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Transactional Memories: a theoretical introduction Selim Arsever & Pascal Perez Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A A<w,r> | A<w,r> |

  1. Transactional Memories: a theoretical introduction Selim Arsever & Pascal Perez

  2. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A A<w,r> | A<w,r> | M<w,r,v> = w<v>.WORK.r(v').[v'=v].A | w<v>.WORK.r(v').[v'=v].A | w(f).M<w,r,f> + r<v>.M<w,r,v>

  3. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<v>.WORK.r(v').[v'=v].A | w(a).M<w,r,f> + r<v>.M<w,r,v>

  4. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<v>.WORK.r(v').[v'=v].A | w(a).M<w,r,a> + r<v>.M<w,r,v>

  5. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<v>.WORK.r(v').[v'=v].A | w(a).M<w,r,a> + r<v>.M<w,r,v>

  6. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<v>.WORK.r(v').[v'=v].A | w(f).M<w,r,f> + r<a>.M<w,r,a>

  7. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<b>.WORK.r(v').[v'=b].A | w(b).M<w,r,b> + r<a>.M<w,r,a>

  8. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<b>.WORK.r(v').[v'=b].A | w(b).M<w,r,b> + r<a>.M<w,r,a>

  9. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[v'=a].A | w<b>.WORK.r(v').[v'=b].A | w(f).M<w,r,f> + r<b>.M<w,r,b>

  10. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[b=a].A | w<b>.WORK.r(v').[v'=b].A | w(f).M<w,r,f> + r<b>.M<w,r,b>

  11. Shared Memory Problems M(w,r,v) := w(f).M<w,r,f> + r<v>.M<w,r,v> A(w,r) := w<v>.WORK.r(v').[v'=v].A → w<a>.WORK.r(v').[b=a].A | w<b>.WORK.r(v').[v'=b].A | w(f).M<w,r,f> + r<b>.M<w,r,b>

  12. Locking is dangerous ● What if a thread fails whilst holding a lock? ● Deadlocks happen! ● Linux pros on http://lwn.net/Articles/86859/

  13. Locking does not scale well Fine grained locked data structures implementation exist of the shelf but… Global knowlegde!

  14. Transaction A tomicity C onsistency I solation D urability

  15. Transaction A + B + C should remain constant under the execution of both transactions in any order. Correct: Wrong: A = A – 10 lock L 1 lock L 1 lock L 2 lock L 1 B = B – 20 A = A – 10 B = B – 20 B = B + 10 unlock L 1 unlock L 1 unlock L 2 unlock L 1 C = C + 20 B = B + 10 C = C + 20

  16. R(0) Transactional Memory W(0) W(1) R(1) W(0) A B C

  17. R(1) Transactional Memory W(0) W(1) R(1) W(0) A B C

  18. Transactional Memory Initial Situation: M T 1 n b TM T 2 T 3

  19. Transactional Memory T 1 gives his chanels to TM: M T 1 n b TM {o,g,a,c,x}

  20. Transactional Memory T 1 gets it’s copie of M: } ’ r , ’ w M’ { M T 1 n b TM {o,g,a,c,x}

  21. Transactional Memory T 1 tries to commit: } ’ r , ’ w M’ { M T 1 n b TM {o,g,a,c,x} T 2 T 3

  22. Transactional Memory A new TM is created: } ’ r , ’ w M 1 { M T 1 n b TM {o,g,a,c,x} M ’ n’’ T 2 TM’ T 3

  23. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  24. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  25. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  26. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  27. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  28. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  29. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  30. Concurrent Commit T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : c 2 .(c 2 + x 2 .T 2 <b>) TM : crash | !... | k.x 1 | k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | c 2 .crash.n 2 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 2 )

  31. Exceptions Enhancement Avoiding Unnecessary Exceptions ● TM := (… | !p(x,cancel).(k.x + cancel)) G := … ( v cancel)(p<x,cancel>. … .(… | cancel.!k) Allowing Needed Exceptions ●

  32. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  33. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  34. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  35. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  36. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  37. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  38. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | p(x).k.x | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  39. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | p(x).k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

  40. Commit while Starting T 1 : c 1 .(c 1 + x 1 .T 1 <b>) T 2 : b<o 2 ,g 2 ,a 2 ,c 2 ,x 2 >.o.g … TM : crash | !... | k.x 1 | p(x).k.x 2 | ! p(x).k.x | c 1 .crash.n 1 ’(w’’,r’’,n’’).(TM<b,n’’>| !k | c 1 ) | b(o 2 ,g 2 ,a 2 ,c 2 ,x 2 ).p<x 2 >.o …

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