© Copyright 1989,
Philip Koopman,
All Rights Reserved.
Stack Computers: the new wave
© Copyright 1989,
Philip Koopman,
All Rights Reserved.
The Forth language is based on an extensible, interactive compiler that creates code for a virtual stack machine. The virtual machine has two stacks. The Data Stack is used for expression evaluation and subroutine parameter passing. The Return Stack is used for subroutine return address saving and for loop control variable storage. The source code for Forth directly reflects the underlying stack machine, and so uses Reverse Polish Notation (RPN) to perform all operations using.
Forth programs are built as a hierarchy of subroutines. Each subroutine is called a "word" in Forth terminology. A program consists of a single Forth word which calls several other Forth words, and so on, forming a tree-structured program. At the lowest level, the leaves of the tree are invocations of Forth primitive words that manipulate the stacks and perform arithmetic.
Below is a glossary of the Forth primitive words found on stack machines discussed in this book. Most of these primitives are actually applicable to any program written in any language on a stack machine (for example, addition of the top two stack elements or swapping the order of the top two stack elements). Forth nomenclature is used in discussions to maintain consistency with an existing standard vocabulary for stack machine operation.
Each Forth word is followed by a "stack picture" on the same line. This stack picture shows the input parameters and output parameters on the Forth Data Stack for the word being described. The values on the left of the "_" indicate the input parameters while those to the right of the "_" indicate output parameters. Each parameter list is ordered with the topmost stack element to the right. Notation in the stack lists is as follows: N1, N2, N3, etc. indicate single-precision integers. D1, D2, etc. indicate double-precision integers, which take up two elements on the data stack. ADDR indicates an address, which may be thought of as a pointer value. FLAG is an integer which is false if zero, true if non-zero. A more detailed glossary of Forth is Haydon's All About Forth (1983).
0 - 0
Push the integer 0 onto the stack.
0< N1 - FLAG
Return a true FLAG if N1 is negative.
0= N1 - FLAG
Return a true FLAG if N1 is zero.
0 N1 - FLAG
Return a true FLAG if N1 is greater than zero.
0BRANCH N1 -
If N1 is false (value is 0) perform a branch to the
address in the next program cell, otherwise continue.
1+ N1 - N2
Add one to N1, returning N2.
1- N1 - N2
Subtract one from N1, returning N2.
2+ N1 - N2
Add two to N1, returning N2.
2* N1 - N2
Multiply N1 by two, returning N2.
2/ N1 - N2
Divide N1 by two, returning N2.
4+ N1 - N2
Add four to N1, returning N2.
< N1 N2 - FLAG
Return a true FLAG if N1 is less than N2.
<> N1 N2 - FLAG
Return a true FLAG if N1 is not equal to N2.
= N1 N2 - FLAG
Return a true FLAG if N1 equals N2.
R N1 -
Push N1 onto the return stack.
> N1 N2 - FLAG
Return a true FLAG if N1 is greater than N2.
! N1 ADDR -
Store N1 at location ADDR in program memory.
+ N1 N2 - N3
Add N1 and N2, giving sum N3.
+! N1 ADDR -
Add N1 to the value pointed to by ADDR.
- N1 N2 - N3
Subtract N2 from N1, giving difference N3.
: -
Define the start of a subroutine. The primitive
[CALL] is compiled every time this subroutine is
reference by other definitions.
; -
Perform a subroutine return and end the definition
of a subroutine. The primitive [EXIT] is compiled.
?DUP N1 - N1 N1 ( if N1 non-zero )
N1 - N1 ( if N1 is zero )
Conditionally duplicate the input N1 if it is
non-zero.
@ ADDR - N1<
Fetch the value at location ADDR in program memory,
returning N1.
ABS N1 - N2
Take the absolute value of N1 and return the result N2.
AND N1 N2 - N3
Perform a bitwise AND on N1 and N2, giving result N3.
BRANCH -
Perform an unconditional branch to the compiled in-line
address.
D! D1 ADDR -
Store the double-precision value D1 at the two memory
words starting at ADDR.
D+ D1 D2 - D3
Return the double precision sum of D1 and D2 as D3.
D@ ADDR - D1
Fetch the double precision value D1 from memory starting
at address ADDR.
DDROP D1 -
Drop the double-precision integer D1.
DDUP D1 - D1 D1
Duplicate D1 on the stack.
DNEGATE D1 - D2
Return D2, which is the two's complement of D1.
DROP N1 -
Drop N1 from the stack.
DSWAP D1 D2 - D2 D1
Swap the top two double-precision numbers on the stack.
DUP N1 - N1 N1
Duplicate N1, returning a second copy of it on the stack.
I - N1
Return the index of the currently active loop.
I' - N1
Return the limit of the currently active loop.
J - N1
Return the index of the outer loop in a nested loop structure.
LEAVE -
Set the loop counter on the return stack equal to the
loop limit to force an exit from the loop.
LIT - N1
Treat the compiled in-line value as an integer constant,
and push it onto the stack as N1.
NEGATE N1 - N2
Return N2, which is the two's complement of N1
NOP -
Do nothing.
NOT FLAG1 - FLAG2
Synonym for 0=. Takes the inverse of a flag value.
OR N1 N2 - N3
Perform a bitwise OR on N1 and N2, giving result N3.
OVER N1 N2 - N1 N2 N1
Push a copy of the second element on the stack, N1, onto
the top of the stack.
PICK ... N1 - ... N2
Copy the N1'th element deep in the data stack to the top.
In Forth-83, 0 PICK is equivalent to DUP , and 1 PICK
is equivalent to OVER .
R> - N1
Pop the top element of the return stack, and push it onto
the data stack as N1.
R@ - N1
Copy the top Return Stack word N1 onto the Data Stack.
ROLL ... N1 - ... N2
Pull the N1'th element deep in the data stack to the top,
closing the hole left in the stack. In Forth-83, 1 ROLL
is equivalent to SWAP , and 2 ROLL is equivalent to ROT.
ROT N1 N2 N3 - N2 N3 N1
Pull the third element down in the stack onto the top of
the stack.
S-D N1 - D2
Sign extend N1 to occupy two words, making it a double
precision integer D2.
SWAP N1 N2 - N2 N1
Swap the order of the top two stack elements.
U< U1 U2 - FLAG
Return a true FLAG if U1 is less than U2 when compared
as unsigned integers.
U U1 U2 - FLAG
Return a true FLAG if U1 is greater than U2 when compared
as unsigned integers.
U* N1 N2 - D3
Perform unsigned integer multiplication on N1 and N2,
yielding the unsigned double precision result D3.
U/MOD D1 N2 - N3 N4
Perform unsigned integer division on D1 and N2, yielding
the quotient N4 and the remainder N3.
XOR N1 N2 - N3
Perform a bitwise exclusive OR on N1 and N2, giving result N3.
NEXT APPENDIX
Phil Koopman --
koopman@cmu.edu