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DEC-08-AJB

December 1969

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Digital Equipment Corporation
Maynard, Massachusetts

ADVANCED FOCAL

TECHNICAL SPECIFICATIONS

D EC-08-AJBB-D L

ADVANCED FOCAL
TECHNICAL SPECI FICATIONS

For additional copies order No. DEC-08-AJBB-DL from Program Library, Digital Equipment
Corporation I Maynard I Mass.
DIGITAL EQUIPMENT

CORPORATION

Price: $5.00
0

MAYNARD

MASSACHUSETTS

1st Printing Apri I 1969

The following are registered trademarks of Digital
Equipment Corporation, Nbynard, Massachusetts:
PDP
FOCAL
COMPUTER LAB

DEC
FLIP CHIP
DIGITAL

CONTENTS
Page
CHAPTER 1
INTRODUCTION
CHAPTER 2
COMMANDS
2. 1

2-1

Type, Ask

2.1.1

Literals

2-1

2.1.2

Numerical Input Formats

2-1

2.1.3

Alphanumeric Input Formats

2-1

2.1.4

Speci a I Characters

2-2

2.1 .5

Print Positions

2-2

2.1.6

Symbol Tab Ie

2-2

2.1.7

Output Formats

2-3

2.1.8

Term i nators

2-3

2.1.9

Off-Line Data Tapes (c.f., Section 4.5.3)

2-3

2.1.10

Corrections

2-3

2.1.11

Roundoff

2-3

2..2

2-4

2.3

Editing and Text Manipulation Facilities

2-4

2.3.1

Command- Input

2-4

2.3.2

ERASE

2-5

2.3.3

MODIFY

2-5

2.4

FOR

2-6

2.5

2-6

2.6

GOTO

2-7

2.7

RETURN

2-7

2.8

QUIT

2-7

2.9

COMMENT

2-7

2. 10

CONTINUE

2-7

2.11

SET

2-7

2.12

High-Speed Reader

2-8

2.12.1

General

2-8

2.12.2

Other Rules

2-8

2.13

2-10

The Functions

iii

CONTENTS (Cont)
Page
2.13.1

General

2-10

2.13.2

Analog to Digital

2-10

2.13.3

Extended Functions

2-11

2.13.4

Random Numbers

2-11

2.13.5

Standard Functions

2-11

2. 13.6

Using the Arctangent

2-12

2.13.7

Boolean Functions

2-13

2.13.8

FNEW - A User Functions

2-13

2.14

2-13

The Li brary Command

2.14.1

L-Command For Single User System

2-13

2. 14.2

LIBRA Command Specifications for Multi-User Systems

2-14

2.14.3

DF32 FOCAL FILE STRUCTURE

2-15

2.15

Write

2-16
CHAPTER 3
FOCAL USAGE

3.1

Requirements

3-1

3.2

Loadi ng Procedure

3-1

3.3

Initial Dialogue

3-1

3.4

Operation

3-1

3.4.1

Restart Procedure

3-1

3.4.2

Keyboard Error Recovery

3-2

3.4.3

Parentheses

3-2

3.4.4

Trace Feature

3-2

3.4.5

Variables, Functions and Numbers

3-2

3.4.6

Error Di agnosti cs

3-2

3.4.7

Arithmetic Priorities

3-3

3.4.8

ASCII data

3-3

3.4.9

Indirect Commands

3-3

3.5

Saving Focal Programs

3-4

3.5.1

Paper Tape

3-4

3.5.2

LINC Tape

3-4

3.5.3

Disk Monitor System

3-4

3.5.4

Disk System and Extended Functions

3-5

CONTENTS (Cont)
Page
3.5.5

Di sk System and Extended Memory

3-6

3.5.6

For 4-user FOCAL SAVE command, see Section 4.6.6

3-7

3.5.7

EAE Patch for FOCAL, 1969

3-7

CHAPTER 4
PROGRAM SPECIFICATIONS
4.1

Machine Requirements

4-1

4.2

Design Specifications

4-1

4.2.1

Design Goals

4-1

4.2.2

Input

4-1

4.2.2.1

Input Format

4-1

4.2.2.2

Character Set

4-1

4.2.3

Output

4-2

4.2.3.1

Output Format

4-2

4.2.3.2

The Input/Output and Interrupt Processor

4-2

4.2.4

Organization

4-3

4.2.4.1

Arithmetic Package

4-3

4.2.4.2

Storage

4-3

4.3

Hardware Errors

4-4

4.4

Internal Environment

4-4

4.4.1

Adding a User's Function; FNEW(Z)

4-4

4.4.2

Internal Subroutine Conventions

4-6

4.4.2.1

Calling Sequences

4-6-

4.4.2.2

Subroutine Organization

4-7

4.4.3

Character Sorti ng

4-7

4.4.4

Language

4-8

4.5

4-9

Notes

4.5.1

Core Uti lization

4-9

4.5.2

Extended Functions

4-9

4.5.3

Error Pri ntouts

4-10

4.5.4

No Interrupts

4-10

4.5.5

Operating HS Reader Without Interrupts

4-10

4.5.6

Non- Typing of Program Tapes During Loading

4-10

4.5.7

Explanation of NAGSW (Not Allor Group Switch)

4-10

CONTENTS (Cont)
Page
4.5.S

4-11

Data Inaccuracies

4-11

4.5.9

4.5.10
4.6

Estimating the Lenght of User's Program

4-11
4-12

FOCA L Systems

4.6.1

FOCAL Systems Assembly

4-14

4.6.2

FOCAL Binary Paper Tapes

4-15

4.6.3

FOCAL Listings

4-15

4.7

4-15

FOCAL Segments

4.7.1

8K Single User Overlay - SK

4-15

4.7.2

Extended Precision Overlay - 4Word

4-15

4.7.2.1
4.7.3

Double Precision Multiply in Four-Word FOCAL

4-16
4-16

Four User Overlay - QUAD

4.7.3.1

Four User Loading and Operating Procedure

4-16

4.7.3.2

Swapping

4-17

4.7.3.3

Workload and Timing

4-17

4.7.3.4

Special Controls

4-17

4.7.3.5

Dialogue

4-17

4.7.4
4.S

Graphics for Circles and Lines - CLIN

4-18

4-22

FOCAL Demonstrations

4.S.1

One-Line Function Plotting

4-22

4.S.2

How to Demonstrate FOCAL's Power Quickly

4-23

4.9

4-23

FOCAL Versus BASIC
CHAPTER 5
ADDITIONAL FOCAL APPLICATIONS

5.1

FOCAL for the LAB-S

5-1

5.1.1

Standard

5-1

5.1.2

Additionsl (Possible) FOCAL Functions for AX-OS

5-1

5.2

5-3

F NEW for Data Arrays

5.2.1

Storage Requirements

5-3

5.2.2

Usage

5-3

5.2.2.1

5-3

5.2.2.2

Ca II i ng Sequence

5-4

5.2.3

5-4

Recursive Calling

CONTENTS (Cont)
Page
5.2.4

Restr ict ions

5-4

5.2.5

Description

5-4

5.3

Dynamic Interrupt Processing via FOCAL, 1969

5-5

5.4

Simultaneous Equations' Solutions

5-6

5.5

Fast Fourier Transforms Programs

5-6

5.6

Travel Voucher to Expense Voucher Conversion Program

5-8

5.7

Twins Demo

5-10
APPENDIX A
FOCAL COMMAND SUMMARY
APPENDIX B
ERROR DIAG NOSTICS
APPENDIX C
EXPLANATION OF NEW INSTRUCTIONS
APPENDIX D
FOCAL CORE LAYOUT
APPENDIX E
SYMBOL TABLE AND OTHER TABLES/LISTS
APPENDIX F
FOCAL SYNTAX
APPENDIX G
ILLUSTRA TIO NS
ILLUSTRA TIO NS

4-1

Figure 4-1

4-8

D-1

FOCAL Core Layout Dynamic Storage

D-4

G- 1 (Sheet 1) Arithmetic Evaluation

G-l

G- 1 (Sheet 2) Arithmetic Evaluation

G-2

G- 1 (Sheet 3) Arithmetic Evaluation

G-3

G-l (Sheet 4) Arithmetic Evaluation (Analysis of Functions)

G-4

G-2

Command/Input

G-5

G-3

Main Control and Transfer

G-6

G-4

DO Command

G-7

G-5 (Sheet 1) Input/Output Commands

G-8

G-5 (Sheet 2) Input/Output Commands

G-9
vii

ILLUSTRATIONS (Cont)
Page
G-6

Iteration Control

G-10

G-7

Conditional Branch Command

G-ll

G-8

Character Editing

G-12

G-9 (Sheet 1) ERASE and Delete

G-13

G-9 (Sheet 2) ERASE and Delete

G-14

G-10 (Sheet 1) Interrupt Hand ler

G-15

G- 10 (Sheet 2) Interrupt Hand ler

G-16

G-ll

Variable Look-up and Enter

G-17

G-12

Character Unpacking

G-18

G-13

IIFINDLNIJ Routine

G-19
TABLES

4-1

FOCAL Source Segments

4-13

4-2

Allowable FOCAL Systems

4-13

4-3

Variations for FOCAL Systems

4-14

8-1

Error Diagnostics of FOCAL, 1969

B-1

C-1

New Instructions

C-3

D-1

FOCAL Core Layout Usage

D-1

D-2

Detai led FOCAL Core Layout

D-2

F-1

Syntax in Backus Norma I Form

F-1

F-2

FOCA L Commands in French

F-2

viii

CHAPTER 1
INTRODUCTION

FOCAL t is a service program for the PDP-8 family of computers, designed to help scientists,
engineers, and students solve numerical problems.
The FOCALT.M·language is used as a tool in a conversational mode; that is, the user creates
his problem step by step, while sitting at the computer; when the steps of the problem have been
completed, they can be executed and the results checked. Steps can be quickly changed, added or
deleted.
One great advantage of a computer is that once a problem has been formulated, the machine
can be made to repeat the same steps in the calculation over and over again. Until now, the job of
generating the program was costly, time-consuming, and generally required the talents of a specialist
called a programmer. For many modest jobs of computation, a person unfamil iar with computers and
programming would use a desk calculator or slide rule to avoid the delays, expense, and bothersome
detail of setting up his problem so that the programmer could understand it.
FOCAL circumvents these difficulties by providing a set of simplified techniques that permit
the user to communicate directly with the computer. The user has the advantages of the computer put
at his disposal without the requirement that he master the intricacies of machine language programming,
since the FOCAL language consists of imperative English statements in standard mathematical notation.
FOCAL is flexible; commands may be abbreviated, and some may be concatenated within
the same line. Each input string or line containing one or more commands is terminated by a carriage
return •
A great deal of power has also been put into the editing properties of the command language.
Normally, deletions, replacements, and insertions are taken care of by the line number which indicates
the replacement or repositioning of lines. If single characters are to be changed within a FOCAL command line, it is not necessary to retype the entire string. The changes may be executed by using the
MODIFY command. Thus, complex command strings may be modified quite easily.
In operation, the program indicates that it is ready to receive input by typing an asterisk.
On-line command/input may be either direct (to be executed immediately) or indirect (to be stored
and executed later) commands. An example of a direct command is
*TYPE
=

5*5*5, 1 (User)
125.000* (PDP-8)

The final asterisk indicates that FOCAL is ready for its next command. All commands may be given in
immediate mode (see Appendix A).
t£ormulating 9n-Line Salculations in ~Igebraic !:.anguage (or FORmula CALculator)
T.M·Trademark of the Digital Equipment Corporation, Maynard, Mass.
1-1

Text input requires that a numerical digit, in the form ab .cd and within a range of 1 .01 to
31 .99, follow the *. The number to the left of the period is called the group number. The nonzero
number to the right is called the specific line or step number. While keying in command/input strings,
the rubout key and the left arrow may be used to delete single characters or to kill the entire line,
respectively.
Since the command decoder is table driven, FOCAL can be modified by a small binary tape
to understand foreign languages commands. (See Appendix F-2)
FOCAL is written especially for the educational and engineering markets and is intended to
be used as a problem solving tool. It gives quick and concise reinforcement, minimizes turnaround
time, and provides an unambiguous printed record.
FOCAL is also an extremely flexible, high accuracy, high resol ution, general-purpose desk
calculator and demonstration program.
This document describes the language, operating procedures for Disk Monitor and FOCAL;
use of High Speed reader; addition of user function FNEW; and many other details of interest. Symbol
tables, lists, and flow-charts are included.
There are also descriptions of the lO-digit overlay, 4 user overlay, and the complete
graphics function.

1-2

CHAPTER 2
COMMANDS

2. 1

TYPE, ASK
The TYPE and the ASK statements are used for output and input of literals, alphanumeric

calculations, and formats. The simplest form of the TYPE statement is a command (e.g., TYPE A *1 .4).
This will cause the program to type =, evaluate the expression, and type out the result. Several
expressions of this kind may be typed from the same statement if the expressions are each ended by
commas.
The ASK statement is similar to the TYPE statement in form, but only single variable names
can be used instead of expressions, and the user types in the values.

2.1.1

Literals
For output of literals, the user may enclose characters in quotation marks. The carriage

return will automatically generate closing quotation marks. The bell may only be inserted during
initial input, not via the MODIFY command.

2.1.2

Numerical Input Formats
Keyboard responses to ASK inputs may
a•

have lead i ng spaces

be preceded by + or - sign if desired or required

be in any fixed point or floating point format

d. be terminated by any terminating character, carriage return, or ALTMODE. It is
recommanded, however, that the space be adopted as the conventional and general purpose input
terminator. The AL TMODE is a special nonprinting terminator that may be used to synchronize the
program with external events. For example, to insert special paper in the teletype before executing
the program, type Ask Ai GO and RETURN, then load the paper, and hit ALTMODE. The value of
the variable used remains unchanged.

2.1.3

Alphanumeric Input Formats
Input data that is in response to an ASK command may take any format, may be signed or

unsigned, and must be terminated by a legitimate terminating character (space, CR, comma, I, etc.).
This means that alphabetic input may also be accepted by an ASK input command (see 3.4.9). This is
done by a simple hash-coding technique so that the program can recognize keyboard responses by a
single comparison. See example under the IF command for an illustration of how to program the

2-1

recognition of the user reply "WAIT". This is possible because the leading zero causes a character
string to be interpreted as a number. (e.g.,
*TYPE OANSWER = 0.26130E+22*).
Any literal word containing the letter "E" twice in one input will cause the ASK statement to be
terminated as the program interprets this letter as an exponent.

2.1.4

Special Characters
The exclamation point (!), percent (%), dollar sign ($), and the number sign (#) may be

used next to quotation marks or by themselves. They cannot be used to terminate alphanumeric
expressions. They may be used in either TYPE or ASK commands.
The TYPE statement precedes its numerical typeouts with an equal sign (=) before beginning
the output conversation process. The ASK statement types a colon (:) when it is ready to receive keyboard data.
To type an expression before its results, the user may enclose the expression in question
marks. This is a special use of the trace feature.
*TYPE ?A *5.2?
A *5.2=+ 10.40

*
2.1.5

Print Positions
Carriage returns are not automatically supplied at the termination of a typeout. To supply

carriage returns within a TYPE or ASK statement, the exclamation mark (!) is used. This is similar to
the use of the slash in FORTRAN format statements.
Occasionally, it is desirable to return the carriage and type out again on the same line
without giving a line feed. A number sign (#) returns the print mechanism to the left hand margin but
does not feed the paper forward. This feature may be used to plot another variable along the same
coordinate.

2.1.6

Symbol Table
TYPE. $ (dollar sign) causes the contents of the symbol table to be typed out with the current

values of all variables created. The symbol table is typed with subscripts and values in chronological
order. The routine then returns as though a carriage return had been encountered in the TYPE statement, thereby terminating the TYPE command. Both the TYPE and the ASK statements may be followed
by a semicolon (;) and other commands, unless a $ is in the string.

2-2

2.1.7

Output Formats
The output format may be changed within a TYPE statement by %X. YY, where X and YY are

positive integers less than 31. X is equal to the total number of digits to be output and YY is equal
to the number of digits to the right of the decimal point.
During output, leading zeroes are typed as spaces. If the number is larger than the field
width indicates, FOCAL wi II convert to E format. E format is also specified by % alone. (Floatingpoint decimal: ±O.XXXXXXXE±Y, where E means "10 to the Yth power".) The current output format
is retained unti I expl i citly changed. If a number is too large for the current format, the E format is
used temporarily.

2.1.8

Terminators
In the ASK statement, arguments are scanned by the GETARG Recursive Routine and may

therefore be terminated by any legitimate terminating character (e.g., space, comma, *, etc.). In
the TYPE statement, arguments are scanned by the EVAL Recursive Routine and must therefore be terminated by comma, semicolon, or carriage return. In either the TYPE or ASK statement, command
arguments may be preceded by format control characters # ! ". Example:
*ASK?A B C ?
A :5, B :6 C :7) *
All commands except WRITE, RETURN, MODIFY, QUIT and ERASE may be combined on the same line
if separated by a semicolon.

2. 1 .9

Off-Line Data Tapes (c.f., Section 4.5.3)
To prepare data tapes off-line, type the data word, the terminating space, and the "here-is"

key. Use backspace and rubout to remove characters off-I i ne .

2. 1 .10

Corrections
For editing input to an ASK command before the input has been terminated, the left arrow

( +-) is used.

2.1.11

Roundoff
Numbers to be typed out are rounded-off to the last significant digit to be printed (i .e.,

the rightmost digit of the requested format) or to the sixth significant digit, whichever is smaller.

2-3

2.2

DO
The DO command is used chiefly to form subroutines from single lines, groups of lines, or

from the entire text buffer. Thus, the instruction DO 3.3makes a subroutine of line 3.3. For a single
line subroutine, control wi" be returned when the end of the I ine is encountered or when the I ine is
otherwise terminated (e.g., by a RETURN statement, or in the case of TYPE, with the $).
One of the most useful features of a command language of this type is the ability to form
subroutines out of entire groups. Thus, the statement DO 5 calls all of group 5 as a subroutine
beginning with the first group 5 line number. Control wi II then proceed through the group numbers
going from smaller to larger. A return or an exit is generated from this type of subroutine by using the
word RETURN, or by encountering the end of that group, or by transferring control out of the group via
a GOTO or IF command. Simi larly, the entire text buffer may be used as a recursive subroutine by
simply using DO or DO ALL.
The DO statement may be concatenated with other legitimate commands by terminating it
with a semicolon. Thus, a single I ine may contain a number of subroutine caUs. In this way, several
forms of complex subroutine groupings may be tested from the console.
The number of DO commands which may be nested linearly or recursively is limited only by
the amount of core storage remaining after inclusion of the text buffer and the variable storage.

NOTE
When a GOTO or IF statement is executed within a DO
subroutine, control is transferred immediately to the
object line of the GOTO command; that line will be
executed and return made to the DO processor. If the
next line number is within the group (if this is a group
subroutine), it will be executed. If, however, a line
number outside of that group is about to be executed,
then a return will be made from the DO subroutine and
if any of the DO command line remains, it will be
processed.

2.3

EDITING AND TEXT MANIPULATION FACILITIES

2.3. 1

Command-Input
A line number which has already been used and is reused in a new input will cause the new

input to replace the line that previously had that number. Insertions are made at the appropriate point
in a numerically-ordered string of lines. For example, line number 1 .01 (the smallest line number)
will be inserted in front of (or above) line number 1 .1. The largest line number is 15.99.

2-4

2.3.2

ERASE
Removal of a single line may be made by using the ERASE command. For example, ERASE

2.2 will cause line 2.2 to be deleted. No error comment will be given if that line number does not
exist. The command ERASE 3 or 3.0 will cause all of group 3 to be erased. To delete all of the text,
one must type the words ERASE ALL.
ERASE, used alone, has the function of merely removing the variables. This may also be
thought of as initializing the values of the variables to zero.
To examine a single line, type WRITE followed by the line number. For example, WRITE
3.3 will cause line 3.3 to be typed out with its I ine number on the Teletype. WRITE 4.0 wi II cause all
of group four to be written on the Teletype. WRITE ALL will cause all of the text to be printed on the
Teletype, left justified, with title and line numbers in numerical order.

2.3.3

MODIFY
When only a few characters of a particular line must be replaced, the MODIFY command is

used to avoid replacing the entire line. For example, to change characters in line 5.41, type MODIFY
5.41. This command is terminated by a carriage return, and the program waits for the user to type that
character at which he wishes to make changes or additions. The program will then type out the contents of that line until the search character is typed. (The search character is not echoed when it is
first keyed in by the user.) The program will now accept input.
At this point, the user has seven options:
a.

type in new characters in addition to the ones that have already been typed out;

b. type a form-feed; this will cause the search to proceed to the next occurrence, if any,
of the search character;
c. type a bell which allows him to change the search character just as he did when first
beginning to use the MODIFY command;
d.

use the rubout key to delete characters going to the left;

type a left arrow to delete the line over to the left margin;

type a carriage return to terminate the line at that point and move the text to the right;

type line-feed to save the remainder of the line.

The ERASE ALL and MODIFY commands are generally used only in immediate mode, as
these commands return to command mode upon completion. The reason for this is that internal pointers
may be changed by these commands.
During command/input, the left arrow wi II delete the line numbers as well as the text.
During the MODIFY command typing the left arrow will not delete the line number.
When the rubout key is struck, a backslash (\) is typed for each character that is deleted.

2-5

NOTE
Any modifications to the text will cause the variables
to be deleted as if an ERASE command had been given.
This is caused by the organization of the data structure.
It is justified by the principle that a change of program
probably means a change of variables as well.

2.4

FOR
This command is used for convenience in setting up program loops and iterations. The

general format is:
FOR A = B, C, D;---.
The index A is initial ized to the value B, then the command string following the semicolon is executed
at least once. When the carriage return is encountered, the value of A is incremented by C and compared to the value of D. If A is less than or equal to D, then the command string after the semicolon
is executed again. This process is repeated until A is greater than D.
Naturally, A must be a single variable; but B, C, and D may all be expressions, variables,
or numbers. The computations involved in the FOR statement are done in floating point arithmetic. If
comma and the value C are omitted, then it is assumed that the increment is one. For example:
SET B = 3; FOR I = 0, 10; TYPE Btl, ! (po'Aer of 3)

2.5

IF
To provide transfer of control after a comparison, we have adopted the IF statement format

from FORTRAN. The normal form of the IF statement contains the word IF, followed by a space, a
parenthesized expression, and three line numbers separated from each other by commas. The program
will GOTO the first line number if the expression is less than zero, the second line number if the
statement has a value of zero, and the third I ine number if the value of the expression is greater than
zero.
Alternative forms of the IF command are obtained by replacing the comma between the line
numbers by a semicolon. In this case, if the condition is met which would normally cause the program
to transfer to a line number past that position, then the remainder of the line will be executed.
Example:
ASK REPLY
IF (REPLY-OWAIT)6.4, 5.01; RETURN
IF (REPLY - OYES) 6.3, 5.02; 6.3

2-6

NOTE
The IF command could occasionally fail to take the
= 0 branch due to internal computation and truncation
errors.

2.6

GOTO
This command causes control of the program to be transferred to the indicated line number.

A specific line number must be given as the argument of the GOTO command. If command is initially

handed to the program by means of an immediately executed GO, control will proceed from low numbered lines to higher numbered lines as is usual in a computer program. Control will be returned to
command mode upon encountering a QUIT command, the end of the text, or a RETURN at the top level.
The operation of the GOTO is slightly more complicated when used in conjunction with a
FOR or a DO statement. Its operation is perfectly straightforward when used with any other statement.

2.7

RETURN
The RETURN command is used to exit from DO subroutines. It is implemented internally by

setting the current program counter to zero. When this situation is encountered by the DO statement
it exits. (Refer to the DO command, Section 3.2.).

2.8

QUIT
A QUIT causes the program to return immediately to command/input mode, type *, and

wait.

2.9

COMMENT
Beginning a command string with the letter C will cause the remainder of that line to be

ignored so that comments may be inserted into the program.

2. 10

CONTINUE
This word is used to indicate dummy lines. For example, it might be used to replace a line

referenced elsewhere without changing those references to that line number.

2. 11

SET
The SET command for arithmetic substitution is used for setting the value of a variable equal

to the result of an expression. The SET statement may contain function calls, variable names, and

2-7

numerical literals on the right hand side of the equal sign. All of the usual arithmetic operations plus
exponentiation, may be used with these operands. The priority of the operators is a standard system:
+-/* t. These, however, may be superseded by the use of parenthetical expressions. The SET statement may be terminated by either a carriage return or a semicolon, in which case it may be followed
by additional commands. For example:
SET AA=B(5+<6+CONST>*AlPHA/ [5/BETA]);GOTO 3.2

2.12

HIGH-SPEED READER

2.12.1

General
The asterisk (*) is also used as a flip-flop control over the selection of the input device to

be used by a FOCAL program. (See the examples that follow.) An out-of-tape condition will return
to low-speed reader input and change the status of the * flip-flop. An error condition, however, does
not change that * flip-flop (see notes below).
For example, typing:

:* ~
will read in a program tape or a series of immediate commands.
**;ASK

ABCDZ

will fill AB with data from tape. If tape is empty, control will return to command mode.
*1 .1*; FOR 1=1, 5; ASK AX(I)

*00 1.1
If the tape contains fewer than 5 pieces of data, then remaining items are taken from keyboard. (See
c below.)

2.12.2

Other Rules
a.

* as a command may be concatenated with other processes [JMP (PROC):

(e.g.,

01.30*; ASK A, B;*)

b. If an out-of-tape condition is encountered while reading commands, then the input
device is switched to keyboard and all is returned to normal. (This occurs when the user has no reader.)
It is equivalent to receipt of a left arrow. [JMP (IBAR)].
c. If an out-of-tape condition occurs while executing an ASK command, then FOCAL
responds as if the end of the command line (carriage return) has been reached. [ISZ PDlXR; POP J]
Thus,
:*; ASK A,B,C,D
produces:::(out of tape on C): and the user is back to normal mode.

2-8

However,
*ERASE
~*; for 1=1, 20; ASK A(I); TYPE I, ! .

:=1.0000
: = 2.0000

: = 3.0000
: (out of tape for 1=4)
: (now accepting from keyboard) 123, = 5.0000
: 345, = 6.0000
: ?01 .00 (Control-C typed)
* TYPE $
I@ (00) = 7.0000
A@ (01) = (data from tape)
A @ (02) = (data from tape)
A @ (03) = (data from tape)
A @ (04) = .0000
A @ (05) = 123.0000
A @ (06) = 345.000

d. When an error occurs from the reader (illegal command, etc.), the code will be typed
out and input device control returned to the low-speed device. However, the device flip-flop (HSPSW)
will still indicate that the reader is active. Consequently, it will be necessary to give two asterisks
before the reader will be activated again.
**
*****?12.83

(Buffer full)

**
**
(reader now active again).
e. It is necessary to have a fairly long timing loop to detect the out-of-tape condition
(slow readers, reatart delays, etc .). As a result, the user of a PDP-8/s may encounter long delays if
there is no high speed reader or when the reader is out of tape. However, the initial dialogue makes
a correction for this when an 8/5 is being used.
f. Since the reader operates with the interrupt on, one may use Control-C to return at
once to keyboard input mode. A manual interrupt via Control-C (?01 .00) or a console restart (?OO.OO)
gives the same effect.
g. All commands, including "*" may be executed in immediate mode from the high speed
reader. This has several beneficial results:
(1) Program tapes may be composed that are self-protecting and self-starting
ERASE ALL
(protection)
01.10 ASK "Power of 2?"REPLY
(input indirect program)
01.30 TYPE 2 REPLY, !, GOTO 1 . 1
(etc)
(starting)
GOTO 1.1
(data)
5, 3, 1
This particular program is an infinite loop and must be stopped by a Control-C
from the keyboard.

2-9

(2) Programs may chain themselves together.
ERASE ALL
3.4 TYPE IINUMBER 111!! !; ASK A
3.5 *
(indirect command)
*; GO
(device restored to low speed and program
started)
The printout from this tape will be:
**
******

(START READER)
NUMBER 1
(Three I ines accepted)
(Erase processed)

: (waiting for keyboard input»)

(user)

(execution of 3.5 * at this point wi" reactivate the high speed reader).
(3) Immediate mode commands on the tape allow maximum storage for variables.
(4) If the interrupts are disabled by the patches shown in Section 4.5.3, then two
tapes may be merged from both high- and low-speed readers by a resident FOCAL
program.

2.13

THE FUNCTIONS

2.13.1

General
The functions are provided to give extended arithmetic capabilities and the potential for

expansion to additional input/output devi ces. There are basically three types of functions. The first
group contains integer parts, sign part, square root, fractional, and absolute value functions. The
second group has the input/output for scope and analog/digital converter functions. The third group
has extended arithmetic computations of trigonometric and exponential functions.
A function call consists of no more than four letters beginning with the letter F and followed
by a parenthetical expression (e.g., FSGN (A-B *2». This expression is evaluated before transferring
to the function process itself.

2. 13.2

Analog to Digital
a.

Input

T~e function FADC(X) is used to take a ra:lding from an analog-to-digital converter.
The value of the function is a 12-bit integer reading. The argument "X II is the channel member (AX08)
in decimal. Additional version of the ADC function could be designed to provide for synchronization
by a c lock or other means. (c. f., Chapter 5)

*SET A=FADC () *5

2-10

Output

The scope function FDIS (expression, expression) is used to set and display an X-V
coordinate on a Model 34 Scope and scope interface. The value returned for each of these functions
is the integer part of the second expression.
*SET Z = FDIS(X,X43/50)

2.13.3

Extended Functions
The extended arithmetic functions (FEXP, FLOG, FATN, FCOS, FSIN) are retained at the

option of the user. They consume approximately 800 characters of text storage area. These arithmetic
functions are adapted from the extended arithmetic functions of the three-word, floating point package.

2.13.4

Random Numbers
A simple random number generator is provided in the basic package as FRANO! An expanded

version could incorporate the random number generator from the DECUS library.
Functions for other devices are provided as overlay tapes (see Appendix H).

2. 13.5

Standard Functions
a.

Trigonometric Functions
All arguments are in radians
FSIN () - the sine functions
FCOS ( ) - the cosine function
FATN ( ) - the arctangent

From these functions, the user may compute all other trigonometric functions. (See FOCAL User1s
Manual)
b.

Logarithmic Functions
FLOG ( ) - log to the base e or Naperian base
FEXP () - e to the pov..e r

Arithmetic Functions
FSQT () - the square root
FSGN ( ) - one (1) with the sign of the argument
FABS () - the absolute value
FITR
() - the next smaller integer part maximum of 1024
LOG
(ARG) = LOGe (ARG) *LOG (e)
10
10
LOG
(e) = 0.434295
10
LOGe (10) = 2.30258
e = 2.71828

where:
1 degree = .0174533 radians
1 rod ian = 57 • 2958 degrees

2-11

2.13.6

Using The Arctangent
An arctan function cycles between + IT/2 and - IT/2. Thus, to get a correct range for 0-2lT

radians from the expression FATN(y/X), we must use the signs of X and Y.
X

FATN(X/y)

O-PI/2

PI/,2 - PI
PI - 3*PI/2
3 *PI/,2 - PI *2

=
=
::

=
=
=
=
=
=
=
=
=
::

=
=
=
=
=
::

=
=
::

=
=

I i..j OEX

0.0f)=

1.00=
0.96=
0.83=
~j. 62=
121.36=
0.07=
0.23=
0.51=
121.74=
0.91=
0.99=
0.99=-

{j. 30=
0.60=
(1).90=
1.20=
1.5')=
1.80=2.110=2.40=2."10=3.100=3.30=3.60=3.910=4.20=4.510=4.80=
5.10=
5.40=
5.70=
6.00=
6.30=
6.60=
6.90=

C-FOCAL

v).90=-

0.73=0.49=0.21=0.09=0.38=0.64=0.84=0.96=1.00=
0.95=
0.82=

0. {1V;=
0.3f,=
0.57=
0.78=
~l. 93=
1.0fi=
0.97=0.86=(;).68=0.43=0.14=0.16=
121.44=
0.69=
0.87=
0.98=
1 .00=0.93=0.77=0.55=0.28=0.02=
121.31=
0.58=

FUNCTION
(7;.000(1nr

0. 300~}0~i

=
=
=
=
=
=
=
=

(/'.600000

0.900000
1.20e,000
1.50vHJ00
1.3.4] 6CO
1. e41 M"~
~).741595

0.441595
0.141595
(1.158403
0.4584'-"2
0.758402
1.05840C;'
1.3584f:ie,
1.483200
1.1832vH:,
0.883196
~j. 583195
0.283198
0.0168~'2

121.316803

0.616800

em'it-' LJ T E [)
P.0CilfHiW0

fl. ~00000
P.6Ci'i!('P00
~l. 900f10~

1 • 2lil000~!
1.5011'0(110
] • R0f,~Hi)fl

2. 1 ~~Ci'l000
2.40f'0(i1C7'
2.70000'"
3.00v'lIif\(ij

=
=
=
=
=
=
=
=
=
=
=
=

3.300t7·0fi
3. 60C?""j0
3.9f':fI 00V
4.2~000(7:

4.500000
4.80000P
5. 100f7,00
5.400000
~h 7f,0~HH)

6. 0000f'o~
0.016802
0.316803
0.616800

8/68

01.05 T !!!!"
INDEX
X
Y
FliNCTION
01.10 FOR I=0~.3~7J TYPE !~%4.02~IJD 2
01.20 TYPE !!!!J~RITE ALL
01.30 QUIT

COMPUTED

02.10 ~ET Y=FSINC!)J SET X=FCOS(I)
02.20 TYPE X~Y~%8.06~rATNCY/<X+IE-10»J DO 13J TYPE ..
13.10 IF CX)13.3~13.2.13.3
13.20 S~T X=lE-100
13.30 S~T TH=FATN(FABS<Y/X»
13.~0 SET PI=3.141596
13.50 IF (Y) 13.61 IF (X) 13.7J RETURN
13.60 IF C~) 13.8JSET TH=PI+PI-THJ RETURN
13.70 SET TH=PI-THJ RETURN
13.80 SET TH=PI+THJ RETURN

•

2-12

.. THJ

2.13.7

Boolean Functions
TRUE is +1
FALSE is -1
*D

15
A B
=-1=-1
=-1= 1
= 1=-1
= 1= 1

AND
=-1 =
=-1 =
=-1 =
=

OR
-1
1
1
1

NOR

1::::
1=

1::::
-1::::

XOR
1
-1
-1

CARRY
::::-1::::-1

SUM

::::-1:::: 1
=-1= 1
= 1=-1

XOR is A*B
NOR is FSGN(-A-B)
OR is FSGN(A+B)
AND is FSGN(A+B-1)
NOT(A) is -A
The result of adding A and B is
CARRY = FSGN(A+B-1)
SUM
= -A*B

*
*WRITE 15
15.05 TYPE II A B AND OR NOR XOR CARRY SUM" !
15.10FORA=-1,2,1;FORB=-1,2,1;TYPEA,B,"
"DO 15.2
15.15 QUIT
15.20 TYPE FSGN(A+B-l),FSGN(A+B),FSGN(-A-B),A*B,"
"FSGN(A+B-1),-A*B,!

*
2. 13.8

FNEW - A User Function
This function name may be used to call a machine language routine for any reason.

(See Section 4.4. 1)

2.14

THE LIBRARY COMMAND
The form and usage of this mass storage command will vary with the computer and FOCAL

system used. (c. f • , 4.6)

2.14.1

L-Command For Single User System
The command may be given in either direct or indirect mode.

Execution of this command

first causes the octal typeout of the contents of four FOCAL pointers: CFRS, BUFR, LASTV, and
BOTTOM, respectively. The second action is to type out whatever characters follow the ilL II to serve
as operating instructions for the user. The third action is to turn off the interrupts and transfer to the
Disk Monitor or a-Library System by jumping to 7600.

2-13

The four octal numbers represent:
a.

the start of text buffer,

the end of text buffer,

the end of the variable list,

the bottom of the push-down list.

These command features will permit optimum usage of available disk storage and be compatible with the Disk Monitor.
After debugging a program, a typical user will execute ERASE and LIB. (This causes Band
C to be equa lin the 4K system.) He will then save the program and restart or call another program.
(See Section 3.4.12)
Manual Chaining may also be done. For example, when a program reaches line 12.3, it
may need to call another routine (as in a series of teaching programs, demos, or math subroutines).
The user, however, must be given instructions on how to proceed:
12.30LlB

.CALL LES2

For example, execution of 12.3 may produce:
3206
3345
3401

4407
.CALL LES2
.CALL LES2
. START

[User types thi s]

*
In the 8K Version, the text and variables are stored independently. For this reason, the 8K
version can have different programs operating on the same data. (See Section 3.4. 14)

2. 14.2

LIBRA Command Specifications for Multi-User Systems*
Four modifiers of the LIBRARY command are implemented to allow automatic program

storage, retrieval, and management in multi -user FOCAL. This extension to the FOCAL system is
implemented under the segment name LIBRA and requires at least an 8K PDP-8 with one DF32.
The LIBRARY command and its variations are:
a.

To save a program on disk,
LI BRA SAVE name

Where IJ name 1/ is a 1 to 4 character identifier and) is described in the FOCAL language specifications.

*Not completed

2-14

Errors:
(1) A program with an identical name has been found in the directory list
(2)

Name missing from command

(3) Disk I/O error (non-recoverable)
b.

To call a program on disk,
LIBRA CALL name

Errors:
(1)

No such program on directory list

(2)

Name missing from command

(3) Disk I/O error (non-recoverable)
c.

To delete a program from disk,
LIBRA

DELETE

name

Errors:

(1)

No such program name in directory list

(2)

Name missing from command

(3)

Disk I/O error

To list the directory
LIBRA

LIST )

Errors:
(1)

Disk I/O error

NOTE
This command will destroy any program by an effective
IIERASE ALL II.

The directory is printed ten across for as many lines as necessary.

2.14.3

DF32 FOCAL FILE STRUCTURE

Programs are stored in blocks 1600 words long. This allows 36 blocks of storage on one
S
DF32 and a directory of 512 words or 256 entries. This directory is sufficient for the maximum DF32
configuration allowable on a PDP-S.

l. Disk

36 blocks

2. Disk

72 blocks

3. Disk

110 blocks

146 blocks

Disk

2-15

The directory is a linear list with a maximum size of 512 words (with 2 words/entry). Word position in
the list corresponds to the block position on the disk. The blocks begin at location lOOOS from the end
of the directory and extend in increments of 1600 to the end of the disk. The end of the list is an
S
entry of ones. Unused blocks are indicated by entries of all zeroes.
The LIBRARY functions swap users in the multiple user system. This diminishes the total
number of blocks by the maximum number of allowed users. A disk program is required to clear the
directory, and to set the maximum number of blocks available.

2. 15

WRITE
The WRITE command is used to list the entire indirect program (WRITE ALL or W), specified

groups, or single lines. When all text is printed, a leader-identifier is given at the top of the listing.
This identifies which major version is being used for the particular indirect program. (FOCAL, 1969;
SK FOCAL @ 1969; 4-word @ 1969).

NOTE
The WRITE command disables the trace.

2-16

CHAPTER 3
FOCAL USAGE

3. 1

REQ UIREMENTS
Any 4K PDP-8 family computer with Teletype may be used with FOCAL: PDP-5, PDP-8,

PDP-8/S, PDP-8II, PDP-8/L, LAB-8, LINC-8, TSS-8, PDP-12.

3.2

LOADING PROCEDURE

a. The RIM or Read-In-Mode Loader must be in memory. (See RIM Loader Manual for a
thorough discussion.)
b. The RIM Loader is used to load the Binary Loader. (See Binary Loader Manual for a
comp Iete descri pt ion • )
c.

The Binary Loader is used to load FOCAL.

Upon halting, press the CONTINUE key, since the program is loaded in two sections.

e. Place 200, the starting address of FOCAL, into the Switch Register when the complete
tape has been loaded.

3.3

Press the LOAD ADDRESS key.

Press the START key.

The initial dialogue will begin.

INITIAL DIALOGUE
The program will identify the DEC 12-bit computer you are using and make appropriate

corrections to itself. If the user determines that extra space is required, the program will permit rejection of extended functions.
FOCAL is ready for commands when it types *.

3.4

OPERATION

3.4.1

Restart Procedure
There are two methods to restart the system.
Method 1 - Type the character control/C at any time; (FOCAL acknowledges this by typing
?01.00).
Method 2 - a.
b.
c.
d.
e.

Put 200 into the Switch Register
Press the STOP key
Press the LOAD ADDRESS key
Press the START key
The program will then type ?OO.OO indicating a manual restart, and an
asterisk indicating it is ready to receive input.

3-1

3.4.2

Keyboard Error Recovery

If an error is made while typing commands to FOCAL, one of the following methods may be
used to recover:
a. Use the RUBOUT key on the teletype keyboard to erase the preceding character. The
RUBOUT key echoes \ for each character removed.
b. Use the MODIFY command, with the modify control characters, to search the command
string for any character in error and alter or delete that character.

3.4.3

Use Left Arrow to delete over to the left margin.

Use Left Arrow to delete input data.

Parentheses
The following parenthetical pairs may be used in any alphanumeric expression: parentheses,

angle brackets «

», and square brackets ( [ ] ). The program checks to see whether the proper

matching terminator has been used at the correct level. Use of these terminators in different configurations provides additional clarity in reading alphanumeric expressions.

3.4.4

Trace Feature
A trace feature may be used to detect errors, follow program control, and create special

formats. To implement the trace feature, insert a question mark into a command string at any point.
Each succeeding character will then be typed out as it is interpreted until another question mark is
encountered or until the program returns to command-input mode.

3.4.5

Variables, Functions and Numbers
A variable name consists of one or two alphanumeric characters, of which the first must be

a letter. The second character may be A-Z, 0-9, II, I . Additional characters are ignored.
Function names are easily distinguished from variable names because they start with the
letter F. A number always begins with a digit 0-9.

3.4.6

Error Diagnostics
Programming errors are indicated by an error diagnostic. The printout is in the form

?XX.XX@ GG.SS. The first number is a specific error number derived from the core address of the
error call. The GG.SS is the number of the line, if any, of the text which contains the error.
The error diagnostic printouts are intended to be efficient yet informative and expl icit.
Used in conjunction with the trace feature, these wi" pinpoint errors precisely. (See Appendix B).

3-2

Example:
*00 2.35?
SET A=5/C + ?28. 72

(Divide by zero, C=O)

*
3.4.7

Arithmetic Priorities

+Operations of equal priority are executed from left to right (e.g., T 2 t3 t2=64 not 512).

3.4.8

ASCII data
ASCII input of A-Z has the values of 1-26 per digit per letter respectively, thus,
*ASK A; TYPE A
:Z=26.00
*A A; T A
:AZ = 36.00
This is also true for internal numerical constants I ike ONO, DYES, etc.
(See the IF command for an example of this feature.)
The technique may also be used to create a kind of associative memory:

3.4.9

*ASK
:DICK

A; ASK GRADE (A) ~
: 95

*ASK
:DICK

A;TYPE GR(A»)
=95

Indirect Commands
If a Teletype I ine is prefixed by a line number, that line is not executed immediately, but

is stored for later execution. Line numbers must be in the range 1.01 to 31.99. The numbers 0.0,
1.00,2.00,3, etc., are illegal line numbers and are used to indicate the entire group. The number
to the left of the point is called the group number; the number to the right is called the step number.
Execution of indirect commands is begun by an immediate GOTO of DO command. The GOTO command causes FOCAL to start the program by executing the command at a specified line number (e.g.,
GOTO 1 .3). The GO command causes FOCAL to go to the lowest numbered line to begin executing
the program and continues until it runs out of program text. FOCAL can automatically cross group
boundaries.

3-3

3.5

SAVING FOCAL PROGRAMS

3 .5. 1

Paper Tape
To save a FOCAL symbolic text, type WRITE ALL, turn on the punch, type @ marks for

leader-trailer, and type carriage return. When all of the program has been typed out, type additional
@ marks for more leader-trailer, turn off the punch, and continue your conversation with the computer.

(To save a FOCAL binary program, see Appendix C.l .)

3.5.2

LINC Tape (see Section 2. 14. 1; TCOl via 8-LIBRARY SYSTEM; PDP-12)
On LINC tape, load FOCAL program as follows:
a.

Load FOCAL binary tape, execute Initial dialog, and call UPDATE.
NAME:
START
SA (OCTAL):
200
MEM LOCATIONS: <4600, 7577 >;

Call UPDATE again.
NAME:
FOCAL
SA (OCTAL):
(none)
MEM LOCATIONS: < 0,

3377 >;

Call ing Sequence:
FOCAL
START

*
d.

Write the desired FOCAL routine.

e. Give an ilL II command. Four octal numbers will be printed, and control will return to
the Library System.
UPDATE
NAME:
(user's choice)
SA (OCTAL):
(none)
MEM LOCATIONS: < 0 > < (A), (B) >;
Where "(A)" and II (B) II mean the first and second octal numbers.

To call a program:
FOCAL
(user's choice)
START

*
3.5.3

Disk Monitor System (see Section 2. 14. 1)
a.

Build the Disk System.

3-4

Load FOCAL into field zero.
(If the computer has 8K, use the binary loader in field 1.)
Alternate procedure: Use PIP to place the binary on disk. Then, use LOAD on the
disk file. (This procedure is faster for a teletype, but uses more disk space.)

Load Address 200, START, and complete the initial dialogue.

Load Address 7600 and START.

Initial ize the disk as follows:
. SAVE
.SAVE

START!4600-7577;200
FOCAL! 0-3377;

Run FOCAL .
. ) FOCAL
.) START
(Create Program)

Save program; return to disk Monitor by giving an L command .
. SAVE (name);O, (A) - (B)

[note saving page zero]

Run a program (after doing either step f or g) •
. FOCAL)
.CALL (name) )
. START) [I inefeed wi II not occur]
*(FOCAL ready)
Steps g and h may be repeated.

3.5.4

Disk System and Extended Functions
To cope with configurations involving deletion of extended functions, proceed as follows:
a.

Load FOCAL and start at 7600;
.SAVE START!4600-7577;200
.SAVE INIT:0,3200-4577;
[note saving page zero]
.CALL INIT
• START
[Dialogue, answer YES]
*L
.SAVE FOCAL !0-3377;

To reinitialize a system without some extended functions, type
.FOCAL
.CALL INIT
• START
[Dialogue, answer NO, YES, i.e., keep sine and cosine]
*L
.SAVE STNY!5200-7577;200

3-5

To create a system without any extended functions, type
.FOCAL
.CALL INIT
• START
[Dialogue, answer NO, NO]
*L
.SAVE STNN !5400-7577;200

Be sure to use the correct START command with each user program.

(1)
[to use no exponential function version]
.FOCAL
.CALL NEXP
.STNY

*
(2) or
[to use no cosine function version]
.FOCAL
.CALL NCOS
.STNN

*
3.5.5

Disk System and Extended Memory (see section 2. 14. 1)
Follow these operations to set up an 8K version of FOCAL on the disk:
[Bui Id Disk System]
[Load FOCAL]
[Start at 200]
[Dialogue, answer questions.]
*L )
0100
(A)
0121
(B)
3217
(C)
XXXX
(D)
.SAVE ST8K! (D) -7577;200
.SAVE FCL81 0 - 3177;
.SAVE NUL8: 10100; 10113
The SAVE command for a finished 8K FOCAL program is
.SAVECODE:1(A) - l(B); 10113

where (A) and (B) are the first and second four digit numbers typed out by the L-command. These are
the field one bounds of the program text. The value of (D) will depend on the functions retained.

3-6

The variables, however, are in field zero. To save a set of data, type:
.SAVE DAT8:0;3200-(C);

[note saving page zero, field zero]

To set up a null program with a particular data set, type:
.FCL8
.CALL DAT8
.CALL NUL8
.ST8K

3.5.6

For 4-user FOCAL SAVE command, see Section 4.6.6.

3.5.7

EAE Patch for FOCAL, 1969
7203
7204
7205
7206
7207
7210
7211
7212

3206
1256
7425

o
3253
7501
3255
5227

DCA
TAD
MQL

.+3
MP2

MUY

o
DCA
MQA
DCA
SNP

MP5
MP3
.+15

3-7

CHAPTER 4
PROGRAM SPECIFICATIONS

4.1

MACHINE REQUIREMENTS
The minimum hardware configuration necessary to run this program is a 4K PDP-8 family

computer with ASR-33.
Scope, an additional 4K memory, and high-speed reader and punch are available options.
Additional PT08s are added for extra users.

4.2

DESIGN SPECIFICATIONS

4.2. 1

Design Goals
FOCAL is a conversational language and operating system for a basic PDP-B. It is designed

to faci litate on-I ine editing and execution of symbol ic programs. (For BNF description, see Appendix
F.)

4.2.2

Input
The keyboard, low-speed reader, or high-speed reader may be used for input of program

text and for commands to be executed immediately. Keyboard input is double buffered.

4.2.2. 1

Input Format - See description of the commands in Chapter 2 for format information.

4.2.2.2

Character Set - Input and output characters are in ASCII teletype code. Interpretive opera-

tions are also done internally in expanded ASCII. The text buffer is packed two characters to a word
as follows.

= represented as: prints as
number
300
= not packed = ignored: @
301 - 336 = 01 - 36: A-Z
337
= not packed - edit control, kill line:
240 - 276 = 40 - 76: symbols
= 37: ?
277
340 - 376 = 7740 - 7776 (extended codes): non-printing
377 = not packed - edit control, delete preceding character; if a character
is deleted, \ (backslash) is typed.
200 = not packed - ignored: Ieader-trailer
210 - 237 = 7701 - 7737: control characters
000 = not packed - ignored: blank tape.
4-

4-1

4.2.3

Output

4.2.3. 1

Output Format - See the TYPE and WRITE statements for format of output. The output

character set is the same as that for input.

4.2.3 .2

The Input/Output and Interrupt Processor - The purpose of the interrupt hand Ier and the I/O

buffers is to permit input and output to proceed asynchronously with calculations. This allows an
optimal use of the computer time. When the interrupt handler finds that the teletype output flag has
been raised, it clears that flag and looks to see whether there are any additional characters in the
te Ietype output buffer to be pri nted • If there are, it takes the next character from the buffer, pri nts
it, clears that location in the buffer, and moves the pointers. Separate pointers are maintained for
both the interrupt processor and for the program output subroutine (XOUTL). If the interrupt handler
finds that there are no more characters to be output on the Teletype, it will clear the teletype inprogress-switch (TELSW). If the interrupt handler does output another character, it sets TELSW to a
nonzero value.
When the program desires to place characters in the buffer for the interrupt processor to
print, it makes a call to XOUTL. This routine first checks to see if TELSW has been set. If TELSW is
zero, no further interrupts are expected by the interrupt processor, and the output routine immediate Iy
types the character itself and sets TELSW to a nonzero value. Otherwise, if the interrupt processor is
in motion, then the output routine places the character into the buffer and increments the pointer. If
there is no room in the buffer for additional characters, the low-speed output routine waits until room
is available. The keyboard input processors are similar in organization to the output routines except
that no in-progress-switch is needed and the input is only double buffered.
Another advantage of the interrupt system is that it enables the user to stop program loops
from the keyboard by typing Control C. The recovery routine will then reset the I/O pointers, type
out the message code ?01.00, and return to command mode. Manual restart via the console switches
also goes to the recovery routine, resets the pointers, and types out message code ?OO.OO. In fact I
all error diagnosti cs go to the recovery routine. Error printing is withheld until prior printing is complete. Otherwise, on occasion, a full buffer could be dumped and the error message could be printed
as many as 16 characters before it should have otherwise occurred. This would be misleading when
using the trace mode to discover specific errors within a character string.
The recovery routine may also be called by the interrupt processor if it discovers that there
is no more room in the keyboard buffer. For example, this could occur if the user continues to type on
the keyboard while the program is making computations. Physical evidence of the error is indicated by
failure of the computer to echo characters as the user types.

4-2

NOTE
This error could also occur when reading a paper tape
program into the text buffer via the low-speed reader.
If the output hardware is slower than the input hardware, more text is read in than is being read out of the
buffer, resulting in failure of the program to empty the
reader buffer as quickly as it is being fj lied up, since
the program synchronizes the reading of the characters
with sending them into the buffers. In other words, the
program synchronizes its side of the I/O buffers, but the
interrupt side of the I/O buffers proceeds at a rate determined by the hardware. To prevent this type of error with
long input tapes, which were prepared off-line, carriage
returns may be followed by some blank tape whi ch is i gnored by the input routines, thereby giving the output
routine time to catch up. This is essentially a hardware
problem since the program is unable to stop the low-speed
reader.

4.2.4

Organization

4.2.4.1

Arithmetic Package - The arithmetic is done in the floating point system. The three-word

floating point package allows six digits of accuracy plus the extended functions. The program wi"
eventually use four words as an option. The exponential range is approximately ten to the six hundredth.
Internal accuracy during computations is 6.924 decimal digits.
The four-word floating point system creates ten digits of accuracy, including roundoff. It
does, however, require more storage for variables and for push-down list data.

4.2.4.2

Storage - The major components of the program occupy locations 1-3200. The remaining

storage 3200 - 4600 is used for text storage, variable storage, and push-down storage, in that order.
The text occupies approximately two characters per register. The variables occupy either five or six
locations per variable depending on whether the three- or four-word option is utilized.
Remaining storage is allocated to the push-down list. Overflow wi" occur only when one
of these lists exceeds the remaining storage. This could happen in the case of complex programs which
have multiple levels or recursive subroutine calls. The push-down list contains three kinds of data.
One of these is a single location for push-jump and pop-jump operations. The content of the accumulator is also pushed into the same list in a single register. The third type of push-down storage is
floating point storage (see Appendix D).

4-3

Thi s important storage allocation scheme permits flexibi I ity in the trade off of text size,
number of variables, and complexity of the program, rather than restricting the user to a fixed number
of statements or characters, or to a fixed number of subroutine calls, or to a limited number of variables.

4.3

HARDWARE ERRORS
The 8/S wi II halt at location EXIT +6 if a parity error occurs.

4.4

INTERNAL ENVIRONMENT

4.4.1

Adding a User's Function;FNEW(Z) (c.f., Section 5.2)
The FOCAL system was designed to be easily interfaced for new hardware such as LAS-8,

multiplexed ADCs real-time clocks, or to software such as a nonlinear function.
The information given below, the symbol table, the various lists, and a core layout are intended to be sufficient for all required modifications and patches. This symbolic approach ensures
greater flexibility and compatibility with DEC modifications to FOCAL, other user's routines, and
assembly via PAL III on a PDP-8.
Example: Suppose we had a scope routine to display characters at a given point on a scope.
We will call this routine from FOCAL as function by FNEW (X, Y I SHOW). Here X and Yare expressions to be used as display coordinates for the start of SHOW.
a.

First, patch the function branch table.
*FNTABF + 15
XFNEW

When control arrives at XFNEW, the X has already been evaluated.
XFNEW,

JMS

INTEGER

DXL
CLA
c.

Now, test for the possibi lity of another argument.
TAD
TAD
SZA
JMP

/make 12 bit integer
in AC
/set X - coor.

CHAR
MCOMMA
CLA
EFUN3I

Move past the separating comma.
GETC
SPNOR

4-4

/no more

Evaluate the second argument.
/this FNEW is
/not recursive

PUSHJ

EVAL
INTEGER
/set Y and intensify

JMS
DYS;CLA
SPNOR
TAD
TAD
SZA
JMP
f.

CHAR
MCOMMA
CLA
EFUN31

Now, pick up the single letters for display until the end of the function is reached.
DCHR, GETC
TAD
TAD
SNA
JMP

CHAR
MRPAR
CLA
EFUN31

Char. display routine called here; (for Tektronics Y002, it is simply PRINTC)
DCHR

JMP
g.

Definitions from the symbol table are available in Appendix E.

Summary:
a. User defined functions must leave their value, if any, in FLAC and return by a
JMP I EFUN3I.
b. The contents of FLAC is converted to an integer in FLAC and in the AC by a
JMS I INTEGER.
c.

The floating point arithmetic interpreter is entered by JMS I 7.

(FOCAL uses its own version of the floating point package.)
d.

The address of the user's function is placed by him in the FNTABF list.

e. Location BOTTOM contains the address of the last location to be used for storage. If
BOTTOM is made to contain 4277, for example, then the user has from 4300 to 4577 for
storage of the function processor. The user should achieve his function implementations
using the information given here and in the symbol table without using the actual listing so
that changes made by different users may be compatible and so that they may also be
relocated easily should any changes be made by DEC. (see Section 4.5.1 for Core
Uti lization List)
f. The argument following the function name is evaluated and left in FLAC before control
is transferred to the particular function handler. Since evaluation is terminated by either
a comma (,) or a right parenthesis, a special function could have more than one argument.
Only in the case of multiple arguments does a user need to worry about saving his
working machine language storage for a possible recursive use of his function. The contents

4-5

of the AC are saved by PUSHA and restored by POP A for this purpose. If there is another
argument, it may be evaluated by PUSHJ; EVAL. Doing a PUSHJ; EVAL-l is equivalent to
GETC;PUSHJ;EVAL.
4.4.2

Internal Subroutine Conventions

4.4.2. 1

Call ing Sequences - The (AC)=O unless it contains information for the subroutines. Upon

returns (AC)=O unless it contains data.
There are six types of routines and subroutines used in the implementation of this program:
a.

Normal subroutines called by an effective
SUBRl

JMS
which contain zero at their entry point
SUBR 1,0
and a return by a

SUBRl

JMP
b.

New instructions called by
PRNTLN

/(to print a line number)

and usually defined by
PRNTLN = JMS I.
XPRNT
where XPRNT is the entry point for a normal subroutine. These new instructions may have
multiple returns/multiple arguments:
SORTJ
LIST6-1
INLIST -LIST 6

/call;
/data list minus one;
/increment to branch table
/return if CHAR is not in LIST6

These new instruction subroutines often have implied arguments, e.g., GETC, READC,
PACKC, TESTC, and SORTC all use the variable CHAR as their argument. The new
instructions SORTJ and PRINTC use CHAR only if the AC is zero. If the AC is nonzero,
then that value is used. Still others use only the AC for their argument:
RTL6, TSTLPR, PUSHA, and TSTGRP, (see Appendix G).
c.

Recursive routines called by
PUSHJ
EVAL

/call
/address
/return

where the address contains the first instruction of the routine. The return address is kept in
the push-down list, and exit is made by use of
/exit subroutine.

POPJ

4-6

Such routines may call each other or themselves in any sequence and/or recursively by
saving data on the push-down list. Others are EVAL, PROCESS, PROC, and GETVAR.
d.

Command processor routines to handle specific command formats are called by
SORT J

/go to command
COMLST-l
COMGO-COMLST
ERROR 3
/i Ilegal command

The individual command routines use only new instructions and recursive routines. They may
exit in one of three possible ways:
(1)

POP J - if C . R. is encountered or

(2) transfer to another command routine or
(3) transfer to START

Floating point groups of interpretive instructions similar to the following format:
/enter floati ng interpreter (i .e., JAS 17)

FI NT
FGET
FMPY

FLARG
PT1

EPUT

FLARG

FXIT

/Ieave floating interpreter

f. Main processor modules to handle text input and keyboard commands. This routine
could be IIl0cked-out II by an instructor to protect and execute a stored or immediate
command program repeated Iy •
IBAR, INPUT X
Similarly, selected commands are easily deleted by the instructor by placing zero in the
appropriate locations in COMLST.
Line number input and explicit replacements are IIshort circuited II by
GONE+ 11, error 3
4.4.2.2

Subroutine Organization - Figure 4-1 illustrates the internal use of various subroutines.

(c. f., Flow Charts in Appendix G).
4.4.3

Character Sorting

If a program must contend with a number of different characters (or 11-bit items) each of
which can initiate different responses, simply look up the address of the action that corresponds to a
given symbol or bit pattern. If the symbols do not form a continuum, the programmer must find the
most efficient method for determining the corresponding address.
The method used in FOCAL is the table sort and branch. This method uses a subroutine to
match up an input character with one member of a list of characters. The call to the subroutine is
followed by

4-7

the address minus one of the list and

b. the difference between that I ist and a second list. The latter list contains the corresponding addresses. Thus, if a match is found in the first list, the difference is added to the address of
that match to compute the address in the second list which contains the name of the action to be
performed.
c.

The next instruction to be executed if a match is not found.

In addition to being simple and concise, although more time consuming than other methods,
this technique has another advantage that is especially useful in a pop-a: the tables may be placed
at page boundaries to take up the slack that often occurs at the end of a page. This results in a more
effi c ient use of ava i Iab Ie core storage.
d. COMMAND ROUTINES
COMMAND

AND

Figure 4-1

4.4.4

language
The program is written in PAL III with floating point commands, as well as program-defined

commands, implemented as subroutine calls. (see Appendix G) The program must be assembled using
PAllO.

4-8

4.5

NOTES

4.5.1

Core Utilization

NAMES

IOBUF:
COMEIN:
FRST:
BEGIN:
FEXP:
ARTN:
FCOS:
TGO:
DECONV:
FLOUTP:
THISD:
FLINTP:
HREAD:
FPNT:
MP4:
XSQRT:
LIBRARY:
XRTD:

Storage of text is

4.5.2

PLACE

SEGMENT

0- 15, 17-166
167-175
176-2572
2573-2577
2600-2724
2725-3117
3120
3140
3206
4420-4577
4430-4577
4620-4776
5000-5166
5200-5345
5400-5577
5600-5773
6000-6157
6160-6176
6200-6317
6320-6377
6400-7177
7200-7377
7400-7502
7503-7556
7557-7576

FOCAL (4K)
8K
FOCAL (4K)
8K
(Interrupt Handler)
FOCAL (4K)
(I/O Buffer)
(Command Buffer)
(Text Buffer)
(Initialization)
CLIN
(Extended Functions)
[11 free]
[32 free]
[ 0 free]
[ 4 free]
(Output Conversion)
8K
(Input Conversion)
(High Speed Reader)
(floating interpreter)
[none free]
[FSQT( ) and format buffer]
(Single user L command)
8K

3200-4577
3200-5177
3200-5377

14 functions
11 functions
9 functions

Extended Functions
Extended Functions may be reinitialized by loading in the second part of main program tape.
Functions are normally deleted by answering the questions asked when FOCAL is initiated.

However, they may also be erased by changing location 0035 to 5377, and locations 401 through
0405 to 2725. Retaining the extended functions allows approximately 1200 characters of text or 170
variables (or any combination in the ratio of 7 characters to one variable). Deleting the extended
functions allows approximately 1800 characters or 250 variables.

4-9

4.5.3

Error Pri ntouts
Errors
and

?01.00
?OO.OO
?11.35

Because these errors are time dependent, they may be followed by nonexistant or false I ine number.

4.5.4

No Interrupts
To read data tapes without running the risk of Keyboard-Input-Buffer overflow (?11.35), it

is necessary to remove the interrupt. This action means that Control-C wi II not work.
To run FOCAL without interrupts, change:
Loc/From

63/2676
64/2666
2732/6001
2762/6046

1353
2413
5336
7000

The high-speed punch will now run in parallel with the low-speed punch!
To run the high speed punch at top speed change:
6021

1356/6041

4.5.5

Operating HS Reader Without Interrupts
To run the high-speed reader without interrupts, make the above patches plus two more:
6011
7410

6324/1037
6325/7700

4.5.6

Non- Typing of Program Tapes During Loading
The "echo" feature for the ASR-33 may be suppressed by changing location 2163 to 7000

(from 4551). This will cause only asterisks to be typed as the tape is read. There will not be line
feeds or carriage returns. (c.f., 4.7.3.4 for multi-user system)
Any output commands w ill be typed out in the usua I manner, as will di agnosti cs, answers,
etc. Entri es from the keyboard wi II not be typed.

4.5.7

Explanation of NAGSW (Not All or Group Switch)
Since LINENO may be modified, a record is needed of whether a specific line number was

given by XX. YY (where XX and YY are nonzero) or whether a group was indicated by XX or XX: or
XX .00 or whether II ALL" text was indicated by either zero, less than one, or a non-numeric argument:

4-10

NAGSW =
4000
0000
0001
4001

For one line
For a group
For all text
Error
PDP-8 code for testing NAGSW:
skip if
Or

All

Group

SMA SZA

ONE

SMA

ALL

SPA SNA

SNA

SMA SZA

SPA SZA

SZA

GROUP

4.5.8

One

Data Inaccuracies
8
The logical conclusion from the inequality 10 < 227 is that the user can represent 8-digit

decimal floating-point numbers accurately by 27-bit floating-point numbers. However, 28 significant
bits are needed to represent some 8-digit numbers accurately. In general, we can show that if
q 1
lOP < 2 - , then q significant bits are always enough for p-digit decimal accuracy. Finally, we can
define a compact 27-bit floating-point representation that will give 28 significant bits, for numbers of
practi cal importance. 1 In FOCAL, 23 bits are used giving 6.9 digit accuracy.

4.5.9

Eliminating = and: in I/O Formats
Leading equal signs and colons in I/O formats are omitted by making the following patch:

4.5.10

Loc/From

1216/4551
6002/4551

7600 /:
7600 /=

Estimating the Length of Userls Program
FOCAL requires five words for each identifier stored in the symbol table and one word for

each two characters of stored program. This may be calculated by

where

c
5s + 2" • 1.01 = Iength of user IS program
s = Number of identifiers defined
c = Number of characters in indirect program

If the total program area or symbol table area becomes too large, FOCAL types an error message.
1Goldberg, B. 118-Digit Accuracy II ,
Communications of the ACM
Vol. 10, No. 2, February, 1967

4-11

FOCAL occupies core locations 1-3300 and 4600 _7576 ' This leaves approximately
S
S
S
70010 locations for the user's program (indirect program, identifiers, and push-down list). The extended functions occupy locations 4600-5377. If the user decides not to retain the extended functions
at load-ti me, there wi" be space left for approximately 110°

characters for the user's program.
10
The L-command may be used to indicate how much core is avai lable for the user.

4.6

FOCAL SYSTEMS
FOCAL systems are designed to take advantage of as many PDP-S configurations as possible.

With this in mind, the system source language is divided into segments which, when loaded together,
fit the needs of a user and his particular configuration. Thus, when a user changes his configuration
or requirements, he does not need to secure an entirely new FOCAL tape but on Iy to load a new segment corresponding to the change in his configuration. The scheme used a Iso has the advantage of
simple maintenance, since changes are made to one source file for all possible systems and in some
cases re-assembly of other segments is not needed.
Two source segments create a FOCAL system for a 4K PDP-S. Others are used to create a
FOCAL system with (1) ten digit arithmetic, (2) SK memory, and (3) circular and linear graphics.
The segments of the FOCAL system and their functions are listed in Table 4-1. The ASCII
source segments FOCAL .ASC and FLOAT .ASC must be assembled with all configurations and the
resulting binary segment, FOCAL.BIN, when loaded makes a one user FOCAL system for a 4K PDP-S.
The segment INIT .ASC is assembled alone, but when INIT. BIN is loaded with FOCAL. BIN
into field zero it gives you the initial dialog. If the extended functions are to be retained, it is not
necessary to load INIT at all. All corrections for machine type will be made anyway. After FOCAL
is started and/or the dialog is completed the user may proceed to load other binary segments.
If a user has an SK PDP-S and wants to create a large program with extended precision
arithmetic, he need only load FOCAL.BIN, start, and then load 4WORD.BIN, and BK.BIN as
indicated in Table 4-2. If he wants to share his PDP-S with three other people, he just loads FOCAL.
BIN and QUAD. BIN into field one and start.
Intra-references between segments is handled by small multiple assemblies, rather than a
large assembly with conditionals for each possible system. For example, to obtain a binary copy of
the segment QUAD.BIN, use PALlO to assemble, QUAD.ASC, FOCAL.ASC, FLOAT.ASC. This
assembly produces only the listing and binary files for QUAD which end with the PSEUDO-op's
"XLIST" and "NOPUNCH ". Tables 4-2 and 4-3 give the allowable combinations of the binary
segments to produce legal configurations of the FOCAL system.

4-12

Table 4-1
FOCAL System Source Segments

Function

ASCII Segment Name

Description

FOCAL*

The interpreter & TTY I/O driver.

FLOAT*

Modified Floating Point Package.

4WORD

Extended precision overlay to FLOAT (give 10 digits).

(4.6.5)

Allows one user to take advantage of an SK PDP-S.

(4.6.4)

QUAD

Allows multiple users (up to 4) to use FOCAL or
SK PDP-So

(4.6.6)

LIBRA t

Allows multiple users (up to 7) to run and save
FOCAL programs on an SK PDP-S with disk.

(2. 14.2)

CLIN

The user may have a scope to interact with FOCAL.

(5.S)

PENT

A variation of QUAD allowing five (5) users.

INIT

The symbolic source for the initial dialog program.

*These two segments must be assembled and loaded together for all configurations. They are
separated for editing convenience.
tNot yet implemented.

Table 4-2
Allowable FOCAL Systems
1 - Must be loaded into field one

o - Must be loaded into field zero
Y - Command may be used if disk system is built
N - Command is illegal
* - Command different
Binary Segment
FOCAL
INIT (optional)
4WORD
SK

Allowed Combinations &
Subsets are indicated by
entries in vertical columns

o0 0 1 1 1 1
0 o 0 0
o0
1
1

0 0

LI BRA (non -SiS)

CLIN (optional)
LIBRARY COMMAND
(for disk monitor)

4-13

SK/PT08s

0 0

SK/PT08s/DF32

Graphics Terminal

YYYY N N * *

FOCAL is always loaded first in the proper field.

o0 0 0

QUAD or PENT (non-SiS)

Minimum Hardware
Required

DF32

Table 4-3
Variations for FOCAL Systems
Any combination of these three sets (2*2*4=16),
a. 8K overlay
4K

b. Disk Monitor
No Disk

c. No Dialogue
No ext. functions
SINe, COSine only
All ext. functions

or QUAD four-user system or PENT five-user system (PENT is obtained by a
modified assembly of QUAD; see listing) may be used with
CLIN graphics (4)
4WORD overlay
Neither
Both
These are formed from only six sections of binary tapes.
The CLIN graphics function can be used for numerical control.
4K FOCAL can be run on the following DEC computers: 5, 8, 8/S, 8/1, 8/L,
LI NC -8, LAB-8, TSS-8, PDP-12.

4.6.1

Load FOCAL & INIT

do initial dialogue

load any or all of 4WORD, 8K, CLIN.

restart and use

FOCAL Systems Assembly
a•

Systems programs

* tC
.RUN T PAL 10
*FOCAL. BIN ,FOCAL .LST"'FOCAL .ZZL,FLOAT .ZZL
*QUAD.BIN,QUAD.LST+QUAD.ZZL,FOCAL .ZZL,FLOAT .ZZL
b.

Initial dialogue

* tC
.RUN T PAL 10
*INIT .BIN,INIT .LST"'INIT .ZZL

*
c.

Overlay routines
.R PAL 10
*4WORD.BIN,4WORD • LST"'4WORD .ZZL,FOCAL .ZZL,FLOAT .ZZL
*8K .BIN,8K • LST"'8K .ZZL,FOCAL.ZZL,FLOAT .ZZL
*CLIN .BIN,CLIN • LST+-CLIN .ZZL,FOCAL .ZZL,FLOAT .ZZL

*
4-14

4.6.2

FOCAL Bi nary Paper Tapes
.AS DSK D
DSK ASSIGNED
.AS PTP
PTP ASSIGNED
.R PIP
*PTP: -II D:Q UAD . BI N
*PTP: -/ID:4WORD. BIN ,8K. BIN ,CLIN. BIN
*PTP: -/ID:FOCAL. BIN, INIT . BIN
tC

4.6.3

FOCAL Listings
*LPT :-D:Q UAD. LST ,4WORD .LST ,8K. LST ,CLIN. LST ,INIT • LST ,FOCAL. LST
*TTY:-/L DTAa:
58: FREE BLOCKS LEFT
FOCAL
.ZZL
FLOAT
.ZZL
QUAD
.ZZL
4WORD .ZZL
8K
.ZZL
CLIN
.ZZL
INIT
.ZZL
PAL 10
.SAV
JR36
JR46

4.7

FOCAL SEGMENTS

4.7.1

8K Single User Overlay - 8K
To increase the size of program, the 8K overlay uses the upper 4K for storage of the user's

source text. The maximum number of variables does not change as they are sti II stored in the lower 8K.
Load the overlay after doing the initial dialogue with the 4K version.

4.7.2

Extended Precision Overlay - 4Word
This overlay provides FOCAL with 10-digit accuracy when the 10th digit goes to enable.

The overlay increases the number of words needed to store a number from three words to four words.
The number of variables that may be stored is decreased accordingly.
Load the overlay after doing the initial dialogue with the 4K version.

4-15

4.7.2. 1

Double Precision Multiply in Four-Word FOCAL
To multiply two numbers, the product of which is greater than ten digits and yet retain the

least significant figures, use a double precision operation.
For example, to multiply:
M = 20243974
by
N = 69732824
let MO = the 1st 4 digits of M and let M1 = the 2nd 4 digits of M. Similarly, NO and N1 are the left
and right halves of N.
Note the correction of an input error in the high order part of N.
*W
C-4WORD@1!69
14. 10
14.20
14.30
14.40
14.50
14.60
14.70
14.80
14.90
14.99
*GO

AS K !, MO ,M 1 , .. *" NO I N 1 , !
SET A=MO*NO
SET B=-NO*M1 + MO*N 1
SET C=M1 *N1
SET Z=FITR(C*lE-4)
SET C=C-Z*lE4
SET B=B+Z
SET Z=FITR(B*lE-4)
SET B=B-Z *1 E4
TYPE ! %8 ,A+Z, 0/04 ,B,C,!

:2024 :3974

:6928+6973

:2824

= 14116694= 7600= 2576

*
4.7.3

Four User Overlay - QUAD
QUAD allows an 8K PDP-8/I, -8/l with up to four teletypes to time-share FOCAL. In

effect, each user has the equivalent of a 4K PDP-8 or PDP-12 with FOCAL. The QUAD overlay is
located in the lower 4K, and the FOCAL interpreter is located in the upper 4K. Users are traded for
one of three other users in the lower 4K. Swapping of users is based upon I/O waits and checkpoints
in the FOCAL interpreter.

4.7.3. 1

Four User loading and Operating Procedure
a.

load 1st binary part into field one. (FOCAL.BIN)

load 2nd binary part into field one. (QUAD .BIN)

4-16

c•

Load address
7600
and START
• SAVE F4UB!0-2177,3000,3600,5400;200
.SAVE F4UA!0-13220, 14600-17577;
(Any errors made here may require reloading field zero.)

(Calling Sequence)
.F4UA
.F4UB
(If any problem occurs hit stop, record the PC and restart at 200 or reload.)

4.7.3.2

Swapping - At certain points in the FOCAL program it is a pure procedure. If swapping

occurs at these times, then only 1K of impure data needs to be saved instead of 4K. This factor of
four considerably improves system performance. Such a point is called a checkpoint.
Each time an operating program reaches a checkpoint the executive routine checks to see
whether another user should be swapped in at that time.
This check is also made if the operating program goes into a state of waiting for input-output,
except for output duri ng use of trace.

4.7.3.3

Workload and Timing

a. Swapping is done on a demand (I/O wait) and a cooperative (checkpoint) basis.
Therefore, no clock is needed. Not having a clock reduces system overhead by about ten percent.
b. Fully asynchronous I/O is backed up by large (over 16 characters) and uniform (easy to
process) character buffers. Serial to parallel conversion of the bit stream is done in external hardware
by PT08 line controllers. This reduces system load by 18 to 30 percent.
c. If each of eight user programs takes less than 100-17 msec to generate one 8-digit
output string, then the system is barely output bound and no delay will be observed in response times.
The 17 msec is average access time to the disk, and one TTY character takes 100 msec to be typed.

4.7.3.4

Special Controls - A control-R character (TAPE) suppresses echo of input tapes except for

the line-feed. A control-T (NOT-TAPE) or Control-C restores the echo of input characters.
It is a good practice to punch a Control-R at the beginning of all off-line tapes. An

alternative is simply to type Control-R manually before setting the low speed reader to RUN.

4.7.3.5

Dialogue - There is no initial dialogue with QUAD.

4-17

4.7.4

Ic£ L I \j

...

Graphics for Circles and Lines - CLIN

RAP'" I CS u VERLAY F 0 k Foe AL , t 2 K

PAL 10

16:01

ICLIN • GRAPHICS OVERLAY FOR

FOCAL.t~K

IFINITE DIFFERENCE EQUATION OF A CIRCLE • FOR FOCAL
11 6 ,2 S p=X~X0;S Q=Y-Y0;s R=FSQT(Qt2~pt2)
11 6 ,3 S ~=FNEW(6,3*R*C,P,Q,X0,Y0,S/R)
116~4

S X0=X;S

Y~=Y

ILl NEAR DIFFERENCE EQUATION OF A LINE
11"1 0 16'21S 2=FNEw(R,P/R,Q/R,X0,Y0,~)JD 1 6 ,4

6057
6053
6067

DXS=6057
DxL=6053
DyS=6067

0035
21035

4437
0407

214217

4440
4440

444~

444
4442
4443
4444
4445
4446
4447
4450
4451
44:S2
4453
4454
4455
44,6
4457
4460
4461
4462
4463
4464
4465
4466
4467
4410

4453
712140
33 4 2
1340
3010
1117
3316
4537
1612
112144
1341
3044
4453

FCIN,

JMS I INTEGER
CMA

DCA R
TAD XXP
DCA AXIN
TAO M5
DCA CT
PuSHJ
TAD EXP
TAD LP
DCA EXP
JMS I INTEGER

7200

CL.A

leJ"~

TAD P13
DCA I AXIN

3410
1045
3410
1046
34.1.0
2316
5241
1046
7640
5343

TAD HORD
DCA I AXIN
TAD LORD
DCA I AXIN
1St CT
JMP GETA
TAD LORD

slA CL,.A
.JMP XFC I R

4-18

ISAvE THE POINT COUNT
1ST ART DATA POINTERS
IFOR 5 MORE ITEMS
ICOMPUTE EACH ARG,
IFOUR FIXED POINT RESULTS

ISAVE UNNORHALllED FORM

ITEST FOR END Or DATA
ITEST FOR CIRCLE OR LINE

ICLl\j

- :;Ht'P-418S OVE.RLAy FOR FOCAL.,tt~
4471
447~

71)0

4474
4475
4476
4477
45 '0
45 -"1
457;2

3331
70J4

447

45~3

4:>:i4
4:> '~5
4:>,J6

±33
__ 32

XFLIN,

PAL1~

13 -~0

1322
60">3
33-50

71 '1[1
13!14
1326

1(6317)- FOR lAB-8

TAD Y01
TAD
DCA
RAL
TAD
TAD

:~334

7:1 ~'4

Y01
Y00

45~7

:1.333

45 u~

13~5

4~11

DCA

Y00

4:>13

6067
3333
23t.2

1St

4514

5~71

Ji'1P

XF\.lN

4:>:1.5

?5,)5

JMP I EFLJN31

4512

14-MAR 6 9 16:01 PAGE 2

IvECTOR PLOT ALGORITHM

elL
TAD X0 1
TAD Pi
!.leA X01
qAL
TAD Xv)0
TAD P0
DXl
DCA X00
Cll

V133

DYS

1(63 0 7)

... FOR LAB-A

I1I11

ITO DISPLAY A POINT X,Y;
SET 2=FDIs<x,Y)
ITO DRA~ lINE X0,Y0 TO X,y:
00 17
ITU 5[T X0,y0=X,Y:
no A,4
ITO ERASE SCREEN :
TYP~ "(ERASE CODE)"
ITO RESET PRINT ORIGIN:
TYPE "(RESrT CODE)"
ITO DRAw A CIRCLt ABOuT X0,Y0 STARTING AT X,Y
lAND GOING COUNTtRClOCKWISE FOR FRACTION
IOF A CIRCLE ALPHA
SET S=+liSET C=ALPHAJD016
ITO GO CLOCK~ISE:
SET S=~lJDO 16
IGROUPS lb AND 17 CREATE OR USE THE VARIABLES
S.
IS MAy BE REPLACED By A 1 IF DESIRED.
IX'Y'X0,Y~,l,R,C'P,Q,K,AND

4-19

leLI\]

:;RAP~I:;S

OVE.F<LAY FOR
CT,

FOCALt~iZK

4~16

007:,2'

4517

~00(ij

(-1
(II

4520

Z0~:'I0

4521
4522
4523

0tL~0

PP.

(71

2102'0

Pel,

00:~f3

Pl,

4524

2!;~ ?l0

QQ,
QeI,

30Z,0

45?6

00J(1I

Ql,

4527

3013

4?31

00 0~~

XX,
X0J,
X01,

1.3

~530

0021 il

45~2

;))013

4533
4534

~~2l~)0

:1020

Y00,
Y01,

0
0

457)5

21100

KK.

4536

~0Z0

4537

00,10

4~25

4540

452~

45~1

3014

4542

~0l0

PAL1~

V133

14-MAR .. 69 16:01 PAGE 3

0
0

(I)

XXP,
LP,

PP-1

ITO USE AN X~Y PLOTTER, CLIN IS NOT NEEDEDJ SIMPLy
lAUD TH£ FOLLOWING LINES TO GROUPS 16 AND 17 I
11 6 ,25 S K=s/R
116.30 ~ 1=0,6.3*R*C;S P=P-Q*K;S Q=Q.P.KJS ~=FDlS(X0+P.Y0+Q)
/17,10 D 16,2;F I=0,RIS X0=X0+P/R;S Y0=Y0+Q/RJS ~=rOIS(X0,Y0)
11 7 ,20 0 16,4

/THE l'£RATION PARAMETER "I" MAY BE TAKEN IN GREATER INCREMENTS
ISGALE rACTOR IS ALSO CHANGED; I.E.
I 'l'1~ DO 16'2JSET K=4/R
7 ,15 rOR I=0,4,RIS X0=X0+K*P;S Y0: Y0+Q*KJS l=roIS(X0,Y0)

4-20

THE

14-MAR-69 16101. PAGE 4
4543
4544
4545
4546
4547
4550
4531
4552
4,53
4554
4555

4487

xrCIR,

~324

4335
6316
21321
2316
6321
1327
002' iZ:

4453
6057

1(6317) - FOR LAS-8

Fl~T

1CLEARS AC

4563

442}7
0321
4335
1324
6324
1332

45~4

Z0Z0

4565
4556
4567

60r,7

7230

FG T PP
FMUL t<K
FAOD QO
FPUT QO
F'AOD YY
FXIT
JMS I INTEGER
OYS
CLA

4570
4571
4572

2342
5343
5535

lSi! R
JMP XFCIR
JMP I EFUN31

4556
4557
4560
4561
4'~2

4453

46210
~0211

IC(RCLE ALGORITHM

FINT
FGET QO
FMUL KK
FPUT CT
FGET PP
FSUB CT
FPUT PP
FADO XX
FXIT
JMS I INTEGER
DXS

NOPUNCH
PAGE
FIELD 1
XLIST

4-21

1(63~7)

- FOR LASeS

4.8

FOCAL DEMONSTRATIONS

4.8.1

One-Line Function Plotting
This example demonstrates the use of FOCAL to present, in graphic form, some given function

over a range of values. In this example, the function used is
- lx
y = 30 + 15(SIN(x»e .
with x ranging from a to 15 in increments of .5. This damped sine wave has many physi ca I applications,
especially in electronics and mechanics (for example, in designing shock absorbers for automobiles) .
In the actual coding of the example, the variables I and J were used in place of x and y,
respectively; any two variables could have been used. The single line 08.01 contains a set of nested
loops for I and J. The J loop types spaces horizontally for the y coordinate of the function; the I loop
prints the * symbol and the carriage return and line feeds for the x coordinate. The function itself is
used as the upper limit of the J loop showing the power of FOCAL commands.
The technique illustrated by this example can be used to plot any desired function. Although
the * symbol was used here, any lega I FOCAL character is acceptable.
08.01 F I=O,.5,15;T "*",!; F J=O,30+15*FSIN(I)*FEXP <-.l*I);T II II

*
*
*DO 8.01

*
*

*
*
*

*
*

*
*
*
*

-lC

*
*
*
*

-lC

*
*
*
*
*

4-22

4.8.2

How To Demonstrate FOCAL's Power Quickly
a.

Load the program and start at 200.

Explain that the initial dialogue gives you options.

Try some other response like MAYBE ) .

Now answer YES J •

e. The preceeding has demonstrated the interactive capabi lities of the language and the
compromises that it permits.

f. In a 4K machine (4096 words) FOCAL gives the user 15 functions and uses only 3K,
leaving enough room to so Ive up to 6th order simultaneous equations.
g.

The asterisk (*) means that FOCAL can now respond to your commands.

The basic command is TYPE:
5 t 2 + FSQT (5) )

*TYPE
i.

Now compute 5 factorial:
*SET
ALPHA=l
*FOR 1=1, 5; SET ALPHA=ALPH *1

The answer is ready when the next asterisk is typed out:
Then type
*TYPE

ALPHA

for the answer.
k.

Now if you are usi ng a PDP-8 or -8/1, demonstrate a large number:
*SET
*FOR

A=l
1=1,

300; SET A=A *1

some time later
*TYPE A
= 0.395
I.

615

Now generate a plot via a stored program:
*1.1 FOR Y=O, .5, 15; TYPE! ; D02
*1.2 QUIT
*2.1 FOR X=O, 12+10*FSIN(Y); TYPE
*2.2 TYPE" * ..
*GO

4.9

Now use the MODIFY Command to change 10* to FEXP ty/6) * and try again.

FOCAL Versus BASIC
FOCAL is superior to BASIC, not only in terms of computing power and ease of use, but also

in maximum use of the memory space, which is so often limited in small computer systems.

4-23

FOCAL contains all the power of BASIC, and in addition provides the following capabi lities:
a. Control of the output format (i .e., precise figure location on a page and graphi ca I
representation) ;
b. An "immediate ll mode, a !lowing the system to operate as a desk calculator and to
execute simple problems without writing a program;
c. The capability of executing individual IIstored program" statements in the immediate
mode for debugging and verification;
d. Bui It-in symbolic editor capable of searching program statements for specified characters
and inserting and deleting characters within a statement, thereby eliminating the retyping
of the entire program statement;
e. Multiple statements may be grouped on each line for more logical ordering of the program;
f.

True multiple level re-entrant subroutining capabilities;

g. A trace feature which types out selected segments of a program (as the program is
executed) to pin point exactly where a program error occurred;
h. Commands may be abbreviated to one letter; this eliminates wasted typing time when
writing a program and- increases the available storage space for use by additional program
statements;
i.

Programs may be saved on disk and chained together;

i· Point plot displays, vector displays, X, Y plotters, and analog to digital converters
may be operated by FOCAL; this capability can be used in an on-line, real-time fashion;
k. FOCAL SYSTEMS a Ilow use of severa I hardware configurations: 8K, 10 digit, di splay,
and mu Iti -user.

4-24

CHAPTER 5
ADDITIONAL FOCAL APPLICATIONS

5. 1

FOCAL FOR TH E LAB-8

5. 1 . 1

Standard
Two commands have been added to FOCAL to implement the A to D converter and the

osci 1I0scope display on the AX08.
a.

A to D Command:
FADC{N) where N is the channel number in decimal.
The command:
SET Z = FADC(28)

gives the variable Z a value of octal channel 34 depending on the position of the upper
righthand potentiometer. The other 3 knobs are channels 29, 30 and 31. A subroutine
in FOCAL to read the A to D in volts is as follows:
15.1

ASK CHAN;C-O, 1,2,3

15.2

SET X=FADC{28+CH)

15.3

IF (X-256)15.Y, 15.4;SET X=X-4096

15.4

SET X=X/255

The input variable is CH for values of a to 3, and the output variable is X with values
±/volt.
b.

Display Command:
The display command has been modified to use only one statement to define X and Y .
SET Z = FDIS{X, Y).

will display a point on the oscilloscope screen defined by points X and Y. X can range
between 0-511 and Y from -255 to +255. The variable Z is a dummy. (It is given the
value of the integer part of Y .). (c. f., Section 5.8 for circle and sector algorithms.)

CAUTION
Since the ADC of the AX08 hardware is an integral part
of the display logic, using both display and A and D,
may result in splatter of the Y direction of the oscilloscope screen.

5.1.2

Additional (Possible) FOCAL Functions for AX-08
FADC

(n):

Converts (decimal) channel n. Returns result of conversion.

FDIS

(x,y):

Loads display X and Y; intensifies point.

5-1

FTIM

(n):

Delays n RC clock pulses (n < 4096)
Returns # of 100 !JS increments since last used.
Xtal c lock interrupt is enabled.
Interrupt servicing for Xtal clock as
follows:
SKXK
JMP OTHERS
CLXK
ISF TIME + 1
JMP .+3
ISF TIME
NOP
ION
JMP I 0
Clock flag servicing will tie up 20% of processor time.

When FTIM is called, do the following sequence:

XTIME,

TAD (1002)
/enable Xtal clock, start RC clock
OTEN
get n
SNA
JMP XTIME
CMA lAC
DCA RCNTR
CLRK
SKRK
JMP
.-1
ISZ
RCNTR
RMP
.-4
PUT TIME, TIME +1 in FLAC
DCA TIME
DCA TIME +1
return to FOCAL

FN EW (a, b, c)
a = 0:
Turn on relays indicated by b (b < 7)
Turn off relays indicated by c (c 7)
as follows:
-

get b
RAL; RTL
AND {70
OTEN
get c
RTL; RAL
AND {70
CMA
ZTEN
CLA
return to FOCAL
a = 1:

lIand II external register with mask
b:
mask (octal)
c:
ignored

5-2

Get characters of b
interpret as octal #
DCA XMASK
XRIN
AND MASK
XRCL
CMA JAC
TAD MASK
SNA CLA
lAC
store in F LAC
return to FOCAL
a = 2:

"orll external register with mask
b:
mask (octal)
c:
ignored
get characters of b
interpret as octal #
DCA XMASK
XRIN
AND MASK
XRCL
SZA CLA
lAC
store in FLAC
return to FOCAL

5.2

FNEW FOR DATA ARRAYS*
A new function for 8-K FOCAL is available which uses field one to store data arrays in

floating double precision, single precision, and signed integer format. This facility is added to
FOCAL via the function call FNEW. The function may be called recursively to any level, and all
of the features of FOCAL are retained. In addition an ERASE or ERASE ALL command will not wipe
out the array. Hence, variables may be stored for use in successive programs.

5.2. 1

Storage Requirements
Fits into unused locations in floating point package

5.2.2

Usage

5.2.2. 1

Loading - Load after FOCAL has been loaded into the machine (and the initial dialogue is

executed). Load the first part of the overlay using the Big Loader. If a single precision floating
array is desired press CONTINUE. A patch should now be read in to allow a 1980 element array in

*Originated by University of Georgia, program not supported by DEC.

5-3

single precision floating point. If an integer array (maximum number = 3047) is desired press
CONTINUE. A patch will now be read in to allow a 3965 element signed integer array.
Restart FOCAL at 200.

5.2.2.2

Calling Sequence - To store a variable Z as array element J:
* S X=FNEW (J,Z)
or
* 4.3 S X=FNEW (J,Z)
In addition, X will be set equal to Z.
To call the array element K and set Z equal to this element:
* S Z=FNEW(K)
i.e., if there is only one argument the instruction is interpreted as a "GET". If there are

two arguments it is interpreted as a "PUTII.

5.2.3

Recursive Call ing
The function FNEW may be called recursively at any level. viz.
* S Z=FNEW [J, FNEW(J+10)J

sets Z=FNEW(J+10) and stores FNEW(J+10) in array element J.
* 3.2 S Z=FDIS (J*1000) , FDIS(FNEW(J)*NORM)
the arguments may be any arithmetic expression. The following are valid:
2
* S Z=FNEW (J*10-3, FEXP(X )*V)
* S Z=FNEW (J,FNEW (K)*FEXP(FNEW(L»)

5.2.4

Restri cti ons
Double precision floating:

0< J < 1320

(23 bits of significance)

Single precision floating:

0< J < 1979

(11 bits of significance)

Integer Array:

0< J < 3965

(11 bits of significance)

I Z I < 2047

5.2.5

Description
The function FNEW protects the binary loader in upper core. The function checks to see if

J is too large, but does not check to see if Z is larger than 2047 in the integer array case (c. f., array
overlay).
The user, of course, may subdivide this array into any number of smaller arrays, keeping
track of his own indices.
5-4

5.3

DYNAMIC INTERRUPT PROCESSING VIA FOCAL, 1969
This simple patch allows real-time interrupts to initiate execution of a specific FOCAL

subroutine (e.g. Group 31) which gains control (i.e., D031) when an interrupt occurs from an external
device. The FOCAL subroutine could sample various channels of the A/D converter, set a few constants, then turn off the interrupt, and return to the main FOCAL program. The main FOCAL program
will carry out the analysis or output of data during the time between these external device interrupts.
The external device could even be an animal and the time between interrupts will be asynchronous and
long (between 1 and 1000 seconds), or the external device will be a clock, in which case the time
between interrupts will probably not be less than 100 ms or greater than 1 sec.

/patch to interrupt processor
(tag assignments from symbol table)
*EXIT
/replaces H. S. Reader*
IOTl
/skip if device
JMP.+3
NOP
/"HINBUF" is cleared
*PCl
JMP I 175

/checkpoint in main program
/ valid for 8K, also

*167
DIPCHK
/Dynamic Interrupt Check
*HINBUF
1
/initialized to non-zero
*HREAD
DIPCHK, TAD HINBUF
SZA CLA
POPJ
TAD PC
/save FOCAL register
PUSHA
TAD SPCLN
/(your group #)
DCA LINENO
DCA NAGSW
ISZ HINBUF
PUSHJ
DO+l
POPA
DCA PC
POPJ
SPCLN, 7600
/(group 31)
The routine in group 31 returns control by "RETURN II. This feature does not operate unti I
main program is started. It will operate during execution of a direct command.

5-5

5.4

SIMULTANEOUS EQUATIONS· SOLUTIONS
This program will work with a set of simultaneous linear equations (in 4K. FOCAL 6 equations

is the limit) and output the solutions. To do this the program requests a value liLli, the number of equations and variables to be processed. The program then requests the coefficients and constants for each
equation, in a matrix like format. The solution values are typed out in a column with the names "X(O)"
through IIX(L -1) II. The program is available through DEC US.

5.5

FAST FOURIER TRANSFORMS PROGRAMS
The FAST FOURIER TRANSFORMS Program is designed to accept samples of a complex wave

pattern as input and, through a FOURIER analysis, describe its component sine and cosine waves in
terms of amplitudes and frequencies.
The user inputs a number IIN", which must be a power of two, (in 4K. FOCAL, "4" is the
limit) and which describes the number of samples to be used in the analysis. Next the samples, which
are wave height measurements taken at regular intervals, are requested. Output is in the form of two
columns (side by side), the left of which describes the cosine wave components whi Ie right hand
column describes the sine wave components.
It should be noted that because the number of samples is always a power of two, the number

of complex multiplications is cut drastically. For this reason computation time is also greatly reduced.

NOTE
In order to use this program, the extra extended
function FX(A, B) must be loaded into memory
via the BIN loader.

FAST FOURIER TRANSFORMS

W
C-FOCAL.,1968
01.08 A "POWER OF 2 II ,NU
01. 10 S N=2 t NU;S TP=2*3. 14159/N
01.18 S S=N/2:, L=l;S Q=5-1;S H=l-NU
01.20 F IlO,N-1;A !;A !,XR(I);S XI(I)=O
01 .22 S SR=XR(Qt-S)+XR(Q);S XR(Q+S)=XR(Q)-XR(Q+S);S XR(Q)=5R
01.24 I (Q) 1.26, 1. 26;S Q=Q-1;G 1.22
01.26 I (L-NU) 1 .28,1 .54,1.28
01.28 S L=L+l;S S=5/2;S H=H+1;S P=N-l;S Z=1/(2t(-H»
01.32 S C=l
01.34 S U=FITR(P*Z);S K=FX(NU,U)*TP
01.36 S CO=FCOS(K);S SN=FSIN(K)
01.38 S GR=CO*XR(P)+SN*XI(P);S GI=CO*XI(P)-SN*XR(P)

5-6

01.405 Q=P-5;5 5R=GR+XR(Q);5 51=GI+XI(Q);5 XR (Q)=XR(Q)-GR
01.42 5 XI(Q)=XI(Q)-GI;5 XR(P)=SR:, XI(P)=SI
01.46 5 P=P-1; I (-FAB5 [C-5J) 1.48; I (P-5+1) 1.52,1.26,1.52
01.48 5 C=C+1;G 1.34
01 .52 5 P=P-5;G 1 .32
01.54 F 1=O,N-1;5 K=FX(NU,I);T !,%3.2,2*XR(K)/N, II

",2*XI(K)/N

*
*C-TRAN5FORM OF INTERFERENCE PATTERN FORMED BY MIXING A 5INE
*C-WAVE OF AMPLITUDE 1 .0 AND A C051NE WAVE OF AMPLITUDE 1 .5

*
*GO
POWER OF 2 :3
: 1.5
:1.768

:1
:-.353

:-1 .5
:-1 .768

:-1
: .353
++0.00
=+1 .50
=+0.00
=+0.00
=+0.00
=+0.00
=+0.00
=+1 .50

=+0.00
=-1 .00
=+0.00
=-0.00
=+0.00
=+0.00
=+0.00
=+-1 .00*

*
/FNEW(u,v) for FFT
*BOTTOM
4377
*FNTABF+1Y
XFX
*4400
XFX, JM5 I INTEGER
Dca U
PU5HJ
EVAl-1
JM5 I INTEGER
CIA
DCA T2
DCA
lORD/low order
TAD
U
Cll
RAR
DCA
U
TAD
lORD
RAl
DCA
lORD
15Z
T2
JMP
.-7
JMP I EFUN31
5-7

5.6

TRAVEL VOUCHER TO EXPENSE VOUCHER CONVERSION PROGRAM
Though FOCAL is not a business oriented language the use of FOCAL in business applications

is not impossible. Such a use is seen in the TRAVEL VOUCHER TO EXPENSE VOUCHER CONVERSION
program with which the user may ease the task of reporting his expenses after a business trip.
Working from the input of the number of the days using the expense account and the categorized input of the expenses encountered (all amounts must be entered in terms of cents rather than dollars)
during that period, the computer tallies and itemizes
a.

the dai Iy expenses and

the totals of the expenses over the entire period.

The data, thus summarized, are very easily transcribed onto an employee expense voucher.

TRAVEL VOUCHER TO EXPENSE VOUCHER
CONVERSION PROGRAM
C-FOCAL., 1969
T !! "EXPENSE ACCOUNTER (fYPE ALL AMOUNTS IN PENNIES)"
01.01
ERASE
01.05
ASK 0/06.02,! "HOW MANY DAYS?" DAYS,!
01 .10
IF (DAYS) 1.1,1.1; FOR 1=1 ,DAYS; DO 5
01.20
01.40T !! II THE TRIP TOTALS ARE";F I=1,30;T II II
01.41T "GRAND"!
SET LO=LTi SET ME=ET
01.60
SET OJ=OT; SET MI=MT; DO 7
01.70
TYPE II $"!!!!!!
01.80
01. 90G 1.05
05.10
05.20
05.30
05.40
05.50
05.60
05.70
05.73
05.75
05.76A
05.77A
05.85
05.90
05.91
05.92
05.93
05.94
05.95
05.96

ASK !! IIBRKFST II B1
ASK "LUNCH II B2
ASK "DINNER II B3
AS K 115 NACKs II B4
ASK IIMILEs TRAVELED? IIB5; SET B5=B5*9; TYPE II $ B5/100; DO 6
ASK "HOTEL II B6
ASK "OTHER II B7
ASK IITELc II B8
A ! "TAXI IIC1
! IIPARKN IIC2
! IITOLL "C3
ASK! IIMISC. II B9
TYPE ! liTHE DAILY TOTALS ARE II !
SET LO=B6; SET ME=B 1+B2+B3+B4
SET OJ=B5+C1; SET MI=B9+B8+B7+c2+C3
TYPE IIDAY NO .11; DO 7.1
TYPE !Ok3,I,1I II; DO 7.2; DO 7.3
SET LT=LT+LOi SET ET=ET+ME
SET OT=OT+OJi SET MT=MT+MI

5-8

06.10

ASK II MISC. TRAV.

? IIB6; SET B5=B5+86

07. lOT II
LODGING
MEALS OTHER TRAV.
MISC.
TOTAL
07.15 T !
07.20T
%8.02, LO/100,1I
IIME/100,1I
IIOJ/100," IMI/lOO,"
07.30 T (LO+ME+OJ+MI)/100

*
*
*G
EXPENSE ACCOUNTER (TYPE ALL AMOUNTS IN PENNIES)
HOW MANY DAYS? :2
BRKFST
: 150
LUNCH
:170
DINNER :645
SNACKS :35
MILES TRAVELED ? :36
$ =+ 3.24 MISC. TRAV.
HOTEL:1400
OTHER :0
TELE
:40
TAXI
:0
PARKN :250
TOLL
:0
MISC. :0
THE DAILY TOTALS ARE
DAY NO.
LODGING
=+
1 =+
14.00

?:O

MEALS
OTHERTRAV.
=+ 10 .00 =+
3 .24
=+

MISC
2 .90 =+

TOTAL
30. 14

BRKFST
:98
LUNCH
:192
DINNER :650
SNACKS :30
MILES TRAVELED ? :23
$=+
2.07
MISC.TRAV.?:O
HOTEL:1400
OTHER
:398
TELE
:285
:0
TAXI
PARKN
:250
TOLL
:0
MISC.
:0
THE DAILY TOTALS ARE
DAY NO.
LODGING
MEALS
OTHER TRAV.
MISC
=+ 9.33
=+ 2
=+
14.00 =+ 9.70
2.07
=+

THE TRIP TOTALS ARE
LODGING
=+
28.00
=+

GRAND
TOTAL
=+ 65.24 $

MEALS
19.70

OTHER TRAV.
=+
=+
5.31

5-9

MISC
12.23

TOTAL
35.10

5.7

TWINS DEMO
The TWINS DEMO Program is an interesting experiment in the applications of plotHng with

a visual scope display unit. It must be noted that several functions must be loaded into memory before
this program will operate. This program is an integral part of curve fitting. The Twins Demo requires

V68/I Control with Tektronix 611 Scope. (i.e., 340 control)
TWINS DEMO
W
C-FOCAL., 1969

01.055
01.105
01.70F
01 .75
01.805

A=FDI5 () + FDX5 () + FNEW(2) + FNEW (256)
A=.2;5 5W=19
T=O, .05,6.284;5 T2=T+3.14159/4;DO 1.8;DO 15
G 2.1
R=4*FSIN(T) +4;5 X=8+R*FCOS(T2);S Y=32+R*FSIN(T2)

02.10

F Y=28.5,A,32;S K=( (Y-30.5)/1.5) t 2;5 X=9-(K*K-K);DO 15

03.10

F X=7.4,A, 10 .5;5 Y=26.5-( (X-9) t2)/2;DO 15

04.10

5 X=10.5;F Y=17,2*A,24.8;DO 15

05.10

F X=7 .2*A,8;5 Y=22-7*(X-7); DO 15

06.10 F

X=10.5 ,A, 15;5 Y=26-F50T(5*(X-10) );DO 15

07.10 F
07.20 F

X=l1 .5 ,A, 14 .5;D 8.5
X=14.5, .2*A, 15;D 8.5

08.10 F

X=3,A,4.6;DO 8.4

08.20 F

X=11 ,A, 12;DO 8.4

08.30

G 9.1

08.40

5 K=X-7;5 Y=12+(K *K)/4;DO 15

08.505

Y-21-F5QT(6.25-(X-12.5) t2);D 15

08.605

Y=(X-7) t2-1;D 15

08.705

X-5+F5IN (3. 14159*(Y -12);7);D 15

09.10 F

Y=O,2*A,16;5 X=12-( (Y-8) t2)/64;DO 15

10.10 F

X=2,A,4.5;5 K=X-3;5 Y=K *(K *( .47*K- .5)+ 1 .03)+26;DO 15

11.10F
11 .20 F

X=2, (.2*A),2 .85;D 8.6
X=4.7,.2*A,6;D 8.6

12.10F

Y=4.5,2*A,12;D 8.7

12.20F

Y =15 ,2 * A ,25; D 8.7

13.10F

X=5 . 3, . 3 *A ,6; 5 Y=-7 * (X -6) ; DO 15

14.10F
14.20F
14.30R

Y=12,2*A,24;5 K=( (Y-15.5}/1l) t2;5 X=5.5+12.5*(K*K-K);DO 15
Y=4,2*A,12;S K=Y-8.5;5 X=8.1-F5QT(27-K*K);DO 15

NOTE
Group 15 must be supplied to scale X, Y and call appropriate display for the device. (c.f., Section 5.8)

5-10

APPENDIX A
FOCAL COMMAND SUMMARY

Command

Abbr

Example of Form

Explanation

TYPE

TYPE FSQT (AL t 3+ FSQT (B) )

Evaluates expression, types out =,
and result in current output format.

TYPE IITEXT STRING II!

Types text. Use! to generate
carriage return line feed.

WRITE ALL

FOCA L pri nts the entire i ndi rect
program.

WRITE 1

FOCAL types out all group 1 lines.

WRITE 1 .1

FOCAL prints line 1 • 1

I F (X) 1 .2, 1. 3 , 1. 4;

Where X is identifier or expression.

WRITE

Control is transferred to the first, second, or third line number if (X) is less than, equal to,
or greater than zero respectively. If the semicolon is encountered prematurely then the remainder of
the line is executed.
MODIFY

MODIFY 1.15

Enab les editi ng of characters on
line 1.15

The next character typed becomes the search character.

FOCAL wi II position itself after

the search character; then the user may
a.

type new text, or

form-feed to go to the next occ urrence, or

bell to change the search character, or

rubout to de lete backwards, or

left arrow to ki II backwards, or

carriage return to end the line, or

line-feed to save the rest of the line.

QUIT

Q un or * or contro I-C

Returns contro I to user.

RETUR~'~

RETURN

Terminates DO subroutines

SET

SET A = 5/B * SCALE(3)

Substitution statement

ASK

ASK ALPHA (I + 2 * J)

FOCAL types a colon for each
variable; the user types a value to
define each variable.

A-1

Command

Abbr

Example of Form

Explanation

If a line begins with the letter C,
the remainder of the line will be
ignored.

COMMENT

C - compute area

CONTINUE

C - ignore temporari Iy

DO 4.14

Execute line 4. 14; return

DO 4

Execute all group 4 lines I return
when group is expanded or when a
RETURN is encountered.

DO ALL

Execute entire indirect text as a
subrouti ne .

ERASE

Erases the symbol table.

ERASE 2

Erases a II group 2 Ii nes .

ERASE 2.1

Deletes line 2. 1 .

ERASE ALL

Deletes all user text.

ERASE

FOR

FOR I = x/Y IZ; TYPE I

The command string following the
semicolon is executed for each value;
X/Y ,Z are constants, variables, or
expressions. x=initial value of I,
Y =value added to I unti I I is greater
than z. y is assumed = 1 if omitted.

Starts indirect program at lowest
numbered line number.

GOTO

GOTO 3.4

Starts indirect program at line 3.4

C - The Fourteen (14) Functions are
FSQT
FABS
FSGN
FITR
FRAN
FEXP
FSIN
FLOG
FDIS
FADC
FNEW
FX

)
- Square Root
)
- Absolute Value
)
- Sign Part of the Expression
( )
- Integer Part of the Expression
( )
- A Noise Generator
( )
- Natura I Base to the Power
( ) and - FCOS ( ) I
FATN (
- Trig Functions
( )
- Naperian Log
- Scope Functions
(X/Y)
( )
- Analog to Digital Input Function
( )
- User Functi on
( )
- Extra User Function
(
(
(

A-2

APPENDIX B
ERROR DIAGNOSTICS*

Table B-1
Error Diagnostics of FOCAL, 1969
Location

Code

0250
0316
0340
0351
0362
0440
0464
0517
0605
0634
1047
1064
1074
1147
1260
1406
1466
1626
1646
1755
1764
2057
2213
2551
2643
5042
5644
6543
7111
7405

?01.00
?01.40
?01.78
?01. 96
?01.: 5
?01.; 4
?02.32
?02.52
?02.79
?03.05
?03.28
?04.34
?04.52
?04.60
?04.: 3
?05.48
?06.06
?06.54
?07.22
?07.38
?07.:9
?07.;6
?08.47
?09.11
?10.:5
?11.35
?20.34
?23.36
?26.99
?28.73
?30.05
?31.<7

?OO.OO

Meaning
Manual Start given from console.
Interrupt from keyboard vi a contro I-C.
Illegal step or line number used.
Group number is too large.
Double periods found in a line number.
Line number is too large.
Group zero is an illegal line number.
Nonexistant Group referenced by 100 I.
Nonexistant line referenced by 1001.
Storage was filled by push-down list.
Nonexistant line used after IGOTO I or lIP.
Illegal command used.
Left of II =II in error in IFOR I or 'SET'.
Excess right terminators encountered.
Illegal terminator in 'FOR ' command.
Missing argument in Display command.
Bad argument to 'MODIFY I .
Illegal use of function or number.
Storage is fj lied by variab les .
Operator missing in expression or double IE'.
No operator used before parenthesis.
No argument given after function call.
Illegal function name or double operators used.
Parenthesis do not match.
Bad argument in 'ERASE ' .
Storage was fi lied by text.
Input buffer has overflowed.
Logarithm of zero requested.
Literal number is too large.
t Power is too large or negative.
Di vi si on by zero requested.
Imaginary square roots required.
Illegal character, unavai lable command, or unavai lable
functi on used.

*The above diagnostics apply only to the version of FOCAL, 1969, issued on tape DEC-08-AJAE-B

B-1

B.1

OBTAINING ERROR CODES VIA ODT36
To obtain error codes via ODT36, proceed as follows:
a.

Start 0 DT at 3600.

User types underlined letters:
to)

(change, from,
4320/1357

1275 (I i ne feed)

4321/4745

3067 (I i ne feed)

(UNENO)

4322/1675

4552 (I i ne feed)

(PRNTlN)

4323/4246

7000 (carriage return)
1355 (C .R.)

63/2676
c.

(OUTDEV, OUTl)

then
M 7777

7777 (line feed)

4273/0001

4400

(C . R.)

4565W

(ERROR 2)

Calling addresses and error codes wi II be printed here. The first two and last error codes
(00.00,01 .00 ,31 . <7) are always the same.

B-2

APPENDIX C
EXPLANATION OF NEW INSTRUCTIONS

C .1

NEW INSTRUCTIONS (see Table C-1)

C.1.1

Push Down Li st Instructi ons
The user1s push down list begins at the start of the floating point package and grows up

toward the last variable. The initial value of the push down list pointer is contained in location
"BOITOM". The pointer is kept in an auto-index labeled "PDLXR". The instructions used to manage
the list are given below:

C.1.2

PUSHA

places the contents of the AC onto the list as the current entry

POPA

adds the current entry of the push down I ist to the AC,

PUSHF

saves a group of data, normally a floating point entry.
This instruction is followed by a pointer to a 3 word (or
4 word) group of data. These 3 or 4 words are placed
on the push down list as the current entry.

POPF

restores a 3 or 4 word group of data from the current
entry on the push down list according to the pointer
which follows the instruction. The location "MFLT"
contains either -3 or -4 and determines the number
of words affected by "PUSH F" and "POPF".

PUSHJ

calls subroutine which is pointed to by the word following the instruction. The return address is placed on the
push down list as the current entry.

POPJ

the current entry is used as a return address from a subroutine.

Character Handling Instructions
These instructions are used to pick-up, save, and print characters for processing by FOCAL.

Characters are fetched from the user's storage area or from the ASR-33 input buffer. Character conversion between 8 and 6 bits and the trace feature are handled by these routines.
PRINTC

is used to print a character. If the AC is zero upon
entry then the character in "CHAR" is printed. If the
AC is non-zero, then the contents of the AC is printed.

READC

Reads a character from the user's input buffer (AS R-33
input) and echos a II characters except line feeds and
rubouts. The character is placed into "CHAR".

PACKC

places the 8-bit character in "CHAR" into the user1s
storage area. If the character is a rubout the previ ous
character is de leted from the user's area and a backslash is echoed via "PRINTC". The character is

C-1

converted into 6-bit code. The auto index
"AXIN" and the flip-flop "XCTIN" are pointers
to the user1s storage area.

C.l.3

GETC

this instruction fetches the next character from the
right or left side of the word pointed to by "AXOUT"
and "XCT II and places it into "CHAR". If a question
mark character is detected the dump switch "DMPSW"
is flipped. If the dump switch is on then the character
in "CHAR" is printed via "PRINTC".

SPNOR

Blanks and leading zeroes are ignored by repeated
calls to "GETC II .

Character Testing Routines
These guide the interpreter through the source text. They are testing routines used through-

out FOCAL in interpreting the program and in other instances.
SORTC

the character in "CHAR II is classified according to
an ASCII list which is pointed to by the location following the instruction. If the character is found in the list
an exit is made to the location following the list pointer.
If no character is found exit is made to the second location
following the list pointer. If the character was found in
the list then "SORTCN" contains the position relative to
zero in the list searched. The list is terminated by a negative
word.

SORTJ

the character in "CHAR" or in the AC is classified according to a list as per IISORTC II . If the character is found in
the ASCII list, then a jump to an address is made from a
second list. The second list is pointed to by the 2nd
location following call. If the character is not found then
exit is made as per IISORTC". "S0RTCN" is not changed,
however.

TESTC

this instruction fetches the next non-space and classifies
it as a terminator, number, function, or letter. The instruction then skips zero, one, two or three cells accordingly.
"CHAR II is classified according to whether it is a period

TESTN

{no skip}, number {skip two}, or other {skip one}. If
"CHAR" is a number then its binary value is in IISORTCN".
TSTLPR

C.l.4

This instruction skips the next instruction if the AC contains
a left parenthesis.

Line Number Handling Instructions
This group is used in manipulating line data and line numbers.

C-2

TSTGRP

PRNTLN

If the group of the line number in the AC is equal
to the group on the line in "LINENO II the next
instruction is skipped.
the coded line in "LINENO II is printed as a decimal

fraction with group number and the step number
separated by a decimal point.
GETLN

JlSPNOR Ii is called and a line number is built in
JlLINENO Ii via calls to IIGETC IJ • IINAGSW II is set
to indicate whether the line number was a group, line,
or "ALLII designator.

FINDLN

the line number coded in IlLINENO Ii is searched for
in the user's text area. If the line is found, -the autoindex IIAXOUT" and IIXCT II are set to point to the
line's text and an instruction is skipped. If the line
is not found, the pointer "AXOUT" is set to point
to the next higher line and no instructions are skipped.
"THISLN" points to the line found on the next larger
line and "LASTLN" points to the previous/less
line.

ENDLN

"ENDLN" links the line in the user's storage area
to the rest of his text. It uses the result of the "FINDLNII
instruction to accomplish this. The new end of the user's
buffer is set-up in IIAXINII. This command is used for
insertion of new text, reconnecting after a deletion,
and reconnecti on after Modify.

Table C-1
New Instructi ons
PUSHJ = JMS I .
XPUSHJ
POPA = TAD I POLXR
POPJ = JMP I .
XPUPJ
PUSHA = JMS I .
XPUSHA
PUSHF = JMS I .
PD2
POPF = JMS I .
PD3
GETC = JMS I .
UTRA
PACKC = JMS I .
PACBUF
SORT J = JMS I .
SORTB
/NUMERICAL LIST -1
/ADDRESS LIST - NUMERICAL LIST

/RECURSIVE SUBROUTINE CALL
/RESTORE AC
/SUBROUTINE RETURN
/SAVE AC
/SAVE GROUP OF DATA
/RESTORE GROUP
/UNPACK A CHARACTER
/PACK A CHARACTER
/SORT AND BRANCH ON AC OR CHAR

C-3

Table C-1 (Cont)
New Instructi ons

SORTC = JMS I .
XSORTC
PRINTC = JMS I .
OUT
READC = JMS I .
CHIN
PRNTLN = JMS I .
XPRNT
GETLN = JMS I .
XGETLN
FINDLN = JMS I .
XFIND
ENDLN = JMS I L
XENDLN
RTL6 = JMS
I.
XRTL6
SPNOR = JMS I. .
XSPNOR
TESTN = JMS I .
XTESTN
TSTLPR = JMS I •
LPRTST
TSTGRP = JMS I •
GRPTST
TESTC = JMS I .
XTESTC
ERROR2 = JMS I .
ERROR3 = JMS I .
ERROR4 = JMS I .
ERR2

/SORT CHAR
/PRINT AC OR CHAR
/READ ASR-33 INTO CHAR AND PRINT IT
/PRINT C (LINENO)
/UNPACK AND FORM A LINENUMBER
/SEARCH FOR A GIVEN LINE
/INSERT LINE POINTERS
/ROTATE LEFT SIX
/IGNORE SPACE AND LEADING ZEROS
/PERIOD: OTHER: NUMBER
/SKIP IS 5 < SORTCN < 11 (I . E. AN L-PAR)
/SKIP IF G(AC) = G (LINENO)
/fERM; NUMBER; FUNCTION; LETTER
/EXCESS SOMETHING ERROR
/MISCELLANEOUS ERROR
/FORMAT ERROR

C-4

APPENDIX D
FOCAL CORE LAYOUT

Table D-1
Foca I Core Layout-Usage

What

Mnemonics

ZERO
START

FOCAL PROPER

BUFBEG

BUFFER AREA

BEGIN

INITIAL DIALOGUE

FEXP
(BET 2+ 3)
ARTN

EXTENDED
FUNCTIONS

(FLAG 3 +1)
FCOS
(FLOA+ll) }
(TEMPO + 1)
DECONV
(I NFIX +5)
FLOUTP
(OUTOG+4)
FLINTP

}

(P43+l)
FPNT

ACMINS
(RAR1+1)
DNORM
(BUFFER +
BINARY
(RIM)

OUTPUT
CONVERSION
INPUT OUTPUT
ROUTINES

FLOATING-POINT
INTERPRETER

10)}

LOADERS

D-1

Table D-2
Detailed FOCAL Core Layout

Miscellaneous
Numbers
Floating-Point Working Area
Constants
New Instruction Pointers
Variables
START
Command/Input
Line Read Routi ne
'DO' Routi ne
Push -POP Routi nes
'GOTO' and 'WRITE' and Misc.
'IF', "SET", 'FOR'andMisc.
'ASK', 'TYPE', 'MODIFY'
"GETARG II - Recursive Routine
"SPNOR", "TESTN", "POPJ"
'RETRUN'
"EVAL" - Recursive Routine
OPNEXT - read operator
ARGNXT - read operand
ETERM - evaluate terminator
FLOP - floating operations called
ENUM - number processor
EFUN - function processor
ELPAR - left parens processor
EFUN3 - function returns
"DELETE" - Recursive Routine
DO K - group de lete
DONE - garbage collection
"FINDLN" - Normal Routine
Find exact match or next larger
'ERASE' command processor
"GETC II - unpack text and trace
"ENDLN", "PRNTLN"
I/O Subrouti nes
Interrupt Processor
ERROR Processor
"PACKC" - pack text
Rubout routi ne

D-2

Table D-2 (Cont)
*3120

T
E
X
T

*4400 -

I/O Buffer
Command Buffer
Text Buffer Begins

Once-On Iy Code
SELF-START

/
V

A
R
I
A
B
L
E
S

CLEAR ALL FLAGS
TYPE MESSAGE

. "/
P

S
H

D
0
W
N
L
I
S
T

*3600

ODT -JR (for X-FUN)

*4600

ODT -JR (for dialogue)

Floating Point Routines
(c.f., Section 4.5.2)
*4600
*5400
*6400
*7600

Extended Functions
I/O Controller
Interpreter
Binary Loader
or 8-SYS LIB Bootstrap
or Disk Monitor Bootstrap
Rim Loader
*7756
End of Field Zero
Field One
Command
Extended Text Storage
Buffer

D-3

FOCAL

CORE

LAYOUT

0000 -------------------------PAGE

FOCAL

ZERO

EXP

FREE
PUSH A
PUSH

PUSH F

4600 r-----------~----------~
EXTENDED

FUNCTIONS

5400 I------------------------~
FLOATING -POINT PACKAGE

LOADERS

7777

Figure D-1 FOCAL Core Layout
Dynamic Storage

D-4

APPENDIX E
SYMBOL TABLE AND OTHER TABLES/LISTS
E. 1

SYMBOL TABLE

If:"OCAL.~lM

PALl"

A
ABSOL
ABSOL2
A8S0L3
ABSOLV
AC1H
AC1L
AC~ I ~'S

7375
5571

ACTI~;G

~7r1

ACTlr:f\J
ACTI\lE
ACTVP
ADn

442e

~"'45

6751
6153
~Z41

;1042
6673

V5l5

1121-APR ... 69
9F'XX
QMOVE
BOTTOM
BUI='BEG
RUF'F"ER
AUF'R
RUF'RS
BurRSP
RurST
C

19138

4556
1255

PAGE 121
OU80lV
DUBLAD
OUMLN2

r.OMLST

31·0
32e!6
1163
0714

COMMF"N

~614

5037
1147

3045
5531
0047

CON1
CaNTIN
CONTIIJ
r:STAQ
CTABS

EBEL.L
ECALL
ECCR
ECHO
ECHOLS
Erop
ErUN
Ef"UN2
EF'UN3
EF'UN31
ELPAR
END
END;I
ENOLN
ENOT
ENUM
[OUT
EP7
EPAA
EPAR2
EA'
ERASE
ERe
[AL
ERR2
EAROR2
EARORJ
ERROR4
ERROR5
ERT
[AV
ERVX
ESCA
ETERM
ETERM1
ETERM2
ETEAMN
EVAL
[Xl
EXASt(
EXCMCK
EXCHE
EXCHEC
EXGO
EXGON
Exn
EXIT1

CO~EtN

COME"'U

~035

CO~GO

3217
7470
"'060
13"'~

Vl~37

C1~k'J

1?!0~6

1143

C140
C144
C2k'l0

2554

DATUM
DA TU~1A
DCONP
DCONT

~061

614~
~123

ADrH~

Ll041(1

ADn~E

6673

C2e0~~

Ql065

AF'
ALF'l
ALF"2
AI.F"l!
ALG,\;
AUGN
ALI ~T
ALlSTP

4677
4760
4763
4755
6570

C260
C3
C5
C7
C9
CCR
CDF'
CDF'l
CEXl
CEXP
CF"
CF'RS
CF"RSX
CHAR
CHARt-I
CHIN

"1113

DCOU~IT

5346
5342
5336
5332
0017
70"'1t!J
6211
651114
6503
4705
"'133
:"1137
0066
C11026
2155
1'1153

["lOTJP
OEBGS\rI
nECK
IjECKP

AI.PH~
AMCU~,'T

AReAlG
ARCRTN
ARGNXT
ARTr-.;
As~rT

ASK
ATE:l
ATfS
ATLIST
ATSw
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~623

1372
;,,,72
1436
6722
4732
5024

1723
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6665
120.2
4465
4513
157e
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:"010
~1i317

~~46

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~ASER

5503

RASES
BASEx
QOUMP

1540

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BETl
~ET2

BETA
BETl
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Rf:"X

~616

~617

0071
4371
~5:54

4442
4771
4774
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4766
47e2
4557

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CHKCON
CHRT
CIA
CIF'
CIF'l
CLA
CI.CU
Cl.F'
Cl.l.
CMA
CML
CNTR
CNTRLC
CNTRI.X
CNTRM
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COM8UF

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OE CO~,IV
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OECR
DELETE
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nGRp
OGRP1
1'1 G
r:lIGIT
DIGITS
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1~52

6133
7041
6202
6212
7200
7421
"'016
7111'121
711140
7020
0057
1'1324
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11'0.4
12'5
11'226

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DOUBLE
OPCVPT
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~1~2

E-l

~11l16

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0353
0041
7102
7252
6303
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6143
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0026
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OJ101
5627
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5533
5521
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5543
5113
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1063
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7036
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631!l'
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56'7

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7261
5133
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7261
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~512

1601
2630
0454
1624
00'6
17.3
1754
2017
0136
1763
111134
6243
.556
0135
1732
",4,.
0121'2
1710
1765
4555
22214
2225
2222
2726
.566
4'66
4566
2725
2214
2217
2237
2'32
1647
1627
1655
1644
1613
"'040
2662
1037
111172
2615
1007
1215
26'6
'8~4

IfOCAL.ti1M

PALl,'

5556
612"1'0
6465
65C1!5

231.3

2165
1041

53!12

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2657
7044

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10"APR .. 69
F'LOUT
F"l.OUTP
F"LPT
F'LSU
F'L TO"1[
F"LTXR
F"LTXR2
F"l.TtER
F"M12
F'NF.:G
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F'NPT
F'NTAPF"

EXIT?
rXIT3
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7363
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1.~14

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F'NTA~L

1171

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F'OP
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"LOG
FLOP

"034

"010
fo.221

6261
1065
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442'7
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6724
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5162
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6563
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GE~D

GERR
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19138

PAGE 121.1

24~5

10101.0
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24~7

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1371
5021
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~316

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KEY
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E-2

"'036
1276
1277
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6321
6324
6364
t'l273
6315
6361
0273
6343

~227

6573
7471
6462
5525
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KRB
KSF"

KSF'l
KSr2
KSF'3
KSF'4
Ll
L2
L3
L4
L8A
L8AX
L8AY
L8B
LASTI.N
I.ASTOP
LASTV
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LG2E
LIBRAR

LINENO
L1ST3
LlST6
LIST1
LISTGO
LlSTI.
LlSTP
L.OG2
LOG5
LOG6
LOG7
LOG8
LOOKUP
LOOPCIl1
LORD
LP?
I.PRTST
M100
Mltl1PT
1'111
M12
1'1137
1'1140
1'1144
M2
MUJ
1'1200
M20M
M240
M240M
M260

2625
60:36
60:51
64~1

6421
6441
6461
5126
5131
5134
5131
4550
4553
4552
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0025
0055
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"311
4113
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1165
5157
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6431
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1556
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6147
0121
2413
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2556
6137
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13056
~114

3146
1526

IF"OCAL.irM
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1527
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l103

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1136

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10-APR .. 69
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NL,2
NL,2000
NL,3777
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NL,7776

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01
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04
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5215
1256
1232
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1256
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72"''''
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4752

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OPTRI
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19138

4724
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PAGE 121-3

"'~32

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1565
11362
1064

2425
11313
~477

~521

etfH0

el011
~012

~013

1553
7365
V'l312
(71011
02112
,,413
21310
~721

1517
4676
5326
7400
1.'l717
~535

1(17910

1533
r;t727
"'7121

0742
2451

PAl-HI

IF'OCAl-.llM

lERO

19'38

V515

6520

ERRORS DETECTED' 0
RUN-TIMEI

32 SECONDS

61( CORE USED

E-5

PAGE 121-4

E.2

OTHER TABLES AND LISTS

ILlsT OF FUNCTION ADJHESSES, (NAMES ARE IN "FNTABL")
0373
~3 73

,1374

,1375
~376

J377

t$~~

!~4?!0

1344

214'1
J4!.J2

50:)0

114713

50410

1.14'4
Z415

5205

J4~6

:'410
1411

7400
2725
2725
2725

1)437

FI\JTABF=,

2014
2010
1161

XA8S
XSGN

XINT
XDYS
XRAN

XAOC
ARTN

FEXP
FLOG
FSIN
FCgS
XSCRT

4620
52210

IAHS
ISGN
IITR
lOIS
IRAN
lADe
IATN
IEXP
ILOG
ISIN

leas
IS T

71~6

eLL RTL

~414

7006

;'4 t 5

7006

RTL
RTl

~416

5612

JMP I XRTL6

0775
0776
0777

0775
0323
0306
0311
0304

COMLST=,
323
306
311

03~7

3"'4
307

10212

0303

303

1~2J3

0301

301

1004

0324
!2I314
°3 0 5

324

t0~7

~10

1011
1e12
1~13

314
3/{)5

~~i~

~i~

0321

321
322

0322
0212

"'SQUARE ROOT
~USER DEFINEO rUNCTIONS

IROTATE AC LEFT SIX"", "RTL6"

~10J0

1 fli1 6

'!!'TRIG FUNCTIONS

ERROR5
ERROR5

1\412

10Z5

-EXPONENTIAL FUNCTIONS

INEW
leOM
IX

ERROR5

)41,3

1';1('10
10211

-ABSOLUTE VALUE'
-SIGN PART
"'INTEGER PART
-DISPLAY AND INTENSlrY
-RANDOM NUMBER
~READ ANALOG TO DIGITAL CONVERTER

212

!E.NbLISH ... FRENCH
ICoMMAND DECODING LIST
!SET
,., ORG~NI~E
IFOR
QUA 0
IIF
- SI
100
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"" VA
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IASK
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ITYPE
.. TAPE
ILIBRARY. ENTREPOSE
IERASE "" BIF"F'E
IwRITE
INSeRIS
IMODIF'Y ... MaDIPIE
IQUIT
.. ARRETE
IRETURN ~ RETQURNE
!(ASTERISK):EXPANDABLE COMMAND

E-6

1164
1165
1160
1167
117~~

1171
1172
1173
ll74
1175
1176
:1.177

1164
1042
1(42
1Vi 14
0417
0604
0615
1203
1204
7503
2204
0636
1257

12~0

el177

12?1
12212

1563
6361

2165

2165
2160
2167
2170
2171
2172
2173
2174
2175
2176
2177
22:3kl
22211
22212
2203

2533

COMGO:, ICOMMANO ROUTINE ADORESSES
SET

FOR
If

DO
GOTO
COMMENT
ASK
TYPE
LIBRARY
ERASE

WRITE

F'NTAB L =,

MODIFY
START
RETRN
HSPX

IRE TURN TO COMMAND MODE VIA 'QUIT'

2533

lABS

265~

2650

2636
2565

2636
2565
2630
2517
2572
2624
2625
2654
2575
2702
2631
2567

263~

2!)17
2572
2624
2625
2654
2575
2702
2631
2567
0330

I(REF'ERENCED)

0330

IACTIVATE THE HIGH SPEED READER

ISGN
IITR
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IRAN
lADe
IATN
IEXP
Il.OG
ISIN
ICOS
ISQT
INEW
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IX

E-7

ILIST OF' COOED rUNCilON NAMES

IQUAD -

~U~TI-JSER

SYSTEM WITH

FOCAL.~rK

PAL10

V133

14'-MAR-69

15149

/CONTROL TABLE.:
:3 354
~355

2'356

0357
0360
21361
21362
~363

21364
21365
21366
el367
~370

0371
21372
0373
0~74

21 75

0376
0377
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iJ4~1

214212
214213
04?J4
2I42J5

04~6

04217
21410
21411
0412
21413

0 451
21355
0456
21333
0326
0333
21333
0333
0456
0333
21333
21467
0333
0467
2J453
0333
~333

~~~~

21345
21333
21351
"333
21333
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21456

~~~~
21451

0451
21451
0456
21453

IL,T.

IGNORE

CTABS:.
ECHO
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CNTRLX
CNTRLX
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ItA-HOME
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IC~END OF' M.ESSAGE
ID
IE
IF
IG '" BELL.
IH
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IK
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IS .. (7((J00) - FOR DEBUGGING

IT-NOT TApE
IU

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4WQRD (10 DIGIT) OVERLAY FOR

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14 WQRO (10 DIGIT) OVERLAY FOR
2'004

21012

21vi 52

14-MARa69

15,54

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7774
3210

3210

Zl355

3211

6427

3212

1722

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5526
5527

5526
7766
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5310

5J14
5320

5310
3755
5314
3755
5320
3755

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TEXT @C-4wORD(il

-DIGITS IEXTENDED LENGTH OF OUTpUT FORMAT
OIGITS+l/RN02
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6402
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64212

654~i

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6736
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6736
7036
7125
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7036
3275
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ICORRECT CONSTANTS

3755
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6143
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6277
31 46

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3755

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ICONSTANT ONE
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4WORO (10 lJJGIT) UvE.RLAY FOR FQCAL.ttK PAL.10
7260
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7271
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7273
7274
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7276
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FJR FJCAL.2lK
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V133

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FOR

14-MAR-69

15:57

PAGE 1

FOCAL.~~K

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TEXT

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6171
6671
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6171
6671
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1ST ART

USER FILE AT T""'IS ADDRESS

TAD 7
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elF p

1~eJ7

3406
6202
5525
6002
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IRE TURN To DISK MONITOR,
7600

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ITOUMP DATA

0000
00021

o
NOPUNCH

XLIST

E-12

APPENDIX F
FOCAL SYNTAX

Table F-l
Syntax in Backus Norma I Form

< i mmedi ate command> : : = < program statement> C . R.
<indirect command>: : = <line # > <program statement> C. R.
<line # >: : = <group no. >. <line no. >
<group no. >: : = 1-31
< line no. > : : = 01-99 11-9
< program statement> : : = <command>

I <command string> J

<program statement >; <program statement>
<command>: : = WRITE
<arguments>: : = ALL

I DO I ERASE I GO I GOTO

I < line # > I <group no. >

I < Library statement> I

<Ask statement> I <If statement>
<Modify statement> I <Set statement>
<For statement> QUIT RETURN I COMMENT

I CONTINUE

FOR <space> <variable> = <expression >, <expression >;
<program statement>
<If statement>: : = IF <space> <subscript> <line # >; I
IF <space> <subscript> <line # >, <line # >; 1
IF <space> <subscript> <line # >, <line # >, <line # >
<Ask statement> : : = ASK <space> <Ask arguments>
<Ask arguments> : : = <operand >, <Ask arguments>

! <Ask arguments> # <Ask arguments> % <format code >, <Ask arguments>
1\

I<null> I

I <null> I <group no. >

< library statement>: : =
LIBRARY <space> < Library Command>
<space> <file NAME>
'<Library Command>: : = CALLI SAVE

I DELETE I LIST
F-1

I :\ @

<special symbols>: : = & \ I

I [200] I <null >

< leader-trai ler >: : = @

<data list>: : = <variable> <variable >, <data list>
<Type statement>: : = TYPE <space> <Type arguments>
<Type Arguments>: : = <Ask arguments> I <expression >\
<Type arguments >, <Type arguments>
<Modify statement>: : = MODIFY <space> <line # >
This command is then followed by keyboard input
characters defined as <search character>
plus
<null> <character string> 1 <control character>
<character string> <control characters>

<control charcter >: : = [bel I] <search character >1
[form] \ [fine-feed] C.R. 1

['l'C]

I [rub-out]

I <constant >\ <subscript> I <function>

I( I [

<expression> <operator> <expression>
<unary>: : =

+\ -

<operator>: : =

t I*

I / I +I-

<Function>: : = F <function code> <subscript>
<function code>: : = SIN· I COS
SQT I ADC
ABS I SGN

LOG I ATN I EXP
DIS I ITR I

RAN

I NEW I

NOTE
Spaces are ignored except when required.

F-2

Table F-2
FOCAL Commands In French

Commandments Francais Pour Le Calculateur Electronique "IGOR"
Eng lish

French

Letter

SET

ORGANIZE

FOR

QUAND

FAIS

GOTO

COMMENT

COMMENTE

ASK

DEMANDE

TYPE

TAPE

LIBRARY

ENTREPOSE

10.

ERASE

BIFFE

1l.

WRITE

INSCRIS

12.

MODIFY

MODIFIE

13.

QUIT

ARRETE

14.

RETURN

RETOURNE

CE N'EST PAS PARFAIT
MAIS "IGOR" EST INTELLIGENT
IL COMPRENDRA

NOTE
"IGOR" refers to PDP-B!I

F-3

APPENDIX G
ILLUSTRA TIO NS

EVAL-1

EVAL

T
ETERM1

N
ENUM

F
EFUN

Figure G-l (Sheet 1)

Arithmetic Evaluation

G-l

Figure G-l (Sheet 2)

Arithmetic Evaluation

G-2

EPAR

ENUM

EPAR2

OPNEXT

ARGNXT

ELPAR

ERROR4

_----_T
ELPAR
ENUM

EPAR2

_----_F
EFUN

_----_v
OPNEXT-2

Analysis of Operands

Analysis of Sub-Expressions and Constants
Figure G-l (Sheet 3)

G-3

Arithmetic Evaluation

EFUN

ASSEMBLE
CODE NAME
FNTABL

FNTABF

r
EFUN2

ERROR4

LIST OF
CODED NAMES

ARG ::::> FLARG
(PT1) ::::> FLARG
CHAR = RPAR.
COMMA OR C. R.

LIST OF
FUNCTION
ADDRESSES

l
TYPICAL FUNCTION

FUNCTION
RETURN

VIA
EFUN31

ERROR4
ILLEGAL
NAME

OPNEXT

Figure G-l (Sheet 4)

Arithmetic Evaluation (Analysis of Functions)

G-4

OR START
INITIAL DIALOG

200

START

ON LINE
COMMAND
PC-O
DNPSW='

IBAR
START
WAIT FOR
INPUT
IGNOR
ASR33

IGNOR+4

G'I >
OJ

LIST 6

(

IBAR

)

L.F.

(

IGNOR+4

)

F.F.

BELL

C.R.

GZERR

(

IGNOR+4

)

(

IGNOR

)

(

IRETN

)

NO
INPUTX

SRETN

Figure G-2

Command/Input

GOTO
MANUAL RESTART VIA LOC 200

ERROR2

START
PROCESS

PROC

BRANCH OR
COMMAND
CHARACTER
GO TO
NEXT
TERMINATOR

ERROR2

Figure G-3

Main Control and Transfer

G-6

CONTINUE
DATA IS
SAVED

ONE

NOT
THERE
ERROR2

DGRP

SAVE NAGSW
DCHAR
LlNEND

PC ., (PC)

DCONT

Figure G-4

DO Command

G-7

ASK
TYPE

REMEMBER
WHICH COMMAND
THIS IS

AL 1ST

TASK

TINTR

)

(

TQUOT

)

(

TCRLF

)

(

TCRLF2

)

(

TDUMP

)

(

TASK4

)

(

TASK4

)

(

PROCESS

)

(

PC1

)

C.R.

Figure G-5 (Sheet 1)

ATLIST

(

0/0

Input/Output Commands

G-8

TYPE 2

TYPE

Figure G-5 (Sheet 2)

Input/Output Commands

G-9

FI NCR

FLiSTl

(

FINCR

)

(

PROCESS

)

(

PCl

)

ERROR4
FLIST2
TLiST

ill

TLiST

G)
I

ERROR4

READ
THE LIM IT

FCONT

Figure G-6

Iteration Control

IF'

GOTO

TUST

lJ
Figure G-7

lUST

(

IF'

)

(

PROCESS

)

(

PCI

)

Conditional Branch Command

G-ll

MODIFY

READ A
LINE NUMBER

SBAR

RESTART
INPUT
POINTERS

SFOUND

ERROR2

NO
SRNLST

LlST6

YES
SGOT

SBAR

)

SCONT

)

SCONT+ 1

)

CARRIAGE - RETURN (

SRETN

)

SEARCH CHARACTER (

SGOT

)

(
FORM- FEED (

BELL (

LINE-FEED (

SCONT

(i)

SCONT+ 1

SCHAR

LlST3

LISTGO

(....._ _
5 R_E_T_N_J)

Figure G-8

Character Editing

ERV

ERASE

ERL

ERRORS

RESET TEXT
POI NTS

ERV
RESET
VAR I ABLE
LI ST

Figure G-9 (Sheet 1)

ERASE and Delete

G-l3

ERL

ENTRY

DELETE

ADD ONE

Figure G-9 (Sheet 2)

ERASE and De lete

G-14

(,-_ _
I N_T_R_PT
_ _) -

TINT

RECOVR

SAVE
ERROR NUMBER
TURN ON TELSW

SAVE
I NPUT DATA

TI NT

EX IT

CLEAR FLAGS

EX IT

Figure G-10 (Sheet 1)

G-15

Interrupt Hand ler

START

XOUTL

ENTRY

~~--~

EXIT XOUTL

XI33

TYPE CHARACTER
AND
~--~~
START PROGRESS

ENTRY

Figure G-10 (Sheet 2)
G-16

Interrupt Handler

EXIT XOUTL

GETARG

ERROR4

)

GETVAR
GFNOl

~::":""'---I~

GSI

ADD THE
VARI ABLE NAME
AND SUBSCRIPT

GFND1

ERROR3

G'I >

-'"
RESTORE NAME

GSl

YES

Fiqure G-ll

Variable Look-up and Enter

UTRA

GET1

ENTRY

UTRA+1

GET3

UT2

200

300 -376

-276

EXTR

UTX

UTa

I
(X)

UTX

YES

CHAR=277

EXIT UTRA

Figure G-12

Character Unpacking

UTa

"FINDLN"

FIND A
PART ICUL AR

LINE FOR A
GIVEN
LI NENUMBER
OR GROUP

"FINDLN~

FINDN

ERROR2

FINDN

Figure G-13

"FINDLN" Routine

G-19

ROUTINE

ADVANCED FOCAL
TECHNICAL SPECIFICAnONS
DEC·08·AJBB·DL

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