1

Structure of a Compiler

• Front end of a compiler is efficient and can be automated

• Back end is generally hard to automate and finding the optimum solution requires exponential time

• Intermediate code generation can effect the performance of the back end

InstructionSelection

InstructionScheduling

RegisterAllocation

Scanner ParserSemantic Analysis

Code Optimization

IntermediateCode

GenerationIR

2

Intermediate Representations

• Abstract Syntax Trees (AST)

• Directed Acyclic Graphs (DAG)

• Control Flow Graphs (CFG)

• Static Single Assignment Form (SSA)

• Stack Machine Code

• Three Address Code

• Hybrid approaches mix graphical and linear representations

– SGI and SUN compilers use three address code but provide ASTs for loops if-statements and array references

– Use three-address code in basic blocks in control flow graphs

high-level

low-level

Graphical IRs

Linear IRs

3

Abstract Syntax Trees (ASTs)

if (x < y)

x = 5*y + 5*y/3;

else

y = 5;

x = x+y;

Statements

<

AssignStmt

+

*

x

IfStmt

AssignStmt AssignStmt

x x y+ yxy

/

5 y 3*

5 y

5

4

Directed Acyclic Graphs (DAGs)

• Use directed acyclic graphs to represent expressions

– Use a unique node for each expression

if (x < y)

x = 5*y + 5*y/3;

else

y = 5;

x = x+y;

Statements

<

AssignStmt

*

IfStmt

AssignStmt AssignStmt

x +y

/

5

3

5

Control Flow Graphs (CFGs)

• Nodes in the control flow graph are basic blocks

– A basic block is a sequence of statements always entered at the beginning of the block and exited at the end

• Edges in the control flow graph represent the control flow

if (x < y)

x = 5*y + 5*y/3;

else

y = 5;

x = x+y;

if (x < y) goto B1 else goto B2

x = 5*y + 5*y/3 y = 5

x = x+y

B1 B2

B0

B3

• Each block has a sequence of statements• No jump from or to the middle of the block• Once a block starts executing, it will execute till the end

6

Stack Machine Code if (x < y)

x = 5*y + 5*y/3;

else

y = 5;

x = x+y;

load x load y iflt L1 goto L2L1: push 5 load y multiply push 5 load y multiply push 3 divide add store x goto L3L2: push 5 store yL3: load x load y add store x

pops the toptwo elements andcompares them

pops the top two elements, multipliesthem, and pushes theresult back to the stack

pushes the valueat the location x to the stack

stores the value at the top of the stack to the location x

7

Three-Address Code

• Each instruction can have at most three operands

• Assignments– x := y– x := y op z op: binary arithmetic or logical operators– x := op y op: unary operators (minus, negation, integer to

float conversion)• Branch

– goto L Execute the statement with labeled L next

• Conditional Branch– if x relop y goto L relop: <, =, <=, >=, ==, !=

• if the condition holds we execute statement labeled L next• if the condition does not hold we execute the statement following

this statement next

Data structures for three address codes

• Quadruples

– Has four fields: op, arg1, arg2 and result

• Triples

– Temporaries are not used and instead references to instructions are made

• Indirect triples

– In addition to triples we use a list of pointers to triples

Quadruples

• A record structure with 4 fields

– op, arg1, arg2 and result

• Examples

– For x := y op z we have:

• y in arg1, z in arg2 and x in result

– For unary operators, arg2 not used

• Content of fields are pointers to ST entries

Triples

• Temps generated in quadruples must be entered in symbol table

• To avoid this, we can refer to a temp value by the location of the relevant statement

– We can have records with only 3 fields

• op, arg1 and arg2

– Fields arg1 and arg2 can be pointers to ST entries or to triple structure for temp values

Indirect Triples

• Listing of pointers to triples, rather than triples themselves

• Example

– We can use an array to list pointers to triples in the desired order

Example

• b * minus c + b * minus c

t1 = minus ct2 = b * t1t3 = minus ct4 = b * t3t5 = t2 + t4a = t5

Three address code

minus*

minus c t3*+=

c t1b t2t1

b t4t3t2 t5t4t5 a

arg1 resultarg2op

Quadruples

minus*

minus c*+=

cb (0)

b (2)(1) (3)a

arg1 arg2op

Triples

(4)

012345

minus*

minus c*+=

cb (0)

b (2)(1) (3)a

arg1 arg2op

Indirect Triples

(4)

012345

(0)(1)

(2)(3)(4)(5)

op353637383940

Examples

1. X=(a+b)*-c/d

13

14

Three-Address Code Generation for a Simple Grammar

Productions Semantic RulesS id := E id.place lookup(id.name);

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.code E1.code;

E.place E1.place;E E1 E.place newtemp();

E.code E1.code || gen(E.place ‘:=‘ ‘uminus’ E1.place);E id E.place lookup(id.name);

E.code ‘’ (empty string)

Attributes: E.place: location that holds the value of expression EE.code: sequence of instructions that are generated for E

Procedures: newtemp(): Returns a new temporary each time it is calledgen(): Generates instruction (have to call it with appropriate arguments)lookup(id.name): Returns the location of id from the symbol table

15

Stack Machine Code Generation for a Simple Grammar

Productions Semantic RulesS id := E id.place lookup(id.name);

S.code E.code || gen(‘store’ id.place);E E1 + E2 E.code E1.code || E2.code || gen(‘add’);

(arguments for the add instruction are in the top of the stack)E E1 * E2 E.code E1.code || E2.code || gen(‘multiply’);E ( E1 )E.code E1.code; E E1 E.code E1.code || gen( ‘negate‘);E id E.code gen(‘load’ id.place)

Attributes: E.code: sequence of instructions that are generated for E(no place for an expression is needed since the result of an expressionis stored in the operand stack)

Procedures: newtemp(): Returns a new temporary each time it is calledgen(): Generates instruction (have to call it with appropriate arguments)lookup(id.name): Returns the location of id from the symbol table

16

Code Generation for Boolean Expressions

• Two approaches

– Numerical representation

– Implicit representation

• Numerical representation

– Use 1 to represent true, use 0 to represent false

– For three-address code store this result in a temporary

– For stack machine code store this result in the stack

• Implicit representation

– For the boolean expressions which are used in flow-of-control statements (such as if-statements, while-statements etc.) boolean expressions do not have to explicitly compute a value, they just need to branch to the right instruction

– Generate code for boolean expressions which branch to the appropriate instruction based on the result of the boolean expression

17

Boolean Expressions: Numerical Representation

Attributes : E.place: location that holds the value of expression E E.code: sequence of instructions that are generated for Eid.place: location for id

Global variable: nextstat: Returns the location of the next instruction to be generated(each call to gen() increments nextstat by 1)

Productions Semantic Rules

E id1 relop id2 E.place newtemp();E.code gen(‘if’ id1.place relop.op id2.place ‘goto’ nextstat+3);

|| gen(E.place ‘:=‘ ‘0’) || gen(‘goto’ nextstat+2)|| gen(E.place ‘:=‘ ‘1’);

E E1 and E2 E.place newtemp();E.code E1.code || E2.code

|| gen(E.place ‘:=‘ E1.place ‘and’ E2.place);

18

Boolean Expressions: Implicit Representation

Productions Semantic Rules

E id1 relop id2 E.code gen(‘if’ id1.place relop.op id2.place ‘goto’ E.true)|| gen(‘goto’ E.false);

E E1 and E2 E1.true newlabel();E1.false E. false; (short-circuiting)E2.true E. true;E2.false E. false;E.code E1.code || gen(E1.true ‘:’) || E2.code ;

Attributes : E.code: sequence of instructions that are generated for EE.false: instruction to branch to if E evaluates to falseE.true: instruction to branch to if E evaluates to true(E.code is synthesized whereas E.true and E.false are inherited)id.place: location for id

can be any relational operator:==, <=, >= !=

These places will be filled with lables later on when they become available

This generated labelwill be inserted to the place for E1.true in the code generated for E1

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Example

100 if x < y goto 103101 t1 := 0102 goto 104103 t1 := 1104 if a = b goto 107105 t2 := 0106 goto 108107 t2 := 1108 t3 := t1 and t2

Input boolean expression:x < y and a == b

Numerical representation:

if x < y goto L1goto LFalse

L1: if a = b goto LTruegoto LFalse...

LTrue:

LFalse:

Implicit representation:

These are the locations ofthree-address code instructions, they are not labels

These labels will be generatedlater on, and will be insertedto the corresponding places

20

Flow-of-Control Statements

If-then-else

• Branch based on the result of boolean expression

Loops

• Evaluate condition before loop (if needed)

• Evaluate condition after loop

• Branch back to the top if condition holds

Merges test with last block of loop body

While, for, do, and until all fit this basic model

Pre-test

Loop body

Post-test

Next block

21

Flow-of-Control Statements: Code Structure

E.code

S1.code

goto S.next

S2.code

to E.true

to E.false

E.true:

E.false:

S.next:

S if E then S1 else S2

if E evaluates to true

if E evaluates to false

E.code

S1.code

goto S.begin

to E.true

to E.false

E.true:

E.false:

S.begin:

S while E do S1

Another approach is to place E.code after S1.code

22

Flow-of-Control Statements

Productions Semantic RulesS 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);

S S1 ; S2 S1.next newlabel();S2.next S.next;S.code S1.code || gen(S1.next ‘:’) || S2.code

Attributes : S.code: sequence of instructions that are generated for SS.next: label of the instruction that will be executed immediately after S(S.next is an inherited attribute)

23

Example

Input code fragment:

while (a < b) { if (c < d) x = y + z; else x = y – z}

L1: if a < b goto L2goto LNext

L2: if c < d goto L3goto L4

L3: t1 := y + zx := t1goto L1

L4: t2 := y – zx := t2goto L1

LNext: ...

24

Backpatching

• E.true, E.false, S.next may not be computed in a single pass (they are inherited attributes)

• Backpatching is a technique for generating labels for E.true, E.false, S.next and inserting them to the appropriate locations

• Basic idea

– Keep lists E.truelist, E.falselist, S.nextlist

• E.truelist: the list of instructions where the label for E.true have to be inserted when it becomes available

• S.nextlist: the list of instructions where the label for S.next have to be inserted when it becomes available

– When labels E.true, E.false, S.next are computed these labels are inserted to the instructions in these lists

25

Flow-of-Control Statements: Case Statements

Case Statements1 Evaluate the controlling expression2 Branch to the selected case3 Execute the code for that case4 Branch to the statement after the case

Part 2 is the key

Strategies

• Linear search (nested if-then-else constructs)

• Build a table of case values & binary search it

• Directly compute an address (requires dense case set)

– Use an array of labels that is addressed by the case value

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Type Conversions

Mixed-type expressions

• Insert conversions as needed from conversion table

– i2f r1, r2 (convert the integer value in register r1 to float, and store the result in register r2)

• Most languages have symmetric conversion tables

Typical Addition

Table

translation of a simple if-statement•

•

Backpatching

• Previous codes for Boolean expressions insert symbolic labels for jumps

• It therefore needs a separate pass to set them to appropriate addresses• We can use a technique named backpatching to avoid this• We assume we save instructions into an array and labels will be

indices in the array• For nonterminal B we use two attributes B.truelist and B.falselist

together with following functions:– makelist(i): create a new list containing only I, an index into the array

of instructions– Merge(p1,p2): concatenates the lists pointed by p1 and p2 and returns

a pointer to the concatenated list– Backpatch(p,i): inserts i as the target label for each of the instruction

on the list pointed to by p

Backpatching for Boolean Expressions•

•

Backpatching for Boolean Expressions• Annotated parse tree for x < 100 || x > 200 && x ! = y

Flow-of-Control Statements

Translation of a switch-statement