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Document:	Focal XVM Language Manual
Order Number:	DEC-XV-LFLGA-A-D
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Pages:	98
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OCR Text

FOCALXVM
LANGUAGE MANUAL
DEC-XV-LFLGA-A-O

FOCALXVM
LANGUAGE MANUAL
DEC-XV-LFLGA-A-D

digital equipment corporation · maynard. massachusetts

First Printing , January 1976

The information in this document is subject to change without notice
and should not be construed as a commitment by Digital Equipment
Corporation.
Digital Equipment Corporation assumes no responsibility
for any errors that may appear in this document.
The software described in this document is furnished under a license
and may be used or copied only in accordance with the terms of such
license.
Digital Equipment Corporation assumes no responsibility for the use or
reliability of its software on equipment that is not supplied by
DIGITAL.

1976 by Digital Equipment Corporation

The postage prepaid READER'S COMMENTS form on the last page of this
document requests the user's critical evaluation to assist us in preparing future documentation.

The following are trademarks of Digital Equipment Corporation:

DIGITAL
DEC
PDP
DECUS
UNIBUS
COMPUTER LABS
COMTEX
DDT
DECCOMM

DECsystem-10
DECtape
DIBOL
EDUSYSTEM
FLIP CHIP
FOCAL
INDAC
LAB-8

MASSBUS
OMNIBUS
OS/8
PHA
RSTS
RSX
TYPESET-8
TYPESET-IO
TYPESET-ll

CONTENTS

Page

Chapter

PREFACE

vii

INTRODUCTION TO FOCAL

1-1

1.1
1.2
1.3
1.4
1.5

"
2

Hardware Requirements
Loading Procedure
Restart Procedure
Saving FOCAL Programs
Data Input/Output

2-1

FOCAL LANGUAGE
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13

1-1
1-1
1-2
1-3
1-3

Elementary Commands
Output Format
Floating-Point Format
Arithmetic Operations and Symbols
Additional Symbol Information
Subscripted Variables
The Erase Command
Handling Text Output
Indirect Commands
Error Detection
Corrections
Abbreviations
Alphanumeric Numbers

2-1
2-2
2-4
2-4
2-5
2-6
2-7
2-7
2-7
2-9
2-9
2-11
2-11

FOCAL COMMANDS
TYPE
3.1
ASK
3.2
WRITE
3.3
SET
3.4
ERASE
3.5
GO
3.6
GOTO
3.7
DO
3.8
IF
3.9
RETURN
3.10
QUIT
3.11
COMMENT
3.12
3.13
FOR
MODIFY
3.14
Using the Trace Feature
3.15
Internal Functions
3 .16

3-1
3-1
3-2
3-3
3-4
3-4
3-5
3-5
3-5
3-6
3-8
3-8
3-8
3-8
3-10
3-12
3-13

EXAMPLES OF FOCAL PROGRAMS

4-1

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

4-1
4-2
4-3
4-5
4-6
4-10
4-11
4-13

Table Generation Using Functions
Formula Evaluation for Circles and Spheres
One-Line Function Plotting
Demonstration Dice Game
Simultaneous Equations and Matrices
Interest Payment Program
Intercept and Plot of Two Functions
Schroedinger Equation Solver

LIBRARY COMMANDS

5-1

5.1
5.1.1

5-1
5-1

Library Output Commands
Library File Initialization

iii

CONTENTS (Cont'd)

Page

Chapter
5.1. 2
5.1.2.1
5.1.2.2
5.1.2.3
5.1.2.4
5.1. 3
5.2
5.3
5.4
5.4.1
5.4.2
5.5
6

Library File Output Operations
Direct Command Output
Single Line Output
Group Output
Program Output
Library File Termination
Library Input Commands
Library .DAT Slot Usage
Common Variables and Arrays
COMMON Format
ERASE COMMON Command
Chaining of FOCAL Programs

5-1
5-1
5-2
5-2
5-2
5-2
5-3
5-4
5-4
5-4
5-5
5-5

USER DEFINED FOCAL FUNCTIONS

6-1

6.1
6.2

6-1
6-3

Example
File FNEW

DATA COMMANDS

7-1

7.1
7.1.1
7.1. 2
7.1. 3
7.2
7.3

7-1
7-1
7-2
7-2
7-2
7-3

DATA Commands
DATA File Initialization and Output
DATA File Termination
DATA Input
DATA .DAT Slot Usage
DATA Command Use

APPENDIX A
FOCAL Command Summary

A-1

APPENDIX B
Error Diagnostics

B-1

APPENDIX C
Estimating the Length of User Programs

C-l

APPENDIX D
Calculating Trigonometric Functions

D-l

APPENDIX E
.DAT Slot and Handler Assignments System in XVM/DOS

B-1

INDEX

Index-l

LIST OF ALL XVM MANUALS

The following is a list of all XVM manuals and their DEC numbers, including the latest version available.

Within this manual, other XVM

manuals are referenced by title only.

Refer to this list for the

DEC numbers of these referenced manuals.
BOSS XVM USER'S MANUAL

DEC-XV-OBUAA-A-D

CHAIN XVM/EXECUTE XVM UTILITY MANUAL

DEC-XV-UCHNA-A-D

DDT XVM UTILITY MANUAL

DEC-XV-UDDTA-A-D

EDIT/EDITVP/EDITVT XVM UTILITY MANUAL

DEC-XV-UETUA-A-D

8TRAN XVM UTILITY MANUAL

DEC-XV-UTRNA-A-D

FOCAL XVM LANGUAGE MANUAL

DEC-XV-LFLGA-A-D

FORTRAN IV XVM LANGUAGE MANUAL

DEC-XV-LF4MA-A-D

FORTRAN IV XVM OPERATING ENVIRONMENT MANUAL

DEC-XV-LF4EA-A-D

LINKING LOADER XVM UTILITY MANUAL

DEC-XV-ULLUA-A-D

MACII XVM ASSEMBLER LANGUAGE MANUAL

DEC-XV-LMLAA-A-D

MACRO XVM ASSEMBLER LANGUAGE MANUAL

DEC-XV-LMALA-A-D

MTDUMP XVM UTILITY MANUAL

DEC-XV-UMTUA-A-D

PATCH XVM UTILITY MANUAL

DEC-XV-UPUMA-A-D

PIP XVM UTILITY MANUAL

DEC-XV-UPPUA-A-D

SGEN XVM UTILITY MANUAL

DEC-XV-USUTA-A-D

SRCCOM XVM UTILITY MANUAL
UPDATE XVM UTILITY MANUAL
VPISA XVM GRAPHICS SOFTWARE MANUAL

DEC-XV-USRCA-A-D
DEC-XV-UUPDA-A-D
DEC-XV-GVPAA-A-D

VTlS XVM GRAPHICS SOFTWARE MANUAL

DEC-XV-GVTAA-A-D

XVM/DOS KEYBOARD COMMAND GUIDE

DEC-XV-ODKBA-A-D

XVM/DOS READERS GUIDE AND
MASTER INDEX

DEC-XV-ODGIA-A-D

XVM/DOS SYSTEM MANUAL

DEC-XV-ODSAA-A-D

XVM/DOS USERS MANUAL

DEC-XV-ODMAA-A-D

XVM/DOS VIA SYSTEM INSTALLATION GUIDE

DEC-XV-ODSIA-A-D

XVM/RSX SYSTEM MANUAL

DEC-XV-IRSMA-A-D

XVM UNICHANNEL SOFTWARE MANUAL

DEC-XV-XUSMA-A-D

PREFACE

FOCAL (Formula CALculator) XVM (FOCAL) is an interactive utility program designed to solve numerical problems of any complexity.

FOCAL

is a component of the XVM/DOS software system.
This manual is designed to allow the reader to master and apply the
FOCAL language within hours.
Chapters 1 through 3 of this manual describe the structure and use of
the FOCAL language (particularly in the formulation and solution of
numeric problems).
Chapter 4 contains demonstration programs which illustrate the many
features and applications of FOCAL.

The reader, by running these pro-

grams uSing different variables, can more fully realize the power and
flexibility of FOCAL.
Chapters 5 and 6 describe advanced user-library storage and retrieval
functions and user-defined FOCAL functions.

The FOCAL library func-

tions permit the storage of lengthy programs by the use of "chaining."
User defined functions enable frequently used operations to be called
(requested and performed) by a single command.
Chapter 7 describes FOCAL data functions which permit the user to
store and then retrieve data on auxiliary Input/Output devices other
than the console terminal.

vii

•

CHAPTER 1
INTRODUCTION TO FOCAL
FOCAL is an on-line, interpretive service program designed to assist
scientists, engineers, and students in solving complex numerical problems.

The language consists of concise, imperative statements;

mathematical expressions are typed in standard notation.
FOCAL puts the full calculating power and speed of the computer at the
user's fingertips.

With FOCAL, the user can easily generate mathe-

matical models, plot curves, solve sets of simultaneous equations in
n-dimensional arrays, and much more.

Examples of various problems

that FOCAL is capable of solving are described in Chapter 4.
1.1

HARDWARE REQUIREMENTS

FOCAL can be run on any XVM or PDP-1S computer which runs XVM/DOS software.
1.2

LOADING PROCEDURE

FOCAL may

be loaded with the Linking Loader after XVM/DOS has been

loaded.
After the bootstrap is loaded XVM/DOS types
XVM/DOS Vnxnnn

$
at the left margin of the console terminal.
The Linking Loader requires assignment of .DAT (Device Assignment)
Table) slots -1 and -4.

FOCAL requires assignment of .DAT slots +3,

+7 (input) and +S, +10 (output).
summarized in Appendix E.)

(.DAT slot assignments for FOCAL are

An example of the required ASSIGN command

is:
$A DPO -1,-4, <SCR> 3,S,7,10.)
On the device assigned to .DAT -1, the Linking Loader, expects to find
the System Library.1

On the device assigned to .DAT slot -4,the

Linking Loader expects to find the relocatab1e binary program, FOCAL
BIN and its external function file, FNEW BIN.

The user should be careful to use the non-floating point FORTRAN
library. If FOCAL is to be used on a system with floating point
hardware, the user should rename the non-floating point library to
.LIBRS BIN and assign .DAT -S to the UIC containing .LIBRS BIN.

1-1

Introduction To Focal

FOCAL uses .DAT slot +3 for the library input function and .DAT slot

+5 for the library output function (see Chapter 5 for FOCAL library
commands).

FOCAL uses .DAT slot +7 for DATA input function and .DAT

slot +10 for DATA output function.

(Refer to Chapter 7 for detailed

information about the DATA commands.)
An example for loading FOCAL follows.

After the .DAT slots are assigned as above, XVM/DOS types another $.
Now type
$GLOAD
and depress the RETURN key.
LOADER XVM

The Loader types

Vnxnnn or BLOADER XVM

Vnxnnn

Now type a P, a back arrow (P+), FOCAL, a comma and FNEW after the
Loader's >,
>P +FOCAL, FNEW
and depress the ALT MODE key.
Teleprinter output format is as follows:
XVM/DOS V1AOOO

$GL..DAD
BL. DADEI:;; XVM V1AOOO
>P ._.FDCAI..., FNEW
p FOCAl...
028 0"71"742
P FNEW
004 0 '7 1:"j:<,-7
p .BH
00~5 O}l473
007 0"71402
P D S OI:~T
001 0 "7 1367
P D~:;IN
002 07:1.:346
P DCO !:;
P DATAN
00:1. 0 7 :1. 3 :.3:3
P [lE XP
00:1. O? 1320
004 0"71 2 72
P DI...DG
006 Ol1.:l.24
F' .DD
004 071004
P .DB
00:3 0}O70:3
P .DE
001 0 7 0~)44
P .DF
001 0 07 047::j
P .DC
012 0 07 04 2 0
P .DA
p .CAll
000 0 "7 03~5:3
P DClUBLE 004 070:1.50
P HEI ... Et-.E lOP 06 07 0:5 :I.
0()4 06 07 0207
f" .Cf!

BFOCAI... XVM V1AO()O
1.3

RESTART PROCEDURE

Restart is accomplished by the use of CTRL P (echoes tP).

However

this may not work if it is typed while output is underway to the teleprinter.
1-2

Introduction To Focal
1.4

SAVING FOCAL PROGRAMS (Refer to Chapter 5 for full description)

To save the current FOCAL program, type the following sequence of
commands; where necessary, wait for FOCAL to type an * on the next
line.

*LIBRARY OUT NAME
*LIBRARY WRITE ·ERASE ALL
*LIBRARY WRITE ALL
*LIBRARY WRITE "*
*LIBRARY CLOSE

*
This sequence does not destroy the current program.

Execute an ERASE

ALL before starting the program to clear all variables and prevent
placing previous programs in the library along with the current program during current library storage (refer to Sections 3.5 and 5.4.2).
When a program is to be saved, Loader assignment must be to the proper
output device.

The assignment described in Section 1.2 will output the

program on DECtape.
To load a saved FOCAL program, type:
*LIBRARY IN NAME
1.5

DATA INPUT/OUTPUT (Refer to Chapter 7 for full description)

To use auxiliary I/O devices for data storage and retrieval, type the
following sequence of commands:
*DATA OUT NAME
*DATA CLOSE
*DATA IN NAME
This sequence will initialize and enter the named file for the data on
a mass storage device, close the named file on that device, and then
initialize a device under the given filename for data retrieval.

1-3

•

CHAPTER 2
FOCAL LANGUAGE
After FOCAL has been loaded, the program types out
FOCAL XVM Vnxnnn

*
to indicate that it is ready to accept commands from the user.

Each

time the user terminates a typed line by depressing the RETURN key, or
after FOCAL has performed a command, an * (asterisk) is typed to tell
the user that FOCAL is ready for another command.
2.1

ELEMENTARY COMMANDS

One of the most useful commands in the FOCAL language is TYPE 1 which
inst.ructs FOCAL to "type out the result of the following expression."
Then, the user types an expression after TYPE (following the asterisk
which FOCAL typed) such as
*TYPE 123.456+9.8765
and presses the RETURN key; FOCAL types the answer.
133.3325*
SET is another useful command, which instructs FOCAL to "store this
symbol and its numerical value; then when this symbol is used in an
expression, insert the numerical value."
*SET A=3.141592;

SET B=23.572;

Thus, the user may type

SET C=485.5

and then use these symbols to identify the values defined in the SET
command.
*TYPE A+B+C
512.2136*
Symbols may consist of one, two, or three alphanumeric characters.
The first character must be a letter, but must not be the letter F
which refers to function names (Refer to Section 3.16).

1Any number appearing in a TYPE command must have its magnitude represented in 35 bits of mantissa, otherwise, FOCAL will type the ?27
error message and ignore your request. This error message will occur
with an 11 or 12 digit or longer number, depending on the magnitude
of the number. The same is applicable for the ASK command.
2-1

Focal Language
FOCAL always checks user input for syntax errors (e.g., invalid commands, illegal formats, etc.).

When an error is detected, FOCAL types

an error message in the form of a question mark and code number to
indicate the type of error.

In the following example,

*:.t.
kHEL..P

no
HYPE 2++4
?2l

HELP is not a valid command and two plus signs (double operators) is
an illegal operation.

The complete list of error messages and meanings

is given in Appendix B.
2.2

OUTPUT FORMAT

The FOCAL program is originally set to produce results showing up to
eight digits, four to the left of the decimal pOint (the integer part)
and four to the right of the decimal point (the fractional part) •
Leading zeros are suppressed, and spaces are shown instead.

Trailing

zeroes are included in the output to the limits of the format, as
shown in the examples below •
.};

*SET A=77.77; SET B=111111.1111; SET C=39
*TYPE A,B,C
77.7700 111111.11
39.0000*

*
The output format may be changed if the user types

*TYPE %x.yz

Where the percent sign (%) is the format operator symbol,x is the
total number of digits to be output and yz is the number of digits to
the right of the decimal pOint.

The values x and yz are positive

integers, and the value of x cannot exceed 63 digits.
always written as a 2 digit number,

(e.g., 03).

The value yz is

For example, if the

desired output format is 2 places to the left of the decimal point and
five to the right, the user types
tTYPE %7.05. 12.222222+2.37184
and FOCAL types
/,..

',1.'

Y 14. :'.'j?406*

2-2

Focal Language
Notice that the format operator (%x.yz) must be followed by a comma,
and that until the user changes the output format all results will be
typed in the last specified format, i.e. %7.05.
The results are calculated to nine digits.

In some circumstances since

rounding may place some uncertainty on the 9th place, the user may
need to account for the rounding.

If the user types

It'

'lTYPE %9.04.

1.234~56. '7B9

FOCAL types
1. 234~.)f.). ?D?*
:+:

*
Of the 9 available digits, priority is given to those to the left of
the decimal point.
In the following examples, the number 2848.5363 is typed out in several
formats.
~<f:)FT A::::284B. ~~)36:'l)
*TYPE %7.03. A
2B4B. ~.'j36*
:+:TYPE %B.04. A
2B4B. ~5363:+:
*TYPE %9. O~:.). A
2B4B. ~:.'i3f.)3()*

*
If the user does not indicate the number of places in the fractional
part of the number, only the integer part is printed.
If the specified output format is too small to contain the integer
portion of the number, FOCAL converts the number to floating pOint
form,

O.LE+mn, where E+mn indicates the mnth power of 10 of the num-

ber L printed as a number between 0.0 and 1.0 (refer to Section 2.3).

•

**TYF'F %3. A
(). 2f:!~::jE+04*

*
If the specified format is larger than the number, FOCAL inserts
leading spaces up to, but not including, the asterisk column.

*TYPE %1 :1.. A
21:149*

Leading blanks and zeros in integers are always ignored by FOCAL,
except for numbers between 0.0 and 1.0, where a zero precedes the
decimal point ..
2-3

Focal Language

*
**rYPE
%8.04, 001 6 , 0. 0 16 v ., 007 0 0
16.0000

2.3

0. 0 160

0 . 0 000

700. 00 00*

FLOATING-POINT FORMAT

The user may request output in exponential form which is called floating-point or E format.

This notation is frequently used in scientific

computations and is the format in which FOCAL performs its internal
computations.

The user requests floating-point format by including a

% followed by a comma in a TYPE command.

FOCAL will print out 0, a

decimal point, a 9-digit number, the letter E, and the number of places
to move the decimal point for standard notation.

Until the user spec-

ifies another output format, all results are typed out in floatingpoint format.
For example,

*
*

*TYPE X,1111
O.111100000Et04*
is interpreted as .1111 times 10

or 1111.

Exponents can be used to

±999.

The largest number that FOCAL can handle is +0.999999983
998
times 10
, and the smallest is -0.999999983 times 10 999 .
If the absolute value of the exponent is 1000 or greater a colon (:)
will replace the higher order digits of the exponent.
of 1021 comes out as :21).

(An

exponent

For example, see the description of FEXP

in Section 3.16.
The user should furthermore note that for systems having EAE only
eight places of accuracy can be guaranteed for numbers larger than
1.0E43.

(In fact, for numbers near 1.0E+998 or 1.0E-999 you only get

7-place accuracy.)
To demonstrate the ability of FOCAL to compute large numbers, find the
value of 449 factorial by typing the following commands:
*S ET A= l
*FOR 1 =1.44 9 ; SET A=A* 1
* r YP E %.A
0.385 1 93052E t 998 *

The FOR statement, which will be explained later, is used to set I
equal to each integer from 1 to 449.
2.4

ARITHMETI~

OPERATIONS AND SYMBOLS

FOCAL performs the usual arithmetic operations (addition, subtraction,
multiplication, division, and exponentiation).
written by using the following symbols:
2-4

These operations are

Focal Language
SYMBOL
t

MATH NOTATION

Exponentiation

3t3 (Power must be a
positive integer)

* Multiplication

3'3

3*3

/ Division

3-:-3

3/3

equal

3+3

priority

3-3

+ Addition
}
Subtraction

These operations may be combined into expressions.

When FOCAL evalu-

ates an expression comprising several arithmetic operations, the priority follows the above list.
Note that addition and subtraction have equal priority.

Expressions

with these two operators are evaluated from left to right.
A+B*C+D is A+(B*C)+D not (A+B) * (C+D) nor {A+B)*C+D
A*B+C*D is (A*B)+(C*D) not A*(B+C)*D nor (A*B+C)*D
X/2*Y is

~
not ( : ) Y
2Y
2

2 t 2 t 3 is 4 3 not 2 8
To perform exponentiation to a negative power, X-A ,use FEXP{A*FLOG<X».
Expressions (except IF) to be evaluated by FOCAL may be enclosed in
any properly paired parentheses, square brackets, or angle brackets.
The IF statements, however, must be enclosed in parentheses .
For expressions without IF statements:
*SET Al

•

= (A+B)*<M+N>*[X+Y]

The left bracket ([) and the right bracket (]) enclosures which do not
appear on certain teletypewriter keys are typed using the SHIFT and K
keys and the SHIFT and M keys, respectively.
For expressions that are nested, FOCAL computes the value of the innermost expression first and then works outward.
*TYPE %,

(2+ < 3 - [1 * 4] + 5 > - 2)

O.400000000F+OI*
Note that this number is expressed in floating-point format, as specified by the unmodified % symbol.
2.5

ADDITIONAL SYMBOL INFORMATION

The value of a symbolic name or identifier is not changed until the
expression to the right of the equal sign is evaluated by FOCAL.
Therefore, before it is evaluated, the value of a symbolic name or
2-5

Focal Language
identifier can be changed by retyping the identifier and assigning
it a new value.
*SET Al=3t2;
*TYPE

SET Al=Al+l

%2, Ai

10*
Symbolic names or identifiers must not begin with the letter F.
(Refer to Section 3.16)
The user can request FOCAL to type out all user defined identifiers,
in the order of definition, by typing a dollar sign ($) after a TYPE
command.
*TYPE

(Refer to Section 3.1)
%7.2,$

The user's symbol table is typed out in the following manner:
A@@(OO)=
8@@(00)=
C@@(OO)=
K@@(OO)=
I@@(OO)=
Al@(OO)=
M@@ (OO)=
N@@( OO)=
X@@(OO)=
Y@@(OO)=

0.3851931E+998
111111.1
39.00000
0.000000
450.0000
10.00000
0.00 0000
0.0 0 0000
0.000000
0.000000

NOTE
"A" and "I" defined in a previous example (on page
2-3) were not erased before going on to the present
example.
If an identifier consists of less than three letters, an @ is inserted
as the second/third character in the symbol table printout, as shown
in the example above.

An identifier may be longer than three char-

acters, but only the first three are recognized by FOCAL and stored
in the symbol table.
2.6

SUBSCRIPTED VARIABLES

FOCAL always allows identifiers, or variable symbols, to be further
identified by Single subscripts in the range ±131071 (2 17 _1), which
are enclosed in parentheses immediately following the identifier.
For example, the following identifiers are subscripted:
A(I)

B(3)

A subscript may also be an expression:
*SET Al(I+3*J)=2.33
*SET X2(S+3*J)=8.20

2-6

Focal Language
The ability of FOCAL to compute subscripts is especially useful in
generating arrays for complex programming problems.

A convenient way

to generate linear subscripts is shown in Section 4.5.
2.7

THE ERASE COMMAND

To delete all of the symbolic names which are defined in the symbol
table, except those in the COMMON area (refer to Section 5.4), type
ERASE.

As FOCAL does not clear the user's symbol table area in core

memory when it is first loaded, it is good programming practice to type

an ERASE command before defining any symbols .
2.8

HANDLING TEXT OUTPUT

Text strings are enclosed in quotation marks (" ... ") and may include
most teletypewriter printing characters and spaces.

The carriage

return, line feed, and leader-trailer characters are not allowed in
text strings.

To instruct FOCAL to type an automatic carriage return

line feed at the end of a text string, the user inserts an exclamation
mark (1).
*TYPE"ALPHA" 1 "BETA" 1 "GAMMA" 1
ALPHA
BETA
GAMMA

*
If only a carriage return without a line feed is desired at the end of
a text typeout, the user inserts a number sign (#).
*TYPE

X Y Z"#"

=11#11

/"1

X+Y = Z

*
The number sign operator is useful in formatting output and in plotting
another variable along the same coordinate (Refer to Section 4.7).
2.9

INDIRECT COMMANDS

Up to this point, only direct commands, executed immediately by FOCAL,
have been discussed.

In contrast, commands may be delayed to alter

sequences, assign all variables or generate a lengthy program.

These

delayed execution statements are called indirect commands which are
prefixed by a line number and are stored by FOCAL for later execution,
usually as part of a sequence of commands.
range 1.01 to 99.99.

Line numbers must be in the

The number to the left of the point is called

the group number; the number to the right is called the step number.
(The numbers 1.00, 2.00, etc., are illegal line numbers; they are used
to indicate an entire group of lines.)

2-7

For example,

Focal Language

1'<
.,K

.:; F I'i (1 ~:; I. ,<\ L L
>i J "I

c:;[ r

(1 <'~

p",n
*l.J TYP[ %2. AtB
*1.,'::"

!'~[T

»:
To execute indirect commands the user types one of the direct commands GO, GOTO, and DO.

The GO command causes FOCAL to go the lowest numbered line to begin
executing the program.

If the user types a direct GO command after

the indirect commands above, FOCAL will start executing at line 1.1.
,GO

11*

The GOTO command causes FOCAL to start the program by executing the
command at a specified line number.
:+UOTO 'I.. ::.:.'
I.:!

FOCAL started executing the program at line,

1.2 SET B=8,

in the above

example, and then continued to line 1.3.
The DO command is used to transfer control to a specified step, or
group of steps, and then return automatically to the command following
the DO command.
).,1:

)j(FR,~SE

ALI

*1.1 SFT A=l;SET B=2
*1.2 TYPE
STARTING·
1.:5

)I(

[II)

~;; .,'

*2.1 TYPE' FINISHED'
*3.1 SET A=3; SET B=4
*3.2 TYPE %1, AtB
*GO

STARTING

FINISHED

*
When the DC command at line 1.3 was reached, the command TYPE %1, A+B
was performed and then the program returned to line 2.1 and continued
-[ L'om there.

ThE' DO cormnand can also cause FOCAL to jump to a group of commands and
~hen

return automatically to the normal sequence.

2-8

•

Focal Language

*ERASE ALL
*1.1 TYPE "A"
*1.2 TYPE "B"
*1.3 TYPE "C"
*1.4 DO 5.0
*1.5 TYPE" END "; GOTO 6.1
*5.1 TYPE "D~
*5.2 TYPE "E"
*6.1 TYPE "."
*GO
ABCDE END .*

*
When the DO command at line 1.4 was reached, FOCAL executed the group 5
lines and then returned to line 1.5.

An indirect command,

with the

proper sequential line number, can be inserted in a program at any time
before the direct execute command.

For example,

**ERASE ALL
*4.8 SET A=1; SET B=2
*6.3 TYPE %8.3, B/C+A
*4.9 SET C=3.4581
*GO
1.5783523*
where line 4.9 will be executed before line 6.3 and after line 4.8.
FOCAL arranges and executes indirect commands in numerical sequence
by line number.
2.10

ERROR DETECTION

FOCAL checks all input commands for a variety of errors.

If an error

is detected, FOCAL types a question mark, followed by an error code
and the appropriate line number if the error is in an indirect command.

A complete list of these error codes is shown in Appendix B.

The WRITE command without an argument causes FOCAL to print out the
entire indirect program so that the user may check it for errors.
The trace feature of FOCAL is valuable in program debugging.

Any

part of an indirect statement or program can be enclosed in question
marks, and when that part of the program is executed, the portion
enclosed in question marks will be printed out.

If only one question

mark is inserted the program is printed out from that point until
completion.

The trace feature is also used to follow program control

and to create special formats
2.11

(Refer to Section 3.15).

CORRECTIONS

If the user types the wrong character, or several wrong characters,
the RUBOUT key, which echoes a backs lash (') for each RUBOUT typed,
is used to delete one character to the left each time the RUBOUT key
is depressed.
2-9

Focal Language

*ERASE ALL..

*1.1 RYPE\\\\TYPE X-Y
*1.2 SET X=:12\3
*WRITE

C FOCAL XVM V1AOOO
01.10 TYPE X---Y
01 .20 BET X::: 1 :-5

Typing CTRL U (echoes an @) deletes everything which appears to its
left on the same line.
*1.3 TYPE A,B,C@
*WRITE

...

C FOCAL XVM V1AOOO
01.10 TYPE X--Y
01.20 SET X==:L3

A line can be overwritten.
new command.

Repeat the same line number and type the

For example, the second instance of line 14.99 replaces

the first:

*14,';'9

~:;ET

C9(N+3)"::I.~::j

*
*
:1<

*
*14.?? TYPE C9/Z~)---2
*WRITE :1.4.99
14.'Y9 TYPE C9/Z~_:_i----2

When WRITE is typed after corrections are made, FOCAL will print the
indirect program as altered.

With this feature, commands can be

checked and a "clean" program printout can be obtained.
all indirect input is printed when WRITE is typed.

Therefore, it is

useful to type ERASE ALL at the start of a new sequence.
Chapter 5 for storing programs.)

Remember that
(Refer to

The ERASE command with an argument

will delete a line or group of lines.

For example, to delete line

2.21, the user types

**ERASE
*

2.21

2-10

Focal Language
To delete all of the lines in group 2, the user types

**ERASE 2.0
*
Used alone, without an argument, the ERASE command causes FOCAL to
erase the user's entire symbol table.

FOCAL does not zero memory

when loaded; consequently, it is good practice to type ERASE before
defining symbols.

The command ERASE ALL erases all user input, except

COMMON variables.
The MODIFY command is another valuable feature.
change any number of characters in

It may be used to

a particular line, as explained

in Section 3.14.
2.12

ABBREVIATIONS

All FOCAL commands (except COMMON and DATA) may be abbreviated to the
first letter of the command.

Thus,

*TYPE 10,!
0.lE+02

*
is equivalent to

**T 10,!
0.IE+02

*
2.13

ALPHANUMERIC NUMBERS (Using Letters as Numbers)

Numbers must start with a numeral but may contain letters.

FOCAL

interprets as a number any character string beginning with a numeral
(0 through 9).

An alphanumeric number is a string of alphanumeric

characters (excluding symbols) which starts with a numeral.

For

example,

**OABC

23BAT

2836Al

?02

Each letter in an alphanumeric number is taken as a number (A through

Z correspond to 1 through 26, respectively) except for E (which denotes
exponentiation) .

2-11

Focal Language

NOTE
E denotes exponentiation; consequently, the number 5
cannot be represented in alphanumeric form.
A=l
B=2
C=3
D=4
E=(exponentiation)
F=6
G=7
H=8
1=9
An

J=10
K=ll
L=12
M=13
N=14
0=15
P=16
Q=17
R=18

S=19
T=20
U=21
V=22
W=23
X=24
Y=25
Z=26

easy way to give FOCAL numerical valued letters is to start the

o
•

number with 0, as in the following example.

*TYPE %.OA[l
0.120000000E+02*

After 0, A=l and B=2; thus, OAB=12.

Alphanumeric characters may be

used in arithmetic operations.
,.

::<TYPE %. OAIHOC
0.150000000E+02*

The letter E denotes exponentiation to base 10 when used in a number.
Alphanumerics after the letter E are taken as the exponent of the
preceding alphanumerics.
Only one E is allowed in anyone alphanumeric number.

*
**TYPE

~:'O,()AEn

10000*
*1YI::'[ %B, OSEe

19000*

*
*
*
Alphabetic characters may be used when assigning numerical values to
identifiers or variables in response to an ASK statement (Refer to
Section 3.9 for a use of this feature and lines 3.20 and 3.30 of
"Intercept and Plot of Two Functions" "in Section 4.7 for an application).

2-12

CHAPTER 3
FOCAL COMMANDS

3.1

TYPE

The TYPE command is used to compute and type out a text string, the
result of an expression, or the value of an identifier.

For example,

*
**4.15 TYPE
*4.14
3.2*6-(36.2*65)/2.348
TYPE
*
*

3~6+(7.23/4.2753)*73.4

Several expressions can be computed by a single TYPE commandi commas
are used to separate each expression.

*1.1 TYPE ~6.03, A1*2, 2~12, 2.28*83.636
*no 1.1
0.000 4096.00 190.690*

*
*

The output format (%) can be included in the TYPE statement as shown
in the example above and as explained in Section 2.2.
The user may request a typeout of all identifiers which he has defined
by typing TYPE $ and pressing the RETURN key.

This causes FOCAL to

type out the identifiers with their values, in the order in which they
were defined.

The $ can follow other statements in a TYPE command,

but must always be the last operation on the line.

*
*

*ERASE ALL
*SET L=33; SET B=22; SET Q=385
*SET A3=94.3; SET A7T=2.485
*TYPE ~5.03,$
l.@(H 00) = 33.000
B@@(OO)= 22.000
Q@@(OO)= 385.00
A3@(00)= 94.300
A7T(00)= 2.485

3-1

Focal Commands
A text string enclosed in quotation marks can be included in a TYPE
command, and a carriage return can replace the closing quotation mark:

*TYPE ·X SQUARED
X SQUARED*

*
A text string or any FOCAL command or group of commands cannot exceed
1
the capacity of a teletype line (72 characters for KSR33 Teletype ).
A command cannot be continued on the following line.

To print out

extended text, each line must start with a TYPE command.
FOCAL does not automatically perform a carriage return after executing
a TYPE command.

To insert carriage return-line feed characters type

an exclamation mark (1).

To insert a carriage return without a line

feed, type a number sign (#).
tation marks.
3.2

To insert spaces, enclose them in quo-

These operations are useful for format output.

ASK

The ASK command is normally used in indirect commands to allow the
user to input data at specific points during the execution of the program.

The ASK command is written in the form:

*11.99 ASK X.Y.Z,

*
When step 11.99 is encountered by FOCAL, it types a colon (:).

Then,

the user types a value in any format for the first identifier, followed
by a carriage return or ALT MODE.
on the same line.

The ALT MODE key continues the text

FOCAL then types another colon, and the user types

a value for the second identifier.

This continues until all the iden-

tifiers or variables in the ASK statement have been given values.
*11.99 ASK X,Y,Z
*DO 11.99

:4:4:8*

*
*
*
In the above example, the user typed 4,4 and 8 as the values, respectively, for X,Y,Z.
FOCAL recognizes each value when its terminator (i.e., carriage return
or ALT MODE) is typed.

Therefore a value can only be changed before

its terminator is typed.

This is done by using RUBOUT or CTRL U.

1Teletype is a registered trademark of the Teletype Corporation.

3-2

Focal Commands
A text string can be

in~luded

in an ASK statement if the string is en-

closed in quotation marks.

**
*ERASE ALL
*1.1 ASK "HOW MANY APPLES DO YOU HAVE?" APPLES
*DO 1.1
HOW MANY APPLES DO YOU HAVE?:25
*TYPE APP
2~j. 000*

*
The identifier APP (FOCAL recognized only the first three characters
of the identifier APPLES.) now has the value 25.
will equal 25.

When APP is used, it

Its value may be reassigned if it is asked for again.

*
*

*ERASE ALL.
*ASI, APP
:30

*TYPE APP
30.000*

Alphabetic characters can be used if numerical values are assigned to
identifiers or variables:

*1.1 ASK A; TYPE %4,A
*DO 1.1
:ABCD
1234*

*
*
*
*
When the user typed ABCD and RETURN, FOCAL typed the numerical value
of ABCD (Refer to "Alphanumeric Numbers", Section 2.13).
Alphabetic responses are especially useful for keyboard responses to
FOCAL statements.

A YES or NO answer can be typed by the user during

program execution in response to a program question, as explained in
Section 3.9.
3.3

WRITE

A WRITE command without an argument causes FOCAL to write out all
indirect statements which the user has typed.

Indirect statements

are those preceded by a line number.
A group of line numbers, or a specific line, can be typed out with the
WRITE command using arguments, as shown below.
:+:7.97 WFnTE 2.0
*7, ';>8 WF,ITE 2.1
*7.9';> WRITE

*
3-3

Focal Commands
3.4

SET

The SET command is used to define identifiers.

When FOCAL executes

a SET command, the identifier and its value, are stored in the user's
symbol table.

When the identifier is encountered in the program, the

value is substituted for the identifier.

**ERASE AL.L.
*4.1 SET A=394.83; SET B=4.373
*4.2 TYPE :r.,AtB
*GO
0.399203000Et03*

**
*

An identifier can be set equal to previously defined identifiers,
which, can be used in arithmetic expressions.

*
*

*3.7 SET

3.5

G=(A+B)*2~6

ERASE

An ERASE command without an argument is used to delete all identifiers
and their values except those in COMMON (Refer to Section 5.4 for the
ERASE COMMON command.) from the symbol table.
If the ERASE command is followed by a group number or a specific line
number, a group of lines or a specific line is deleted from the program.

*ERASE 2.0
*ER,~SE 7. 11

*
The ERASE ALL command erases all the user's input.

In the following

example, an ERASE command is used to delete line 1.50.

*ERASE AL.L
U.2 SET B=2
U.3 SET C=34
U.4 TYPE BtC
U.5 TYPE C-B
*ERASE 1.5
*WRITE
C FOCAL V3AOOO
01.20 SET B=2
01.3() SET C=34
01.40 TYPE BtC

3-4

Focal Commands
The ERASE ALL command is generally used only in immediate mode because
it returns to command mode upon completion.
3.6

The GO command is used to execute the program which starts with the
lowest numbered line.
number sequence.
3.7

The remainder of the program is executed in line

Line numbers must be in the range 1.01 to 99.99.

GOTO

The GOTO command causes FOCAL to transfer control to a specific line
in an indirect program.

It must be followed by a specific line number.

After executing the command at the specified line, FOCAL continues to
the next higher line number, executing the program sequentially.

**
**ERASE Al.l.

*1.1 TYPE "A"
*1.2 TYPE "B"
*1.3 TYPE "C"
U.4 TYPE "[I"
*GOTO 1

.. .
'0)

3.8

The DO command transfers control momentarily to a single line, a group
of lines, or an entire indirect program.

If transfer is made to a

Single line, the statements on that line are executed, and control is
transferred back to the statement following the DO command.

Thus, the

DO command makes a subroutine of the lines to which control is transferred, as shown in the following example:

*
*

*ERASE Al.L
*1.1 TYPE "F"
*1.2 [10 2.3; TYPE "C"
*1.:3 TYPE "A"
*1.4 TYPE "l."
U.5 (WIT

*2.:3 TYPE "a"
*GO
FOCAl.*

*
**
If a DO command transfers control to a group of lines, FOCAL executes
the group sequentially and returns control to the statement following
the DO command.

3-5

Focal Commands
If DO is written without an argument, FOCAL executes the entire indirect program in the same manner as a GO command.
DO commands cause specified portions of the indirect program to be
executed as closed subroutines.

These subroutines can also be ter-

minated by a RETURN command.
A GO TO or an IF statement within a DO subroutine modifies the program
execution sequence.
3.9

To transfer control after a comparison, FOCAL contains a conditional
IF statement in the form IF (m)x,y,z; m is an expression or variable,
and x,y,z,are three line numbers.

The expression is evaluated, and

the program transfers control to the first number, x, if the expression
is less than zero; to the second line number, y, if the expression
equals zero; or to the third line number, z, if the value of the expression is greater than zero.

*
*

* 2. 1 TYPE "LESS THAN ZERO"; QUIT
* 2. 2 TYPE "EQUAL TO ZERO"; QUIT
* 2 .3 TYPE "GREATER THAN ZERO"; QUIT
*IF (25- 25 ) 2 .1 .2 .2~2 . 3
EQUAL TO ZE RO*

*
*
In the above example, the parenthetical expression equals zero; consequently, line 2.2 is executed.

Note that an IF statement must be

enclosed in parentheses.
The IF statement can be shortened by terminating it with a semicolon
or carriage return after the first or second line number.

If a semi-

colon follows the first line number, the expression is tested, and
control is transferred to that line if the expression is less than
zero.

If the expression is not less than zero, the program continues

with the next statement.

*
*

*2.20 IF(X)1.8;TYPE ·C·
In the above example, when line 2.20 is executed, if X is less than
zero, control is transferred to line 1.8.

3-6

If not, C is typed out.

Focal Commands

*3.19 IF(B)1.8,1.9
*3.20 TYPE B

*
*
In the above example, if B is less than zero, control goes to line 1.8,
if B is equal to zero, control goes to line 1.9.

If B is greater than

zero, control goes to the next statement (in this case, line 3.20), and
the value of B is typed.
In programs that require a keyboard response (as in Section 4.7 line
3.2), it is useful to determine if the answer by the user to an ASK
question is YES or NO.

Alphabetic responses used with an IF statement

permit one of two possible commands to be executed, depending on the
user's answer.

For example:

IF (answer-OYes)1.1,2.1,1.1
where answer is YES or NO, as typed by the user.

The next command

depends on whether answer is YES (in which case, answer-OYES equals 0,
and line 2.1 is executed) or NO (producing a nonzero result and moving
program execution to line 1.1).
For example,
*1.1 TYPE "DO YOU WANT A LINE?",!
*1.2 ASK "TYPE YES OR NO",ANS,!
*1.3 IF (ANS-OYES) 2.1,2.2,2.1
*2.1 QUIT
*2.2 TYPE "-------------------",!
*2.3 GOTO 1.1
*GO
DO YOU WANT A LINE?
TYPE YES OR NO:YES
DO YOU WANT A LINE?
TYPE YES OR NO:NO
If a GOTO or an IF command is executed within a DO subroutine, two
actions are possible:
a. If a GOTO or IF command causes transfer to a line inside the

DO group, the remaining commands in that group are executed as in
any subroutine before returning to the command following the DO
command.

3-7

Focal Commands
b. If transfer is to a line outside the DO group, that line is
executed and control is returned to the command following the DO
command unless that line contains another GOTO or IF.

**ERASE ALL

*1.1 TYPE "A"; SET X=-l; DO 3.1; TYPE "D"; DO 2
*1.2 DO 2.0
*2.1 TYPE "G"
*2.2 IF (X) 2.5,2.6,2.7
*2.5 TYPE "H"
*2.6 TYPE "I"
*2.7 TYPE "J"
*2.8 TYPE "K"
*2.9 TYPE % 2.01,X; TYPE" "; SET X=Xtl
*3.1 TYPE "B"; GOTO 5.1; TYPE "F"
*5.1 TYPE "C"
*5.2 TYPE "W"
*GO
ABCDGHIJK-l.0 GIJK 0.0 GJK 1.0 BCW*

*
**
*
*
3.10

RETURN

The RETURN command is used to exit from a DO subroutine.

When a

RETURN command is encountered during execution of a DO subroutine,
the program exits from its subroutine status and returns to the command following the DO command that initiated the subroutine status.
3.11

QUIT

A QUIT command causes the program to halt and return control to the
user.

FOCAL types an asterisk and the user can type another command.

3.12

COMMENT

Beginning a command string with the letter C (except for COMMON) will
cause the remainder of that line to be ignored to allow insertion of
comments into the program.

Such lines are skipped over when the pro-

gram is executed, but are typed out by a WRITE command.

A program

that is well documented with comments is more meaningful and easier
to understand than one without comments.
3.13

FOR

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

The general format is

*FOR A=B,C,D; (COMMANDS)

3-8

Focal Commands
The identifier A is initialized to the value B.

Then, the commands

following the semicolon up to the line terminator are executed.

When

the commands have been executed, the value of A is incremented by C
and compared to the value of D.

If A is less than or equal to D, the

commands after the semicolon are executed again. This process is repeated until A is greater than D; then, FOCAL goes to the next sequential line.
The identifier A must be a single variable.
expressions, variables, or numbers.

B,C, and D can be either

If a comma and the value Care

omitted, it is assumed that the increment is one.

If C,D is omitted,

it is handled like a SET statement and no iteration is performed.
The computations involved in the FOR statement are done in floatingpoint arithmetic, and it may be necessary, in some circumstances to
account for this type of arithmetic computation.
Example 1 below is a simple example of how FOCAL executes a FOR command.

Example 2 shows the FOR command combined with a DO command.

Example l:

*ERASE ALL
*3.11 SET A=383.383
*3.12 FOR B=20,10,70; TYPE
*60
B IS
403.383
B IS
413.383
B IS
423.383
B IS
433.383
B IS
443.383
B IS
453.383

~7.03,

**
Example 2
*1.1 FOR X==1,2.9; [10 2.0
*1.2 GOTO 3.1
-i!5, "X" X
*2.1 TYPE ! "
*2.2 SET A==X+100.00
"~5,
"A" A
*2.3 TYPE I "
*3.1 QUIT
*60
X
A
X
A
X
A
X
A
X
A

1
101
3

103
5
105
7

107
9
109*

3-9

"B IS " BfA,!

Focal Commands

If two FOR statements are put on one line, the second FOR statement
is performed in full for each incrementation in the first FOR statement.

Any number of FOR statements may appear on one line.

3.14

MODIFY

Frequently, only a few characters in a particular line require changes.
To facilitate this job, and to eliminate the need to replace the entire line, FOCAL has

a MODIFY command.

For example, to modify the

characters in line 5.41, the user types MODIFY 5.41 and then depresses
the RETURN key.

The program then waits for the user to type the char-

acter he wishes to modify.

After the user has typed the search char-

acter, the program types out the contents of that line until the search
character is typed.
At this point, the user has seven options:
a.

Type in new characters in addition to the ones that have
already been typed out.

Type ALT MODE to continue the search to the next occurrence,
if any, of the same search character.

To change the search character, type CTRL BELL and the new
search character as at the beginning of the MODIFY command.

Use the RUBOUT key to delete one character to the left each
time RUBOUT is depressed.

Type a CTRL U to delete the line over to the left margin,
but not the line number.

Type carriage return to terminate the line at that point,
removing the text to the right.

Type a LINE FEED to save the remainder of the line.

3-10

Focal Commands
The MODIFY command is generally used only in immediate mode because it
returns to command mode upon completion.
During command input, CTRL U deletes the line numbers as well as the
text if the CTRL U is the right-most character on the line.

However,

when using the MODIFY command the line number is not deleted by the
use of CTRL U.

Note the error in line 7.01.

*7.01 JACK AND HILL WRNT UP THE GILL
*MODIFY 7.01
H JACK AND H\JRIll WR\EGNT UP THE G\H
ILL
*WRITE 7.01
07.01 JACK AND JILL WENT UP THE HILL
*ERASE ALL

*
~

To modify line 7.01, the user typed an H to indicate the character to
be changed.

FOCAL stopped typing when it encountered the search

character H.

The user typed the RUBOUT key to delete the H, and then

typed the correct letter, J.

The user then typed the CTRL BELL key

followed by the R, the next character to be changed.

The RUBOUT

deleted the R and the user typed E.

was made (this

Again

time for the G), and the G was changed to H.

a search

The user typed a line

feed to save the remainder of the line.
When the MODIFY command (or another command which alters the stored
indirect program) is used, the values in the user's symbol table
(except those defined as COMMON) are reset to zero.

Therefore, if

the user defines his symbols in direct statements and then uses a
MODIFY command, the values of his symbols are erased and must be redefined.
However, if the user defines his symbols by indirect statements prior
to using a MODIFY command, the values are not erased because these
symbols are not entered in the symbol table until the statements
defining them are executed.
In the following example, notice that the values of Y and Z were set
using direct statements.

The use of the MODIFY command resets their

values to zero and lists them after the defined symbols:

3-11

Focal Conunands

*ERASE ALI...
*SET Z=9
*SET Y=8
U.1. SET X=::3
*1..2 SET W::::4
*1.3 TYPE W+X+Y+Z; TYPE!; TYPE $
*MODIFY 1..1.
S SET X::::5

X@(~ (O(»

::::

W@(~ (O(»

:":

Y(~(~ (00) ::::

()

zr~)(() (O(»

()

:":

*
*
3.15

USING THE TRACE FEATURE

As noted in Section 2.10, the trace feature is useful in checking an
operating program.

Those parts of the program which are enclosed in

question marks are printed out as they are executed.
In the following example, parts of three lines are printed.

*
**ERASE ALL
U.1 SET A=2
U.2 SET 8=5
U.3 SET C=3
*1.4 TYPE ~2, ?A+B-C?,!
*1.5 TYPE ?8+A/C?,!
*1.6 TYPE ?8-C?
*1.6 TYPE ?B-C/A?
*60

A+B-C
B+A/C
B-C/A

4
6

*
Also, GO? will trace the program starting with the lowest numbered
line, provided no other question marks are present in the program.

3-12

Focal Commands
3.16

INTERNAL FUNCTIONS

The internal functions provide extended arithmetic capabilities.
defined external functions are described in Chapter 6.

User

A standard

function call consists of four letters, beginning with the letter F,
and followed by a parenthetical expression.
The following are the internal functions:
a.

The square root function (FSQT) computes the square root of
the expression within parentheses.

*
**TYPE %,FSQT(43.489)
0.659461902E+Ol*
*TYPE FSQT(2.333)
0.152741612E+Ol*
*TYPE FSQT (371. 8)
0.609754049E+02*

**
b,

The absolute value function (FABS) outputs the absolute or
positive value of the number in parentheses.

*
*
*TYPE
%, FABS(-394)
0.394000000E+03*
*TYPE FABS (""-.93)
0.930000000[+00*
*TYPE FABS(73)
0.730000000E+02*

*
*
c.

The sign part function (FSGN) outputs the sign part (+ or -)
of a number and the integer part becomes a 1.
sidered a positive number.

*TYPE %. FSGN(-283.3)
-0.100000000E+Ol*
HYPE FSGN(O.OO)
0.100000000E+Ol*
*TYPE FSGN(-0.38)
-0.100000000E+Ol*

*
**
*

3-13

Zero is con-

Focal Commands
d.

The integer part function (FITR) outputs the integer part of
a number up to ±131071(2 17 _1).

*
*

*TYPE %,FITR( - 34.8)
- 0 . 340000000E+02*
*TYPE FITRCO.73)
O.OOOOOOOOOE+OO*
*TYPE FITR(374.92)
0.374000000E+03*

*
**
The random number generator function (FRAN) computes a nonstatistical pseudo-random number between -1 and +1 (most
numbers fall in the range 0 to +1.).

Another random number

generator function (FRNO) is provided in the external function
file FNEW and is described in Section 6.2.

*
**TY PE %, FRAN( )
0.719269147E - 02*
*TYPE FRANC )
0.549454402E-01*

**
*
f.

The exponential function (FEXP) computes e

(e=2.718281) to

the power within parentheses.

*
**
*TYPE Z, FEXP(27)
0.532048241E+12*
*TYPE FEXP(2.348)
0.104646196E+02*
*TYPE FEXP (0.374)
0.145353715E+01*

*
**
In floating-point format (%) you only get correct results for
FEXP(X) if

2300?X~-2302.

If X is not between these limits the expon-

ent of the result will not be between ± 999, and a colon will replace
its high order digits as described in Section 2.3.
Example:
*T FEXP (23 00)0.7538907IE+999*
*T FEXP (2301)0.20492876E+:00

3-14

Focal Commands
The 727 error message does not appear as it applies only to mantissas
with more than 35 binary bits (11 or 12 decimal digits) while the above
limitation relates to exponents, not mantissas.
g.

The sine function (FSIN) calculates the sine of an angle
expressed in radians.
)I(

*
**TYPE
Z, FSINC3.10)

0.415806618E-01*
*TYPE FSINCO.278)
0.27443::.'<?86E+OO*
*TYPE FSINC1.272)
O. 9~:j!::j691 !::i07E+OO*

**
FOCAL requires that angles be expressed in

radians~

thus, to find a

function of an angle in degrees, the conversion factor n/180, must be
used.

To find the sine of 10 degrees:

**SET PI =3.14159; TYPE rSINC10*PI/180)
O· 1 736 4D033E+OO*

The cosine function (FCOS) calculates the cosine of an angle
expressed in radians.

*TYPE %.
FCOSC2*PI)
O.100000000E+01*
*TYPE FCOS(.3628)
0.934?06 7 B9E+OO*
>nYPE FeDS Cj, .:37)
().19 9 44<17211::+00*

*
i.

The arctangent function (FATN) calculates the angle in radians
the tangent of which is the argument within parentheses.
tTYPE %. FATNC1.000)
(). 7B5~598164E +()O*
.TYPE FATNC23.44)
O.15 2 816007E+01*
*TYPE FATNCO.728)
0.629271798E +00*

()

j .

The logarithm function (FLOG) computes the natural logarithm
(loge) of the number within parentheses.
*TYPE %, FLOG(238.48467)
o 547430!,)03E+OU
*TYPE FLDGCO.2876)
- 0.124618465E+Ol*
*TYPE Fl..DGC1.23)
O.207014169E+00*
t

3-15

•

CHAPTER 4
EXAMPLES OF FOCAL PROGRAMS
4.1

TABLE GENERATION USING FUNCTIONS

The ability to evaluate simple arithmetic expressions and to generate
values with the aid of internal functions is one of the first benefits
to be derived from learning the FOCAL language.

In the example that

follows, a table of sine, natural logarithm, and exponential values
is generated for a series of arguments.

As the user becomes more

familiar with these functions, he can easily combine them with standard arithmetic operations and evaluate any given formula for a single
value or for a range of values.
In this example, line *1.01 outputs the desired column headings.
Line *1.10 is the loop to generate values for I, beginning with the
value 1.00000000 and continuing in increments of .00000010 through the
value 1.00000100; the DO 2.05 command at the end of this second line
causes the various functions to be executed for the I arguments.

The

output format %9.08 in line 2.05 specifies that all output results up
to the next % symbol are to appear in fixed-point format with one digit
position to the left of the decimal point and eight digit positions
to the right; the second % symbol reverts the output mode back to
floating point for the remaining values FLOG and FEXP.Line 01.20
(optional) returns control to the user.
The following techniques are apparent in line *2.05 of this example:
a.

FOCAL commands can be abbreviated to the first letter of the
command followed by a space, as shown by the use of T instead
of TYPE.

This technique can be used to shorten command

strings.
b.

Arguments can be enclosed in various ways.

This feature is

useful in matching correctly when a number of enclosures
appear in a command.
c.

Spaces can be inserted in an output format by enclosing the
appropriate number of spaces within quotation marks.

This

procedure is recommended to improve the readability of the
output results.
d.

The use of very small loop increments (in this example
.0000001) eliminates the need to interpolate between table
values of trigonometric functions.

FOCAL is usually accur-

ate to eight significant digits but rounding in certain cases
may place some uncertainty on the 8th place.

Thus, the user,

in some circumstances, may need to account for the rounding.

4-1

Examples Of Focal Programs
*1.01
*1.10
*1.20
*2.05

T"
I
SINE
LOG
FOR I=1,.0000 001, 1 .0000 01; DO 2.05
QUIT
T %9 . 08,I,· ",FSINCI)," ",%,FLOG< I) • ",FEXPEIJ.l

I
1.00000000
1.00000010
1.00000020
1.00000030
1.00000040
1.00000050
1.00000060
1.00000070
1 . 00000080
1.00000090
1.00000100

SINE
0.84147099
0.84147104
0.84147109
0.8 414 7115
0.84147120
0.84 1 47126
0.84 14 713 1
0.8 414 7136
0.84147142
0.84147147
0.84 1 47153

LOG
0.806929521E-10
0.999785677[-07
0.199 8 76442 [-06
0.2997339 7 1E-06
0.399631845[-06
0.499529720[-06
0 .59 9427595E-06
0.69 92851 23[ -0 6
0.799182998[-06
0.899040526[-06
0.998978747[-06

[" 1

0.27 1 828183E+01
0.27 1828210Et01
0.271828237E+01
0.271828264Et01
0.271828292[t01
0.271827319Et01
0.271828346E+01
0.271828373[t01
0.271828400[+01
0.271828427[+01
0.271828454 [+0 1

4.2

FORMULA EVALUATION FOR CIRCLES AND SPHERES

In this example, FOCAL is used to calculate, label, and output geometric values for an indefinite number of radii typed in by the user.
Given a radius, R, FOCAL can calculate such values as:

circle diameter: 2R

circle area: nR

circle circumference: 2nR

d.
e.

3
sphere volume: 4nR /3

sphere surface area: 4nR

Although inches are used in this example, conversions to other systems
(metric, for example) could be easily incorporated into the program,
without the need for hand-calculated conversions.
The program is very straightforward.

ASK is used to allow the user to

type in the radius value to be used in the calculations.
to supply the value of n.
put.

SET is used

TYPE is used for all calculations and out-

If a value (e.g., nin this example) is to be entered once and

then used in repeated calculations, it should be entered by a SET
command which is outside the calculation loop; otherwise, the variable
must be set at the beginning of each pass through the loop.

If the

value of the variable changes during each iteration, however, then it
must be calculated either by a SET or TYPE command within the loop.
The use of the GOTO command (line *1.50) results in an infinite loop
of lines *1.10 through *1.50.

This technique is used when the number

of desired repetitions is not known.

4-2

The looping process can be ter-

Examples Of Focal Programs
minated at any time by typing CTRL P.

If, however, the number of

desired repetitions is known (e.g., 10), the following method can
be used.

:t.f..,ET PI""3 .1.4l~:)9
*:1. ,:I. (.l~:"< , . ,

*
*!::L.6 TYPE I!! I !
*FDR I

()

= 1,10; DO l

The ability to choose between these methods provides great flexibility

in actually running FOCAL programs •
~c FOCAL XVM V1AOOO
*1.01 SET PI=3.14l59
*:1..10 ASK" A RADIUS OF ·,R, ·INCHES"
1.20 TYPE %B. 04, I.' GENEF~ATE~; {., CIRCLE OF: ',!
*l •. :':!:J. TYPE "
[lIAMETEI:~",
2*F~,'
INCHES·,!
*1.30 TYPE·
AREA", PI*R-2,' SQUARE INCHES',!
*1.31 TYPE·
CIRCUMFERENCE", 2*PI*R,· INCHES·,!
* 1.40 TYPE I, ",;ND A SPHEF~E DF:·.!
U .47 TYPE"
VOLUME". (4/3)*F·I*F~r·3,· CUBIC INCHES', I
*1.50 TYPE! I I I I; GOTD 1.1

~(GO

A RADIUS OF :26.39INCHES
GENERATES A CIRCLE OF:
D I t,r1ETEF~
:';i2 • 7800 I NCI . tI::~:;
AREA 21B7.9041 SQUARE INCHES
CIRCUMFERENCE 165.8131 INCHES
AND ,;

OF:
VOLUME 769B5.053 CUBIC INCHES

SPHEI~E

A RADIUS OF :0.73INCHES
GENERATES A CIRCLE OF:
DIAMETER
l.4600 INCHES
AREA
:1..6742 SQUARE INCHES
CIRCUMFERENCE
4.5867 INCHES
(iND ,;

~:;PI"IEF(E

OF:

l)OLI..JI'lE
4.3

:1..6295 CUBIC INCHES

ONE-LINE FUNCTION PLOTTING

This example demonstrates the use of FOCAL to present, in graphic
form, some given function over a range of values.
the function used is
y=30+l5[sin(x)]e- O • 1X

4-3

In this example,

Examples of Focal Programs
with x ranging from 0 to 15 in increments of .5.

This damped sine

wave has many physical applications, especially in electronics and
mechanics (for example, in designing automobile shock absorbers).
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 1.10 contains a set of nested loops for I and

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, again 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 legal

FOCAL character is acceptable.

*1.1 F I~O •• 5.15; T "*D,!; F J=O.30t15*FSINCI)*FEXPC-.1*I); T • •
*DO 1.1

*
*
*
**
*

*
**
*
*

* *
**

*
**
*

4-4

*
*
*

**
*

Examples Of Focal Programs
4.4

DEMONSTRATION DICE GAME

Occasionally, the computer user will apply the computer to tasks solely
for his own enjoyment.

Because such pastimes are usually keyboard

oriented, FOCAL lends itself nicely to these ends.

The following exam-

ple uses the random number generator, FRAN ( ), to produce dice combinations, as well as IF logic to check bets and winning combinations.
Note again the use of initials to abbreviate commands throughout the
example (remember that each such abbreviation must be followed by a
space) •
The random number generator must be modified for use with statistical
or simulation programs to achieve true randomness.

However, it is

sufficiently random for most applications in its present form.
NOTE
DEC does not assume any responsibility for the
use of this routine or any similar routines.
C FOCAL XVM VIAOOO
01.10 S B=O;T ""DICE GAME"' ,"HOUSE LIMIT IS 51000"
01 • 13 T ". MIN. BET I ~3 51.00" I I
01.20 ASK "YOUR BET IS"A;I (1000-A) 3.10
01.22 I (A-1)3.40.1.26.1.26
01.26 IF (A-FITR(A»)3.50.1.30.3.50
01.30 ASK M;DO 2;SET D=C;DO 2;T • ";SET D=DtC
01.32 I (D-7)1.42,3.20,1.42
01.40 I (D-2)1.50.3.30.1.50
01.42 I (D-11)1.40,3.20.1.40
01.50 I (D-3) 1.60.3.30,1.60
01.60 ASK M;DO 2;S E=C;DO 2;T " ";S E=EtC
01.72 I (E-7) 1.74.3.30,1.74
01.74 I (E-D) 1.60.3.20.1.60
02.10 SET C=FITR(10*FABSCFRANC»));IF (C-6)2.20,2.20.2.10
02.20 I CC-l)2.10~T %1." "C; RETURN
03.10 T "HOUSE LIMITS ARE 51000" I I ; G 1.20
03.20 ~:; B""B+A;T %6.0. '"YOU WIN. YOUI'~ l')INNINGf:; t'iI:~F
".D.II.G 1.;:'
03. 30 ~:; B""B"-A.-r %6.0. I" f:;ol:my YOU I",DE'I":.
YOl.m WI NN ING!:; Al'n:'
". n, I I ; G 'I. :.:,'
03.40 T "MIN. BET IS 51"' I;G 1.2
03. ~,)O T "NO PENN IE!:;, PLEA!:;E" I I ; GOTO 1.::>'

4-5

Examples of Focal Programs

I1ICE GAME
HOUSE LIMIT IS $1000. MIN, BET IS $1.00
YOUR BET IS: .50
MIN. DET IS $1.
YOUR BET IS: 1 '"

f::"

""
""
'"
YOU'" WIN.
.J

.,J
ro:
o

YOUI:~

WINNINGS

AI'~E

:1, ~.';

'" '" :
YOU'" WIN. YDUF~ WINNING~:; AI:;:E

YOUR BET IS: ~j
0::-

1::-

r::"

l::'

YOUf( BET IS:3
0:.-

,,)

r,",::.

YOU WIN.

YDUI:~

WINNING S AI:;:E

YOUR BET IS:l'LL QUIT WHILE I'M AHEAD. THANKSI
4.5

SIMULTANEOUS EQUATIONS AND MATRICES

Many disciplines use subscripted variables for vectors in one, two, or
more dimensions to store and manipulate data.

A common use is the 2-

dimensional array or matrix for handling sets of simultaneous equations.
For example,
Given

lX l + 2X

+ 3X 3

4X l + 3X

+ 2X 3 = 1

Find: The values of Xl' X2 , and X3 to satisfy all three equations
simultaneously.
The solution can be reduced to simple mathematics between the various
elements of the rows and columns until correct values of X are found.
Each individual quantity in an array is referred to in terms of its
position within the array.

This identifier is a subscript.

The

notation A(I) refers to element I of array A.
FOCAL uses only a single subscript.

Thus, the handling of two or more

dimensions requires the generation

of a linear subscript which repre-

sents the correct position if it were stored in normal order, i.e.,
leftmost subscript moving fastest.

4-6

Examples of Focal Programs
For example:

In one dimension:
ARRAY ( 0) A

Element D could be represented as

ARRAY (3); any element in this array

(2 ) C

can be represented by a subscript in

(3)

the range 0 through 4.

(1 )

(4) E

The first ele-

ment in an array always has a subscript
of O.

o
In two dimensions:
ARRAY (row,column) or A(I,J)
This must be reduced to the form A(G).

Because subscripts are lin-

ear, G is a function of I and J; that is, A(I,J)=A(G).

Consider the

diagram
J=
I

This array has five rows and three columns; thus, two values can be
defined:
IMAX

JMAX

To generate the number (G)

in any box, using the corresponding values

of I and J, the formula
G=I+IMAX*J or A(G)=A(I+IMAX*J)
can be used.
area.

Each element in

a 2-dimensional array represents an

The example for solving simultaneous equations, above, uses

this algorithm for subscripts, merely by replacing I, IMAX, and J
with J, L, and K, respectively, to form the equation
A (J+L*K)
In three dimensions
ARRAY (row,column,plane)=A(I,J,K)=A(G)

4-7

Examples of Focal Programs
Three dimensions can be illustrated as a rectangular solid.

K=O

JaO

This rectangular solid has dimensions of five rows, three columns,
and four planes; thus, IMAX=5,JMAX=3, and KMAX=4.

Each plane is

numbered exactly as in the 2-dimensional example, except 15 times
K (with K = the number of planes back from the first)

is added to

each subscript in the first plane.
Example:
Upper lefthand square, back one plane from the first

I=Q,J=Q,K=1;I+(IMAX*J)+(IMAX*JMAX*K)=15=G
or
A(Q,Q,1)=A(15)
In four dimensions:
ARRAY (row,column,plane,cube)=A(I,J,K,L)=A(G)
Assign the values for IMAX, JMAX, KMAX; a method similar to the one
above yields
G=I+(IMAX*J)+(IMAX*JMAX*K)+(IMAX*J~~X*KMAX*L)

This process can theoretically be extended indefinitely to n-dimensions.

4-8

Examples of Focal Programs

C FOCAL XVM V1AOOO
01.02 TYPE '"ROUTINE TO SOLVE MATRIX EQ. AX=B FOR X"'
01.04 ASK "ENTER DIMENSION OF A, THEN
01.05 TYPE "ENTER COEFF'S ACJ,K) ••• A(J,N> AND B(J)',
01.10 ASK L,';SET N=L-l; SET 1=-1
01.11 FOR K=O,N; SET RCK)=K+l
01.12 FOR J=O,N; TYPE'; FOR K=O,L; ASK ACJ+L*K)
01.14 SET M=lE-6
01.16 FOR J=O,N; FOR K=O,N; DO 4
01.17 SET R[Pl=O.
01.18 FOR K=O,L; SET A[P+L*Kl=A[P+L*Kl/M
01.20 FOR J=O,N; DO 5
01.22 SET 1=1+1
01.23 IF CI-N) 1.14, 1.26 , 1.14
01.26 FOR J=O,N; FOR K=O,N; DO 7
01.28 FOR K=O,N;TYPE 'X2,'XC'K,") ·,X8.05,X(K)
01.29 TYPE "; GoTo 1.02
04.05 IF (R{J» 0, 4.3, 4.1
04.10 IF (FABSCA(J+L*K» - FABS[M]) 4.3;
04.20 SET M=A(J+L*K)
04.22 SET P=J; SET Q=K
04.30 RETURN
05.10 IF (J-P) 5.2,5.4,5.2
05.20 SET D=A(J+L*Q)
05.30 FOR K=O,L; SET A{J+L*K)=A{JtL*K)-A{PtL*K>*D
05. 40 RETUF~N
07.10 IF (lE-6-FABS[A(JtL*K)]) 7.2; RETURN
07.20 SET X(K)=A(JtL*L)

ROUTINE TO SOLVE MATRIX EQ. AX=B FOR X
ENTER DIMENSION OF A, THEN
ENTER COEFF'S A(J,K) ••• A(JyN) AND B(J)
:3

o + 2~500()
1.75000

o. 7~5000

ROUTINE TO SOLVE MATRIX EQ. AX=B FOR X
ENTER DIMENSION OF A, THEN
ENTER COEFF'S A(J,K) ••• A(J,N) AND B(J)

~j. OO()()O

4.00000

1 • ~:)OOOO

4-9

Examples of Focal Programs
4.6

INTEREST PAYMENT PROGRAM

This is an example of a business-oriented FOCAL program.

It is desig-

ned to completely describe the payments to be made on a loan, with
interest, on an installment plan basis.
Under program control, the computer requests as input the amount of a
loan, the percentage of interest on that loan, and the length of time
over which the loan is to be paid.

The computer than calculates and

types the amount of monthly payments to be paid, the total amount of
interest to be paid, and a table showing interest paid, amount applied
to principal, and balance due after each payment.

C FOCAL XVM V1AOOO
01 +02 TYPE I I , %7.0::'.
01.20 TYPE" THIS PROGRAM WILL COMPUTE MONTHLY PAYMENTS AND THE"
01+21 TYPE" CONTRIBUTION OF EACH"
01.22 TYPE I 'PAYMENT TO INTEREST AND PRINCIPAL. PLEASE ANSWER THE"
01.23 TYPE" FOLLOWING:"?! I
01.:30 A!3K "',.JHtIT I!:) THE (lhOUi··1T OF THE PF~INCIP(:ii . "''' PF~INCIP(l!...
01.31 ASK "WHAT IS THE RATE OF INTEREST"'" INTEREST
01.32 ASK "WHAT IS THE TERh OF THE LOAN IN MONTHS?" TERM
01.33 TYPE I I
01.40 SET D=1t({INTEREST/12>*.01)
01.41 FOR A=1.1.TERM; DO 1S.99
01.42 !3ET C"'PF~:;:NCIF(lL/.F{
OS+01 SET BALANCE~PRINCIPAl.
05.02 TYPE "PRINCIPAL"
05.03 TYPE PRINCIPAL; TYPE"
05.04 TYPE "PAYMENTS"; TYPE C; TYPE I I I
OS.OS TYPE·
PAYMENT"; TYPE"
OS.06 TYPE "INTEREST"; TYPE"
OS.07 TYPE "PRINCIPAL"; TYPE·
05.08 TYPE "BALANCE"; TYPE"
"; TYPE
06.01 FOR M=1,1.TERM; DO 7.00
06.02 TYPE I I !; ·fYPE "
•
06.03 TYPE "TOTAL INTEREST",%6.02
06.04 TYPE TOT INTEREST
06.0!"j TYPE I I I
06.06 G()TO :1.02
07.0:1 SET CINTEREST=BALANCE*(INTEREST/l::'.)*.01
07.0::'. SET TOTINTEREST=10TINTEREST t CINTEREST
07.03 SET CPRINCIPAL=C-CINTEREST
07.04 SET BALANCE=BALANCE-CPRINCIPAL
07.0S TYPE %7.02,h.%14.02
07+07 TYPE CINTEREST,CPRINCIPAL.BALANCE, I
15.99 SET B=Bt(1/{D>~A)
II

THIS PROGRAh WILL COMPUTE MONTHLY PAYMENTS AND THE CONTRIBUTION OF
EACH PAYMENT TO INTEREST AND PRINCIPAL. PLEASE ANSWER THE FOLLOWING:
WHAT IS THE AMOUNT OF THE PRINCIPAL?:2000
WHAT IS THE RATE OF INTEREST?:6.4
WHAT IS THE TERM OF THE LOAN IN MONTHS"':1::'.
PRINCIPAL

2000.00

PAYr1ENT~:)

4-10

1."72 + ~::.iO

Examples of Focal Programs

PAYMENT

10.6'7

2.00

9.DO
B.94

3.()0
4.00

PI:;:INC I PAl...
16:1. .134
1 (',2.70

INTEF~EGT

1.()()

163.~.)'1

B.06
'7.19
6.31

164.44
165.:32

:1.:347.47

1M,.20

:1.01~5.%

~.'i. 42

:L67.00

0413.B7

167.97

:l (). O()

4. ~5:'5
3.63
2.7:'5

:1.:1.00
12.00

:I. • f:l ::~
O. (12

6BO.90
512.03
342.26
:L 71.5(1
0.00

~;j <-

6.0()
'7 . 0()

O.()O
r,' • 00

:1.6,8.137
:l69. '7'7
:L 70.613
171.~5(1

TOTAL INTEF<E!3T

4.7

BALANCE
:1.13 :3 f:l • :1. '1
:L675.47
:I ~:):I. :1. • ('Y 0
:L :LO::!. :I.~)

70.0:1.

INTERCEPT AND PLOT OF TWO FUNCTIONS

Values are first computed and printed for two monotonic functions.
Then these curves are plotted within specified limits.

Non-monotonic

functions must be plotted using the method of residuals.

C FOCAL XVH V1AOOO
01..()1 T /.8.04
01.02 ASK "LOWER LIMIT",LL,' "UPPER LIHIT",UL, , "INCREHENT",IN, I
01.10 SET Yl=O; SET Y2=O;
01..20 FOR X=LL,IN,UL; SET Yl=-X-3; SET Y2=3t4*X- X-2; DO 2.0
02.10 IF (Y2-Yl) 2.3,2.2,2.3
02.20 TYPE "THE POINT OF INTERSECTION IS ""
02.30 TYPE "Xl:",X,"
","Yl=",Yl, ',"X2=",X,"
","Y2=",Y2,"
03.10 TYPE "DO YOU WANT A PLOT?"
03.20 A!:11\ "( TYPE Y FOF~ YES + TYPE N FOF~ NO) ", AN, , ,
03.30 IF (AN-OY)9.1,4.1,9.1
04.10 FOR X=LLyIN,UL; DO 5.0
05.01 IF (X) 5.1.5.02y5.1
O~j. 02 TYPE •
Y••••• , ••• + • + • • • • • • • • • • • • • • • • • • • • • • • • • • • • Y" , t
05.10 FOR Y=O.30; TYPE· •
05.20 TYPE ",n.t
05.30 FOR Y=O.30t(-X-3); TYPE
05.40 TYPE "*",t
05.50 FOR Y=0.30t(3+4*X-X~2); TYPE
0:'5.60 TYPE
09.:1. () CHJIT

"*".,

4-11

Examples of Focal Programs
*GO
L.OWEf~

LIMIT: ··· lO

UF'F' Ef~

LIMIT: lO

INCRE~1ENT: 1

Xl ::::-'
X2= ···

lO.OOOO
lO.O()()O

Y:t.::::
7.00()O
Y2::::···· :tT? ,OO O()

Xl ::::"·
X2::: ··

9.0000
9.0000

Y1::::
Y2::::····

:1. :I. 4.0000

Xl. ::: ..•
X 2 :::·'·

8.00()O
8.0000

Yl. ::::
Y? ::::····

:~;. O()OO
93.00()O

Xl ::::'·'
X2 ::: ····

?OOOO
7.()00O

Y:I. ::::
Y2::::····

4.0()OO
74.000()

X 1:::·X2:::····

6.0000
6.0000

Yl::::
Y2::::····

3.0000
::.:;-; ' • 0000

Xl =·X2=-

5.0000
5. ()O()()

Yl. ::::
Y2 =·-

?O()OO
4 2 .0()()O

Xl :::: ....

X2::: ....

4.0()()0
4. ()()()()

Yl.::::
Y2= ....

:1. • O()OO
?9.0 000

Xl::::....
X2=::""

3.()OOO
:3.00()O

Y:I.::::
Y2 :::: ....

0.0000
If.l.OO()O

Xl "::.-

2.0000
2.000()

Yl :::: ...
Y2 :::: ....

1 .0000
CJ . O()O O

X2 :::: ....

6.0000

THE POINT OF INTERSECTION IS
Xl =l..OOOO Yl=?OOOO
X2=:t..OOOO Y? =?OOOO
Xl::::

O,OO()()
O.O()OO

Y:I. :::: ....
Y2=::

:,':1 ,0000
3.0000

Xl::::

:t. .()OOO

Yl:::: ....

X2::::

1 .OO()()

y;?::::

4.00()()
6.0()OO

Xl ,,::
X2:::

2.0000
2.0()O()

Y1:::: ....

~,:;,

Y?::::

"'J

Xl::::

:,'~ • 000 ()
:·' .O()OO

Y:I. :::: ....

6,OO()()

'(2::::

6,0000

4,()()()O
4. ()()()O

yl:::: ....

'7 ,O ()()O

Y2::::

:·} .OOO O

0.0000
2.()O()O

X2=

X2::::
Xl::::
X;.~:::

0000

.O() O()

Xl::::

:::;.O()()O

'i1:::: ....

X;:'>:::'

~.:; • 0000

Y2 :::: ....

Xl ::::

6.00()()
6.0()O()

y1::" ....

?OO()O
/ .O()OO

y:I.::::....

lO.O()()()

Y2:::: ....

1G,OO()()

X2"::
Xl""

X2="

..,

y;?::" ....

?O()()()
9.00 00

4-12

Examples of Focal Programs
Xl ,,:

•

X2""

8.00()()
8.0()O()

X 1. ::::
X2"7.

Y:I.:::: ·"·

Y2:::: ""

I.I.OOOO
::'.9.000()

<f.O()()O
9.000()

YI. ::::"-

12. ()()()O

Y2::::·-

42.()OOO

Xl I:::
X2=

1.0. ()()OO
IO.()()()()

Y:I.::::""
Y2::::""

~)? •

Xl::::
X2=

11.00()()
1.1..00()()

Yl ::::-..

:L3.0()()()

Y2:::: "..

~.)?

:1.:3 • O()OO

O()OO
0000

DO YOU WANT A PLOT?(T¥PE Y FOR YES. TYPE N FOR NO) :Y

**
**
**
*

*
*
*
*
4.8

**
*
*
..* **
*
*
*
*.
*.
y •••••••••••••••• * ..... * ................. Y
*
*
*
*
*
*
.*
*
* *
*
*
*
*
*
*
*

SCHROEDINGER EQUATION SOLVER

This program is designed to aid the user in searching for possible
energy-states of an electron in a potential well.
most compex equations yet written in FOCAL.

This is one of the

It calculates and plots

the energy levels of an electron within specified boundary conditions.
C FOCAL XVM V1A000
01 01 T ' ." SCH~: (iE[O I NCiEf;: EG~'-'FIT I ON SOL\"EF: _."., '
01. 02 T ' ., "
-[:'ELSG~'-'FtPEC' F'S I + FI:': :t: P::; I :: E :+: PS I "., ' ,
O~ 0:: A " T I L TED SG'UAPE ~<IELL Pf':OE:LEM ~"ITH ~,~ I C'HI" ., :« 1.. '
1~11. 0::: A "~'4E L L TI LT SLOPE FI" ., F11 ., " "TI;: I FIL. ENE~:(;'T' E" ., E:1,. ,
01.09 A "NUt'1E:EF: OF STU'S"., NT ., '
01. 11 S VF=0; S SL=l
01 70 S P ( 0 ) =0, S DX=XO/NT ; S P ( 1 ) =SL:+:[OX; S PO=0
(11 . 75 .:' t,/F=(1
1~1 1. :::0 :;
p(1=e
01 . 90 F N=e, 1 , NT- 2; D 6
til 9 : T ' ., " PS I ZEF:OS" :.;;2 . I). PI;1
1211 . 95 GOTO 7 . 02

4-13

Examples of Focal Programs

05. 10 T I., ~.;::;:. ~), p:.:., " P~; I "., ~';., P (F':':)., ". "
~)5. 20 ::' PZ=F I H::: Pt'1*SC).;
S PE=:F I TP{': P( P:': ]+Pt1) *::;C>
05. 3:0 F ::<=1 . 1 ., PZ-1.; T " "
~j5. 4~~1 T " . "., #.;
F ::<=1.,1.., F'E+;;::.:L T " "
~;15. 5~;1

TII:+:".i

06.10 S P(N+2)=«-B1+A1*DX*[N+1J)*DX~2+2>*P(N+1)-P(N)
06.20 I (NT-N-2) 12.90.6.9.6.}
06. 3:0 S F:E:=F' (N+2) *F' (N+1).; I .: F:E:) 0:;. 4. 6. 4. 0:;. 9
06. 40 S F'0=F'0+1 ; P
~J6. 90 CO/HINUE
(17 . 02 S CF=(F'(NT>/F'<1»~2; T"
CONY IND"%. CF
~J7.

ND~ E '~'" N'T'
05 A"
~)7
I (NY-9) 7 . 9.7.08.7. 9
07. 08 I (VF) 7. 09. 7. 8. 7. 09

(17.

07.09 I (CF-100) 7.1.7.1.7. 8
10 S F:2=F' <tH) :t:',iF,; I (F:2) 7'. 7:1: " 7, :::0. 7, ::::;
07. 73 S 08=-0. 5*DB; GOTO 7. 85
(17. ::a~1 S 08=(1. 1
07. :::5 S E:1=E:1:t: (1-+(:OE:).; T E:1; :.=; ',iF (NT).; G 1. :::(1
07 90 DO 14; GOTO 12. 01
12. 01 T I ., I " "E I GEN E" E:l.; ~; HF'=:E:1,··' (FI1.:.:::<(1)
12. 20 T" EN,··· t'1FI:x: F'OT" HF'., I
:12. 9~~1 C~UIT
14.10 S F'M=(1; S F'F'=(1; F PX=1.1.NT; D 15
14. 20 S PS=F'M+F'F'; S SC=45/PS
14. 3:0 T '! I.; F F'::<=L 1., 7(1.; T ". "
14.40 F F'X=0.1 . NT; D 5
14. 50 T ,; F P::<=1., L 7(1.; T ". "
14. 6(1 T I J .; P
15.10 I (F'(PX]) 15.2 . 15.9.15.5
15.20 I (F'M+F'(PX» 15.3.15.4.15. 4
15.30 S F'M=FABS(F'(F'X])
15. 40 PETUPN
15.50 I (P(PX>-PP) 15.9.15. 9.15. 6
15. 60 S PP=P'; P::-:)
15. 9(1 F:ETUF.:N
~j7.

:+:130

SCHROEDINGER EQUATION SOLVEP -DELSQUAPED PSI

-I-

AX * PSI

= E * PSI

TILTED SQUARE WELL PROBLEM WITH WIDTH 1
WELL TILT SLOPE A: 40
TRIAL ENERGY E . 50
NUMBER OF STEPS : 15
PSI ZEROS

CONY IND 0.501}26462E+01

4-14

NEW E?Y

Examples of Focal Programs

o PSI 0. 000000000E+00.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

PSI 0. 666666667E-01.
PSI 0. 119308642E+00.
PSI 0. 148265643E+00.
PSI 0. 149546390E+00.
PSI 0. 124684213E+00.
PSI 0. 795031267E-01.
PSI 0. 223082351E-01.
PSI-0. 379932849E-01.
PSI-0. 934541789E-01.
PSI-0. 138115924E+00.
PSI-0. 168454535E+00. *
PSI-0. 183320286E+00~
PSI-0. 183520414E+00~
PSI-0. 171213965E+00. *
PSI-0. 149268805E+00.

EIGEN E 0. 500000000E+02

*
*

EN/MAX POT 0. 125000000E+01

4-15

•

CHAPTER 5
LIBRARY COMMANDS
FOCAL LIBRARY commands allow the user to save and then call programs
by name.

These commands cause files consistent with the XVM/DOS file

format to be produced and accepted.

These files, which use lOPS ASCII

data mode, can be manipulated by other XVM/DOS programs such as PIP
and EDITOR.

In addition to the library commands, a COMMON command and

an ERASE COMMON command are available.

These commands allow the effec-

tive segmentation (chaining) of FOCAL programs, with the COMMON area
defining those variables which
5.1

are to be used by all segments.

LIBRARY OUTPUT COMMANDS

Three operations are required to produce a file with the FOCAL library
commands:
a.

File initialization

File output

File termination

5.1.1

Library File Initialization

The command

*
*

*LIBRARY OUT NAME

initializes a file' on the output device associated with .DAT slot 5.
If the device is directoried (i.e., has named files), then the file
name NAME is used.

NAME can be up to six alphanumeric characters

and is terminated by a carriage return.

The extension FCL is supplied

by the system.
5.1.2

Library File Output Operations

Commands of the form

*LIBRARY WRITE nnn

*
cause information to be entered into the library file.
string nnn can take four forms which
5.1.2.1

The character

are explained below.

Direct Command Output

If the character string nnn, in the example above, begins with quotation marks ("), the command indicates that the character string
following the quotation marks is to be inserted into the file.
character string may be any FOCAL command.

5-1

This

Library Commands
For example, the command here is an *, a FOCAL symbol typed by the
user to signal termination of input from the device associated with
.DAT slot 3.

*
*

*LIBRARY WRITE "*; GO

causes the command

to be inserted into the library file as a direct command.

This will

start the program when the file is later called for execution by

library input command.
5.1.2.2

Single Line Output

If the character string nnn is a legal line number which is present in
the program in core, this command causes a single line to be inserted
into the file.

For example, the command

*
*

*LIBRARY WRITE 10.02

causes line 10.02 to be inserted into the currently opened output file.
5.1.2.3

Group Output

If the character string nnn is a legal group number, this command
causes the entire group of lines to be inserted into the file.

For

example, the command

**LI8RARY WRITE 2 00
causes all group 2 lines to be inserted into the current output file.
5.1.2.4

Program Output

If the character string nnn is ALL or A, then the entire indirect program is inserted into the current output file.
5.1.3

Library File Termination

After using the appropriate library output commands, it is necessary
to issue the command

*LI8RARY CLOSE

to complete file output and enter the file name into the directory

5-2

Library Commands
of the mass storage unit of the system.

The LIBRARY CLOSE command

allows an input or output file to be closed.

An error message "?35"

will be printed if a file has not be opened.

If the LIBRARY CLOSE

command is not issued, the user remains in library mode and all other
commands are illegal.

However, to leave library mode without actually

finishing the output file, the command

*
**L I E: F.: AF.:'T' f< ILL
is used.

After using this command, the user is in command mode, and

the file which had been started by the library output commands is
lost.
5.2

LIBRARY INPUT COMMANDS

To load a library file which has been output from FOCAL or which has
been prepared off-line, the command

*
**LIE:RARY IN NAME
is used where NAME follows the conventions used for library output.
The library input from the device associated with .DAT slot 3 is terminated by an end of file or end of tape condition on the input file.
It is also terminated by the presence of a direct command of asterisk
(*), supplied during a LIBRARY WRITE command within the library file.
If none of these three conditions occurs, FOCAL assumes that subsequent
input (e.g., for ASK command) will corne from the device associated
with .DAT slot 3.
which

This direct command can be a multiple command

can provide automatic program starting.

For example, a direct

command to terminate input and to start a program at line number 8.21
would

be
..;,

*"".;

GOTO :::. 21

This command can be inserted at the end of the library output by the
command
,t,

*LIBRARY WRITE "*;

GOTO 8. 21

5-3

Library Commands
5.3

LIBRARY .DAT SLOT USAGE

The FOCAL LIBRARY commands assume input on .DAT slot 3 and output on
.DAT slot 5, and the FOCAL DATA commands assume input on .DAT slot 7
and output on .DAT slot 10.

The recommended assignment to the Linking

Loader is the System Library located on system disk unit O.
The following table shows a typical set of device assignments where
the system software is on disk pack unit 0, input is from DECtape
unit 1 and output is to DECtape unit 2.
.DAT Slot

Contents

.DAT -1

System Library

DPO

.DAT -4

FOCAL binary program
plus FNEW binary

DPO

.DAT 3

FOCAL library input

DTI

.DAT 5

FOCAL library output

DT2

.DAT 7

FOCAL data input

DTl

.DAT 10

FOCAL data output

DT2

SamQle Assignment

FOCAL data commands are described in Chapter 7, and .DAT slot assignments are again summarized in Appendix E.
5.4

COMMON VARIABLES AND ARRAYS

The COMMON command allows the user to define permanent FOCAL variables
and arrays which are saved with their current values when the user
modifies the stored indirect program.

Thus, the caution at the MOD-

IFY command (refer to Section 3.14) does not apply to COMMON variables.
The COMMON command is legal only if no other variables have been defined in the symbol table. Thus, it is good programming practice to
precede a COMMON definition by an ERASE command to clear the symbol
table.

If any non-COMMON variables have been defined when the COMMON

command is executed, it will be treated as a COMMENT and ignored.
5.4.1

COMMON Format

Three types of variables can be defined in a COMMON command as the
following example shows.

:+:COt-lI'10N 11 .. E: 0:: 5 :' ., ( C .. L L J:::-

The first variable, A, defines a single non-subscripted variable.

The

second variable, B(5), defines a single array element to be COMMON.
All other elements of the array B are non-COMMON.

The third variable

(C.l.I.3) defines a series of array elements as COMMON by using a

5-4

Library Commands
notation similar to the FOR statement.

Thus, the command

*
*

*COMMON (C,1,1.5)
is equivalent to the command

*'
*'
*CONt'10N C(1) .. C(2).· C(]:) .. (:(4) .. (:(5)
but much shorter.

Note that, because COMMON and COMMENT both have the

initial letter C, the COMMON command must not be abbreviated.
5.4.2

ERASE COMMON Command

The ERASE COMMON command must be used to clear the COMMON area if a
user wishes to define a completely new COMMON area.

It will clear

both the COMMON area and all variables in the symbol table, but not
the program itself.

If, however, the user simply wants to add to the

current COMMON area, it is only necessary to erase any non-COMMON
variables by using ERASE.

The ERASE ALL command has no effect on the

COMMON area variables and does not change their values.
5.5

CHAINING OF FOCAL PROGRAMS

For FOCAL programs that exceed the capacity of user's core memory, it
is possible to segment the program.

By combining the library input

and COMMON commands, one segment can call another by name.

ALL COM-

MON variables are retained in core memory for access to them from
all segments of the program.

New COMMON variables can be added to

the permanent table from any segment.

The command LIBRARY IN NAME

brings in the next segment to core memory and provides access to the
COMMON table for the operations in this segment of the program.
NOTE
Ensure that a segment does not exceed its alloted
memory location or the overflow will begin to
erase the compiler core.
The following example shows three FOCAL segments and the operations
required to provide the segments with linkage capability.

The first

segment, named CH1, defines a COMMON area and initializes the variables.

If CHl is called again, it checks for the values in the second

part of the COMMON area which were defined in CH2 and QUITS.

The

second-segment, CH2 defines more COMMON variables, checks the original
COMMON values created in CH1, and initializes the additional COMMON
variables.

The third segment checks all the COMMON values and calls

the first segment again.

5-5

Library Commands
*WRITE

C FOCAL XVM ~lA000
01.05 TYPE "CH1 READY·,
01. H3 COMMON A., 8, C, (AE:C, 1. 5)
01.20 IF (A) 20.1,1.3,20.1
01. 30 SET A=l
01. 40 SET 8=2; SET C=3
01. %} FO~: X=1. 5.; SET AE:C (:.:) =:·: :.:113
~31. 55 T'T'PE "CHi NINE
CALLI NI3 CH2·., !
01.60 LIBRARY IN CH2
20 . 10 IF (0-10) 20.2,20. ],20. 2
2~3 . 20 T'T'PE "CIJt1t10N E~:~:(lR ON 2N[;o CAL.L OF CH1", !
2~3. 30 T'T'PE "ALL DONE", ,;
G~ U IT

Listing
of CHl

•

*LIBRARY OUT CHi
*LIBRARY WRITE "ERASE ALL
*LI BRAR'T' WI<: I 11::. f"il L
:.'L I BRA":'T' WI': I TE ":.:;
130

Library
Output
of CHl

*
*HRITE ALL
C FOCAL XVM V1A000
~::11. 1~::1 P,'PE "CH2 I<:EAC,'T'''., !
01.20 COMMON Q, (ABC,5,1,10)
01.30 FOR X=6,10; S ABC(X)=X*10
01.40 FOR X=l, 10; DO 25.0
01.50 IF (A+B+C-6) 1.6,1. 7,1 . 6
01 . 60 TYPE "CH2 COMMON ERROR - SUM = ",A+B+C,
01 . 70 TYPE "CH2 DONE
CALL I NI3 CHJ: N., !
81. 80 LIBRARY IN CH3
25. 10 IF CABC(X)-10*X) 25. 2,25. 3,25.2
25. 20 TYPE "ERROR AT X = ",X," ABC ARRAY = ",ABC ( X), I
25. 3:~::1 I<:ETUI<:N

*LIBRARY OUT CH2
*LIBRARY WRITE "ERASE ALL
*LIBRARY WRITE ALL
*LIBRARY WRITE "*; 130
*L I B~:AR'T' CLOSE

Listing
of CH2

Library
Output
of CH2

*
*WRITE ALL

C FOCAL XVM V1A000
01. 10 TYPE "CH] READY",
01.20 FOR X=l, 10; DO 25.0
01. 3:(1 SET G~=l(1
~31 . 4~3 T','PE 10 CH3: C'ONE
CALl. I NCi CHl AI3A IN"., I
01 . 50 LIBRARY IN CHl
25. 10 IF CABCCX)-10*X) 25.2,25. 3, 25 . 2
25. 2(1 T','PE 10 EF:I<:01<: AT :x:
"., :X: ., " AE:C AI<: ~:A'T' = "., AE:C (:X:)., !
25. 3:(1 I<:ETURN

5-6

Listing
of CH3

Library Commands

*lI8RARY OUT CHJ
*lIBRARY WRITE "ERASE 1 . 00
*lIBRARY WRITE 1 . 00
*lIBRARY WRITE "*; GO
*l I E:I':AI':'T' CLOSE

Library
Output
of CH3

*
BFOCAl XVM V1A000
*ERASE COm'lON
*l 181':AR'T' IN CH1
CHi I':EACo'T'
CH1 [)ONE
CH2 REACo'T'
CH2 C'ONE
CH]: REACo'T'
CH3: CoONE
CH1 I':EAC,'T'
All CoONE
*T'T'PE f.
A11'11' «(10) =
811'11' (0(1) =

CI]lI]I ( OO)=
A8C «(11)=
A8C(02)=
A8(:«(1})=
A8C(134 )=
A8(: ( 05)=
Q@@(OO ) =
A8(: ( 06)=
A8(:(07)=
A8(: ( 08)=
A8(: ( 09)=
A8(:(10)=

CALLING CH2
CALL I NG (:H3:
CALLING (:Hi AGAIN

1. (1(1(1(1
2 . 0(11)(1
] :. (1(11)(1
1(1. (1(1(11)
20. (1(11;11;1
3:0 . 1)(1(11)
4 O. (1 (11;11;1
50. 0000
10. 0000
60. 0000
70. 0000
80. 0000
90. 0000
100. 0000

Library
Input and
Execution of
Chained Programs CHI,
CH2 and CH3

Dump of
COMMON
Symbols

5-7

•

CHAPTER 6
USER DEFINED FOCAL FUNCTIONS
The ability to write FOCAL functions in MACRO assembly language and
subsequently interface these functions with the FOCAL interpreter is
an important feature which allows real-time use of FOCAL.

These func-

tions are processed in the same way as the normal internal functions
supplied with the interpreter (i.e., FSIN,FITR,etc.).

Some external

functions are provided in the FNEW file (Refer to Section 6.2).

User-

defined functions can be incorporated into the source file of FNEW
and then reassembled by MACRO.

The process is described in the XVM/

DOS System Installation Guide.

The interface of external functions is

accomplished by:
a.

Use of a function table which contains the three letter
function name in .SIXBT (6-bit ASCII) and a jump to the
function processor.

Use of .GLOBL definitions which allow the function processors to use character processing and expression evaluation routines which are in the interpreter.

The following detailed example shows the operations necessary to
write an external FOCAL function in MACRO assembler language and to
merge it into the external function file, FNEW, described in Section 6.2.
6.1

EXAMPLE

A scope routine has been generated to display characters at a given
point on a scope.
XYC (X,Y,SHOW).

This routine is called from FOCAL as a function by
Here, X and Yare expressions to be used as display

coordinates for the start of SHOW.
First, the function name and transfer instruction must be added to
the .NEWF function table within FNEW.
.SIXBT

/XYC/

SETXYC

Refer to page 6-6.

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

JMS*

.AX

DXL

/make 18 bits
/set X coordinate

6-1

User Defined Focal Functions
Now, check for the second argument and give an error if no second
argument is given.
JMS*
SAD
JMP
.DEC
LAW
.OCT
JMP*

XSPNOR
(254
+3

/skip spaces
/is it a comma?
/yes

/?Ol error

FUNERR

/function error

Move past the separating comma.
JMS*

UTRA

Evaluate the second argument.
LAC

EVAL

DAC
JMS*
XX

+2
XPUSHJ

/address of evaluation
routine

The second argument must be made into an lS-bit quantity and the y
coordinate set:
.AX

JMS*
DYL
Test for a

comma~

JMS*
SAD
JMP
.DEC
LAW
.OCT
JMP*
JMS*

i f present,

bypass it to get to the character string.
XSPNOR
(254
+3

/skip spaces
lis it comma?
/yes

/?Ol error

FUNERR
UTRA

/error return
/skip comma

Now, pick up the single ASCII characters and display them.

(This

example assumes the character display routine is called DYCHAR.):
DCLOOP

LAC *
JMS
JMS*
SAD
JMP*
JMP

CHAR
DYCHAR
UTRA
(251
EFUN3
DCLOOP

6-2

/get character
/display it
/get next char
lis it end?
/yes-return
/no-go display next
character

User Defined Focal Functions
6.2

FILE FNEW

The following functions are supplied in FNEW (where N cannot be
another function):
FUNCTION

MEANING

FDXS(N)
FDIS (M)

Set the x coordinate of the 34H display
Set the y coordinate of the 34H display
and itensify the point
Set the x and y coordinates and intensify.
Set the multiplexer of the A/D converter
and perform one conversion
Set the D/A converter to the specified
value.
If N=-l, clear the relay buffer (M should
not be specified)
I f N=O to 17, set the appropriate bit of
relay buffer according to the value
of M(O or 1).
Start a sequence of random numbers in the
range of -1.0 less than or equal N
less than or equal +1.0 based on the
value of N. The value N may be any
valid arithmetic expression. FRND
always generates the same number for
the same value of N.
If N is either
o or L....I (a space), a random number
will be generated based upon the
previously generated number. The
first time FRND is called, if with a
o or L....I argument, it produces a value
of 1.0000.

FDXY(N,M)
FADC (N)
FDAC (N)
FRLE(N,M)

FRND(N)

The following points should be noted:
1,

Other names for the 34H display are the RM503 Scope or the
VP15E Scope.

The proper way to use these functions is as follows:
SET J

FDXY (N,M)

(What J will be set to is immaterial, and other letters
may be used in place of J.)
FDXY (N,M)
3.

You cannot use:

The 34H display is a refresh-type scope.

This fact, combined

with the time it takes to interpret and execute the graphics
functions,

limits them to a maximum of 75-100 points on the

screen, before the first point put out begins to diappear.
Hence, they are suitable for putting out graphs consisting
of a set of points.

They are not suitable for putting out

"continuous line" drawings, in which many points spaced close
together look like a continuous line.

6-3

User Defined Focal Functions
The functions are supplied to provide the user with additional examples in the method of coding external functions.
The listing that follows is representative of the source code in the
file FNEW is supplied by DEC but may not exactly match what is available •

./
;,,"

/D()'v'E i...EN::: ·(

,. . EDIT

O(){~

GL. .nf:L..
.. Gi... UE-; I...
.:. Ci i... Cj :c.; L.

/.F;'U~:)H ..l

.. GLUF{L

F L;i\!i:::F.:F;~
i:::r:' UN:'::)

;::·:;:... l::iI:~ L..
~. Ci i... C) B i...
~ Cii...ChL.
.~ ;3 LC)f·: L.
,. t~l: . D~:,:.: ~
,. C;I .U:C';i..
... L •.. U:C.;L.

./ I::' l...t ~::: ;"1

',." .,: i'I, "

•

l<;:"U~:;;·-:{.1

F' D ::.::

1'"

1\1

' "

:;. : ' -'

•

C d {:: ;::~

Ei)()!...

~. H L..

.,/ i: '· . ", :' J
i ,

r ,'. ,' .1. <'!'

. j

r:
i-- t-"iUi ... ·::,:) I,) !.. ..

~::

n I i..,.l:: ii(;<j() :... '.

r: (.! f) i:;~ ;;:: ? 0 <> () C 0

•
,/

~ .. { I C:.

:'.) (,i...

DHC

.. .... ::~H

'r HE::

H(~;:~ Dt"I(:·Jr;.:E

~.1 r-.'! ::::. ?i<

(iCCij('-iUL (:: 'r t::!F:

(F>t.!';::: H (:'; j

><F' U ~:~ H {:i

I ,"

. 1.....

6-4

User Defined Focal Functions
/

IPUSH FLOATING ACCUMULATOR (PUSHF.AA)
/
LAC
.AA
/
DAC
.+2
/
JMS*
PD2
/
XX
/P OP FLOATING ACCUMULATOR (POPF .AA)
I
I...f~C
• AA
/
DAC
.+2
/
JMS*
PD3
/
XX
/

I PUSH FLOATING VARIABLE (PUSHF VAR)
/
JMS*
PD2
/
/ WHERE VAR IS THE FIRST OF
IT HREE(3) REGISTER BLOCK
/~

/ POP FLOATING VARIABE (POPF VAR)
JMS*
PD3

/S AME AS FOR PUSHF VAR

/
/

I FETCH CURRENT CHARACTER
/
LAC*
CHAR
IFETCH NEXT CHARACTER (GETC)
JMS*
UTRA

IC HARACTER IN BOTH CHAR AND AC

IIG NORE LEADING SPACES AND ZEROS (SP NOR)
/
JMS*
XSPNOR
INEXT CHARACTER IN BOTH CHAR AND AC
./

I INDICATE A FUNCTION ERROR (ERROR NN)
/
, DEC
,"
i.Jl~J
/NN=TWO DIGIT (DECIMAL) ERROR CODE
.OCT
,..1111"'*
I ERROR WILL HAVE DOUBLE QUESTION MARK
./

/ RETURN FROM FU NCTIO N (RETURN)
,/
EFUN3

iV ALUE OF FUNCTION IN FLOATING AC

! E~TER

/
i
/
,/

FLOA TING POINT INTERPRETER (JMS FIN T)
Jh~:;*: IN T
/TFWI'i HEF~E UN (.I,.. ;.., INf:;nWCTIONS
FNN
A
/AR E ASSUMED TU BE FLOATING POINT
FNN:t:
/ UNTIL FXIT IS REACHED - FNN
C
I REF ERS TO FLOATING POINT OPERATIONS
FXIT
/L I~;;TED NEXT.

/ FLOATING POINT OPERATION S ( USE
F'FD~!

',H~h

Ft,DD

lJ(d:;:

r::;UB

\,-'(d:(

•./

FhUL
FDIlJ
i::'GET

',)(.~F:

FPL.!T
Fi-"'jDh:

'.)(1"':

V{1i:~
')(~F(

FXIT

* FOR INDIRECT)

/ RAISE F.P. AC TO VAR/CONSTANT
/A DD F.P. VARIABLE/CONSTANT TO F.P. AC
IS UBTRACT FROM F.P. AC
/ MULTIPLY THE F.P. AC
I DIVIDE INTO THE F.P . AC
/ LOAP INTO THE F.P. AC
/S TORE THE F.P . AC
INO RMALI ZE THE F.P. AC
/ EXIT FROM FLOATING POINT MODE

I NEGAfE THE FLOATING ACCUM UL ATOR
,,/

/
~ FIX

THE FLO AT ING ACCUMULATOR INTO THE HARDWARE ACCUMULATOR

6-5

User Defined Focal Functions
I
IFLOAT THE HARDWARE ACCUMULATOR INTO THE FLOATING ACCUMULATOR
I
JMS*
.AW
I
I

IEXTERNAL FUNCTION TABLE FORMAT
WORD 0: TWO'S COMPLEMENT COUNT OF NUMBER OF ENTRIES
WORDS 1 TO 2N: N TWO WORD ENTRIES
EACH ENTRY:
WORDO: .SIXBT THREE LETTER FUNCTION NAME
WORD1: JMP TO FUNCTION ADDRESS

I
I
I
I
I
I

.EJECT
I

ITABLE OF NAME S OF EXTERNAL FUNCTIONS
I

.NEWF

.NEWFE=.

.NEWFE-.-1/2\777777+1
.SIXBT IDXSI
JMP
SETX
.SIXBT IDISI
JMP
SETYI
.SIXBT IDXYI
JMP
SETXYI
.SIXBT I ADC I
JMP
SETADC
. SIXBT IDACI
JMP
SETDAC
.SIXBT IRLBI
JMP
SE TRLB
.SIXBT IRNDI
JMP
RAND

ITWO'S COMP COUNT OF NAMES
IS £T X COORDINATE

ISET Y COORDINATE AND INTENSIFY
ISET X AND Y AND INTENSIFY
15ET MULTIPLEXER AND CONVERT

ILOAD DIA CONVERTER
18£T RELAY BUFFER

IRANDOM NUMBER ROUTINE

I I OT DEFI NIT ION S
I

DYL=7 006 06
DXS=700546
AD SF=7013 01
ADSC =701304
ADRB= 70 1312
AD SM=70 11 03
DAL1=70550 1
ORC=70 2 101
ORS =702 10 4

ILOAD Y COORDINATE
I LOAD X COORDINATE AND INTENSIFY
15KIP ON AID FLAG
ISE LECT AND CONVERT
IREAD AID BUFFER
ISE1 MULTIPLEXER
ILD AD D/A CHANNEL ONE
ICLEAR RELAY BUFFER
/8ET RELAY BUFFER

SETX
SETYl

SETXYI

SETADC

.EJEC T
JM S*
DA C
JMP*
JMS*
DYL
LAC
DXS
JMP*
JMS*
DAe
JMS
JMP
JM S*
ADSM
IOF
I SA +l 0
ADSC
ADSF

.A X
XCDORD
EFUN3
.A X
XCODRD
EFUN3
.A X
XCO ORD
GETARG
SETYI
.A X

ISET X COORDINATE
ISAVE
I RE TURN
ISET Y COORDINATE
ILOAD REG WITH Y
ILOAD WITH X AND INTENSIFY
/RETURN
/5ET X COORDINATE
ISA VE
I NOW SAME AS FDIS
IGET MULTIPLEXER CHANNEL
INOTE: WILL USE LOW ORDER
I SIX BITS AS CHANNEL NUMBER
ITURN OFF INTERRUPT SYSTEM
/SELECT AND CONVERT
/WAIT FOR FLAG
6-6

User Defined Focal Functions
.II'll'"

. .... :1.

ADRB
I READ AID BUFFER
II//C ODE REMOVED WHICH PROPAGATED SI GN BI T AUSUM. 12 BIT AID
I//WAD AUGUST 1969 •••
f(ESULT

/F LCl ,~;T

': 400000

ION

(~)(

Dt1i... :i.

..)1'11"'*
SETr'::LB

/i'a:l um'~
/G~,

VALUE AS iNTEGER

[FUN::>

Jh~" *

GI'iA

ITURN ON INTEVVUPT SYSTEM

IUE l V(.1 L.. U::::
.. ' I ::) IT l'i 1 NU!:)

J~lP

.+4

DZi'i

F~EL(~YB

OI:;:C
..JhP*

EFUN3

/YES - CLEAR WHOLE RELAY BUFF ER
/F;:ETU;:(f'.!

Cl"i(.i
D(.le

TEMF

I FOf(M ONE: !:) COMF
/~:;{" l.JE t,~; CClUrH

(10

/MUST BE RELAY 0 fa 17

I NC - UD

~INr

~[T

POSITION

.DEC
Tr.)!:'

,OCT
/IS IT LEGAL POSITION

~:; r1A

..JMP
.DEC
L(\W
. DCT
,.J I"iP*

,.,

.,,;:,

INC)

FUNEj:;:f;:

/'O"i'0 2

EHF~D!';:

[Lt, ' eLL.. ' ChL

,/INITI(.\i...IZE '!lC

1:( Af;:

1 ~:;Z

TEhP

,j f'lP

•.... ,..::."\

D(~C

TEMP
GE'rf:\i'(G
TE1'il':'

..Jh~:;

LAC

/PUT BI T IN kLGHf
/SAVE BIl POSITION

/CLEAR OLD RELAY VALUE

Ci"iA
,'~ND

I'(EI...(\YB

D(.\C

F:EI...(,YD

..JH~:;*

• (\)(

LAC

lEi"!!'"
F([I...J"\Y·I)
F;:El...t·, ··,.,B

I CLEAR OR SET RELAY
XDh:
D(.~C

./L.D(\D DU;::·F!::.F;:

DF(~:;

.Jr1P*

/11' i'iClN lEI:::!) SET

EFUN3

~3(1D

/'F(ETUF:N
/GET

("f(GUMENT

if;I<JP

~:;F(\C[~:;

/ I !:j 1 T (', cm-1M":1?

..Jr-lP
.DEC

.+3

L.. (')l~

:I.

INCl ....

FUNEF(I:(

iEXTEf(NAL FUNCTION [Rf(Of(
/~:;I< I I'" C(Jr-jM(~

. OCT
,.J HP*
,.Jf''I~:;*

1...(\[

UTW~
EV(~I...

Di~C

.+2

,.JhS*

XPUSH.J

/YE::>
'i' TO!.

Ef::I:Wf(

ICAlL EXPf(ESSIDN EVAI...UATOf(

XX
..Jl'1P*

IF(ETUf(N

xcoc:mD

()

IX COOf(DINATE STORAGE

I,(EI...f-IYB

()

/ HEI...AY BUFFER STORAGE

TEMP

ITEMPORARY STORAGE

6-7

User Defined Focal Functions
IROUTINE TO GENERATE A RANDOM NUMBER
I!DEC. 1970
INUMBER SEGUENCE CAN BE INITIALIZED
IBY HAVING A NON-ZERO FUNCTION ARGUMENT
/

IUSES A SIMULATED 18BIT SHIFT REGESTER
/WHICH IS SHIFTED 1 BIT RIGHT WITH FEEDBACK
IFROM THE 7'TH&18'TH STAGES TO THE l'ST STAGE
ITHROUGH AN EXCLUSIVE BR GATE
I

RAND

STGEN

JMS*
SZA
JMP
LAC
SNA
LAW
DAC

.AX

lIS IT 0

STGEN
RANPT

I NO GENERATE RANDOM NUMBER
I YES IS LAST RANF'T 0

-- 1

IYES INITIriLIZE RANF'T
ISTA RT TO GENERATE
I NEW RANDOM NUMBER
IBY SHIFTING ONE BIT RIGHT
IGET BITl7 AND STORE (STAGE18)

RANPT

RCF~

DAC
GLK
DAC
LAC
RTR
RTR
RTR
RTR
RTR
AND
XOR
SZA
TAD
TAD
DAC
DAC*
DZM*
DZM*
JMF'*
BITSAV
RANPT

IGET AFWUMENT IN AC

RANF'T

•

BITSAV
RANF'T
I GET 8IT6 (STAGE 7)
ISETUP TO FEEDBACK TO BITO
!(STAGE 1) THROUGH XOR GATE
(1

BITSAl)
(377777
RANPT
F<ANPT
.AB
.AA
.,:'.jC

EFUN3

IFEEDBACK {O, ONE
/MAKEUP NEW RANDOM NUMBER
/STORE FOR FUTURE USE
/SET SIGN AND HIGH ORDER MANTISSA
IS ET EXPDNENT"'O
ISET LOW ORDER MANTISSA =O
IEXI T TO FUNCTION RETURN

0
0

.END

6-8

CHAPTER 7
DATA COMMANDS
FOCAL data commands allow the user to store and then retrieve substantial amounts of data through the use of auxiliary Input/Output
devices other than the Teletype.

The steps for processing the data

need not be incorporated in the FOCAL program itself.

The commands

cause files consistent with the XVM/DOS format to be produced and
accepted: and as with the library commands, the files can be manipulated by other XVM/DOS programs such as PIP and EDITOR, as may be
noted from the examples at the end of this chapter.
Data commands

are used with other FOCAL commands and follow the

same conventions with only minor exceptions.

The DATA command,

because of the conflict with the DO command, cannot be abbreviated.
Also, under some conditions, library commands are illegal as with
DATA OUT or DATA CLOSE (see 7.1.1 and 7.1.2).
7.1

DATA COMMANDS

Three operations are required to produce a file with the FOCAL data
commands:

7.1.1

file initialization

file output

file termination
DATA File Initialization and Output

The command
*DATA OUT NAME
initializes and enters a filename on the device associated with .DAT
slot 10.

The name can be up to six alphanumeric characters and is

terminated by a carriage return.

The extension FCL is supplied by

the system.
Every TYPE or WRITE command issued after DATA OUT NAME will output
data to the device assigned to .DAT slot 10.

For example with the

following .DAT slots assigned:
$A DPO -1,-4/DT1 3,5,7,10
data is output to .DAT 10 on DECtape unit 1, until a DATA file termination command is given.
If a LIBRARY command is issued while in the DATA OUT mode, error
message "?31" will be output to the teletype.

What has already been

output to the DATA file can then only be saved if a DATA CLOSE command is issued.

7-1

Data Commands
7.1.2

DATA File Termination

After the appropriate DATA output commands are used, it is necessary
to issue the command
*DATA CLOSE
to complete file output and enter the filename and data into the device
associated with .DAT slot 10.
put files to be closed.

DATA CLOSE commands allow input or out-

If a file has not been opened, FOCAL will

output the "?35" error message on the teletype.

The DATA CLOSE com-

mand also returns the user to the teletype mode.
If the command is not issued, the user remains in the data mode.

How-

ever, to leave the data mode without finishing the output file the
user may type
*DATA KILL
which aborts the output file and returns the user to the teletype mode.
The file started by the DATA output command is lost when DATA KILL is
issued.
7.1.3

DATA Input

The command
*DATA IN NAME
function is related to its use in indirect programs.

When DATA IN

NAME is used in an indirect program (e.g., 1.10 DATA IN filename),

initializes the device associated with .DAT slot 7 for data input
from an ASK command.

Recall that the ASK command is normally used in

indirect commands and that its use is to input data at specific points
during the execution of an indirect program.

Thus, when a line num-

ber and a DATA IN command such as
*1.10 DATA IN filename
is inserted in a program,

.DAT slot 7 is initialized for data input

when an ASK command such as
*2.10 ASK X,Y,Z
is encountered during program execution.
7.2

DATA .DAT SLOT USAGE

Data commands, as previously stated, assume input on .DAT slot 7 and
output on .DAT slot 10.

The recommended assignment to the Linking

Loader is the system library located on unit O.

7-2

Recommended FOCAL

Data Commands
program and user input/output assignments for DECtape and Disk are:
,DAT Slot

contents

Sample Assignment

.DAT -1
.DAT -4

System Library
FOCAL binary program
plus FNEW binary
FOCAL library input
FOCAL library output
FOCAL DATA input
FOCAL DATA output

DPO
DPO

.DAT 3
.DAT 5
.DAT 7
.DAT 10
7.3

DTO
DTO
DTO
DTO

DATA COMMAND USE

Some of the data commands so far described are used in the following
examples.

Also demonstrated are the commands for loading FOCAL with

the Linking Loader and for use of PIP for a Directory listing and output of data on the teletype.
XVM/DOS Vnxnnn
$A DPI -4,3,5,7,10

/Prior .. DAT slot assignment

$GLOAD
LOADER XVM

Vnxnnn

FOCAL
FOCAL XVM Vnxnnn
*1.10 DATA IN INDISK

/Type indirect program

*1.20 ASK A,B,C,D,E

/File INDISK contains the input
Data.

*1.30T A+B+C+D+E,!

/See PIP listing of INDISK below.

*GO
15,0000
*LO SHOW

/Save indirect program.

*LWA
*LC
*LI Show
*WA

/Recall indirect program

C FOCAL XVM Vnxnnn
o

01.10 DATA IN INDISK

/List program on the teletype.

01.20 ASK,A,B,C,D,E
01.30 T A+B+C+D+E, !
*GO
15,0000
*TA
1. 0000*

*TB, !
2,0000

7-3

Data Commands
* DATA OUT OUTDT

/Output data onto DECtape using

*TA

/the TYPE command

*TB
*TC
*TD
*TE,l
/Close the output file.

* DATA CLOSE
* C
XVM/DOS Vnxnnn
SPIP
XVM Vnxnnn

/Examination of files created
and input

PIP XVM Vnxnnn
LTT

DT1

DIRECTORY LISTING
1042 FREE BLKS
4 USER FILES
10

SYSTEM BLKS

INDISK

FCL

FOCAL

BIN

SHOW

FCL

OUTDT

FCL

3
4

1
1

T TT

DT1 INDISK FCL(A)

1.0
2.0
3.0
4.0
5.0
C FOCAL XVM Vnxnnn
01.10 DATA IN INDISK

•

01.20 ASK A,B,C,D,E
01.30 T A+B+C+D+E.!
T TT

DT1 OUTDT FCL(A)
1. 0000

2.0000

3.0000

XVM/DOS Vnxnnn

7-4

4.0000

5.0000

APPENDIX A
FOCAL COMMAND SUMMARY
Corrunand

Example of Form

Explanation

ASK

ASK X,Y,Z

FOCAL types a colon for
each variable, user then
types a value to define each
variable.

COMMENT

If a line begins with the
letter C, but not COMMON,
the remainder of the line is
ignored during program execution.

COMMON

none

COMMON A,B,
(C,1,2,20)

Assigns COMMON variables to
be stored in indirect program.

CONTINUE

Durruny lines.

DATA

none

DATA OUT NAME

Initializes the device
assigned to .DAT 10 and, if
file-oriented, enters the
filename in the file directory.

DATA CLOSE
NAME

Closes the output file and
returns the user to the
teletype mode.

DATA KILL

Aborts the output file and
returns the user to the
teletype mode.

DATA IN NAME

Initializes the device
assigned to .DAT 7 and
reads in the file named.

DO 4.1

Execute line 4.1, return to
corrunand following DO command.

DO 4.0

Execute all group 4 lines,
return to corrunand following
DO corrunand, or when a RETURN is encountered.

DO ALL

Execute entire indirect
program

ERASE

Erases 1user 's entire symbol
table

ERASE 2.0

Erases all lines in group 21

ERASE 2.1

Erases line 2.1 1

ERASE ALL

.
1
Deletes all user lnput

ERASE COMMON

Deletes all COMMON variables

.")

Abbreviation

ERASE

1Has no effect
A-1

Appendix A (Cont'd)

Corronand

FOR

Abbreviation
F

Example of Form

FOR I=X,Y,X,
(corronands)

Explanation

Where the corronand following
is executed at each new
value.
X=initial value of I.
Y = value added to I until
I is greater than Z.
Y
1, if not defined.

Starts indirect program at
lowest numbered line number.

GO?

Starts at lowest numbered
line number and traces entire indirect program until
another question mark (7) or
an error is encountered, or
until completion of program.

GOTO

GOTO 3.4

Starts indirect program
(transfers control to line
3.4); must have argument.

IF (X)Ln,Ln,Ln

Where X is a defined identifier, a value or an expression, followed by three
numbers/corronands.

IF (X)Ln,Ln;
(corronands)
IF (X)Ln;
( corronands )

If X is less than zero, control is transferred to the
first line number.
If X is equal to zero, control is transferred to the
second line number or command.
If X is greater than zero,
control is transferred to
the third line number or
corronand.

LIBRARY

LIBRARY OUT
NAME

Initializes a file on the
output device.

LIBRARY WRITE
NNN

Inserts NNN in library output file.

LIBRARY WRITE
2.01

Inserts line 2.01 in output
file.

LIBRARY WRITE
2.00

Inserts group 2 lines in
library output file.

LIBRARY WRITE
ALL

Inserts entire indirect program in library output file.

A-2

Appendix A (Cont'd)

Command

Example of Form

Explanation

LIBRARY CLOSE

Causes file name to be entered in directory.

LIBRARY KILL

Returns user to command mode
& file is deleted.

LIBRARY IN NAME

Loads library file NAME.

MODIFY

MODIFY 1.15

Enables editing of any character on line 1.15 (see
below) •

QUIT

Returns control to the user.

RETURN

Terminates DO subroutines,
returning to the original
sequence.

SET

SET A=5/B*C

Defines identifiers in the
symbol table. Each occurrence of A is replaced by
the value of the expression.

TYPE

TYPE A+B - C

Evaluates expression and
types out result in current
output format.

TYPE A-B,C/E

Computes and types each expression separated by commas.

TYPE "TEXT
STRING"

Types text, can be followed
by exclamation point (!) to
generate carriage returnline feed or by # to generate carriage return only.

WRITE
WRITE ALL

FOCAL types out the entire
indirect program.

WRITE 1.0

FOCAL types out all group
1 lines.

WRITE 1.1

FOCAL types out line 1.1

WRITE

,..

Abbreviation

FOCAL Operations
Operation
To set output format

Command

Explanation

TYPE% x.yz

Where x is the total number
of digits, and yz is the
number of digits to the
right of the decimal point.

TYPE % 6.3,
123.456

FOCAL types: 123.456

TYPE

Resets output format to
floating pOint.

A-3

Appendix A (Cont'd)

Operation

Command

TO type symbol table

TYPE $

Explanation
Other statements may not
follow on this line.

To produce carriage
return-line feed
Carriage return only

Modify Operations
After a MODIFY command, the user types a search character, and FOCAL
types out the contents of that line until the search character is
typed.

The user can then perform any of the following optional oper-

ations.
a.

Type in new characters.
point of insertion.

FOCAL adds these to the line at the

Type an ALT MODE.
FOCAL proceeds to the next occurrence of
the search character.

Type a CTRL BELL.
character.

Type RUBOUT. This deletes characters to the left; one character for each time the user strikes the RUBOUT key.

Type CTRL U. Deletes the line over to the left margin, but
not the line number.

Type RETURN. Terminates the line, deleting characters over
to the right margin.

Type LINE FEED. Saves the remainder of the line from the
point at which LINE FEED is typed over to the right margin.

After this, the user can change the search

Summary of Internal Functions
Function
Square Root

FOCAL Representation
FSQT(x)

Operation
Focal computes ..Jx where x is a
positive number or expression
greater than zero.

Absolute Value

FABS(x)

FOCAL ignores the sign of x.

Sign Part

FSGN(x)

FOCAL evaluates the sign part
only with 1 as integer.

Integer Part

FITR(x)

FOCAL operates on the integer
part of x, ignoring any fractional part.

Random Number
Generator

FRAN

FOCAL generates a random number.

Exponential
Function
(eX)

FEXP (x)

(

FOCAL generates e to the power
x.
(2. 718281828 x ) .

A-4

Appendix A (Cont'd)
Function

FOCAL Representation

Operation

Sine

FSIN(x)

FOCAL generates the sine of angle
x expressed in radians.

Cosin

FCOS (x)

FOCAL generates the cosine of
angle x expressed in radians.

Arc Tangent

FATN(x)

FOCAL generates the arc tangent
of angle x expressed in radians.

Logarithm

FLOG (x)

FOCAL generates log (x).
e

A-5

•

APPENDIX B
ERROR DIAGNOSTICS
MEANING

CODE

700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
77nn

Function not implemented
Illegal character at beginning of line
Group number illegal as line number
Group number too large
Illegal type/ask format
Too many periods
Line number too large
Line number missing
Illegal group number
Push-down list overflow
Illegal command
Illegal IF format
Left of equals in error on FOR or SET
Excess right parenthesis
Illegal FOR format
Illegal variable name
Text/variable buffer overflow
Illegal expression format
Operator missing before parenthesis
Missing left parenthesis
Illegal function name
Double operator
Parenthesis error
ERASE or WRITE argument error
Negative line number
Zero argument for log
Input overflow
Number too large
Negative power illegal
Division by zero illegal
Square root of a negative number
Illegal command during library or data output
Illegal library command
Illegal file name
File not found
No file open
.OTS error from arithmetic package
COMMON statement format error
User defined function error

•

B-1

•

APPENDIX C
ESTIMATING THE LENGTH OF USER PROGRAMS
FOCAL requires five words for each identifier stored in the symbol
table, and one word for each three characters of stored program.
This may be calculated by
5s+(
where

1 ·1.01) = length of user's program

= Number of identifiers defined

= Number of characters in indirect program

If the total program area or symbol table area becomes too large,
FOCAL types the error message
116
The following routine allows the user to find out how many core
locations remain for his use.
tEOR

I ~ 1.50 0 0;

S ET A(I) = I

?1 6

tTYPE %4. It5.
"LOCATIONS LEFT"
8 16 0 LOCA1IONS LEFT*

(Wait for FOCAL to type
the error message.)

At the end of this routine, use ERASE to clear all the variables A(I)
from the symbol table.
NOTE
The upper limit on I varies with the
amount of core memory in the user's
system.

C-1

•

APPENDIX D
CALCULATING TRIGONOMETRIC FUNCTIONS

Function

FOCAL
Representation

Sine
Cosine
Tangent

FSIN(A)
FCOS (A)
FSIN(A)/FCOS(A)

Secant

l/FCOS (A)

Cosecent
Cotangent

Argument
Range
O.:;.IAI <10 t 4
0~IAI<10t4

0< IA' <10t4
I A ~ (2N+1hr/2
O~ I AI <10t4

IAI~(2N+1)1T/2
0~IAI<10t4

l/FSIN (A)

IAI~2N1T

FCOS(A)/FSIN(A)

Arc sine
FATN(A/FSQT(1-A t 2)
Arc cosine
FATN(FSQT(1-At2)/A)
Arc tangent
FATN (A)
Arc secant
FATN(FSQT(At2-1»
Arc cosecant
FATN(1/FSQT(At2-1»
Arc cotangent
FATN (l/A)
Hyperbolic sine (FEXP(A)-FEXP(-A»/2
Hyperbolic
(FEXP(A)+FEXP(-A»/2
cosine
Hyperbolic
(FEXP(A)-FEXP(-A»/
tangent
(FEXP(A)+FEXP(-A»
Hyperbolic
2/(FEXP(A)+FEXP(-A»
secant
Hyperbolic
2/(FEXP(A)-FEXP(-A»
cosecant
Hyperbolic
(FEXP(A)+FEXP(-A»/
cotangent
(FEXP(A)-FEXP(-A»
Arc hyperbolic FLOG(A+FSQT(At2+1»
sine
Arc hyperbolic FLOG(A+FSQT(At2-1»
cosine
Arc hyberbolic
(FLOG(1+A)-FLOG(1-A»/2
tangent
Arc hyperbolic FLOG«1/A)+FSQT«1/Af2)-1»
secant
Arc hyperbolic FLOG«1/A)+FSQT«1/At2)+1»
cosecant
Arc hyperbolic
(FLOG(X+1)-FLOG(X-1»/2
cotangent

D-1

0~IAI<10t4
IAI~2N1T

Function
Range
O~IFI~l
O~IFI~l

0~IFI<10t6

1s.IFI<10t6
1~IFI<10t6
0~IFI<10t440

O~ 'AI <1
O<IA .s..1
0S.As.10t6
1S.A<10t6
1 <A<lO BOO
0<A<10t615
0S.IAI<700
0S.IAI<700

0S.IFIS.1T/2
0S.F<1T/2
0S.F<1T/2
0<F<1T/2
0<F<1T/2
0S.IFIs.5*10t300

0S.IAI<700

OS.IFIs.l

0S.IAI<700

O<F~l

0<IAI<700

0<IFI<10t7

0<IAI<700

1~IFI<10t7

0~IFI~1T/2

1~F<5*10BOO

-10t5<A<10t600 -12<F<1300
l:::A<lOBOO

0S.Fs.700

O~IAI<l

0S.IFI<8.31777

O<IAI~l

0S.F<700

0<IAI<10t300

0S.IFI<1400

1S.A<10t616

0S.F<8

•

APPENDIX E
.DAT SLOT AND HANDLER ASSIGNMENTS
SYSTEM IN XVM/DOS

The .DAT slots to be assigned with FOCAL are
.DAT

Typical Device Assignments*

Function

-1

System Library

-4

FOCAL binary program
plus FNEW binary

DPO <SYS>
DPO <SYS>

Library input

DPO <UIC>

Library output

rDPO <UIC>

Data input

DPO <UIC>

Data output

DPO <UIC>

*Here the system disk is assumed to be disk pack.
If it is cartridge
disk, substitute RK for DP in the assignments. Similarly, for fixedhead disk, substitute DK for DP.

E-l

•

INDEX
Abbreviated commands, 2-1], 4-1
Absolute value function (FABS),
3-13
Addition, 2-5
Alphanumeric characters, 2-12
Alphanumeric numbers, 2-11
Angle brackets, 2-5
Arctangent function (FATN),
3-15
Arithmetic operations and
symbols, 2-4
Arrays, COMMON, 5-4
ASK command, 3-2, 3-3, 7-2
* (asterisk) usage, 2-1, 3-8
as plotting character, 4-4
@ (at sign) used in symbol
table, 2-6
Auxiliary I/O devices, 1-3

Commands (cont.),
IF, 3-7
LIBRARY CLOSE, 5-3
LIBRARY WRITE, 5-3
MODIFY, 2-11, 3-10
RETURN, 3-8
SET, 2-1, 3-4
summary, A-I
TYPE, 2-1, 3 -1, 7-1
WRITE, 2-9, 2-10, 3-3, 7-1
COMMENT lines, 3-8
COMMON command, 5-1, 5-4
format, 5-4
variables, 5-5
Corrections in typing, 2-9, 2-10,
3-11
Cosine function (FCOS), 3-15
CTRL P, 1-2
CTRL U, 2-10, 3-11

Brackets, 2-5

DATA CLOSE command, 7-1, 7-2
Data commands, 7-1, 7-3
DATA IN command, 7-2
Data input/cutput, 1-3
Data I/O .DAT slots, 1-2
DATA KILL command, 7-2
.DAT slots, 1-1, E-l
data, 7-2
library, 5-4
Deleting characters, 2-9
Deleting lines, 2-10
Device assignment table, 1-1
Dice game, 4-5
Direct command output, library, 5-1
Division, 2-5
DO command, 2-8, 3-5

Chaining, 5-5
Character deletion, 2-9
Characters, alphanumeric, 2-12
Circles and spheres, formula
evaluation for, 4-2
(colon) usage, 3-2
Commands,
abbreviations for, 2-11, 4-1
data input, 7-2
data output, 7-1
library input, 5-3
library output, 5-1
Commands,
ASK, 3-2, 3-3, 7-2
COMMON, 5-1, 5-4
DATA CLOSE, 7-1, 7-2
DATA IN, 7-2
DATA KILL, 7-2
DO, 2-8, 3-5
ERASE, 2-7, 2-10, 2-11, 3-4
ERASE COMMON, 5-1, 5-5
FOR, 3-8
GO, 2-8, 3-5
GOTO, 2-8, 3-5, 3-7

EAE number accuracy, 2-4
E format, 2-4
Equations, 4-6
ERASE command, 2-7, 2-10, 2-11, 3-4
ERASE CO~~ON command, 5-1, 5-5
Error detection, 2-9
Error diagnostics, B-1
Errors,
syntax, 2-2

Index-l

Errors (cont.),
typing, 2-9
Examples of FOCAL programs, 4-1
Exponential function (FEXP),
3-14
Exponentiation, 2-4, 2-5, 2-12
Expressions, 2-5

File initialization,
data, 7-1
library, 5-1
File termination,
data, 7-2
library, 5 -- 2
Floating-point
arithmetic, 3-9
format, 2-3, 2-4, 3-14
hardware, 1-1
FNEW functions, 6-3
FOR command, 3-8
Formula evaluation for circles
and spheres, 4-2
FORTRAN library, 1-1
FOCAL language, 2-1
Functions,
FNEW, 6-3
internal, 3-13
names of, 2-1
trigonometric, D-l
user-defined, 6-1

GO command, 2-8, 3-5
GOTO command, 2-8, 3-5, 3-7
Group output, library, 5-2

Hardware, 1-1

IF command, 3-7
IF statement, 3-6
Indirect commands, 2-7
Initialization of library file,
5-1
Input commands,
data, 7-2
library, 5-3
Integer part function (FITR),
3-14
Intercept and plot of two
functions, 4-11
Interest payment program, 4-10
Internal functions, 3-13

Length of program, C-l
LIBRARY CLOSE command, 5-3
Library .DAT slot usage, 1-2, 5-4
Library files,
initialization, 5-1
output, 5-1
termination, 5-2
Library, FORTRAN, 1-1
LIBRARY WRITE command, 5-3
Line deletion, 2-10
Line numbers, 2-7
Linking loader, 1-1
Loading, 1-1, 1-3
Logarithm function (FLOG), 3-16
Looping process, 4-2

Matrices, 4-6
MODIFY command, 2-11, 3-10
Multiplication, 2-5

Names of
symbols, 2-1
functions, 2-1
Nested expressions, 2-5
Non-subscripted variable, 5-4
Number representation in TYPE
command, 2-1
Numbers, alphanumeric, 2-11
Number sign (#) usage, 2-7

One-line plotting, 4-4
Operators, arithmetic, 2-5
Output,
data files, 7-1
library files, 5-1
Output format, 2-2

Parentheses, 2-5, 3-6
Percent sign (%) usage, 2-2, 3-1
Plotting, 4-4
Program chaining, 5-5
Program length, C-l
Program output,
data, 7-1
library, 5-2

Question marks in program, 2-9
Quotation marks, 4-1
in command string, 3-2
in text output, 2-7

Leading zeros, 2-2

Index-2

Random number generator function
(FRAN), 3-14
Restart, 1-2
RETURN command, 3-8
Rounding, 2-3, 4-1
RUBOUT, 2-9

Saving programs, 1-3
Schroedinger equation solver,
4-13
Scope routine example, 6-1
Semicolon in IF statement, 3-6
SET command, 2-1, 3-4
Sign part function (FSGN), 3-13
Sine function (FSIN), 3-15
Single line output, library,
5-2
Spheres, formula evaluation for
circles and, 4-2
Square brackets, 2-5
Square root function (FSQT),
3-13
Statement, IF, 3-6
Subroutines, 3-6
Subscripted variables, 2-6, 4-6
Subtraction, 2-5
Symbol names, 2-1
Symbols, arithmetic, 2-5
Symbol table, 2-6
Symbol table values, 3-11
Syntax errors, 2-2

Table generation using functions,
4-1
Termination of
data files, 7-2
library files, 5-2
Text output, 2-7
Trace feature, 2-9, 3-12
Trailing zeros, 2-2
Trigonometric functions, D-l
TYPE command, 2-1, 3-1, 7-1

User-defined functions, 6-1

Variables,
nonsubscripted, 5-4
subscripted, 2-6, 4-6

WRITE command, 2-9, 2-10, 3-3,
7-1

Zeros in output format, 2-2

Index-3

•

FOCAL XVH Language Hanual
DEC-XV-LFLGA-A-D
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