Compiler Design Spring 2017

Transcription

1 Compiler Design Spring Live variables Dr. Zoltán Majó Compiler Group Java HotSpot Virtual Machine Oracle Corporation

2 Live variables Foundations for several optimizations If a variable is not live, it s dead. No need to store value in dead variables Outline Data flow problem Transfer function Examples 2

3 Wishlist Given a statement S dest = operand 1 operand 2 Compiler would like to know at point P if there is a further use of dest I.e., there is a statement S that uses dest and there is a path from P to P before_s One interesting point is P after_s or P after_b (with B the basic block of S) But every point could be interesting Like to know if some operand i is used again in another statement 3

4 Data flow problem Similar to reaching definitions but not interested what has happened prior to reaching P but what happens after P Consider all paths that start at P and go to EXIT A variable V is live at point P if there is a path from P to EXIT that contains a statement S that uses V, and there is no definition of V on this path between P and S. Path can start anywhere Often we care about paths that start after a definition of V A single path with a use is enough for V to be live at P A variable that is not live is called dead Recall that we assume all statements have clearly identifiable operands and destinations 4

5 Live variables Live variable analysis determines for all points P the set of variables that are live We care primarily about live variables at the end of a basic block. Handling a basic block is easy if we know what s live at the end There are many optimizations that are based on live variable analysis If a variable is dead at P then it s not necessary to store the variable If a register is needed and one of the registers contains a dead variable, this register can be used right away no need to save the current content 5

6 No need to store value computed by S 2 in variable W If expr has no side effect stmt can be removed V is local to basic block B If Y is in a register this register can be released after S 4 S 1 : V = S 2 : W = expr S 3 : = X V S 4 : = Y 1 S 5 : = Z Live = {X, Z} B 6

7 Transfer function d: = var B var is live at the start of basic block B if there is no stmt in B prior to d that defines var 7

8 Transfer function d: = var d : var = B var is live at the start of basic block B if there is no stmt in B prior to d that defines var 8

9 Transfer function d : var = d: = var B var is not live at the start of basic block B as there is a stmt in B prior to d that defines var Definition d 9

10 Transfer function d: = var B Define for basic block B def B = { var var is defined in B prior to any use of var in B } use B = { var var is used in B prior to any definition of var in B } Definitions and uses of a variable: must be conservative In def only if we are sure the variable is set In use if there is a chance that the value is used 10

11 12

12 Running example def = {i, j, a} use = {m, n } def = {} use = {i, j} ENTRY d 1 : i = m 1 d 2 : j = n d 3 : a = d 4 : i = i + 1 d 5 : j = j - 1 def = {a} use = d 6 : a = def = {i} use = d 7 : i = From Aho et al Compilers, p 604 EXIT 13

13 Transfer function Notice we may be interested in the set of live variables at the start of a basic block So far: local analysis def and use determine effect of statements for basic block in isolation Global information determined by statements in basic block and statements in subsequent basic blocks Eventually we also figure out what s live at the end of a basic block Set of live variables at the end of a basic block Determined by statements in subsequent basic blocks Another term: live == downward exposed 14

14 Transfer function How do we extend transfer function to consider subsequent basic blocks? 15

15 Transfer function IN(B) = {v 1, v 2,, v n } d: = var For a basic block B we define IN(B) = { var var live at P before_b } OUT(B) = { var var live at P after_b } OUT(B) = {v 1, v 2,, v m } Variable v IN(B) v is used in B prior to any definition, i.e. v use B v OUT(B) and v not set by statements in B, i.e. v def B IN(B) = use B (OUT(B) def B ) 16

16 Transfer function B2 B3... B1 Given IN(B1) What should be OUT(B2) and OUT(B3)? OUT(B2) = IN(B1), OUT(B3) = IN(B1) 17

17 18

18 Transfer function... B1 B2 B3 Given IN(B2) and IN(B3) What should be OUT(B1)? A variable var is live at a point P if there is a path from P to EXIT such that var is used along that path prior to any definition Must consider all paths starting at P 19

19 20

20 Transfer function... B1 B2 B3 Given IN(B i ) OUT(B) = B i, Bi is successor of B in CFG IN(B i ) 21

21 Finding IN and OUT def B and use B capture what happens inside a basic block 22

22 Running example def = {i, j, a} use = {m, n } def = {} use = {i, j} ENTRY d 1 : i = m 1 d 2 : j = n d 3 : a = d 4 : i = i + 1 d 5 : j = j - 1 def = {a} use = d 6 : a = def = {i} use = d 7 : i = From Aho et al Compilers, p 604 EXIT 23

23 Finding IN(B) and OUT(B) N basic blocks, 2 N sets IN / OUT System with 2 N unknowns Solve by iterating until a fixed point is found How to start iteration? Safe assumption IN[EXIT] = Nothing is live at the end 24

24 Finding live variables IN[EXIT] = Initialize IN[B] = for B EXIT while (changes to any IN(B)) { for (each basic block B EXIT) { OUT(B) = Bi, Bi is successor of B in CFG IN(Bi) IN(B) = use B (OUT(B) def B ) } } 25

25 Finding live variables IN[EXIT] = Initialize IN[B] = for B EXIT while (changes to any IN(B)) { for (each basic block B EXIT) { OUT(B) = Bi, Bi is successor of B in CFG IN(Bi) IN(B) = use B (OUT(B) def B ) } } 26

26 Initialize IN[B] = while (changes to any IN(B)) { for (each basic block B EXIT) { OUT(B) = Bi, Bi is successor of B in CFG IN(Bi) IN(B) = use B (OUT(B) def B ) } def = {i, j, a} use = { m, n } ENTRY d1: i = m 1 d2: j = n d3: a = IN(B1) = OUT(B1) = def = {} use = {i, j} d4: i = i + 1 d5: j = j - 1 IN(B2) = OUT(B2) = d6: a = IN(B3) = def = {a} use = def = {i} use = OUT(B3) = d7: i = IN(B4) = OUT(B4) = From Aho et al Compilers, p 604 EXIT IN(EXIT) 29

27 Incomplete example to be continued. zmajo 30