CS143 Handout #29
Autumn 2001
TAC
Handout written by Maggie Johnson and revised by me.
Three address code
Three-address code (TAC) will be the intermediate representation used in our Decaf compiler,It is
essentially a generic assembly language that falls in the lower-end of the mid-level IRs,Some
variant of 2,3 or 4 address code is fairly commonly used as an IR,since it maps well to most
assembly languages.
Our TAC is a sequence of instructions,each of which can have at most three operands,The
operands could be two operands to a binary arithmetic operator and the third the result location,or
an operand to compare to zero and a second location to branch to,and so on,For example,below
on the left is an arithmetic expression and on the right,is a translation into TAC:
a = b * c + b * d _t1 = b * c;
_t2 = b * d;
_t3 = _t1 + _t2;
a = _t3;
Notice the use of temp variables created by the compiler as needed to keep the number of operands
down to three,Of course,it's a little more complicated than the above example,because we have to
translate branching and looping instructions,as well as function and method calls,Here is an
example of the TAC branching instructions used to translate an if-statement:
if (a < b + c)
a = a - c;
c = b * c;
_t1 = b + c;
_t2 = a < _t1;
IfZ _t2 Goto _L0;
_t3 = a - c;
a = _3;
_L0:_t4 = b * c;
c = _t4;
And here is an example of the TAC translation for a function call and array access:
int n;
n = ReadInteger();
Binky(arr[n]);
n = LCall _ReadInteger;
_t1 = 4;
_t2 = _t1 * n;
_t3 = arr + _t2;
_t4 = *(_t3);
PushParam _t4;
LCall _Binky;
2
Decaf TAC instruction formats
The convention followed in the examples below is that t1,t2,and so on refer to variables (either
from source program or temporaries) and L1,L2,etc,are used for labels,Labels are attached to the
instruction that serve as targets for goto/branch instructions and are used to identify
function/method definitions and vtables.
Assignment:
t2 = t1;
t1 = "abcdefg";
t1 = 8;
(rvalue can be variable,or string/int
constant)
Arithmetic:
t3 = t2 + t1;
t3 = t2 - t1;
t3 = t2 * t1;
t3 = t2 / t1;
t3 = t2 % t1;
(not all arithmetic operators are present,
must synthesize others using the primitives
available)
Relational/equality/logical:
t3 = t2 == t1;
t3 = t2 < t1;
t3 = t2 && t1;
t3 = t2 || t1;
(must synthesize other ops as necessary)
Labels and branches:
L1:
Goto L1;
IfZ t1 Goto L1;
(take branch if value of t1 is zero)
Function/method calls:
PushParam t1;
(before call,params are individually
pushed right to left)
LCall L1;
t1 = LCall L1;
ACall t1;
t0 = ACall t1;
(LCall used for a function label known
at compile-time,ACall for a computed
function address,most likely from vtable.
Each has two forms that differ in void vs
non-void return value)
The built-in functions from Decaf
standard library (Alloc,ReadLine,
PrintInt,Halt,etc.) are invoked via LCall
Function definitions:
BeginFunc;
EndFunc;
Return t1;
Return;
Memory references:
t1 = *(t2);
t1 = *(t2 + 8);
*(t1) = t2;
*(t1 + -4) = t2;
(optional offset must be integer constant,
can be positive or negative)
Array indexing:
To access arr[5],add offset multiplied by
elem size to base and deref
Object fields,method dispatch:
To access ivars,add offset to base,deref
To call method,retrieve function address
from vtable,invoke using ACall
Data specification:
VTable ClassName = L1,L2,...;
3
Here is an example of a simple Decaf program and its TAC translation:
void main() {
int a;
int b;
int c;
a = 1;
b = 2;
c = a + b;
Print(c);
}
main:
BeginFunc;
_t0 = 1;
a = _t0;
_t1 = 2;
b = _t1;
_t2 = a + b;
c = _t2;
PushParam c;
LCall _PrintInt;
EndFunc;
What we have to do is figure out how to get from one to the other as we parse,This includes not
only generating the TAC,but figuring out the use of temp variables,creating labels,calling
functions,etc,Since we have a lot to do,we will make the mechanics of generating the TAC as easy
as possible,In our parser,we will create the TAC instructions one at a time,We can immediately
print them out or store them for further processing,We will simplify the Decaf language a little by
excluding doubles for code generation and internally treating bools as 4-byte integers,Classes,
arrays,and strings will be implemented with 4-byte pointers,This means we only ever need to deal
with 4-byte integer/pointer variables.
As each production is reduced,we will create the necessary instructions,This strategy makes our
code-generation a bit limited—particularly for the way we would have to do switch statements—but
we can translate more-or-less any language structure into an executable program in a single pass,
without needing to go back and edit anything,which is pretty convenient.
To see how a syntax-directed translation can generate TAC,we need to look at the derivation,and
figure out where the different TAC statements should be generated as the productions are reduced.
Let’s start with a trivial program:
void main() {
Print("hello world");
}
main:
BeginFunc;
_t0 = "hello world";
PushParam _t0;
LCall _PrintString;
EndFunc;
Notice that we call the built-in library function labelled _PrintString to do the actual printing,The
library functions are called like any ordinary global function,but the code is provided by the
compiler as part of linking with the standard library,Here is the derivation of the source program.
The trick is to identify where and what processing occurs as these productions are reduced to
generate the given TAC:
Type -> void
Formals ->
StmtList ->
Constant -> stringConstant
Expr -> Constant
ExprList -> Expr
PrintStmt -> Print ( ExprList )
Stmt -> PrintStmt ;
StmtList -> StmtList Stmt
StmtBlock -> { StmtList }
FunctionDefn -> Type identifier ( Formals ) StmtBlock
4
Decl -> FunctionDefn
DeclList -> Decl
Program -> DeclList
Here is another simple program with a bit more complex expression:
void main() {
int a;
a = 2 + a;
Print(a);
}
main:
BeginFunc;
_t0 = 2;
_t1 = _t0 + a;
a = _t1;
PushParam a;
LCall _PrintInt;
EndFunc;
Here is the derivation,Again,consider where the instructions above must be emitted relative to the
parsing activity:
Type -> void
Formals ->
StmtList ->
Type -> int
Variable -> Type identifier
VariableDecl -> Variable ;
Stmt -> VariableDecl
StmtList -> StmtList Stmt
OptReceiver ->
LValue -> OptReceiver identifier
Constant -> intConstant
Expr -> Constant
OptReceiver ->
LValue -> OptReceiver identifier
Expr -> LValue
Expr -> Expr + Expr
SimpleStmt -> LValue = Expr
Stmt -> SimpleStmt ;
StmtList -> StmtList Stmt
OptReceiver ->
LValue -> OptReceiver identifier
Expr -> LValue
ExprList -> Expr
PrintStmt -> Print ( ExprList )
Stmt -> PrintStmt ;
StmtList -> StmtList Stmt
StmtBlock -> { StmtList }
FunctionDefn -> Type identifier ( Formals ) StmtBlock
Decl -> FunctionDefn
DeclList -> Decl
Program -> DeclList
5
What additional processing would need to be added for a program with a complex expression like:
void main() {
int b;
int a;
b = 3;
a = 12;
a = (b + 2)-(a*3)/6;
}
main:
BeginFunc;
_t0 = 3;
b = _t0;
_t1 = 12;
a = _t1;
_t2 = 2;
_t3 = b + _t2;
_t4 = 3;
_t5 = a * _t4;
_t6 = 6;
_t7 = _t5 / _t6;
_t8 = _t3 - _t7;
a = _t8;
EndFunc;
Now let’s consider what needs to be done to deal with arrays (note the TAC code below doesn't do
array bounds checking,that will be your job to implement!)
void Binky(int[] arr) {
arr[1] = arr[0] * 2;
}
_Binky:
BeginFunc;
_t0 = 1;
_t1 = 4;
_t2 = _t1 * _t0;
_t3 = arr + _t2;
_t4 = 0;
_t5 = 4;
_t6 = _t5 * _t4;
_t7 = arr + _t6;
_t8 = *(_t7);
_t9 = 2;
_t10 = _t8 * _t9;
*(_t3) = _t10;
EndFunc;
Before we deal with classes,we should look at how function calls are implemented,This will
facilitate our study of methods as they are used in classes,A program with a simple function call:
int foo(int a,int b) {
return a + b;
}
void main() {
int c;
int d;
foo(c,d);
}
_foo:
BeginFunc;
_t0 = a + b;
Return _t0;
EndFunc;
main:
BeginFunc;
PushParam d;
PushParam c;
_t1 = LCall _foo;
EndFunc;
6
Now for a class example with both fields and methods (notice how this is passed as a secret first
parameter to a method call)
class Animal {
int height;
void InitAnimal(int h) {
this.height = h;
}
}
class Cow extends Animal {
void InitCow(int h) {
InitAnimal(h);
}
}
void Binky(class Cow betsy) {
betsy.InitCow(5);
}
_Animal.InitAnimal:
BeginFunc;
*(this + 4) = h;
EndFunc;
VTable Animal =
_Animal.InitAnimal,;
_Cow.InitCow:
BeginFunc;
_t0 = *(this);
_t1 = *(_t0);
PushParam h;
PushParam this;
ACall _t1;
EndFunc;
VTable Cow =
_Animal.InitAnimal,
_Cow.InitCow,;
_Binky:
BeginFunc;
_t2 = 5;
_t3 = *(betsy);
_t4 = *(_t3 + 4);
PushParam _t1;
PushParam betsy;
ACall _t4;
EndFunc;
7
How about some TAC that implements control structures,for example,such the if statement below?
void main() {
int a;
a = 23;
if (a == 23)
a = 10;
else
a = 19;
}
main:
BeginFunc;
_t0 = 23;
a = _t0;
_t1 = 23;
_t2 = a == _t1;
IfZ _t2 Goto _L0;
_t3 = 10;
a = _t3;
Goto _L1;
_L0:
_t4 = 19;
a = _t4;
_L1:
EndFunc;
Or the even snazzier while loop (for loops are left an exercise for the reader):
void main() {
int a;
a = 0;
while (a < 10) {
Print(a % 2 == 0);
a = a + 1;
}
}
main:
BeginFunc;
_t0 = 0;
a = _t0;
_L0:
_t1 = 10;
_t2 = a < _t1;
IfZ _t2 Goto _L1;
_t3 = 2;
_t4 = a % _t3;
_t5 = 0;
_t6 = _t4 == _t5;
PushParam _t6;
LCall _PrintBool;
_t7 = 1;
_t8 = a + _t7;
a = _t8;
Goto _L0;
_L1:
EndFunc;
8
Using TAC with other languages
The TAC generation that we have been looking at is fairly generic,Although we have talked about
it in the context of Decaf,a TAC generator for any programming language would generate a similar
sequence of statements,For example,in the dragon book,the following format is used to define the
TAC generation for a while loop,(P,469 Aho/Sethi/Ullman)
S -> while E do S1
{ S.begin = newlabel;
S.after = newlabel;
S.code = gen(S.begin ':')
E.code
gen('if' E.place '=' '0' 'goto' S.after)
S1.code
gen('goto' S.begin)
gen(S.after ':')
}
One last idea before we finish..,A nice enhancement to a TAC generator is re-using temp variable
names,For example,if we have the following expression:
E -> E1 + E2
Our usual steps would be to evaluate E1 into t1,evaluate E2 into t2,and then set t3 to their sum.
Will t1 and t2 be used anywhere else in the program? How do we know when we can reuse these
temp names? Here is a method from Aho/Sethi/Ullman (p,480) for reusing temp names:
1) Keep a count c initialized to 0.
2) Whenever a temp name is used as an operand,decrement c by 1
3) Whenever a new temp is created,use this new temp and increase c by one.
x = a * b + c * d - e * f
(c = 0) T0 = a * b
(c = 1) T1 = c * d (c = 2)
(c = 0) T0 = T0 + T1
(c = 1) T1 = e * f (c = 2)
(c = 0) T0 = T0 - T1
x = T0
Note that this algorithm expects that each temporary name will be assigned and used exactly once,
which is true in the majority of cases.
Bibliography
J.P,Bennett,Introduction to Compiling Techniques,Berkshire,England,McGraw-Hill,1990.
S,Muchnick,Advanced Compiler Design and Implementation,San Francisco,CA,Morgan
Kaufmann,1997.
A,Pyster,Compiler Design and Construction,New York,NY,Van Nostrand Reinhold,1988.