Digital PDFs

DEC-9A-KFZA-D

April 1968

114 pages

Original

2.8MB

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
Revision:
Pages:	114
Original Filename:	http://bitsavers.org/pdf/dec/pdp9/DEC-9A-KFZA-D_FORTRANIV.pdf

OCR Text

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
Equipment Corporation, Maynard, Massachusetts:
PDP
FOCAL
COMPUTER LAB

DEC
FLIP CHIP
DIGITAL

April 196B
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 Variab les

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

Re lational 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-Sca Ie 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 Statement's Read in at Object Time

1-32

5.2.8

Printing of a Formatt'ed Record

1-32

5.3

Auxiliary I/O Statements

1-33

5.3. 1

BACKSPACE Statement

1-33

5.3.2

REWIND 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 N

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
SY MBOL TABLE SIZES (F4 V3A)

I-59

ILLUSTRATIONS
1-1

FORTRAN Coding Form

1-3

TABLES
.!'age

1--1

Intrinsi c Functions

1-41

1--2

External Functions

1-43

Part II: FORTRAN IV OBJECT - TIME SYSTEM
11-1

Introducti on
OTS Binary Coded Input/Output

11-3

OTS Binary Input/Output

11-6

OTS Auxiliary Input/Output

11-8

OTS lOPS CommunicCltion

11-10

OTS Calculate Array Element Address

11-12

OTS Computed GOTO

JI-14

OTS Stop

11-15

OTS Pause

11-16

OTS Octal Print

11-17

OTS Errors

11-18

Fi Ie Commands

H-19

Clock Handling

11-21

Adjustable Dimensionilng

11-23
TABLES

U-1

OTS Errors

11-2

Part III: PDP-9 SCIENCE LIBRARY
UI-1

Introduction
Intrinsic Functions

111-1

Externa I Functi ons

111-1

Sub-Functions

111-1

The Arithmetic Package

111-1

Accumulators

111-2

A-Register

111-2

Floating Accumulator

111-2

Held Accumulator

111-3

Calling Sequences

111-3

Algorithm Descriptions

111-10

TABLES

Page

111-1

PDP-9 Science Library

111-5

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, LINC-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 DECUS 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: DEC US Office,
Digital Equipment Corporation,
Maynard, Mass. 01754
Please send DECUS installation membership information.
Please send DECUS individual membership information.
Please add my name to the DECUSCOPE non-member mai I ing list.
Name
Company
Address
(Zip Code)

PREFACE

This manua I describes the FORTRAN IV language and compi ler system for the PDP-9 computer.

rt provides the user with the necessary information for writing FORTRAN programs for compi la-

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.

IIA

Guide to FORTRAN IV Programming, II 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
compi led FORTRAN statements, parti cu larly I/O statements, at execution time.
Part III, PDP-9 Science Library, provides deta i led 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

eng ineer to learn the machine language for specifi c 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 seque'nces 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. The trans-

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

It is in a binary-coded form that the

machine can understand.

1 .2

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

A, B, C, D, E, F, G, H, I, J, K, L, M,
N, 0, P, Q, R, S, T, U, V, W, X, Y, z.
the 10 digits:

0, 1, 2, 3,4, 5, 6, 7, 8, 9
and 11 specia I characters:
Blank
Equals
Plus
Minus
Asterisk
Slash
Left Parent~es is
Right Parenthesis
Comma
Decimal Point
Dollar Sign

/
(
)

1-1

1 .2. 1

Card Format (I BM Mode I 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, I ine continuation field, statement field,.
and identification field.
The FORTRAN statement is written in columns 7-72.

If the statement is too long for om~

I inEl, 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 iSinored.

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 mCJY be
used for program identification, sequencing, or any other purpose desired by the user. Comments may
be iincluded in the program by putting a "C" in column 1 of each line containing a comment (or continuation of a comment). The compi ler ignores ,these comments except for printing them.
Blanks may be used to aid 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 prapared on paper tape, the sequence of'

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

For statement con-

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

Each line is terminated with a carriage

return, I ine feed.
The TAB key can increase the speed of wri ting FORTRAN stalrements on paper tape. A TAB
followed by an a Iphabeti c 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 fivedigif's,
followed by a TAB, places the next character in column 6 if it is a digiJ, or in column 7 if it is a letter.

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

1-2

CODER

FORTRAN

DATE

PAGE

PROBLEM

CODING FORM

[CC;;-:;;"e' I ~!----IS Syrnbo ~ Ie

!B.~B.o~,le,o:li:

FORTRAN STATEMENT

-------+--_

_ _' _ _
_
_ _ _
k:--~L~- 5 6 I 7 8 9 1011 12 ~1~~:.21_2~~3 24 2~ 31 3233 3435363738394041424344454647484950 51 52535455565758596061626364656667686970n 72 TJ74757677787980

~,+,,+----------v

:+-,--+-

-++-+-+-+-+--+ I I I ' I I I ' I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I

t:±f~==~~=~~:: :::'::':::' '::':: : : :::::::::::::::::: I::::::: I
l.
,~ l "
I
'j I

L-"--'--4-+

LtL~-f-~-+-H-~

:::::::::::::::::::::::::::::::::::1:::::::1

~-t ----+----+-+-+-+-+-+-+-+-+--+---r--+---t- I

I I I I I I

l
!

I~-

r-'

~'-i-

-+-+--+---t-+-+-+-+--+-+--+--+-+-+--+--t--+

r---+-+----'---+~+_+___+_I

i
L

T
w

+-+-+ I I I

I I

I I I

I I I I I I I I I I I

I I I I

I I I I I I I I I I I I I

I I I I I

I I

~-r~

+-+-+-+-+--+--+-+-

, ,

, , I , , I "

__~r~-~-+-f-r~~-r+-~~H-r~-+~H~+4-r~-+

~-+-4++++-" I I I I I :
I

, ,

I I I I I

I I I I I I

-+-+ I I I I I I I +-+ ' I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

~+-+---t+--+-+--+-+--+-+

II
I I I] I ,
[ ' TT~I
j

.' 1i "j

:+-,.-+-+-H I I I I I

~'~+-IIIII

" " "

••

I
J
I
TTI-'--~~~-'

11111111111111111111111111111

~.:.'d::::.!..lk..---L......L...-....L-::::l
~~_?__ 3___ 4 ~~ _s.!_~-'-l~~~~~~ ~~?021222324 252627282930 3132'33 34 3~363738J94041 42434U546"748"950 51 52S35.t5SS657SS596061 62636" bS66676161' 70 n 72. 7'374757677711'910
......L.....l

__
, _ _
,
_ ,_ ' _ ' _ '

DIGITAL EQUIPMENT CORPORATION

Figure I-1

•

MAYNARD, MASSACHUSETTS

FORTRAN Coding Form

100 ,12f04

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, logi cal, 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
17
be less than or equal to 131071 (2 -1).
Example:
+97

o
-2176
576
If the magnitude>2

-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
50 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
(2'S COMP.)

LOW ORDER
MANTISSA

SIGN OF
MANTISSA

- - - -'---'-~
HIGH ORDER MANTISSA
~

L-._L--_

Negative mantissae are indi cated 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 exponl~nt 1

indicated by the letter D and a 1- or 2-digit constant with magnitude! not greater than 76. A + orsign may precede the constant and may also precede the scale factor. A decimal point within the
c:onstant is optiona I. A double-precision constant is interpreted identically to a real constant 1 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:

C-_-_-_-_'-_______:___EX_PO_NEN~

(2',S__
CO_M_P,_)_ _ _ _ _ _ _ _ _ __

]
,7

SIGN OF
MANTISSA

-f-j

HIGH ORDER MANTISSA

]

LOW ORDER MANTISSA

2.1.4

_ _ _ _ _ _ _ _ _,_ _ _ _

NEGATIVE
MANTISSAE
ARE
INDICATED
WITH A
CHANGE
OF
SIGN

J
'7

Logical Constants
The two logical constants are the words TRUE and FALSE, I~ach both preceded and followed

by a decimal point.
. TRUE.
. FALSE.

777777

o
/-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, whi ch 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:
1HA
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 IS 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
X12345
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 Logi cal Variables
A type specification statement is the only way to assign a vClriable value to one of these two

types. This is done with either a double precision statement or a logic(ll 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 (3 sub·script. For example,
A (3)

represents the third element in a one-dimensional array named A. To ~Ieneralize further, in an array A
with n elements, A (I) represents the Ith element of the array A where I = 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 sepclrated from the next by a comma. For example,
B (1, 3)

represents the value located in the first row and the third column of a two-dimensional array namE~d 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 stomge locations. The array i:; storc~d

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

ascending absolute
storage locations

1-8

2.3.2

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

V
IC
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)
BET A (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: arithmeti c
and logical.

2.4.1

Arithmetic Expressions
An arithmetic expression consists of arithmeti c elements jo ined by the arithmeti c operators +,

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

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

1-9

function name). An expression enclosed in parentheses· is considered a ::;ingle 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 double-

precision constants or variables produce a double-precision mode. The mode of an arithmeti c 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 (::mother mode in the same expression. There are, however, exceptions to this rule.
a. The follow ing examples show the modes of the val id arithmetic expressions involvin!~ the
use of the arithmetic operators +, -, *, and /.

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

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

I+ I
R+ R
R+ D

D+ R ~
D + D.

Integer result
Real result
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 integ.~r, real, and double-preci:;ion.
1**1
R**/
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 detE~rmine the order of computcltion"
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-D{I,J) + E**F*G-H
interpreted as,
F
FUNC + ({A*B)/C) - D{I,J) + (E * G) - H
2.4.1 .3

Rules for Constructing Arithmetic Expressions a. Any expression may be enclosed in parentheses.
b.

Expressions may be preceded by a + or - sign.

Simple expressions may be connected to other simple expressions to form a compound

expression, provided that:

(1)

No two operators appear together.

(2)

No operator is assumed to be present.

d. Only val id mode combinations may be used in an expression (described under Mode of an
Expression, Section 2.4.1.1).

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

3
A{I)
B + 7.3
C*D
A + (B*C) - D**2 + 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 (»
Equal to (=)
Not equal to (r)
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 logiical quantity th(lt
follows.

.AND.

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

.OR.

Logical OR generates a logical resul,t 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 e!xpression enclosed in parenthesc~s.

b. The logical operator. NOr. 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 expressiion fClr
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 quantil"y.

/-12

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

thesis 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.

Evaluation of functions

b. **{Exponentiation}
c. Evaluation of unary minus quantities
d. * and/ {multiplication and division}
e. + and - {addition and subtraction}
f.

. LT., . LE., . EQ., . NE. I

•

GT. I

•

GE.

g . . NOT.
h . . AND. and .OR.
i.

= Replacement operator

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

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

gram. There are four categories of statements provided for by the FORTRAN language:
a. Arithmeti c statements define a numeri ca I ca Icu lat ion.
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.

Specifi cation statements define the properties of variables, functions, and arrays appear-

ing in the source program. They also enable the user to control the a Ilocation 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 logica I, 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.
cases an automati c conversion takes place.

In such

The rules for the assignment of an expression E to a variable

V are as follows:
E Mode

V Mode

Assi~nment 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 eva 1uate and real assign

Double-precision

Integer

Double-precision float
and assign

Double-precision

Real

Double-precision eva 1uate and ass ign

Double-precision

Assign

Logical

Assign

Mode conversions involving logical quantities are illegal unless the mode of both V and E is
log i ca I.

Examples of an assignment statement:
ITEM = ITEM + 1
A(I) = 8(1) + ASSIN (C (I) )
V = .FALSE.
X =A.GT.B.AND.C .LE. G
A=B

I-15

CHAPTER 4
CONTROL STATEMENTS

The statements of a FORTRAN program norma Ily are executed as written.

However, it is

frequently desirable to a Iter the norma I 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 whi ch
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 l' n , .... , n m)
2

where i is a nonsubscripted integer variable reference appearing in a previously executed ASSI GN
statement, and n , n , .... , nm are the statement numbers which the ASSIGN statement may legally
1 2
assign to i. Examples:
ASSIGN 13 TO KAPPA
GO TO KAPPA, (l, 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 l' n2' .... , n m)' i

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

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

Exclmple:
GO TO (3, 17, 25, 50, 66), ITEM
If t-he value of ITEM is 2 at the time this GO TO statement is executed,r the statement to which control
is t-ransferred 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

where e is an arithmetic expression and n , n , n3 are statement numbers. The IF statement evaluates
1 2
the expression in parentheses and transfers control to one of the referenced statements. If the value of
the expression (e) is less than, equal to, or greater than zero, control i's transferred to n , n , or n3
1 2
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 log i ca I expression and s is any executable statement other than a DO statement or another
10~J i ca I IF statement.

The logi ca I expression is eva luated, 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 state'ment s is a CALL statement, in wh i ch case contro I is transferred to the next statement after return from
the subprogram).

If the log i ca I expression e is fa Ise, statement s is ignored and contro I is transfelrred to

the statement following the IF statement.

1-18

Example:
IF (L l) I = I + 1
IF (L. LE. k) GO TO 17
IF (LOG.AND. (.NOT.LOGl)) 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 = m , m , m3
1
2
or

where n is a statement number representing the terminal statement or the end of the IIrange ll ; i is a nonsubscripted integer variable known as the II index ll ; and m , m , and m3 are unsigned nonzero integer
1
2
constants or nonsubscripted integer variables, which represent the lIinitial, II IIfinal, II and lIincrement li
values of the index.

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

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

1-19

Example:
DO 72 I :::: 1, 10, 2
DO 15 K:::: 1, 5
DO 23 I :::: 1, 1 1, 4
Any FORTRAN statement may appear within the range of a DO statement, including an()ther
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 sCltisfying this rule is called a nest of DOs.

It is possible for a terminal stah:~ment to be the terminal stcJte-

ment for more than one DO statement. The following configuration, where brackeh are used to represent the range of the DOs, indi cates the pel'missible and illega I nesting procedures.

PERMISSIBLE , - - - - -

ILLEGAL . - - - - - - - - DO

~DO

LL-

--DO

Transfer of control from within the range of a DO statement 1'0 outside ii's 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 val id and inval id

transfers.

VALID

INVALID

c-~

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., GO TO, arithmetic IF, RETURN, STOP, PAUSE, or DO, or a 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 , The integer n is typed out on the console
8
Teletype for the purpose of determining which of several PAUSE statements was encountered. Program
execution is resumed, by typing contro I P (1 P), starting with the first statement fo Ilowing the PAUSE
statemen t"

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 77777778" 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 a /lowed in subprograms.
4.11

END STATEMENT
The END statement is placed a't the physical end of a program or subprogram. The form con-

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

1-21

It signals the compiler

A control transfer type statemf~nt, a STOP statement, or a RETURN sf'atement must immedilately precede END. This will be checked by the compiler.

1-22

CHAPTER 5
INPUT/OUTPUT STATEMENTS

The input/output (J/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 whi ch comprises a user's optimum physical record varies for each
I/O device, as follows:
Unit
or
Device
Typewriter
(input and output)

Formatted Physi ca I
Record Definition

Unformatted
(Binary) Physical
Record Definition

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

Undefined

Line printer

One I ine 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 I ine image of 630 characters

252 words

Disc/drum/
DECtape

One I ine 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
REA D (u, f) list
requests one logical record from the device associated with slot u in the device assignment table.
The statement descriptions in this section use u to identify a specific I/O unit, f as the statement number of the FORMAT statement describing the type of data conversion, and Iist as a 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 devi ces.

5. 1 . 1

Input/Output Argument Lists
An I/O statement which calls for the transmission of informajrion includes a I ist of quan'tities

to be transmitted.

In an input statement this I ist consists of the variabl'9s to which the incoming data i$

to be assigned; in an output statement the liist consists of the variables whose values are to be transmittE~d
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 devi ce. Any number of items may appear in a sing Ie list.
The same statement may transmit integer and real quantities.

If the daf'a to be transmitted exceeds the

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

Conversely, if the items in the I ist exceed the data to be transmitted,

suc:ceeding superfluous records are transmitted unti I a II items specified in the Iist have been transmitted.
5. 1 . 1 . 1

Simple Lists - The Iist uses the form
C , C , .... , C
1
2
n

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

as Iist items. The I ist reads from left to right. When an array identifil~r appears in the list, the Emtire
array is to be transmitted before the next Hem in the list.

Examples of Simple Lis,ts:

Y,Y, Z
A, B (3), C, D (I + 1, 4)
5. 1 . 1 .2

DO-Impl ied Lists - Indexing similar to that of the DO statement may be used to contred the

number of times a group of simple I ists is to be repeated. The Iist elements thus controlled, and i-he
index control itself, are enclosed in parentheses, and the contents of the parentheses are regarded as
a sing Ie item of the I/O list.
Example:
W, X (3), (Y (I), Z (I, K), I = 1, 10)

5.1.2

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

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
REA D (u, f) list

or
READ (u, f)
Execution of this statement causes input from device u to be converted as specified by format statement
f, the resulting values to be assigned to the items specified by list, if any.
Examples:
READ (3, 13) A, B, C
READ (2,10) A, (8 (/), 1= 1,5)
READ (1,3)

5.1.2.2

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

or
READ (u)
Execution of this statement causes input from devi ce 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 WR ITE 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 devi ce u.

I-25

5.1.3.2

Unformatted WRITE - The unformatted WRITE statement has lrhe general form
WR ITE (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 blclnks.

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

Exolmples of WR ITE:

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

FORMAT STATEMENTS
These statements are used in conj unction with the genera I I/O statements. They specify the

type of conversion whi·ch 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

~ecifying FORMAT

The general 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 d(lta c(mversion will be performed according to the same specification. This is also known as the repeat coun1'.
If n is equal to 1, it may be omitted. The control character k indica1'es which type of conversion will
be performed. This character may be I IE, F, G, D, P, L/A, H I or X. The nonzero integer constant w specifies the width of the fie Id. The integer constant d indi cates the number of dig its to the right of the
decimal point.
Six of the nine control characters listed above provide for data conversion between internell
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

Logi cal variable

Letter T or F

Alphanumeric

Alphanumeric (BCD) characters

External

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

Purpose

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

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

Designates Hollerith fields.

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

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

given a statement number.
Commas (,) and slashes (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 beg inn ing or the end of the

FORMAT specifi cations, the number of input records skipped or blank Iines 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 OIS 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 va lue wi II 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 specifi cations are used again until the list is complete.

1-27

Field descriptors (except H and X) are repeated by preceding the descriptor with an unsigne!d
integer constant (the repeat count). A group repeat count is used to enable the repetition of a group (,f
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 specificai"ion)
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:
FORMA T (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 1'0 a binary integer. A minus sign

indicates a negative number. A plus sign, indicating a positive numher, is optional. The decimal
point is illegal.

If there are blanks, they must precede the sign or fir:st digit. All imbedded blanks are

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

If the number is smaller than the field w

If an integer is tOCI large, the most significant digiits

Negative numbers have a minus sign just preceding their most significanlr digi·t

if suffi cient spaces have been reserved.

No sign indicates a positive number.

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

5.2.2.2

bbbbb
-b5
bbb12345

Internal

Output

+00000
-05
+12345

bbbbO
b-5
bbb12345

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

spaces reserved for the digits to the right of the decimal point. The w includes field d, spaces f,or a
sign, the decimal point, plus four spaces for the exponent (written E j: 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
\.'igits containing an optional decimal point, followed by an exponent.

Input data can be any number

vf digits in length, although it must fall within the range of 0 to ± 10±39
E output consists of a minus sign if negative (blank if positive), the digit 0, a decimal point,
a string of digits rounded to d 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 decima I point.
Input for F-type conversion is basically the same as that for E-type conversion, described
above.
The output consists of a minus sign if the number is negative (blank if positive), the integer
portion of the number, a decimal point, and the fractional part of the number rounded to d significant
digits.
Examples:
Format Descriptor
F6.3
F6.3
F9.2
F7.2
5.2.2.4

bl3457
313457
-21367.
-21367.

Internal

Output

13.457
313.457
-21367.
-21367-

13.457
13.457
-21367.00
1367.00

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

appears, or is to appear, internally as a 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 interna I floating-po int
number. Comparison is made between the exponent (e) of the internal value and the number of signifi cant dig its (d) specified by the format descriptor.

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

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

1-29

The 4X represents four blank spaces that are always appended to the va lue.
sented is less than .1

If the va lue to be replre-

,the E-type conversion is always used.

Examples:

5.2.2.5

Format Descriptor

Interna I

Output

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

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

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

D-Type Conversion - Field descriptor: Ow.d or nDw.d
The number of characters specified by w is converted as a do,uble-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 excep~ that a D is used in
plclce of the E in the exponent.
Examples:
Format Descriptor
bb+21345D 03
b+3456789012
-12345.6D-02

D12.6
D12.6
D12.6
5.2.3

Intemal

Output

21 .345
3456.789012
-123.456

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

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

D-·type conversions.

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

processed, the sca Ie factor establ ished by 11 rema ins in effect for a II subsequent E, F, and D descriptor$
within the same FORMAT statement unti I another sca Ie factor is encountered.
For E, F, G I and D input conversions (when no exponent exists in the externa I fie Id) khe
scale factor is defined as external quantity = internal quantity x 1On .
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. IFor E
and D output, the fractional part is multipl ied by 1On and the exponent is reduced by n.
Examples:
Format Descriptor

Sca Ie Factor

Internal
--

Output

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

123456
123456
12.3456

-3
-3
+1

+123456.
+12345.6
+1 .23456

2:L456
bbO.0001E+08
1 ,,2345D+00

1-30

5.2.4

Conversion of Alphanumeric Data

5.2.4. 1

A-Type Conversion (7-Bit ASC II, 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

a a ... a
1 2 3
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 logical quantity is Tor F. The internal format of a logical quantity

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

Leading blanks are ignored. A

nonblank character is illegal.
For L output, if the internal value is 0, an F is output. Otherwise a T is output. The F or T
is preceded by w-l leading blanks.
5.2.6

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

ignored. On X output, n spaces are output.

1-31

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
stcltements have the general form:
READ (u, name)
READ (u, name) lUst
WRITE (u, name)
WR ITE (u, name) I ist
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 descriptolr may
not be used. The FORMAT specification may be inserted into the array by using a data initialization
stcltement, 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 ,:)f
cards to be read. The first card of the deck wou Id conta in the format :itatement,
1

10
( (I 7 ,F 10.3)
the subsequent cards would contain data in the general form,

(

7
xx

17
xxxx

DIMENSION AA (10)
13 FORMAT (10A5)
READ (3, 13) (AA( I), 1=1, 10)
READ (3,AA) JJ, BOB
With the card reader assigned to device number 3, the first READ places the format stoltement
from the first card into the array AA, and the second READ statement causes data from the subsequent
cards to be read into JJ and BO B with format specifi cations 17 and FlO. 3, respectively.
5.2.8

Printing of a Formatted Record
When formatted records are prepared for output on a hard-copy devi ce I 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 STATEMENT~
These statements man ipulate the I/O fi Ie oriented devi ces. 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 ENDFILE statement has the general form
ENDFILE u

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

1-33

CHAPTER 6
SPECIFICA nON STATEMENTS
Specification statements are nonexecutable because they do not generate instructions in the
object program. They provide the compiler with information about the nature of the constants and variables used in the program. They also supply the information required to allocate locations in storage for
certain variables and/or arrays. All SPECIFICATION statements must appear before any executable code
generating statement. They must appear in this order: type statements, DIMENSION statements,
COMMON statements, and EQUIVALENCE statements. EXTERNAL and DATA statements must appear
after a II other specification statements and before executable-code-generating statements and FORMAT
statements.
6.1

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

where a, b, 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
REA L A (2,4), I,.J, K
DOUBLE PRECISION ITEM, GROUP
LOGICAL TRUE, FALSE
Any functi on references (statement functi ons, i ntri nsi c functions, 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
wou Id be generated by the compi ler and no error di agnosti c 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 form of the DIMENSION statement is:

where each V is the name of an array and each i is composed of one, two, or three unsigned intefJer
constants separated by commas. The number of constants represents the number of dimensions the IJrray
contains; the va lue 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, or a DIMENSIOI'I
statement; however, di mensi oning information should on Iy be given onc:e.
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 calling program.
6.3

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

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

where each x is a variable whi ch is a COMMON block name, or it can be blank.
fir:st 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 statElment.
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 withiin the program. The entries so
assigned are strung together in the given COMMON block in order of j·heir appearance.

Labeled

COMMON blocks with the same name appearing in several programs or subprograms executed togl9ther
must contain the same number of total words. The elements within the blocks, however, need not agree
in name I mode, or order. A blank COMMON may be any length.

1-36

Examples:
COMMON A, Bf 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 I ist of two or more variables or subscripted variables separated by commas.
Each element in the I ist is assigned the same memory storage location.
An 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 EQU IVALENCE statement, they may not both appear in COMMON statements within the same program.
Example:
EQUIVALENCE (A,B), (C(10), 0(10), E(15))
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(l 00), B(50)
COMMON A
EQUIVALENCE (A(l), B(l) )

1-37

The above example shows a legClI EQUIVALENCE statement. If, however, the statem,snt
were changed to read
EQUIVALENCE (A (50) , B(l))
the statement would cause an error di agnosti c •

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 (ISUM,A,B)
CA LL DEB UG (I SUB, 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 j"ime

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 noj~ contain dummy arguments.

There must be a one-to-one correspondence between the name: list and the data list, except

where the data I ist consists of a sequence of identica I constants.

In slJch a case, the constant need be

written only once, preceded by an integer constant indicating the number of repeats and an asterisk.

A Hollerith constant may appear in the data list.
Variable or array elements appearing in a DATA statement may not be in blank COMMON.
They may be in a labeled COMMON block and initially defined only in a BLOCK DATA sUbprO!3ram.
Example:
DATA A, B,C/3*2.0/
DATA X(1), X(2), X(3), X(4)/0.O, 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
Externa I 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 call ing 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 sing Ie statement simi lar in form to that of an arithmeti c

assignment statement.

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

Statement

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

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

I-39

a. Non-Hollerith constants
b. Variable references
c. Intrinsic function references
d. References to previously defined statement functions
e. External function references
A statement function is ca lied any time the name of the function appe(Jrs in any FORTRAN arithmeti c
expression.

The actual arguments must agree in order, number, and type with the corresponding dummy

arguments.
Execution of the statement function reference results in the computations indicated by the
function definition.

The resulting quantity is used in the expression whi ch conta ins the function refer-

ence.
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 FORTR,A,N

system library.

The type of each intrinsi c function and its arguments Clre predefined and cannot be

changed.
An intrinsic function is referenced by using its function name with the appropriate arguments
in an arithmetic statement. The arguments may be arithmetic expressi,ons, subscripted or simple varia··
biles, constants, or other intrinsi c functions (see table 1-1).
Examples:

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

J = IF IX (R)

1-40

Table 1-1 .
Intrinsi c Functions

Intrinsic Functions

Definition

Absolute value

No. of
Arguments

Truncation

Sign of a times largest
integer ~ I a I

Remaindering*

Symbolic
Name

Type of
Argument

Type of
Function

ABS
lABS
DABS

Real
Integer
Double

AINT
INT
IDINT

Real
Real
Double

Real
Integer
Integer

(mod O )
2

AMOD
MOD

Real
Integer

Choosing largest
value

Max (0 ,0 , ... )
1 2

AMAXO
AMAX1
MAXO
MAX1
DMAX1

Integer
Real
Integer
Real
Double

Real
Real
Integer
Integer
Double

Choosing smallest
value

Min (0 ,0 " .. )
1 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 times
2

SIGN
ISIGN
DSIGN

Real
Integer
Double

DIM
IDIM

Real
Integer

Obtain most signifi cant part of double
precision argument

SNGL

Double

Real

Express single precision argument in
double precision
form

DBLE

Real

Double

I 1I
0

Positive difference

- Min (0

)
2

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

1-41

7.3

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

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

FUNCTION NAME (a ,a ,··· ,an)
1 2
(FORTRAN statements)

NAME = final calculation
RETURN
END
where t is either INTEGER, REAL, DOUBL.E PRECISION, LOGICAL, or is blank; NAME is the symbol ic name of the function to be defined; and the a's are dummy arguments whi ch are nonsubscripted
vClriable names, array names, or other external function names.
The first letter of the function name imp I i citly determines the type of function.
letter is I, J, K, L, M, or N, the va lue of the function is INTEGER.

If tholt

If it is any other letter, the

v(llue 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 FUNCT ION 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 subprogmm, 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 statE~ment in the subprogram is
encountered is called the va lue of the function.
There must be at least one argument in the FUNCTION stalrement. These must be nonsubscripted variable names.

If a dummy argument is an array name, an appropriate DIMENSION st(Jtememt

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

It, of course, cannot contain any

si'atement which references itself, either directly or indirectly.
A function subroutine must contain at least one RETURN stcltement. The general form is:
RETURN
This signifies the logical end of the subprogram and returns control and the computed value to thl~ calling
plrOgram. 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 compi ler 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 cor-

respond in number, order, and type to the dummy arguments. An actua I argument may be one of the
following:
a.
b.
c.
d.
e.

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

Example:
DIMENSION A(l 00), B(lOO)

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

Type of
Argument

Type of
Function

EXP
DEXP

Real
Double

Symbol ic
Name

Exponent ia I

Natura I logarithm

log (a)
e

ALOG
DLOG

Real
Double

Common logarithm

log10(a)

ALOG10
DLOG10

Real
Double

Trigonometric sine

sin (a)

SIN
DSIN

Real
Double

Trigonometric cosine

cos (a)

COS
DCOS

Real
Double

Hyperbolic tangent

tanh (a)

TANH

Real

Square root

(a) 1/2

SQRT
DSQRT

Real
Double

I-43

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

Definition

Arctangent

arctan (a)

Remaindering*

No. of
Arguments

Symbolic:
Name

Type of
Argument

Type of
Function

arctan (a 1/a2)

1
2
2

ATAN
DATAN
ATAN2
DATAN2

Reali
Double
Real
Double

Real
Double
Real
Double

DMOD

Double

(mod a )
2

*The function DMOD (a ,a ) is defined as a - [a /a ] a , where [ x] is the integer whose
1 2
1 2
1
2
magnitude does not exceed the magnitude of x and whose sign is the s,ame as the sign of x.
7.4

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

It is similclr to

an external function in that both contain the same sort of dummy arguments, and both require at Ileast
one RETURN statement and an END statement. A subroutine, however, may have multiple outputs.
The general form of a subroutine is:
SUBROUTINE NAME (a ,a , ... ,an)
1 2
or
SUBROUTINE NAME
where NAME is the symbol ic name of the subroutine subprogram to be defined; and the als are dummy
arguments (there need not be any) which are nonsubscripted variable names, array names, or the dummy
name of another subroutine or externa I function.
The name of a subroutine consists of one to six alphanumeric characters, the first of wlhichis
a Iphabeti c. The symbol i c names of the subroutines cannot appear in any statement of the subroutine
except the SUBROUTINE statement itself.
The dummy variables represent input and output variables. Any arguments used as output
variables must appear on the left side of an arithmeti c statement or an input Iist with in 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

or
CALL NAME
where NAME is the symbol ic 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 SUBROUTINE subprogram. The array sizes must be the same. An actual argument in the CALL statement may be one of the
following:
a.
b.
c.
d.
e.
f.
7.5

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

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

block during compilation.

A BLOCK DATA statement takes the form

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

It cannot contain any executable statements.

It can be used to initialize data 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 BLOC K DATA Subprogram
BLOCK DATA
DIMENSION X (4) , Y(4)
COMMON/NAME/A, B, C, I,J ,X, Y
DATA A,B,C/3*2.0/
DATA X(l), X(2), X(3), X(4)/0.0, 0.1, 0.2, 0.3;Y(1), Y(2)
2Y (3), Y (4)/1 •OE2, 1. OE-2, 1 .OE4, 1 .OE-4/
END
1-45

APPENDIX 1
SUMMARY OF PDP-9 FORTRAN IV STATEMENTS

CONTROL STATEMENTS
ASSIGN n to i

1-15

CALL nome (° ,° , ••• )
1 2
CONTINUE • • • . • • .

1-42

• • • .

1-19

DO n i=m ,m ,m
••••••.
1 2 3
GO TO n • • • • • • •

1-17

GO TO i, (n ,n , ... )
1 2
GO TO (n ,n , ••. ), i
1 2
IF (e ) n ,n ,n . •
1 1 2 3
IF (e) 5 •

1-15

1-16
1-16

• ••.

1-16

PAUSE •

1-19

PAUSE n

1-19

STOP

1-19

STOP n

1-19

END

1-19

RETURN

1-39

SUBROUTINE NAME (° ,° ,., .on)
1 2
FUNCT ION NAME (° ,° , •.. on)
1 2

1-41
1-39

INPUT/OUTPUT STATEMENTS
BACKSPACE u •.

1-31

ENDFILEu

1-31

FORMAT (5 ,5 ,., .,sn)
1 2
READ (u,f)

1-24

REA D (u, f) list

1-23

••••

READ (u) • • • •
READ (u) list

1-23

•••••

1-23

READ (u, nome)

1-30

READ (u,nome) list

1-30

REWIND u

1-31

••

1-23

WRITE (u,f) list • • •

1-47

WRiTE(u,f)

1·,23

WR IT E (u) list

1-·24

WR ITE (u, name) . .

1-·30

WRITE (u, name) list

1-·30

SPECIF ICATION STATEMENTS
COMMON /x 1/a 1/xia 2/·· ./xn/a n . .

1··33

DATA k1/d 1/, k2/d /, • •• kn/d n/ . •
2
DIM ENS 10 N V 1(i 1)' V2(i 2) , • •• Vn(i n)

1··35

DOUBLE PREC ISION a, b, c • • • • •••

1··32

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

1··34

INTEGER a, b, c • •

1··32

lOG ICAl a,b, c ••

1··32

REAL a,b, c

1--32

BLOCK DATA • . •

1--42

1··32

1··34

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 arithmeti care i lIega I.

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 compi ler that allows DECtape input and output in an 8K system.
F4A operates under control of the Keyboard Monitor on Iy, 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 avai lable in the F4 version:

o
S
L

Object code listing
Symbol table printout
Source listing

In paper tape systems, the FORTRAN compiler along with necessary I/O device handlers and
an appropriate version of the I/O Monitor are punched on a tape in absolute format, referred to as a
"system tape. II At the beginning of the system tape is a Bootstrap Loader. The system tape can be loaded
by setting the starting address of the Loader (17720 for 8K systems, 37720 for 16K) on the console address
switches, pressing I/o RESET, and then pressing the READIN switch.

(Refer to the I/O Monitor Guide

for Paper Tape Systems, DEC-9A.-NGAA-D.)
In larger systems with a bulk storage device such as DECtape, the Keyboard Monitor accepts
direct keyboard commands to load the com pi ler in a device-independent environment.

(Refer to Keyboard

Mon itor Guide, DEC-9U-N GAA-D.) Th is 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 Moni tor Guide (I/O Monitor of Keyboard Mon itor) 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 dec laration 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 which
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
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

MINl
MIN2

o
JMS*

.DA

JMP

.+3

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

0
0
MINl
MIN2
MIN 1
MIN2
MINl
(400000
MIN2
MIN

/ENTRY/EXIT
fUSE THE F4 GENERAL GET ARGUMENT
/SUBPROGRAM TO LOAD THE ARGUMENTS
/JUMP AROUND REGISTERS LEFT FOR
/ ARGUME NT 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 sing Ie-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
A

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

When the program is loaded, the address (plus re location fClctor) of A is stored in location
00015 (plus relocation factor) and the address of B in 00016 (plus relocation factor). When .DA is
called from the MACRO-9 subprogram, it stores these addresses in MI N 1 and MIN2 (plus re locaf'ion
fClctor).

Thus MIN1 must be referenced indirectly to get the value of A (a direct· reference would gel

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: subrouf'ines
return the argument directly to the calling program, while functions rleturn arguments through accumulators.
The MACRO-9 program set-up for a FORTRAN IV subroutine is basically that described in
Part III of th is manua I 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+1
ADDR OF ARG1
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

call ing program. The following is an example of an expansion of the beginn ing 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 values, and. AP stores double precision values.

Since the A-register is the standard hardware accumulator,

a DAC instruction wi \I 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.

I-53

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 separate Iy, with i ntersegment communi cation of data accomp Ii shed 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 segment number to be called. The chain number (N) is established at chain-build time
(refer to the CHAIN section of the Keyboard Monitor Guide, DEC-9U-NGBA-D).
than or less than but not equal to the current chain number.

Only var,iables 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 CA LL CHAI N (N) statement rather than a STOP
statement i mmedia1'e Iy precedi ng the END statement wi II
cause an I error duri ng compi lati on (i II ega I 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 coiled).

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

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

CALL CHAI N (3)
END
I-55

N can be greater

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

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

I-56

APPENDIX 5
FORTRAN IV ERROR LIST

These letter-coded error messages apply to all versions of F4 and F4A. Refer to page 11-2
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.

Statemen t number 'error

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

Argument/subscript error

Missing argument or subscript, illegal use of subscripts, i lIega I 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.

Charac ter/ statemen t/
term error

I1lega I character, unrecogn izable statement, i Ilega 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 itude 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

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

FUNCTION/SUBROUTIN E/
EXTERNAL/CALL statement
error

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

Hollerith error

Hollerith data illegal in th is statement or i lIega I of
Hollerith constant.

I-57

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, ppe -

189 symbols (deci ma I)

DTe, TTA, ppe -

62 symbols (deci ma I)

PRB, TTA, ppe -

407 symbols (decimal)

DTe, TTA, ppe -

278 symbols (decimal)

DTB, TT A, DTB -

54 symbols (decimal)

F4A

I-59

FORTRAN IV OBJ ECT - TIME SYSTEM

INTRODUCTION
Part" describes the subprograms included in the PDP-9 FORTRAN IV Object Time System.
The Object Time System is a group of subprograms that process compiled FORTRAN IV statements,
particularly I/O statements, at execution time. The compiler outputs calls in the form of globals to
various subprograms, depending upon the content of the FORTRAN program. When the compiled program is loaded via the Linking Loader, the Loader attempts to satisfy these globa Is 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.
the object time system which are described in Table /1-1 .
The following information is given for each program:
a.
b.
c.
d.
e.

Class
Purpose
Ca II ing sequence
Externa I ca lis
Size
Error conditions

11-1

There are eight error messages output by

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 Arg ument

DSQRT

Illegal Index in Computed GO TO

.GO

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,

112

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 1,0

*Only those routines whose calls are generated by the compiler are Iiste!d.

11-2

OTS Binary Coded Input/Output
BCDIO
1. Class:

Object - Time System

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:

Purpose:

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

ENTRY

LOOPl
ARGl

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

.FP, .FR,.FE,.FF,.FW
3,4
.FP
/Initia lize I/O device status table.
.FR
/Initialize device 3 for input
(3)
/under control of FORMAT statement
FRMTl
/FRMT 1 and read first record into line
/buffer.
/Set loop counter to 8.
-lfJ
COUNT
(ARRAY) /Set element address to first word
ARGl
lin the array.

JMS*

.FE

fJ
ISZ
ISZ
ISZ
JMP
JMS*

ARGl
ARGl
COUNT
LOOPl
.FF

JMS*
.DSA
. DSA
LAW
DAC

.FW
(4)
FRMT2
-lfJ
COUNT

11-3

/Convert next Iine 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/Ou'tput

LOOP2
ARG2

LAC
DAC
JMS*

/Set element address to first
/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.

y5
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.

2y5
'(8Fl O. 5) I
'(8E12.5)'

y5
.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 staf'ement or allray.

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 De:scriptor Block.

d. To terminate the current logical record:
JMS*

.FF

All BCDIO routines util ize the F lOPS object-time package to perform a"
I/O data transfers between devices and the FlOPS Iline buffer. Device level
commun i cation is never employed.
e.

External Calls:
FlOPS, OTSER, REAL ARITHMETIC

Size:

2773 octal locations

11-4

OTS Binary Coded Input/Output
g. Error Conditions:
OTS ERROR 1,0' - Illegal I/O Device Number
OTS ERROR 11 - Bad Input Data (lOPS Mode Incorrect)
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 asso1ciated with the WRITE statements that generates the log i ca I record.
Each WRITE statement generates one logical record.
Each READ statement reads one logical record, regardless of the length of its I/O
I ist. For this reason, it is the responsibil ity of the FORTRA N programmer to ensure
that I/O I ists for WR ITE and READ statements are compatible.

3. Calling Sequences:
a. To initialize a device for binary input (output):

JMS*
.DSA

. FS (.FW)
DEVICE

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

JMS*
.DSA

.FI
address of the element

c. To input(or output) 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
f.

.FL
address of the element

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

LOGICAL
RECORD

PHYSICAL RECORD
FOR ID (OCTAL)

Externa I Ca lis:
F lOPS I OTSER

5. Size:
I

244 octal locations

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

1/-7

OTS Auxiliary Input/Output
AUXIO
1.

Class:

2. Purpose:

Object - Time System
Auxi I iary Input/Output consists of the processors fol' the three C:lUxii iary I/O statements in FORTRAN IV: BACKSPACE, REWIND, and ENDFILE.
These statements are normally used to control MagnE~tic Tape Transports which are
being used by unformatted READ and WRITE statements (BIN 10).

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

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

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

3.. Ca II ing 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
4.

.FV
DEVICE

External Calls:
FlOPS

11-8

OTS Auxil iory Input/Output
5.

Size:

64 octal locations

Error Conditions:
OTS ERROR 1,0' - Illegal I/O Device Number

1/-9

OTS lOPS Communi cation
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 (Inifrialize I/O Device). IniticJliza'tion of all slots is maintained in the device status tClble. The first time that .FC is
called for any device, the appropriate .INIT call i~, made to lOPS. The buffer size
and input/output flag are stored in the status word table. Then all subsequent co lis
to . FC for the same devi ce suppress another . IN IT un less the input/output flag has
changed.
One Iife buffer is used by a II FORTRA N 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.II A .\NAIT
is a Iways performed.
The .FP routine is called at the beginning of all FORTRAN main programs. This
routine sets all words in the device status table to zero, indicating that all devices
are uninitialized.

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

.FP

b. To specify input:
DZM*

• FH

c. To specify output:

(1)

LAC
DAC*

.FH

d. To select device:
LAC
JMS*

DEV ICE (address of slot number)
.FC

e. To input or output the I ine 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 .FI'-l+377 .
8

11-10

OTS lOPS Communication
3}
4}

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

4. External Calls:
OTSER
5. Size:
6.

530 octo I locations

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

/1-11

OTS CCllculate Array Element Address
.sS
1. Class:

Object - Time System

To calculate the array element address.
as follows:

Purpose:

wd 1

ARRAY

I 000 I MI Size
0

wd 2

]
17

2 345
IN* Imax

wd 3

wd 4

The Array Descriptor Block is constructed

N* 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
11

01
02
03
01

integer
real
double precisic'n
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) * I * n + (k - 1) * I * J 'k n
'-y--J

'--y--J

•

wd 4

wd 2

wd 3

1-dimension array

~------------------~y-----------------'

2-dimension array
~-------------------------w----·-----------------~

3-dimension array
3. Call ing Sequence;
.GLOBL
JMS*
.DSA

ARRAY
.SS
ARRAY

LAC
LAC
LAC
DAC

51
52
53

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

//-12

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

57 octa I locations

6. Error Conditions:
None.

11-13

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

Object - Time System

To compute the index of a computed GO TO

Purpose:

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

/Index value in A-re~~ister
/Number of statemenjr addresses

STMT ADDR (N)

4. Externa I Ca lis:
OTSER

5. Size:
6.

26 octal locations

Error Conditions:
OTS ERROR 7 if the indE~x is illegal (equal to or les$ than zero).

/1-14

ors 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:
6.

13 octal locations

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 kl:!Yboard, control is returned to the program.

Co II ing Sequence:
LAC
JMS*

(Octal number to be printed)
.PA

External Calls:
SPMSG (. SP)

5" Size:
6..

14 octal locations

Error Conditions:
None

11-16

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. Ca" ing Sequence:
LAC
JMS*
. DSA
LAC
LAC
LAC
LAC
LAC
LAC
4.

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

Externa I Ca lis:
None

5. Size:
6.

74 octal locations

Error Conditions:
None

11-17

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 fi of the error number is a 1, the error is recoverable and program control
is returned to the ca II ing program at the first loc(]tion follow ing the error number.

If bit fi of the error number is a fi, the error is unrecoverable and program cc:>ntrol
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 return ing contro I to the ca Iler.

If the error is a bad format statement (unrecoverable), the current 5/7 ASCI/
word pair of the erroneous format statement is printed in addition to the errc>r
number.

3. Calling Sequence:

JMS*
ERROR #12
only

.DSA
LAC
LAC

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

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

External Calls:
None

5. Size:
6.

117 octal locations

Error Conditions:
None

/1-18

Additions to the PDP-9 FORTRAN IV Subroutine Library
Fi Ie Commands
FILE
1. Class
2. Purpose:

Externa I S ubrouti ne
To provide the device-independent .lOPS commands SEEK, ENTER, CLOSE, FSTAT,
RENAM, and DLETE. These commands are used to allow the FORTRAN IV Object Time
System to communicate with .IOPS file-oriented devices.
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 fi Ie 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 lIing Sequences:
a.

To seek a named fi Ie:
CALL SEEK (N ,A)
where N = device number
A = array name containing the 9-character 5/7
ASCII fi Ie name and extension.
The file array has the following format for the named file FILNAM EXT:
DIMENSION FILEN (2)
DATA FI LEN(1), FI LEN (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 file:
CALL CLOSE (N)
where N is the same as for SEE K.

11-19

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 fi Ie not found and I = 0 (. TRUE.) if fi Ie found and action complete.

To rename a fi Ie 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. External Calls
FlOPS, .DA, .SS, .SEEK, .ENTER, .CLOSE, .FSTAT, .RENAM, .DLETE
5. Size
322 octa I locations
6. Error Condi ti ons
.OTS Error 10 if I/O device number is illegal
.IOPS Error 13 if fi Ie not found on SEEK
.IOPS Error 14 if direc:tory 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. Ca lIing Sequence:
CALL TIME (IMIN, ISEC, IOFF)
This call causes the clock 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 II cause the time taken to execute the code at A to be output.
4. External Calls:
.DA, .TIMER
5. Size:
53 octa I Iocati ons
6. Error Conditi ons:
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 .. Calling Sequence:
CALL TIME10 (IMIN, ISEC, ISEC10, IOFF)
Thi s ca II causes the c loc:k to be started and the elapsed ti me to be recorded as
mi nutes, seconds, and t,enths of seconds in IMI N, ISEC, and ISEC10 respectiv '3Iy.
To stop the clock, set IOFF to non-zero. Only one~ call at TIME10 or TIME CCJn
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 condi ti ons:
None

11-22

Adjustable Dimensioning
ADJ1
1. Class:

Externa I S ubrouti ne

2. Purpose:

To provide dimension adjustment on a one dimensional array

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

(B,A)

Where B is the array whose storage begi ns at A. A must be an array element (such
as C (200)) wi th suffi ci ent storage beyond A to a Ilow 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)
CALLADJ1 (B,A(lOl))
CALL ADJl (C,A(201))
After the ca lis to ADJ 1 , the arrays Band C may be referenced as if they had been
di mensi oned as (100) each. No further ca lis to ADJ 1 have to be made.

4. Externa I ca lis:
.DA
5. Size:
17 octa I locati ons
6. Error Conditions:
None

II-23

Adjustable Dimensioning
ADJ2
1. Class:

Externa I Subroutine

2. Purpose:

To provi de di mensi on aclj ustment for a two di mensi on array.

3. Ca Iii ng Sequence:
DIMENSION B(l, 1)
CALL ADJ2 (B ,A, NR)
where NR is the number of rows to appear in array B.
See ADJ1 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
di mensi oned (10, 10) and (20, 10) respecti ve Iy. No further ca lis to ADJ2 have to
be made.
4. External Ca lis:
DA, .AD
5. Size:
36 octa I locati ons
6. Error Conditi ons:
None

11-24

Adjustable Dimensioning
ADJ3
1. Class:

Externa I Subroutine

2. Purpose:

To provide dimension adjustment for a three dimension array

3. Ca IIing Sequence:
DIMENSION B (1, 1, 1)
CALL ADJ3 (B, A, NR, NC)
where NR and NC are i'he number of rows and columns respectively to appear in array
B. See ADJ 1 for comments on B and A.
Example:
See ADJ1 and ADJ2
4. Externa I Ca lis:
.DA, .AD
5. Size:
41 octo I locati ons
6. Error Conditions:
None

11-25

PDP-9 SCIENCE LIBRARY

INTRODUCTION
All mathematica I routines in the PDP-9 Sc ience Library are descri bed in Part III. Most of the
descri ptive material is Iisted in Table III-l; in cases where detai led ca leu lations or a Igorithms are involved, a reference (,6) is made in column 1 to detailed descriptions following the table.

Information

given in Table 111-1 for each routine includes the routine name, mnemonic, calling sequence, function,
mode, errors, accuracy and timing (where available), storage requirements, and external calls.

Rou-

tines are categorized by Intrinsic Functions, External Functions, Sub-Functions, or part of the Arithmeti c Package and are I isted in the table accordingly.

Intrinsi c Functions
Intrinsi c 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 FORTRA N statement.
Example:

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

EClch External Function accepts one or more numerical arguments

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

All basic

Externa I Functions suppl ied with the FORTRAN system are described in Table III -1 .
Sub-Functions
Sub-Functions are called by Intrinsic and External Functions, but are not directly accessible
to the user via FORTRAN.

For example, the Sub-Function

. EB is called by the External Function SIN,

and performs the actual computation of the sine.
The Arithmeti c Package
The Arithmetic Package contains all arithmetic routines required for integer, real, and
double precision arithmetic.

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

11/-1

Accumulators
There are three accumulators referred to in the CALLING SEQUENCE column of the hlble.
These include the A-register, the floatnng accumulator, and the held (]ccumulator.

The A-register is the standard h::lrdware accumulator and is used in some of the computations
that involve integer values.
Floating Accumulator
The floating accumulator is a software accumulator that is included in the REAL ARITHMETIC
package.

It is a 3-word accumulator, .AA being the label of the firsl" word, .AB the second, and .AC

the third.

Numbers are stored in this accumulator in the following format:

.AA

EXPONENT (2 1s COMP .)

17
SIGN OF MANTISSA

f i , H ORDER MANTISSA

.AB

.AC

LOW ORDER MANTISSA

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

Single precision numbers have a different format and must be converted before clnd

after use in the floating accumulator.

The format of single precision numbers is:

EXPONEI~

I L O W ORDER
LMANTISSA

----EI

SIGN OF
MANTISSA

(2IsCOM~

89
HIGH ORDER MANTISSA

-~
17

111-2

Held Accumulator
The held accumulator has the same format as the floaHng 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 call ing sequences, given in the third column of Table 3-1, assume in some
cases where there are two arguments, that the appropriate accumulator has been loaded with the first
argument.

If the first argument is an integer value, it can be loaded into the A-register 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 I ibrary routines that are used in MACRO-9 programs must be declared with a
. G LOBL 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 wi II be loaded.

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

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

" 1-3

Table 111-1
PDP-9 Science Library
t

ROUTI NE NAME

Mnemonic

Calling Sequence

Function

Mode

Errors

Accur.
Bits

Timing
NonEAE
EAE

I**K

1=1**1

None

N.A.

Note 1

A**K

R=R**I

#13, if base ~O

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 ~O

23.0 ms

.EE,.EF,REAL

A**B

D=R**D

#13, if base ..20

27.6 ms

· EE, . DF, DOUBLE

Storage
(Octal}

Externa I Ca lis

INTRINSIC FUNCTIONS

.BB

{tc

Real Base, Integer Exponent

.BC

DP Base, Integer Exponent

.BD

Exponentiation:
Integer Base, Integer Exponent

Real Base, Real Exponent

.BE

Real Base, DP Exponent

. BF

JMS*
LAC

-< JMS*
.DSA

....,

SUBR
ADDR of ARG2
(exp.)

INTEGER

DP Base, Real Exponent

.BG

A**B

D=D**R

#14, if base..20

27.6 ms

· DE,. DF, DOUBLE

DP Base, DP Exponent

.BH

A**B

D=D**D

#14, if base ~

26.6 ms

· DE, . DF, DOUBLE

Absolute Value:

ARGl (ba~)}
. BB
ARG2 (exp)

-.,

Real Absolute Value

ABS

IAI

R=ABS(R)

None

N.A.

120 fJS

.DA,REAL

Integer Absolute Value

lABS

I=IABS(I)

None

N.A.

64 fJS

.DA

DP Absolute Value

DABS

IAI

D=DABS(D)

None

N.A.

120 fJS

.DA,DOUBLE

of integer
A Hm"}
~~est

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

None
None
None

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

365 fJS
180 fJS
180 fJS

15
13
13

· DA,REAL
· DA,REAL
· DA,REAL, DOUBLE

· DA,REAL

JMS*
-< JMP
.DSA

lJl

SUBR
.+2
ADDR of ARG

Truncation:
AINT
INT
IDINT

Real to Rea I Truncation
Real to Integer Truncation
DP to Integer Truncation

Remaindering:
Real Remaindering

AMOD

Note 2

R=AMOD(R,R)

None

N.A.

3015 fJs

Integer Remaindering

MOD

Note 2

I=MOD(I,I)

None

N.A.

477 fJs

· DA, INTEGER

DP Remaindering

DMOD

Note 2

D=DMOD(D, D)

None

N.A.

3335 fJs

.DA, DOUBLE

None
None
None

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

198 fJS
81 fJS
192 fJS

26
20
26

· DA, REAL
.DA
.DA,DOUBLE

Real Transfer of Sign

SIGN

Integer Transfer of Sign

ISIGN

DP Transfer of Sign

DSIGN

tor}

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

Real Positive Difference

DIM

A1-MIN(A1,A2)

R=DIM(R,R)

None

N.A.

794 fJs

.DA,REAL

Integer Positive Difference

IDIM

Il-MIN(11,12)

I=IDIM(I,I)

None

N.A.

85 fJs

· DA, INTEGER

A .... I

R=FLOAT(I)

None

N.A.

246 fJs

· DA,REAL

I ..... A

I=IFIX(R)

None

N.A.

180 fJs

· DA,REAL

A.... B

R=SNGL(D)

None

N.A.

144 fJS

.DA,DOUBLE

A.... B

D=DBLE(R)

None

N.A.

115 fJS

.DA,REAL

JMS*
JMP
DSA
.DSA

Transfer of Sign:

-< .

SUBR
.+3
ADDR of ARG1
ADDR of ARG2

Sign of A2

Positive Difference:

Conversion:

Its.

Integer to Real Conversion

FLOAT

Real to Integer Conversion

IFIX

DP to Real Conversion

SNGL

Real to DP Conversion

I DBLE

NOTES:
1.
2.

I
I

JMP
.DSA

SUBR
}
.+2
ADDR of ARG

- _ . _ ... _._-

Timing indicated in this column is estimated unless indicated to be otherwise with a dagger (I). 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 fJS times n, where n is the largest power of 2 in the exponent.
Remaindering is defined as A 1 - LA 1/A2 ] A2, where [A 1/A2 ] is the integer whose magnitude does not exceed the magnitude of A 1/A2 and whose sign is the same as Al/A2.

Table 111-1
PDP-9 Sc ience Library (Cont)

j
I

I
IMnemonic

ROUTINE NAME

Function

Calling Sequence

Errors

Mode

lAo,", ~~-----l Storage
I EAE

I Bits

(Octal) I External Calls

INTRINSIC FUNCTIONS (Cont)
-..,

Maximum/Minimum Value:

Integer to Integer Max.

MAXO

Integer to Integer Min.

MINO

MAXO,MINO,
AMAXO, or AMINO
.+n+1
JMP
.DSA ADDR of ARGI
(IMax. Value
.DSA ADDR of ARG2
Min. Value

LDSA ADDR of ARGn

Integer Maximum/Minimum

Integer to Rea I Max.

AMAXO

Integer to Real Min.

AMINO

Real Maximum/Minimum

RMNMX

Real to Real Max

AMAXI I

Real to Real Min.

AMINI

Real to Integer Max.

MAXI

Real to Integer Min.

MINI

i r:,

---

AMAXI,AMINI,
MAXI,orMIN2
.+n+l
JMP
.DSA ADDR of ARGI
.DSA ADDR of ARG2

I=MAXO(lI, ... , In)

None

I=MINO(II, ... ,In)

None

Max. Value

R=AMAXO(I1, ... ln)

None

Min. Value

R=AMINO(ll, .•• ln)

None

N.A·I Note 3
Note 3

N.A·I
N.A. Note 4
N.A. Note 4

JMS*

117 IINTEGER, REAL

.DSA ADDR of ARGn

>,Max. Value

I R=AMAX1(Rl, ...Rn)

None

N.A.

Note 5

Min. Value

R=AMIN1(RI, .. .Rn)

None

I=MAX1(Rl, ... Rn)

None

Min. Value

I=MIN1(Rl, ... Rn)

None

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

Note 5

Max. Value

DP Maximum

~:;:~~1 DMll'111s I
JMP
I:Yv\NMY
t'MS*
DMAXI
.DSA A~DR of ARGI
IMax. Value

DP Minimum

DMINI

DP ~y~aximum;.vdnimurn

106 IINTEGER, REAL

IMNMX JMS*

I
D=DMAX1(Dl, ... Dn) None

Note 6

105 IDOUBLE

N.A.

Note 7

Min. Value

D=DMINI (DI, ... On) None

N.A.

Note 7

X 1/ 2

R=SQRT(R)

#5,ARG < 0

t 6. 657ms It 3. 584 ms

66 I.DA,oER,REAL

XI /2

D=DSQRT(D)

#6,ARG < 0

t 8.191 ms t 4.094 ms

R=EXP(R)

#13, ARG:£O 126

t 15.489 msl t 4.672 ms

13 I.DA,.EF,.ER,REAL

D=DEXP(D)

#14, ARG ~O

t 17.664 ms t7.223ms

.DA,DF,.ER,
DOUBLE

R=ALOG(R)

#13, ARG <0126

t 8.197 ms It 4.092 ms

· DA, . EE, . ER, REAL

D=DLOG(D)

#14, ARG <0

t 15.489 ms t 4.095 ms

· DA, . DE, . ER,
DOUBLE

:
.DSA ADDR of ARGn

0-.

EXTERNAL FUNCTIONS
Square Root:

ill
DP Square Root ill

......

SQRT

Real Square Root

DSQRT

. DA, . ER, DOUBLE

Exponential:
Real Exponential
DP Exponential

&::,
&::,

EXP

DEXP

Natural Logarithm:

Real Natura I logarithm

DP Natural logarithm

JMP

.+2

~I~::

DLOG

Common Logarithm:
Real Common Logarithm
DP Common Logarithm

DP Sine
Cosine:
Reo! Cosine

DP Casine
.... 1r\TCC'.

1"III"-'IL..,..l.

..,
"'.

4.
5.

&
&

ALOG1~

loglO X

R=ALOG 1O(R)

#13, ARG<O 1 26

t 8.197 ms It 4.094 ms

· DA, . EE, . ER, REAL

DLOGl

Log

D=DLOG I O(D)

#14, ARG <0

t ll . 7ms

.DA,.DE,.ER,
DOUBLE

&
&

SIN

IA\

COS
OCOS

Sine:
Real Sine

SUBR

. DSA ADDR of ARG

ALOG

JMS*

DSIN

57 jis + 40 rS fOi each uigumsiit .
242 fJS + 40 I-'s for each argument.
168 fJs + 624 I-'s for each argument.

j
6.
7.

t i t

Sin (X)

R=SIN(R}

None

10.368 mSI '4.094 ms

.DA,.EB,REAL

Sin (X)

I D=SIN(D)

None

t 16.383 ms t 5.632 ms

· DA, DB, DOUBLE

Cos (X)

None
None

26
34

t 11.02S msl t 4.901 ms
t 16.383 msl t 6.145 ms

20
21

.DA, .EB,REAL
· DA, . DB, DOUBLE

Cos (X)

233;:: + 624 rS fer ecch c:"g~~e~t.
163 fJs + 607 fls for each argument.

~~~'~)

Table 111-1
PDP-9 Science Library (Cont)

ROUTINE NAME

Mnemonic

Calling Sequence

Timing
NonEAE
EAE

Mode

Errors

Accur.
(Bits)

R=ATAN(2)

None

16.352 ms

D=DATAN(D)

None

14.6 ms

· DA,. DD, DOUBLE

R=ATAN2(R,R)

None

12.4 ms

· DA, .ED,REAL

D=DATAN2(D, D)

None

16.2 ms

· DA, . DD, DOUBLE

tanh (a)

R=TANH(R)

None

16.383 ms

.DA,.EF,REAL

Function

Storage
(Octal) Externa I Ca lis

EXTERNAL FUNCTIONS (Cont)
Arctangent:

ATAN

&
Real Arctangent (x/y) &

ATAN2

Real Arctangent
DP Arctangent

DP Arctangent (x/y)
Hyperbolic Tangent

ATAN 0, DATAN} tan -1 (a)
~MS'
JMP

tan -1 (a)
-1
S ATAN2 0' DATA] tan (x/y)
JMP
.+3
-1
.DSA' ADDR of ARG1
tan (x/y)
.DSA ADDR of ARG2

DATAN

&
!b

.DSA ADDR or ARG

DATAN2

TANH
~MS'
.+2
JMP

TANH

.DSA

ADDR OF ARG

7.233 ms

.DA, .ED,REAL

.....

SUB-FUNCTIONS

}

5.632 ms

Sine Computation:
Real Sine
DP Sine

'-...J

ill
&

.EB

Sin (a)

R=.EB(R)

None

9.3 ms

100

· EC, .REAL

.DB

Sin (a)

D=.DB(D)

None

10.8 ms

116

· DC,. DOUBLE

.ED

1
tan- (a)

R=.ED(R)

None

11.0 ms

· EC, .REAL

tan -1 (a)

D=.DD(D)

None

14.5 ms

144

· DC,. DOUBLE

1092 a
1092 a

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

#13, ARG:5: 0 26
#14, ARG:5: 0 32

9.0 ms
10.7 ms

71
101

· ER, .REAL
· ER, . DOUBLE

R=. EF(R)

None

12.2 ms

116

REAL

D=. DF(D)

None

15.0 ms

137

DOUBLE

R=.EC(R ,R ,
2 1
... R )
n

None

N.A.

Note 8

REAL

D=. DC(D , D ,
2 1
... D)
n

None

N.A.

Note 8

DOUBLE

Arctangent Computation:
Real Arctangent
DP Arctangent

&
&\

.DD

1-< JMS*

Logarithm (Base 2) Computation:
Real Log
DP Log

ill

SUBR

NOTE
.EE

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

Exponential Computation:
Real Exponential
DP Exponentia I

. EF

.DF

....,

Polynomial Evaluation:
Real Polynomial Evaluation

DP Polynomial Evaluation

ill

JMS*
CAL

.EC

.EC or .DC
PLIST

X
X

n
~

i=O
C
Z2i+1
2i+1
PLIST

.DC

1-<

-N
C

/-No. of
terms +1
/Iast term

n
Cn-1 /next to last

i=O
Z2i+1
C
2i+1

I
!

I
I
I

Cn
I

NCiES:

2.0 ms T 1.3 ms for each coefficient.

\...

/2nd term

/lst term

I
I

------l

Table III-l
PDP-9 Science Library (Cont)
TiminR
Accur.
ROUT!NE NA~AE

~Anemonic

CeIling Sequence

Mode

Function

Errors

Bits

NonEAE

t
Storage
(n~~~I\

EAE

\'-"

............ ,

Externa! Ca!! s

SUB-FUNCTIONS (Cont)
I

General Get Argument

Routine that calls
Callins Routine

.DA

jMS*
JMP
.DSA
.DSA

SUBR
.+n+1
ARG1
ARG2

DSA

ARGn

Cal i;!:'l!

ROUHn~

N.A.

I
None

I N.A.

Note 9

None

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

(address of ARGn)
ARITHMETIC PACKAGE
Integer Arithmetic:
Multiplication
Division
Reverse Division
Subtraction
Reverse Subtraction

.AD
.AE
.AF
.AY
.AZ

Double Precision Arithmetic:

DOUBLE

I
::::
I

Multiplicand
Dividend
Divisor
Minuend
Subtrahend

ARG2i
Multiplier

II 1* J

Divisor
Dividend
SUbtrahej
Minuend

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

ARG2

Value
Augend
Minuend

Address
Address
Addend
Subtrahend

Reverse Subtract
Multiply
Divide
Reverse Divide

.AU
.AS
.AT
.AV

Subtrahend
Multiplicand
Dividend
Divisor

Minuend
Multiplier
Divisor
Dividend

Reverse Subtract
Multiply
Divide
Reverse Divide

ARGl
FL.ACC.

SUBR
ARG2

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

I' 352 f-ls

t 48 iJS
t 55 f.is

I
REAL

142

.AO
.AP
.AQ
.AR

REAL

JMS*
LAC

Note 11

t 281 flS

.....,

ARGl
FL.ACC.

Load
Store
Add
Subtract

Real Arithmetic (Includes
Floating):
Load
Store
Add
Subtract

I
I

ARGl
A-Resister

INTEGE

JMS*
.DSA

SUBR
ARG2

N.A.
N.A.

~70 f-lS
: 72 f.iS
'255 f.iS
t 324 f-ls

t 2.047 ms t 272 f.iS
t 1.537 ms t 352 f-lS

-."

ARG2

---

.AG
.AH
. AI
.AJ

Value
Augend
Minuend

Address
Address
Addend
Subtrahend

.AM
.AK
.AL
.AN

Subtrahend
Multiplicand
Dividend
Divisor

Minuend
Multiplier
Divisor
Dividend

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=R/R
R=R/R

None
None
None
None

N.A.
N.A .

t 67 f.is
} 70 fJs
'280 f.iS
t 385 fJs

tl 9"'"
t 264 fJS
't"
0/ ms
1.327 ms t 324 fJS

I
NOTES:

37 fJS + 15 f.is for each argument.

10.

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

11.

1308 for EAE, 164 for non EAE.
8
764 for EAE, 733 for non EAE.
8

12.

Table III-l
PDP-9 Sc ience Library (Cont)

Timing
Mode

Errors

A-I
I -A
A--A

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

None
None
None

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

Function

Calling Sequence

Mnemonic

Accur.
Bits

NonEAE

185 fJS
65 f.JS
10 f.JS

EAE

Storage
(Octal)

External Calls

ARITHMETIC PACKAGE (Cont)
A-Re!ijister

FL.ACC. }

Float
Fix
Negate

.AW
.AX
.BA

Integer

F.P. No.
F.P. No.

FL.ACC.

HELDAC

Multiply

.CA

Multiplicand

Multiplier

A*B

R=R*R

None

774 f.JS

Divide

.CI

Divisor

Dividend

AlB

R=R/R

None

1124 f.JS

Floating Arithmetic

JMS*

SUBR

(avg)
(real)
1444fJS

(DP)
A+B

R=R+R

None

Value

N.A.

R=. CD(R)

None

N.A.

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.

16 f.JS
30 f.JS
30 f.JS

N.A.

R=.CB(R)

None

N.A.

28 f.JS

Add

.CC

Augend

Normalize

.CD

Hold
Round & Sign
Sign Control

. CF
.CH
.CG

Short Get Argument

.CB

Addend

JMS*

SUBR

300 f.JS

-0

(avg)
160 f.JS

(avg)

Value

~CAL
JMS* 0 .CB
CAL

.DSA 0
_L...-

}

PDP-9 SCIENCE LIBRARY ALGORITHM DESCRIPTIONS
1.

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

(EXP-1 )

+ ARG

Po = .5

If the exponent (EXP) of the argument is even:
(EXP _

+ ARG

Newton's iterative approximation is then appl ied three times.

Pi+ 1 = 2'

(P. + ARG )
I

P.
I

EXPONENTIAL (EXP, DEXP, .EF, .DF)
e
Th e funeti on eX is ea Ie u loted as 2 x log 2 , where x log 2e
wi II have an integra I porf'i on (I) and a fraeti ona I porti on (F). Then

where

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

The values of Care:
Co

1.0

0.34657359

C
2
C
3
C
4
C
5
C
6
C7 =
C8

0.06005663
0.00693801
0.00060113
0.00004167
0.00000241
0.00000119

= 0.000000518

III-l0

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 fractiona I 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 +
2
2

i=O

C
2i + 1

Z2i+1\
)

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

1
3
5

DLOG & DLOG10

2.8853913

0.96147063

0.59897865

C
C

1
3
5
7

2.8853900
0.96180076
0.57658434
0.43425975

Finally,
log

X = (1092 X) (log 2), for A LOG & DLOG
e

and
10910 X = (l092 X) (l0910 2 ), for ALOG10 & DLOG10.

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

Quadrant

Modified Value (Z)

00
01
10
11

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

"
III
IV

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

=(~

i=O

2i +

C2i + 1 Z

1,\
)

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

111-11

DP ROUTINES

REAL ROUTINES

C
C
C

1
3
5

= 1.570796318

C 1 = 1. 5707932680

= -0.645963711

= 0.079689677928

C = 0.06969262601
5
C = -0. 004681752998
7
C = 0.0001604:3839964
9
C11 =-0.000003595184353
C = 0.000000054465285
13

C = - O. 0046737655"7
7
C = O. 0001 5148419
9

= -0.6459640975

The argument for COS and DCOS routines is adjusted by adding '1'1'/2.

The sin sub-

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

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

~ (.~

C
2i+1

1=-=0

Z2i+1\
)

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

For X greater than 1,

Z == 1IX, and:

arctangent X = :!!2 -

C~
i=O

C2i + 1 Z

2i+1,
)

where n = 8 for REAL routines and n = 3 for DP routines.

The va lues of C are as

follows.
REAL ROUTINES

DP ROUTINES

C 1 = 0 .9999993329
C

3
C5

= -

0.3332985605

= 0.9992150
1
C3 = -0. 321 1819

0 . 1994653599

= - 0.1390853351
7
C 9 = 0 .0964200441

ell = -0.0559098861
C
C

0.0218612288

15 = - 0 .0040540580

III-12

5
C
7

0.1462766

-0.0389929

HYPERBOLIC TANGENT (TANH)

tanh

IX I=1;-.
21 X I "\
~ l+e
-;

e , calculated as 2

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

fractional portion (F), then:

where

2F =

and n = 6

i=O
The va lues of C are as follows.
C

1.0

C
2
C3

0.34657359

C
4
C
5
C
6
C
7

0.00693801

O. 06005663

0.000601 '13
0.00004167
0.00000241

LOGARITHM, BASE 2 (. EE, . DE)
The exponent of the argument is saved as one greater than the integer portion of the
result.
1 and 2.

The fractional portion of the argument is considered to be a number between

Z is computed as fo Ilows.

x-02

Z=----

X+02

Then
log

X = -1 +

'-0
1-

C2i + 1 Z

2i+l)

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

III-13

.EE

C
3
C
5

.DE

2.8853913

0.96147063

C
3
C
5
C
7

0.59897865

2.8853900
0.96180076
0.57658434
0.43425975

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

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

III-J 4

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

READER'S COMMENTS
Digital Equipment Corporation maintains a continuous effort to improve the quality and usefulness of its publications.
To do this effectively, we need user feedback: your critical evaluation of this manual and the DEC products described.
Please comment on this publication. For example, in your judgment, is it complete, accurate, well-organized, wellwritten, usable, etc? _______________________________________

Did you find this manual easy to use? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __

What is the most serious fault in this manual? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __

What single feature did you like best in this manual?

Did you find errors inth~manuan Pleasedescribe.~_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _~

Please describe your position. _ __
Name_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Organizationl-_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
Street"~

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ State_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Zip!-----_ _

........................................................................................... Fold H.ere ..................................................................................... ..

............................................................................. Do Not Tear - Fold Here and Staple ............................................................ ..

FIRST CLASS
PERMIT NO. 33
MAYNARD, MASS.
BUSINESS REPLY MAIL
NO POSTAGE STAMP NECESSARY IF MAILED IN THE UNITED STATES

..................................................................
Postage will be paid by:

Digital Equipment Corporation
Software Quality Control
Building 12
.
146 Main Street
Maynard, Mass. 01754