Symbolic Bounds Analysis of Pointers, Array Indices, and Accessed Memory Regions Radu Rugina and Martin Rinard

1
Symbolic Bounds Analysis of Pointers, Array
Indices, and Accessed Memory RegionsRadu Rugina
and Martin Rinard

• 6/6
• AMO????????
• M1 ?? ??

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Introduction

• ????????????????????????????????
• ???????????????????????????????????
• Symbolic ??????
• ??????????????????
• ???????????
• ????????????
• ???????
• ????????????????

3
?????

• ??????????
• ???????????
• ?????????
• ??
• ??????????
• ??

4
???????

• ????????????????????????
• ????????
• Cilk (C?????????) ???

5
?????

• ?Procedure ??????????????????
• ?????????????????
• allocation blocks
• ????????????
• symbolic regions
• ??block?????????
• ????????
• ?????????????(??????)

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????

• dcInc ( int q, int m) ???
• allocation block a (l.24)???? symbolic
  region????p0, p0 n0 - 1 ?????
• ???? l.15 ? l.16 ??????????????????
• top-level ???????(l.26) ???A ???? A, A size -
  1 ??????????????????????????????

7
?????????

• ?????
• ???????????????????????????????????
• ??????allocation block ???symbolic region ????
• ?????????????????????????
• ?????????????????????????????????????

8
????????
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Pointer and Read-Write Sets Analysis

• R. Rugina and M. Rinard 99
• ??????????????????Procedure ????????
  ?????(????????)????????

10
Symbolic Analysis

• ?????????????????????????????
• ???????? allocation block ???????????????????
• Symbolic Analysis ????3?????????
• Intraprocedural Bounds Analysis
• Intraprocedural Region Analysis
• Interprocedural Region Analysis

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Symbolic Analysis ???

• Intraprocedural Bounds Analysis
• ???????????????????????????????
• Intraprocedural Region Analysis
• 1. ?????????procedure ? allocation block
  ?????????????????
• Interprocedural Region Analysis
• ????????????????procedure ????????????????????????
  ????????

12
Intraprocedural Bounds Analysis (1/4)????

• ???procedure f ????? B Bj 1 ? j ? L
  ?????
• ?????????????? ?? uv,j ? ?? lv,j ??????

13
Intraprocedural Bounds Analysis (2/4)?????????

• ????????????????????????
• ???????????????
• ????????
• ????????????????????????

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Intraprocedural Bounds Analysis (3/4)????????

• ?????
• ???????B1????????????? v ????????
  v0(??????)??????????????
• ??????????
• ????????????????????????????????????????????????
  ??
• ????
• ????????????????????????
• min ?v?lj2 (uv,j - lv,j )

15
????????????
16
Intraprocedural Bounds Analysis (4/4)????????

• ??????????????????????
• li,2 c1q0 c2m0 c3 li,3 c4q0 c5m0 c6
• ???????????????????
• ??????? li,2 lt li,3 ?? c1ltc4, c2ltc5, c3ltc6
• ??????????????????????????????????????????????
• ??????????????????
• ????? Cn ????????
• ????????????????????

17
???????????

• ????????????? li,3 0 ui, 3 m0-1??? ?l.7
  ???? i ?????? 0,m0 - 1?????

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Region Analysis

• Intraprocedural Region Analysis
• ??????????????????? f ? allocation block a
  ????????RRlocalf,a ?RWlocalf,a ????
• ????????????????????????????????????????
• Interprocedural Region Analysis
• ????????????(call site)????????????????????????
• ???????????????????????(Symbolic Unmapping)

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symbolic unmapping ??

• l.13?????(cs1 call site 1???)?unmapping???SUcs1
  (RWbaseInc,a) p0, p0 n0 - 1 ???

20
???Symbolic Unmapping(1/2)

• ???????????????
• ?????????????????????????????????????????
• ???????????????????????????????????
• Symbolic Bounds Analysis ???????????????
• ???????????????????????????????????????????

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???Symbolic Unmapping(2/2)

• ??????? f ??????? RRlocalf,a ?RWlocalf,a ?????
• ??????????????????
• RRf,a lrd f,a,1, urd f,a,1... lrd f,a,j,
  urd f,a,j
• RWf,a lwr f,a,1, urd f,a,1... lwr f,a,j,
  urd f,a,j
• ???????
• RRlocalf,a ? RRf,a
• ?????????????????????
• SUcs(RRg,a )? RRf,a
• ??????????????????
• ????????????????????????????????????

22
???Symbolic Unmapping??

• dcInc ??
• l13, l15, l16 ????????????????
• dcInc ??? allocated block ????????????????????????
  ????
• lwrdcInc,a p0, uwrdcInc,a P0 n0 - 1???

23
???????

• ??????????????allocation blocks
  ???????????????????????????????
• RRbaseInc,a RRbaseInc,a q0, q0 m0 - 1
  
• RRdcInc,a RRdcInc,a p0, p0 n0 - 1
• RRmain,a RRmain,a -8, 8
• ????????????????????????????

24
?????????

• ????
• ???????????????????????????????????????????
• ???????
• ???????????????????????????????????????????
• ????????
• ??????????????????????????????
• ?????????????????????????????

25
????????

• ????????????????
• ????????????????????????
• ????????????????
• ?????????????????????????
• ??????????????????????
• ??????????????????????????????????????????

26
?????

• ?????????????????????????????
• ?????????????????????????
• ????????????????Ghost allocation blocks
  ??????????????
• ????????????????????????

27
??

• SUIF ?????????????
• Cilk ? C ??????????
• Cilk ?????????????
• C ??????????????
• ?????????????????????
• ??????????????????????????????????????????????????
  ??

28
???????

• Fibonacci
• QuickSort
• MergeSort
• Heat(?????????)
• Knapsack
• BlockMul (??????????????????)
• NoTempMul(?????????????)
• LU

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??(1/3)

• Knapsack ?????????????????????????????????????????
  
• Knapsack ??????????????????????
• ?????
• Sun Ultra Enterprize (8CPUs)
• 8,000,000 numbers ????
• 10241024?????
• ??????????????????

30
??(2/3)
(????????????????????????????)
31
??(3/3)

• ???????
• ??????????????????????????????????????????????
• ??????????????????????????????????

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????(1/4)

• Symbolic Memory Access Region Analysis
• ?????
• ?????????????????????????? ad hoc ?????????
• ??????????
• ????????????????
• ??????????????????????????????????????
• ????????????????????????????????????????

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????(2/4)

• Array Bounds Check Elimination
• ?????
• ?????????????
• ?????????????????
• ???????????????????????????????????
• ???????????????????
• ?????????????????????????????????????????
• ???????????????????
• ?????????????????????

34
????(3/4)

• Race Detection
• ?????
• ??????????????????????????????
• ?????Signal/wait ???????????????
• Lock ??????????????????????????????????
• ??????????
• ??????????????????????????????????????????

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????(4/4)

• Parallelizing Compiler
• ??????????????????????????????
• ??????????????????????????????????
• ?????????????????????????????????????
• ???Shape analysis ??Commutativity analysis
  ?????????

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??Reference

• R. Rugina and M. Rinard. Pointer analysis for
  multithreaded programs. In Proceedings of the
  SIGPLAN '99 Conference on Program Language Design
  and Implementation, Atlanta, GA, May 1999.
• F. Gustavson. Recursion leads to automatic
  variable blocking for dense linear-algebra
  algorithms. IBM Journal of Research and
  Development, 41(6)737-755, November 1997.
• J. Frens and D. Wise. Auto-blocking
  matrix-multiplication or tracking BLAS3
  performance from source code. In Proceedings of
  the 6th ACM SIGPLAN Symposium on Principles and
  Practice of Parallel Programming, Las Vegas, NV,
  June 1997.
• S. Chatterjee, A. Lebeck, P. Patnala, and M.
  Thottethodi. Recursive array layouts and fast
  matrix multiplication. In Proceedings of the 11th
  Annual ACM Symposium on Parallel Algorithms and
  Architectures, Saint Malo, France, June 1999.