Advanced Compilers Introduction to Dataflow Analysis by Example. Fall Chungnam National Univ. Eun-Sun Cho

Transcription

1 Advanced Compilers Introduction to Dataflow Analysis by Example Fall Chungnam National Univ. Eun-Sun Cho 1

2 Dataflow Analysis + Optimization r1 = r2 + r3 r6 = r4 r5 r6 = r2 + r3 r7 = r4 r5 r4 = 4 r6 = 8 Classical optimization examples Common subexpression elimination r2 + r3? r4 - r5? Register allocation (live range anlysis) Can virtual registers r1 and r7 be allocated in a same actual register? Control flow analysis Considering basic blocks as black boxes Concerns only branches Data flow analysis Collecting information about constructions/destructions of each data value in a program Look inside basic blocks and check each operations cf. CFA note: (virtual) registers == (user-defined or temporary) variables

3 Live Variable (Liveness) Analysis r1 = r2 + r3 r6 = r4 r5 r6 = r2 + r3 r7 = r4 r5 r4 = 4 r6 = 8 r6(=8) is dead Others are live r1,r2,r3,r4 and r5 are live r6 (=r4-r5) is dead r4 and r6(=r4-r5) are dead others are live Live variable analysis : to see (at a specific program point) if the current value of a variable is to be used in the future Conclusions : r6 = r4 r5 is useless!

4 Live Variable Analysis Algorithms Collecting following sets USE/DEF inner basic block USE = set of external variables consumed in the BB DEF = set of variables defined in the BB IN/OUT inter basic blocks IN = set of variables that are live at the entry point of a BB OUT = set of variables that are live at the exit point of a BB note) It is better to evaluate IN/OUT backward IN/OUT are defined by USE/DEF At the entry of a BB, registers except for IN had better be freed, At the exit of a BB, registers except for OUT had better be freed.

5 Compute USE/DEF Sets For Each BB (When an instruction is Equal to a BB) for each basic block X, do DEF(X) = dest : = src 1 +src 2 USE(X) = for each operation in sequential order in X, op, do for each source operand of op, src, do USE(X) += src DEF(X) += dest

6 Compute USE/DEF Sets For Each BB (In General) for each basic block X, do DEF(X) = dest : = src 1 +src 2 USE(X) = for each operation in sequential order in X, op, do for each source operand of op, src, do if (src not in DEF(X)) then USE(X) += src endif DEF(X) += dest DEF : all the LHS in the block USE : the values from outside which are used before redefined in the block

7 Example DEF/USE Calculation r1 = MEM[r2+0] r2 = r2 + 1 r3 = r1 * r4 USE = r2,r4 DEF = r1,r2,r3 USE = r1,r5 DEF = r1,r3,r7 r1 = r1 + 5 r3 = r5 r1 r7 = r3 * 2 r2 = 0 r7 = 23 r1 = 4 USE = DEF = r1,r2,r7 r8 = r7 + 5 r1 = r3 r8 r3 = r1 * 2 USE = r3,r7 DEF = r1,r3,r8

8 Compute IN/OUT Sets For All BBs initialize IN(X) to for all basic blocks X change = 1 while (change) do change = 0 for each basic block, X, do old_in = IN(X) OUT(X) = Y successor(x) IN(Y) IN(X) = USE(X) + (OUT(X) DEF(X)) if (old_in!= IN(X)) then change = 1 endif IN : live variables at the entry point of the block the variables of which values at the entry point are used in the USE(X) + the variables of which values are not updated in this block, while they are to be used in some following blocks OUT(X) DEF(X) OUT : collection of IN(Y)s from direct successor blocks Y

9 Example IN/OUT Calculation r1 = MEM[r2+0] r2 = r2 + 1 r3 = r1 * r4 USE = r2,r4 DEF = r1,r2,r3 IN = r2,r4,r5 OUT = r1,r3,r5 USE = r1,r5 DEF = r1,r3,r7 IN = r1,r5 OUT = r3,r7 r1 = r1 + 5 r3 = r5 r1 r7 = r3 * 2 r2 = 0 r7 = 23 r1 = 4 USE = DEF = r1,r2,r7 IN = r3 OUT = r3,r7 r8 = r7 + 5 r1 = r3 r8 r3 = r1 * 2 USE = r3,r7 DEF = r1,r3,r8 IN = r3,r7 OUT = liveness analysis = finding out the set of registers which retain meaningful values at a specific program point (like the entry point of a block, the exit point of a block..),

10 Reaching Definition Analysis (rdefs) 1: r1 = r2 + r3 2: r6 = r4 r5 Definition of a variable an (assignment) expression which has the variable at its lhs 5: r6 = r2 + r3 6: r7 = r4 r5 3: r4 = 4 4: r6 = 8 defs 1 and 2 reach this point defs 1, 3, 4 Definition d reaches a program point (point) p from right after d to p, there exists a path d which does not kill d reach this point Definition d is killed between two def 2 is killed by 4 program points on the path between the two points, there exist other definitions of the same variable that d defines eg) r1=r2+r3 kills all the previous definition (although they are not shown in the figure) of r1 defs 1, 3, 5, 6 reach this point defs 2, 4 are killed by 5

11 Reaching Definition Analysis - Algorithms Collecting following sets GEN/KILL inner basic block GEN = set of definitions generated in the BB KILL = set of definitions killed in the BB IN/OUT inter basic blocks IN = set of definitions reaching the BB entry OUT = set of definitions reaching the BB exit note) It is better to evaluate IN/OUT forward IN/OUT are defined by GEN/KILL

12 Compute Rdef GEN/KILL Sets For Each BB (When an instruction is Equal to a BB) for each basic block X, do GEN(X) = dest : = src 1 +src 2 KILL(X) = for each operation in sequential order in X, op, do GEN(X) += op KILL(X) = {all ops which define dest}

13 Compute Rdef GEN/KILL Sets For Each BB (In General) for each basic block X, do GEN(X) = dest : = src 1 +src 2 KILL(X) = for each operation in sequential order in X, op, do G = op K = {all ops which define dest} GEN(X) = G + (GEN(X) K) KILL(X) = K + (KILL(X) G)

14 Example Rdef GEN/KILL Calculation 1: r1 = MEM[r2+0] 2: r2 = r : r3 = r1 * r4 GEN = 1,2,3 KILL = 4,5,7,9,11,12 GEN = 4,5,6 KILL = 1,3,8,9,11,12 4: r1 = r : r3 = r5 r1 6: r7 = r3 * 2 7: r2 = 0 8: r7 = 23 9: r1 = 4 GEN = 7,8,9 KILL = 1,2,4,6,11 10: r8 = r : r1 = r3 r8 12: r3 = r1 * 2 GEN = 10,11,12 KILL = 1,3,4,5,9

15 Compute Rdef IN/OUT Sets for all BBs initialize OUT(X) = for all basic blocks X change = 1 while (change) do change = 0 for each basic block X, do old_out = OUT(X) IN(X) = Y predessor(x) OUT(Y) OUT(X) = GEN(X) + (IN(X) KILL(X)) if (old_out!= OUT(X)) then change = 1 endif IN = set of definitions reaching the entry of BB OUT = set of definitions leaving BB

16 Example Rdef IN/OUT Calculation 1: r1 = MEM[r2+0] 2: r2 = r : r3 = r1 * r4 GEN = 1,2,3 KILL = 4,5,7,9,11,12 IN = OUT = 1,2,3 GEN = 4,5,6 KILL = 1,3,8,9,11,12 IN = 1,2,3 OUT = 2,4,5,6 4: r1 = r : r3 = r5 r1 6: r7 = r3 * 2 7: r2 = 0 8: r7 = 23 9: r1 = 4 10: r8 = r : r1 = r3 r8 12: r3 = r1 * 2 GEN = 10,11,12 KILL = 1,3,4,5,9 GEN = 7,8,9 KILL = 1,2,4,6,11 IN = 1,2,3 OUT = 3,7,8,9 IN = 2,3,4,5,6,7,8,9 OUT = 2,6,7,8,10,11,12

17 Application Live Ranges in Register Allocation C from CMU Compiler Web site 17

18 r1 = r2 + r3 r6 = r4 r5 r6 = r2 + r3 r7 = r4 r5 Available Expressions r4 = 4 r6 = 8 r2+r4 is available r4-r5 is available r2+r3 is available r4- r5 is not available r2+r3 is available r4-r5 is not available Goals to reuse the values of syntactically same expressions which were evaluated before Availability Consider all the (syntactic) expressions Is an expression already evaluated? = Is this expression available? expression e is killed between two program points on the path between the two points, there exist definitions of the variable used in e: the previous value is not usable eg) r4=4 kills the expression r4-r5 in r6=r4-r5

19 Available Expression Analysis - Algorithms Collecting following sets E_GEN/E_KILL inner basic block E_GEN = set of expressions generated in the BB E_KILL = set of expressions killed in the BB IN/OUT inter basic blocks IN = set of expressions available at the BB entry OUT = set of expressions available at the BB exit note) It is better to evaluate IN/OUT forward IN/OUT are defined by E_GEN/E_KILL

20 Compute AvailExp. GEN/KILL Sets For Each BB for each basic block X, do E_GEN(X) = dest : = src 1 +src 2 E_KILL(X) = for each operation in sequential order in X, op, do if (dest is not FV of src 1 +src 2 ) G = src 1 +src 2 K = {all exprs which contains dest in FV} E_GEN(X) = G + (E_GEN(X) K) E_KILL(X) = K + (E_KILL(X) G) FV (e): set of free variables of e exprs eg.. FV(x+1) = {x} FV(2+x+y+3) = {x, y}

21 Example AvailExp. GEN/KILL Calculation r1 = MEM[r2+0] r2 = r2 + 1 r3 = r1 * r4 E_GEN = r1*r4 E_KILL = r2+1, r1+5, r5-r1, r3*2, r3-r8, E_GEN = r5-r1 r3*2 E_KILL = r1*r4, r1+5, r3-r8, r7+5 r1 = r1 + 5 r3 = r5 r1 r7 = r3 * 2 r2 = r3*2 r7 = 23 r1 = 4 E_GEN = r3*2 E_KILL =r2+1, r7+5, r1*r4, r1+5, r5-r1 r8 = r7 + 5 r1 = r3 r8 r7 = r3 * 2 E_GEN = r3-r8, r3*2 E_KILL = r1*r4, r1+5, r5-r1, r7+5

22 Compute AvailExp. IN/OUT Sets for all BBs initialize OUT(X) = U for all basic blocks X change = 1 while (change) do change = 0 for each basic block X, do old_out = OUT(X) IN(X) = Y predessor(x) OUT(Y) OUT(X) = E_GEN(X) + (IN(X) E_KILL(X)) if (old_out!= OUT(X)) then change = 1 endif IN = set of expressions available the entry of BB OUT = set of available expressions leaving BB

23 Example AvailExp. IN/OUT Calculation r1 = MEM[r2+0] r2 = r2 + 1 r3 = r1 * r4 E_GEN = r1*r4 E_KILL = r2+1, r1+5, IN = OUT = r1*r4 r5-r1, r3*2, r3-r8, E_GEN = r5-r1 r3*2 E_KILL = r1*r4, r1+5, r3-r8, r7+5 IN = r1*r4 OUT = r5-r1, r3*2 r1 = r1 + 5 r3 = r5 r1 r7 = r3 * 2 r8 = r7 + 5 r1 = r3 r8 r7 = r3 * 2 r2 = r3*2 r7 = 23 r1 = 4 E_GEN = r3*2 E_KILL = r2+1, r7+5, r1*r4, r1+5, r5-r1 IN = r1*r4 OUT = r3*2 E_GEN = r3-r8, r3*2 E_KILL = r1*r4, r1+5, r5-r1, r7+5 IN = r3*2 OUT = r3-r8, r3*2

24 Summary of Three Dataflow Problems Live Variables Reaching Definition Available Expressions Domain Sets of variables Sets of definitions Sets of expressions Direction Backwards Forwards Forwards Main Logic IN = USE + (OUT DEF) OUT = GEN + (IN KILL) OUT = GEN + (IN KILL) Transfer function F B (x) = use B (x def B ) F B (x) = gen B (x kill B ) F B (x) = e_gen B (x e_kill B ) Boundary IN(Exit) = OUT(Entry) = OUT (Entry) = Meet( ) Initialize IN(X) = OUT(X) = OUT(X) = U universe Equation in(b) = F B (out(b)) out(b) = Q Succ(B) in(q) out(b) = F B (in(b)) in(b) = Q Pred(B) out(q) out(b) = F B (in(b)) in(b) = Q Pred(B) out(q) 24