1 CMPSC 160 Translation of Programming Languages Fall 2002 Lecture-Modules 17 and 18 slides derived from Tevfik Bultan, Keith Cooper, and Linda Torczon Department of Computer Science University of California, Santa Barbara

2 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 Instruction Selection Instruction Scheduling Register Allocation ScannerParser Semantic Analysis Code Optimization Intermediate Code Generation IR

3 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

4 Abstract Syntax Trees (ASTs) if (x < y) x = 5*y + 5*y/3; else y = 5; x = x+y; Statements < AssignStmt + * x IfStmt AssignStmt xxy+ yx y / 5 y 3 * 5 y 5

5 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 x+y / 5 3

6 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 B 1 else goto B 2 x = 5*y + 5*y/3y = 5 x = x+y B1B1 B2B2 B0B0 B3B3 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

7 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 L2 L1: push 5 load y multiply push 5 load y multiply push 3 divide add store x goto L3 L2: push 5 store y L3: load x load y add store x pops the top two elements and compares them pops the top two elements, multiplies them, and pushes the result back to the stack JVM: A stack machine In the project we generate assembly code for JVM which is converted to bytecode by Jasmin assembler JVM interpreter executes the bytecode on different machines JVM has an operand stack which we use to evaluate expressions JVM provides local variables for each method The local variables are like registers so we do not have to worry about register allocation Each local variable in JVM is denoted by a number between 0 and (x and y in the example will be assigned unique numbers) pushes the value at the location x to the stack stores the value at the top of the stack to the location x

8 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 yop: unary operators (minus, negation, integer to float conversion) Branch –goto LExecute the statement with labeled L next Conditional Branch –if x relop y goto Lrelop: =, ==, != if the condition holds we execute statement labeled L next if the condition does not hold we execute the statement following this statement next

9 Three-Address Code if (x < y) x = 5*y + 5*y/3; else y = 5; x = x+y; if x < y goto L1 goto L2 L1:t1 := 5 * y t2 := 5 * y t3 := t2 / 3 x := t1 + t2 goto L3 L2:y := 5 L3:x := x + y Temporaries: temporaries correspond to the internal nodes of the syntax tree Variables can be represented with their locations in the symbol table Three address code instructions can be represented as an array of quadruples: operation, argument1, argument2, result triples: operation, argument1, argument2 (each triple implicitly corresponds to a temporary)

10 Three-Address Code Generation for a Simple Grammar ProductionsSemantic Rules S  id := Eid.place  lookup(id.name); S.code  E.code || gen(id.place ‘:=‘ E.place); E  E 1 + E 2 E.place  newtemp(); E.code  E 1.code || E 2.code || gen(E.place ‘:=‘ E 1.place ‘+’ E 2.place); E  E 1 * E 2 E.place  newtemp(); E.code  E 1.code || E 2.code || gen(E.place ‘:=‘ E 1.place ‘*’ E 2.place); E  ( E 1 )E.code  E 1.code; E.place  E 1.place; E   E 1 E.place  newtemp(); E.code  E 1.code || gen(E.place ‘:=‘ ‘uminus’ E 1.place); E  id E.place  lookup(id.name); E.code  ‘’ (empty string) Attributes:E.place: location that holds the value of expression E E.code: sequence of instructions that are generated for E Procedures:newtemp(): Returns a new temporary each time it is called gen(): Generates instruction (have to call it with appropriate arguments) lookup(id.name): Returns the location of id from the symbol table

11 Stack Machine Code Generation for a Simple Grammar ProductionsSemantic Rules S  id := Eid.place  lookup(id.name); S.code  E.code || gen(‘store’ id.place); E  E 1 + E 2 E.code  E 1.code || E 2.code || gen(‘add’); (arguments for the add instruction are in the top of the stack) E  E 1 * E 2 E.code  E 1.code || E 2.code || gen(‘multiply’); E  ( E 1 )E.code  E 1.code; E   E 1 E.code  E 1.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 expression is stored in the operand stack) Procedures:newtemp(): Returns a new temporary each time it is called gen(): Generates instruction (have to call it with appropriate arguments) lookup(id.name): Returns the location of id from the symbol table

12 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

13 Boolean Expressions: Numerical Representation Attributes :E.place: location that holds the value of expression E E.code: sequence of instructions that are generated for E id.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) ProductionsSemantic Rules E  id 1 relop id 2 E.place  newtemp(); E.code  gen(‘if’ id 1.place relop.op id 2.place ‘goto’ nextstat+3); || gen(E.place ‘:=‘ ‘0’) || gen(‘goto’ nextstat+2) || gen(E.place ‘:=‘ ‘1’); E  E 1 and E 2 E.place  newtemp(); E.code  E 1.code || E 2.code || gen(E.place ‘:=‘ E 1.place ‘and’ E 2.place);

14 Boolean Expressions: Implicit Representation ProductionsSemantic Rules E  id 1 relop id 2 E.code  gen(‘if’ id 1.place relop.op id 2.place ‘goto’ E.true) || gen(‘goto’ E.false); E  E 1 and E 2 E 1.true  newlabel(); E 1.false  E. false; (short-circuiting) E 2.true  E. true; E 2.false  E. false; E.code  E 1.code || gen(E 1.true ‘:’) || E 2.code ; Attributes :E.code: sequence of instructions that are generated for E E.false: instruction to branch to if E evaluates to false E.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 label will be inserted to the place for E 1.true in the code generated for E 1

15 Example 100if x < y goto t1 := 0 102goto t1 := 1 104if a = b goto t2 := 0 106goto t2 := 1 108t3 := t1 and t2 Input boolean expression: x < y and a == b Numerical representation: if x < y goto L1 goto LFalse L1:if a = b goto LTrue goto LFalse... LTrue: LFalse: Implicit representation: These are the locations of three-address code instructions, they are not labels These labels will be generated later on, and will be inserted to the corresponding places

16 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

17 Flow-of-Control Statements: Code Structure E.code S 1.code goto S.next S 2.code    to E.true to E.false E.true: E.false: S.next: S  if E then S 1 else S 2 if E evaluates to true if E evaluates to false E.code S 1.code goto S.begin    to E.true to E.false E.true: E.false: S.begin: S  while E do S 1 Another approach is to place E.code after S 1.code

18 Flow-of-Control Statements ProductionsSemantic Rules S  if E then S 1 else S 2 E.true  newlabel(); E.false  newlabel(); S 1.next  S. next; S 2.next  S. next; S.code  E.code || gen(E.true ‘:’) || S 1.code || gen(‘goto’ S.next) || gen(E.false ‘:’) || S 2.code ; S  while E do S 1 S.begin  newlabel(); E.true  newlabel(); E.false  S. next; S 1.next  S. begin; S.code  gen(S.begin ‘:’) || E.code || gen(E.true ‘:’) || S 1.code || gen(‘goto’ S.begin); S  S 1 ; S 2 S 1.next  newlabel(); S 2.next  S.next; S.code  S 1.code || gen(S 1.next ‘:’) || S 2.code Attributes : S.code: sequence of instructions that are generated for S S.next: label of the instruction that will be executed immediately after S (S.next is an inherited attribute)

19 Example Input code fragment: while (a < b) { if (c < d) x = y + z; else x = y – z } L1:if a < b goto L2 goto LNext L2:if c < d goto L3 goto L4 L3:t1 := y + z x := t1 goto L1 L4:t2 := y – z x := t2 goto L1 LNext:...

20 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

21 Flow-of-Control Statements: Case Statements Case Statements 1 Evaluate the controlling expression 2 Branch to the selected case 3 Execute the code for that case 4 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

22 Type Conversions Mixed-type expressions Insert conversions as needed from conversion table –i2f r 1, r 2 (convert the integer value in register r 1 to float, and store the result in register r 2 ) Most languages have symmetric conversion tables Typical Addition Table

23 Memory Layout Placing run time data structures Alignment and padding Machines have alignment restrictions –32-bit floating point numbers and integers should begin on a full-word boundary (32-bit boundary) Place values with identical restrictions next to each other Assign offsets from most restrictive to least If needed, insert padding (space left unused due to alignment restrictions) to match restrictions CodeCode S G t l a & o t b i a c l HeapHeap StackStack 0 high Stack and heap share free space Fixed-size areas together For compiler, this is the entire picture

24 Memory Allocation P  D D  D; D D  id : T T  char | int | float | array[num] of T | pointer T Attributes: T.type, T.width Basic types: char width 4, integer width 4, float width 8 Type constructors: array(size,type) width is size * (width of type) pointer(type) width is 4 Enter the variables to the symbol table with their type and memory location Set the type attribute T.type Layout the storage for variables Calculate the offset for each local variable and enter it to the symbol table Offset can be offset from a static data area or from the beginning of the local data area in the activation record

25 A Translation Scheme for Memory Allocation P  {offset  0;} D D  D; D D  id : T {enter(id.name,T.type, offset); offset  offset + T.width; } T  char { T.type  char; T.width  4; } | int { T.type  integer; T.width  14; } | float { T.type  float; T.width  8; } | array[num] of T 1 { T.type  array(num.val, T 1.type); T.width  num.val * T 1.width; } | pointer T { T.type  pointer(T 1.type); T.width  8; } Note that if the size of the array is not a constant we cannot compute its width at compile time In that case allocate the memory for the array in the heap and allocate the memory for the pointer to the heap at compile time

26 Memory Allocation for Nested Procedures Use two stacks: –Stack for symbol table: top(tblptr) points to current symbol table –Stack for offset: top(offset) gives the value of the offset in the current symbol table addwidth(table,width) stores the cumulative width of all the entries in the symbol table in the header of the symbol table mktbl(previous) creates a new symbol table linked to the previous enter(table, name, type, offset) enters a variable to the symbol table enterProc(table,name,newtable) enters a procedure to the symbol table P  D D  D; D D  id : T | proc id; D; S

27 Memory Allocation for Nested Procedures P  {t  mktable(nil); push(t,tblptr); push(0, offset)} D {addwidth(top(tblptr), top(offset)); pop(tblptr); pop(offset);} D  D; D D  proc id ; { t  mktable(top(tblptr)); push(t,tblptr); push(0,offset); } D ; S { t  top(tblptr); addwidth(t, top(offset)); pop(tblptr); pop(offset); D  id : T {enter(top(tblptr), id.name, T.type, top(offset)); top(offset)  top(offset) + T.width; }

28 Array access: How does the compiler handle A[ i ][ j ] ? First, must agree on a storage scheme Row-major order (most languages) Lay out as a sequence of consecutive rows Rightmost subscript varies fastest A[1,1], A[1,2], A[1,3], A[2,1], A[2,2], A[2,3] Column-major order (Fortran) Lay out as a sequence of columns Leftmost subscript varies fastest A[1,1], A[2,1], A[1,2], A[2,2], A[1,3], A[2,3] Indirection vectors (Java) Vector of pointers to pointers to … to values Takes more space Trades indirection for arithmetic (in modern processors memory access is more costly than arithmetic) Locality may not be good if indirection vectors are used

29 Laying Out Arrays The Concept Row-major order Column-major order Indirection vectors 1,11,21,31,42,12,22,32,4 A 1,12,11,22,21,32,31,42,4 A 1,11,21,31,4 2,12,22,32,4 A 1,11,21,31,4 2,12,22,32,4 A These have distinct & different cache behavior  The order of traversal of an array can effect the performance

30 Computing an Array Address A[ i + ( i - low )  sizeof(A[1]) What about A[i 1 ][i 2 ] ? Row-major order, two + (( i 1 - low 1 )  (high 2 - low 2 + 1) + i 2 - low 2 )  sizeof(A[1]) Column-major order, two + (( i 2 - low 2 )  (high 1 - low 1 + 1) + i 1 - low 1 )  sizeof(A[1]) Indirection vectors, two dimensions *(A[i 1 ])[i 2 ] — where A[i 1 ] is, itself, a 1-d array reference Expensive computation! Lots of +, -, x operations int A[1:10]  low is 1 Make low 0 for faster access (save a subtraction ) Almost always a power of 2, known at compile- time  use a shift for speed Base of A (starting address of the array)

31 Optimizing Address Calculation for A[ i ][ j ] In row-major + (i-low 1 )(high 2 -low 2 +1)  sizeof(A[1][1]) + (j - low 2 )  sizeof(A[1][1]) Which can be factored + i  (high 2 -low 2 +1)  sizeof(A[1][1]) + j  sizeof(A[1][1]) - (low 1  (high 2 -low 2 +1)  sizeof(A[1][1]) + low 2  sizeof(A[1][1])) If low i, high i, and sizeof(A[1][1]) are known, the last term is a constant 0 - (low 1  (high 2 -low 2 +1)  sizeof(A[1][1]) + low 2  sizeof(A[1][1])) And len 2 as (high 2 -low 2 +1) Then, the address expression 0 + (i  len 2 + j )  sizeof(A[1][1]) Compile-time constants

32 Array References What about arrays as actual parameters? Whole arrays, as call-by-reference parameters Need dimension information  build a dope vector Store the values in the calling sequence Pass the address of the dope vector in the parameter slot Generate complete address polynomial at each reference Some improvement is possible Save len i and low i rather than low i and high i Pre-compute the fixed terms in prolog sequence What about call-by-value? Most call-by-value languages pass arrays by low 1 high 1 low 2 high 2

33 Structure of a Compiler Instruction Selection Instruction Scheduling Register Allocation ScannerParser Semantic Analysis Code Optimization Intermediate Code Generation