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OPA A
LET'S BUILD A COMPILER!
By
Jack W. Crenshaw, Ph.D.
24 July 1988
Part II: EXPRESSION PARSING
PA A
*****************************************************************
* *
* COPYRIGHT NOTICE *
* *
* Copyright 1988 (C) Jack W. Crenshaw. All rights reserved. *
* *
*****************************************************************
GETTING STARTED
If you've read the introduction document to this series, you will
already know what we're about. You will also have copied the
cradle software into your Turbo Pascal system, and have compiled
it. So you should be ready to go.
The purpose of this article is for us to learn how to parse and
translate mathematical expressions. What we would like to see as
output is a series of assembler-language statements that perform
the desired actions. For purposes of definition, an expression
is the right-hand side of an equation, as in
x = 2*y + 3/(4*z)
In the early going, I'll be taking things in _VERY_ small steps.
That's so that the beginners among you won't get totally lost.
There are also some very good lessons to be learned early on,
that will serve us well later. For the more experienced readers:
bear with me. We'll get rolling soon enough.
SINGLE DIGITS
In keeping with the whole theme of this series (KISS, remember?),
let's start with the absolutely most simple case we can think of.
That, to me, is an expression consisting of a single digit.
Before starting to code, make sure you have a baseline copy of
the "cradle" that I gave last time. We'll be using it again for
other experiments. Then add this code:
{---------------------------------------------------------------}
{ Parse and Translate a Math Expression }
procedure Expression;
begin
EmitLn('MOVE #' + GetNum + ',D0')
end;
{---------------------------------------------------------------}
And add the line "Expression;" to the main program so that it
reads:A*A*
- 2 -
PA A
{---------------------------------------------------------------}
begin
Init;
Expression;
end.
{---------------------------------------------------------------}
Now run the program. Try any single-digit number as input. You
should get a single line of assembler-language output. Now try
any other character as input, and you'll see that the parser
properly reports an error.
CONGRATULATIONS! You have just written a working translator!
OK, I grant you that it's pretty limited. But don't brush it off
too lightly. This little "compiler" does, on a very limited
scale, exactly what any larger compiler does: it correctly
recognizes legal statements in the input "language" that we have
defined for it, and it produces correct, executable assembler
code, suitable for assembling into object format. Just as
importantly, it correctly recognizes statements that are NOT
legal, and gives a meaningful error message. Who could ask for
more? As we expand our parser, we'd better make sure those two
characteristics always hold true.
There are some other features of this tiny program worth
mentioning. First, you can see that we don't separate code
generation from parsing ... as soon as the parser knows what we
want done, it generates the object code directly. In a real
compiler, of course, the reads in GetChar would be from a disk
file, and the writes to another disk file, but this way is much
easier to deal with while we're experimenting.
Also note that an expression must leave a result somewhere. I've
chosen the 68000 register DO. I could have made some other
choices, but this one makes sense.
BINARY EXPRESSIONS
Now that we have that under our belt, let's branch out a bit.
Admittedly, an "expression" consisting of only one character is
not going to meet our needs for long, so let's see what we can do
to extend it. Suppose we want to handle expressions of the form:
1+2
or 4-3
or, in general, <term> +/- <term>
(That's a bit of Backus-Naur Form, or BNF.)ABAB
- 3 -A*A*
PA A
To do this we need a procedure that recognizes a term and leaves
its result somewhere, and another that recognizes and
distinguishes between a '+' and a '-' and generates the
appropriate code. But if Expression is going to leave its result
in DO, where should Term leave its result? Answer: the same
place. We're going to have to save the first result of Term
somewhere before we get the next one.
OK, basically what we want to do is have procedure Term do what
Expression was doing before. So just RENAME procedure Expression
as Term, and enter the following new version of Expression:
{---------------------------------------------------------------}
{ Parse and Translate an Expression }
procedure Expression;
begin
Term;
EmitLn('MOVE D0,D1');
case Look of
'+': Add;
'-': Subtract;
else Expected('Addop');
end;
end;
{--------------------------------------------------------------}
Next, just above Expression enter these two procedures:
{--------------------------------------------------------------}
{ Recognize and Translate an Add }
procedure Add;
begin
Match('+');
Term;
EmitLn('ADD D1,D0');
end;
{-------------------------------------------------------------}
{ Recognize and Translate a Subtract }
procedure Subtract;
begin
Match('-');
Term;
EmitLn('SUB D1,D0');
end;
{-------------------------------------------------------------}A6A6
- 4 -A*A*
PA A
When you're finished with that, the order of the routines should
be:
o Term (The OLD Expression)
o Add
o Subtract
o Expression
Now run the program. Try any combination you can think of of two
single digits, separated by a '+' or a '-'. You should get a
series of four assembler-language instructions out of each run.
Now try some expressions with deliberate errors in them. Does
the parser catch the errors?
Take a look at the object code generated. There are two
observations we can make. First, the code generated is NOT what
we would write ourselves. The sequence
MOVE #n,D0
MOVE D0,D1
is inefficient. If we were writing this code by hand, we would
probably just load the data directly to D1.
There is a message here: code generated by our parser is less
efficient than the code we would write by hand. Get used to it.
That's going to be true throughout this series. It's true of all
compilers to some extent. Computer scientists have devoted whole
lifetimes to the issue of code optimization, and there are indeed
things that can be done to improve the quality of code output.
Some compilers do quite well, but there is a heavy price to pay
in complexity, and it's a losing battle anyway ... there will
probably never come a time when a good assembler-language pro-
grammer can't out-program a compiler. Before this session is
over, I'll briefly mention some ways that we can do a little op-
timization, just to show you that we can indeed improve things
without too much trouble. But remember, we're here to learn, not
to see how tight we can make the object code. For now, and
really throughout this series of articles, we'll studiously
ignore optimization and concentrate on getting out code that
works.
Speaking of which: ours DOESN'T! The code is _WRONG_! As things
are working now, the subtraction process subtracts D1 (which has
the FIRST argument in it) from D0 (which has the second). That's
the wrong way, so we end up with the wrong sign for the result.
So let's fix up procedure Subtract with a sign-changer, so that
it readsA9A9
- 5 -A*A*
PA A
{-------------------------------------------------------------}
{ Recognize and Translate a Subtract }
procedure Subtract;
begin
Match('-');
Term;
EmitLn('SUB D1,D0');
EmitLn('NEG D0');
end;
{-------------------------------------------------------------}
Now our code is even less efficient, but at least it gives the
right answer! Unfortunately, the rules that give the meaning of
math expressions require that the terms in an expression come out
in an inconvenient order for us. Again, this is just one of
those facts of life you learn to live with. This one will come
back to haunt us when we get to division.
OK, at this point we have a parser that can recognize the sum or
difference of two digits. Earlier, we could only recognize a
single digit. But real expressions can have either form (or an
infinity of others). For kicks, go back and run the program with
the single input line '1'.
Didn't work, did it? And why should it? We just finished
telling our parser that the only kinds of expressions that are
legal are those with two terms. We must rewrite procedure
Expression to be a lot more broadminded, and this is where things
start to take the shape of a real parser.
GENERAL EXPRESSIONS
In the REAL world, an expression can consist of one or more
terms, separated by "addops" ('+' or '-'). In BNF, this is
written
<expression> ::= <term> [<addop> <term>]*
We can accomodate this definition of an expression with the
addition of a simple loop to procedure Expression:AQAQ
- 6 -A*A*
PA A
{---------------------------------------------------------------}
{ Parse and Translate an Expression }
procedure Expression;
begin
Term;
while Look in ['+', '-'] do begin
EmitLn('MOVE D0,D1');
case Look of
'+': Add;
'-': Subtract;
else Expected('Addop');
end;
end;
end;
{--------------------------------------------------------------}
NOW we're getting somewhere! This version handles any number of
terms, and it only cost us two extra lines of code. As we go on,
you'll discover that this is characteristic of top-down parsers
... it only takes a few lines of code to accomodate extensions to
the language. That's what makes our incremental approach
possible. Notice, too, how well the code of procedure Expression
matches the BNF definition. That, too, is characteristic of the
method. As you get proficient in the approach, you'll find that
you can turn BNF into parser code just about as fast as you can
type!
OK, compile the new version of our parser, and give it a try. As
usual, verify that the "compiler" can handle any legal
expression, and will give a meaningful error message for an
illegal one. Neat, eh? You might note that in our test version,
any error message comes out sort of buried in whatever code had
already been generated. But remember, that's just because we are
using the CRT as our "output file" for this series of
experiments. In a production version, the two outputs would be
separated ... one to the output file, and one to the screen.
USING THE STACK
At this point I'm going to violate my rule that we don't
introduce any complexity until it's absolutely necessary, long
enough to point out a problem with the code we're generating. As
things stand now, the parser uses D0 for the "primary" register,
and D1 as a place to store the partial sum. That works fine for
now, because as long as we deal with only the "addops" '+' and
'-', any new term can be added in as soon as it is found. But in
general that isn't true. Consider, for example, the expression
1+(2-(3+(4-5)))ABAB
- 7 -A*A*
PA A
If we put the '1' in D1, where do we put the '2'? Since a
general expression can have any degree of complexity, we're going
to run out of registers fast!
Fortunately, there's a simple solution. Like every modern
microprocessor, the 68000 has a stack, which is the perfect place
to save a variable number of items. So instead of moving the term
in D0 to D1, let's just push it onto the stack. For the benefit
of those unfamiliar with 68000 assembler language, a push is
written
-(SP)
and a pop, (SP)+ .
So let's change the EmitLn in Expression to read:
EmitLn('MOVE D0,-(SP)');
and the two lines in Add and Subtract to
EmitLn('ADD (SP)+,D0')
and EmitLn('SUB (SP)+,D0'),
respectively. Now try the parser again and make sure we haven't
broken it.
Once again, the generated code is less efficient than before, but
it's a necessary step, as you'll see.
MULTIPLICATION AND DIVISION
Now let's get down to some REALLY serious business. As you all
know, there are other math operators than "addops" ...
expressions can also have multiply and divide operations. You
also know that there is an implied operator PRECEDENCE, or
hierarchy, associated with expressions, so that in an expression
like
2 + 3 * 4,
we know that we're supposed to multiply FIRST, then add. (See
why we needed the stack?)
In the early days of compiler technology, people used some rather
complex techniques to insure that the operator precedence rules
were obeyed. It turns out, though, that none of this is
necessary ... the rules can be accommodated quite nicely by our
top-down parsing technique. Up till now, the only form that
we've considered for a term is that of a single decimal digit.A6A6
- 8 -A*A*
PA A
More generally, we can define a term as a PRODUCT of FACTORS;
i.e.,
<term> ::= <factor> [ <mulop> <factor ]*
What is a factor? For now, it's what a term used to be ... a
single digit.
Notice the symmetry: a term has the same form as an expression.
As a matter of fact, we can add to our parser with a little
judicious copying and renaming. But to avoid confusion, the
listing below is the complete set of parsing routines. (Note the
way we handle the reversal of operands in Divide.)
{---------------------------------------------------------------}
{ Parse and Translate a Math Factor }
procedure Factor;
begin
EmitLn('MOVE #' + GetNum + ',D0')
end;
{--------------------------------------------------------------}
{ Recognize and Translate a Multiply }
procedure Multiply;
begin
Match('*');
Factor;
EmitLn('MULS (SP)+,D0');
end;
{-------------------------------------------------------------}
{ Recognize and Translate a Divide }
procedure Divide;
begin
Match('/');
Factor;
EmitLn('MOVE (SP)+,D1');
EmitLn('DIVS D1,D0');
end;AKAK
- 9 -A*A*
PA A
{---------------------------------------------------------------}
{ Parse and Translate a Math Term }
procedure Term;
begin
Factor;
while Look in ['*', '/'] do begin
EmitLn('MOVE D0,-(SP)');
case Look of
'*': Multiply;
'/': Divide;
else Expected('Mulop');
end;
end;
end;
{--------------------------------------------------------------}
{ Recognize and Translate an Add }
procedure Add;
begin
Match('+');
Term;
EmitLn('ADD (SP)+,D0');
end;
{-------------------------------------------------------------}
{ Recognize and Translate a Subtract }
procedure Subtract;
begin
Match('-');
Term;
EmitLn('SUB (SP)+,D0');
EmitLn('NEG D0');
end;ANAN
- 10 -A*A*
PA A
{---------------------------------------------------------------}
{ Parse and Translate an Expression }
procedure Expression;
begin
Term;
while Look in ['+', '-'] do begin
EmitLn('MOVE D0,-(SP)');
case Look of
'+': Add;
'-': Subtract;
else Expected('Addop');
end;
end;
end;
{--------------------------------------------------------------}
Hot dog! A NEARLY functional parser/translator, in only 55 lines
of Pascal! The output is starting to look really useful, if you
continue to overlook the inefficiency, which I hope you will.
Remember, we're not trying to produce tight code here.
PARENTHESES
We can wrap up this part of the parser with the addition of
parentheses with math expressions. As you know, parentheses are
a mechanism to force a desired operator precedence. So, for
example, in the expression
2*(3+4) ,
the parentheses force the addition before the multiply. Much
more importantly, though, parentheses give us a mechanism for
defining expressions of any degree of complexity, as in
(1+2)/((3+4)+(5-6))
The key to incorporating parentheses into our parser is to
realize that no matter how complicated an expression enclosed by
parentheses may be, to the rest of the world it looks like a
simple factor. That is, one of the forms for a factor is:
<factor> ::= (<expression>)
This is where the recursion comes in. An expression can contain a
factor which contains another expression which contains a factor,
etc., ad infinitum.
Complicated or not, we can take care of this by adding just a few
lines of Pascal to procedure Factor:ABAB
- 11 -A*A*
PA A
{---------------------------------------------------------------}
{ Parse and Translate a Math Factor }
procedure Expression; Forward;
procedure Factor;
begin
if Look = '(' then begin
Match('(');
Expression;
Match(')');
end
else
EmitLn('MOVE #' + GetNum + ',D0');
end;
{--------------------------------------------------------------}
Note again how easily we can extend the parser, and how well the
Pascal code matches the BNF syntax.
As usual, compile the new version and make sure that it correctly
parses legal sentences, and flags illegal ones with an error
message.
UNARY MINUS
At this point, we have a parser that can handle just about any
expression, right? OK, try this input sentence:
-1
WOOPS! It doesn't work, does it? Procedure Expression expects
everything to start with an integer, so it coughs up the leading
minus sign. You'll find that +3 won't work either, nor will
something like
-(3-2) .
There are a couple of ways to fix the problem. The easiest
(although not necessarily the best) way is to stick an imaginary
leading zero in front of expressions of this type, so that -3
becomes 0-3. We can easily patch this into our existing version
of Expression:AKAK
- 12 -A*A*
PA A
{---------------------------------------------------------------}
{ Parse and Translate an Expression }
procedure Expression;
begin
if IsAddop(Look) then
EmitLn('CLR D0')
else
Term;
while IsAddop(Look) do begin
EmitLn('MOVE D0,-(SP)');
case Look of
'+': Add;
'-': Subtract;
else Expected('Addop');
end;
end;
end;
{--------------------------------------------------------------}
I TOLD you that making changes was easy! This time it cost us
only three new lines of Pascal. Note the new reference to
function IsAddop. Since the test for an addop appeared twice, I
chose to embed it in the new function. The form of IsAddop
should be apparent from that for IsAlpha. Here it is:
{--------------------------------------------------------------}
{ Recognize an Addop }
function IsAddop(c: char): boolean;
begin
IsAddop := c in ['+', '-'];
end;
{--------------------------------------------------------------}
OK, make these changes to the program and recompile. You should
also include IsAddop in your baseline copy of the cradle. We'll
be needing it again later. Now try the input -1 again. Wow!
The efficiency of the code is pretty poor ... six lines of code
just for loading a simple constant ... but at least it's correct.
Remember, we're not trying to replace Turbo Pascal here.
At this point we're just about finished with the structure of our
expression parser. This version of the program should correctly
parse and compile just about any expression you care to throw at
it. It's still limited in that we can only handle factors
involving single decimal digits. But I hope that by now you're
starting to get the message that we can accomodate further
extensions with just some minor changes to the parser. You
probably won't be surprised to hear that a variable or even a
function call is just another kind of a factor.A*A*
- 13 -
PA A
In the next session, I'll show you just how easy it is to extend
our parser to take care of these things too, and I'll also show
you just how easily we can accomodate multicharacter numbers and
variable names. So you see, we're not far at all from a truly
useful parser.
A WORD ABOUT OPTIMIZATION
Earlier in this session, I promised to give you some hints as to
how we can improve the quality of the generated code. As I said,
the production of tight code is not the main purpose of this
series of articles. But you need to at least know that we aren't
just wasting our time here ... that we can indeed modify the
parser further to make it produce better code, without throwing
away everything we've done to date. As usual, it turns out that
SOME optimization is not that difficult to do ... it simply takes
some extra code in the parser.
There are two basic approaches we can take:
o Try to fix up the code after it's generated
This is the concept of "peephole" optimization. The general
idea it that we know what combinations of instructions the
compiler is going to generate, and we also know which ones
are pretty bad (such as the code for -1, above). So all we
do is to scan the produced code, looking for those
combinations, and replacing them by better ones. It's sort
of a macro expansion, in reverse, and a fairly
straightforward exercise in pattern-matching. The only
complication, really, is that there may be a LOT of such
combinations to look for. It's called peephole optimization
simply because it only looks at a small group of instructions
at a time. Peephole optimization can have a dramatic effect
on the quality of the code, with little change to the
structure of the compiler itself. There is a price to pay,
though, in both the speed, size, and complexity of the
compiler. Looking for all those combinations calls for a lot
of IF tests, each one of which is a source of error. And, of
course, it takes time.
In the classical implementation of a peephole optimizer,
it's done as a second pass to the compiler. The output code
is written to disk, and then the optimizer reads and
processes the disk file again. As a matter of fact, you can
see that the optimizer could even be a separate PROGRAM from
the compiler proper. Since the optimizer only looks at the
code through a small "window" of instructions (hence the
name), a better implementation would be to simply buffer up a
few lines of output, and scan the buffer after each EmitLn.
o Try to generate better code in the first placeA6A6
- 14 -A*A*
PA A
This approach calls for us to look for special cases BEFORE
we Emit them. As a trivial example, we should be able to
identify a constant zero, and Emit a CLR instead of a load,
or even do nothing at all, as in an add of zero, for example.
Closer to home, if we had chosen to recognize the unary minus
in Factor instead of in Expression, we could treat constants
like -1 as ordinary constants, rather then generating them
from positive ones. None of these things are difficult to
deal with ... they only add extra tests in the code, which is
why I haven't included them in our program. The way I see
it, once we get to the point that we have a working compiler,
generating useful code that executes, we can always go back
and tweak the thing to tighten up the code produced. That's
why there are Release 2.0's in the world.
There IS one more type of optimization worth mentioning, that
seems to promise pretty tight code without too much hassle. It's
my "invention" in the sense that I haven't seen it suggested in
print anywhere, though I have no illusions that it's original
with me.
This is to avoid such a heavy use of the stack, by making better
use of the CPU registers. Remember back when we were doing only
addition and subtraction, that we used registers D0 and D1,
rather than the stack? It worked, because with only those two
operations, the "stack" never needs more than two entries.
Well, the 68000 has eight data registers. Why not use them as a
privately managed stack? The key is to recognize that, at any
point in its processing, the parser KNOWS how many items are on
the stack, so it can indeed manage it properly. We can define a
private "stack pointer" that keeps track of which stack level
we're at, and addresses the corresponding register. Procedure
Factor, for example, would not cause data to be loaded into
register D0, but into whatever the current "top-of-stack"
register happened to be.
What we're doing in effect is to replace the CPU's RAM stack with
a locally managed stack made up of registers. For most
expressions, the stack level will never exceed eight, so we'll
get pretty good code out. Of course, we also have to deal with
those odd cases where the stack level DOES exceed eight, but
that's no problem either. We simply let the stack spill over
into the CPU stack. For levels beyond eight, the code is no
worse than what we're generating now, and for levels less than
eight, it's considerably better.
For the record, I have implemented this concept, just to make
sure it works before I mentioned it to you. It does. In
practice, it turns out that you can't really use all eight levels
... you need at least one register free to reverse the operand
order for division (sure wish the 68000 had an XTHL, like the
8080!). For expressions that include function calls, we wouldA6A6
- 15 -A*A*
PA A
also need a register reserved for them. Still, there is a nice
improvement in code size for most expressions.
So, you see, getting better code isn't that difficult, but it
does add complexity to the our translator ... complexity we can
do without at this point. For that reason, I STRONGLY suggest
that we continue to ignore efficiency issues for the rest of this
series, secure in the knowledge that we can indeed improve the
code quality without throwing away what we've done.
Next lesson, I'll show you how to deal with variables factors and
function calls. I'll also show you just how easy it is to handle
multicharacter tokens and embedded white space.
*****************************************************************
* *
* COPYRIGHT NOTICE *
* *
* Copyright 1988 (C) Jack W. Crenshaw. All rights reserved. *
* *
*****************************************************************AIAI
- 16 -A*A*
@
