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Borrowed from J. N. Amaral, slightly modified cs.ualberta/~amaral/courses/680

LIVE-IN: k j. g. g := mem[j+12]. h. h := k -1. f. f := g + h. e. e := mem[j+8]. m. m := mem[j+16]. b. b := mem[f]. c. c := e + 8. d. d := c. k := m + 4. j := b. LIVE-OUT: d k j.

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Borrowed from J. N. Amaral, slightly modified cs.ualberta/~amaral/courses/680

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  1. LIVE-IN: k j g g := mem[j+12] h h := k -1 f f := g + h e e := mem[j+8] m m := mem[j+16] b b := mem[f] c c := e + 8 d d := c k := m + 4 j := b LIVE-OUT: d k j Borrowed from J. N. Amaral, slightly modified http://www.cs.ualberta.ca/~amaral/courses/680 k j k j CMPUT 680 - Compiler Design and Optimization

  2. Example:Simplify (K=4) stack f (h,no-spill) e j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  3. Example:Simplify (K=4) stack f (g, no-spill) (h, no-spill) e j k b m d c g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  4. Example:Simplify (K=4) stack f (k, no-spill) (g, no-spill) (h, no-spill) e j k b m d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  5. Example:Simplify (K=4) stack f (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) e j b m d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  6. Example:Simplify (K=4) stack (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) e j b m d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  7. Example:Simplify (K=4) stack (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) j b m d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  8. Example:Coalesce (K=4) stack (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) j b d c Why can’t we simplify? Cannot simplify move-related nodes. CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  9. Example:Coalesce (K=4) stack (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) j b d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  10. Example:Simplify (K=4) stack (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) j b c-d CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  11. Example:Coalesce (K=4) stack (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) j b CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  12. Example:Simplify (K=4) greedy-4-colorable stack (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) b-j CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  13. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  14. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  15. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  16. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  17. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  18. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  19. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  20. Example:Select (K=4) stack f e (b-j, no-spill) (c-d, no-spill) (m, no-spill) (e, no-spill) (f, no-spill) (k, no-spill) (g, no-spill) (h, no-spill) R1 R2 j k b m R3 d R4 c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  21. LIVE-IN: k j g := mem[j+12] h := k -1 f := g + h e := mem[j+8] m := mem[j+16] b := mem[f] c := e + 8 d := c k := m + 4 j := b LIVE-OUT: d k j Example:Allocation with 4 registers k j g h f e m b c d k j CMPUT 680 - Compiler Design and Optimization

  22. LIVE-IN: k j g := mem[j+12] h := k -1 f := g + h e := mem[j+8] m := mem[j+16] j := mem[f] d := e + 8 k := m + 4 LIVE-OUT: d k j Example:Allocation with 4 registers k j g h f e m j d k CMPUT 680 - Compiler Design and Optimization

  23. Could we do the allocation in the previous example with 3 registers? CMPUT 680 - Compiler Design and Optimization

  24. Example:Simplify (K=3) stack f (h,no-spill) e j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  25. Example:Simplify (K=3) stack f (g, no-spill) (h, no-spill) e j k b m d c g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  26. Example:Freeze (K=3) stack f (g, no-spill) (h, no-spill) e j k b m Coalescing may make things worse (not always). George’s rule would coalesce the move d-c, Briggs’ rule would freeze. d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  27. Example:Simplify (K=3) stack f (c, no-spill) (g, no-spill) (h, no-spill) e j k b m d c CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  28. Example:Potential Spill (K=3) stack f (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e j k b m Neither coalescing nor freezing help us. At this point we should use some profitability analysis to choose a node as may-spill. d CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  29. Example:Simplify (K=3) stack f (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) j k b m d CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  30. Example:Simplify (K=3) stack (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) j k b m d CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  31. Example:Coalesce (K=3) stack (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) j k b d CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  32. Example:Coalesce (K=3) stack (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) j-b k d CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  33. Example:Coalesce (K=3) stack (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) j-b k CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  34. Example:Coalesce (K=3) stack (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) j-b CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  35. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  36. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  37. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  38. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  39. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  40. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g This is when our optimism could have paid off. CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  41. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  42. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  43. Example:Select (K=3) stack f (j-b, no-spill) (k, no-spill) (d, no-spill) (m, no-spill) (f, no-spill) (e, may-spill) (c, no-spill) (g, no-spill) (h, no-spill) e R1 R2 j k b m R3 d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  44. So, is it possible for K=3? f e j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  45. Example:Simplify (K=3) f e j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  46. Example:Simplify (K=3) f e j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  47. Example:Simplify (K=3) f e j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  48. Example:Simplify (K=3) f e Impossible! But only 3 variables are live at any time…there may be a way? j k b m d c h g CMPUT 680 - Compiler Design and Optimization (Appel, pp. 237)

  49. LIVE-IN: k j g := mem[j+12] h := k -1 f := g + h e := mem[j+8] m := mem[j+16] b := mem[f] c := e + 8 d := c k’ := m + 4 j’ := b LIVE-OUT: d k’ j’ Example as basic block:3 Registers by renaming k & j k j g h f e m b c d k’ j’ CMPUT 680 - Compiler Design and Optimization

  50. LIVE-IN: k j g := mem[j+12] h := k -1 f := g + h e := mem[j+8] m := mem[j+16] j’ := mem[f] d := e + 8 k’ := m + 4 LIVE-OUT: d k’ j’ Example as basic block:3 Registers by renaming k & j k j g h f e m j’ d k’ CMPUT 680 - Compiler Design and Optimization

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