r FORTH
Dimensions
Volume 6. Number 3
September/October 1984
$2.50
Continued
Fractions
Re-Defining a Colon Word
Write Li Ice a Fox
Forth-79 Programs Forth-83
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FORTH Dimensions
2
Volume VI, No. 3
FORTH Dimensions
Published by the
Forth Interest Group
Volume VI, Number 3
September/ October 1984
Editor
Marlin Ouverson
Production
Jane A. McKean et al.
Forth Dimensions solicits editorial ma-
terial, comments and letters. No responsi-
bility is assumed for accuracy of material
submitted. Unless noted otherwise, mate-
rial published by the Forth Interest Group
is in the public domain. Such material
may be reproduced with credit given to
the author and the Forth Interest Group.
Subscription to Forth Dimensions is
free with membership in the Forth Inter-
est Group at $15.00 per year ($27.00 for-
eign air). For membership, change of
address and/ or to submit material for
publication, the address is: Forth Interest
Group, P.O. Box 1105, San Carlos, Cali-
fornia 94070.
Symbol Table
Simple; introductory tu-
torials and simple appli-
cations of Forth.
Intermediate; articles
and code for more com-
plex applications, and
tutorials on generally dif-
ficult topics.
Advanced; requiring stu-
dy and a thorough under-
standing of Forth.
I
1
■Ml
79
■
Code and examples con-
form to Forth-83 stand-
ard.
Code and examples con-
form to Forth-79 stand-
ard.
Code and examples con-
form to fig-FORTH.
Deals with new propos-
als and modifications
to standard Forth sys-
tems.
1
Dimensions
FEATURES
10
1
20
I
23
I
26
I
Long Divisors and Short Fractions
by Nathaniel Grossman
This article presents both an analysis to show that the continued fraction
algorithm can be implemented in double-precision integer Forth and an
implementation in Forth-83.
Re-Defining a Colon Word
by £d Schmauch
This program development aid allows one to re-define a Forth word so that
higher-level words which already use it will now reference the new version.
Think Like a User, Write Like a Fox
by Michael Ham
Designing systems to accommodate users' individual typing habits may
seem antithetical to data integrity, or just too much work to bother with.
But for those times when "the computer should have known what I meant,"
this code will help.
Upgrading Forth-79 Programs to Forth-83
by Robert Berkey
When you are ready to integrate your existing applications with Forth-83,
this thorough approach will get you standard in short order.
DEPARTMENTS
4 Authors
5 Letters
7 Editorial: Credit Where It's Due
9 President's Letter: Operations by Robert R. Reiling
30 Ask the Doctor: Astronomical Problems by William F. Ragsdale
32 Techniques Tutorial: Debugging, Part Two by Henry Laxen
35 Chapter News by John D. Hall
38 FIG Chapters
Volume VI, No. 3
3
FORTH Dimensions
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the Authors
Robert Berkey is a systems software
engineer at Dysan Corporation. He is
the treasurer of the Forth Standards
Team, participated on the fig-FORTH
implementation team and is the author
of the Alpha Micro fig-FORTH listing.
Nathaniel Grossman is a professor of
nathematics at UCLA where he teaches
)oth graduate and undergraduate stu-
ients. He uses Forth for personal and
,emi-professionaI purposes, and enjoys
eading, thinking and fussing over a
mall model railroad.
John D. Hall is the National Chapter
Zoordinator for the Forth Interest
jroup.
Michael Ham is manager of customer
iatisfaction at Dysan Corporation, and
ists documentation design as one of his
esponsibilities of interest. He designed
I national data base of continuing edu-
cation records, and wrote a college
iearch program in Forth.
Henry Laxen is Vice-President of
^.esearch and Development for Para-
lise Systems, Inc. He worked on the
)perating system for the Panasonic/
Quasar HHC, the world's first hand-
leld computer. He will soon participate
n a tango competition, and has a cat
lamed Sophie who sounds like a bird.
William F. Ragsdale was the found-
ng President of the Forth Interest
jroup. As the author of fig-FORTH
installation Manual and Model, his
vork has been translated to run on
ileven processors.
Ed Schmauch is a research chemist
with Conoco,Inc. where he investigates
methods of controlling corrosion during
the production of petroleum products.
He has developed on a portable compu-
ter various real-time Forth programs
which were in turn used as debugging
aids for other computer systems.
FORTH Dimensions
Volume VI, No. 3
Value Needn't Be Pricey
Dear FIG:
I would like to thank Henry Laxen
and Michael Perry for their F83 imple-
mentation. It is receiving considerable
support in the Minnesota FIG Chapter.
Its inclusion of complete source code is
a great benefit few vendors offer. Its
many enhancements and low price make
it an unbeatable system. The under-
standable lack of support could largely
be compensated for if a user network of
some kind develops. Suggestions,
anyone?
I must comment on Bill Ragsdale's
comments on the price of a software
package as an indicator of its value
(V/ 6). While it is a clue, I don't think the
conclusion drawn ("...Forth... has only
one-fifth the value [of] a C system.") is
justified. Price is also an artifact of the
market system. The simplicity and ele-
gance of Forth makes it easier to imple-
ment with fewer development resources,
which results in cheaper implementa-
tions being possible. I hope vendors
don't conclude that if they only charge
more they will sell more, clearly a falla-
cious conclusion. Personally, I think
software should be priced near the cost
of the medium on which it resides, and
programmers should be remunerated
from the proceeds of some other finan-
cial mechanism.
Fred H. Olson
1221 Russell Avenue N.
Minneapolis, Minnesota 5541 1
A Cure is in Sight
Editor:
I am very pleased with the new format
for Forth Dimensions. It certainly makes
things easier to read and to find articles
at my level.
I have one suggestion. In your column
"Ask the Doctor" could you make the
"Rx" stand out in some manner. I find
that sometimes I am into the answer
before I realize I left the question.
Keep up the good work.
Sincerely,
David H. Lawson
219 N. Vanderhurst
King City, California 93930
We aim to please — this month 's column
format should be a bit easier to
read... -Ed.
A Bibliography of
Forth
References
A Bibliography of Forth References contains
over 1,000 references to articles, books, and
papers on Forth. Listed by author and subject.
2nd Edition. September 1984. $15.
Outside North America please add $5 for air-
freight. Published by The Institute for Applied
Forth Research, Inc., P.O. Box 27686,
Rochester, NY 14627.
_ , THE JOURNAL OF
Forth
Application and
Research
Volume 2 will have articles on Forth in silicon, utilizing
large address spaces, image processing, and telescope
control. Journal issues also contain book reviews,
technical notes, algorithms, and calendar events.
Subscriptions Volume 2 1984
Corporate/ Institute $100 Individual $40
Subscriptions outside North America please add $20 airmail
postal charge. Back issues: Volume I. 1983, Robotics; Data
Structures, two issues, $30, outside North America $40.
Checks should be in U.S. Dollars on a U.S. bank, payable
to The Journal of Forth Application and Research,
P.O. Box 27686, Rochester, New York, 14627 USA.
Published Quarterly by
The Institute for Applied Forth Research, Inc.
Volume VI, No. 3
5
FORTH Dimensions
Sixth Annual
Forth National Convention
November 16-17, 1984
Hyatt Palo Alto
4290 El Camino Real, Palo Alto, CA 94306 USA
Learn about Forth and make your life easier. The convention will show you how!
• Exhibits
• Speakers
• Tutorials
• Vendor Meetings
• Panel Discussions
Equipment Demonstrations
Discussion Groups
Worldwide FIG Meeting
Banquets
Awards
Forth is for everyone. The Forth computer language is used in video games, operating systems, real-time control,
word processing, spread sheet programs, business packages, DBMS, robotics, engineering and scientific calculations
and more.
Coverage of Forth applications, Forth-based instruments. Forth-based operating systems, and more.
Speak at the convention. Those wishing to participate and be speakers and/or panelists are urged to contact the
program coordinator immediately. (Telephone the FIG hotline 415/962-8653.)
PROGRAM
SATURDAY, November 17
EXHIBITS 9 am — 5 pm
Forth Resources
Education
Lunch
FRIDAY, November 16
EXHIBITS Noon — 6 pm
1 1 :30 am Registration
1 pm Forth Systems
2 pm Data Base Developments
3 pm Forth-Based Products
4 pm Forth-Based Products
5 pm 32 Bit Systems
6 pm Exhibits Close
10 am
11 am
Noon
1 pm
2 pm
3 pm
4 pm
5 pm
Forth Chips and Computers
Business Applications
Forth Chapters
Forth-83 Standard, FORML Preview
Exhibits Close
BANQUET
7 pm Saturday — Reservation and payment required — $30,00
Convention preregistration is $10.00; or $15.00 at the door. Special convention room rates are available at the
Hyatt Palo Alto. Telephone direct to Hyatt reservations by calling (800) 228-9000 and request the special Forth
Interest Group Convention rates for November 16th and 17th.
The Forth Convention is sponsored by the Forth Interest Group (FIG). The Forth Interest Group is a non-profit
organization of over 4800 members and 50 chapters worldwide, devoted to the dissemination of Forth-related
information. FIG membership of $15.00/year ($27.00 overseas) includes a one-year subscription to FORTH
Dimensions, the bimonthly publication of the group.
□ Yes! I will attend the Forth Convention.
□ Number of pre-reglstered admissions x $10.00 each
□ Number of Banquet Tickets x $30.00 each
□ Yes! I want to join FIG and receive FORTH Dimensions ($1 5.00 US, $2700 foreign)
TOTAL CHECK TO FIG
□ I want to exhibit; please send exhibitor information.
Name
Address
Company
City
Phone (
State .
Zip
Return to: Forth Interest Group, RO. Box 1105, San Carlos, CA 94070 • 415/962-8653
FORTH Dimensions
6
Volume VI, No. 3
Credit Where It's Due
Forth Dimensions is evolving along
with the Forth Interest Group, and it
requires the care and labor of a fairly
large group of people, mostly FIG board
members, attendees at the monthly FIG
business meetings, correspondents and
other volunteers. It seems a good idea to
let you know how it all manages to come
together.
We receive letters and articles (but
never enough!) in the mail. These are
collected by Shepherd Associates (who
is also responsible for all the advertising
content) and are passed to me along
with press releases, requests for reprint
privileges and other miscellaneous mail
for the editor. Often included among
this material are requests for specific
information about a Forth system: from
how to save blocks to diskette on an
Apple system, to which headerless com-
piler is right for a given application.
Unfortunately, except for items ans-
wered in Bill Ragsdale's "Ask the Doc-
tor" column, we cannot always give the
kind of individual attention we'd like.
The best source of such information is
often the vendor, a users group, the
local FIG chapter, the FIG hotline, the
FIG Tree or any class on Forth
programming.
Material under consideration for pub-
lication is taken to Forth experts who
offer technical and literary criticism.
Ray Duncan and Kim Harris have often
assisted graciously in this task, although
a considerably larger number contrib-
utes as needed. We look for sound pro-
gramming technique, clarity of both the
code and the text, interesting new solu-
tions which demonstrate the problem-
solving process, small applications
which illustrate one or more Forth
techniques, and good tutorials. Fre-
quently frowned at are articles which
simply re-hash an old subject with little
new to offer. The reviewers also usually
shy away from code presented in dia-
lects of Forth that few readers can use
directly, or which contains undocu-
mented non-standard words and exten-
sions. Sometimes the reviewers will like
the basic concepts of a piece but will
make suggestions to the author and ask
him to consider revising the piece. Well-
written tutorials for beginners are rarely
received, but are almost always received
enthusiastically.
Articles accepted for publication are
tentatively scheduled for a particular
issue. In the interests of timeliness,
Forth Dimensions does not work as far
ahead as some periodicals, but we are
always about two issues ahead of our
readers in terms of the ones we are put-
ting together. When you receive this
issue we will be preparing Volume VI,
Number 4 for the printer, Number 5 will
be waiting in the wings and we will be
planning and reviewing articles for
Number 6.
Jane McKean is the one responsible
for taking the abstract concept of the
new design of Forth Dimensions and
turning it into the concrete form you
hold in your hands. After an article's
spelling is corrected, the capitalization
fixed and all questions answered, it is
transmitted to Jane's computer via
modem or is handed to her as hard
copy. She then enters formatting codes
and uploads it to a nearby commercial
typesetter. The typeset articles come
back on long pages called galleys, and
are proofread by yours truly before a
final version is run off. Jane then tries to
make the brew we've concocted fit within
the given length of the magazine, a labor
sometimes only requiring a shoe horn,
but often calling for a crowbar wielded
with surgical skill (my eyes are some-
times bigger than the plates). If you can
imagine a combination of a crossword
and fifteen-tile puzzle with elements of
Risk and Rubik's Cube, you have a taste
of what it's Hke to do the physical pro-
duction of a magazine.
There is one more inspection of the
entire issue before it goes to the printer.
Labels are generated by C.J. Street &
Associates, who provides our mailing
list service; and the issue is printed and
bound by Technical Publishing just as
editorial and production are starting to
put the next issue together.
In a nutshell, that is how each issue
gets put together. Of course, I haven't
mentioned our faithful columnists who
endure my preaching about the signifi-
cance of deadlines. (I really do need it by
Friday, gang, no kidding!) The names
John Hall, Henry Laxen, Bill Ragsdale
and Robert Reiling appear regularly.
Not mentioned often enough are the
many other authors whose work also is
freely given to improve the body of
Forth literature and tools. Perhaps the
best way to thank them is to return the
favor!
— Martin Ouverson
Editor
Volume VI, No. 3
7
■
FORTH Dimensions
THE MOST ADVANCED VERSION OF FORTH
IS NOT ON THIS 5 1/4" DISK.
IT'S UNDERNEATH IT!
When you pay $300 for some languages all you get is a $3.00 disk. When you buy the
NMIX-0012 RSC-FORTH System from New Micros, Inc. you not only get the language, you
get a complete computer system. It has features that you can't expect from a disk based
language, like an RS 232 serial interface, 40 individually programmable input/output lines
(5 parallel ports), two counter/timers, RAM, ROM and a EEPROM/EPROM programmer. For
that matter, disks don't usually come with their own power supplies, and almost none are
packaged in rugged metal cases! You would expect a disk to come with hundreds of pages
of documentation — our system certainly does. With a disk, you have to tie up your whole
computer to run the program. After storing your program in our system, it can be dedicated
to a task without the support of your PC, or you can communicate with it over the same serial
channel used to program it. On top of all this our FORTH has advanced features, like built-in
target compilation, CASE statements, PROM programming words and, believe it or not, disk
access functions. The NMIX-0012 is 100 millimeters on a side, smaller than a disk, priced
at $290 complete. The "100 Squared"™ is the logical choice! Substantial quantity discounts.
ORDER NOW FROM: New Micros, Inc.
808 Dalworth
Grand Prairie, Texas 75050
(214) 642-5494
FORTH Dimensions
8
Volume VI. No. 3
p
Operations
Have you ever wondered how the Linda Kahn. She is in contact with mag-
Forth Interest Group accompUshes all azine editors regularly in order to alert
its member service activities? Dedicated them to current events and new infor-
volunteers perform many functions; for mation about Forth. If you have an arti-
example, the Board of Directors and cle about Forth, Linda can probably
Officers are all volunteer positions. But suggest a publisher who would be inter-
this group cannot provide all the sup- ested in it. She also sends a regular
port needed to keep the Forth Interest stream of press release material to the
Group running smoothly; therefore, they press.
have entered into agreements with spe- These are some of the support func-
cialists who are able to perform the tions that are contracted by the Forth
ongoing daily tasks that are necessary. Interest Group. They keep things going.
Early this year the Board selected an — Robert Reiling
association management firm, Shepherd President
Associates, to perform association ser-
vices for the Forth Interest Group. For
the past several years. Martens and
Associates had performed this service,
but because of other commitments they P-S. Don't forget the upcoming
wanted to stop. Shepherd Associates is events: the Sixth Annual Forth Interest
experienced in association work and Group Convention November 16-17,
now handles the daily activities of the 1984 at the Hyatt Palo Alto in Palo
Forth Interest Group, doing such things Alto, California; and the FORML Con-
as entering Forth Dimensions suhscrip- ference to be held at Asilomar, Pacific
tion renewals and new subscriptions, fill- Grove, California, November 23-25,
ing orders for publications and prod- 1984.
ucts, and answering the hot line. They
help the Chapter Coordinator, John
Hall, do mailings to chapter coordina-
tors throughout the world. They also
solicit advertising for insertion in Forth
Interest Group publications. In July, the
Board extended the initial contract to
the end of 1984.
The editor of Forth Dimensions, Mar-
lin Ouverson, is one of the professionals
supporting the Forth Interest Group.
He is responsible for editing Forth Di-
mensions and making certain that it is
ready for the printer on schedule. You
probably have noticed some of the new-
look features that Marlin has added to
Forth Dimensions. Unique department
headings, the thermometer to indicate
the technical level of an article, and
symbols to indicate the Forth dialect,
for example.
Spreading the word about the Forth
Interest Group activities is publicist
The ProgramiiiBr's
Quiz
Question:
Name one 32 bit Realtime
Operating / Development
System for wtiich 128 kb of
RAM and Floppy Disk is an
enormous computer.
Answer:
4XF0RTH for the MC68000,
a complete ROM based
operating system with
multi-user & tasking,
dynamically selectable
system's device.
error checking assembler,
ring buffered input,
ram disk, ami much more.
4xrORTH which meets the
'83 Forth Standard, except
with 32 bit variables.
4xF0RTH. a realtime tool
for the professional
programmer.
by
The Dromon CUoup, Vnc
148 Poca Fork Road
Elkview, WV 25071
304/965-5571
Long Divisors and Short Fractions
Nathaniel Grossman
Los Angeles, California
Readers of Starting Forth, Forth Tools
and Forth Dimensions understand the
power of the scahng operation */ and will
value the convenience of simple rational
approximations to thirty-two-bit float-
ing-point constants. Starting Forth [5, p.
122] contains a short table of useful
approximations. Forth Tools [2, p. 104]
and Forth Dimensions [6] contain similar
tables.
For example, sjl = 1.4142135624.
Starting Forth suggests the approxima-
tion 19601/13860 = 1.4142135642. The
method to be explained in this article
obtains the approximation 19601/13860
as well as better approximations, among
them 47321/33461=1.4142135621, which
has an error = 3X 10"'". This method, part
of the theory of continued fractions and
well known to mathematicians, furnishes
simple, iterative algorithms for grinding
out short, rational approximations to
long and complicated rational numbers
and even to other classes of numbers such
as square roots of integers. Implementa-
tion of these algorithms on specific com-
puters may run into difficulties when the
arithmetic overflows the capacity of the
built-in calculator routines. If, however,
the numerical givens and the iterative
schemes are carefully analyzed, the diffi-
culties are seen to be removable.
This article presents both an analysis to
show that the continued fraction algo-
rithm can be implemented in double-
precision integer Forth and, best of all, an
implementation in Forth-83. By loading
the implementation, any Forth user can
unleash continued fraction power.
The rest of this article is in two parts.
To get the full power from the algorithms,
the standard Forth arithmetic arsenal
must be extended by a word UD/MOD that
expects unsigned double dividend and
divisor and returns their unsigned double
quotient and remainder. (Thus, UD/MOD
is a superword of /MOO.) At the same
time, it is convenient to introduce a new
class of stack manipulators that I call
long pair words. These words, distin-
guished by the prefix LP, move pairs of
adjacent double numbers around the
stack. The LP words and UD/MOD have an
independent value outside the continued
fraction calculations. They can be viewed
as quadruple-precision words of a sort,
but I decided not to use David Beers'
quadruple precision words [3] because I
did not need triple and quadruple addi-
tion and subtraction or signed multiplica-
tion and division. These matters compose
Part I.
Part II begins with a short introduc-
tion to continued fractions in just enough
detail to justify their use in constructing
rational approximations. Both strengths
and weaknesses are included. This leads
into a discussion of the specific algorithm
and of its implementation in Forth.
Part II requires Part I, but the first part
can stand alone as a useful addition to the
Forth dictionary. You may be wavering
about reading either or both. In that case,
turn first to the Intermezzo between the
two parts. You will find there a single,
stand-alone screen. Load it and read the
description; run it and you will get a con-
cise demonstration of the power of the
full continued fraction program.
Parti
Long Pairs and Long Division
Although the Forth Required Word
Set and the Double Number Extension
Word Set are rich in arithmetic words, no
words are included to carry out the divi-
sion of one (signed or unsigned) double
integer by another. Such words are
needed occasionally. The Forth way to
fill such a need is clear: extend the dic-
tionary with new words. Indeed, two tries
at writing double division words are
available in back issues of Forth Dimen-
sions. L.H. Bieman [4] wrote screens of
double precision mathematics words, but
an accompanying commentary on the
words by Robert L. Smith indicates that
Bieman 's word D/ for division of double
by double can produce errors of several
units in the least significant digit of the
quotient. Because I need full accuracy in
the quotient, Bieman 's D/ is of no help to
me. (I continue to use his word U*/ with
gratitude.) And, as I have already men-
tioned, David Beers' quadruple words [3]
are too lush for my needs. Therefore, I
have written a word UD/MOD to fill my
needs exactly.
A Long Division Algorithm
The goal is a word UD/MOD that expects
unsigned double dividend and divisor
and returns the unsigned double quotient
and remainder from the division.
Of course, the literature contains many
descriptions of multi-precision division
algorithms. I read the appropriate section
in Knuth's standard treatise [8] but I did
not feel that the algorithm Knuth recom-
mends would be best for implementing in
Forth. Nevertheless, I could make good
use of some of the many goodies with
which Knuth lards his text. The algo-
rithm I implemented is improved by a
long division algorithm (for use on geared
mechanical calculators) presented in a
mathematical handbook [I, p. 21]. Algo-
rithms with such provenance usually
require an additional logical co-processor
— the human brain! It is toward doing
away with human intervention that the
tidbits from Knuth are applied.
Suppose that u and v are integers, with
v positive, u non-negative, and both less
than 2" (double integers). It is required to
divide u by v and return the quotient and
remainder as unsigned double integers.
Knuth advises using the division of a
two-digit integer by a two-digit integer as
a model. His algorithm requires exten-
sion of the dividend to a three-digit
integer, and I want to avoid this higher
precision extension. Now, thirty-two
binary digits seem more than two, but
they are not really much more from the
right point of view. Introduce a i^perfea^e
b = 2 = 65336. Any double integer may
then be written as u = uo * b + u, where
< uo < b and < ui < b; uo and ui are
the "superdigits." Similarly, v = vo * b +
vi and u/ V = (uo * b + ui)/(vo * b + Vi).
FORTH Dimensions
10
Volume VI, No. 3
u _ d * u
V w
^ d * (uo * b + u^)
Wo * b + wi
= d ^ Up * b + ui
Wo * b 1 + (wi / Wo * b)
= -inr* {uo*b + u,} */i-_^ + e|
Wo * b ( Wo * b }
= -J— * L- "° * - aiw, + u * eI
Wo * b I Wo Wo * b j
Figure One
The problem would be essentially done if
Forth, which can talk in so many bases,
could manipulate in base b. But it cannot.
The next step is analytic. There is a
simple formula: (1 + x)~' = 1 - x + error,
where if < x < 1 then < error < x^.
Before we use this formula, we are going
to scale the fraction u/ v for a reason that
will be easier to explain a few paragraphs
farther along. We want to multiply divi-
dend and divisor by a scaling integer d
that makes dv close to b^ = 2 ^, so close
that Vib^ < dv < b^. The exact choice of d
is not crucial: I take Knuth's suggestion,
selecting d = [b/ (vo + 1 )] (where [x] is the
floor of x, the largest integer not bigger
than x). Let w = dv and write w = wo * b
+ Wi; now '/4b < wo < b and u/v = (d *
u)/w. (We do not multiply d and u to-
gether immediately to form a new divi-
dend because there is no guarantee that d
* u will not stretch to more than thirty-
two bits.)
With this preparation, the analytic
unfolding of the division is easy (see
figure one).
Now we will show that the last two
terms in the braces can be omitted if we
want only the quotient [u/v]. This is
where the scaling is important. We know
that l<d<b,0<w<b,0<ui<b, and
Vzb < Wo. Also, < E < (wi/wo * b)'.
Then
and
Thus
because the two terms neglected are small
(and of opposite signs, which will not be
needed here). Having the quotient in
hand, we find the remainder simply as
u - V * [u/v].
The actual calculation of [u/v] is now
easy using the arithmetic operations built
into Forth, but the terms must be evalu-
ated in the correct order to ensure full
precision. First calculate the bracket as a
double integer — Bieman's U*/ is useful
for this — then multiply/ divide by d/wo,
again using U*/. Division by the super-
base b = 2" is then performed by drop-
ping the least significant sixteen bits of
the penultimate result.
Implementation of Long Division
The algorithm described above does
not call for a complicated implementa-
tion. There is one place to take care. Even
though the divisor is called thirty-two
bits wide, the sixteen high bits may be
zero. If this happens, the number wo will
be zero and the algorithm will call on
division by zero. To avoid zero divisions,
the algorithm lays down a double track.
The screens are composed in Forth-83,
specifically MicroMotion MasterFORTH.
The screens should run in Forth-79 if
UM* is replaced by U* and UM/MOD by
U/MOD. MasterFORTH contains a file
system and I have placed these screens in
the file LONGWORDS.
Screen #2: These are the long pair — LP —
words for moving pairs of double num-
bers around the stack. They are ana-
logues of one-cell and two-cell stack
words, and their actions should be clear
from the stack diagrams.
Screen #3: Here are Bieman's useful
words T*, T/ and u*/.
Screen #4: If the divisor in fact fits into
sixteen bits, then [u/v] can be computed
with no further extension of the diction-
ary by the word NARROW_UD/ MOD. The
word US>D converts an unsigned single
to a double, and it is necessary because
S>D reads the sixteenth bit as a - (minus)
sign and extends to a double accordingly.
Note the double constant SUPERBASE.
Volume VI, No. 3
11
FORTH Dimensions
Screen #5: The actual long division be-
gins on this screen. The word UD/ MOD_
TUCK disassembles the high and low parts
of the dividend and divisor and saves
those cells needed later. Then UD/MOD_
DENSCALE calculates the number d, which
SCALE-^DEN uscs to scale the denomina-
tor. The quotient, at least if w needs thirty-
two bits, is a consequence of WIDE_QU0T,
which carries out the algorithm worked
out above.
Screen #6: WIDE_UD/MOD carries out the
full thirty-two-bit division operation and
returns quotient and remainder.
Screen #7: Enter double numbers, divi-
dend first and then the divisor, and exe-
cute UD/MOD. The stack holds the re-
mainder inside the quotient. Example:
3141592654. 1000000000. CF D. D. prints
first 3 and then 141592654.
(See "Intermezzo, "page 15.)
SCR
a
1
2
3
4
5
h
7
8
9
\Z
11
12
13
14
15
SCR » 3
* 2
. LONGWORDS
> For Ranipulating groups of
FORTH 33 B9MAR84Ne
double nuabers
UPSWAP \
>R >R 2SWAP
>R >R 2SWAP
LPDUP \
2DUP >R >R
LPOVER
>R >R
LPROT
>R >R
LPDROP
>R
>R
Dl D2 D3 04 D3 D4 Dl D2
>R >R 2SWAP R> R> R> R> 2SlilAP
R> R> i
Dl D2 Dl D2 Dl 02
20VER R> R> ;
\ Dl D2 03 04 01 02 03 04 01 D2
>R LPDUP R> R> R> R> LPSWAP j
\ 01 02 03 04 05 06 — 03 04 05 D6 Dl
>R LPSWAP R> R> R> R> LPSWAP ;
\ 01 02 —
02
DROP DROP DROP DROP
FORTH 83 iaf1AR84NG
1
2
3
4
5
6
7
8
9
18
U
12
13
14
15
\ LONGWORDS
\ words for aanipulating double nuabers
\ double-triple words after L. H. BIEHAN, FORTH Diaensions,
V-1
UM/ \ UD UN — UN
un/noo SWAP drop ;
T* \ UD UN — UT
DUP ROT UM* >R >R
UN*
R> R> 0+ i
T/ \ UT UN UD
>R Re UH/NOD SWAP
ROT a Re un/noo swap
ROT R> UH/MOD SWAP DROP
a 2SWAP SWAP 0+ ;
U*/ \ UD UN UN — UD
>R T* R> T/ ;
divide UD by UN and drop reaainder
SCR » 4
a \ LONGWORDS F0RTH83 ianAR84NG
1 \ words for dividing double by double
2
3 : NARROW. UD/NOD
4 \ UOividend UNdivisor — UOreaainder UOquotient
5 DROP >R 20UP Re \ shuck high cell of divisor
6 t SWAP U«/ \ UOguotient
7 2SWAP 20VER R> 1 U*/ D- 2SWAP j \ UDrea UOquot
8
9 VARIABLE NUMH VARIABLE DENH VARIABLE DENL VARIABLE DENSCALE
IB 2VARIABLE NUN 2VARIABLE DEN
11 65536. 2C0NSTANT SUPERBASE
12
13 ! US>D \ convert unsigned 16bit to 32bit
14 a ;
15
FORTH Dimensions
12
Volume VI, No. 3
SCR » 3
a \ L0N6U0RDS FORTH 93 ianAR84NG
1 \ Mords ior dividing oi double by double
2
3 ; UD/I10D_TUCK \ UD UD — save parts o+ num and den
4 2DUP DEN 2! DENH ! DENL !
5 2DUP NUM 2! NUHH ! DROP ;
i ; UD/MOD DENSCALE \ — UN for scaling-up den
7 SUPERBA5E DENH i I* Un/
9 DENSCALE ! |
9 i SCALE. DEN \ iultiply deno»inator by scale factor
10 DEN is DENSCALE 8 1 U*/
U DENH '. DENL ! ;
12 i WIDE.QUOT \ UD if divisor needs more than 16 bits
13 NUIl'29 NUMH 9 US>D
U DENL 9 DENH 9 U»/ D-
15 DENSCALE 9 DENH 9 U*/ SWAP DROP i
SCR » 6
9 \ LONSWORDS FORTH 83 iaMAR84NG
1 \ Hords for dividing double by double
2
3 : 7NARR0W. DIVISOR \ D — flag is divisor < 65536 ?
4 DUP ;
5 I WIDE.REH \ UD reiiainder in wide division
6 DUp'nUH 29 ROT DEN 29
7 ROT 1 U*/ D- ROT US>D ;
9 : WIDE UD/MOD \ UDdividend UDdivisor — UDren UDquot
9 UD/iioD.TUCK
la UD/MOD. DENSCALE
11 SCALE DEN
12 WIDE QUOT
13 WIDE REM ;
14
15
SCR # 7
a \ LONGWORDS FORTH 83 iaMAR94NG
1 \
division
of double by
doubl e
2
3 !
UD/MOD
\ UDdividend
UDdivisor -
— UDreiiainder
4
?NARRbH
.DIVISOR
5
IF
6
NARROW
.UD/MOD
7
ELSE
9
WIDE UD/MOD
9
THEN
la :
UDMOD
\ UDdividend
UDdivisor -
— UDremainder
11
UD/MOD.
2DR0P ;
12 !
UD/
\ UDdividend
UDdivisor -
• — UDquotient
13
UD/MOD
2SWAP 2DR0P
!
14
15
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and transcendental functions.
•String extensions including LEFTS,
RIGHTS, and MID$.
•Full feature screen editor and
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•Compatible with VIC peripherals
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•Expanded 167 page manual with
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PERFORMANCE
MICRO
PRODUCTS
770 Dedham Street,
Canton, MA 02021
(617) 828-1209
Volume VI, No. 3
13
FORTH Dimensions
Sixth FORML Conference
Forth Modification Laboratory
November 23-25, 1984
CALL FOR PAPERS
FORML is a technically advanced conference of Forth practitioners. The topics to be discussed will affect the future
evolution of Forth. All conference participants are encouraged to write a paper for oral or poster presentation.
Topics Suggested for Presentation
Forth in 64K and l)eyond Forth on the 32 bit machine
Forth expert systems Forth in the future
Forth on the IMacintosh Forth for robot control
Forth advanced applications Forth programming style
Registration and Papers
Complete the registration form, selecting
accommodations desired, and send with
your payments to FORML Include a 100
word abstract of your proposed paper. A
complete author's packet will be sent to
you. The deadline for abstracts and paid
registrations is October 15, 1984. Com-
pleted papers are due November 1, 1984.
About Asilomar
Asilomar is an ideal conference location. It is
situated on the tip of the Monterey Peninsula
overlooking the Pacific Ocean. Asilomar
occupies 105 secluded acres of forest and
dune. The secluded setting and clustered
meeting and accommodation areas make it
ideal for group meetings. Asilomar's excel-
lent meals are complemented by Asilomar's
homemade bread and pastries. Accommo-
dations are excellent and deluxe rooms have
been reserved for FORML attendees.
Sweeping ocean views are available from
decks or balconies. Asilomar is a Unit of the
California State Park System.
Registration Form
Complete and return with check made out to:
FORML, RO. Box 51351, Palo Alto, CA 94303
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Company .
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Prices include coffee breaks, wine and cheese parties, use of Asilomar facilities,
rooms Friday and Saturday nights, and meals from lunch Friday through lunch
Sunday. Conference participants receive notebooks of papers presented.
Conference attendees, share a double room:
number of people x $250 = $
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number of people x $300 = $
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number of people x $200 = $
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Options: Vegetarian meals? .
Non-smoking roommate? .
FORML, P.O. Box 513S1, Palo Alto, California 94303, U.S.A.
FORTH Dimensions
14
Volume VI, No. 3
Intermezzo
Short Continued Fraction
This interlude is a sampler. You can
load one screen and see a cut-down ver-
sion of the continued fraction program in
action. If you like what you see, you
can plunge into Part II — explanations,
screens, and all.
Begin by loading figure two, the screen
#8 of the file NUMBTHY. It is over-
stuffed and has no comments, but they
will be found in abundance in Part II.
Enter 31416 10000 SCF and execute. You
will soon be viewing three columns
headed PARTIAL_QUOT, NUMERATOR and
DENOMINATOR. Ignore the first column
for the moment and inspect the second
and third. They list the numerator and
denominator of a sequence of fractions,
one or more of which you may recognize.
If you enter a pair as <numerator> 10000
<denominator> */, execute, and inter-
pret the result as an integer followed by
four decimal places, you will surely rec-
ognize the sequence of fractions as giving
approximations to a well-known number.
You can repeat with 14142 10000 SCF
and 6931 10000 SCF to generate rational
numbers approximating sjl and In 2.
Return now to 31416 10000 SCF for a
closer look. The partial quotients in the
left column fit together to create con-
tinued fractions:
3 + -
7 +
16
3+-
3/1
22/7
355/113
3927/1250
7 +
16+-
Notice also that 3927/1250 is just the
fraction 31416/ 10000 reduced to lowest
terms.
The word SCF accepts integers p and q
no bigger than 32767 and returns the par-
tial quotients and corresponding frac-
tions (called convergents) of the con-
tinued fraction for p/q.
The goal of Part II is a word CF that
would accept, say, 3141592654. and
1000000000. and return a sequence of
fractions affording increasingly better
approximations to the floating point num-
ber 3.141592654. From this sequence, we
can select one whose numerator and
denominator each fit into sixteen bits and
test it using U*/ to see if the quotient
approximates 3. 141592654 to the desired
precision.
If you see possibilities from this dem-
onstration, continue on to Part II.
DASH, FIND
Our company, DASH. FIND & ASSOCIATES,
is in the business of placing FORTH Program-
mers in positions suited to their capabilities.
We deal only with FORTH Programmers
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FORTH Programmer, contact us or
send your resume to:
DASH. FIND & ASSOCIATES
808 Dalworth. Suite B
Grand Prairie TX 75050
(214)642-5495
Committed to Excellonce
SCR » S
8 \ NUNBTHY FORTH 33 17MARS4NG
1 \ short version oi continued friction
2 VARIABLE SB. BIN VARIABLE SQ.BIN VARIABLE ?R.BIN
3 : SCF \ nI N2 — continued fraction of N1/N2
4 CR PARTIAL. QUQT" .* NUMERATOR" ." DENOMINATOR"
5 1 a 2SWAP a I 2SWAP
6 BE5IN
7 SWAP OVER /MOD DUP S>D CR 12 D.R
8 SB. BIN ! SR. BIN ! SQ.BIN I
9 2SWAP 20VER
la SB. BIN 9 • ROT + DUP S>D 11 D.R
11 ROT ROT SB. SIN 9 • + DUP S>D 13 D.R
12 SMAP SQ.BIN 9 SR. BIN 9 DUP a«
13 UNTIL
14 6 a DO DROP LOOP ;
15
Figure Two
Volume VI, No. 3
15
FORTH Dimensions
Part II
Continued Fraction
If you have not read the previous
Intermezzo, you may wish to do so now
to get an idea of where this part will go.
Then return here to continue reading.
Every real number can be approxi-
mated to arbitrary precision by rational
numbers. If the real number is itself
rational, then it is its own approximation
to arbitrary precision, but in that case
there are still approximations by rational
numbers with smaller denominators. We
must carefully distinguish the ideal set of
real numbers from machine numbers,
those entities that a given computer uses
to mimic the real numbers and, even
more so, machine arithmetic from the
ideal of real number arithmetic. Most
computer-users believe they are doing
real arithmetic and, if the computer is
well-designed, they will be reasonably
safe in that belief.
In carrying out actual arithmetical
computations, we never calculate other
than with rational numbers. Irrational
numbers such as \/2 and ir must be
represented by rational surrogates. For
example, we may represent tt as the
decimal approximation 3.1416, that is,
the rational number 31416/ 10000. Com-
putation with decimal fraction approxi-
mations proceeds by famiUar repetitive,
simple steps. However, decimal fraction
representatives are not the only forms in
which to present a rational number and
are not always the most efficient for spe-
cific calculations.
A decimal number no.nin2n3. . ., pos-
sibly non-terminating, is a conventional
abbreviation for an infinite sum 2k=o
nk lO '', each nk being an integer between
and 9 inclusive. Another type of represen-
tation is by a (possibly) infinite product,
for example Wallis' product
JL= 2 2 4 4 6 6
2 1 3 3 5 5 7
(I have used a product decomposition in
an earlier Forth algorithm [7].) Product
representations are useful in forming
products of two numbers, but they are
not well-adapted for addition and
subtraction.
Our goal in this part is an implementa-
tion of continued fraction expansions of
double precision rational numbers. Con-
tinued fractions — to be described presently
— correspond to real numbers in a
(nearly) one-to-one fashion, but they are
not convenient for any of the usual
arithmetic operations. They can, how-
ever, be used to produce approximating
rational numbers — optimal in a sense to
be described — which can be substituted
for real numbers in machine computa-
tions of given precision and upon which
arithmetic can be carried out as usual. If
the original real number is irrational, the
associated continued fraction is unique.
If the original number is rational, the
continued fraction is almost unique: there
are two such associated continued frac-
tions differing only trivially. In the ra-
tional case, the continued fraction en-
genders an infinite sequence of rational
numbers approximating the given rational
to increasing and, finally, to infinite pre-
cision. The decimal fraction form of one
of these approximants may agree with
that of the original to the precision
required and yet the approximant may
have drastically smaller numerator and
denominator than the original fraction.
Continued Fractions
Here is the place to define continued
fractions and describe their properties
useful to us. In fact we will describe a
subclass, the simple continued fractions.
(The word "simple" is merely a technical
term.) A simple continued fraction is a
symbol
f=bo + S
b, + S
— [bo; bi, b2, bs,. . .].
The first version gives an idea of the
meaning of the symbol. The second ver-
sion is a conventional representation for
the sake of the typographer. The first
version indicates that f is the limit of a
sequence of rational fractions (called
convergents).
bo = bo/ 1
bo + -rr =(bo*bi + l)/bo
bi
. , 1_ ^ bo * bi ♦ b2 + bp * bi + b2
""^^ ^ 1 (b,*b2 + b,)
01+-;—
b2
and so on. By conventions. & partial quo-
tient bk can equal only if all the follow-
ing partial quotients are 0. In this case the
convergents stabilize and f, the Umiting
value, is a rational number if all the par-
tial quotients are integers. If the sequence
of partial quotients never terminates, and
if the partial quotients are integers, the
limiting value f always exists and it is an
irrational number. (It can be shown that
the sequence of integer partial quotients
is eventually periodic exactly when f is a
number of the form (P + qVD)/R,
where P, Q, R, and D are integers, R 0,
and D is positive and not a square.) For
example, the continued fraction [1; 1,2,
3] — the trailing entries are suppressed
— gives the sequence of rationals 1/1,
2/ 1 , 5/ 3, 17/ 10, and the last is the value of
the continued fraction. (Note that [ 1 ; 1 , 2,
3] = [1; 1, 2, 2, 1], illustrating the trivial
non-uniqueness of terminating fractions.)
Proofs of the following assertions will
be found in almost every book whose title
contains one of the strings "Theory of
Numbers" or "Number Theory." The
notafion is keyed to the standard refer-
ence [1, 3.10.1] with one minor change
that will be pointed out later.
If f = [bo; bi, b2, bs, . . ■ ], then the finite
section f„ = [bo; bi, b2, . . . ,bn] is called the
nth convergent. When all the bk's are
integers (and this is the only case we con-
sider from now on), the nth convergent
simplifies into a rational number of the
form fn = An/Bn, where the numerator
and denominator may have any common
divisors removed. The limit f = lim An/ Bn
always exists. If f is irrational, the partial
quotients are uniquely determined. If f is
rational, they are determined except for
the last: the last partial quotient can be
decreased by 1 and a further partial quo-
tient 1 appended. (For example, [1; 1,2,
3] = [1;1,2, 2, 1].)
The convergents bracket the value of
the continued fraction according to the
inequalities
f2k < f2k+2 < f < fjk+l < f2k-l
Furthermore,
|f-An/B„| < 1/BS,
FORTH Dimensions
16
Volume VI, No. 3
and there is no better approximation to f
by a fraction A/B with B < Bn.
If we set A-i =1, A-2 = 0, B-i =0, and
B 2 = 1, then the value of the Ak and Bk
can be found for k > from the partial
quotients by the recurrences
Ak = bk * Ak-i + Ak-2
Bk = bk * Bk-i + Bk-2
Conversely, given f, the partial quotients
can be generated from the convergents by
the formula
bk = [Bk-i/(Ak i-f*Bk-i)].
Euclidean Algorithm
As we are aiming only for continued
fractions of rational numbers, we can
take an important path along the Eucli-
dean algorithm. If u and v are integers,
u non-negative and v positive, then the
Euclidean algorithm consists of the
sequence of divisions
u =
bo * V + ri
v =
bi * ri -1- r2
ri =
b2 * r2 + rs
r2 =
bi* T3 + u
r„-2 =
b„-i * rn-i + r
rn-i =
b„ * rn
r„-i/r„ =
b„.
In this presentation, the Euclidean algo-
rithm states exactly that u/v — [bo; bi,
b2,...,b„]!
We can, therefore, implement the Eu-
clidean algorithm and draw from it both
greatest common divisor and continued
fractions.
Two remarks will be useful. It should
be clear from inspection of the Euclidean
algorithm that it will terminate after
finitely many steps. How many steps will
be required? G. Lam€ proved that the
algorithm will require no more than
about five times the larger of the numbers
of decimal digits in the two terms u and v.
When the terms u and v are double preci-
sion integers of at most thirty-two bits,
this means that the Euclidean algorithm
will cycle at most fifty times or, in other
words, that the continued fraction for
u/v will contain at most fifty non-zero
partial quotients.
What numbers will stretch the algo-
rithms to their limits? Further inspection
of the Euclidean algorithm shows that
this will happen if the numbers u and v
produce the sequence of partial quotients
1; 1, 1, 1,.... When the ones run on
forever to produce f = [1; 1, 1, 1,. . .],
then f= (1 + V5)/2, the golden section
(or its reciprocal). Furthermore, the con-
vergents to f can be calculated by the
recurrences Ak = Ak-i + Ak-2, A-2 = 0,
A-, = 1 , and Bk = Bk-i + Bk-2, B-2 = 1 , B-i
= 0. Thus, both Ak and Bk run along the
sequence of Fibonacci numbers Fk defined
by the recurrence Fk = Fk-i + Fk-2, Fi = 1 ,
F2 = l.
Implementation of the Algorithm
The algorithm as I have implemented it
calls upon the word UD/MOD and its satel-
lites defined in Part I, as well as the long
pair (LP) words. All of the calculations
are in double precision and the screens
are essentially the expansion to double
precision of the single precision screen
presented during the Intermezzo.
Again the screens have been composed
in MicroMotion MasterFORTH, an im-
plementation of Forth-83 with file sys-
tem. These screens are from my file
NUMBTHY. They should run in Forth-
79 if the word ABORT" in screen #3 is
adjusted. Here is a description of the
screens.
Screen #2: For convenience, the greatest
common divisor, calculations for which
are embedded in the continued fraction
algorithm, is given without encumbranc-
es by the word DGCD acting on double
integers. The Fibonacci numbers are use-
ful for many purposes — including gener-
ation of demonstration continued frac-
tions of maximal stretch — so the word
FIB is included to list them as far as D. will
print them.
Screen #3: The numbers Ak, Bk, and bk
all can be genuinely thirty-two-bit inte-
gers. As the recurrence formulas for gen-
erating the convergents call on products
bk * Ak-i and bk * Bk-i, it is conceivable
that quadruple precision multiplication
could be required. In fact, this worst case
can never happen, and this is clear from a
close look at the recurrence formulas.
Each of the Ak, Bk and bk is non-negative,
so that bk * Ak-i < Ak < u and bk * Bk-i <
Bk < u. Therefore, bk and Ak-i cannot be
both wider than sixteen bits and the same
is true of bk and Bk-i: at most one of the
factors can be double width. I wrote the
word CF* to exploit this special circum-
stance. It calculates the product of UDl
and UD2 using Bieman's multiplication/
division U*/. Because U*/ is not commuta-
tive, CF* orders the factors and issues an
error message if both are wider than six-
teen bits.
Screens #4, 5, and 6: The actual calcula-
tion begins here in the mode of the Eucli-
dean algorithm. I've written short words
with long names in a try at cutting down
on comment lines. The words should be
easy to follow through on screen #6,
where the stack at BEGIN holds Bk-2, Ak-2,
Bk-i, Ak-i, rk-i, rk.
Screen #7: If I have chosen word names
well, all that remains to explain is that the
last line of CF cleans the stack. (I could
have used the Forth-83 word CLEAR, but
that might clear other numbers deeper in
the stack.)
Using CF
The word CF ideally is used interac-
tively. For example, suppose we are to
calculate integer products [xtf], where x
is a double integer and [xtt] is to be a
double integer. The evaluation will be
carried out by finding a rational u/v
approximating tt, then computing [xtt]
by the sequence xuvU*/. If x is much
wider than sixteen bits, it is important to
approximate tt in such precision that low
precision digits in the product are not
distorted.
We know that tt = 3.141592654, so
enter 3141592654. 1000000000. CF. The
latest convergent both of whose elements
fit into sixteen bits each is 355/113. This
gives TT = 3.1415929..., good to six
rounded places.
We can do better. The next entry is
104348/33215 s 3.141592654, the exact
rounded value to nine decimal places. But
Volume VI, No. 3
17
FORTH Dimensions
104348 needs more than sixteen bits.
Even so we can obtain [xtt] by the
procedure
X 52174 33215 U*/ 2DUP D+.
Observe that the expansion given here
for 355/ 1 13 = [3; 7, 15, 1], while SCF gives
355/ 1 13 = (3; 7, 16]. This is an instance of
the only almost uniqueness of the con-
tinued fraction for rational numbers, and
arises because only finitely many digits of
TT are being manipulated.
References
1. Abramowitz, M., and I. A. Stegun, Handbook
of Mathematical Functions, National Bureau
of Standards Applied Mathematics Series, 55.
(Re-printed by Dover Publications.)
2. Anderson, Anita, and Martin Tracy, Forth
Tools, Volume One, MicroMotion, Inc., 1984.
3. Beers, David A., "Quadruple Word Simple
Arithmetic," Forth Dimensions, IV/ 1, p. 17.
4. Bieman, L.H., "Double-Precision Math
Words," Forth Dimensions, V/ 1, p. 16.
5. Brodie, Leo, Starting Forth, Prentice-Hall,
Inc., 1981
6. Corry, Robert T., "Closer Approximations,"
Forth Dimensions, IV/4, p. 4.
7. Grossman, Nathaniel, "Fixed-Point Loga-
rithms," Forth Dimensions, V/5, p. 11
8. Knuth, D.E., The Art of Computer Program-
ming, Volume Two, Addison- Wesley Publish-
ing Co., 1973.
SCR # 2
a \ NUMBTHY FORTH 3J 15l1Afia4NG
1 \ double nuaber greatest coaaon divisor and -flbonacci nuabers
2
3 i DSCD \ Dl D2 — qcd of Dl and D7
4 BE5IN
5 2SWAP 2QVER UDMOD 2DUP Da«
6 UNTIL 2DR0P D. j
7
8 ; FIB \ N — -first N fibonacci numbers, N < 47
9 >R a. I. R> 1+ I CR
la DO
U SPACE SPACE I .
12 2DUP D. SPACE 126 EMIT
13 2SWAP 2QVER D+
14 LOOP i
15
SCR » 3
a \ NUMBTHY
1 \ product of double -factors Mh
2
3 : CF» \ UOl UD2 UD
4 ?DUP
3 IF
6 2SWAP ?DUP
7 IF CR ABORT" OVERFLOW"
8 ELSE 1 U*/
9 THEN
IB ELSE 1 U*/
11 THEN j
FORTH 33 14MAR84N6
en one Is really single
\ is UD2 Mider than ib bits?
\ yes, so see if UDl is
\ also wider than 1& bits
\ both Mide ■> all done
\ but at least one is narrow
\ peraits aul t i pi i cat i on
\ with 32 bit product
SCR # 4
a \ NUMBTHY FORTH 33 15MAR84NG
1 \ words for continued fraction see scr #7
2
3 2VARIABLE B.BIN 2VARIABLE Q.BIN 2VARIABLE R.BIN
4
5 ! .CF HEADING
6 CR ." PARTIAL. QUOT" NUMERATOR" .' DENOMINATOR" ;
7
8 : INIT'IZE. RECURRENCE
9 1. a. LPSWAP a. 1. LPSWAP j
la ! GET. PARTIAL. QUOTIENT
11 2SWAP 20VEi UD/MOD ;
12
J3 ; .PARTIAL. QUOTIENT
14 CR 2DUP 12 D.R ;
15
FORTH Dimensions
18
Volume VI, No. 3
SCR i 3
i \ NUMBTHY F0RTH83 15MAR84NG
i \ words ior continued fraction see scr #7
2
3 ! SAVE. SCO. ELEMENTS
4 B_BIN 2! R.BIN 2! Q.BIN 2! j
5
6 i INIT' IZE. TO. CALC. CONVERGENT
7 LPSWAP LPOVER ;
3
9 : GET. NUMERATOR
la B.BIN 28 CF» 2R0T D+ f
1 1
12 ! .NUMERATOR
13 2DUP 12 D.R i
14
15
SCR » 6
a \ NUMBTHY FORTH 93 15nAR84NG
1 \ words -for continued fraction see scr #7
2
3 ! SET. DENOMINATOR
4 2R0T 2R0T B BIN 29 CP* D+ i
5
(, : .DENOMINATOR
7 2DUP 12 D.R ;
3
9 i REINIT' IZE. RECURRENCE
la 2SMAP Q.BIN 28 R.BIN 28 |
11
12 ; 7END.GCD. ALGORITHM
13 2DUP DB» !
14
15
SCR » 7
a \
NUMBTHY
FORTH S3
1 \
continued fraction algoritha
2
3
CF
4
.CP. HEADING INIT'IZE.
RECURRENCE
5
BEGIN \ euclidean gci
algoritha loop
i
SET PARTIAL QUOTIENT
.PARTIAL QUOTIENT
7
SAVE. 6CD. ELEMENTS
INIT 'IZE. TO. CALC. CONVERGENT
3
GET NUMERATOR
.NUMERATOR
9
GET. DENOMINATOR
.DENOMINATOR
la
REliilT' IZE. RECURRENCE
7END.GCD. ALGORITHM
11
UNTIL
12
6 a DO 2DR0P LOOP i
13
14
15
Volume VI, No. 3
19
FORTH Dimensions
Re-Defining a Colon Word
E.H. Schmauch
Ponca City, Oklahoma
Although Forth offers may signifi-
cant advantages over BASIC, there is
one characteristic of BASIC which
makes it easier for me to use in program
debugging. To change any line in a
BASIC program, all I do is re-enter that
line and the program is ready to run. In
Forth, I can interactively re-define any
word; however all words which already
reference this word will still reference
the old version. To have the new version
of the re-defined word referenced, 1
must re-load all words which reference
the re-defined word. As programs be-
come more complicated, the successive
editing and re-loading of screens begins
to resemble the old Fortran program
development cycle, something I would
like to avoid.
Forth purists may insist that proper
planning and bottom-up development
will eliminate the type of problem I am
describing; however, I found myself
wishing to re-define a Forth word, when
higher-level words have been developed,
sufficiently often to warrant the devel-
opment of RE: and RE; which are shown
in screens 42 and 43. By using RE: and RE;
instead of : and ; I can re-define a word
and previously defined words will refer-
ence the new version. This allows me to
interactively debug the word. When I
am satisfied with the modifications, I
edit the screen and re-load everything
just once, instead of once for each test
run during debugging.
RE: and RE; do not overwrite the old
definition, but rather compile a new
parameter field at the top of the diction-
ary. (The parameter field is the list of
words in the definition.) At run time,
execution is directed to the new parame-
ter field. RE: is identical to : except RE-
CREATE is used instead of CREATE. (For
definitions of : and ; consult All About
Forth by Glenn Haydon.) RE-CREATE
finds the word and replaces the value in
the PFA with the current top of the
dictionary. RE: then puts the address of
DOCOL at the top of the dictionary and
SCR #42
( REDEFINING A COLON WORD — CRC=53915
1
2 ' : CPA iS CONSTANT DOCOL
EHS 06AUGa3 FORTH-79 )
6
7
8
9
10
1 .1
12
13
14
15
RE-CREATE ( )
-FIND NOT IF
HERE COUNT TYPE NOT FOUND" ABORT
THEN
DROP DUP CPA 3 DOCOL = NOT IF
HERE COUNT TYPE ." NOT A COLON WORD" ABORT
THEN
HERE SWAP .' ;
RE-EXIT (
R> R) 2DR0P
)
SCR #43
< REDEFINING A COLON WORD — CRC= 4982
1
2 : RE: ( )
3 SP3 CSP !
4 CURRENT 3 CONTEXT !
5 RE-CREATE DOCOL , ] ;
6
7 : RE; ( )
a ?CSP
9 COMPILE RE-EXIT
10 C COMPILE] C !
11 IMMEDIATE
12
13
14
15
EHS 06AUBa3 FORTH-79 )
enters the compile mode. Now the first
word in the old definition is a colon
word at the top of the dictionary. The
word at the top of the dictionary will
only have code and parameter fields, not
name or link fields. Next the re-defmition
is compiled at the top of the dictionary.
When the re-definition is complete, RE;
is used instead of ;.
RE; is identical to ; except it compiles
RE-EXIT instead of EXIT. RE-EXIT serves
the same function as EXIT except it pops
the return stack an extra time. EXIT
would transfer program execution to
the third byte of the parameter field of
the original definition. The extra pop of
the return stack in RE-EXIT causes pro-
gram execution to properly return to the
point after the word was called. SMUDGE
is not used in RE: or RE; since the word
being re-defined, in general, will not be
on top of the dictionary.
There is a performance penalty with
words re-defined with RE: and RE; since
DOCOL must be executed twice for each
execution of the re-defmed word. Once I
am satisfied with the definition, I will
edit the screen and re-load everything,
eliminating the performance penalty.
RE: and RE; can also be used to easily
change colon words in the Forth kernel
without meta-compilation.
RE: and RE; demonstrates one of the
greatest advantages of Forth over other
languages: the ease with which a charac-
teristic of a Forth system can be modi-
fied in Forth.
FORTH Dimensions
20
Volume VI, No. 3
PUBLICATIONS
The FORTH Interest Group Order Form (on the reverse side of this page) has 11 newly added publications selected
by the FIG Publications Committee:
All About FORTH Threaded Interpretive Languages
Beginning FORTH Understanding FORTH
FORTH Encyclopedia The Journal of FORTH Applications and Research, V. 1,#1
FORTH Fundamentals, Volume 1 The Journal of FORTH Applications and Research, V. 1, #2
FORTH Fundamentals, Volume 2 Dr. Dobb's Journal, 9/84
Thinking FORTH (Soft and Hard cover)
Here are brief descriptions of 4 of them:
THINKING FORTH,
A Language and Philosophy for Solving noblems
by Leo Brodie
The best-selling author of
STARTING FORTH (Prentice Hall,
1981) is back again! — this time
with the first guide to using
FORTH to program applications.
This book captures the Philosophy
of the language to show users how
to write more readable, better
maintainable applications.
Both beginning and experienced
programmers will gain a better
understanding and mastery of
such topics as:
• FORTH style and conventions
• decomposition
• factoring
• handling data
• simplifying control structures
• and more.
And, to give you an idea of how
these concepts can be applied.
Thinking FORTH contains
revealing interviews with real-life
users and with FORTH's creator,
Charles H. Moore.
To program intelligently,you
must first thinl< intelligently, and
that's where Thinking FORTH
comes in.
Leo Brodie is a writer,
programmer, consultant, teacher
and world-renowned authority on
FORTH.
BEGINNING FORTH
by Paul M. Chirlian
Here's a clear, self teaching
introduction to FORTH. It starts
with the very basic ideas you need
to know to begin programming,
then builds to the most complex
FORTH programming procedures.
FORTH Fundamentals,
Voiume 1: Language Usage
by C. Kevin McCabe
A complete guide to the two
major versions of FORTH, fig-
FORTH and FORTH-79. The book
gives you nontechnical
descriptions of FORTH words and
programming methods, and it
explores the language's internal
operation and use of memory.
FORTH Fundamentals,
Voiume 2: iJinguage Giossary
by C. Kevin McCabe
Organized by core FORTH word
names, this comprehensive fig-
FORTH and FORTH-79 glossary
gives you all the applicable
vocabularies and pronounciation.
Each word is fully defined, with
notes on the differences between
the two FORTH versions.
Volume VI, No. 3
21
FORTH Dimensions
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REFERENCE
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FORTH Dimensions
22
Volume VI, No. 3
Think Like a User
Write Like A Fox
Michael Ham
Scotts Valley, California
Good design consists in large part of
anticipating the user's inclinations and
accommodating them, at the same time
ensuring that the user is as friendly to
your program as your program is to the
user. This article describes the word DIG-
ITS, written to conform to this precept.
DIGITS collects numeric data of a speci-
fied number of digits. 3 DIGITS, for exam-
ple, will allow entry of at most three
numeric digits and will ignore all keys
except for numerals, backspace and the
enter (or return) key - and those keys
allowed by FIX.
A computer will follow its instructions
exactly but users are not so cooperative.
It is better to observe users and then
make your program conform to their
habits and expectations than to attempt
the reverse. FIX is a word to accommo-
date the users.
Whenever a user can validly complain,
"The computer should have known what
I meant," the design is bad. For example,
typists generally use the lower-case letter
L for the number one; if an L is typed in
the context of numeric entry, "one" is
clearly intended. The word L->1 thus
accommodates the user in this regard.
Similarly, the letter O and the numeral
zero not only share the same form, they
also occupy adjacent keys on the key-
board. If the user is a hunt-and-peck
typist, it is likely that the letter O in a
numeric context is meant as a zero and
0->0 again accommodates the user.
If the program displays the numeric
entry field (e.g., the numbers are being
entered in an inverse video rectangle that
defines the maximum number of charac-
ters), then some users will automatically
space over instead of entering leading
zeroes. That is, if they are to enter the
number seven in a three-digit field, they
normally will want to enter the seven in
the units position and will press the space
bar twice to move the cursor over.
Rather than fight this natural tendency.
Words to collect clean numeric data
1
2
3
4
5
6
7
8
9
1
1 1
1 2
1 3
1 4
1 5
1
2
3
4
5
6
7
8
9
1
1 1
1 2
13
1 4
1 5
C Numeric Input 1 of 2
: BS? < n - f > 12 = ;
: CR? ( n - f ) 13 = ;
Michael Warn
6/28/84 )
BACK
BSP
SP->0
L->1
O->0
FIX
OK?
«?
aaSCR?
-2 CURSOR ♦ ! i
BACK SPACE BACK
DUP 32 =
DUP 76 =
DUP 79 =
SP->0 L'
or n 1 )
) DUP 47
IF DROP 48 THEN ;
OVER 108 = OR IF DROP 49 THEN
OVER 111 = OR IF DROP 48 THEN
■>1 0->0 i
IF 1 ELSE BELL DROP THEN !
> OVER 58 < AND !
) «? OVER BS? OR OVER CR? OR
GETttBSCR ( -
GET»BSCR ( -
asc 1 1
asc i i
) BEGIN KEY FIX «BSCR? OK? UNTIL ;
) BEGIN DROP KEY FIX »BSCR? UNTIL
<, Numeric Input 2 of 2
Michael Ham
6/28/84 )
( n = max « of digits to collect; m = « of digits entered)
: DIGITS ( n - d m > DUP 1 ♦
DO BEGIN GET«BSCR DUP BS?
( bksp: ) IF DROP I IF BSP R> 1- >R ELSE BELL THEN
ELSE DUP PAD I * C! DUP CR?
( cr: ) IF DROP 1 LEAVE
( nmbr!) ELSE OVER I = IF DROP BELL ELSE EMIT 1
THEN THEN THEN UNTIL LOOP DROP ( n)
PAD 1- CONVERT PAD - ;
( NOTE: Delete 1 in line 7 if LEAVE is 83-Standard . )
it is easy to interpret spaces as zeroes.
"Space, space, seven" can be accepted
and displayed as "007". (Of course, if
they simply enter the seven (in the hun-
dreds place) and then hit enter, the pro-
gram should accept the number as seven,
not as 700.) If the entry field does not
have a visibly defined length, delete
SP->0 from the definition of FIX.
Note that FIX is unobtrusive. Users
who restrict themselves to the numeric
keys will never know that FIX is present
and even those who use FIX will be
unaware of it. For them, the computer is
simply doing what they would expect.
BS? and CR? test for backspace and
carriage return. This was written using
Forth Technology's Forth/ level 2, which
interprets the backspace key as ASCII
12. Most Forths use another value, typi-
cally 8. To find out what your Forth
does, type the sequence
KEY . <enter> <backspace>
The number displayed is the key-code
for your backspace key. Use it in place of
"12" in the definition of BS?.
BACK moves the cursor back one posi-
tion by decrementing the contents of
CURSOR, which in Forth/ level 2 deter-
mines the cursor position. In Forth/ level
2, EMITting a control code to the screen
displays a character instead of triggering
the specified function. In particular, that
system's 8 EMIT (which in some Forths
Volume VI, No. 3
23
FORTH Dimensions
acts as a backspace and thus could be
used as the definition of BACK) prints a
rectangular blob. Once you have defined
BACK you can then define BSP, which
moves the cursor back one position and
erases the character above it.
#? checks to see whether the value on
the stack is in the range of the ASCII
values of decimal digits. #BSCR? extends
#? to allow ENTER and backspace as
valid characters also. I factored out #?
for separate definition because it is use-
ful in other contexts to check for purely
numeric values.
OK? is a general-purpose word for
dropping bad input with a beep, sounded
by BELL (substitute your Forth's equi-
valent). A beep can be useful if the user
will be doing head-down data entry. If
the user is probably going to be looking
at the screen, however, I prefer to ignore
invalid keystrokes without the beep:
unnecessary noise is distracting in an
office. I thus give two versions of
GET#BSCR; the second version, on line
fifteen of the first screen listing, will not
beep. Instead, the DROP immediately
after the BEGIN will get rid of invalid
input after the UNTIL has eaten the flag
left by #BSCR?. The zero preceding BEGIN
is to give DROP something to drop the
first time through the loop.
You pick the version of GET#BSCR
that you want to use. Both will loop
until the user enters an acceptable value.
From the point of view of the user,
invalid keys (for example, most of the
alphabetic keys) simply don't work.
The above words are used to define
DIGITS, which itself requires a number:
the maximum number of digits to be
allowed in the number the user will enter.
DIGITS leaves two numbers on the stack:
the count of digits the user actually typed
and, beneath that, the entered number
(as a double-precision number occupy-
ing two cells on the stack). By having the
count of digits typed, your program can
check whether a number was input or
whether the enter key was pressed imme-
diately, with no digits entered.
The trick in writing DIGITS was seeing
that to collect a five-digit number, for
example, the loop must allow for six
repetitions - but the sixth time through
the loop, enter and backspace are the
only valid input.
DIGITS first duplicates the number of
digits allowed. It uses one copy to deter-
mine when it is in the last cycle of the
loop; it adds one to the other copy and
uses that as the limit for the loop. DIGITS
refuses to backspace on the first cycle of
the loop and refuses numeric input on
the last cycle (when only enter or back-
space are allowed). For these two errors,
I decided that a beep was warranted
because these keys are normally accept-
able; it is only under these special cir-
cumstances that they are invalid. If you
don't want the beep, eliminate the word
BELL.
The DO loop in DIGITS contains a
BEGIN-UNTIL construct - the routine es-
capes the BEGIN-UNTIL only when either a
valid digit is collected or enter is pressed.
If GET#BSCR delivers a backspace, the
value is dropped from the stack; then if
the backspace is invalid (trying to back-
space past the beginning of the number)
a beep is sounded or, if the backspace is
valid, the backspace is performed and
the loop index is picked up, decremented
by one and put back. By setting back the
index by one, the routine will collect
again the previous digit. In either case,
the backspace leaves a zero on the stack
so that the routine will not escape the
BEGIN-UNTIL but will go back to
GET#BSCR.
If the input was not a backspace, it is
stored in the scratch area PAD. The index
is used to locate the proper byte within
PAD so that the ASCII string representa-
tion of the number is built digit by digit.
Note that the ASCII value for enter (13)
will be stored as the last character of the
string.
If GET#BSCR delivers an ASCII 13 (the
enter key), that value is stored in the
string, then dropped from the stack and
the DO loop is exited with LEAVE.
If GET#BSCR delivers the ASCII value
for a number - the next digit of the
entered number - a check is made to see
whether this is the last time through the
loop (when only a backspace or enter
will be accepted). If so, the digit's ASCII
value is dropped from the stack, the
computer beeps and zero is left on the
stack so that the routine will repeat the
BEGIN-UNTIL loop; if not, EMIT displays
the digit on the screen and a one is left on
the stack to escape the BEGIN-UNTIL and
go through the next cycle of the DO loop.
Extraneous digits - digits that were
backspaced over or entered (incorrectly)
on the last cycle through the DO loop
— are left in the string in PAD. They can
be left there because they will be overlaid
either by the correct digit or by the
ASCII 13 stored when enter is pressed.
The ASCII 13 marks the end of the valid
digits.
When the routine escapes the DO loop,
it drops the number that was kept on the
stack to check the index. CONVERT con-
verts a number expressed as an ASCII
string into numeric representation, add-
ing it to a double-precision number on
the stack. The two zeroes (which amount
to one double-precision zero) are put on
the stack so that CONVERT will be adding
to zero, and PAD 1- provides the correct
address for CONVERT. CONVERT leaves on
top of the stack the address of the first
non-numeric character it encountered in
the string (which will be the ASCII 13
from the enter). By subtracting PAD (the
address of the beginning of the string),
the top of the stack will show the number
of digits entered.
If fewer than five digits are collected,
the number will be a single-precision
number. DIGITS can then be followed by
2DR0P to get a single-precision number -
without showing the number of digits
collected. If you want a single-precision
result but also want to know the number
of digits entered (so you can distinguish
an entered zero from no entry), follow
DIGITS with SWAP DROP.
Once you have received the result of
DIGITS, you can subject it to any other
edits your application might demand -
maximum or minimum legal values or
the like. DIGITS cooperates with the user,
but also delivers a clean number for you
to work with.
FORTH Dimensions
24
Volume VI, No. 3
SUPER FORTH 64
By Elliot B. Schneider
TOTAL CONTROL OVER YOUR COMMODORE-64"
USING ONLY WORDS
MAKING PROGRAMMING FAST, FUN AND EASY!
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Volume VI, No. 3
25
FORTH Dimensions
Upgrading Forth-79 Programs
Robert Berkey
Palo Alto, California
Given a set of code developed under
the 79-Standard, several choices exist
concerning translating to Forth-83. The
approach considered in this article is to
integrate the application with the new
standard, and the changes needed are
reviewed. After upgrading, each word
used within the application will then be
used in a Forth-83 manner.
The discussion is based on having a
79-Standard program needing transla-
tion onto a Forth-83 system. Actual
programs may use system-dependent ex-
tensions but the standard word set pro-
vides a basis from which to work. A
general knowledge of the changes to
Forth-79 is expected for following the
discussion; these changes have been docu-
mented in previous issues oi Forth Dimen-
sions. Only the required word set of
Forth-79 is considered, not the exten-
sion word sets. Users upgrading fig-
FORTH applications will also need to
consider the differences between fig-
FORTH and Forth-79.
Integrating the Code
The largest programming task is to
examine the output of each flag (eight
exist in the standard, and a typical
application uses additional flag produc-
ers), and determine whether its output is
used in other than a zero or non-zero
way. If in doubt, NEGATE or ABS can be
inserted in-line following the flag result.
ABS will work with either a 79flag or an
83flag, whereas NEGATE will be slightly
faster; but don't ignore efficient alterna-
tives. The phrase 79flag + can be re-
coded 83flag -. 79flag * is the same as
83flag AND. The phrase
flag IF + ELSE DROP THEN
is the same as
83flag AND +
NOT must be examined to see if its
input is a pure flag. If in doubt, it should
be changed to 0=. Indeed, it is simplest to
globally change each NOT to 0=, although
I find this to be stylistically undesirable.
Uses of LEAVE should be examined for
code that would have executed follow-
ing the LEAVE and before the loop termi-
nates; such code includes +LOOP itself,
since +LOOP removes a value from the
stack. Note that the only word needed
after the 83-Standard LEAVE is THEN.
For example,
IF (a) LEAVE ELSE (b) THEN
can be re-coded as
IF (a) LEAVE THEN (b)
Wherever ' is used, the ticked word must
be followed with >BODY. Cases of ' used
in a colon definition must be changed to
['] and, as just mentioned, >BODY must
be added after the ticked word.
My own experience in doing a major
conversion was to successfully examine
all the flags, NOTs, tick-values and LEAVES
and to forget to convert the few cases
involving PICK and ROLL. Some modifi-
cations are less common but can be rou-
tinely checked for. U* must be re-named
UM* and U/MOD must be re-named
UM/MOD. FIND translates directly by re-
placing its occurrences in colon defini-
tions with the following phrase:
32 WORD FIND 0= IF DROP THEN
If FIND is being interpreted on a load
screen it can usually be replaced with '
(tick).
Several words have different imme-
diate flags. COMPILE LEAVE gets changed
to [COMPILE] LEAVE. FORTH, when used
in a colon definition, must be replaced
with [ FORTH ]. Likewise, EDITOR is no
longer immediate and should be replaced
with [ EDITOR ]. The phrases [COMPILE]
FORTH and [COMPILE] EDITOR should
have the [COMPILE] removed for stylistic
reasons.
The formerly state-smart words pres-
ent special problems when preceded
with [COMPILE]. Consider the phrase
[COMPILE] '. Will the word containing
the [COMPILE] ' be used (1) when STATE
is true, (2) when STATE is false, or (3)
both? For case (1) use [COMPILE] [']. For
case (2) remove the [COMPILE]. For any
of the three cases a state-smart phrase
can be substituted:
STATE @ IF [COMPILE] ['] ELSE '
THEN [COMPILE] ."
can have the following phrase substi-
tuted:
STATE @ IF [COMPILE] ." ELSE
34 WORD COUNT TYPE THEN
[COMPILE] LITERAL can have the follow-
ing phrase substituted:
STATE @ IF [COMPILE] LITERAL THEN
The considerations from here until
the end of the paper will become increas-
ingly unusual, but any bug in an algo-
rithm is too much of a bug, so here goes.
This material is also of increasing inter-
est to work intended to be transportable
across all standard systems.
A number of other changes affect few
programs. These include division pro-
ducing negative quotients when the re-
mainder is not zero, unusual DO inputs,
the trailing character left by WORD and
trailing null characters left by EXPECT.
None of these was a problem in the
application I converted.
SCR, LISTand EMPTY-BUFFERS are no
longer required by the standard but this
is unlikely to be a problem, both because
standard programs don't typically use
these words and because standard sys-
tems have them around anyway. If they
are unavailable in the FORTH vocabulary
check in the EDITOR vocabulary. If avail-
able in the FORTH vocabulary they can
be depended upon to conform with the
Controlled Reference Words of
Forth-83.
QUERY is no longer required but is
typically implemented. It is regulated by
the Controlled Reference Word Set but
FORTH Dimensions
26
Volume VI, No. 3
it should be noted that the Forth-83
QUERY sets >IN and BLK to zero. The
word ? is no longer supported but is
easily defined:
: ? ( a - ) @ . ;
Block buffers may be a subtle prob-
lem because in Forth-83 changes can be
written to disk even if not UPDATEd
although I don't know of any systems
that exhibit this property. The phrase
SAVE-BUFFERS EMPTY-BUFFERS
can be re-coded FLUSH. Forth-79 algo-
rithms that make other use of EMPTY-
BUFFERS or that write to block buffers
without updating are candidates for
re-designing.
Some usages that are now non-stand-
ard will nonetheless work on some imple-
mentations; included in this group are
(1) ticking a CONSTANT and modifying
its contents, (2) using COMPILE in con-
junction with , (comma) to put a literal
value into the threaded code as with
COMPILE [ , ]
and (3) using the output of KEY without
stripping the high bits.
If the application is to be portable,
each of these cases should be reviewed
and eliminated. For the case of ticking a
CONSTANT and modifying the contents,
it may be useful to define a new class of
words:
: VALUE ( ~ 16b ) ( creating: 16b ~)
CREATE , DOES> @ ;
If any CONSTANT which is being ticked
is re-defined using VALUE, the problem is
resolved. A similar solution exists for
KEY.
: ASKEY ( ~ char ) KEY 127 AND ;
This, of course, requires altering refer-
ences to KEY to become ASKEY. If your
application is dependent on structures
of the class
COMPILE [ , ]
no standard mechanism is available for
translation. The significance here is that
the threaded code of a colon definition
may be kept outside of the Forth address
space. In practice there will be alternate
programming approaches available or,
for any particular system, a simple sys-
tem-dependent word (or words) provid-
ing equivalent functions.
Multi-programming has been speci-
fied in Forth-83. If the application will
run on only one system and that system
is not multi-tasking, then there is no
problem. But if the application is to be
portable, multi-programming must be
considered. A likely problem area is typ-
ing from block buffers.
Yet another problem can exist if the
requirements of the standard program
exceed the capacity of the standard sys-
tem. Systems can be considered stand-
ard with as few as 2000 bytes of applica-
tion dictionary, sixty-four bytes of data
stack, forty-eight bytes of return stack
and thirty-two mass storage blocks.
Another area to be considered is non-
standard practices that worked on the
older system but that will not run on a
Forth-83 system. One potential problem
is confusing I and R@. Similarly, the
function I' might have been used to
extract the loop limit. For many Forth-
83 systems the loop hmit can be retrieved
as a function of the top two elements of
the return stack, but the specific func-
tion varies widely among systems. Addi-
tional unknown effects will involve vocab-
ularies. CONTEXT and CURRENT are no
longer in the required word set; in
Forth-83 they are in the System Exten-
sion Word Set. In fig-FORTH, CON-
TEXT @ could be used to preserve the
entire search order. In Forth-83 systems
with a vocabulary stack, CONTEXT @
may preserve only the first vocabulary
in the search order. FORGET now uses the
compilation vocabulary, not the CON-
TEXT search-order.
The standard permits loop stacks,
and the loop stack need support only
three concurrent loops in the program.
The number of loops in use at any one
time is not something a Forth pro-
grammer would normally consider.
Some non-standard techniques will
work only on an indirect threaded code
system, while others will work only on a
subset of indirect threaded code sys-
tems; in either case these techniques
would not have worked on certain
Forth-79 systems and won't work on
some Forth-83 systems. Here is an exam-
ple of problems involving non-standard
techniques. Consider the following
definitions:
: 79DEFINER CREATE COMPILE
[ HERE 6 - @ , ]
FIND , FIND , COMPILE EXIT
DOES> EXECUTE 8 * ;
A superficially Forth-83 implementation
of the same idea follows:
: NEST ( apf ~ ) 2+ >R ;
: 83DEFINER CREATE ['] NEST @ ,
' , ' , COMPILE EXIT
DOES> NEST 8 * ;
These are used in the form:
79DEFINER MUNCH PAD @
83DEFINER MUNCH PAD @
On a post-increment indirect threaded
system, MUNCH will fetch the value at
PAD and multiply it by eight.
But the above definitions comprise a
rogues' gallery of non-standard prac-
tices. The definitions use the following
Forth-83 non-standard practices.
• Reaching into the header of the Forth
definition and knowing what is there.
• Requiring that the code field of a
colon definition be exactly two bytes.
(With a direct threaded system the code
field might well be three, four or more
bytes.)
• Leaving the return stack unbalanced
in a colon definition.
• Assuming knowledge of whether the
system has a pre-increment or a post-
increment IP.
• Assuming that the threaded code is
kept in the Forth address space, i.e.,
assuming that execution of COMPILE will
modify the value of HERE by two (HERE
might in fact be modified by zero, one,
two, three or four).
Volume VI, No. 3
27
FORTH Dimensions
• Assuming that the compilation address
is a Forth address. (A compilation add-
ress might be any sixteen-bit value that
is somehow contained in the threaded
code and understood by the address
interpreter. In addition, the compilation
address is not necessarily the address of
a code field.)
• Assuming that the sixteen-bit compi-
lation address is the only component of
the threaded code. (A jump-subroutine
system would have an additional one or
two bytes; a byte-token system would
only have one byte.)
• Assuming that the address used by the
address interpreter is a Forth byte add-
ress. (It could be a cell address or
another number, such as an 8086 seg-
ment.)
• Assuming that the address used by the
address interpreter is kept on the return
stack and is only one cell deep. (The part
of the return stack accessible with R>
may well have a return address of zero,
one or two cells in length.)
• Assuming knowledge of the physical
relationship of the address of the code
field and the address of the parameter
field. (>80DY converts the compilation
address to the address of the parameter
field for words whose parameter fields
are known to exist in the Forth address-
space — CREATE and VARIABLE and user-
defined words that execute CREATE —
but no mechanism is standardized for
going from the parameter field to the
compilation address or from the param-
eter field to the address of the code
field.)
Because of the actual structure in-
volved, these definitions could be stand-
ardized in this way:
: EXECUTE2 ( apf — ) DUP >R @
EXECUTE R> 2+ @ EXECUTE ;
: 83DEFINER CREATE ' , ' ,
DOES> EXECUTE2 8 * ;
This article has shown one approach
to translating a Forth-79 program onto
a Forth-83 system. The customized
changes described above produce effi-
cient and compact code. The next issue
of Forth Dimensions presents another
approach, a program interface that min-
imizes man-hours required to translate
at the cost of efficiency and size of the
program.
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FORTH Dimensions
28
Volume VI, No. 3
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Volume VI, No. 3
29
FORTH Dimensions
Astronomical Problems
William F. Ragsdale
Hayward, California
"Ask the Doctor" is Forth Dimen-
sions' health maintenance organization
devoted to helping you use and under-
stand Forth. Questions about problems
you have, references you need or con-
temporary techniques are most appro-
priate. When needed, our columnist will
call in specialists. Published letters will
receive a pre-print of the column as a
direct reply.
Walter Milton of Camden, New Jer-
sey has just begun to use the popular
Forth from Texas Instruments on his TI
99/ 4 A. He offers a request that the good
doctor hopes will stir thoughts for new
application programs in the mind of at
least one programmer looking for a
challenge.
"I am an amateur astronomer and
would appreciate any help or direction
you can supply. I would like to write
programs to do the following: 1) Code
the celestial mechanics equations for
planetary motion within the solar sys-
tem. 2) Generate plots specifically for
Jupiter and the four bright (Galilean)
satellites. 3) I would also like to input
my observations of Halley's comet and
compare with others' reports."
Rx: Forth had early use in the astro-
nomical community due to Charles
Moore's association with the National
Radio Astronomical Observatory and
the Kitt Peak National Observatory.
His work aided research there, at Owens
Valley Radio Observatory and at other
observatories world wide. One can sur-
mise that astronomers were limited by
funds and hardware, and depended on
Forth to extend their resources.
Two proponents of Forth are Roger
Stapleton at St. Andrews and Hans
Nieuwenhuijzen at the State University
at Utrecht. At this moment, I am being
tantalized by a listing from St. Andrews
for the measurement titled "Lunar
Occultation of Aldebaran." This is
exchange material from 1979, sent by
Roger. Since the application is quite
specific to his hardware and support
software, it serves to inspire rather than
to provide specific guidance. I trust that
both of these educators could provide a
short list of references on the appro-
priate calculation methods and practical
approaches.
While not programmed in Forth, the
program TellStar (from Information
Unlimited Software of Sausalito, Cali-
fornia) will produce customized viewing
charts for your site and time from an
internal data base and planetary calcu-
lations. The product also presents the
constellations of the Southern Hemis-
phere, so you may explore, in simula-
tion, portions of the heavens only avail-
able otherwise by extended travel.
Who would like to combine the ele-
ments of Julian date, star coordinates
and planetary motion, yielding a Forth
simulation system?
The gentlemen mentioned above may
be contacted at:
Dr. J. Roger Stapleton
University Observatory
Buchanan Gardens
St. Andrews, Fife
Scotland
Dr. Hans Nieuwenhuijzen
Sterrewacht Sonnenborgh
Zonnenburg 2
3512 NL Utrecht
The Netherlands
Frans Van Duinen of Toronto, Can-
ada, graciously writes: "Firstly, let me
express my appreciation for all the good
work you and the many other Figgers
have done and are still doing. Thanks!
In the original fig-FORTH Model
(vl.l), as in the Forth-83 Standard, the
colon changes the first vocabulary in the
search order to the one receiving the new
definitions (CURRENT). Why is that?
There are good reasons, no doubt,
but for the life of me I see none, only a
disadvantage. When I set the search
order to CP/M FORTH DBASE ONLY I don't
appreciate the system changing it to
DBASE FORTH DBASE ONLY just because I
happen to be adding definitions to
DBASE. Your comments, please."
Rx: A small number of reasons come
to mind for this characteristic. I'm unsure
if they are compelling. A broader dis-
cussion could bring to light additional
aspects, favorable or not. The short
answer is that it's always been that way.
The contemporary practice is reflected
in Forth, Inc. products, fig-FORTH,
and the Forth-78, Forth-79 and Forth-
83 Standards.
A more satisfying reason is that dur-
ing testing you may switch to another
vocabulary; when resuming compilation,
you might now compile identically
named words from that other vocabu-
lary. If colon (:) did not move back to
your application vocabulary, you would
compile the editor I, which would be
quite inappropriate inside a DO...LOOP.
Forth program development is highly
interactive. You move from testing to
editing to compiling in a matter of
seconds. Many would find it irritating to
have to type in the application vocabu-
lary name at the end of editing. You
presently just have to load the next
application block and the editor is re-
placed by the application vocabulary.
The restoration of the CURRENT vocab-
ulary was much more important back in
the days when the search order was spec-
ified in the order in which vocabularies
were defined. (This is compile-time
chaining as contrasted to the contem-
porary method of run-time chaining
with ONLY and ALSO.) Since the editor
chained only to FORTH in those systems,
without the automatic switch you would
search EDITOR, then FORTH and then the
CURRENT vocabulary. Since your appli-
cation would be searched last, any syn-
onyms in EDITOR or in FORTH would be
found first.
We see in compile-time-chained sys-
tems that the context shift at the start of
L
FORTH Dimensions
30
Volume VI, No. 3
compiling is needed for uniform behav-
ior. The importance is reduced, but not
eliminated, in run-time-chained systems.
Forth is a very fluid environment.
Vended systems can be extended or
modified. Ross Grable is concerned
about validation. He writes, "Dear Col-
league: Is there any software that can
verify the operation of a version of
Forth? I am looking for a program that
will verify a system against a glossary or
a standard. It seems that this would be
an extrememly useful tool, particularly
since cross-computer portability is a
strong feature of the language. Testing
Forth automatically would certainly
raise some interesting questions, such as
how to test the hmitations of compila-
tion and defining words."
Rx: In early 1982 a team of four sys-
tem implementors formed in Northern
California to develop a validation pack-
age for Forth-79. By the time they were
under way, the prospect of Forth-83
suggested that their work was prema-
ture. However, they didn't resume their
effort upon the release of Forth-83.
The field appears to be wide open,
even invited by the standard itself. Sec-
tion 7.2 of Forth-83 gives the required
hardware configuration for testing (2000
bytes of memory, thirty-two disk blocks,
stacks of sixty-four and forty-eight bytes,
and an ASCII terminal). Some of the
steps likely to be in a validation suit
would be to inventory all words, classify
if immediate or non-immediate, verify
that the validation source code has not
been altered and check characteristics of
the words. Typical subtleties would in-
clude tests that IF...THEN branches can
branch further than 127 bytes, and that
CREATE DOES> words are of the specified
construction. FIND classifies words as
immediate, non-immediate or missing.
Prospects of testing prompted this Stand-
ards Team choice. Such a validation
program could be the basis of a product,
or at least a very hvely conference paper.
David Fu of San Diego, California,
has set his sights at the high end of the
hardware spectrum. He queries, "I want
to know whether anybody put Forth on
the CDC Cyber, using the Compass lan-
guage. I'd like to try it."
In August of 1978, your faithful prac-
titioner received a listing of Forth in
Compass Assembler for the CDC 6600.
This was submitted to the Forth Imple-
mentation Workshop by Gregory
Walker of the Population Research Cen-
ter of the University of Texas at Austin.
About thirty-five words were written in
code. Only ten were complex. Mr.
Walker's method was to write the text
interpretation words in machine code
and to compile most of what is usually
code nucleus words in high-level form.
This inverts the usual form but is ideal
from a portability standpoint. The initial
vocabulary is in the general form
@ ! : ; INTEGER INTERPRET EXECUTE STATE
NUMBER FIND NAME LOAD + - * / OR AND
XOR EQZ LTZ CURRENT PUTDICT
A beautiful touch was his method for
the common stack operations. Gregg
discards into a variable called TRASH in
this fashion:
INTEGER TRASH
INTEGER TOP
: DROP TRASH ! ;
: DUP TRASH ! TRASH @ TRASH @ ;
: SWAP TOP ! TRASH ! TOP @ TRASH @ ;
We were not able to include Gregg's
work in the FIG implementations since
the market acceptance was uncertain
and our CDC 6600 was unavailable for
testing.
MicroMotion
MasterFORTH
If s here - the next genera-
tion of MicroMotion Forth.
• Meets all provisions, extensions and
experimental proposals of the FORTH-
83 intemationai Standard.
• Uses the host operating system file
stnjcture (APPLE DOS3.3 & CP/M 2,x).
• Built-in micro-assembler with numeric
local labels.
• A full screen editor is provided which
includes 16 x 64 format, can push &
pop more than one line, user defin-
able controls, upper/ lower case key-
board entry, A COPY utility moves
screens within & between lines, line
stack, redefinable control keys, and
search & replace commands,
• Includes all file primitives described
in Kernigan and Plauget's Software
Tools .
• The editor, assembler and screen copy
utilities are provided as relocatable
object modules. They are brought
into the dictionary on demand and
may be released with a single com-
mand,
• Many key nucleus commands are
vectored. Error handling, number par-
sing, keytxxard translation and so on
can be redefined as needed by user
programs. They are automatically re-
turned to their previous definitions
when the program is forgotten,
• The string-handling package is the
finest and most complete available,
• A listing of the nucleus is provided as
part of the documentation,
• The language implementation ex-
actly matches the one described in
R3RTH TOOLS , by Anderson & Tracy.
This 200 page tutorial and reference
is included with MasterfORTH,
• The input and output streams are
fully redirectable,
• Floating Point & HIRES options avail-
able.
• Available for APPLE ll/ll-l-/lle& CP/M
2,x users.
• MasterFORTH - S100.00. FP & HIRES -
$40.00 each
• Fliblications
• FORTH TOOLS - $20,00
• 83 International Standard- $15.00
• FORTH-83 Source Listing 6502, 8080,
8086 - $20.00 each.
Contact;
MicroMotion
12077 Wilshire Blvd,. Ste. 506
Los Angeles, CA 90025
(213) 821-4340
Volume VI, No. 3
31
FORTH Dimensions
Part Two
Debugging Techniques
Henry Laxen
Berkeley, California
Last time, we looked at machine-
independent ways of debugging in Forth.
We implemented the word UNRAVEL
which, when executed, prints on the
terminal the current nesting structure of
Forth. This is very useful for run-time
error checking. Now we are going to
look at what kind of debugging tools we
can implement if we are willing to
descend to the depths of assembly
language, and if we have a working
knowledge of the internal structure of
Forth. I will assume that you know how
Forth works and will not endeavor to
explain the workings of NEXT or NESTing
or UNNESTing. If these things are un-
familiar to you, I suggest you refer to
Tracy's Forth Tools or to Brodie's
Starting Forth for further information.
If you are unfortunate enough to own an
IBM PC or compatible, you may be able
to mindlessly use the code I am pre-
senting. These same tools can be imple-
mented on other CPUs but the code
words must be modified, of course.
Mike Perry and I have implemented
these debugging words in our Forth-83
system on the 8080, 8086 and 68000
CPUs with little or no difficulty.
All of the following techniques will
only work if NEXT is not executed in-
line, but is jumped to. The techniques
rely on patching NEXT to perform addi-
tional functions besides incrementing
the IP and jumping to the next word to
execute. Because of that, the run time of
the system will be affected. By judicious
use of code, this overhead can be kept to
well under fifty percent, which is not
bad for debugging.
The first and most useful debugging
tool allows you to selectively single-step
trace through the Forth word of your
choice. One of the very nice things
about this implementation is that you
need not re-compile anything in order
\ Debugging - Lohi Leuel
1
HEX
2
UflRlfiBLE 'DEBUG ( Holds CFR of TRRCE
routine )
3
UflRlfiBLE <IP ( Loiuer 1 imlt of IP
during tracing )
4
IIPRIftRI F IP> i ilnnpn limit of IP
Hup i na t rac i no )
5
CODE GOTO ( n - ) IP POP flX LODS flX
u nou [u] jnp C;
6
CODE UNBUG ( - )
7
BVTE OfiD « >NEXT «) HOU 0D88B « >HEXT
1+ » nOU NEXT C;
8
RSSEtlBLER LABEL DEBNEXT
9
<ip «) IP cnp U> IF
10
ip> ») IP cnp u<= IF
11
•DEBUG «) U nOU [ti] JIIP
12
THEN THEN ' GOTO c- 1+ «) JIIP ( Bock
to NEXT )
13
CODE PNEXT ( -- )
H
BVTE 0E9 » >NEXT ») nOU
15
DEBNEXT >HEXT 3 + - « >NEXT 1+ «) HOU
NEXT C; DECinftL
Figure One
\ Debugging - High Level
1 ; L. id' ( cfQ len - )
2 OUER >NfinE DUP .ID ROT 1- - + SPACES ;
3 : 'UNNEST ( pfa - pfo' )
4 BEGIN 1+ OUP c- ['] UNNEST = UNTIL ;
5 UflRlfiBLE RES ( Used to RESUHE tracing )
6 : TRACE ( -- )
7 UNBUG CR R> DUP c- 10 L.ID >R ,S SPACE KEV UPC
8 flSCl I F OUER = IF
9 RES OFF DROP BEGIN QUERV RUN RES c- UNTIL THEN
10 ASCII OUER = IF DROP QUIT THEN
11 DROP PNEXT A> GOTO ; ' TRACE 'DEBUG !
12 ; DEBUG ( - )
13 UNBUG ' DUP <IP I 'UNNEST IP> ! PNEXT ;
H ; RESUHE ( - n )
15 RES ON ;
Figure Two
FORTH Dimensions
32
Volume VI, No. 3
\ l-lcitch Q flsiflopy Local ion
1
UftRiftBLE UfiT['H-FTllHT fl
1 1 ) I 1 1 1 U' Li L. W 1 I 1 t.' 1 1 1 villi L' f
2
ASSEMBLER LABEL UHEXT
3
UATCH-pniNT «) BX tlOU FBXl flX llfiii
" I p 1 k-- 1 1 ■■-■rill / L.'i I 1 HJv L *- ' ' J 1 1 f 1 ML' -.-
UflTCH-POINT 2+ «) AX CHP 0<> IF
5
AX UATCH-POIHT 2+ ») HOU ' LIHRAUEL
» u nou [u] jnp
THEN ' nriTfl a 1+ tt^ IMP ( ficmulnn
lit ft 1 /
7
CODE PNEXT ( -- )
8
HEX BVTE 0E9 « >NEXT «) HOU DEC 1 HAL
UNEXT >NEXT 3 + - « >NEXT 1+ «) I10U
NEXT C;
10
UATCH ( oddr - )
11
DLIP UATCH-POIHT ! c- NATCH-POINT 2+ 1
PNEXT J
12
13
H
15
Figure Three
to trace it. You can retroactively decide
what to trace and, in fact, can change
your mind in the middle of the trace and
begin tracing a different word. This abil-
ity to debug previously compiled words
is very powerful and usually requires
hardware help. It is possible in Forth
because the user has power over Forth 's
virtual machine, namely NEXT, and can
modify it according to his whim.
The idea, then, is to modify NEXT so
that in addition to incrementing the IP
and jumping to the next word, it checks
to see if the IP is within a certain range.
If it is, it calls a special word that
initiates debugging, instead of the word
that it was going to execute. The idea is
very simple but the implementation is
complicated by the fact that the special
word that NEXT is caUing must itself use
NEXT in order to implement the tracing
function. Furthermore, we want to exe-
cute step-by-step the word being traced,
so we sometimes need to turn off this
special NEXT.
Now let's take a look at figures one
and two. The variables <IP and IP> hold
the range of IP values we are interested
in tracing. Whenever the actual IP is
between these two values, we will initiate
tracing. Fortunately, the structure of
high-level Forth words is such that they
are contiguous in memory. Thus, while
we are executing a particular high-level
Forth word, the IP will always be
greater than the code field address of
that word, and less than the address of
the UNNEST code field that was compiled
by ;. The label DEBNEXT is the new ver-
sion of NEXT that gets jumped to when
tracing is enabled. It simply compares
the IP value to the contents of the varia-
bles <IP and IP>. If the IP is between
these values, the high-level word pointed
to by the variable 'DEBUG is executed. If
the IP is not in that range, then a normal
NEXT is executed and Forth proceeds as
though nothing had happened. The
words UNBUG and PNEXT are inverses of
each other. PNEXT patches NEXT to point
to DEBNEXT, and UNBUG restores NEXT
back to how it used to be. 0E9 is a JMP
instruction on the 8080, and AD880D is
what NEXT normally is on an 8088. The
last code word we need to worry about
is GOTO, which is simply a high-level
branch. It has its own in-line NEXT to
avoid the problem of recursively tracing
the same code field forever.
The high-level work is done in figure
two. L.ID prints the name of a word left-
justified in a fixed-length field. 'UNNEST
searches for the code field of UNNEST
given a starting address, and returns the
address found. In F83, the ; word com-
piles the code field of UNNEST while EXIT
compiles a different code field that does
the same thing. This allows F83 to imple-
ment this debugging feature and a nifty
decompiler very simply, since colon
definitions are now terminated by a
unique code field.
Now let's take a look at TRACE. The
first thing it does is turn off debugging.
This is just in case you happen to be
tracing a word that is being used inside
TRACE. You would get very confused, I
assure you. Next, the name of the word
about to be executed is printed, along
with the current parameter stack con-
tents. The R> on line seven gives us the
address inside the word we are tracing
of the code field of the word about to be
executed. Thus, when we fetch it, we
have the actual code field of the next
word to be executed. Notice that our
DEBNEXT version of NEXT has not yet
incremented the IP; thus, the current
address on the return stack is really the
address of the current word that was
about to be executed. We must replace
this address on the return stack with the
>R before printing out the parameter
stack, or else confusion will again result.
Next we wait for a KEY. At this point the
user has three choices. If you want to
continue single-stepping through the
word, press any key other than Q or F.
If you press Q for Quit, tracing will
cease and you will be returned to the
Forth interpreter. If you press F, you
will re-enter the Forth interpreter, but
will be able to continue tracing right
where you left off if you type the word
RESUME.
Let's take a look at how this works
and what it really means. First, the vari-
able RES is turned OFF, meaning it gets
set to zero. The following DROP throws
away the character you typed. Thus,
what is on the stack at this point is
exactly what was there when tracing
began. The BEGIN. ..UNTIL loop repeatedly
gets a line of input from the terminal
with QUERY and then executes it with
RUN. (On your system, INTERPRET may
Volume VI, No. 3
33
FORTH Dimensions
have to be substituted for RUN.) This
continues until the variable RES is set to
a non-zero value. Looking at RESUME,
that is precisely what it does, as well as
leaving a value on the stack to make up
for the DROP that threw away the key-
stroke. This ability to re-enter Forth
and then RESUME debugging is extremely
powerful. At any point while .you are
tracing, you have the full power of
Forth at your disposal. For example,
you could examine variables, dump
memory, list screens, or anything you
want, right in the middle of executing a
word. And then, by typing RESUME you
can pick up right where you left off
before re-entering Forth. One note of
caution! If you make a mistake while
you have re-entered Forth, the error
handling of Forth will take over and
you will wind up back in the Forth
interpreter and unable to RESUME debug-
ging of the word you were in. Such is
life.
The user interface to all of this is the
word DEBUG. It should be followed by
the name of the word you want to
debug; for example, DEBUG WORDS.
Then the next time WORDS is executed,
it will be single-step traced. All DEBUG
does is set up the variables <IP and IP>,
and patch NEXT to point to DEBNEXT.
Needless to say, you can make your own
custom version of TRACE and simply
place its code field address in the varia-
ble 'DEBUG. Then it will receive control
whenever the IP is within the range
specified. The possibilities are only
limited by your imagination.
Finally, a totally different but some-
times invaluable tool is presented in fig-
ure three. Again NEXT is patched to
point to WNEXT. WNEXT monitors a par-
ticular memory word whose address is
at WATCH-POINT and whose initial con-
tents is at WATCH-POINT 2+. If the value at
that memory location differs from
WATCH-POINT 2+ then we call UNRAVEL,
which will give us a trace of our return
stack. Thus, we will be able to see
exactly where we were at the time the
location changed. This is an incredible
tool usually found only in hardware
emulators. It allows us to catch a "ran-
dom store" bug almost immediately, in
fact before the execution of the next
high-level word: and the cost is one
screen of code.
I hope these debugging ideas will
come in handy for you: They have saved
me countless hours. Good luck, and
may the Forth be with you.
Copyright ® 1984 by Henry Laxen.
All rights reserved.
33 KFLOPS
Use your IBM PC (or compatible) to mul-
tiply two 1 28 by 1 28 matrices at ttie rate
of 33 thousand floating-point operations
per second (kflops)! Calculate the
mean and standard deviation of 16,384
points of single precision (4 byte) float-
ing-point data in 1.4 seconds (35
kflops). Perform thie fast Fourier trans-
form on 1024 points of real data in 6.5
seconds. Near PDP-1 1/70 performance
when running the compute intensive
Owen benchmark.
WL FORTH-79
FORTH-79 by WL Computer Systems is
a powerful and comprehensive pro-
gramming system which runs on the
IBM PC (and some compatibles). If your
computer has the 8087 numeric data
processing chip (NDP) installed, then
this version of FORTH-79 will unleash
the awesome floating-point processing
power which is present in your system.
If you haven't gotten around to installing
the 8087 NDP coprocessor in your com-
puter, you can still use WL FORTH to
write applications using standard
FORTH-79.
8087 support and other features
WL FORTH features extremely fast float-
ing point calculations because it uses
the 8087 hardware stack to store inter-
mediate results and achieve 16 to 18
digits precision. The system includes a
large set of transcendental functions,
such as SIN, COS, TAN, ASIN, ACOS,
ATAN, yZ, LN, LOG, SORT. FORTRAN
like conversion specification words
allow the user to specify output field
width, places beyond the decimal point
and fixed or scientific notation.
The FORTH assembler allows the user
to code time critical words in 8087/8088
assembly language and includes struc-
tured branch and looping constructs.
The entire 1 Mb address space is avail-
able for array storage. Definitions can
include SWITCH to different screen
files, thereby allowing dynamic switch-
ing of screen files. SAVE allows current
system to be saved as a .COM file and
ZAP prevents your applications from
being decompiled. The system in-
cludes interrupt driven exception hand-
lers for both the 8087 and 8088, and the
programmer can select the desired
number of screen buffers.
But can I get the source?
Unlike most other products, the com-
pletesource is available at a very
affordable price.
Package 1 includes FORTH-79 ver-
sions with and without 8087 support.
Included are screen utilities, 8087 and
8088 FORTH assemblers. $100
Package 2 includes package 1 plus the
assembly language source for the WL
FORTH-79 nucleus. $150
Package 3 includes package 2 plus the
WL FORTH-79 source screens used to
add the 8087 features to the vocab-
ulary. $200
Starting FORTH book. $22
WL Computer Systems
1910 Newman Road
W. Lafayette, IN 47906
(317) 743-8484
Visa and Master Card accepted.
IBM is a trademark of International Business Ma-
chines
FORTH Dimensions
34
Volume VI, No. 3
John D. Hall
Oakland, California
We have five new chapters. That makes
sixty-two!
Kodiak Area FIG Chapter, Kodiak,
Alaska
Monterey/ Salinas FIG Chapter, Sali-
nas, California
Fort Wayne FIG Chapter, Fort Wayne,
Indiana
Albuquerque FIG Chapter, Albuquer-
que, New Mexico
Cincinnati FIG Chapter, Cincinnati,
Ohio
Arizona FIG Chapter
May 24: Charles Moore attended! He
discussed his Forth computer chip's
architecture in detail. At the time, he
was in Arizona testing prototypes of the
chip prior to production runs. An over-
flow crowd attended and the meeting
was video-taped. The tapes may be
available for distribution after approv-
als are obtaiiied.
Orange County FIG Chapter
February 22: Wil Baden presented his
FIX-FORTH which fixes the F83 Model
so that it will meet the 83 Standard.
John Broderick presented a program for
cross-referencing words and where they
are used.
March 28: Dan Slater spoke to the
group and presented a slide show of the
work he did at TRW, and a robot
camera he worked on for Hollywood
space movies. The group was very
impressed with the work he was able to
turn out. Wil Baden reported that he
spoke on the virtues of Forth to the
Rockwell Space Systems Group at the
Lunch Hour Computer Club.
April 4: Dave Harralson presented a
paper on the generalization of Forth
control structures. Wil Baden also spoke
about control logic.
Sacramento FIG Chapter
May 22: Fifteen people attended,
including Jack Park, author of MVP's
Expert System. We discussed our rea-
sons for attending a FIG meeting and
tried to identify areas of mutual interest.
Mr. Park identified an area of concern
for the chapters: that of reconciling our
levels of experience in Forth. If a topic
or speaker addresses a subject at an
expert level, the less experienced won't
be able to follow and will become bored.
If it is addressed at a novice level, the
more experienced won't need to follow
and will become bored. Tom Ghormley
is sure that their chapter is not the first
to address this. Any suggestions? (J.H.:
This sounds like a discussion of the
blind leading the blind and the faithful
only talking to the faithful. In reality, it
shouldn't be this polarized. A chapter
meeting is a place to discuss, criticize
and learn by all. It 'snot a place to accept
someone 's ideas as the "truth "any more
than it is a place to present the "true"
solution. In all cases, papers and presen-
tations are tutorials for the author as
well as for the audience, and the process
to obtain the solution should be the
main message, not the product. With
this attitude, both "novices " and "ex-
perts "are learning, and the only distinc-
tion is how far along each is in the learn-
ing process. As soon as the topic changes
slightly, the role of "novice "and "expert "
will possibly change. The test of the
strength of the Forth community and
chapter then becomes how well those
further along can assist those earlier in
the process.)
June 12: Walt Winter of Engineering
Logic gave a talk on his Forth-operated
TM990 control system. Wes Lane gave a
talk on the 83 Standard experimental
proposed words ONLY and ALSO as well
as a short exposition of direct, indirect
and tokenized threaded code. Tom
Ghormley passed around his article on
Forth for comments and corrections. It
appeared in the July issue of the Sacra-
mento Valley Computer News.
July 10: Twenty-two people attended
the meeting, several because of Tom
Ghormley's article. A demonstration of
Forth application using a Commodore
64 and several J&J instruments had to
be postponed because of a bad disk. Bob
Nash was rushed into service and gave a
short comparison of three versions of
Forth available for the Commodore 64
as well as a more in-depth look at
SuperForth 64, complete with demo.
Connecticut FIG Chapter
May 4: The first FIG meeting of the
Connecticut chapter was held at the
Meridan Public Library. The group had
an excellent assortment of personalities
and programming experience, and was
especially fortunate to have in attend-
ance two very knowledgeable and expe-
rienced Forthers (Forthites, Forthies...?):
John Moran, a software group leader;
and Bryan Lockwood, an independent
consultant. John told the group about
the trials and tribulations of getting
Forth in ROM and his use of a meta-
compiler to do so. He also discussed his
experience getting Forth up on the VAX.
Bryan explained some of the problems
and limitations of trying to access more
than 64K of address space from a six-
teen-bit bus. He also gave a short talk on
headerless code as a means of saving
memory. Dan Kern-Ekins, an indepen-
dent consultant and president of a local
Commodore 64 club, told us about his
version of Forth for that machine, and
described some of the peculiarities of his
disk operation. Tom Evans, a software
engineer, spoke of his use of Forth at
work for data acquisition and analysis
of optical surfaces. Mike Davis talked
about the new IBM-PC he got at work
and his plans to get Forth for the NEC-
8201 A. Jean-Pierre Jaborska surprised
many of the group when he commented
that the Commodore Pet, his Forth
machine, is still being manufactured.
Jean-Pierre, who is from France, was
disappointed that so many Forth arti-
cles are at the system level, and so few
talk about real-world applications — a
good point. Charlie Krajewski outlined
Volume VI, No. 3
35
1
FORTH Dimensions
a Forth project in which he hooked his
bicycle to an 8088-based computer for
indoor winter training. Unfortunately,
the project was finally completed in
early May.
Forth Gesellschaft
April 28: Sixteen people got together
to get the ball rolling for a German FIG
chapter. Three of us are "old FIG hands"
who, once upon a time, keyed the FIG
listings into their machines. We are going
to work as a chapter under the name of
Forth Gesellschaft and we will pubHsh a
newsletter under the name of Vierte
Dimension. The first issue will be mailed
by the end of May and will feature a
translation of Bill Ragsdale's interview
from Forth Dimensions ( V / 6) . Six work-
ing groups constituted themselves:
1) Forth-83: we will be distributing
Laxen and Perry's F83 and work is
underway to translate the documenta-'
tion into German.
2) Leibniz: one of the major difficulties
in gaining wide acceptance for Forth is
constituted by the language barrier.
Hence, we are going to create a "new"
programming language, under the name
of Leibniz, which will have German
names and will follow the Forth-83
Standard semantically. Leibniz will be
derived from the version of Forth which
was developed by Klaus Scheisiek and it
will be put into the public domain.
3) One working group will keep tabs on
Forth publications and products, and
will compile an index.
4) Newsletter: Vierte Dimension will be
published approximately four times a
year as a forum and communications
vehicle for Forth users in Germany.
Initial subscription is 23,- DM for indi-
viduals and 55,- DM for corporations.
5) Fifth Dimension: this is a "brain-
storming" group which is going to envi-
sion the future development of Forth
toward friendly and not necessarily
Forth-like user interfaces and higher-
level constructs. We will see what they
are going to come up with. They want to
use Forth as a base on which to build
more sophisticated structures.
6) Operations and management: Horst-
GUnter Lynsche was elected secretary of
Forth Gesellschaft and he will be respon-
sible for the management aspects —
keeping tabs on the subscribers, publish-
ing Vierte Dimension, etc.
TOTAL CONTROU
FORTH: FOR Z-80®, 8086, 68000, and IBM® PC
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• FORTH is interactive and conver-
sational, but 20 times faster than
BASIC.
• FORTH programs are highly struc-
tured, modular, easy to maintain.
• FORTH affords direct control over
all interrupts, memory locations, and
i/o ports.
• FORTH allows full access to DOS
files and functions.
• FORTH application programs can
be compiled into turnkey COM files
and distributed with no license fee.
• FORTH Cross Compilers are
available for ROM'ed or disk based ap-
plications on most microprocessors.
Trademarks; IBM, International Business l^^achines
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include interpreter/compiler with virtual memory
management and multi-tasking, assembler, full
screen editor, decompiler, utilities, and 130 +
page manual. Standard random access files
used for screen storage, extensions provided for
access to all operating system functions.
Z-80 FORTH for CP/I^®2.2 or MPIM II, $50,00;
8080 FORTH for CP/M 2.2 or MP/M II, $50.00;
8086 FORTH for CP/M-86 or MS-DOS, $100.00;
PC/FORTH for PC-DOS, CP/M-86, or CCPM,
$100.00; 68000 FORTH for CP/M-68K, $250.00.
FORTH + Systems are 32 bit implementations
that allow creation of programs as large as 1
megabyte. The entire memory address space of
the 68000 or 8086/88 is supported directly.
PC FORTH -t- $250.00
8086 FORTH -Hfor CP/M-86 or MS-DOS $250.00
68000 FORTH + for CP/M-68K $400.00
Extension Packages available include; soft-
ware floating point, cross compilers, INTEL
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or graphics, custom character sets, symbolic
debugger, telecommunications, cross reference
utility, B-tree file manager. Write for brochure.
I I
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Laboratory Microsystems Incorporated
4147 Beethoven Street. Los Angeles, CA 90066
Phone credit card orders to (213) 306-7412
FORTH Dimensions
36
Volume VI, No. 3
New Chapters in Formation
Here are more of the new chapters
that are forming. If you live in any of
these areas, contact these people and
offer your support and help in form-
ing a FIG chapter. You are not
expected to be one of the "experts."
Bruce N. Collins
c/o Malemute Software
P.O. Box 81746
College, AK 99708
Gary Smith
Hawg Wild Software
P.O. Box 7668
Little Rock, AR 72217
Herman B. Gibson
8014 Gondola Dr.
Orlando, FL 32809
Alexander Luoma
P.O. Box 10432
Talahassee, FL 32302
Richard Wagner
728 E. Colfax Ave.
South Bend, IN 46617
Michael G. Waldon
Inst, of Environmental Studies
Rm. 42, Atkinson Hall
Louisiana State University
Baton Rouge, LA 70803-5705
504/388-8521
Claude W. Hesselman
2545 Bainbridge Blvd.
Chesapeake, VA 23324
804/545-1240
Jean-Marc Bertinchamps
Rue N. Monnom, 2
B-6290 NaUnnes
Belgium
Darryl C. Oliver
Pacer Electronics
2302 Marengo
New Orleans, LA 70115
504/899-8922
Tom Chrapkiewicz
P.O. Box 1056
Dearborn, MI 48121
313/524-2100
The job of organizing a chapter can
be done as well by people who are
better at organizing than at program-
ming, or by people who are in need of
the help and support that a chapter
can return. Lend a hand!
Gene Embry
Route 1, Box 151-H
Morrisville, NC 27560
Bill Morrissey
Rio Grande Electronics
1595 W. Picacho, Ste. 28
Las Cruces, NM 88005
J. Rennie
1809 N.W. 34th
Oklahoma City, OK 73118
Phillip A. Marciner
243 Judith Dr.
Johnstown, PA 15905
Bard Ermentrout
5464 Upsal Place
Pittsburgh, PA 15206
Terry L. Wallis
322 Haverford
San Antonio, TX 78217
Al Amway
Rare Earth Services, Inc.
3115 Willow Rd. N.W.
Roanoke, VA 24017
David Caulkins
Mad Apple FIG
P.O. Box 5103
Madison, WI 53705
Ray St. Laurent
P.O. Box 95
Vars, ON KOA 3H0
Canada
Jan Langerad
Loebpakken 1
3520 Sarum
Denmark
Mrs. J.J. van der Hoek
Forth Interesse Groep
MedembUkpad 70
8304 CZ Emm6loord
The Netherlands
Multiuser/Multitasking
for 8080, Z80, 808.6
Industrial ^|
Strength
FORTH i
TaskFORTH.
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Full Feature FORTH
System at a micro price*
LOADS OF TIME SAVING
PROFESSIONAL FEATURES:
■A- Unlimited number of tasks
■ir Multiple thread dictionary,
superfast compilation
■iV Novice Programmer
Protection PackageiM
■Cz Diagnostic tools, quick and
simple debugging
•tz starting FORTH, FORTH-79,
FORTH-83 compatible
■A- Screen and serial editor,
easy program generation
^ Hierarchical file system with
data base management
• starter package $250. Full package $395- Single
user and commercial licenses available.
If you are an experienced
FORTH programmer, this is the
one you have been waiting for!
If you are a beginning FORTH
programmer, this will get you
started right, and quickly too!
Available on 8 inch disk
under CP/M 2.2 or greater
also
various SVa" formats
and other operating systems
FULLY WARRANTED,
DOCUI^ENTED AND
SUPPORTED
DEALER
INQUIRES
INVITED
Shaw Laboratories, Ltd.
24301 Southland Drive, #216
Hayward, California 94545
(415) 276-5953
Volume VI, No. 3
37
FORTH Dimensions
U.S.
. ALASKA
Kodiak Area Chapter
Call Norman C. Mcintosh
907/486-4843
. ARIZONA
Phoenix Chapter
Call Dennis L. Wilson
602/956-7678
Tucson Chapter
Twice Monthly, 2nd & 4th Sun., 2 p.:
Flexible Hybrid Systems
2030 E. Broadway #206
Call John C. Mead
602/323-9763
. CALIFORNIA
Berkeley Chapter
Monthly, 2nd Sat., 1 p.m.
10 Evans Hall
University of California
Berkeley
Call Mike Perry
415/644-3421
Los Angeles Chapter
Monthly, 4th Sat., II a.m.
Allstate Savings
8800 So. Sepulveda Boulevard
1/2 mile North of LAX
Los Angeles
Call Phillip Wasson
213/649-1428
Monterey/Salinas Chapter
Call Bud Devins
408/633-3253
Orange County Chapter
Monthly, 4th Wed., 7 p.m.
Fullerton Savings
Talbert & Brookhurst
Fountain Valley
Monthly, 1st Wed., 7 p.m.
Mercury Savings
Beach Blvd., & Eddington
Huntington Beach
Call Noshir Jesung
714/842-3032
San Diego Chapter
Weekly, Thurs., 12 noon.
Call Guy Kelly
619/268-3100 ext 4784
Sacramento Chapter
Monthly, 2nd Tues., 7 p.m.
I70B 59th St., Room C
Call Tom Ghormley
916/444-7775
Silicon Valley Chapter
Monthly, 4th Sat., 1 p.m.
Dysan Auditorium
5201 Patrick Henry Dr.
Santa Clara
Call Glenn Tenney
415/574-3420
Stockton Chapter
Call Doug Dillon
209/931-2448
. COLORADO
Denver Chapter
Monthly, 1st Mon., 7 p.m.
Call Steven Sams
303/477-5955
. CONNECTICUT
Central Connecticut Chapter
Monthly, 1st Thurs., 7 p.m.
Meriden Public Library
Call Charles Krajewski
203/344-9996
. FLORIDA
Southeast Florida Chapter
Miami
Call John Forsberg
305/252-0108
• ILLINOIS
Central Illinois Chapter
Urbana
Call Sidney Bowhill
217/333-4150
Fox Valley Chapter
Call Samuel J. Cook
312/879-3242
Rockwell Chicago Chapter
Call Gerard Kusiolek
312/885-8092
. INDIANA
Central Indiana Chapter
Monthly, 3rd Sat., 10 a.m.
Call Richard Turpin
317/923-1321
Fort Wayne Chapter
Call Blair MacDermid
219/749-2042
. IOV\IA
Iowa City Chapter
Monthly, 4th Tues.
Engineering Bldg., Rm. 2128
University of Iowa
Call Robert Benedict
319/337-7853
. KANSAS
Wichita Chapter (FIGPAC)
Monthly, 3rd Wed., 7 p.m.
Wilbur E. Walker Co.
532 S. Market
Wichita, KS
Call Ame Flones
316/267-8852
. MASSACHUSETTS
Boston Chapter
Monthly, 1st Wed.
Mitre Corp; Cafeteria
Bedford, MA
Call Bob Demrow
617/688-5661 after 7 p.m.
. MINNESOTA
MNFIG Chapter
Even month, 1st Mon., 7:30 p.m.
Odd Month, 1st Sat., 9:30 a.m.
Vincent Hall Univ. of MN
Minneapolis, MN
Call Fred Olson
612/588-9532
. MISSOURI
Kansas City Chapter
Monthly, 4th Tues., 7 p.m.
Midwest Research Inst.
Mag Conference Center
Call Linus Orth
816/444-6655
St. Louis Chapter
Monthly, 3rd Tues., 7 p.m.
Thomhill Branch of
St. Louis County Library
Call David Doudna
314/867-4482
. NEVADA
Southern Nevada Chapter
Suite 900
101 Convention Center Drive
Las Vegas, NV
Call Gerald Hasty
702/452-3368
. NEW MEXICO
Albuquerque Chapter
Call Rick Granfield
505/296-8651
WiUiam Edmonds
804/898^99
. NEW YORK
FIG, New York
Monthly, 2nd Wed., 8 p.m.
Queens College
Call Tom Jung
212/432-1414 ext. 157 days
212/261-3213 eves.
Rochester Chapter
Bi-monthly, 4th Sat,, 2 p.m.
Hutchison Hall
Univ. of Rochester
Call Thea Martin
716/235-0168
Syracuse Chapter
Monthly, 1st Tues., 7:30 p.m.
Call C. Richard Comer
315/456-7436
. OHIO
Athens Chapter
Call Isreal Urieli
614/594-3731
Cleveland Chapter
Call Gary Bergstrom
216/247-2492
Cincinatti Chapter
Call Douglas Bennett
513/831-0142
Dayton Chapter
Twice monthly, 2nd Tues &
4th Wed., 6:30 p.m.
CFC 1 1 W. Monument Ave.
Suite 612
Dayton, OH
Call Gary M. Granger
513/849-1483
. OKLAHOMA
l^Isa Chapter
Monthly, 3rd Tues., 7:30 p.m.
The Computer Store
4343 South Peoria
Tulsa, OK
Call Art Gorski
918/743-0113
. OREGON
Greater Oregon Chapter
Monthly, 2nd Sat., 1 p.m.
Computer & Things
3460 SW 185th, Aloha
Call Timothy Huang
503/289-9135
. PENNSYLVANIA
Philadelphia Chapter
Monthly, 3rd Sat.
LaSalle College, Science Bldg.
Call Lee Hustead
215/539-7989
. TEXAS
Dallas/Ft. Worth
Metroplex Chapter
Monthly, 4th Thurs., 7 p.m.
Software Automation, Inc.
14333 Porton, Dallas
Bill Drissel
214/264-9680
FORTH Dimensions
38
Volume VI, No. 3
Houston Chapter
Call Dr. Joseph Baldwin
713/749-2120
t VERMONT
Vermoiit FIG Chapter
Monthly. 3rd Mon., 7:30 p.m.
Vicrgennes Union High School
Rm. 210, Monkton Rd.
Vfergennes, VT
Call Hal Clark
802/877-2911 days
802/452^2 eves
• VIRGINIA
Norfolk FIG Chapter
Call William Edmonds
804/898-4099
Potomac Chapter
Monthly, 1st Tues., 7 p.m.
Lee Center
Lee Highway at Lexington St.
Arlington, VA
Call Joel Shprentz
703/437-9218 eves.
Richmond Forth Group
Monthly, 2nd Wed., 7 p.m.
Basement, Puryear Hall
Univ. of Richmond
Call Donald A. Full
804/739-3623
FOREIGN
. AUSTRALIA
Melbourne Chapter
Monthly, 1st Fri., 8 p.m.
Contact: Lance Collins
65 Martin Road
Glen Iris, Victoria 3146
03/29-2600
Sydney Chapter
Monthly, 2nd Fri., 7 p.m.
John GoodseU Bldg.,
Rm. LG19
Univ. of New South Wales
Sydney
Contact: Peter Tregeagle
10 Binda Rd., Yowie Bay
02/524-7490
% BELGIUM
Belgium Chapter
Monthly, 4th Wed., 20«)h
Contact: Luk Van Loock
Lariksdreff 20
2120 Schoten
03/658-6343
Southern Belgium FIG Chapter
Contact: Jean-Marc Bertinchamps
Rue N. Monnom, 2
B-6290 Nalinnes
Belgium
071/213858
. CANADA
Nova Scotia Chapter
Contact: Howard Harawitz
227 Ridge Valley Rd.
Halifax, Nova Scotia B3P 2E5
902/477-3665
Southern Ontario Chapter
Monthly, 1st Sat., 2 p.m.
General Sciences Bldg.
Rm. 312
McMaster University
Contact: Dr. N. Solntseff
Unit for Computer Science
McMaster University
Hamilton, Ontario L8S 4K1
416/525-9140 ext. 2065
Toronto FIG Chapter
Contact: John Clark Smith
P.O. Box 230, Station H
Toronto, ON M4C 5J2
. COLOMBIA
Colombia Chapter
Contact: Luis Javier Parra B.
Aptdo. Aereo 100394
Bogota
214-0345
. ENGLAND
Forth Interest Group — U.K.
Monthly, 1st Thurs., 7 p.m., Rm. 408
Polytechnic of South Bank
Borough Rd., London
Contact: Keith Goldie-Morrison
Bradden Old Rectory
Towchester, Northamptonshire
NN12 8ED
. FRANCE
French Language Chapter
Contact: Jean-Daniel Dodin
77 rue du Cagire
31100 Toulouse
(16-61)44.03
. GERMANY
Hamburg FIG Chapter
Monthly, 4th Sat., 1500 hrs.
Contact: Horst-Gunter Lynsche
Holstenstr. 191
D-2000 Hamburg 50
> IRELAND
Irish Chapter
Contact: Hugh Dobbs
Newton School
Waterford
051/75757
051/74124
> ITALY
FIG Italia
Contact: Marco Tausel
Via Gerolamo Fomi 48
20161 Milano
02/645-8688
. REPUBLIC OF CHINA
R.O.C.
Contact: Ching-Tang Tzeng
P.O. Box 28
Lung-Tan, Taiwan 325
. SWITZERLAND
Swiss Chapter
Contact: Max Hugelshofer
ERNI & Co. Elektro-lndustrie
Stationsstrasse
8306 Bruttisellen
01/833-3333
SPECIAL GROUPS
Apple Corps Forth
Users Chapter
Twice Monthly, lst&
3rd Tues., 7:30 p.m.
1515 Sloat Boulevard, #2
San Francisco, CA
Call Robert Dudley Ackerman
415/626-6295
Baton Rouge Atari Chapter
Call Chris Zielewski
504/292-1910
Detroit Atari Chapter
Monthly, 4th Wed.
Call Tom Chrapkiewicz
313/524-2100
FIGGRAPH
Call Howard Pearlmutter
408/425-8700
Volume VI, No. 3
39
FORTH Dimensions
ANNOUNCING
ORDER FROM THE FORTH INTEREST GROUP
COMPLETE ORDER FORM ON PAGE 22
FORTH INTEREST GROUP
P.O. Box 1105
San Carlos, CA 94070
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