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Semelhante a (Relative) Safety Properties for Relaxed Approximate Programs
Semelhante a (Relative) Safety Properties for Relaxed Approximate Programs (20)
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(Relative) Safety Properties for Relaxed Approximate Programs
- 1. (Relative) Safety Properties for Relaxed Approximate Programs Michael Carbin and Martin Rinard MIT EECS and CSAIL
- 2. Approximate Computing Media Processing, Machine Learning, Search
- 3. Fuzzy = Tradeoff of Accuracy and Cost Accuracy Time/Resources/Cost 0% 100% Highly Accurate, Expensive Less accurate, Inexpensive
- 4. Standard Program Model Accuracy Time/Resources/Cost 0% 100% One point in tradeoff space
- 5. Relaxed Program Model Accuracy Time/Resources/Cost 0% 100% Admits executions at multiple points in tradeoff space Relaxed programs can dynamically and automatically adapt
- 6. Producing Relaxed Programs Task Skipping/Loop Perforation - Rinard ICS ‘06, Misailovic ICSE ‘10 Dynamic Knobs - Hoffmann ASPLOS ‘11 Approximate Memories - Lui ASPLOS ‘11, Sampson PLDI ‘11 Approximate Memoization - Chaudhuri FSE ‘11 Unsynchronized Parallelization - Misailovic MIT-TR ‘10, Rinard RACES ‘12
- 7. Unsynchronized Parallelization When is this acceptable?
- 8. Defining Acceptable IntegrityAccuracy Key: any implementation that satisfies the stated acceptability properties is acceptable Acceptability Properties
- 9. Defining Acceptable IntegrityAccuracy Key: any implementation that satisfies the stated acceptability properties is acceptable Acceptability Properties Safety
- 10. How do we verify the safety of relaxed programs?
- 11. Program Logic (Hoare Logic) {x = 1} x = x + 1 {x = 2} If we know P is true of the program, then after execution of s, Q is also true }{}{ QsP Standard Hoare Logic doesn’t capture what we want
- 12. General Model for Relaxed Programs A general primitive for relaxed sequential programs [1]: relax (n) st (n <= old(n)); for (uint i = 0; i < n; ++i) {...} [1] Proving Acceptability Properties of Nondeterministic Relaxed Approximate Programs. Carbin, Kim, Misailovic, Rinard. PLDI ‘12 Modified Variables Relaxation Predicate Loop Perforation!
- 13. Applying Standard Hoare Logic • Note: relaxation doesn’t modify y • If S(y) holds in the original program, then it also holds in relaxed program <...> { P(x, y) && Q(y) } relax (x) st (true); { Q(y) } <...> { R(x, y) && S(y)} assert R(x, y) && S(y); Lose P because x is modified Prove both R and S
- 14. Relational Program Logic {x<r> == x<o> && y<r> == y<o>} relax (x) st (true); {y<r> == y<o>} relrel QsP
- 15. Applying Relational Program Logic <...> {x<r> == x<o> && y<r> == y<o>} relax (x) st (true); { y<r> == y<o> } <...> {R(x<r>, y<r>) && y<r> == y<o> } assert R(x, y) && S(y) ; x different but y the same Only prove R If S(y<o>) is true and y<r> == y<o> then S(y<r>) is true Relational reasoning is the bridge
- 16. If original program satisfies all assertions, then the relaxed program satisfies all assertions Relative Safety More in our RACES paper: • Small formalization of unsynchronized parallelization • Formal statement of relative safety • Simple example from the Jade Benchmarks suite Established through any means: verification, testing, code review
- 17. Takeaway Relax Semantics. Preserve Safety. Reuse Proofs
Notas do Editor
- We are being exposed to a a lot more applications that are being built for approximate computing
- What I mean by approximation is there is larger space of potential solutions to a problem, each with differing accuracy versus cost, where cost is in terms of time, or power, or storage. A developer’s task is often to identify some set of solutions that gives the majority of the accuracy for some given or reasonable amount of time.
- What I mean by approximation is there is larger space of potential solutions to a problem, each with differing accuracy versus cost, where cost is in terms of time, or power, or storage. A developer’s task is often to identify some set of solutions that gives the majority of the accuracy for some given or reasonable amount of time.
- How do we verify properties like these for relaxed programs in general?
- As we can see, it’s entirely possible to verify the program outright. Let P, Q, and R be properties in first order logic describing states of the program. The relax statement has the semantics of a non-deterministic assignment
- Keep track of relations between original and relaxed program.
- FOCUS: Don’t need to restablish S(y).This is great. Relational reasoning allows us to transfer properties we’ve proved of the original program to the relaxed program in cases where we do not interfere.
- This addresses the key problem. Address how we can hope to verify large programs, because we can using whatever means necessary to verfy