

None

N.A.

3015 ~s

.DA,REAL

Integer Remaindering

MOD

Note 2

I=MOD(I,Q

None

N.A.

477 ~s

· DA, INTEGER

DP Remo indering

DMOO

Note 2

D=DMOD(D, D)

None

N.A.

3335 ~s

.OA,DOUBLE

None
None
None

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

198 ~s
81 ~s
192 ~s

26
20
26

.DA,REAL
.DA
.OA,DOUBLE

Transfer of Sign:

JMS* SUBR
JMP
.+3
DSA ADDR of ARGl
.DSA ADDR of ARG2

Integer Transfer of Sign

ISIGN

DP Transfer of Sign

DSIGN

{"'T'}

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

Real Positive Difference

DIM

Al-MIN(Al,A2)

R=DIM(R,R)

None

N.A.

794 ~s

.OA,REAL

Integer Positive Oifference

IDIM

I1-MIN(ll,12)

I=IDIM(I,Q

None

N.A.

85 ~s

· DA, INTEGER

A .... I

R=FLOAT(I)

None

N.A.

246 ~s

.DA,REAL

I+-A

I=IFIX(R)

None

N.A.

180 ~s

.DA,REAL

A .... B

R=SNGL(D)

None

N.A.

144 ~s

.DA,DOUBLE

A.... B

D=DBLE(R)

None

N.A.

115 ~s

· DA,REAL

Real Transfer of Sign

SIGN

-< .

Sign of A2

Positive Difference:

Conversion:

Integer ta Real Conversion
Real to Integer Conversion
DP to Real Conversion
Real ta DP Conversion

FLOAT
IFIX
SNGL
DBLE

to SU~

}
.+2
JMP
.DSA ADDR of ARG

NOTES:
1.
2.

Timing indicated in this column is estimated unless indicated ta 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 approximately equal to 335 ~s times n, where n is the largest power of 2 in the exponent.
Remaindering is defined as A 1 - [A 1/A21 A2, where [A 1/A21 is the integer whose magnitude does not exceed the magnitude of A1/A2 and whose sign is the some as A1/A2.

Timing t
ROUTINE NAME

Calling Sequence

Mnemonic

Function

Mode

Errors

Accur.
Bits

Non-

EAE

Storage

EAE

(Octal)

External Calls

106

INTEGER, REAL

117

INTEGER, REAL

105

DOUBLE

INTRINSIC FUNCTIONS (Cant)

Integer Maximum/Minimum

IMNMX

JMS'

Integer to Integer Max.

MAXO

-< . DSA

JMP
.DSA
Integer to Integer Min.

MINO

Integer to Real Max.

AMAXO

Integer to Real Min.

AMINO

Real Maximum/Minimum

RMNMX

JMS'

Real to Real Max

AMAXl

Real to Real Min.

AMINI

Real to Integer Max.

MAX1

Real to Integer Min.

MINl
DMNMX

DP Maximum/Minimum

-I

0..

....,

Maximum/Minimum Value:

DP Maximum

DMAXl

DP Minimum

DMINl

.DSA

MAXO,MINO,
AMAXO, or AMINO
.+n+l
ADDR of ARGl
::> Max. Value
ADDR of ARG2
Min. Value
ADDR of ARGn

None

N.A.

Note 3

I~MINO(ll, ... , In)

None

N.A.

Note 3

Max. Value

R~AMAXO(ll , ... In)

None

N.A.

Note 4

Min. Value

R~AMINO(ll , ... In)

None

N.A.

Note 4

AMAXl ,AMINI,
MAX1, or MIN2

.+n+1
JMP
.DSA ADDR of ARGl
-< . DSA ADDR of ARG2

.DSA

I~MAXO(ll, •.. , In)

>- Max. Value

R~AMAX1(Rl, ... Rn)

None

ADDR of ARGn
-'

~"~'N}

JMP
.+n+1
M
.DSA
ADDR of ARG1
"
.DSA ADDR of ARGn

N.A.

Note 5

Min. Value

R~AMIN1(Rl, ...Rn)

None

N.A.

Note 5

Max. Value

I~AX1(Rl, •.. Rn)

None

N.A.

Note 6

Min. Value

I~MIN1(R1, ... Rn)

None

N.A.

Note 6

Max. Value

None

N.A.

Note 7

Min. Value

D~DMAX1(D1, ... Dn)
I
D~DMIN1(Dl, ... Dn)

None

N.A.

Note 7

EXTERNAL FUNCTIONS
Square Root:
Real Square Root
DP Square Root

&
&

....,

Xl / 2

R~SQRT(R)

#5,ARG < 0

t6.657ms

t 3.584 ms

· DA,. ER,REAL

DSQRT

Xl/2

D~DSQRT(D)

#6,ARG < 0

t 8.191 ms

t 4 . 094 ms

· DA, . ER, DOUBLE

EXP

R~EXP(R)

#13, ARG ::s.0

t 15.489 ms t4.672ms

· DA, .EF, .ER,REAL

D~DEXP(D)

#14, ARG .sO

t 17.664 ms t7.223ms

.DA,DF, .ER,
DOUBLE

Loge X

R~ALOG(R)

#13, ARG <0

t 8.197 ms t 4 . 092 ms

· DA, . EE, . ER, REAL

Log X
::> e

D~DLOG(D)

#14, ARG <0

t 15.489 ms t 4.095 ms

.DA, .DE, .ER,
DOUBLE

SQRT

Exponentia I:

Real Exponential
DP Exponential

&
&

DEXP

Natural Logarithm:

&
&

Real Natural Logarithm
DP Natural Logarithm

ALOG

JMS'

SUBR

JMP

.+2

.DSA ADDR of ARG

DLOG

1-<

X
X

Common Logarithm:

Real Common Logarithm
DP Common Logarithm

&
&

Lo9 10 X
Log 10 X

R~A LOG 1O(R)

#13, ARG<O

t8.197ms t 4.094 ms

· DA, . EE, . ER, REAL

DLOG1C

D~DLOG 1O(D)

#14, ARG<O

t ll . 7ms

.DA, .DE, .ER,
DOUBLE

ALOG1C

Sine:

&,
&,

SIN

Sin (X)

R~SIN(R)

None

tlO.368ms t 4 . 094 ms

· DA,. EB, REAL

DP Sine

DSIN

Sin (X)

D~SIN(D)

None

t 16.383 ms t 5 . 632 ms

· DA, DB, DOUBLE

Cosine:
Real Cosine

COS
DCOS

Cos (X)
Cos (X)

R~COS(R)

None
None

26
34

t II .025 ms t 4 . 901 ms
t16.383ms t 6. 145 ms

20
21

· DA, . EB, REAL
· DA, . DB, DOUBLE

Real Sine

DP Cosine
NOTES:

3.
4.
5.

57 ~s + 40 I's for each argument.
2421's + 40 ~s for each argument.
168 ~s + 624 ~s for each argument.

D~COS(D)

6.
7.

2331'S + 6241'5 for each argument.
163 ~s + 607,,, for each argument.

Table III-l
PDP-9 Science library (Cont)

Timing
NonEAE
EAE

Mode

Errors

Accur.
(Bits)

(a)

R=ATAN(2)

None

16.352 ms

(a)

D=DATAN(D)

None

R=ATAN2(R,R)

None

D=DATAN2(D, D)

Nane

tanh (a)

R=TANH(R)

None

.EB

Sin (a)

R=. EB(R)

.DB

Sin (a)

D=. DB(D)

ill

.ED

tan

(a)
(a)

ROUTINE NAME

Calling Sequence

Mnemonic

Function

Storage
(0 cto I) External Calls

EXTERNAL FUNCTIONS (Cont)
Arctongent:

ill
DP Arctangent
ill
Real Arctangent (x/y) ill
DP Arctangent (x/y) It
Hyperbolic Tangent

ATAN
~MS'
JMP

ATAN

Real Arctongent

DATAN

.DSA ADDR or ARG

tan

-1
-1

-1
ATAN' 0' DATAN} tan (x/y)
MS
JMP
.+3
-1
.DSA' ADDR of ARGl
tan (x/y)
.DSA ADDR of ARG2

ATAN2
DATAN2

tan

0' DATAN }

TANH
MS
JMP
* .+2
.DSA ADDR OF ARG

TANH

.DA, .ED,REAL

14.6 ms

· DA,. DD, DOUBLE

12.4 ms

.DA, .ED,REAL

16.2 ms

· DA,. DD, DOUBLE

16.383 ms

.DA,.EF,REAL

None

9.3 ms

100

· EC, .REAL

None

10.8 ms

116

· DC,. DOUBLE

R=. ED(R)

None

11.0 ms

· EC, .REAL

D=. DD(D)

None

14.5 ms

144

· DC,. DOUBLE

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 2 , R1,

None

N.A.

Note 8

REAL

None

N.A.

Note 8

DOUBLE

7.233 ms

....,

SUB-FUNCTIONS

}

5.632 ms

Sine Computation:
Real Sine
DP Sine

'-J

ill

Arctangent Computation:
Real Arctangent
DP Arctangent

.DD

1-< JMS*

Logarithm (Base 2) Computation:
Real Log
DP Log

ill

SUBR

tan

-1
-1

NOTE
.EE

Enter with argument in
floating accumulator.
Returns with result in
float ing a ccumu lator .

1092 a
1092 a

Exponentia I Computation:
Real Exponential
DP Exponential

ill
ill

. EF

. DF

Polynomial Evaluation:
Real Polynomial Evaluation

DP Polynomial Evaluation

ill
ill

JMS*
CAL

.EC

.DC

PLiST

2.0 ms + 1.3 ms for each coefficient.

-N
C

/-No. of
terms +1
/Iast term

n
Cn_1 /next to last

'8.

.....
. EC or . DC
PLiST

n
L
i=O

2i+l
C2i +1 Z

1-<

NOTES:

X
X

/2nd term

/1 st term

D=. DC(D2 , D1,

n
L
i=O

C2i +1 Z

... Rn)

... D)
n
2i+l

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

r Imln
',g t
ROUTINE NAME

Mnemonic

Colling Sequence

SUB-FUNCTIONS (Cont)

.DA

Mode

Errors

N.A.

None

N.A.

NonEAE

Note 9

EAE

Storoge
(Octo I)

Externol Calls

None

....,

Generol Get Argument

Function

Accur.
Bits

Routine that calls
Ca Iling Routine

Calling Routine

JMS*
JMP
-< . DSA
.DSA

SUBR
.+n+1
ARGI
ARG2

DSA

ARGn

SUBR CAL 0
JMS* .DA
JMP
.+n+1
~
(address of ARGI)
(address of ARG2)

(address of ARGn)
ARITHMETIC PACKAGE
INTEGE

ARGI
A-Resister

Multipl i cation
Division
Reverse Division
Subtroction
Reverse Subtroction

.AD
.AE
.AF
.AY
.AZ

Multiplicand
Dividend
Divisor
Minuend
Subtrohend

Double Precision Arithmetic:

DOUBLE

Integer Arithmeti c:

......
......
......
I

Note 11

ARG2
Multiplier
Divisor
~
Dividend
JMS* SUBR
Subtrohend LAC ARG2
Minuend --'
ARG2

.AO
.AP
.AQ
.AR

Value
Augend
Minuend

Address
Address
Addend
Subtrohend

Reverse Subtroct
Multiply
Divide
Reverse Divide

.AU
.AS
.AT
.AV

Subtrohend
Multiplicand
Dividend
Divisor

Minuend
Multiplier
Divisor
Dividend __

Reverse Subtroct
Multiply
Divide
Reverse Divide

ARGI
FL.ACC.

ARG2

.AG
.AH
.AI
.AJ

Value
Augend
Minuend

Address
Address
Addend
Subtrohend

.AM
.AK
.AL
.AN

Subtrohend
Multiplicand
Dividend
Divisor

Minuend
Multiplier
Divisor
Dividend

REAL

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

None
None
None
None
None

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

D=.AO(D)
D=.AP(D)
D=D-D
D=D-D

None
None
None
None

B-A
A*B
A/B
B/A

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

None
None
None
None

t 281 fJS
t 352 fJs

t 48 fJS
t 55 fJS

....,

ARGI
FL.ACC.

Load
Store
Add
Subtroct

Real Arithmetic (Includes
Floating):
Load
Store
Add
Subtroct

I*J
I/J
J/I
I-J
J-I

142

JMS*
.DSA

SUBR
ARG2

N.A.
N.A.

t 70 fJS
t72 fJs
t 255 fJS
t 324 fJS
t2.047ms t 272 fJS
tl.537 ms t 352 fJs

Note 12

JMS*
.DSA

SUBR
ARG2

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

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

None
None
None
None

B-A
A*B
A/B
B/A

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

None
None
None
None

N.A.
N.A.

t 67 fJS
t 70 fJs
t280 fJS
t 385 fJs
tt 1.937 ms t 264 fJS
1.327 ms t 324 fJS

-------_ .. _---

NOTES:

37 fJS + 15 fJs for eoch argument.

10.

The sign of the result (the exclusive OR of the sign bits of .AB and CE02) is stared in .CE. The sign of .AB is saved in CE05.

II.

1308 for EAE, 1648 for non EAE.
7648 for EAE, 733 for non EAE.

12.

REAL

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

Timing
Calling Sequence

Mnemonic

Mode

Errors

Accur.
Bits

A-I
I-A
A--A

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

None
None
None

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

Function

NonEAE

185 fJs
65 fJs
10 fJS

ARITHMETIC PACKAGE (Cont)
A-Resister

Floating Arithmetic

FL.ACC. }
F.P. No .
F.P. No.

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.

774 fJS
(avg)
1124 fJS
(real)
1444 fJs
(DP)
300 fJS
(avg)
160 fJS
(avg)
16 fJS
30 fJs
30 fJS

Short Get Argument

.CB

N.A.

R=.CB(R)

None

N.A.

28 fJS

JMS*

SUBR

-.0

{LO

JMS* .CB
CAL 0
.DSA 0

Value

}

EAE

Storage
(Octal)

Externa I Co lis

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:
( EXP-l,

-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.
1

(P. + ARG )
I

EXPONENTIAL (EXP, DEXP, .EF, .DF)
The function eX is calculated as 2 x lo92 e

where x log e

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

where

l=(;

and n ,= 6 for EXPand .EF,
or
n = 8 for DEXP and .DF.

i=O

The values of Care:

1.0

C1
C2

0.34657359

C3
C4
C5
C6

0.06005663
0.00693801
0.00060113
0.00004167
0.00000241

C7 = 0.00000119
Cs = 0.00000051S

III-10

NATURAL AND COMMON LOGARITHMS (ALOG, ALOG10, DLOG, DLOG10)
The exponent of the argument is saved as one greater than the integra I portion of the
result. The fractional portion of the argument is considered to be a number between
1 and 2. Z is computed as fo lIows.

x - .[2
Z=--X + .J2
Then

log X = -1 +
2
2

i=O

Z2i+i\

2i + 1

)

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

DLOG & DLOG10

2.8853913

2.8853900

0.96147063

0.96180076

C5 = 0.59897865

0.57658434

0.43425975

Finally,
log X = (log 2 X) (log 2), for ALOG & DLOG
e
e
and
10910 X = (l092 X) (log 102) , for ALOG1 0 & DLOG10.

SINE AND COSINE (SIN, COS, DSIN, DCOS, .EB, .DB)
The argument is converted to quarter circles by multiplying by 2/1Y. The low two bits
of the integra I 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

I
II
III
IV

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

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-ll

REAL ROUT INES

DP ROUTINES

C 1 = 1.570796318

C 1 = 1.5707932680

C 3 =-0.645963711

C 3 = -0.6459640975

C 5 = 0.079689677928

= 0.06969262601

= -0. 00467376557

C 7 =-0.004681752998

= O. 0001 5148419

C 9 = 0.00016043839964
C 11 = -0.000003595184353
C 13 = 0.000000054465285

The argument for COS and DCOS routines is adjusted by adding 'h' /2.

The sin sub-

function is then used to compute the cosine according to the following relationship:
cos x = sin (~ + x)
5.

ARCTANGENT (ATAN, DATAN, ATAN2, DATAN2, .ED, .DD)
ForX less than or equal to 1, Z=X, and:
arctangent X =

(.~

C2i + 1 Z

1=0

2i+l\

)

where n = 7 for REAL routines and n = 3 for DP routines.

For X greater than 1,

Z = l/X, and:

arctangent X =

¥-(.~

1=0

C 2i + 1 Z

2i+l\
)

where n = 8 for REAL routines and n = 3 for DP routines. The values of C are as
follows.
REAL ROUTINES
C1 =

DP ROUTINES

0 .9999993329

C1 =

O. 9992150

C 3 = - 0.3332985605

C 3 = -0.3211819

C5 =

0 • 1 994653599

C 7 = - 0.1390853351
C9 =

0 .0964200441

'C 11 = -0.0559098861
C 13 =

0.0218612288

C 15 = - 0 .0040540580

III-12

0.1462766

C7 = -0.0389929

HYPERBOLIC TANGENT (TANH)

tanh

IX I =~- ~2~'\
l+e 2\X \ -.;

e ,calculated as 2

x log e
2 , where x 1092e will have an integral portion (I) and a

fractional portion (F), then:

where

2 =

and n = 6

1=0
The values of C are as follows.
C1

1.0

0.34657359

0.06005663

0.00693801

C 5 = 0.00060113

0.00004167

O. 00000241

LOGARITHM, BASE2(.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=--X+~2

Then
log X = -1 +

.-0
1-

C 2i +1 Z

2i+1'\
)

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

III-13

.EE

C1
C3

2.8853913

0.59897865

.DE

0.96147063

C1
C3

2.8853900

C5
C7

0.57658434

0.96180076
0.43425975

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

x = Z (C o + Z2 (C 1 ... +Z2 (C n Z2 + Cn- 1)))

III-14

UTILITY PROGRAMS
ADVANCED SOFTWARE SYSTEM
PROGRAMMER'S REFERENCE MANUAL
DEC-9A-KFZA-D

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