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PDP-SII

FOCAL

Programming Manual

DEC-08-AJAB-D

FOCAL

Programming Manual
for
PDP-S
PDP-SIS
PDP-S/I
LAB-S
LINC-S

For additional copies Order No. DEC-08-AJAB-D from Program Library,
Digital Equipment Corporation, Maynard, Mass. Price $1.00
DIGITAL EQUIPMENT CORPORATION. MAYNARD. MASSACHUSETTS
Printed in U.S.A.

CONTENTS

CHAPTER 1
AN INTRODUCTION TO FOCAL
1.1

Equipment Requirements

1-1

1.2

Loading Procedure

1-1

1.3

Restart Procedure

1-3

1.4

Saving Focal Programs

1-3
CHAPTER 2
FOCAL LANGUAGE

2. 1

Simple Commands

2-1

2.2

Output Format

2-2

2.3

Floating-Point Format

2-3

2.4

Arithmetic Operations

2-4

2.5

More About Symbols

2-5

2.6

Subscripted Variables

2-6

2.7

The ERASE Command

2-6

2.8

Handling Text Output

2-6

2.9

Indirect Commands

2-7

2.10

Error Detection

2-9

2.11

Corrections

2-9
CHAPTER 3
FOCAL COMMANDS

3. 1

TYPE

3-1

3.2

ASK

3-2

3.3

WRITE

3-2

3.4

SET

3-3

3.5

ERASE

3-3

3.6

3-4

3.7

GOTO

3-4

3.8

3-4

3.9

3-5

3.10

RETURN

3-6

3.11

QUIT

3-6

3.12

COMMENT

3-6
iii

CONTENTS (cont.)
3.13

FOR

3-6

3.14

MODIFY

3-8

3.14.1

Caution

3-9

3.15

Using the Trace Feature

3-9

3.16

Functions

3-10

CHAPTER 4
EXAMPLES OF FOCAL PROGRAMS

4. 1

Table Generation Using Library Functions

4-1

4.2

Formula Evaluation for Circ les and Spheres

4-2

4.3

Tem perature Convers ion

4-4

4.4

One-Line Function Plotting

4-5

4.5

Extensions to Plotting

4-6

4.6
4.7

Demonstration Dice Game

4-7

Simultaneous Equations and Matrices

4-9

APPENDIX A
FOCAL COMMAND SUMMARY

A-1

APPENDIX B
ERROR DIAGNOSTICS

B-1

APPENDIX C
ESTIMATING THE LENGTH OF USER'S PROGRAM

C-1

APPENDIX D
CALCULATING TRIGONOMETRIC FUNCTIONS IN FOCAL

D-1

APPENDIX E
OPERATING HINTS

E-l

APPENDIX F
LOADERS

F-1

ILLUSTRATION
1-1

1-2

FOCAL Loading Procedure

HOW TO OBTAIN REVISIONS AND CORRECTIONS

Notification of changes and revisions to currently available Digital software
and of new software manuals is available from the DEC Program Library for the
PDP-5, 8, 85, 81, Linc 8, the PDP-4, 7 and 9 is currently published in DECUSCOPE,
the magazine of the Digital Equipment Computer User IS Society (DECUS). This
information appears in a section of DECUSCOPE called IIDigital Small Computer

Revised software products and documents are shipped only after the Program
Library rece ives a spec ifie request from a user.
DECUSCOPE is distributed periodically to both DECUS members and to nonmembers who request it. If you are not now receiving this information, you are
urged to return the request form below so that your name will be placed on the
mailing list.

~~~----------------------------~~---~~-~~-~~~~

To:

DECUS Office,
Digital Equipment Corporation,
Maynard, Mass. 01754

Please send DECUS installation membership information.

o Please send DECUS individual membership information.
o

Please add my name to the DECUSCOPE non-member mailing list.
Name ____________________________
Company __________________________
Address __________________________

(Zip Code)

PREFATORY NOTE
The purpose of this manual is to introduce FOCAL to
the scientific and engineering, and educational fraternities.

Later, Digital will publish two specialized

FOCAL manuals; one for professional scientists and
engi neers, the other for students.

CHAPTER 1
AN INTRODUCTION TO FOCAL*

FOCAL (for ~ormulating .Qn-Line ~alculations in ~Igebraic !:.anguage) is an on-line,
conversational, service program for the PDP-8 family of computers, designed to help scientists,
engineers, and students solve numerical problems. The language consists of short imperative English
statements which are relatively easy to learn. Mathematical expressions are typed, for the most part,
in standard notation. The best way to learn the FOCAL language is to sit at the Teletype and try the
commands, starting with the examples given in this manual.
FOCAL puts the full calculating power and speed of the computer at your fingertips. FOCAL
is used for simulating mathematical models, for curve plotting, for handling sets of simultaneous
equations in n-dimensional arrays, and many other kinds of problems. Some of the kinds of problems
that have been solved by FOCAL are described in Chapter 4, Sample Programs.

1.1

EQUIPMENT REQUIREMENTS
FOCAL operates on a 4K PDP-8/1, PDP,,:,8, PDP-8/S, LAB-8, or LlNC-8 computer with

ASR 33 Teletype. Optional: Analog-to-Digital Converter (AF01A)i Oscilloscope Display (VC8/1 or 340).

1.2

LOADING PROCEDURE
The Binary Loader is used to load FOCAL. Check to see if the Binary Loader is in core. If

location 7777 contains 5301, the Binary Loader is in corei if not, refer to Appendix F.
The procedure for loading FOCAL is detailed below.
a.

Place the FOCAL binary tape in the tape reader.

Put 7777 (the starting address of the Binary Loader) in the SWITCH REGISTER.

Press the LOAD ADDress key.

To use the high speed paper tape reader, set bit 0 of the SWITCH REGISTER to O.
d.

Press the START key.

e. The tape will stop twice during loading because the program is loaded in three sections
for additional checksum protection. After each halt, the contents of the accumulator (AC) should be 0i
if the AC -F 0, reload the previous section of tape. If the AC is 0, press the CONTinue key and the
tape will continue loading.
f. Place 200 (the starting address of FOCAL) in the SWITCH REGISTER when the tape is
completely loaded.

* FOCAL is a trademark of Digital Equipment Corporation.
1-1

Press the LOAD ADDress key.

h. Press the START key. The initial dialogue will begin. This is a question and answer
sequence, with FOCAL asking questions and the user providing the answers. The first question offers
an option. If you want a full explanation, press the RETURN key on your Teletype. The present
version of FOCAL operates in 4K, and so states; future versions will include an option to uti! ize an
additional 4K of memory.
i. FOCAL is correctly loaded and ready for user input when it types an asterisk. If
FOCAL is incorrectly loaded, reload the FOCAL tape starting with step a above.
The FOCAL loading procedure is illustrated in the flowchart (Figure 1-1).

FOCAL IS READY
FOR USER INPUT

Figure 1-1

CHECKSUM ERROR

FOCAL Loading Procedure

1-2

1.3

RESTART PROCEDURE
Two methods for restarting the system are outl ined below.

a. The CTRL/C keys at any time. 1 FOCAL will type ?01 .00 indicating a keyboard
restart, and an asterisk on next Iine indicating it is ready for user input.
b.

From the computer console:

(1) Depress the STOP switch.
(2) Put 0200 in the SWITCH REGISTER
(3)

Depress the LOAD ADDress switch

(4)

Depress the START switch

(5) FOCAL will then type *?OO.OO indicating a manual restart, and an asterisk on the
next Iine indicating it is ready for user input.

1.4

SAVING FOCAL PROGRAMS
To save a FOCAL program on-line, the user should
a.

Respond to * by typing WRITE ALL (do not depress the RETURN key).

b•

Turn on tape punch

c. Type several @ signs to get leader tape {press the Shift, REPEAT, and P keys in that
order; release in the reverse order}.
d.

Depress RETURN key

When the user's program has been typed and punched out
e.

Type several more @ signs to get trailer tape.

Turn off tape punch

The user may now continue with another FOCAL program. The previous FOCAL program is
still in the computer and waiting to operate on user input.

1 CTRL/C indicates holding down the Control key while depressing the C key. This convention is
used throughout this manual.

1-3

CHAPTER 2
FOCAL LANGUAGE

After the initial dialogue has been concluded, FOCAL types

*
indicating that the program is ready to accept commands from the user. Each time the user completes
typing a Teletype line, which is terminated 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

SIMPLE COMMANDS
One of the most useful commands in the FOCAL language is TYPE. To FOCAL this means

"type out the result of the following expression."

If you type (following the asterisk which FOCAL

typed),
*TYPE 6.4318+8.1346

and then press the RETURN key, FOCAL types
=+

14.5664*

Another useful command is SET, which tells FOCAL "store this symbol and its numerical
value. When I use this symbol in an expression, insert the numerical value." Thus, the user may type,
*SET A=3.14159; SET B=428.77; SET C=2.71828

*
The user may now use these symbols to identify the values defined in the SET command. Symbols may
consist of one or two alphanumeric characters. The first character must be a letter, but must not be
the letter F.
*TYPE A+B+C
=+ 434.6300 *
Both the TYPE and SET commands will be explained more fully in the next chapter.
FOCAL is always checking user input for invalid commands, illegal formats, and many
other kinds of errors, and types an error message indicating the type of error detected. In the example,

2-1

*HELP
?02 .29
*TYPE 2++4
?04.; 9

*
HELP is not a valid command and two plus signs (double operators) are illegal. The complete list of
error messages and their 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 zeros are included in the
output, as shown in the examples below.
*SET A=77.77; SET 8=1111.1111; SET C= 39
*TYPE A,8,C
=+
77.7700=+1111.1100=+
39.0000*

The results are calculated to six significcmt digits. Even though a result may show more than
six digits, only six are significant, as shown above in SET B = 1111.1111, which FOCAL typed as

=+ 1111.1100.
The output format may be changed if the user types
TYPE

%x.yz

where x is the total number of digits to be output and yz is the number of digits to the right of the
decimal point. x and yz are positive integers, and x cannot exceed 19 digits. When first loaded,
FOCAL is set to produce output having eight digits, with four of these to the right of the decimal point
(%8.04). For example, if the desired output format is mm.nn

the user may type

and FOCAL will type
=+14.59*

2-2

Notice that the format operator (%) must be followed by a comma.
In the following examples, the number 67823 is typed out in several different formats.

*SET A=67823
*TYPE %6.01, A
=+67823.0*
*TYPE %5, A
=+67823*

*T YP E %8 .0 3, A
=+67823.000*

If the specified output format is too small to contain the number, FOCAL types XiS, as shown
below.

*TYPE %3,
=+xxx*

67823

If the specified format is larger than the number, FOCAL inserts leading spaces:

*TYPE %7, 67823
=+
67823*

Leading blanks and zeros in integers are always ignored by FOCAL.

*TYPE %8.04, 0016,0.016,
=+
16.0000=+
0.0160=+

2.3

.,007
0.0000=+

FLOATING-POINT FORMAT
To handle much larger and much smaller numbers, 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 floatingpoint format by including a % followed by a comma, in a TYPE command. From that point on, until
the user again changes the output format, results will by typed out in floating-point format.

*TYPE %, 11
=+0.110000E+02*

This is interpreted as .11 times 102 , or simply 11. Exponents can be used to ±619. The largest number
that FOCAL can handle is +0.999999 times 10619 , and the smallest is -0.999999 times 10 619 •

2-3

To demonstrate FOCAL's power to compute large numbers, you can find the value of 300
factorial by typing the following commands. (The FOR statement, which will be explained later, is
used to set I equal to each integer from 1 to 300.)

*SET A=l
*FOR 1=1 .. 300; SET A=A* I
*TYPE %.. A
=+0.306051E+615*

2.4

(wait for FOCAL to type *)

ARITHMETIC OPERATIONS
FOCAL performs the usual arithmetic operations of addition, subtraction, multiplication,

division, and exponentiation. These are written by using the following symbols
FOCAL

Symbol

Math Notation

1 Exponentiation

* Multipl ication

3·3

313 (Power must be a
positive integer)
3*3

/ Division

3+3

3/3

+ Addition

3+3

- Subtraction

3-3

These operations may be combined into expressions. When FOCAL evaluates an
expression, which may include several arithmetic operations, the order of precedence is the same as
that in the list above. That is, exponentiation is done first, followed by multiplication and division,
followed by addition and subtraction. Expressions with the same precedence 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 2<2Y
Expressions are combinations of arithmetic operations or functions which may be reduced
by FOCAL to a single number. Expressions may be enclosed in properly paired parentheses, square
brackets, and angle brackets (use the enclosures of your choice; FOCAL is impartial and treats them
all merely as enclosures).

2-4

For example,
*SET Al=(A+B)*<C+D>*[E+G]

*
The [and J enclosures are typed using Shift/K and Shift/M, respectively.
Expressions may be nested. FOCAL computes the value of nested expressions by doing the
innermost first and then working outward.

*TYPE %~ [2+(3-<1*1>+5)+2]
=+0.110000E+02*

Note that this number is expressed in floating-point format.

2.5

MORE ABOUT SYMBOLS
The value of a symbol ic name or identifier can be changed by retyping the identifier and

giving it a new value.
*SET A1=312;
*TYPE %2~ Al
=+10*

SET A1=Al+l

The user may request FOCAL to type out all of the user defined identifiers, in the order of
definition, by typing a dollar sign ($).
*TYPE %6.5~

The user's symbol table is typed out Iike this

A@(00)=+XXXXXX
B@ (00 ) =+ 111 1 .1 1
C@ (00) =+39 .0000
I@ (00) =+30 1 .0eJeJ
Al (00)=+10.0000
D@ (00) =+0.00000
E@ (00 ) =+0.00000
G@ (00) =+0.00000

2-5

If an identifier consists of only one letter, an @ is inserted as a second character in the symbol table
printout, as shown in the example above. An identifier may be longer than two characters, but only
the first two will be recognized by FOCAL and thus stored in the symbol table.

2.6

SUBSCRIPTED VARIABLES
FOCAL always allows identifiers, or variable symbols, to be further identified by subscripts

(range ±2047) which are enclosed in parentheses immediately following the identifier. A subscript may
also be an expression:

*SET AlCI+3*J)=2.71; SET X1<5+3*,J)=2.79

*
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 4.7.

2.7

THE ERASE COMMAND
It is useful at times to delete all of the symbolic names which you have defined in the symbol

table. This is done by typing a single command: ERASE. Since 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 Teletype printing

characters and spaces. The carriage return, Iine feed, and leader-trailer characters are not allowed
in text strings. In order to have FOCAL type an automatic carriage return-line feed at the end of a
text string, the user inserts an exclamation mark (! ) •

*TYP E "ALP HA" ! "BETA" ! "DELTA" !
ALPHA
BETA
DELTA

*
To get a carriage return without a Iine feed at the end of a text typeout, the user inserts a
number sign (#) as shown below.

2-6

I-=----=---_-~:::~~s

r - .-

x Y
~

3 SPACES

r - - - - - - - - - - - - - - 5 SPACES
r - - - - - - - - - - - 2 SPACES
r - - - - - 8 SPACES

*TYPE !"
X+Y

Z"#"

="#"

/"!

*
The number sign operator is useful in formatting output and in plotting another variable along the same
coordinate (see Section 4.5).
2.9

INDIRECT COMMANDS
Up to this point we have discussed commands which are executed immediately by FOCAL.

Next, we shall see how indirect commands are written.
If a Teletype line is prefixed by a line number, that line is not executed immediately, instead,
it is stored by FOCAL for later execution, usually as part of a sequence of commands. Line numbers
must be in the range 1.01 to 15.99. The numbers 1.00, 2.00,etc., are illegal line numbers; they are
used to indicate the entire group. The number to the left of the point is called the group number; the
number to the right is called the step number. For example,
*ERASE
*1.1 SET A=l
*1.3 SET B=2
*1.5 TYPE %1, A+B

*
Indirect commands are executed by typing GO, GOTO, or DO commands, which may be
direct or indirect.
The GOTO command causes FOCAL to start the program by executing the command at a
spec ified line number. If the user types
*GOTO 1.3
=+2*

FOCAL started executing the program at the second command in the example above.
The GO command causes FOCAL to go to the lowest numbered Iine 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 •

2-7

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.
*ERASE ALL
*1.1 SET A=11 SET 8=2
*1.2 TYPE " START! NG "
* 1 .3 DO 3.2
*2.1 TYPE" FINISHED"
*3.1 SET A=31 SET 8=4
*3.2 TYPE %1, A+8
*GO
STARTING =+3 FINISHED =+7*

When the DO command at line 1.3 was reached, the command TYPE %1, A+B was performed and then
the program returned to line 2.1 •
The DO command can also cause FOCAL to jump to a group of commands and then return
automatically to the normal sequence, as shown in the example below.
*ERASE ALL
* 1 • 1 TYPE "A "
* 1 .2 TYPE "8 "
* 1 .3 TYPE ftC "
* 1 .4 DO 5.0
*1 .5 TYPE " END"l GOTO 6.1
*5.1 TYPE "D "
*5.2 TYPE "E "
*5.3 TYPE "F "
*6.1 TYPE "
"
*GO
A 8 C D E F END. *

When the DO command at line 1.4 was reached, FOCAL executed lines 5.1, 5.2, and 5.3 and then
returned to line 1 .5.
An indirect command can be inserted in a program by using the proper sequential I ine number.
For example,
*ERASE ALL
*4.8 SET A=I; SET 8=2
*6.3 TYPE %5.4, 8/C+A
*4.9 SET C=I.31*.29
*GO
=+6.2645*

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, starting with the smallest line number and
going to the largest.

2-8

2.10

ERROR DETECTION
FOCAL checks for a variety of errors, and if an error is detected, types a question mark

followed by an error code. A complete Iist of these error codes is shown in Appendix B. The group
number of an error message indicates the class or general type:
?OO

Manual restart from console

?01

Interrupt from keyboard via CTRL/C

?02

Excessive number or illegal mathematical operation.

?03

Miscellaneous

?04

Format errors

?05

Function or command not loaded

The WRITE command without an argument can be used to cause FOCAL to print out the
entire indirect program so the user can visually check it for errors.
The trace feature is invaluable in program debugging. Any part of an indirect statement or
program may be enclosed in question marks, and when that part of the program is executed that portion
surrounded by question marks will be printed out. If only one question mark is inserted, the trace
feature becomes operative, and the program is printed out from that point until completion.
The trace feature may also be used to follow program control and to create special formats
(see Section 3.15).

2.11

CORRECTIONS

If the user types the wrong character, or several wrong characters, he can use the RUBOUT
key, which echoes a backslash (\) for each RUBOUT typed, to erase one character to the left each
time the RUBOUT key is depressed. For example,

*ERASE ALL

* 1 • 1 P \ T YP E X - Y
*1.2 SET $=13\\\\X=13
*WRITE
C -FOCAL.,

o 1 • 10

1968

T YP E X - Y

01.20 SET X=13

*
The left arrow (....) erases everything which appears to its left on the same line.

2-9

*1.3 TYPE A~ 8~
*WRITE
C-rOCAL. ~ 1968

01.10 TYPE X-Y
01.20 SET X=13

*
A Iine can be overwritten by repeating the same Iine number and typing the new command.
*14.99 SET

C9(N~3)=15

*
is replaced by typing
*14.99 TYPE C9/Z5-2
*WRHE 14.99
14.99 TYPE C9/Z5-2

*
A line or group of lines may be deleted by using the ERASE command with an argument. For
example, to delete line 2.21·, the user types

*ERASE 2.21

*
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 user1s
entire symbol table. Since FOCAL does not zero memory when loaded, it is good practice to ERASE
before defining symbols. The command' ERASE ALL erases all user input.
The MODIFY command is another valuable feature. It may be used to change any number of
characters in a particular line, as explained in Section 3.14.

2-10

CHAPTER 3
FOCAL COMMANDS

3.1

TYPE
The TYPE command is used to request that FOCAL compute and type out a text string, the

result of an expression, or the value of an identifier. For example
*4.14 TYPE 8.1+3.2-(29.3*5)/2.517
* 4 • 1 5 T YP E (2.2 + 3 • 5 H (7 .2/3 ) /59 • 1 13

*
Several expressions may be computed in a single TYPE command, with commas separating
each expression.
*ERASE
*9.19 TYPE %4.01, A1*2, E+215, 2.51*81.1
*DO 9019
=+
0.0=+
32.0=+ 204*

The output format may be included in the TYPE statement as shown in the example above and as explained
in Section 2.6.
The user may request a typeout of all identifiers which he has defined by typing TYPE $ and
a carriage return. This causes FOCAL to type out the identifiers with their values, in the order in which
they were defined. The $ may follow other statements in a TYPE command, but must be the last operation
on the line.
*ERASE
*SET L=33; SET B=87; SET Y=55;
*TYPE $
L@(00)=+
33.0
B@ (00 )=+
87.0
Y@(00)=+
55.0
C9(00)=+
91.0

SET C9=91

*
A text string enc lased in quotation marks may be inc luded in a TYPE command. A carriage
return may replace the terminating quotation mark, as shown below:
*1.2 TYPE "X SQUARED =

*
A text string or any FOCAL command or group of commands may not exceed the capacity of
a Teletype line, which is 72 characters on the ASR33 Teletype. A line may not be continued on the
following line. To print out a longer text, each line must start with a TYPE command.

3-1

FOCAL does not automatically perform a carriage return after executing a TYPE command.
The user may insert a carriage return-line feed by typing an exclamation mark (!). To insert a carriage
return without a line feed, the user types a number sign (#). Spaces may be inserted by enclosing them
in quotation marks. These operations are useful in formatting output.

3.2

ASK
The ASK command is normally used in indirect commands to allow the user to input data at

specific points during the execution of his program. The ASK command is written in the general form,
*11.99 ASK X,

*
When step 11.99 is encountered by FOCAL, it types a colon (;). The user then types a value or expression for the first identifier, followed by a comma or a space. FOCAL then types another colon and
the user types a value for the second identifier. This continues until all the identifiers or variables in
the ASK statement have been given values,
*1 .02 TYPE "X SQUARED =
*11.99 ASK X, Y, Z
*DO 11.99

:5, :4, :3,*
where the user typed 5,4, and 3 as the values, respectively, for X, Y, and Z.
A text string may be inc luded in an ASK statement by enclosing the string in quotation marks.
*1.10 ASK "HOW MANY APPLES DO YOU HAVE?" APPLES
*00 1.10
HOW MANY APPLES DO YOU HAVE? :25 (user typed 25)

*
The identifier AP (FOCAL recognizes the first two characters only) now has the value 25.

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, may be typed out with the WRITE command using
arguments, as shown below.
(FOCAL types all group' 2 lines)
(FOCAL types line 2.1)
(FOCAL types all numbered lines)

*7 .97 WR ITE 2.0
*7. 98 WR ITE 201
*7. 99 WRITE

*
3-2

3.4

SET
The SET command is used to define identifiers. When FOCAL executes a SET command, the

identifier and its value is stored in the user's symbol table, and that value will be substituted for the
identifier when the identifier is encountered in the program.
*ERASE ALL
*3.4 SET A=2.55; SET B=8.05
*3.5 TYPE %, A+B
*GO
=+0.106000E+02*

An identifier may be set equal to previously defined identifiers, which may be used in arithmetic expressions.
*3.7 SET G=(A+B)*2.2t5

*
3.5

ERASE
An ERASE command without an argument is used to delete all identifiers, with their values,

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
*ERASE 7.11

(deletes all group 2 lines)
(deletes line 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 ALL
*1 .20 SET B=2
*1.30 SET C=4
*1 .40 TYPE B+C
*1.50 TYPE B-C
*ERASE 1.50
*WRITE ALL
C-F"OCAL., 1968
01 .20 SET B =2
01 .30 SET C =4
01.40 TYPE B+C

3-3

3.6

GO
The GO command requests that FOCAL execute the program which starts with the lowest

numbered line. The remainder of the program will be executed in line number sequence. Line numbers
must be in the range 1 .01 to 15.99.

3.7

GOTO
The GOTO command causes FOCAL to transfer control to a specific line in the indirect pro-

gram. 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 ALL
* 1 • 1 TYPE "A"
* 1 .2 TYPE "8"
* 1 .3 TYPE "C"
*1 .4 TYPE "0"
*GOTO 1 .2
BCD*

3.8

DO
The DO command transfers control momentarily to a single line, a group of lines, or the 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 commands transferred to, as shown in this example,
*ERP,SE ALL
1 • 1 T YP E "X"
*1.2 DO 2 .3; TYPE "yrv
*1.3 TYPE "Z"
*2.3 TYPE "A"
*GO
XAYZA*

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.

If Do is written without an argument, FOCAL execute the entire indirect program.

DO commands cause specified portions of the indirect program to be executed as closed subroutines. These subroutines may also be terminated by a RETURN command.

If a GOTO or IF command is executed within a DO subroutine, two actions are possible:

3-4

1. If a GOTO or IF command transfers to a line inside the DO group, the remaining commands
in that group will be executed as in any subroutine before return ing to the command following the DO.

2. If transfer is to a line outside the DO group, that line is executed and control is returned
to the command following the DO; un less that line contains another GOTO or IF.
*ERASE ALL
*1.1 TYPE "A"; SET X=-I; DO 3.1; TYPE "0";
*i.2 DO 2

*2.1
*2.2
*2.5
*2 • 6
*2.7
*2.8
*2.9

TYPE "G"
IF (X)2.5,2.6,2.7
TYPE "H"
T YP E "I"
TYPE "J"
TYPE "K"
TYPE %2.£:'11, X; TYPE"

*
*
TYPE "e"
*5.I

*3.1 TYPE "8",; GOTO 5.1 ;

DO 2

"; SET X=X+l

TYPE "F'''

*5.2 TYPE "E"
*5.3 TYPE "L"
*GO

(FOCAL types the answer)
ABCDGEIJK=-1.0

3.9

GIJK=+0.0

GJK=+1.0

BCEL*

IF
In order to transfer control after a comparison, FOCAL contains a conditional IF statement.

The normal form of the IF statement consists of the word IF, a space, a parenthesized expression or
variable, and three line numbers in order, separated by commas.

The expression is evaluated, and the

program transfers control to the first line number if the expression is less than zero, to the second line
number if the expression has a value of zero, or to the third line number if the value of the expression
is greater than zero.
The program below transfers control to line number 2.10, 2.30, or 2.50, according to the
value of the expression in the IF statement.
*2.1 TYPE "LESS THAN ZERO"; QU IT
*2.3 TYPE "EQUAL TO ZERO"; QUIT
*2.5 TYPE "GREATER THAN ZERO"; QUIT
*IF (25-25)2.1,2.3,2.5
EQUAL TO ZERO*

The IF statement may be shortened by terminating it with a semicolon or carriage return after
the first or second Iine number. If a semicolon follows the first line number, the expression is tested

3-5

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

(X)} .S;

TYPE "Q"

*
In the above example, when line 2.20 is executed, if X is less than zero, control is transferred to line 1.8. If not, Q is typed out.
*3.19 IF (B)1 .S,I.9
*3.20 TYPE B

*
In this 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, which in this case is
line 3.20, and the value of B is typed.

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 in itiated 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 may type another command.

3.12

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

ignored so that comments may be inserted into the program. Such lines wi II be skipped over when the
program is executed, but wi II be typed out by a WRITE command.

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;(COMMAND)

3-6

The identifier A is initialized to the value B, then the command following the semicolon is executed.
When the command has 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 command after the semicolon is executed again. This process
is repeated until A is greater than D, and FOCAL goes to the next sequential line.
The identifier A must be a single variable. B, C, and D may be either expressions, variables,
or numbers. If comma and the value C are 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.
Tbe computations involved in the FOR statement are done in floating-point 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 1:
*ERASE ALL
*1.1 SET A=100
*1.2 FOR B=I .1,5; TYPE %5.02, "8 IS" B+A,!
*GO
B IS =+101.00
B IS =+102.00
B IS =+103.00
B IS =+104.00
B IS =+105.00

*
Example 2:

*1.1 FOR X=I,I,5; DO 2.0
*1.2 GOTO 3.1

**2.1 TYPE! "

" %3, "X "X
*2.2 SET A=X+100.000
*2.3 TYPE ! "
" %5.02, "A "A

**3.1 QUIT
*GO
X
A
X
A
X
A
X

=+
=+101.00
=+
2
=+102.00
=+
3
=+103.00
4
=+
A =+104.00
X =+
5
A =+105.00*

3-7

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, the FOCAL programmer may use the MODIFY
command. Thus, in order to modify the characters in line 5.41, the user types MODIFY 5.41. This
command is terminated by a carriage return whereupon the program waits for the user to type that
character in the position in which he wishes to make changes or additions. This character is not printed.
After he has typed the search character, 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.

b. Type a form-feed (CTRL/L); this will cause the search to proceed to the next occurrence,
if any, of the search character.
c. Type a CTRL/BELL; this allows the user to change the search character just as he did
when first beginning to use the MODIFY command.
d.

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

Type a left arrow (~) to delete the line over to the left margin.

Type a 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.

The ERASE ALL and MODIFY commands are generally used on Iy in immediate mode since they
return to command mode upon completion. (fhe reason for this is that internal pointers may be changed
by these commands.)
During command input, the left arrow wi II delete the line numbers as well as the text if the
left arrow is the right most character on the line.
Notice the errors in line 7.01 below.

*7.01 JACK AND BILL W$NT UP THE HALL
*MODIFY 7.01
JACK AND B\JILL W$\ENT UP THE HA\ILL
*\I:RITE 7.01
07.01 JACK AND JILL WENT UP THE HILL

*
To modify line 7.01, a B was typed by the user to indicate the character to be changed. FOCAL stopped
typing when it encountered the search character, B. The user typed the RUBOUT key to delete the B,
and then typed the correct letter J.

He then typed the CTRL/BE LL keys followed by the $, the next

character to be changed. The RUBOUT deleted the $ character, and the user typed an E. Again a
search was made for an A character. This was changed to I. A LINE FEED was typed to save the remainder of the line.

3-8

3.14.1

Caution
When the MODIFY command is used the values in the user's symbol table 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 means of indirect statements prior to using a
MODIFY command, the values will not be erased because these symbols are not entered in the symbol
table until the statements defining them are executed.
Notice in the example below that the values of A and B were set using direct statements. The
use of the MODIFY command reset their values to zero and listed them after the defined symbols.

*ERP,SE ALL
*SET A=l
*SET B=2
*1.lSETC=3
*1.2 SET 0=4
*1.3 TYPE A+B+C+O;
*MODIFY 1.1
SET C=3'5
*GC
=+
9.012
C@ (012) =+
5.00
O@ (012 ) =+
4.00
A@(00)=+
0.00
B(ll(00)=+
0.00

TYPE

TYPE $

*
3.15

USING THE TRACE FEATURE
As stated in Section 2.10, the trace feature is useful in checking an operating program.

Those parts of the program which the user has enclosed in question marks will be printed out as they are
executed.
In the following example, parts of 3 I ines are printed.

*ERASE ALL
* 1 .1 SET A = 1
*1.2 SET B=5
*1.3 SET C=3
*1.4 TYPE %1, ?A+B-C?,!
*1.5 TYPE ?B+A/C?,!
1 • 6 T YP E ? B - C I A ?
*GO
A+B-C=+3
B+A/C =+5
B-C/A.=+2*

Also GO? Will trace the entire program.

3-9

3.16

FUNCTIONS
The functions are provided to give extended arithmetic capabi lities and to give the potential

for expansion to additional input-output devices. A standard function call always consists of four letters
beginning with the letter F and followed by a parenthetical expression.
FSGN(A-B*2)
There are three basic types of functions; two of which are included in the basic FOCAL program. The first type contains integer part, sign part, and absolute value functions.
In the second type, the extended arithmetic functions, are loaded at the option of the user.
They will consume approximately 800 locations of the users program storage area. These arithmetic
functions are adapted from the extended arithmetic functions of the PDP-8 three-word floating-point
package and are fully described with their limitations in the pertinent document.
The input-output functions are the third type. These include a nonstatistical random number
generator (FRAN). This function uses the FOCAL program itself as a table of random numbers. An expanded version could incorporate the random number generator from the DECUS library. Following are
examples of the functions now avai lable.
a.
parentheses.

The square root function (FSQT) computes the square root of the expression with in

*TYPE %21 FSQT(4)
=+ 2*

HYPE FSQT (9)
=+ 3*

*TYPE FSQT (144)
=+12*

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

*TYPE FABS(-66)
=+66*

*TYPE FABS C-23 )
=+23*

*TYPE FABSC-99)
=+99*

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

3-10

",TYPE FSGNC4-6)
=- 1 *
",TYPE FSGNC4-4)
=+ 1 *
",TYPE FSGNC-7)
=- 1 *

The integer part function (FITR) outputs the integer part of a number up to 2046.
",TYPE F ITR C5.2)
=+ 5*
",TYPE F ITR C55.66)
=+55*
",TYPE FITR(77.434)
=+77*
",TYPE FITRC-4.t )
=- 5*

e. The random number generator function (FRAN) computes- a nonstatistical pseudo-random
number between ± 1 •
*TYPE %~ FRANC )
=-0.250000E+00*
*TYPE FRAN C )
=-0. 623535E+00 *

The exponential function (FEXP) computes e to the power within parentheses. (e = 2.718281)
",TYPE FEXPC6.66953E-1)
=+0 .194829E+01 *
",TYPE FEXPC.666953)
=+0 .194829E+01 *
",TYPE FEXPC1 .23456)
=+0 .343687E+01 *
",TYPE FEXP C-1 • )
= +0 • 3 67879 E +0 0 *

The sine function (FSIN) calculates the sine of an angle in radians.
*TYPE %~ FSIN(3.14159)
=+0.238419E-05*
*TYPE FSIN(1.400)
=+0. 985450E+00 *

3-11

Since FOCAL requires that angles be expressed in radians, to find a function of an angle in degrees,
the conversion factor, 'if/lBO, must be used. To find the sine of 15 degrees,
*SET PI=3.14159J TYPE fSIN(15*PI/180)
=+0.258819E+00*
*TYPE fSIN(45*3.14159/180)
=+0.7137106E+00*

The cosine function (FCOS) calculates the cosine of an angle in radians.
*TYPE fCOS(2*3.141592)
=+13 .1000130E+01 *
*TYPE fCOS(.501300)
=+0. 877582E+00 *
*TYPE fCOS(45*3.141592/180)
=+0.707107E+130*

i. The arc tangent function (FATN) calculates the angle in radians whose tangent is the
argument within parentheses.
*TYPE fATN <1 • )
=+0.785398E+00*
*TYPE fATN(.31305)
=+0.3133386E+00*
*TYPE fATN(3.141592)
=+0 .126263E+01 *

i. The logarithm function (FLOG) computes the natural logarithm (log ) of the number
• h'In parentheses.
e
Wit
*TYPE fLOG(1.001300)
=+0.000000E+130*
*TYPE fLOG(1.98765)
=+0.686953E+130*
*TYPE %5.031 fLOG(2.065)
=+ 0.725*

3-12

CHAPTER 4
EXAMPLES OF FOCAL PROGRAMS

4.1

TABLE GENERATION USING LIBRARY FUNCTIONS
The ability to evaluate simple arithmetic expressions and to generate values with the aid of

library functions is one of the first benefits to be obtained from learning the FOCAL language. In this
example, a table of the sine, cosine, natural logarithm, and exponential values is generated for a series
of arguments. As one becomes familiar with these and other library functions, it becomes easy to combine them with the standard arithmetic operations of addition, subtraction, multiplication, division, and
exponentiation. The user should then be able to evaluate any given formula for a single value or for a
range of values as in this example.
Although FOCAL allows the typing of more than one command per line, each command in this
example has been typed on a separate line to maintain clarity and because of the length of several of the
commands. In this example, line 01.05 outputs the desired column headings. Line 01.10 is the loop to
generate values for I, beginning with the value 1.00000 and continuing in increments of .00001 up
through the value 1.00010; the DO 2.05 command at the end of this second line causes line 02.05 to be
executed for each value of I. Line 02.05 is the command to evaluate the various library functions for the
I arguments; the %7.06 specifies that all output results up to the next % symbol are to appear in fixedpoint format with one digit position to the left of the decimal point and six digit positions to the right:
the second % symbol reverts the output mode back to floating point for the remaining values - FLOG(I)
and FEXP(I).

Line 01.20 (optional) returns control to the user.

Several techniques can be noted in line 02.05 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 ability is useful in
matching correctly when a number of such enclosures appear in a command.
c. Spaces can be inserted in an output format by enclosing the appropriate number of spaces
within quotation marks. Such use of spacing is recommended to improve the readability of the output
results.
d. FOCAL allows accuracy of six significant digits, which makes possible the use of very
small loop increments (in this example, .00001); this should eliminate the need to interpolate between
table values of trigonometry functions in most cases. With modifications, FOCAL can give results
having an accuracy of up to ten significant digits.

4-1

01.05 T " I
SINE
01.10 FOR 1=1,.00001,1.0001; DO 2.05
01.20 QU IT
o 2 .0 5 T %7 .0 6, I , "

" , F SIN ( I ) , "

COSINE

" , Fe 0 S < I > , "

LOG

" , %, FLO G [ I ],"

E"!

" , FE XP ( I ) , !!

**
*GO
I
=+1.000000

SINE
=+0.841471

COSINE
LOG
=+0.540302
=+0.000000E+00

E
= +0 .27 1 82 8E +0 1

=+1.000010

=+0.841476

=+0.540294

=+0.977508E-05

= +0 • 2 7 1 83 1 E +0 1

=+1.000020

=+0.841481

=+0.540285

=+0.195501 E-04

=+0.271834E+01

=+1.000030

=+0.841487

=+0.540278

=+0.293250E-04

=+0.271836E+01

=+1.000040

=+0.841492

=+0.540269

=+0.390998E-04

=+0.271839E+01

=+1 .000050

=+0.841497

=+0.540261

=+0.488744E-04

=+0.271841 E+01

=+1 .000060

=+0.841502

=+0.540252

=+0.586491E-04

=+0 .271844E+0 1

=+1.000070

=+0.841508

=+0.540244

=+0.68423 6E -0 4

=+0.271847E+01

=+1.000080

=+0.841513

=+0.540236

= +0 • 781 980 E -04

=+0.271849E+01

=+ 1 .000090

=+0.84151 8

=+0.540228·

=+0.879723E-04

=+0.271852E+01

=+1.000100

=+0.841524

=+0.540220

=+0.977465E-04

=+0.271855E+01

4.2

FORMULA EVALUATION FOR CIRCLES AND SPHERES
In this example, FOCAL is used to calculate, label, and output the following values for an

indefinite number of radii typed in by the user.
Given: radius(R)
Program calculates:

circle diameter
circle area

1rR2

circle circumference
sphere volume

21rR

4/31rR

sphere surface area

41rR

Although the American system of inches is used in this example, conversions to other systems
(metric, for example) could be very easily incorporated into the program, thus eliminating any need for
hand-ca Icu lated 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. SET is used to supply the value of 1r (PI). TYPE is used for all calculations

4-2

and output. Note that if a value (such as PI in 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,
otherwi se, the variable wou Id be set at the beginning of each pass through the loop. However, if the
value of the variable changes during each iteration, then it must be calculated either by a SET or TYPE
command within the loop.
The use of the GOTO command (line 01.60) results in an infinite loop of lines 01.10 through

.01.60. This technique is used when the number of desired repetitions is not known. The looping process
can be terminated at any time by typing CTRL/C • If, however, the number of desired repetitions is known
(e.g., 10), the following method can be used.
*SET PI=3.14159
*1.1 ASf<.•••

*1 .6 TYPE 1!!!!

*FOR 1=1,10; DO

(Eliminate GOTO 1.1)
(Direct command; causes all
steps in group 1 to be executed 10 times)

The ability to choose between these methods provides great flexibility in actually running
FOCAL programs.

01 .01 SET PI=3.141592
01 .10 ASK "A RADIUS OF", R, " INCHES"
!, " GENERATES A CIRCLE OF:", !
01 .20 TYPE
DIAMETER", 2*R,"
INCHES",
01 .21 TYPE "
AREA", PI*Rt2," SQUARE INCHES",
01.30 TYPE "
CIRCUMFERJ;:NCE", 2*PI*R,"
INCHES",
01 .35 TYPE "
01 .40 TYPE !, " AND A SPHERE OF:", !
VOLUME", (4/3)*PI*Rt3,"
CUBIC INCHES",
01 .49 TYPE "
AND SURFACE AREA", 4*PI*Rt2," SQUARE INCHES"
01 ~ 50 TYPE "
01 .60 TYPE !!!!!; GOTO 1.1

*
*
*

*GO
A RADIUS OF:l
INCHES
GENERATES A CIRCLE OF:
DIAMETER=+
2.0000
INCHES
AREA=+
3.1416 SQUARE INCHES
CIRCUMFERENCE=+
6.2832
INCHES
AND A SPHERE OF:
VOLUME=+
4.1888 CUBIC INCHES
AND SURFACE AREA=+ 12.5664 SQUARE INCHES

4-3

A RADIUS OF:l.414 INCHES
GENERATES A CIRCLE OF:
DIAMETER=+
2.8280
INCHES
AREA=+
6.2813 SQUARE INCHES
CIRCUMFERENCE=+
8.8844
INCHES
AND A SPHERE OF:
VOLUME=+ 11.8423 CUB I C I NC HE S
AND SURFACE AREA=+ 25.1252 SQUARE INCHES

A RADIUS OF: ••••

4.3

TEMPERATURE CONVERSION
Measurement system conversions are time consuming in many lines of work. A short FOCAL

program, such as the one illustrated in the following example, eliminates hours of repeated calculations.
In this particular example, the problem is to convert temperatures from degrees Fahrenheit to degrees
Centigrade, using the formula:

This routine is quite similar in structure to the "Table Generation" example. The one basic
difference is that here the user can input the loop parameters wh ich govern the generation of the output.
Thus, provision has been made for output of properly labeled requests for starting, ending, and incrementing values and their input for use by the program.
The ability for loop parameters to be negative, zero, fractional, or expressions, provides
power beyond many other similar languages in simplifying the routine's structure. It also reemphasizes
the flexibility and control over FOCAL programs at the time they are run.

02.10 ASK "FROM" .. START .. " TO" .. END .. " DEGREES FAHRENHEIT" .. !
02.20 ASK"
IN INCREMENTS OF" .. INCR .. " DEGREES" .. !
02.30 TYPE "THE APpROPRIATE FAHRENHEIT TO CENTIGRADE CONVERSIONS ARE:"
02.40 FOR T=START .. INCR .. END;TYPE !; DO 2.5
02.45 QUIT
02.50 TYPE"
" .. T .. "FAHR. DEG •••••• " .. <T-32)*5/9 .. " CENTIGRADE DEG."
*DO ~
FROM:-40 TO:80 DEGREES FAHRENHEIT
IN INCREMENTS OF:20 DEGREES
THE APPROPRIATE FAHRENHEIT TO CENTIGRADE CONVERSIONS ARE:
=- 40.0000FAHR. DEG •••••• =- 40.0000 CENTIGRADE DEG.
=- 20.0000FAHR. DEG •••••• =- 28.8889 CENTIGRADE DEG.
=+
0.0000FAHR. DEG •••••• =- 17.7778 CENTIGRADE DEG.
=+ 20.0000FAHR. DEG •••••• =6.6667 CENTIGRADE DEG.
=+ 40.0000FAHR. DEG •••••• =+
4.4444 CENTIGRADE DEG.
=+ 60.0000FAHR. DEG •••••• =+ 15.5556 CENTIGRADE DEG.
=+ 80.0000FAHR. DEG •••••• =+ 26.6667 CENTIGRADE DEG.*

4-4

4.4

ONE-LINE FUNCTION PLOTTING
This example demonstrates the use of FOCAL to present, in graphic form, some given function

over a range of values. In this example, the function used is
y = 30 + 15(SIN(x»e- .1x
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 the shock absorbers of a car).
In the actual coding of the example, the variables I and J were used in place of x and y,
respectively; any two variables could have been used. The single line 08 .01 contains a set of nested
loops for I and J. The J loop types spaces horizontally for the y coordinate of the function; the I loop
prints the * symbol and the carriage return and I ine 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.
08.01 r

I=0~.5~15;

T "*"~!; r

J=0~30+15*rSIN(I)*rEXP<-.I*I>;T

*
*DO 8.01
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*

4-5

" "

4.5

EXTENSIONS TO PLOTTING
In this next example, the wave form is the same as that shown under One-Line Function

Plotting, i.e., a damped sinusoid, however, both the x and y axes have been added to increase the
readability of the output. Since amplitude and the damping factor can be varied, a series of such plots
shows their relative effects and can be used as a learning tool, or for trial and error solutions.
Another FOCAL command, IF, is used to position the x axis in the output. Two different
options are used once the comparison within the parentheses is made. In line 02.10, the statement numbers separated by commas indicate where to branch if the expression is negative, zero, or positive,
respectively. However,in line 03.10a branch is made to 3.3 if the expression is negative, or 3.2 if
the expression is zero, but for the positive case (J is less than 31) the remainder of the line is executed.
Whereas, in previous examples only single lines were executed as subroutines by DO commands (e.g.,
DO 2.05). This routine contains DO commands which execute a group of lines as a subroutine
before returning to the statement following the DO (e.g., DO 2, DO 3).
It is often useful to superimpose one function plot upon another. This ,can be accomplished
in FOCAL by replacing the exclamation point (representing a carriage return, line feed) with the number
sign

(representing a carrige return only)

in certain TYPE commands. A very large number of functions

using different plot symbols could be superimposed in this way. Often it is useful to follow each line in
a function plot with the value of the function at that point, thus producing analog and digital output
together. One can see from the spacing of the dots on the x and y axes that the Teletype produces a
scale with a horizontal to vertical ratio of 5-to-3 (i .e., five horizontal spaces = 3 vertical line feeds).
This factor must be taken into account when plotting closed curves such as circles.
It should be noted that FOCAL library functions already provide for output displays on oscilloscopes as well as for analog-to-digital conversions.

01.03
01.04
01.05
01.06
01.07
01.11

ASK "SINE WAVE AMPLITUDE" ~ AMPL~ !
ASK "DAMPING FACTOR COEFFICIENT"~ T~
FOR K=0~60; TYPE "."
TYPE !; FOR I=0,.5~15; DO 1.11; TYPE "*"; DO 3
QUIT
FOR J=0~30+AMPL*FSIN(I>*FEXP(-T*I); DO 2; T " "

02010 IF (J-32)
02.20 TYPE "."
02.30 RETURN

2.3~

2.2~

o3 • 1 0 I F ( 3 1 - J ) 3. 3, 3. 2
03.20 TYPE "."
03.30 TYPE !; RETURN

2.3

;

FOR K = J , 30 ;

*GO
SINE WAVE AMPLITUDE:15
DAMPING FACTOR COEFFICIENT:.135

4-6

T YP E .. ..

.............................................................
*.

*
*

* ·
*

* ·
*
*

·*

4.6

DEMONSTRATION DICE GAME
Sooner or later, people who have access to a computer wi II try to "match brains" with it or

use it for their own enjoyment. Such pastimes are usually keyboard oriented and FOCAL lends itself
nicely to these ends. The following example uses the random number generator, FRAN( ), to produce
dice combinations, plus 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). Lines beginning with a C indicate that the line
is to be treated as a comment and is not to be interpreted or executed. If a comments statement is preceded by a statement number, the line is stored as part of the program but does not affect the program
logic.

4-7

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
We naturally cannot assume any responsibility for the use
of this or any similar routines.
*01.10
*01.13
*01.20
*01.22
*01.26
*01.30
*01.32
*01.40
*01.42
*01.50
*01.60
*0 1 • 72
*01.74

S B=0;T ! !"DICE GAME"! .. "HOUSE LIMIT OF $1000
T"
MINIMUM BET IS $1"!!
ASK "YOUR BET IS"AH <l000-A) 3.1
I (A-l )3.4 .. 1.26 .. 1.26
IF (A-FITR(A))3.5 .. 1.3 .. 3.5
ASK M;DO 2;SET D=C;DO 2;T " ";SET D=D+C
I <0-7)1.42 .. 3.2 .. 1.42
I <0-2)1.5 .. 3.3 .. 1.5
1<0-11)1.4 .. 3.2 .. 1.4
1<0-3) 1.6 .. 3.3,1.6
ASK M;DO 2;S E=C;DO 2;T " ";S E=E+C
I (E -7) 1. 74,3 .3, 1 • 74
I (E-D)I.6 .. 3.2 .. 1.6

**02.10 SET C=FITR(10*FABS(FRAN()));IF (C-6)2.2 .. 2.2,2.1
*02.20

(C-l)2.1;T %1,"

"C; RETURN

*03.10 T "HOUSE LIMITS ARE $1000"!!; G 1.2
*03.20 S B=B+A;T %7, !"YOU WIN. YOUR WINNINGS ARE
"B .. !!;G 1.2
*03.30 S B=B-A;T %7,!"SORRY .. YOU LOSE.
YOUR WINNINGS ARE"B,!!;G 1.2
*03.40 T "MINIMUM BET IS $1"!!;G 1.2
*03.50 T "NO PENNIES, PLEASE"! !;GOTO 1.2
**
**C-ONCE YOU PLACE A BET, FOLLOW THE OTHER CO~ONS WITH A
**C
CARRIAGE RETURN TO INDICATE THE COMMAND: "ROLL THE DICE".

*GO

o ICE GAME
HOUSE LIMIT OF $1000.

MINIMUM BET

YOUR BET IS:.50 MINIMUM BET
YOUR BET IS: 1 5 : 7
=+6
=+3
=+1
=+4 :
=+4
=+5
YOU WIN. YOUR WINNINGS ARE
YOUR BET IS;5
=+2
=+2
=+1
=+6
SORRY, YOU LOSE.

IS $1

YOUR WINNINGS ARE=+

YOUR BET IS:3
=+6
=+5
YOU WIN. YOUR WINNINGS ARE
YOUR BET IS:

IS $1

I'LL QUIT WHILE

I'M AHEAD. THANKS!

4-8

4.7

SIMULTANEOUS EQUATIONS AND MATRICES
Many disciplines use subscripted variables for vectors in one, two, or more dimensions to

store and man ipulate data. A common use is the 2-dimensional array or matrix for handling sets of
simultaneous equations. For example,
Given:

1X 1 + 2X 2 + 3X 3 = 4
4X 1 +3X 2 +2X 3 = 1
lX 1 + 4X 2 + 3X 3 = 2

Find: The values of Xl' X 2 , 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.
Since FOCAL uses only a single subscript, the handling of two or more dimensions requires
the generation of a linear subscript which represents the correct position if it were stored in normal
order; i.e., leftmost subscript mov ing fastest.
In one dimension:
ARRAY(

'E lement D could be represented as ARRAY(3);

any element in this array can be represented

by a subscript in the range 0 through 4. The

first element in an array always has a sub-

script of O.

In two dimensions:
ARRAY (row ,column} or A(I,J}
This must be reduced to the form A(G). Since subscripts are linear, G is a function of I and
J; that is, A(I,J) = A(G). Consider the diagram

J=
1=0

012
0 5
10
1

4-9

This array has five rows and three columns, so two values can be defined:
IMAX = 5;
JMAX = 3.
To generate the number (G) in any box, using the corresponding values of I and J, the formula
G

1+ IMAX* J

A(G)

A.(I + IMAX* J)

can be used. Each element in a 2-dimensional array represents an area. 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, so as to form the equation
A(J+L* K).
In three dimensions:
ARRAY(row,column,plane) = A(I,J,K) = A(G)
Three dimensions can be illustrated as a cube.

I =0

This cube has d,imensions 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 with the addition
of 15 times K (with K = the number of planes back from the first) to each subscript in the first plane.
Example:
Upper lefthand square, back one plane from the first = 15
1=0, J = 0, K = 1;

I+(IMAX*J)+(IMAX*JMAX*K) = 15 = G
or
A(O,O, 1) = A(15)

4-10

In four dimensions:
ARRAY(row,column,plane,cube) = A(I,J,K,L) = A(G)
Assign the values for IMAX, JMAX, KMAXi a method similar to the one used above yields
G = I+(IMAX* J)+(IMAX* JMAX* K)+(IMAX* JMAX* KMAX* L)
This process can theoretically be extended indefinitely to n-dimensions.

01.02 TYPE !"ROUTINE TO SOLVE MATRIX EQ. AX=B F'OR X"!
01 .04 ASK "ENTER D IMENS ION OF' A~ THEN
01.05 TYPE !"ENTER COEF'F"S ACJ .. K) ••• ACJ .. N) AND BCJ)"!
01.10 ASK L .. !;SET N=L-1;-SET 1=-1
01.11 F'OR K=0~N; SET RCK)=K+l
01.12 F'OR J=0,N; TYPE !; F'OR K=IO~L; ASK ACJ+L*K)
01.14 SET M=IE-6
01.16 F'OR J=0~N; F'OR K=0~N; DO 4
o 1 • 1 7 SET R [P ] =0 •
01.18 F'OR K=0~L; SET A[P+L*K]=A[P+L*K]/M
01.20 F'OR J=IO~N; DO 5
01.22 SET 1=1+1
01.23 IF' Cl-N) 1.14~ 1.26 ~ 1.14
01.26 F'OR J=0~NI FOR K=0~N; DO 7
o 1 .28 F'O R K=0 , N; T YP E ! %2 ~ " XC" K ~ " ) " ~ %8 .0 5, X CK )
01.29 TYPE!!; QUIT
04.05
04.10
04.20
04.22
04.30

IF' CR<J» 0~ 4.3~ 4.1
IF' CF'ABSCA(J+L*K)) - F'ABS[M]) 4.3;
SET M=ACJ+L*K)
SET P=J; SET Q=K
RETURN

05.10 IF' CJ-P) 5.2~5.4~5.2
05.20 SET D=ACJ+L*Q)
05.30 F'OR K=0~L; SET A<J+L*K>=A<J+L*K>-A<P+L*K>*D
05.40 RETURN
07.10 IF' CIE-6-F'ABS[ACJ+L*K)]) 7.2; RETURN
07.20 SET XCK)=ACJ+L*L)

**GO
ROUTINE TO SOLVE MATRIX EQ. AX=B F'OR X
ENTER DIMENSION OF' A~ THEN
~NTER COEF'F"S ACJ~K) ••• ACJ~N) AND BCJ)
:3
; 1 ;2 ;3
;3 ;2
: 1 :4 :3
XC=+ 0)
XC=+ 1 )
XC=+ 2)
;4

:4
;1
:2
=+
=
=+

0.10100100
1 .010101010
2.000010

4-11

APPENDIX A
FOCAL COMMAND SUMMARY

Command

Abbreviation

Example of Form

Explanation

X, Y, Z

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

ASK

COMMHH

COMMENT

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

CONTINUE

Dummy lines

DO 4.1

Execute line 4.1; return to command
following DO command,

DO 4.0
DO ALL

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

ERASE

Erases the symbol table.

ERASE 2.0

Erases all group 2 lines.

ERASE 2.1

De letes line 2. 1 .

ERASE ALL

De letes a II user input.

FOR i=x,y,zi(commands)

Where the command following is executed
at each new value.

ERASE

FOR

FOR i= x, Zi (commands)

x=initial value of i
y=value added to i until i is greater
than z.
GO

Starts indirect program at lowest numbered I ine number.

GOTO

G3.4

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

I F (X) Ln, Ln, Ln

Where X is a defined identifier, a va I ue,
or an expression, followed by three
I ine numbers.

IF (X)Ln, Lni(commands)
IF (X)Lni(commands)

If X i·s less than zero, control is transferred to the first line number

If X is equal to zero, control is to the
second I ine number.
If X is greater than zero, control is to
the th ird Iine number.
MODIFY

MODIFY 1.15

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

QUIT

Returns control to the user.

A-1

Command

Abbreviation

Example of Form

Explanation

RETURN

Terminates DO subroutines, returning to
the original sequence.

SET

SET A=5/B*C;

Defines identifiers in the symbol table.

TYPE

TYPE A+B-C;

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

TYPE A-B, C/E;

Computes and types each expression
separated by commas.

TYPE "TEXT STRING"

Types text. May be fo I lowed by ! to
~enerate carriage return-line feed, or
to generate carriage return.

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 .

TYPE %x.y

where x is the total number of digits,
and y 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.

TYPE $

Other statements may not follow on this
line

WRITE

FOCAL Operations
To set output format,

To type symbol table,

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 may then perform any of the following
option a I operations.
a.

Type in new characters. FOCAL will add these to the line at the point of insertion.

Type a CTRL/L. FOCAL will proceed to the next occurrence of the search character.

Type a CTRL./BELL. After this, the user may change the search character.

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

Type

• 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.

g. Type LINE FEED. Saves the remainder of the line from the point at which LINE FEED
is typed over to the right margin.
A-2

Summarl of Functions
Square Root

FSQT(x)

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 .0000 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.

* Sine

FSIN(x)

FOCAL generates the sine of x in radians.

*Cosine

FCOS(x)

FOCAL generates the cosine of x in radians.

* Arc Tangent

FATN(x)

FOCAL generates the arc tangent of x in
radians.

* Logarithm

FLOG(x)

FOCAL generates loge (x) .

Ana log-to-Digita I

FADC(n)

FOCAL reads from an analog-to-digital channel, the value of the function is that integer
reading.

FDIS(y)

Displays y coordinate on scope and intensifies
x-y point.

FDXS(x)

Displays x coordinate on scope.

(2.71828 X )

Scope Functions

ASK/TYPE CONTROL CHARACTERS

Format delimiter

Text delimiter
Carriage return and line feed

Carriage return on Iy

Type the symbol table contents

SPACE

Terminator for names
Terminator for expressions
Terminator for commands

RETURN

Terminator for lines

*These are known as extended functions.

A-3

APPENDIX B
ERROR DIAGNOSTICS

Code

Meaning

*?OO.OO
*?01.00

Manual start from console
Interrupt from keyboard via CTRL/C

*?02.07
*?02.24
* ?02 .28
*?02.29
*?02.44
*?02.46

Bad line number format
Keyboard input buffer overflow
Group number or literal too large
Illegal command used
Line number too large
Imaginary square roots, or nonexistent line
referenced by DO
Nonexistent group referenced by DO
Bad argument for MODIFY
Division by zero
Command input buffer exceeded
Illegal step number
Number too large to be made an integer
Illegal or misspelled function name

*?02.61
*?02.67
*? 02 .80
*?02.87
*?02.;0
*?02.;3
*?02.;7
*?03.10
* ?03.42
*?03.50
*?03.79

Bad argument for ERASE
Log of zero requested
Improper step number
Variable storage exceeded, or exponent not
a positive integer

*?04.12
*704.13
*?04.18
*?04.33
*?04.39
*?04.45
*?04.53
*?04.61
*?04.93
*?04.;0
*?04.;2
*?04.;9

Bad argument in IF command
Missing operator in an expression, or illegal
E format on input or literal
Bad argument in FOR, SET, or ASK
Operator missing before parenthesis
Error to left of equal sign
Parentheses do not match
Excess right parenthesis
Illegal character in FOR
Double periods in a line number
Function not followed immediately by parens
Multiple periods in a line number
Double operators in an expression

*?05.11
*?05.28
*?05.60
*?05.;6

No argument in IF command
Command not available
Error in FOR command format
Function not loaded into core

NOTE
The above diagnostics apply only to the version of FOCAL, 1968
issued on tape DEC-08-AJAB-D.

B-1

APPENDIX C
ESTIMATING THE LENGTH OF USER'S PROGRAM

FOCAL requires five words for each identifier stored in the symbol table, and one word for
each two characters of stored program. This may be calculated by

5s + 2" • 1.01 = length of user's program
where

s = Number of identifiers defined
c = Number of characters in indirect program
If the total program area of symbol table area becomes too large, FOCAL types the error

message
?03.79
FOCAL occupies core locations 1-33008 and 46°°8-75768' This leaves approximately 100010
locations for the user's program {indirect program, identifiers, and push-down list}. The extended functions occupy locations 4600-5277. If the user decides not to retain the extended functions at load-time,
there will be space left for approximately 180010 characters for the user's program.
The following routine allows the user to find out how many core locations are left for his use.
*FOR 1=1,300; SET ACI)=I
?03.79
(disregard error code)
*TYPE %4, 1*5, " LOCATIONS LEFT"
=+ 705 LOCATIONS LEFT *

C-l

APPENDIX D
CALCULATING TRIGONOMETRIC FUNCTIONS IN FOCAL

Function

Argument
Range

FOCAL Representation

Function
Range

Sine

FSIN(A)

O~IA 1<1 ot 4

O~IF 1~1

Cosine

FCOS(A)

0~IAI<10t4

O~IF ts1

Tangent

FSIN (A)/FCOS(A)

O~IA 1<10t4

O~IF 1<10t6

IA 11(2N+l )1r/2
Secant

O~IA 1< lOt 4

l/FCOS(A)

l~IF 1<10t6

1A 11(2N+ 1)1r/2
Cosecant

O~IA 1<10t4

l/FSIN(A)

l~IF 1<10t6

IA 112N1r
Cotangent

O~!A 1<10t 4

FCOS(A)/FSIN(A)

O~ IF 1< lOt 440

IA 112N1r
Arc sine

FATN(A/FSQT(l-A t2)

O~IA 1<1

O~IF 1':S1r/2

Arc cosine

FATN(FSQT(l-A t2)/A)

O<IAbl

O~IF 1:1r/2

Arc tangent

FATN(A)

0<A<10t6

0~<n/2

Arc secant

FATN(FSQT(A t2-1))

1<A<1 ot 6

0~F<1r/2

Arc cosecant

FATN(l/FSQT(A t2-1)

1<A<l Ot300

0<F<1r/2

Arc cotangent

FATN(l/A)

0<A<10t615

0<F<1r/2

Hyperbolic sine

(FEX P(A)-FEXP( -A))/2

O~IA ~700

O~ IF 1'55* lOt 300

Hyperbolic cosine

(FEXP(A)+FEXP(-A»/2

0~IAI<700

1<F<5* 10t300

Hyperbolic tangent

(FEXP(A)-FEXP(-A»/
(FEX P(A)+FEX P(-A))

~IAI<700

O~ IF 1~1

Hyperbolic secant

2/(FEX P(A)+FEX P(-A»

~IA ~700

O<F<l

Hyperbolic cosecant

2/(FEXP(A)-FEXP(-A) )

0< IA 1<700

0< IF 1<10t7

Hyperbolic cotangent

(FEXP(A)+FEXP(-A»/
(FEXP(A)-FEX P( -A))

0< IA 1<700

l~IF 1<10t7

Arc hyperbolic sine

FLOG(A+FSQT(A t 2+ 1»

-lOt 5<A<1 ot 600

-12<F<1300

Arc hyperbolic cosine

FlOG(A+FSQT(A t 2-1»

1~A<10t300

0<F<700

Arc hyperbolic tangent

(FLOG(l +A)-FLOG (l-A) )/2

~IAI<l

0~IFI<8.31777

Arc hyperbolic secant

FLOG((l/A)+FSQT((l/At 2)-1»

0< IA bl

O<F<700

Arc hyperbolic
cosecant

FLOG((l/A)+FSQT((l/A t 2)+1»

0< IA 1<10 t300

~IFI<1400

Arc hyperbo I ic
cotangent

(FLOG(X+l)-FLOG(X-l);2

1<A<10t616

O<F<8

D-l

APPENDIX E
OPERATING HINTS 1

OVERLOAD RECOVERY
When the program and symbol table areas become too large the error diagnostic ?03.79 will
be typed out. The user should then do one of the following.
a.

Restart at location 0200.

Restart at location 2216, if ?03.79 follows a legitimate command. This erases all variables.

As a last resort, restart at 2213. Th is erases the text.

LOADING PROGRAM TAPES
When loading a long program tape into FOCAL the user can suppress the echo (printing)
feature by changing the content of location 2475 to 7000. This will cause only asterisks to be typed as
the tape is being read; there will not be a carriage return-line feed at the end of the line.
Entries from the keyboard will not echo unless each entry is preceded by a TYPE command.
Output wi II be typed' in the norma I manner.
To restore the echo feature, depress the STOP key on the computer console and deposit 4277
into location 2475.

1These hints apply only to FOCAL, 1968, issued on tape DEC-08-AJAB-D.

E-1

APPENDIX F
LOADERS

READ-IN MODE {RIM} LOADER
The RIM Loader is a program used to load the Binary Loader. The RIM Loader must be toggled
into memory using the switches on the computer console.
To load the RIM Loader, fo Ilow the procedure be low.
a. Check to see if the RIM Loader program is in memory correctly by examining the following
locations for the appropriate instructions {contents}.

Location

ASR33 Reader

7756
7757
7760
7761
7762
7763
7764
7765
7766
7767
7770
7771
7772
7773
7774
7775
7776

6032
6031
5357
6036
7106
7006
7510
5357
7006
6031
5367
6034
7420
3776
3376
5356
0000

Instructi on
High Speed Reader
6014
6011
5357
6016
7106
7006
7510
5374
7006
6011
5367
6016
7420
3776
3376

5356
0000

b. If the instruction in any location does not agree with the above list, deposit the correct
instruction into that location (see User1s Handbook, F-85, for detai Is) .

BINARY FORMAT (BIN) LOADER
The BIN Loader is a program used to load FOCAL into memory. The BIN Loader tape is loaded
by the RIM Loader as explained below.
The BIN Loader is loaded into locations 7612-7616, 7626-7752, and 7777, with its starting
address at location 7777. A detailed description of the BIN Loader is in the User1s Handbook, F-85.
To load the BIN Loader, follow the procedure below.
a.
b.
blank tape).

Check the RIM Loader for correctness, and correct if necessary.
Put Binary Loader tape in reader (always put leader-trailer code over reader head, never

F-1

Turn reader ON.

Set Switch Register (SR) to 7756 (the starting address of the RIM Loader).

Depress LOAD ADDress switch on computer console.

Depress START switch on computer console.

Tape should begin reading in, if not, check the RIM Loader and start again at step a.

After program is read in, depress STOP switch on the computer console.

F-2

FOCAL PROGRAMMING MANUAL
DEC-08-AJAB-D

READER'S COMMENTS
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