1. 1 Control Flow Analysis Topic today Representation and Analysis Paper (Sections 1, 2) For next class: Read Representation and Analysis Paper (Section 3) Do problems 1 and 2 from the representation and analysis paper

2. 2 Intermediate Representations Program analyses grew out of the compiler world, where they were used to help optimize code. Many optimizations depend on analyses of intermediate representations of software, such as: o Parse trees o Abstract syntax trees o Three-address code

3. 3 Intermediate representation Code Compilation and Analysis Parsing, lexical analysis Source program Code generation, optimization Target code Code execution Intermediate representation Analyze intermediate representation, perform additional analysis on the results Use this information for code optimization techniques

4. 4 Tree Representations Representations Parse trees represent concrete syntax Abstract syntax trees represent abstract syntax Concrete versus abstract syntax Concrete syntax shows structure and is language-specific Abstract syntax shows structure

5. 5 Example: Grammar Example 1.a := b + c 2.a = b + c; Grammar for 1 stmtlist  stmt | stmt stmtlist stmt  assign | if-then | … assign  ident “:=“ ident binop ident binop  “+” | “-” | … Grammar for 2 stmtlist  stmt “;” | stmt”;” stmtlist stmt  assign | if-then | … assign  ident “=“ ident binop ident Ÿ binop  “+” | “-” | …

6. 6 Example: Parse Tree Example 1.a := b + c 2.a = b + c; Parse tree for 1Parse tree for 2

7. 7 Example: Parse Tree Example 1.a := b + c 2.a = b + c; stmt stmtlist ident assign a ident“:=“binop cb ident “+” stmt stmtlist ident assign a ident“=“binop cb ident “+” “;” Parse tree for 1Parse tree for 2

8. 8 Example: Abstract Syntax Tree Example 1.a := b + c 2.a = b + c; Abstract syntax tree for 1 and 2 assign a add bc

9. 9 Three Address Code General form: x := y op z May include temporary variables (intermediate values) May reference arrays: a[t1] Specific forms (examples) Assignment Binary: x := y op z Unary: x := op y Copy: x := y Jumps Unconditional: goto (L) Conditional: if x relational-op y goto (L) …

10. 10 Example: Three Address Code if a > 10 then x = y + z else x = y – z … 1.if a > 10 goto (4) 2.x = y – z 3.goto (5) 4.x = y + z 5.… Source code Three address code

11. 11 Larger Example: 3 Address Code (1)i := m-1 (2)j := n (3)t1 := 4*n (4)v := a[t1] (5)i := i+1 (6)t2 := 4*I (7)t3 := a[t2] (8)if t3 < v goto (5) (9)j := j-1 (10)t4 := 4*j (11)t5 := a[t4] (12)if t5 > v goto (9) (13)if I >= j goto (23) (14)t6 := 4*I (15)x := a[t6] (16) t7 := 4*I (17) t8 := 4*j (18) t9 := a[t8] (19) a[t7] := t9 (20) t10 := 4*j (21) a[t10] := x (22) goto (5) (23) t11 := 4*I (24) x := a[t11] (25) t12 := 4*I (26) t13 := 4*n (27) t14 := a[t13] (28) a[t12] := t14 (29) t15 := 4*n (30) a[t15] := x

12. 12 Control Flow Graph One of the most basic program representations Nodes represent statements or basic blocks Edges represent flow of control between nodes To build a CFG:  Construct basic blocks  Join blocks together with labeled edges

13. 13 Basic Blocks A basic block is a sequence of consecutive statements in which flow of control enters at the beginning and leaves at the end without halt or possibility of branch except at the end A basic block may or may not be maximal For compiler optimizations, maximal basic blocks are desirable For software engineering tasks, basic blocks that represent one source code statement are often used

14. 14 Computing Basic Blocks (algorithm) Input: a sequence of procedure statements Output: A list of basic blocks with each statement in exactly one block Method:  Determine the set of leaders: the first statements of basic blocks, using the following rules: oThe first statement in the procedure is a leader oAny statement that is the target of a conditional or unconditional goto statement is a leader. oAny statement that immediately follows a conditional or unconditional goto statement is a leader.  Construct the basic blocks using the leaders. For each leader, its basic block consists of the leader and all statements up to but not including the next leader or the end of the procedure.

15. 15 (1)i := m-1 (2)j := n (3)t1 := 4*n (4)v := a[t1] (5)i := i+1 (6)t2 := 4*I (7)t3 := a[t2] (8)if t3 < v goto (5) (9)j := j-1 (10)t4 := 4*j (11)t5 := a[t4] (12)if t5 > v goto (9) (13)if I >= j goto (23) (14) t6 := 4*l (15) x := a[t6] (16) t7 := 4*I (17) t8 := 4*j (18) t9 := a[t8] (19) a[t7] := t9 (20) t10 := 4*j (21) a[t10] := x (22) goto (5) (23) t11 := 4*I (24) x := a[t11] (25) t12 := 4*I (26) t13 := 4*n (27) t14 := a[t13] (28) a[t12] := t14 (29) t15 := 4*n (30) a[t15] := x Example: Compute Basic Blocks on this 3 Address Code

16. 16 (1)i := m-1 (2)j := n (3)t1 := 4*n (4)v := a[t1] (5)i := i+1 (6)t2 := 4*I (7)t3 := a[t2] (8)if t3 < v goto (5) (9)j := j-1 (10)t4 := 4*j (11)t5 := a[t4] (12)if t5 > v goto (9) (13)if I >= j goto (23) (14) t6 := 4*I (15) x := a[t6] (16) t7 := 4*I (17) t8 := 4*j (18) t9 := a[t8] (19) a[t7] := t9 (20) t10 := 4*j (21) a[t10] := x (22) goto (5) (23) t11 := 4*I (24) x := a[t11] (25) t12 := 4*I (26) t13 := 4*n (27) t14 := a[t13] (28) a[t12] := t14 (29) t15 := 4*n (30) a[t15] := x Example: Compute Basic Blocks on this 3 Address Code: leaders

17. 17 (1)i := m-1 (2)j := n (3)t1 := 4*n (4)v := a[t1] (5)i := i+1 (6)t2 := 4*I (7)t3 := a[t2] (8)if t3 < v goto (5) (9)j := j-1 (10)t4 := 4*j (11)t5 := a[t4] (12)if t5 > v goto (9) (13)if I >= j goto (23) (14) t6 := 4*I (15) X := a[t6] (16) t7 := 4*I (17) t8 := 4*j (18) t9 := a[t8] (19) a[t7] := t9 (20) t10 := 4*j (21) a[t10] := x (22) goto (5) (23) t11 := 4*I (24) x := a[t11] (25) t12 := 4*I (26) t13 := 4*n (27) t14 := a[t13] (28) a[t12] := t14 (29) t15 := 4*n (30) a[t15] := x Example: Compute Basic Blocks on this 3 Address Code: blocks

18. 18 Computing Control Flow Graph from Basic Blocks (algorithm) Input: a list of basic blocks Output: A list of control-flow graph (CFG) nodes and edges Method:  Create entry and exit nodes; create edge (entry, B1); create (Bk, exit) for each Bk that represents an exit from program  Add CFG edge from Bi to Bj if Bj can immediately follow Bi in some execution, i.e., oThere is a conditional or unconditional goto from the last statement of Bi to the first statement of Bj or oBj immediately follows Bi in the order of the program and Bi does not end in an unconditional goto statement  Label edges that represent conditional transfers of control as “T” (true) or “F” (false); other edges are unlabeled

19. 19 (1)i := m-1 (2)j := n (3)t1 := 4*n (4)v := a[t1] (5)i := i+1 (6)t2 := 4*I (7)t3 := a[t2] (8)if t3 < v goto (5) (9)j := j-1 (10)t4 := 4*j (11)t5 := a[t4] (12)if t5 > v goto (9) (13)if I >= j goto (23) (14) t6 := 4*I (15) X := a[t6] (16) t7 := 4*I (17) t8 := 4*j (18) t9 := a[t8] (19) a[t7] := t9 (20) t10 := 4*j (21) a[t10] := x (22) goto (5) (23) t11 := 4*I (24) x := a[t11] (25) t12 := 4*I (26) t13 := 4*n (27) t14 := a[t13] (28) a[t12] := t14 (29) t15 := 4*n (30) a[t15] := x Example: Compute Control Flow Graph from Basic Blocks B1 B2 B3 B4 B5 B6

20. 20 Example: Compute Control Flow Graph from Basic Blocks B1 B2 B3 B4 B6 B5 T F T T F F Entry Exit

21. 21 Computing Control Flow from Source Code (example) Procedure AVG S1 count = 0 S2 fread(fptr, n) S3 while (not EOF) do S4 if (n < 0) S5 return (error) else S6 nums[count] = n S7 count ++ endif S8 fread(fptr, n) endwhile S9 avg = mean(nums,count) S10 return(avg)

22. 22 Computing Control Flow from Source Code (example) Procedure AVG S1 count = 0 S2 fread(fptr, n) S3 while (not EOF) do S4 if (n < 0) S5 return (error) else S6 nums[count] = n S7 count ++ endif S8 fread(fptr, n) endwhile S9 avg = mean(nums,count) S10 return(avg) S1 S2 S3 S4 S5S6 S7 S8 S9 S10 entry exit F T F T

23. 23 Computing Control Flow from Source Code (maximal basic blocks) Procedure AVG S1 count = 0 S2 fread(fptr, n) S3 while (not EOF) do S4 if (n < 0) S5 return (error) else S6 nums[count] = n S7 count ++ endif S8 fread(fptr, n) endwhile S9 avg = mean(nums,count) S10 return(avg) S1 S2 S3 S4 S5S6 S7 S8 S9 S10 entry exit F T F T

24. 24 Computing Control Flow from Source Code (another example) Procedure Trivial S1 read (n) S2 switch (n) case 1: S3 write (“one”) break case 2: S4 write (“two”) case 3: S5 write (“three”) break default S6 write (“Other”) endswitch end Trivial

25. 25 Computing Control Flow from Source Code (another example) Procedure Trivial S1 read (n) S2 switch (n) case 1: S3 write (“one”) break case 2: S4 write (“two”) case 3: S5 write (“three”) break default S6 write (“Other”) endswitch end Trivial S1 S2 S3S4 S5S6 entry exit

26. 26 Computing Control Flow from Source Code (maximal basic blocks) Procedure Trivial S1 read (n) S2 switch (n) case 1: S3 write (“one”) break case 2: S4 write (“two”) case 3: S5 write (“three”) break default S6 write (“Other”) endswitch end Trivial S1 S2 S3S4 S5S6 entry exit

27. 27 Applications of Control Flow Program understanding: In CFGs, program structure and flow are explicit Complexity: Cyclomatic (McCabe’s) Computed in several ways: Edges –nodes +2 Number of regions in CFG Number of decision statements + 1 (if program is structured) Indicates number of test cases needed; indicates difficulty of maintaining 1 23 45 6 7 8

28. 28 Applications of Control Flow Testing: branch, path, basis path Branch: must test 1  2, 1  3, 4  5, 4  8, 5  6, 5  7 Path: infinite number because of loop Basis path: set of paths such that each path executes at least one more edge (cyclomatic complexity gives max necessary); example: 1,2,4,8; 1,3,4,5,6,7,4,8 1 23 45 6 7 8

29. 29 Applications of Control Flow Support for Other Analyses: Dominator Postdominator Data dependence Control dependence Points-to Regression test selection 1 23 45 6 7 8

30. 30 Terminology: Levels of Analysis Local: within a single basic block or statement Intraprocedural: within a single procedure, function, or method (sometimes intramethod) Interprocedural: across procedure boundaries, procedure call, shared globals, etc. Intraclass: within a single class Interclass: across class boundaries...

31. Exercise How would we represent interprocedural control flow; that is, control flow involving an entire program containing several procedures? 31 Procedure A begin S3 call B() S4 end Procedure Main begin S1 if (P1) then call A() else call B() endif call A() S2 end Procedure B begin S5 end

32. Step 1: Draw individual CFGs 32

33. Step 2: Connect CFGs (how?) 33