Partial Redundancy Elimination and SSA Form
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1 Topic 5a Partial Redundancy Elimination and SSA Form \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic- 7b.ppt 1
2 References Robert Kennedy, Sun Chan, Shin-ming Liu, Raymond Lo, Pend Tu, Fred Chow. Partial redundancy elimination in SSA Form. ACM Trans. On Programming Languages and Systems, 21(3), May 1999: Drechsler K. and Stadel M. A variation of Knoop, Ruthing, and Steffen s lazy code motion. SIGPLAN Notices, 28(5), May, 1993: Keith Cooper, Linda Torczon. Engineering a compiler \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 2
3 Outline Partial Redundancy Elimination (PRE) SSAPRE (a short summary) \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 3
4 KCC Compiler Infrastructure Front end Middle end Back end Machin ne Model Fortran C C++ fe90 gfec gfecc Very High WHIRL High WHIRL Middle WHIRL Low WHIRL Very Low WHIRL CGIR Asm file Source to IR (Scanner Parser RTL WHIRL) VHO (Very High WHIRL Optimizer) Standalone Inliner W2C/W2F IPA (inter-procedural analysis & opt) LNO (Loop unrolling/fission/fusion/tiling/peeling etc) PREOPT (point-to analysis etc) WOPT - SSAPRE (Partial Redundancy Elimination) - VNFRE (Value numbering based full redundancy elim.) RVI-1 (Register Variable Identification) RVI-2 Some peephole opt Cflow (control flow opt) EBO (extended block opt.) PQS (predicate query system) Loop Opt (Unrolling + SWP) GCM (global code motion), HB sched (hyperblk schedule) GRA/LRA (global/local register alloc) \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 4
5 Important Observation An operand of a φ function is regarded as occurring at the end of its corresponding predecessor block. The result of a φ function is regarded as occurring at the beginning of the block that contains it \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 5
6 Partial Redundancy Elimination B 1 t x*y a t Is the program in SSA form before and after PRE? a x*y t x*y B 2 X*y is partially redundant here X*y is made redundant here b x*y b t B \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 6
7 Problem Formulation for PRE For an expression, identify its partially redundant occurrences Safely insert occurrences (to new temporaries) at some points Delete the original partially (now fully) redundant occurrences. Replace them by loads from a temporary variable \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 7
8 PRE Basics Availability: An expression, say, x*y, is available at a program point p if EVERY path from entry to p evaluates the expression before reaching p And there are no assignments to x or y after the (last) evaluation but before p (on all paths). Availability implies full redundancy \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 8
9 PRE Basics (Cont.) Partial availability: An expression, say, x*y, is partially available at a program point p if SOME paths from entry to p evaluates the expression before reaching p And there are no assignments to x or y after the (last) such evaluation but before p. Partial availability implies partial redundancy \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 9
10 PRE Basics (Cont.) Anticipatability: An expression e is anticipatable ( down-safe ) at a program point p if it appears (without redefinition) along ALL paths from p to an exit of the program X*y is anticipatable here B 1 B 2 a x*y b x*y B \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 10
11 Safe Placement - Safe insertion: If an inserted computation occurs at a point where the computation is anticipated. - Unsafe insertion: means that some original path in the program did not contain this computation. May increase the execution time of the program May cause exceptions \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 11
12 Safe Placement: Example x*y Safe Not safe x*y This is called an critical edge. Allowable if we can insert computations on an edge. Otherwise, need split \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 12
13 Optimal Placement (Cont d) Computationally optimal If no other safe placement can result in fewer occurrences of the computation along any path from entry to exit in the program \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 13
14 Optimal Placement (cont d) Lifetime optimal Minimize the lifetimes of the introduced temporaries. Intuition: delay an expression to the latest point (Lazy Code Motion [KnoopEtal92, DrechslerStadel93]) \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 14
15 Outline Partial redundancy elimination (PRE) SSAPRE (a short summary) \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 15
16 SSAPRE \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 16
17 SSAPRE: Motivation Traditional data flow analysis based on bit-vectors do not interface well with SSA representation \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 17
18 Before PRE Traditional Partial Redundancy Elimination B 1 a x*y B 2 b x*y B 3 SSA form After PRE t x*y B 1 t x*y B 2 a t b t B 3 Not SSA form! \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 18
19 SSAPRE: Motivation (Cont.) Traditional PRE needs a postpass transform to turn the results into SSA form again. SSA is based on variables, not on expressions \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 19
20 SSAPRE: Motivation (Cont.) Representative occurrence Given a partially redundant occurrence E 0, we define the representative occurrence for E 0 as the nearest to E 0 among all occurrences that dominate E 0. Unique and well-defined \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 20
21 FRG (Factored Redundancy Graph) E E E E Control flow edge E =Φ(E, Φ E, ) Redundancy edge E E E E Without factoring Factored \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 21
22 FRG (Factored Redundancy Graph) E E t 0 x*y t 1 x*y E =Φ(E, E, ) t 2 Φ(t 0, t 1, t 3 ) E E Assume E=x*y t 2 t 2 Note: This is in SSA form \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 22
23 Observation Every use-def edge of the temporary corresponds directly to a redundancy edge for the expression \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 23
24 Intuition for SSAPRE Construct FRG for each expression E Refine redundant edges to form the use-def relation for each expression E s temporary Transform the program For a definition, replace with t E For a use, replace with t Sometimes need also insert an expression \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 24
25 An Example a 1 a 2 φ(a 4, a 1 ) B 1 B 2 a 1 t 1 a 1 + b 1 t2 φ φ(t 4, t 1 ) a 2 φ(a 4, a 1 ) B 1 B 2 a 2 +b a 3 B 3 t 2 a 3 t 3 a 3 + b 1 a 4 φ(a 2, a 3 ) a 4 +b B 4 t 4 φ(t 2, t 3 ) a 4 φ(a 2, a 3 ) t 4 B 4 exit B 5 exit \course\cpeg421-08s\topic-5a.ppt\course\cpeg421-07s\topic-7b.ppt 25
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