ref: d8e023787209c17f2849a1418ec279a87cca80f8
dir: /doc/primer.txt/
A Beginner's Guide to Forth
by
J.V. Noble
Contents
0. Preliminaries
1. Getting started
The structure of Forth
2. Extending the dictionary
3. Stacks and reverse Polish notation (RPN)
3.1 Manipulating the parameter stack
3.2 The return stack and its uses
4. Fetching and storing
5. Comparing and branching
6. Documenting and commenting Forth code
7. Arithmetic operations
8. Looping and structured programming
9. CREATE ... DOES> (the pearl of Forth)
9.1 Defining "defining" words
9.2 Run-time vs. compile-time actions
9.3 Dimensioned data (intrinsic units)
9.4 Advanced uses of the compiler
10. Floating point arithmetic
0. Introduction
Forth is an unusual computer language that has probably been applied
to more varied projects than any other. It is the obvious choice when
the project is exceptionally demanding in terms of completion sched-
ule, speed of execution, compactness of code, or any combination of
the above.
It has also been called "...one of the best-kept secrets in the com-
puting world." This is no exaggeration: large corporations have pur-
chased professional Forth development systems from vendors such as
Laboratory Microsystems, Inc., Forth, Inc. or MicroProcessor Engineer-
ing, Ltd. and sworn them to secrecy.
Some speculate (unkindly) that corporate giants prefer to hide their
shame at using Forth; but I believe they are actually concealing a
secret weapon from their rivals. Whenever Forth has competed directly
with a more conventional language like C it has won hands down, pro-
ducing smaller, faster, more reliable code in far less time. I have
searched for examples with the opposite outcome, but have been unable
to find a single instance.
1. Getting started
We will use Win32Forth for these illustrations. Download the file
w32for35.exe
and double-click on it to install on any Windows 95-equipped machine.
The compressed files will then decompress themselves. They should also
install a program group on your desktop.
Now start Win32Forth by opening the program group and clicking on the
appropriate icon.
It should respond by opening a window and writing something like
32bit Forth for Windows 95, and NT
Compiled: July 23rd, 1997, 5:11pm
Version: 3.5 Build: 0008 Release Build
Platform: Windows 95 Version: 4.0 Build: 16384
491k bytes free
2,719 Words in Application dictionary
1,466 Words in System dictionary
4,185 Words total in dictionaries
8,293 Windows Constants available
Loading Win32For.CFG
*** DON'T PANIC, Press: F1 NOW! ***
Win32Forth is case-insensitive.
Now type
BYE <cr>.
The Win32Forth window immediately closes.
What just happened? Forth is an interactive programming language con-
sisting entirely of subroutines, called "words".
A word is executed (interactively) by naming it. We have just seen
this happen: BYE is a Forth subroutine meaning "exit to the operating
system". So when we entered BYE it was executed, and the system re-
turned control to Windows.
Click on the Win32Forth icon again to re-start Forth.
Now we will try something a little more complicated. Enter
2 17 + . <cr> 19 ok
What happened? Forth is interpretive. An "outer interpreter" continu-
ally loops, waiting for input from the keyboard or mass storage de-
vice. The input is a sequence of text strings separated from each
other by blank spaces --ASCII 32decimal = 20hex-- the standard Forth
delimiter.
When the outer interpreter encounters text it first looks for it in
the "dictionary" (a linked list of previously defined subroutine
names). If it finds the word, it executes the corresponding code.
If no dictionary entry exists, the interpreter tries to read the input
as a number.
If the input text string satisfies the rules defining a number, it is
converted to a number and stored in a special memory location called
"the top of the stack" (TOS).
In the above example, Forth interpreted 2 and 17 as numbers, and
pushed them both onto the stack.
"+" is a pre-defined word as is ".", so they were looked up and exe-
cuted.
"+" added 2 to 17 and left 19 on the stack.
The word "." (called "emit") removed 19 from the stack and displayed
it on the standard output device (in this case, CRT).
We might also have said
HEX 0A 14 * . <cr> C8 ok
(Do you understand this? Hint: DECIMAL means "switch to decimal arith-
metic", whereas HEX stands for "switch to hexadecimal arithmetic".)
If the incoming text can neither be located in the dictionary nor in-
terpreted as a number, Forth issues an error message. Try it: say X
and see
X
Error: X is undefined
or say THING and see
THING
Error: THING is undefined
2. Extending the dictionary
The compiler is one of Forth's most endearing features. Unlike
all other high-level languages, the Forth compiler is part of the
language. (LISP and its dialects also make components of the com-
pilation mechanism available to the programmer.) That is, its com-
ponents are Forth words available to the programmer, that can be
used to solve his problems.
In this section we discuss how the compiler extends the
dictionary.
Forth uses special words to create new dictionary entries, i.e.,
new words. The most important are ":" ("start a new definition")
and ";" ("terminate the definition").
Let's try this out: enter
: *+ * + ; <cr> ok
What happened? The word ":" was executed because it was already
in the dictionary. The action of ":" is
> Create a new dictionary entry named "*+" and switch from
interpret to compile mode.
> In compile mode, the interpreter looks up words and
--rather than executing them-- installs pointers to
their code. (If the text is a number, rather than
pushing it on the stack, Forth builds the number
into the dictionary space allotted for the new word,
following special code that puts it on the stack
when the word is executed.)
> The action of "*+" will be to execute sequentially
the previously-defined words "*" and "+".
> The word ";" is special: when it was defined a bit
was turned on in its dictionary entry to mark it as
IMMEDIATE. Thus, rather than writing down its
address, the compiler executes ";" immediately. The
action of ";" is first, to install the code that
returns control to the next outer level of the
interpreter; and second, to switch back from compile
mode to interpret mode.
Now try out "*+" :
DECIMAL 5 6 7 *+ . <cr> 47 ok
This example illustrated two principles of Forth: adding a new word to
the dictionary, and trying it out as soon as it was defined.
3. Stacks and reverse Polish notation (RPN)
We now discuss the stack and the "reverse Polish" or "postfix" arith-
metic based on it. (Anyone who has used a Hewlett-Packard calculator
should be familiar with the concept.)
Virtually all modern CPU's are designed around stacks. Forth effi-
ciently uses its CPU by reflecting this underlying stack architecture
in its syntax.
But what is a stack? As the name implies, a stack is the machine ana-
log of a pile of cards with numbers written on them. Numbers are
always added to the top of the pile, and removed from the top of the
pile. The Forth input line
2 5 73 -16 <cr> ok
leaves the stack in the state
cell # contents
0 -16 (TOS)
1 73 (NOS)
2 5
3 2
where TOS stands for "top-of-stack", NOS for "next-on-stack", etc.
We usually employ zero-based relative numbering in Forth data struct-
ures (such as stacks, arrays, tables, etc.) so TOS is given relative
#0, NOS #1, etc.
Suppose we followed the above input line with the line
+ - * . <cr> xxx ok
what would xxx be? The operations would produce the successive stacks
cell# initial + - * .
0 -16 57 -52 -104
1 73 5 2
2 5 2
3 2 empty
stack
The operation "." (EMIT) displays -104 to the screen, leaving the
stack empty. That is, xxx is -104.
3.1 Manipulating the parameter stack
Forth systems incorporate (at least) two stacks: the parameter stack
and the return stack.
A stack-based system must provide ways to put numbers on the stack, to
remove them, and to rearrange their order. Forth includes standard
words for this purpose.
Putting numbers on the stack is easy: simply type the number (or in-
corporate it in the definition of a Forth word).
The word DROP removes the number from TOS and moves up all the other
numbers. (Since the stack usually grows downward in memory, DROP mere-
ly increments the pointer to TOS by 1 cell.)
SWAP exchanges the top 2 numbers.
DUP duplicates the TOS into NOS.
ROT rotates the top 3 numbers.
These actions are shown below (we show what each word does to the ini-
tial stack)
cell | initial | DROP SWAP ROT DUP
0 | -16 | 73 73 5 -16
1 | 73 | 5 -16 -16 -16
2 | 5 | 2 5 73 73
3 | 2 | 2 2 5
4 | | 2
Forth includes the words OVER, TUCK, PICK and ROLL that act as shown
below (note PICK and ROLL must be preceded by an integer that says
where on the stack an element gets PICK'ed or ROLL'ed):
cell | initial | OVER TUCK 4 PICK 4 ROLL
0 | -16 | 73 -16 2 2
1 | 73 | -16 73 -16 -16
2 | 5 | 73 -16 73 73
3 | 2 | 5 5 5 5
4 | | 2 2 2
Clearly, 1 PICK is the same as DUP, 2 PICK is a synonym for OVER, and
2 ROLL means SWAP.
3.2 The return stack and its uses
We have remarked above that compilation establishes links from the
calling word to the previously-defined word being invoked. The linkage
mechanism --during execution-- uses the return stack (rstack): the
address of the next word to be invoked is placed on the rstack, so
that when the current word is done executing, the system knows to jump
to the next word. (This is so in most, but not all Forth implement-
ations. But all have a return stack, whether or not they use them for
linking subroutines.)
In addition to serving as a reservoir of return addresses (since words
can be nested, the return addresses need a stack to be put on) the
rstack is where the limits of a DO...LOOP construct are placed.
The user can also store/retrieve to/from the rstack. This is an ex-
ample of using a component for a purpose other than the one it was
designed for. Such use is discouraged for novices since it adds the
spice of danger to programming. See "Note of caution" below.
To store to the rstack we say >R , and to retrieve we say R> . The
word R@ copies the top of the rstack to the TOS.
Why use the rstack when we have a perfectly good parameter stack to
play with? Sometimes it becomes hard to read code that performs com-
plex gymnastics on the stack. The rstack can reduce the complexity.
Alternatively, VARIABLEs --named locations-- provide a place to store
numbers --such as intermediate results in a calculation-- off the
stack, again reducing the gymnastics. Try this:
\ YOU DO THIS \ EXPLANATION
VARIABLE X <cr> ok \ create a named storage location X;
\ X executes by leaving its address
3 X ! <cr> ok \ ! ("store") expects a number and
\ an address, and stores the number to
\ that address
X @ . <cr> 3 ok \ @ ("fetch") expects an address, and
\ places its contents in TOS.
However, Forth encourages using as few named variables as possible.
The reason: since VARIABLEs are typically global --any subroutine can
access them-- they can cause unwanted interactions among parts of a
large program.
Although Forth can make variables local to the subroutines that use
them (see "headerless words" in FTR), the rstack can often replace
local variables:
> The rstack already exists, so it need not be defined anew.
> When the numbers placed on it are removed, the rstack shrinks,
reclaiming some memory.
A note of caution: since the rstack is critical to execution we mess
with it at our peril. If we use the rstack for temporary storage we
must restore it to its initial state. A word that places a number on
the rstack must remove it --using R> or RDROP (if it has been defined)
-- before exiting that word. Since DO...LOOP also uses the rstack,
for each >R folowing DO there must be a corresponding R> or RDROP
preceding LOOP. Neglecting these precautions will probably crash
the system.
4. Fetching and storing
As we just saw, ordinary numbers are fetched from memory to
the stack by @ ("fetch"), and stored by ! (store).
@ expects an address on the stack and replaces that address by
its contents using, e.g., the phrase X @
! expects a number (NOS) and an address (TOS) to store it in, and
places the number in the memory location referred to by the address,
consuming both arguments in the process, as in the phrase 3 X !
Double length numbers can similarly be fetched and stored, by
D@ and D!, if the system has these words.
Positive numbers smaller than 255 can be placed in single bytes of
memory using C@ and C!. This is convenient for operations with strings
of ASCII text, for example screen and keyboard I/O.
5. Comparing and branching
Forth lets you compare two numbers on the stack, using relational
operators ">", "<", "=" . Ths, e.g., the phrase
2 3 > <cr> ok
leaves 0 ("false") on the stack, because 2 (NOS) is not greater than 3
(TOS). Conversely, the phrase
2 3 < <cr> ok
leaves -1 ("true") because 2 is less than 3.
Notes: In some Forths "true" is +1 rather than -1.
Relational operators consume both arguments and leave a "flag"
to show what happened.
(Many Forths offer unary relational operators "0=", "0>" and "0<".
These, as might be guessed, determine whether the TOS contains an
integer that is 0, positive or negative.)
The relational words are used for branching and control. For example,
: TEST CR 0 = NOT IF ." Not zero!" THEN ;
0 TEST <cr> ok ( no action)
-14 TEST <cr>
Not zero! ok
The word CR issues a carriage return (newline). Then TOS is compared
with zero, and the logical NOT operator (this flips "true" and
"false") applied to the resulting flag. Finally, if TOS is non-zero,
IF swallows the flag and executes all the words between itself and the
terminating THEN. If TOS is zero, execution jumps to the word
following THEN.
The word ELSE is used in the IF...ELSE...THEN statement: a nonzero
value in TOS causes any words between IF and ELSE to be executed, and
words between ELSE and THEN to be skipped. A zero value produces the
opposite behavior. Thus, e.g.
: TRUTH CR 0 = IF ." false" ELSE ." true" THEN ;
1 TRUTH <cr>
true ok
0 TRUTH <cr>
false ok
Since THEN is used to terminate an IF statement rather than in its
usual sense, some Forth writers prefer the name ENDIF.
6. Documenting and commenting Forth code
Forth is sometimes accused of being a "write-only" language, i.e. some
complain that Forth is cryptic. This is really a complaint against
poor documentation and untelegraphic word names. Unreadability is
equally a flaw of poorly written FORTRAN, PASCAL, C, etc.
Forth offers programmers who take the trouble tools for producing ex-
ceptionally clear code.
6.1 Parenthesized remarks
The word ( -- a left parenthesis followed by a space -- says "disre-
gard all following text until the next right parenthesis in the
input stream". Thus we can intersperse explanatory remarks within
colon definitions.
6.2 Stack comments
A particular form of parenthesized remark describes the effect of a
word on the stack. In the example of a recursive loop (GCD below),
stack comments are really all the documentation necessary.
Glossaries generally explain the action of a word with a
stack-effect comment. For example,
( adr -- n)
describes the word @ ("fetch"): it says @ expects to find an address
(adr) on the stack, and to leave its contents (n) upon completion.
The corresponding comment for ! would be
( n adr -- ) .
6.3 Drop line (\)
The word "\" (back-slash followed by space) has recently gained favor
as a method for including longer comments. It simply means "drop ev-
erything in the input stream until the next carriage return". Instruc-
tions to the user, clarifications or usage examples are most naturally
expressed in a block of text with each line set off by "\" .
6.4 Self-documenting code
By eliminating ungrammatical phrases like CALL or GOSUB, Forth pre-
sents the opportunity --via telegraphic names for words-- to make code
almost as self-documenting and transparent as a readable English or
German sentence. Thus, for example, a robot control program could con-
tain a phrase like
2 TIMES LEFT EYE WINK
which is clear (although it sounds like a stage direction for Brun-
hilde to vamp Siegfried). It would even be possible without much dif-
ficulty to define the words in the program so that the sequence could
be made English-like: WINK LEFT EYE 2 TIMES .
7. Arithmetic operations
The 1979 or 1983 standards require that a conforming Forth system con-
tain a certain minimum set of pre-defined words. These consist of
arithmetic operators + - * / MOD /MOD */ for (usually) 16-bit signed-
integer (-32767 to +32767) arithmetic, and equivalents for unsigned (0
to 65535), double-length and mixed-mode (16- mixed with 32-bit) arith-
metic. The list will be found in the glossary accompanying your
system, as well as in SF and FTR.
Try this example of a non-trivial program that uses arithmetic and
branching to compute the greatest common divisor of two integers using
Euclid's algorithm:
: TUCK ( a b -- b a b) SWAP OVER ;
: GCD ( a b -- gcd) ?DUP IF TUCK MOD GCD THEN ;
The word ?DUP duplicates TOS if it is not zero, and leaves it alone
otherwise. If the TOS is 0, therefore, GCD consumes it and does
nothing else. However, if TOS is unequal to 0, then GCD TUCKs TOS
under NOS (to save it); then divides NOS by TOS, keeping the remainder
(MOD). There are now two numbers left on the stack, so we again take
the GCD of them. That is, GCD calls itself. However, if you try the
above code it will fail. A dictionary entry cannot be looked up and
found until the terminating ";" has completed it. So in fact we must
use the word RECURSE to achieve self-reference, as in
: TUCK ( a b -- b a b) SWAP OVER ;
: GCD ( a b -- gcd) ?DUP IF TUCK MOD RECURSE THEN ;
Now try
784 48 GCD . 16 ok
8. Looping and structured programming
Forth has several ways to loop, including the implicit method of re-
cursion, illustrated above. Recursion has a bad name as a looping
method because in most languages that permit recursion, it imposes
unacceptable running time overhead on the program. Worse, recursion
can --for reasons beyond the scope of this Introduction to Forth-- be
an extremely inefficient method of expressing the problem. In Forth,
there is virtually no excess overhead in recursive calls because Forth
uses the stack directly. So there is no reason not to recurse if that
is the best way to program the algorithm. But for those times when
recursion simply isn't enough, here are some more standard methods.
8.1 Indefinite loops
The construct
BEGIN xxx ( -- flag) UNTIL
executes the words represented by xxx, leaving TOS (flag) set to TRUE
--at which point UNTIL terminates the loop-- or to FALSE --at which
point UNTIL jumps back to BEGIN. Try:
: COUNTDOWN ( n --)
BEGIN CR DUP . 1 - DUP 0 = UNTIL DROP ;
5 COUNTDOWN
5
4
3
2
1 ok
A variant of BEGIN...UNTIL is
BEGIN xxx ( -- flag) WHILE yyy REPEAT
Here xxx is executed, WHILE tests the flag and if it is FALSE
leaves the loop; if the flag is TRUE, yyy is executed; REPEAT then
branches back to BEGIN.
These forms can be used to set up loops that repeat until some
external event (pressing a key at the keyboard, e.g.) sets the
flag to exit the loop. They can also used to make endless loops
(like the outer interpreter of Forth) by forcing the flag
to be FALSE in a definition like
: ENDLESS BEGIN xxx FALSE UNTIL ;
8.2 Definite loops
Most Forths allow indexed loops using DO...LOOP (or +LOOP or /LOOP).
These are permitted only within definitions
: BY-ONES ( n --) 0 TUCK DO CR DUP . 1 + LOOP DROP ;
The words CR DUP . 1 + will be executed n times as the lower
limit, 0, increases in unit steps to n-1.
To step by 2's, we use the phrase 2 +LOOP to replace LOOP, as with
: BY-TWOS ( n --) 0 TUCK
DO CR DUP . 2 + 2 +LOOP DROP ;
8.4 Structured programming
N. Wirth invented the Pascal language in reaction to program flow
charts resembling a plate of spaghetti. Such flow diagrams were
often seen in early languages like FORTRAN and assembler. Wirth
intended to eliminate line labels and direct jumps (GOTOs), thereby
forcing control flow to be clear and direct.
The ideal was subroutines or functions that performed a single
task, with unique entries and exits. Unfortunately, programmers
insisted on GOTOs, so many Pascals and other modern languages now have
them. Worse, the ideal of short subroutines that do one thing only is
unreachable in such languages because the method for calling them and
passing arguments imposes a large overhead. Thus execution speed re-
quires minimizing calls, which in turn means longer, more complex sub-
routines that perform several related tasks. Today structured program-
ming seems to mean little more than writing code with nested IFs in-
dented by a pretty-printer.
Paradoxically, Forth is the only truly structured language in common
use, although it was not designed with that as its goal. In Forth word
definitions are subroutine calls. The language contains no GOTO's so
it is impossible to write "spaghetti code". Forth also encourages
structure through short definitions. The additional running time
incurred in breaking a long procedure into many small ones (this is
called "factoring") is typically rather small in Forth. Each Forth sub-
routine (word) has one entry and one exit point, and can be written
to perform a single job.
8.5 "Top-down" design
"Top-down" programming is a doctrine that one should design the entire
program from the general to the particular:
> Make an outline, flow chart or whatever, taking a broad overview
of the whole problem.
> Break the problem into small pieces (decompose it).
> Then code the individual components.
The natural programming mode in Forth is "bottom-up" rather than "top-
down" --the most general word appears last, whereas the definitions
must progress from the primitive to the complex. This leads to a some-
what different approach from more familiar languages:
> In Forth, components are specified roughly, and then as they are
coded they are immediately tested, debugged, redesigned and
improved.
> The evolution of the components guides the evolution of the outer
levels of the program.
9. CREATE ... DOES> (the pearl of FORTH)
Michael Ham has called the word pair CREATE...DOES>, the "pearl of
Forth". CREATE is a component of the compiler, whose function is to
make a new dictionary entry with a given name (the next name in the
input stream) and nothing else. DOES> assigns a specific run-time ac-
tion to a newly CREATEd word.
9.1 Defining "defining" words
CREATE finds its most important use in extending the powerful class of
Forth words called "defining" words. The colon compiler ":" is such
a word, as are VARIABLE and CONSTANT.
The definition of VARIABLE in high-level Forth is simple
: VARIABLE CREATE 1 CELLS ALLOT ;
We have already seen how VARIABLE is used in a program. (An altern-
ative definition found in some Forths is
: VARIABLE CREATE 0 , ;
--these variables are initialized to 0.)
Forth lets us define words initialized to contain specific values: for
example, we might want to define the number 17 to be a word. CREATE
and "," ("comma") can do this:
17 CREATE SEVENTEEN , <cr> ok
Now test it via
SEVENTEEN @ . <cr> 17 ok .
Remarks:
> The word , ("comma") puts TOS into the next cell of the dic-
tionary and increments the dictionary pointer by that number of
bytes.
> A word "C," ("see-comma") exists also -- it puts a character into
the next character-length slot of the dictionary and increments
the pointer by 1 such slot. (If the character representation is
ASCII the slots are 1 byte--Unicode requires 2 bytes.)
9.2 Run-time vs. compile-time actions
In the preceding example, we were able to initialize the variable
SEVENTEEN to 17 when we CREATEd it, but we still have to fetch it to
the stack via SEVENTEEN @ whenever we want it. This is not quite what
we had in mind: we would like to find 17 in TOS when SEVENTEEN is
named. The word DOES> gives us the tool to do this.
The function of DOES> is to specify a run-time action for the "child"
words of a defining word. Consider the defining word CONSTANT , de-
fined in high-level (of course CONSTANT is usually defined in machine
code for speed) Forth by
: CONSTANT CREATE , DOES> @ ;
and used as
53 CONSTANT PRIME <cr> ok
Now test it:
PRIME . <cr> 53 ok .
What is happening here?
> CREATE (hidden in CONSTANT) makes an entry named PRIME (the
first word in the input stream following CONSTANT). Then ","
places the TOS (the number 53) in the next cell of the dic-
tionary.
> Then DOES> (inside CONSTANT) appends the actions of all words be-
tween it and ";" (the end of the definition) --in this case, "@"--
to the child word(s) defined by CONSTANT.
9.3 Dimensioned data (intrinsic units)
Here is an example of the power of defining words and of the distinc-
tion between compile-time and run-time behaviors.
Physical problems generally involve quantities that have dimensions,
usually expressed as mass (M), length (L) and time (T) or products of
powers of these. Sometimes there is more than one system of units in
common use to describe the same phenomena.
For example, U.S. or English police reporting accidents might use
inches, feet and yards; while Continental police would use centimeters
and meters. Rather than write different versions of an accident ana-
lysis program it is simpler to write one program and make unit conver-
sions part of the grammar. This is easy in Forth.
The simplest method is to keep all internal lengths in millimeters,
say, and convert as follows:
: INCHES 254 10 */ ;
: FEET [ 254 12 * ] LITERAL 10 */ ;
: YARDS [ 254 36 * ] LITERAL 10 */ ;
: CENTIMETERS 10 * ;
: METERS 1000 * ;
Note: This example is based on integer arithmetic. The word */
means "multiply the third number on the stack by NOS, keeping
double precision, and divide by TOS". That is, the stack com-
ment for */ is ( a b c -- a*b/c).
The usage would be
10 FEET . <cr> 3048 ok
The word "[" switches from compile mode to interpret mode while com-
piling. (If the system is interpreting it changes nothing.) The word
"]" switches from interpret to compile mode.
Barring some error-checking, the "definition" of the colon compiler
":" is just
: : CREATE ] DOES> doLIST ;
and that of ";" is just
: ; next [ ; IMMEDIATE
Another use for these switches is to perform arithmetic at compile-
time rather than at run-time, both for program clarity and for easy
modification, as we did in the first try at dimensioned data (that is,
phrases such as
[ 254 12 * ] LITERAL
and
[ 254 36 * ] LITERAL
which allowed us to incorporate in a clear manner the number of
tenths of millimeters in a foot or a yard.
The preceding method of dealing with units required unnecessarily many
definitions and generated unnecessary code. A more compact approach
uses a defining word, UNITS :
: D, ( hi lo --) SWAP , , ;
: D@ ( adr -- hi lo) DUP @ SWAP 2 + @ ;
: UNITS CREATE D, DOES> D@ */ ;
Then we could make the table
254 10 UNITS INCHES
254 12 * 10 UNITS FEET
254 36 * 10 UNITS YARDS
10 1 UNITS CENTIMETERS
1000 1 UNITS METERS
\ Usage:
10 FEET . <cr> 3048 ok
3 METERS . <cr> 3000 ok
\ .......................
\ etc.
This is an improvement, but Forth permits a simple extension that
allows conversion back to the input units, for use in output:
VARIABLE <AS> 0 <AS> !
: AS TRUE <AS> ! ;
: ~AS FALSE <AS> ! ;
: UNITS CREATE D, DOES> D@ <AS> @
IF SWAP THEN
*/ ~AS ;
\ UNIT DEFINITIONS REMAIN THE SAME.
\ Usage:
10 FEET . <cr> 3048 ok
3048 AS FEET . <cr> 10 ok
9.4 Advanced uses of the compiler
Suppose we have a series of push-buttons numbered 0-3, and a word WHAT
to read them. That is, WHAT waits for input from a keypad: when button
#3 is pushed, for example, WHAT leaves 3 on the stack.
We would like to define a word BUTTON to perform the action of pushing
the n'th button, so we could just say:
WHAT BUTTON
In a conventional language BUTTON would look something like
: BUTTON DUP 0 = IF RING DROP EXIT THEN
DUP 1 = IF OPEN DROP EXIT THEN
DUP 2 = IF LAUGH DROP EXIT THEN
DUP 3 = IF CRY DROP EXIT THEN
ABORT" WRONG BUTTON!" ;
That is, we would have to go through two decisions on the average.
Forth makes possible a much neater algorithm, involving a "jump
table". The mechanism by which Forth executes a subroutine is to
feed its "execution token" (often an address, but not necessarily)
to the word EXECUTE. If we have a table of execution tokens we need
only look up the one corresponding to an index (offset into the table)
fetch it to the stack and say EXECUTE.
One way to code this is
CREATE BUTTONS ' RING , ' OPEN , ' LAUGH , ' CRY ,
: BUTTON ( nth --) 0 MAX 3 MIN
CELLS BUTTONS + @ EXECUTE ;
Note how the phrase 0 MAX 3 MIN protects against an out-of-range
index. Although the Forth philosophy is not to slow the code with un-
necessary error checking (because words are checked as they are de-
fined), when programming a user interface some form of error handling
is vital. It is usually easier to prevent errors as we just did, than
to provide for recovery after they are made.
How does the action-table method work?
> CREATE BUTTONS makes a dictionary entry BUTTONS.
> The word ' ("tick") finds the execution token (xt) of the
following word, and the word , ("comma") stores it in the
data field of the new word BUTTONS. This is repeated until
all the subroutines we want to select among have their xt's
stored in the table.
> The table BUTTONS now contains xt's of the various actions of
BUTTON.
> CELLS then multiplies the index by the appropriate number of
bytes per cell, to get the offset into the table BUTTONS
of the desired xt.
> BUTTONS + then adds the base address of BUTTONS to get the abso-
lute address where the xt is stored.
> @ fetches the xt for EXECUTE to execute.
> EXECUTE then executes the word corresponding to the button pushed.
Simple!
If a program needs but one action table the preceding method suffices.
However, more complex programs may require many such. In that case
it may pay to set up a system for defining action tables, including
both error-preventing code and the code that executes the proper
choice. One way to code this is
: ;CASE ; \ do-nothing word
: CASE:
CREATE HERE -1 >R 0 , \ place for length
BEGIN BL WORD FIND \ get next subroutine
0= IF CR COUNT TYPE ." not found" ABORT THEN
R> 1+ >R
DUP , ['] ;CASE =
UNTIL R> 1- SWAP ! \ store length
DOES> DUP @ ROT ( -- base_adr len n)
MIN 0 MAX \ truncate index
CELLS + CELL+ @ EXECUTE ;
Note the two forms of error checking. At compile-time, CASE:
aborts compilation of the new word if we ask it to point to an
undefined subroutine:
case: test1 DUP SWAP X ;case
X not found
and we count how many subroutines are in the table (including
the do-nothing one, ;case) so that we can force the index to
lie in the range [0,n].
CASE: TEST * / + - ;CASE ok
15 3 0 TEST . 45 ok
15 3 1 TEST . 5 ok
15 3 2 TEST . 18 ok
15 3 3 TEST . 12 ok
15 3 4 TEST . . 3 15 ok
Just for a change of pace, here is another way to do it:
: jtab: ( Nmax --) \ starts compilation
CREATE \ make a new dictionary entry
1- , \ store Nmax-1 in its body
; \ for bounds clipping
: get_xt ( n base_adr -- xt_addr)
DUP @ ( -- n base_adr Nmax-1)
ROT ( -- base_adr Nmax-1 n)
MIN 0 MAX \ bounds-clip for safety
1+ CELLS+ ( -- xt_addr = base + 1_cell + offset)
;
: | ' , ; \ get an xt and store it in next cell
: ;jtab DOES> ( n base_adr --) \ ends compilation
get_xt @ EXECUTE \ get token and execute it
; \ appends table lookup & execute code
\ Example:
: Snickers ." It's a Snickers Bar!" ; \ stub for test
\ more stubs
5 jtab: CandyMachine
| Snickers
| Payday
| M&Ms
| Hershey
| AlmondJoy
;jtab
3 CandyMachine It's a Hershey Bar! ok
1 CandyMachine It's a Payday! ok
7 CandyMachine It's an Almond Joy! ok
0 CandyMachine It's a Snickers Bar! ok
-1 CandyMachine It's a Snickers Bar! ok
10. Floating point arithmetic
Although Forth at one time eschewed floating point arithmetic
(because in the era before math co-processors integer arithmetic
was 3x faster), in recent years a standard set of word names has
been agreed upon. This permits the exchange of programs that will
operate correctly on any computer, as well as the development of
a Scientific Subroutine Library in Forth (FSL).
Although the ANS Standard does not require a separate stack for
floating point numbers, most programmers who use Forth for numer-
ical analysis employ a separate floating point stack; and most of
the routines in the FSL assume such. We shall do so here as well.
The floating point operators have the following names and perform
the actions indicated in the accompanying stack comments:
F@ ( adr --) ( f: -- x)
F! ( adr --) ( f: x --)
F+ ( f: x y -- x+y)
F- ( f: x y -- x-y)
F* ( f: x y -- x*y)
F/ ( f: x y -- x/y)
FEXP ( f: x -- e^x)
FLN ( f: x -- ln[x])
FSQRT ( f: x -- x^0.5)
Additional operators, functions, trigonometric functions, etc. can
be found in the FLOATING and FLOATING EXT wordsets. (See dpANS6--
available in HTML, PostScript and MS Word formats. The HTML version
can be accessed from this homepage.)
To aid in using floating point arithmetic I have created a simple
FORTRAN-like interface for incorporating formulas into Forth words.
The file ftest.f (included below) illustrates how ftran111.f
should be used.
\ Test for ANS FORmula TRANslator
marker -test
fvariable a
fvariable b
fvariable c
fvariable d
fvariable x
fvariable w
: test0 f" b+c" cr fe.
f" b-c" cr fe.
f" (b-c)/(b+c)" cr fe. ;
3.e0 b f!
4.e0 c f!
see test0
test0
: test1 f" a=b*c-3.17e-5/tanh(w)+abs(x)" a f@ cr fe. ;
1.e-3 w f!
-2.5e0 x f!
cr cr
see test1
test1
cr cr
: test2 f" c^3.75" cr fe.
f" b^4" cr fe. ;
see test2
test2
\ Baden's test case
: quadroot c f! b f! a f!
f" d = sqrt(b^2-4*a*c) "
f" (-b+d)/(2*a) " f" (-b-d)/(2*a) "
;
cr cr
see quadroot
: goldenratio f" max(quad root(1,-1,-1)) " ;
cr cr
see goldenratio
cr cr
goldenratio f.
0 [IF]
Output should look like:
: test0
c f@ b f@ f+ cr fe. c f@ fnegate b f@ f+ cr fe. c f@ fnegate b f@
f+ c f@ b f@ f+ f/ cr fe. ;
7.00000000000000E0
-1.00000000000000E0
-142.857142857143E-3
: test1
x f@ fabs 3.17000000000000E-5 w f@ ftanh f/ fnegate b f@ c f@ f* f+
f+ a f! a f@ cr fe. ;
14.4682999894333E0 ok
: test2
c f@ noop 3.75000000000000E0 f** cr fe. b f@ f^4 cr fe. ;
181.019335983756E0
81.0000000000000E0 ok
: QUADROOT C F! B F! A F! B F@ F^2 flit 4.00000 A F@
C F@ F* F* F- FSQRT D F! B F@ FNEGATE D
F@ F+ flit 2.00000 A F@ F* F/ B F@ FNEGATE
D F@ F- flit 2.00000 A F@ F* F/ ;
: GOLDENRATIO flit 1.00000 flit -1.00000 flit -1.00000
QUADROOT FMAX ;
1.61803 ok
with more or fewer places.
[THEN]