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Scalable Points-to Analysis. Rupesh Nasre. Advisor: Prof. R. Govindarajan. Comprehensive Examination. Jun 22, 2009.

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Outline. Introduction (points-to analysis). Issues involved in context-sensitive analyses. Bloom filter. Points-to analysis with bloom filter. Experimental evaluation. Future work.

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What is Pointer Analysis? Pointer analysis is the mechanism of statically finding out possible run-time values of a pointer and relation of various pointers with each other.

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Why Pointer Analysis? for parallelization: fun(p); fun(q); for common subexpression elimination: x = p + 2; y = q + 2; for dead code elimination. if (p == q) { fun(); } for other optimizations.

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Introduction. Flow sensitivity. Context sensitivity. Field sensitivity. Unification based. Inclusion based.

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Flow sensitivity. p = &x; p = &y; label:... flow-sensitive, at label: {(p, y)}. flow-insensitive: {(p, x), (p, y)}.

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Context sensitivity. caller1() { caller2() { fun(int *ptr) { fun(&x); fun(&y); a = ptr; } } } context-insensitive: {(a, x), (a, y)}. context-sensitive: {(a, x)} along call-path caller1, {(a, y)} along call-path caller2.

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Field sensitivity. a.f = &x; field-sensitive: {(a.f, x)}. field-insensitive: {(a, x)}.

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Unification based. one(&s1); one(struct s*p) { two(struct s*q) { one(&s2); p->a = 3; q->b = 4; two(&s3); two(p); } } unification-based: {(p, &s1), (p, &s2), (p, &s3), (q, &s1), (q, &s2), (q, &s3)}.

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Inclusion based. one(&s1); one(struct s*p) { two(struct s*q) { one(&s2); p->a = 3; q->b = 4; two(&s3); two(p); } } inclusion-based: {(p, &s1), (p, &s2), (q, &s1), (q, &s2), (q, &s3)}

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Related work. Scalable points-to analyses. B. Steensgaard, Points-to Analysis in Almost Linear Time, POPL 1996. J. Whaley and M. S. Lam, Cloning-Based Context-Sensitive Pointer Alias Analysis Using Binary Decision Diagrams, PLDI 2004. B. Hardekopf and C. Lin, The ant and the grasshopper: fast and accurate pointer analysis for millions of lines of code, PLDI 2007. V. Kahlon, Bootstrapping: a technique for scalable flow and context- sensitive pointer alias analysis, PLDI 2008.

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Issues with context-sensitivity. main() { f(a) { g(b) { S1: f(&x); S3: g(a);... S2: f(&y); S4: g(z);... } } } ff gggg main S1 S2 S3S4S3S4 Invocation graph. Exponential number of contexts.

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Issues with context-sensitivity. Storage requirement increases exponentially. Along S1-S3-S5-S7, p points to {x1, x3, x5, x7}. Along S1-S3-S5-S8, p points to {x1, x3, x5, x8}. Along S1-S3-S6-S7, p points to {x1, x3, x6, x7}. Along S1-S3-S6-S8, p points to {x1, x3, x6, x8}. Along S1-S4-S5-S7, p points to {x1, x4, x5, x7}. Along S1-S4-S5-S8, p points to {x1, x4, x5, x8}. Along S1-S4-S6-S7, p points to {x1, x4, x6, x7}. Along S1-S4-S6-S8, p points to {x1, x4, x6, x8}. Along S2...

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Tackling scalability issues. How about not storing complete contexts? How about storing approximate points-to information? Can we have a probabilistic data structure that approximates the storage? Can we control the false-positive rate?

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Bloom filter. A bloom filter is a probabilistic data structure for membership queries, and is typically implemented as a fixed-sized array of bits. To store elements e1, e2, e3, bits at positions hash(e1), hash(e2) and hash(e3) are set. 11 e1, e3e2

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Points-to analysis with Bloom filter. A constraint is an abstract representation of the pointer instruction. p = &xp.pointsTo(x). p = qp.copyFrom(q). *p = qp.storeThrough(q). p = *qp.loadFrom(q). Function arguments and return values resemble p = q type of statement. Note, each constraint also stores the context.

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Points-to Analysis with Bloom filter. If points-to pairs (p, x) are kept in bloom filter, existential queries like “does p point to x?” can be answered. What about queries like “do p and q alias?”? What about context-sensitive queries like “do p and q alias in context c?”? How to process assignment statements p = q? How about load/store statements *p = q and q = *p?

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Multi-Bloom filter. Points-to pairs are kept in a bloom filter per pointer. A bit set to 1 represents a points-to pair. Example (diagram on the next slide): Points-to pairs {(p, x), (p, y), (q, x)}. hash(x) = 5, hash(y) = 6. Set bit numbers: p.bucket[5], p.bucket[6], q.bucket[5]. Can hash(x) and hash(y) be the same? Yes.

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Multi-Bloom filter. 00000110 05 6 (p, x)(p,y) 0000010 0 5 (q, x) p.bucket. q.bucket. 00 0 0

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Multi-Bloom filter. Each pointer has a fixed number of bits for storing its points-to information, called as a bucket. Thus, if bucket size == 10, all pointees are hashed to a value from 0 to 9. This notion is extended to have multiple buckets for each pointer for multiple hash functions.

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Handling p = q. Points-to set of q should be added to the points- to set of p. Bitwise-OR each bucket of q with the corresponding bucket of p. Example on the next slide.

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Example. h1(x) = 0, h2(x) = 5, h1(y) = 3, h2(y) = 3.

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Handling p = *q and *p = q. Extend multi-bloom to have another dimension for pointers pointed to by pointers. The idea can be extended to higher-level pointers (***p, ****p, and so on). We implemented it only for two-level pointers. Example on the next slide.

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Another example. h(x) = 1, h(y) = 4, hs(p1) = 1, hs(p2) = 2.

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Alias query: context-sensitive. If the query is DoAlias(p, q, c), for each hash function ii { hasPointee = false; for each bucket-bit jj if (p.bucket[c][ii][jj] and q.bucket[c][ii][jj]) hasPointee = true; if (hasPointee == false) return NoAlias; } return MayAlias;

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Alias query: context-insensitive. If the query is DoAlias(p, q), for each context c { if (DoAlias(p, q, c) == MayAlias) return MayAlias; } return NoAlias;

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Experimental evaluation: Time.

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Experimental evaluation: Memory.

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Experimental evaluation: Precision.

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Summary. Bloom filters offer an effective way to represent points-to information. Precision can be as close to exact, still saving storage. Parameters can be configured for an application usage.

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Future work. Flow-sensitive analysis using counting bloom filter. need to support kill operation. require resetting bits. may introduce false negatives. storage requirement of flow-sensitive analysis is an issue.

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Future work. Adaptive bloom filter parameters. not all pointers require same number of bits. bits saved from one pointer can be used by another. storage required for counters representing number of bits for each pointer. bitwise operations are not straightforward.

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Future work. Efficient flow-insensitive analysis. approach similar to wave/deep propagation¹. similarity with flow-sensitive analysis. preliminary results show that the number of iterations to reach a fix-point can be reduced, e.g., on an example set of programs, total number of iterations are reduced from 180 (deep) to 148. ¹ F M Q Periera, Daniel Berlin, Wave Propagation and Deep Propagation for Pointer Analysis, CGO 2009.

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Scalable Points-to Analysis. Rupesh Nasre. Advisor: Prof. R. Govindarajan. Comprehensive Examination. Jun 22, 2009.

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Approach. Start from main(). Add constraints for each pointer statement. Flow-insensitive. Jump to the called function, process it and return. Continue with the caller. A function called multiple times is processed multiple times. Keep context along with each constraint. Recursion is handled by iterating over the cycle until a fix- point. This is context-insensitive. At the end, iterate over constraints to extract points-to information in context-sensitive manner. Iteration makes it flow-insensitive.

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Example. main() {f(a) { S1:r1 = f(p)return a S2:r2 = f(q)} S3:r3 = g(p)g(b) { S4:r4 = h()c = b} h() { p = &x q = &y } Only realizable paths. Along main-S1, r1 points to x. Along main-S2, r2 points to y. Even though main-S3 and main- S4 are different contexts, we merge context-information. Thus, c points to x. Since main-S1 and main-S2 call the same function, we do not merge the information. Thus, r1 does not alias with r2.

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Experimental evaluation: Mod/Ref.

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