14-Intermediate code generation - Variants of Syntax trees - Three Address Code-14-06-2023.pdf

UNIT III – INTERMEDIATE CODE GENERATION
INTRODUCTION
The front end translates a source program into an intermediate representation from which
the back end generates target code.
Benefits of using a machine-independent intermediate form are:
1. Retargeting is facilitated. That is, a compiler for a different machine can be created by
attaching a back end for the new machine to an existing front end.
2. A machine-independent code optimizer can be applied to the intermediate representation.
Position of intermediate code generator
intermediate
code
INTERMEDIATE LANGUAGES
Three ways of intermediate representation:
 Syntax tree
 Postfix notation
 Three address code
The semantic rules for generating three-address code from common programming language
constructs are similar to those for constructing syntax trees or for generating postfix notation.
Graphical Representations:
Syntax tree:
A syntax tree depicts the natural hierarchical structure of a source program. A dag
(Directed Acyclic Graph) gives the same information but in a more compact way because
common subexpressions are identified. A syntax tree and dag for the assignment statement a : =
b * - c + b * - c are as follows:
parser static
checker
intermediate
code generator
code
generator
NOTES.PMR-INSIGNIA.ORG

assign assign
a + a +
* * *
b uminus b uminus b uminus
c c c
(a) Syntax tree (b) Dag
Postfix notation:
Postfix notation is a linearized representation of a syntax tree; it is a list of the nodes of
the tree in which a node appears immediately after its children. The postfix notation for the
syntax tree given above is
a b c uminus * b c uminus * + assign
Syntax-directed definition:
Syntax trees for assignment statements are produced by the syntax-directed definition.
Non-terminal S generates an assignment statement. The two binary operators + and * are
examples of the full operator set in a typical language. Operator associativities and precedences
are the usual ones, even though they have not been put into the grammar. This definition
constructs the tree from the input a : = b * - c + b* - c.
PRODUCTION SEMANTIC RULE
S  id : = E S.nptr : = mknode(‘assign’,mkleaf(id, id.place), E.nptr)
E  E1 + E2 E.nptr : = mknode(‘+’, E1.nptr, E2.nptr )
E  E1 * E2 E.nptr : = mknode(‘*’, E1.nptr, E2.nptr )
E  - E1 E.nptr : = mknode(‘uminus’, E1.nptr)
E  ( E1 ) E.nptr : = E1.nptr
E  id E.nptr : = mkleaf( id, id.place )
Syntax-directed definition to produce syntax trees for assignment statements

The token id has an attribute place that points to the symbol-table entry for the identifier.
A symbol-table entry can be found from an attribute id.name, representing the lexeme associated
with that occurrence of id. If the lexical analyzer holds all lexemes in a single array of
characters, then attribute name might be the index of the first character of the lexeme.
Two representations of the syntax tree are as follows. In (a) each node is represented as a
record with a field for its operator and additional fields for pointers to its children. In (b), nodes
are allocated from an array of records and the index or position of the node serves as the pointer
to the node. All the nodes in the syntax tree can be visited by following pointers, starting from
the root at position 10.
Two representations of the syntax tree
aaaaaaaaaaaaa 0
1
2 2
3
4
5
6
7
8
9
10
(a) (b)
Three-Address Code:
Three-address code is a sequence of statements of the general form
x : = y op z
where x, y and z are names, constants, or compiler-generated temporaries; op stands for any
operator, such as a fixed- or floating-point arithmetic operator, or a logical operator on boolean-
valued data. Thus a source language expression like x+ y*z might be translated into a sequence
t1 : = y * z
t2 : = x + t1
where t1 and t2 are compiler-generated temporary names.
assign
id a
+
* *
id b id b
uminus uminus
id c id c
id b
id c
uminus 1
* 0 2
id b
id c
uminus 5
* 4 6
+ 3 7
id a
assign 9 8

Advantages of three-address code:
 The unraveling of complicated arithmetic expressions and of nested flow-of-control
statements makes three-address code desirable for target code generation and
optimization.
 The use of names for the intermediate values computed by a program allows three-
address code to be easily rearranged – unlike postfix notation.
Three-address code is a linearized representation of a syntax tree or a dag in which
explicit names correspond to the interior nodes of the graph. The syntax tree and dag are
represented by the three-address code sequences. Variable names can appear directly in three-
address statements.
Three-address code corresponding to the syntax tree and dag given above
t1 : = - c t1 : = -c
t2 : = b * t1 t2 : = b * t1
t3 : = - c t5 : = t2 + t2
t4 : = b * t3 a : = t5
t5 : = t2 + t4
a : = t5
(a) Code for the syntax tree (b) Code for the dag
The reason for the term “three-address code” is that each statement usually contains three
addresses, two for the operands and one for the result.
Types of Three-Address Statements:
The common three-address statements are:
1. Assignment statements of the form x : = y op z, where op is a binary arithmetic or logical
operation.
2. Assignment instructions of the form x : = op y, where op is a unary operation. Essential unary
operations include unary minus, logical negation, shift operators, and conversion operators
that, for example, convert a fixed-point number to a floating-point number.
3. Copy statements of the form x : = y where the value of y is assigned to x.
4. The unconditional jump goto L. The three-address statement with label L is the next to be
executed.
5. Conditional jumps such as if x relop y goto L. This instruction applies a relational operator (
<, =, >=, etc. ) to x and y, and executes the statement with label L next if x stands in relation

relop to y. If not, the three-address statement following if x relop y goto L is executed next,
as in the usual sequence.
6. param x and call p, n for procedure calls and return y, where y representing a returned value
is optional. For example,
param x1
param x2
. . .
param xn
call p,n
generated as part of a call of the procedure p(x1, x2, …. ,xn ).
7. Indexed assignments of the form x : = y[i] and x[i] : = y.
8. Address and pointer assignments of the form x : = &y , x : = *y, and *x : = y.
Syntax-Directed Translation into Three-Address Code:
When three-address code is generated, temporary names are made up for the interior
nodes of a syntax tree. For example, id : = E consists of code to evaluate E into some temporary
t, followed by the assignment id.place : = t.
Given input a : = b * - c + b * - c, the three-address code is as shown above. The
synthesized attribute S.code represents the three-address code for the assignment S.
The nonterminal E has two attributes :
1. E.place, the name that will hold the value of E , and
2. E.code, the sequence of three-address statements evaluating E.
Syntax-directed definition to produce three-address code for assignments
PRODUCTION SEMANTIC RULES
S  id : = E S.code : = E.code || gen(id.place ‘:=’ E.place)
E  E1 + E2 E.place := newtemp;
E.code := E1.code || E2.code || gen(E.place ‘:=’ E1.place ‘+’ E2.place)
E  E1 * E2 E.place := newtemp;
E.code := E1.code || E2.code || gen(E.place ‘:=’ E1.place ‘*’ E2.place)
E  - E1 E.place := newtemp;
E.code := E1.code || gen(E.place ‘:=’ ‘uminus’ E1.place)
E  ( E1 ) E.place : = E1.place;
E.code : = E1.code
E  id E.place : = id.place;
E.code : = ‘ ‘

Semantic rules generating code for a while statement
S.begin:
E.code
if E.place = 0 goto S.after
S1.code
goto S.begin
S.after: . . .
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 ‘:’)
 The function newtemp returns a sequence of distinct names t1,t2,….. in response to
successive calls.
 Notation gen(x ‘:=’ y ‘+’ z) is used to represent three-address statement x := y + z.
Expressions appearing instead of variables like x, y and z are evaluated when passed to
gen, and quoted operators or operand, like ‘+’ are taken literally.
 Flow-of–control statements can be added to the language of assignments. The code for S
 while E do S1 is generated using new attributes S.begin and S.after to mark the first
statement in the code for E and the statement following the code for S, respectively.
 The function newlabel returns a new label every time it is called.
 We assume that a non-zero expression represents true; that is when the value of E
becomes zero, control leaves the while statement.
Implementation of Three-Address Statements:
A three-address statement is an abstract form of intermediate code. In a compiler,
these statements can be implemented as records with fields for the operator and the operands.
Three such representations are:

 Quadruples
 Triples
 Indirect triples
Quadruples:
 A quadruple is a record structure with four fields, which are, op, arg1, arg2 and result.
 The op field contains an internal code for the operator. The three-address statement x : =
y op z is represented by placing y in arg1, z in arg2 and x in result.
 The contents of fields arg1, arg2 and result are normally pointers to the symbol-table
entries for the names represented by these fields. If so, temporary names must be entered
into the symbol table as they are created.
Triples:
 To avoid entering temporary names into the symbol table, we might refer to a temporary
value by the position of the statement that computes it.
 If we do so, three-address statements can be represented by records with only three fields:
op, arg1 and arg2.
 The fields arg1 and arg2, for the arguments of op, are either pointers to the symbol table
or pointers into the triple structure ( for temporary values ).
 Since three fields are used, this intermediate code format is known as triples.
op arg1 arg2 result op arg1 arg2
(0) uminus c t1 (0) uminus c
(1) * b t1 t2 (1) * b (0)
(2) uminus c t3 (2) uminus c
(3) * b t3 t4 (3) * b (2)
(4) + t2 t4 t5 (4) + (1) (3)
(5) : = t3 a (5) assign a (4)
(a) Quadruples (b) Triples
Quadruple and triple representation of three-address statements given above

A ternary operation like x[i] : = y requires two entries in the triple structure as shown as below
while x : = y[i] is naturally represented as two operations.
op arg1 arg2 op arg1 arg2
(0) [ ] = x i (0) = [ ] y i
(1) assign (0) y (1) assign x (0)
(a) x[i] : = y (b) x : = y[i]
Indirect Triples:
 Another implementation of three-address code is that of listing pointers to triples, rather
than listing the triples themselves. This implementation is called indirect triples.
 For example, let us use an array statement to list pointers to triples in the desired order.
Then the triples shown above might be represented as follows:
statement op arg1 arg2
(0) (14) (14) uminus c
(1) (15) (15) * b (14)
(2) (16) (16) uminus c
(3) (17) (17) * b (16)
(4) (18) (18) + (15) (17)
(5) (19) (19) assign a (18)
Indirect triples representation of three-address statements
DECLARATIONS
As the sequence of declarations in a procedure or block is examined, we can lay out
storage for names local to the procedure. For each local name, we create a symbol-table entry
with information like the type and the relative address of the storage for the name. The relative
address consists of an offset from the base of the static data area or the field for local data in an
activation record.

Declarations in a Procedure:
The syntax of languages such as C, Pascal and Fortran, allows all the declarations in a
single procedure to be processed as a group. In this case, a global variable, say offset, can keep
track of the next available relative address.
In the translation scheme shown below:
 Nonterminal P generates a sequence of declarations of the form id : T.
 Before the first declaration is considered, offset is set to 0. As each new name is seen ,
that name is entered in the symbol table with offset equal to the current value of offset,
and offset is incremented by the width of the data object denoted by that name.
 The procedure enter( name, type, offset ) creates a symbol-table entry for name, gives its
type type and relative address offset in its data area.
 Attribute type represents a type expression constructed from the basic types integer and
real by applying the type constructors pointer and array. If type expressions are
represented by graphs, then attribute type might be a pointer to the node representing a
type expression.
 The width of an array is obtained by multiplying the width of each element by the
number of elements in the array. The width of each pointer is assumed to be 4.
Computing the types and relative addresses of declared names
P  D { offset : = 0 }
D  D ; D
D  id : T { enter(id.name, T.type, offset);
offset : = offset + T.width }
T  integer { T.type : = integer;
T.width : = 4 }
T  real { T.type : = real;
T.width : = 8 }
T  array [ num ] of T1 { T.type : = array(num.val, T1.type);
T.width : = num.val X T1.width }
T  ↑ T1 { T.type : = pointer ( T1.type);
T.width : = 4 }

Keeping Track of Scope Information:
When a nested procedure is seen, processing of declarations in the enclosing procedure is
temporarily suspended. This approach will be illustrated by adding semantic rules to the
following language:
P  D
D  D ; D | id : T | proc id ; D ; S
One possible implementation of a symbol table is a linked list of entries for names.
A new symbol table is created when a procedure declaration D  proc id D1;S is seen,
and entries for the declarations in D1 are created in the new table. The new table points back to
the symbol table of the enclosing procedure; the name represented by id itself is local to the
enclosing procedure. The only change from the treatment of variable declarations is that the
procedure enter is told which symbol table to make an entry in.
For example, consider the symbol tables for procedures readarray, exchange, and
quicksort pointing back to that for the containing procedure sort, consisting of the entire
program. Since partition is declared within quicksort, its table points to that of quicksort.
Symbol tables for nested procedures
sort
to readarray
to exchange
readarray exchange quicksort
partition
header header
i
header
a
x
readarray
exchange
quicksort
nil header
i k
v
partition
header
j

The semantic rules are defined in terms of the following operations:
1. mktable(previous) creates a new symbol table and returns a pointer to the new table. The
argument previous points to a previously created symbol table, presumably that for the
enclosing procedure.
2. enter(table, name, type, offset) creates a new entry for name name in the symbol table pointed
to by table. Again, enter places type type and relative address offset in fields within the entry.
3. addwidth(table, width) records the cumulative width of all the entries in table in the header
associated with this symbol table.
4. enterproc(table, name, newtable) creates a new entry for procedure name in the symbol table
pointed to by table. The argument newtable points to the symbol table for this procedure
name.
Syntax directed translation scheme for nested procedures
P  M D { addwidth ( top( tblptr) , top (offset));
pop (tblptr); pop (offset) }
M  ɛ { t : = mktable (nil);
push (t,tblptr); push (0,offset) }
D  D1 ; D2
D  proc id ; N D1 ; S { t : = top (tblptr);
addwidth ( t, top (offset));
pop (tblptr); pop (offset);
enterproc (top (tblptr), id.name, t) }
D  id : T { enter (top (tblptr), id.name, T.type, top (offset));
top (offset) := top (offset) + T.width }
N  ɛ { t := mktable (top (tblptr));
push (t, tblptr); push (0,offset) }
 The stack tblptr is used to contain pointers to the tables for sort, quicksort, and partition
when the declarations in partition are considered.
 The top element of stack offset is the next available relative address for a local of the
current procedure.
 All semantic actions in the subtrees for B and C in
A  BC {actionA}
are done before actionA at the end of the production occurs. Hence, the action associated
with the marker M is the first to be done.

 The action for nonterminal M initializes stack tblptr with a symbol table for the
outermost scope, created by operation mktable(nil). The action also pushes relative
address 0 onto stack offset.
 Similarly, the nonterminal N uses the operation mktable(top(tblptr)) to create a new
symbol table. The argument top(tblptr) gives the enclosing scope for the new table.
 For each variable declaration id: T, an entry is created for id in the current symbol table.
The top of stack offset is incremented by T.width.
 When the action on the right side of D  proc id; ND1; S occurs, the width of all
declarations generated by D1 is on the top of stack offset; it is recorded using addwidth.
Stacks tblptr and offset are then popped.
At this point, the name of the enclosed procedure is entered into the symbol table of its
enclosing procedure.
ASSIGNMENT STATEMENTS
Suppose that the context in which an assignment appears is given by the following grammar.
P  M D
M  ɛ
D  D ; D | id : T | proc id ; N D ; S
N  ɛ
Nonterminal P becomes the new start symbol when these productions are added to those in the
translation scheme shown below.
Translation scheme to produce three-address code for assignments
S  id : = E { p : = lookup ( id.name);
if p ≠ nil then
emit( p ‘ : =’ E.place)
else error }
E  E1 + E2 { E.place : = newtemp;
emit( E.place ‘: =’ E1.place ‘ + ‘ E2.place ) }
E  E1 * E2 { E.place : = newtemp;
emit( E.place ‘: =’ E1.place ‘ * ‘ E2.place ) }
E  - E1 { E.place : = newtemp;
emit ( E.place ‘: =’ ‘uminus’ E1.place ) }
E  ( E1 ) { E.place : = E1.place }

E  id { p : = lookup ( id.name);
if p ≠ nil then
E.place : = p
else error }
Reusing Temporary Names
 The temporaries used to hold intermediate values in expression calculations tend to
clutter up the symbol table, and space has to be allocated to hold their values.
 Temporaries can be reused by changing newtemp. The code generated by the rules for E
 E1 + E2 has the general form:
evaluate E1 into t1
evaluate E2 into t2
t : = t1 + t2
 The lifetimes of these temporaries are nested like matching pairs of balanced parentheses.
 Keep a count c , initialized to zero. Whenever a temporary name is used as an operand,
decrement c by 1. Whenever a new temporary name is generated, use $c and increase c
by 1.
 For example, consider the assignment x := a * b + c * d – e * f
Three-address code with stack temporaries
statement value of c
0
$0 := a * b 1
$1 := c * d 2
$0 := $0 + $1 1
$1 := e * f 2
$0 := $0 - $1 1
x := $0 0
Addressing Array Elements:
Elements of an array can be accessed quickly if the elements are stored in a block of
consecutive locations. If the width of each array element is w, then the ith element of array A
begins in location
base + ( i – low ) x w
where low is the lower bound on the subscript and base is the relative address of the storage
allocated for the array. That is, base is the relative address of A[low].

The expression can be partially evaluated at compile time if it is rewritten as
i x w + ( base – low x w)
The subexpression c = base – low x w can be evaluated when the declaration of the array is seen.
We assume that c is saved in the symbol table entry for A , so the relative address of A[i] is
obtained by simply adding i x w to c.
Address calculation of multi-dimensional arrays:
A two-dimensional array is stored in of the two forms :
 Row-major (row-by-row)
 Column-major (column-by-column)
Layouts for a 2 x 3 array
first column
first row
second column
second row
third column
(a) ROW-MAJOR (b) COLUMN-MAJOR
In the case of row-major form, the relative address of A[ i1 , i2] can be calculated by the formula
base + ((i1 – low1) x n2 + i2 – low2) x w
where, low1 and low2 are the lower bounds on the values of i1 and i2 and n2 is the number of
values that i2 can take. That is, if high2 is the upper bound on the value of i2, then n2 = high2 –
low2 + 1.
Assuming that i1 and i2 are the only values that are known at compile time, we can rewrite the
above expression as
(( i1 x n2 ) + i2 ) x w + ( base – (( low1 x n2 ) + low2 ) x w)
Generalized formula:
The expression generalizes to the following expression for the relative address of A[i1,i2,…,ik]
(( . . . (( i1n2 + i2 ) n3 + i3) . . . ) nk + ik ) x w + base – (( . . .((low1n2 + low2)n3 + low3) . . .)
nk + lowk) x w
for all j, nj = highj – lowj + 1
A[ 1,1 ]
A[ 1,2 ]
A[ 1,3 ]
A[ 2,1 ]
A[ 2,2 ]
A[ 2,3 ]
A [ 1,1 ]
A [ 2,1 ]
A [ 1,2 ]
A [ 2,2 ]
A [ 1,3 ]
A [ 2,3 ]

The Translation Scheme for Addressing Array Elements :
Semantic actions will be added to the grammar :
(1) S  L : = E
(2) E  E + E
(3) E  ( E )
(4) E  L
(5) L  Elist ]
(6) L  id
(7) Elist  Elist , E
(8) Elist  id [ E
We generate a normal assignment if L is a simple name, and an indexed assignment into the
location denoted by L otherwise :
(1) S  L : = E { if L.offset = null then / * L is a simple id */
emit ( L.place ‘: =’ E.place ) ;
else
emit ( L.place ‘ [‘ L.offset ‘ ]’ ‘: =’ E.place) }
(2) E  E1 + E2 { E.place : = newtemp;
emit ( E.place ‘: =’ E1.place ‘ +’ E2.place ) }
(3) E  ( E1 ) { E.place : = E1.place }
When an array reference L is reduced to E , we want the r-value of L. Therefore we use indexing
to obtain the contents of the location L.place [ L.offset ] :
(4) E  L { if L.offset = null then /* L is a simple id* /
E.place : = L.place
else begin
E.place : = newtemp;
emit ( E.place ‘: =’ L.place ‘ [‘ L.offset ‘]’)
end }
(5) L  Elist ] { L.place : = newtemp;
L.offset : = newtemp;
emit (L.place ‘: =’ c( Elist.array ));
emit (L.offset ‘: =’ Elist.place ‘*’ width (Elist.array)) }
(6) L  id { L.place := id.place;
L.offset := null }
(7) Elist  Elist1 , E { t := newtemp;
m : = Elist1.ndim + 1;
emit ( t ‘: =’ Elist1.place ‘*’ limit (Elist1.array,m));
emit ( t ‘: =’ t ‘+’ E.place);
Elist.array : = Elist1.array;

Elist.place : = t;
Elist.ndim : = m }
(8) Elist  id [ E { Elist.array : = id.place;
Elist.place : = E.place;
Elist.ndim : = 1 }
Type conversion within Assignments :
Consider the grammar for assignment statements as above, but suppose there are two
types – real and integer , with integers converted to reals when necessary. We have another
attribute E.type, whose value is either real or integer. The semantic rule for E.type associated
with the production E  E + E is :
E  E + E { E.type : =
if E1.type = integer and
E2.type = integer then integer
else real }
The entire semantic rule for E  E + E and most of the other productions must be
modified to generate, when necessary, three-address statements of the form x : = inttoreal y,
whose effect is to convert integer y to a real of equal value, called x.
Semantic action for E  E1 + E2
E.place := newtemp;
if E1.type = integer and E2.type = integer then begin
emit( E.place ‘: =’ E1.place ‘int +’ E2.place);
E.type : = integer
end
else if E1.type = real and E2.type = real then begin
emit( E.place ‘: =’ E1.place ‘real +’ E2.place);
E.type : = real
end
else if E1.type = integer and E2.type = real then begin
u : = newtemp;
emit( u ‘: =’ ‘inttoreal’ E1.place);
emit( E.place ‘: =’ u ‘ real +’ E2.place);
E.type : = real
end
else if E1.type = real and E2.type =integer then begin
u : = newtemp;
emit( u ‘: =’ ‘inttoreal’ E2.place);
emit( E.place ‘: =’ E1.place ‘ real +’ u);
E.type : = real
end
else
E.type : = type_error;

For example, for the input x : = y + i * j
assuming x and y have type real, and i and j have type integer, the output would look like
t1 : = i int* j
t3 : = inttoreal t1
t2 : = y real+ t3
x : = t2
BOOLEAN EXPRESSIONS
Boolean expressions have two primary purposes. They are used to compute logical
values, but more often they are used as conditional expressions in statements that alter the flow
of control, such as if-then-else, or while-do statements.
Boolean expressions are composed of the boolean operators ( and, or, and not ) applied
to elements that are boolean variables or relational expressions. Relational expressions are of the
form E1 relop E2, where E1 and E2 are arithmetic expressions.
Here we consider boolean expressions generated by the following grammar :
E  E or E | E and E | not E | ( E ) | id relop id | true | false
Methods of Translating Boolean Expressions:
There are two principal methods of representing the value of a boolean expression. They are :
 To encode true and false numerically and to evaluate a boolean expression analogously
to an arithmetic expression. Often, 1 is used to denote true and 0 to denote false.
 To implement boolean expressions by flow of control, that is, representing the value of a
boolean expression by a position reached in a program. This method is particularly
convenient in implementing the boolean expressions in flow-of-control statements, such
as the if-then and while-do statements.
Numerical Representation
Here, 1 denotes true and 0 denotes false. Expressions will be evaluated completely from
left to right, in a manner similar to arithmetic expressions.
For example :
 The translation for
a or b and not c
is the three-address sequence
t1 : = not c
t2 : = b and t1
t3 : = a or t2
 A relational expression such as a < b is equivalent to the conditional statement
if a < b then 1 else 0

which can be translated into the three-address code sequence (again, we arbitrarily start
statement numbers at 100) :
100 : if a < b goto 103
101 : t : = 0
102 : goto 104
103 : t : = 1
104 :
Translation scheme using a numerical representation for booleans
E  E1 or E2 { E.place : = newtemp;
emit( E.place ‘: =’ E1.place ‘or’ E2.place ) }
E  E1 and E2 { E.place : = newtemp;
emit( E.place ‘: =’ E1.place ‘and’ E2.place ) }
E  not E1 { E.place : = newtemp;
emit( E.place ‘: =’ ‘not’ E1.place ) }
E  ( E1 ) { E.place : = E1.place }
E  id1 relop id2 { E.place : = newtemp;
emit( ‘if’ id1.place relop.op id2.place ‘goto’ nextstat + 3);
emit( E.place ‘: =’ ‘0’ );
emit(‘goto’ nextstat +2);
emit( E.place ‘: =’ ‘1’) }
E  true { E.place : = newtemp;
emit( E.place ‘: =’ ‘1’) }
E false { E.place : = newtemp;
emit( E.place ‘: =’ ‘0’) }
Short-Circuit Code:
We can also translate a boolean expression into three-address code without generating
code for any of the boolean operators and without having the code necessarily evaluate the entire
expression. This style of evaluation is sometimes called “short-circuit” or “jumping” code. It is
possible to evaluate boolean expressions without generating code for the boolean operators and,
or, and not if we represent the value of an expression by a position in the code sequence.
Translation of a < b or c < d and e < f
100 : if a < b goto 103 107 : t2 : = 1
101 : t1 : = 0 108 : if e < f goto 111
102 : goto 104 109 : t3 : = 0
103 : t1 : = 1 110 : goto 112
104 : if c < d goto 107 111 : t3 : = 1
105 : t2 : = 0 112 : t4 : = t2 and t3
106 : goto 108 113 : t5 : = t1 or t4

Flow-of-Control Statements
We now consider the translation of boolean expressions into three-address code in the
context of if-then, if-then-else, and while-do statements such as those generated by the following
grammar:
S  if E then S1
| if E then S1 else S2
| while E do S1
In each of these productions, E is the Boolean expression to be translated. In the translation, we
assume that a three-address statement can be symbolically labeled, and that the function
newlabel returns a new symbolic label each time it is called.
 E.true is the label to which control flows if E is true, and E.false is the label to which
control flows if E is false.
 The semantic rules for translating a flow-of-control statement S allow control to flow
from the translation S.code to the three-address instruction immediately following
S.code.
 S.next is a label that is attached to the first three-address instruction to be executed after
the code for S.
Code for if-then , if-then-else, and while-do statements
to E.true
to E.false
to E.true E.true:
E.true : to E.false
E.false:
E.false : . . .
S.next: . . .
(a) if-then (b) if-then-else
S.begin: to E.true
to E.false
E.true:
E.false: . . .
(c) while-do
E.code
S1.code
E.code
S1.code
goto S.next
S2.code
E.code
S1.code
goto S.begin

Syntax-directed definition for flow-of-control statements
S  if E then S1 E.true : = newlabel;
E.false : = S.next;
S1.next : = S.next;
S.code : = E.code || gen(E.true ‘:’) || S1.code
S  if E then S1 else S2 E.true : = newlabel;
E.false : = newlabel;
S1.next : = S.next;
S2.next : = S.next;
S.code : = E.code || gen(E.true ‘:’) || S1.code ||
gen(‘goto’ S.next) ||
gen( E.false ‘:’) || S2.code
S  while E do S1 S.begin : = newlabel;
E.true : = newlabel;
E.false : = S.next;
S1.next : = S.begin;
S.code : = gen(S.begin ‘:’)|| E.code ||
gen(E.true ‘:’) || S1.code ||
gen(‘goto’ S.begin)
Control-Flow Translation of Boolean Expressions:
Syntax-directed definition to produce three-address code for booleans
E  E1 or E2 E1.true : = E.true;
E1.false : = newlabel;
E2.true : = E.true;
E2.false : = E.false;
E.code : = E1.code || gen(E1.false ‘:’) || E2.code
E  E1 and E2 E.true : = newlabel;
E2.true : = E.true;
E.code : = E1.code || gen(E1.true ‘:’) || E2.code
E  not E1 E1.true : = E.false;
E1.false : = E.true;
E.code : = E1.code
E  ( E1 ) E1.true : = E.true;

E.code : = E1.code
E  id1 relop id2 E.code : = gen(‘if’ id1.place relop.op id2.place
‘goto’ E.true) || gen(‘goto’ E.false)
E  true E.code : = gen(‘goto’ E.true)
E  false E.code : = gen(‘goto’ E.false)
CASE STATEMENTS
The “switch” or “case” statement is available in a variety of languages. The switch-statement
syntax is as shown below :
Switch-statement syntax
switch expression
begin
case value : statement
. . .
default : statement
end
There is a selector expression, which is to be evaluated, followed by n constant values
that the expression might take, including a default “value” which always matches the expression
if no other value does. The intended translation of a switch is code to:
1. Evaluate the expression.
2. Find which value in the list of cases is the same as the value of the expression.
3. Execute the statement associated with the value found.
Step (2) can be implemented in one of several ways :
 By a sequence of conditional goto statements, if the number of cases is small.
 By creating a table of pairs, with each pair consisting of a value and a label for the code
of the corresponding statement. Compiler generates a loop to compare the value of the
expression with each value in the table. If no match is found, the default (last) entry is
sure to match.
 If the number of cases s large, it is efficient to construct a hash table.
 There is a common special case in which an efficient implementation of the n-way branch
exists. If the values all lie in some small range, say imin to imax, and the number of
different values is a reasonable fraction of imax - imin, then we can construct an array of
labels, with the label of the statement for value j in the entry of the table with offset j -
imin and the label for the default in entries not filled otherwise. To perform switch,

evaluate the expression to obtain the value of j , check the value is within range and
transfer to the table entry at offset j-imin .
Syntax-Directed Translation of Case Statements:
Consider the following switch statement:
switch E
begin
case V1 : S1
case V2 : S2
. . .
case Vn-1 : Sn-1
default : Sn
end
This case statement is translated into intermediate code that has the following form :
Translation of a case statement
code to evaluate E into t
goto test
L1 : code for S1
goto next
L2 : code for S2
goto next
. . .
Ln-1 : code for Sn-1
goto next
Ln : code for Sn
goto next
test : if t = V1 goto L1
if t = V2 goto L2
. . .
if t = Vn-1 goto Ln-1
goto Ln
next :
To translate into above form :
 When keyword switch is seen, two new labels test and next, and a new temporary t are
generated.
 As expression E is parsed, the code to evaluate E into t is generated. After processing E ,
the jump goto test is generated.
 As each case keyword occurs, a new label Li is created and entered into the symbol table.
A pointer to this symbol-table entry and the value Vi of case constant are placed on a
stack (used only to store cases).

 Each statement case Vi : Si is processed by emitting the newly created label Li, followed
by the code for Si , followed by the jump goto next.
 Then when the keyword end terminating the body of the switch is found, the code can be
generated for the n-way branch. Reading the pointer-value pairs on the case stack from
the bottom to the top, we can generate a sequence of three-address statements of the form
case V1 L1
case V2 L2
. . .
case Vn-1 Ln-1
case t Ln
label next
where t is the name holding the value of the selector expression E, and Ln is the label for
the default statement.
BACKPATCHING
The easiest way to implement the syntax-directed definitions for boolean expressions is
to use two passes. First, construct a syntax tree for the input, and then walk the tree in depth-first
order, computing the translations. The main problem with generating code for boolean
expressions and flow-of-control statements in a single pass is that during one single pass we may
not know the labels that control must go to at the time the jump statements are generated. Hence,
a series of branching statements with the targets of the jumps left unspecified is generated. Each
statement will be put on a list of goto statements whose labels will be filled in when the proper
label can be determined. We call this subsequent filling in of labels backpatching.
To manipulate lists of labels, we use three functions :
1. makelist(i) creates a new list containing only i, an index into the array of quadruples;
makelist returns a pointer to the list it has made.
2. merge(p1,p2) concatenates the lists pointed to by p1 and p2, and returns a pointer to the
concatenated list.
3. backpatch(p,i) inserts i as the target label for each of the statements on the list pointed to
by p.
Boolean Expressions:
We now construct a translation scheme suitable for producing quadruples for boolean
expressions during bottom-up parsing. The grammar we use is the following:
(1) E  E1 or M E2
(2) | E1 and M E2
(3) | not E1
(4) | ( E1)
(5) | id1 relop id2
(6) | true
(7) | false
(8) M  ɛ

Synthesized attributes truelist and falselist of nonterminal E are used to generate jumping code
for boolean expressions. Incomplete jumps with unfilled labels are placed on lists pointed to by
E.truelist and E.falselist.
Consider production E  E1 and M E2. If E1 is false, then E is also false, so the statements on
E1.falselist become part of E.falselist. If E1 is true, then we must next test E2, so the target for the
statements E1.truelist must be the beginning of the code generated for E2. This target is obtained
using marker nonterminal M.
Attribute M.quad records the number of the first statement of E2.code. With the production M 
ɛ we associate the semantic action
{ M.quad : = nextquad }
The variable nextquad holds the index of the next quadruple to follow. This value will be
backpatched onto the E1.truelist when we have seen the remainder of the production E  E1 and
M E2. The translation scheme is as follows:
(1) E  E1 or M E2 { backpatch ( E1.falselist, M.quad);
E.truelist : = merge( E1.truelist, E2.truelist);
E.falselist : = E2.falselist }
(2) E  E1 and M E2 { backpatch ( E1.truelist, M.quad);
E.truelist : = E2.truelist;
E.falselist : = merge(E1.falselist, E2.falselist) }
(3) E  not E1 { E.truelist : = E1.falselist;
E.falselist : = E1.truelist; }
(4) E  ( E1 ) { E.truelist : = E1.truelist;
E.falselist : = E1.falselist; }
(5) E  id1 relop id2 { E.truelist : = makelist (nextquad);
E.falselist : = makelist(nextquad + 1);
emit(‘if’ id1.place relop.op id2.place ‘goto_’)
emit(‘goto_’) }
(6) E  true { E.truelist : = makelist(nextquad);
emit(‘goto_’) }
(7) E  false { E.falselist : = makelist(nextquad);
emit(‘goto_’) }
(8) M  ɛ { M.quad : = nextquad }

Flow-of-Control Statements:
A translation scheme is developed for statements generated by the following grammar :
(1) S  if E then S
(2) | if E then S else S
(3) | while E do S
(4) | begin L end
(5) | A
(6) L  L ; S
(7) | S
Here S denotes a statement, L a statement list, A an assignment statement, and E a boolean
expression. We make the tacit assumption that the code that follows a given statement in
execution also follows it physically in the quadruple array. Else, an explicit jump must be
provided.
Scheme to implement the Translation:
The nonterminal E has two attributes E.truelist and E.falselist. L and S also need a list of
unfilled quadruples that must eventually be completed by backpatching. These lists are pointed
to by the attributes L..nextlist and S.nextlist. S.nextlist is a pointer to a list of all conditional and
unconditional jumps to the quadruple following the statement S in execution order, and L.nextlist
is defined similarly.
The semantic rules for the revised grammar are as follows:
(1) S  if E then M1 S1 N else M2 S2
{ backpatch (E.truelist, M1.quad);
backpatch (E.falselist, M2.quad);
S.nextlist : = merge (S1.nextlist, merge (N.nextlist, S2.nextlist)) }
We backpatch the jumps when E is true to the quadruple M1.quad, which is the beginning of the
code for S1. Similarly, we backpatch jumps when E is false to go to the beginning of the code for
S2. The list S.nextlist includes all jumps out of S1 and S2, as well as the jump generated by N.
(2) N  ɛ { N.nextlist : = makelist( nextquad );
emit(‘goto _’) }
(3) M  ɛ { M.quad : = nextquad }
(4) S  if E then M S1 { backpatch( E.truelist, M.quad);
S.nextlist : = merge( E.falselist, S1.nextlist) }
(5) S  while M1 E do M2 S1 { backpatch( S1.nextlist, M1.quad);
backpatch( E.truelist, M2.quad);
S.nextlist : = E.falselist
emit( ‘goto’ M1.quad ) }
(6) S  begin L end { S.nextlist : = L.nextlist }

(7) S  A { S.nextlist : = nil }
The assignment S.nextlist : = nil initializes S.nextlist to an empty list.
(8) L  L1 ; M S { backpatch( L1.nextlist, M.quad);
L.nextlist : = S.nextlist }
The statement following L1 in order of execution is the beginning of S. Thus the L1.nextlist list is
backpatched to the beginning of the code for S, which is given by M.quad.
(9) L  S { L.nextlist : = S.nextlist }
PROCEDURE CALLS
The procedure is such an important and frequently used programming construct that it is
imperative for a compiler to generate good code for procedure calls and returns. The run-time
routines that handle procedure argument passing, calls and returns are part of the run-time
support package.
Let us consider a grammar for a simple procedure call statement
(1) S  call id ( Elist )
(3) Elist  E
Calling Sequences:
The translation for a call includes a calling sequence, a sequence of actions taken on entry
to and exit from each procedure. The falling are the actions that take place in a calling sequence :
 When a procedure call occurs, space must be allocated for the activation record of the
called procedure.
 The arguments of the called procedure must be evaluated and made available to the called
procedure in a known place.
 Environment pointers must be established to enable the called procedure to access data in
enclosing blocks.
 The state of the calling procedure must be saved so it can resume execution after the call.
 Also saved in a known place is the return address, the location to which the called
routine must transfer after it is finished.
 Finally a jump to the beginning of the code for the called procedure must be generated.
For example, consider the following syntax-directed translation
(1) S  call id ( Elist )
{ for each item p on queue do
emit (‘ param’ p );

emit (‘call’ id.place) }
{ append E.place to the end of queue }
(3) Elist  E
{ initialize queue to contain only E.place }
 Here, the code for S is the code for Elist, which evaluates the arguments, followed by a
param p statement for each argument, followed by a call statement.
 queue is emptied and then gets a single pointer to the symbol table location for the name
that denotes the value of E.

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