1. Data-parallel Abstractions for Irregular Applications Keshav Pingali University of Texas, Austin

2. Motivation Multicore processors are here –but no one knows how to program them A few domains have succeeded in exploiting parallelism –Databases: billions of SQL queries are run in parallel everyday –Computational science Both these domains deal with structured data –Databases: relations –Computational science: mostly dense and sparse arrays “Universal” parallel computing –Unstructured data is the norm: graphs, trees, lists,… What can we do to make it easier for programs that manipulate unstructured data to exploit multicore parallelism?

3. Organization of talk Two case studies –Delaunay mesh refinement –Agglomerative clustering  Irregular programs have “generalized” data-parallelism Exploiting irregular data-parallelism: Galois system –Programming model –Implementation Experimental evaluation Ongoing work –Exploiting locality –Scheduling

4. Two case studies

5. Delaunay Mesh Refinement Meshes useful for –Finite element method for solving PDEs –Graphics rendering Delaunay meshes (2-D) –Triangulation of a surface, given vertices –Delaunay property: circumcircle of any triangle does not contain another point in the mesh In practice, want all triangles in mesh to meet certain quality constraints –(e.g.) no angle > 120° Mesh refinement: –fix bad triangles through iterative refinement

6. Refinement Algorithm { pick a bad triangle add new vertex at center of circumcircle gather all triangles that no longer satisfy Delaunay property into cavity re-triangulate affected region, including new point // some new triangles may be bad themselves } while there are bad triangles

7. Refinement Example Original MeshRefined Mesh

8. Sequential Algorithm Mesh m = /* read in mesh */ WorkList wl; wl.add(mesh.badTriangles()); while (true) { if ( wl.empty() ) break; Element e = wl.get(); if (e no longer in mesh) continue; Cavity c = new Cavity(e);//determine new cavity c.expand(); c.retriangulate();//re-triangulate region m.update(c);//update mesh wl.add(c.badTriangles()); }

9. Properties of algorithm Actual code is far more complex –boundaries, especially non-convex boundaries are a pain Average work per triangle (measured on Itanium) –1M instructions, 100K floating-pt instructions Don’t-care non-determinism –Cavities of bad triangles may overlap –Therefore final mesh may depend on order in which bad triangles are processed –Any order will end up with a good mesh (in 2-D) Number of bad triangles fixed by algorithm may be different for different orders –Heuristics for ordering bad triangles for processing are known –Not widely used

10. Parallelization Opportunities Unit of work: fixing a bad triangle Bad triangles with non-overlapping cavities can be processed in parallel. No obvious way to tell if cavities of two bad triangles will overlap without actually building cavities  compile-time parallelization will not work

11. Agglomerative Clustering Input: –Set of data points –Measure of “distance” (similarity) between them Output: dendrogram –Tree that exposes similarity hierarchy Applications: –Data mining –Graphics: lightcuts for rendering with large numbers of light sources

12. Clustering algorithm Sequential algorithm: iterative –Find two closest points in data set –Cluster them in dendrogram –Replace pair in data set with a “supernode” that represents pair Placement of supernode: use heuristics like center of mass –Repeat until there is only one point left

13. Key Data Structures Priority queue: –Elements are pairs where p is point in data set n is its nearest neighbor –Ordered by increasing distance kdTree: –Answers queries for nearest neighbor of a point –Convention: if there is only one point, nearest neighbor is point at infinity (ptAtInfinity) –Similar to a binary search tree but in higher dimensions

14. Clustering algorithm: implementation kdTree := new KDTree(points); pq := new PriorityQueue(); for each p in points (pq.add( )); while (true) do { if (pq.size() == 0) break; pair := pq.get(); //get closest pair ………. Cluster c := new Cluster(p,n); //create supernode dendrogram.add(c); kdTree.remove(p); //update kdTree kdTree.remove(n); kdTree.add(c); Point m := kdTree.nearest(c); //update priority queue …………. pq.add( ); }

15. Clustering algorithm: details kdTree := new KDTree(points); pq := new PriorityQueue() for each p in points (pq.add( ) while (true) do { if (pq.size() == 0) break; pair := pq.get(); if (p.isAlreadyClustered()) continue; if (n.isAlreadyClustered()) { pq.add( ); continue; } Cluster c := new Cluster(p,n); dendrogram.add(c); kdTree.remove(p); kdTree.remove(n); kdTree.add(c); Point m := kdTree.nearest(c); if (m!= ptAtInfinity) pq.add( ); }

16. Parallelization Opportunities Natural unit of work: processing of a pair in PQ Algorithm appears to be sequential –pair enqueued in one iteration into PQ may be the pair dequeued in next iteration However, in example, and can be clustered in parallel Cost per pair in graphics app –100K instructions, 4K floating-point operations

17. Take-away lessons Irregular programs have data-parallelism –Data-parallelism has been studied in the context of arrays –For unstructured data, data-parallelism arises from work-lists of various kinds Delaunay mesh refinement: list of bad triangles Agglomerative clustering: priority queue of pairs of points Maxflow algorithms:list of active nodes –Boykov-Kolmogorov algorithm for image segmentation –Preflow-push algorithm Approximate SAT solvers ……. Data-parallelism in irregular programs is obscured within while loops, exit conditions, etc. –Need transparent syntax similar to FOR loops for structured data- parallelism

18. Take-away lessons (contd.) Parallelism may depend on “data values” –whether or not two potential data-parallel computations conflict may depend on input data (e.g.) Delaunay mesh generation: depends on shape of mesh Optimistic parallelization is necessary in general Compile-time approaches using points-to analysis or shape analysis may be adequate for some cases In general, runtime conflict-checking is needed Handling of conflicts depends on the application Delaunay mesh generation: roll back all but one conflicting computation Agglomerative clustering: must respect priority queue order

19. Current approaches to optimistic parallelization

20. Manual approaches Time-warp (1986) –Optimistic event-driven simulation –Distributed-memory computing model –Buffering of speculative state/roll-backs/commits implemented manually for particular application Pthreads + hand-coded optimistic parallelization –Most current implementations of Delaunay mesh refinement use this approach –Writing correct fine-grain locking code is tricky code tends to be very unstructured and complex tripled software costs for Unreal game engine

21. System support Hardware/software support for – buffering speculative state – detecting dependence violations by tracking reads and writes to memory locations –rollback/commit Implementations: –Thread-level speculation (TLS) –Transactional memory TLS: –Speculative execution of DO-loops with irregular array accesses (Padua/Rauchwerger/Torrellas/…) –Most implementations do not target while loops Only data speculation, no control speculation –Hardware support can be fairly complex –Mis-speculations limit speed-up (SUIF study) Transactional memory –Leverage cache-coherence hardware (Herlihy/Moss) –Support for optimistic synchronization in explicitly parallel programming model

22. Limitations of TLS/TM Applications require unbounded while-loops –Most algorithms involve a work-list of some kind –Detect more work as you traverse data structure to perform work Detecting dependence violations by tracking reads and writes to memory locations results in lots of spurious conflicts –Example: Delaunay mesh refinement Regardless of how worklist is implemented, there must be a location “head” that points to next bad triangle in list Every thread must read and write this location to get work When should update made a thread be made visible to other threads? –As soon as thread pulls work from worklist: cascading roll-backs are possible –Only after thread finishes its work: only one bad triangle can be processed at time –Other data structure manipulations (PQ,kdTree,graph) may have similar problems

23. Galois programming model and implementation

24. Beliefs underlying Galois system Optimistic parallelism is the only general approach to parallelizing irregular apps –Static analysis can be used to optimize optimistic execution Concurrency should be packaged within syntactic constructs that are natural for application programmers and obvious to compilers and runtime systems –Libraries/runtime system should manage concurrency (cf. SQL) –Application code should be sequential Crucial to exploit abstractions provided by object- oriented languages –in particular, distinction between abstract data type and its implementation type Concurrent access to shared mutable objects is essential

25. Components of Galois approach 1)Two syntactic constructs for packaging optimistic parallelism as iteration over sets 2)Assertions about methods in class libraries 3)Runtime system for detecting and recovering from potentially unsafe accesses by optimistic computations

26. (1)Concurrency constructs: two set iterators for each e in Set S do B(e) –evaluate block B(e) for each element in set S –sequential implementation set elements are unordered, so no a priori order on iterations there may be dependences between iterations –set S may get new elements during execution for each e in PoSet S do B(e) –evaluate block B(e) for each element in set S –sequential implementation perform iterations in order specified by poSet there may be dependences between iterations –set S may get new elements during execution

27. Galois version of mesh refinement Mesh m = /* read in mesh */ Set wl; wl.add(mesh.badTriangles()); // non-deterministic order for each e in Set wl do { //unordered iterator if (e no longer in mesh) continue; Cavity c = new Cavity(e);//determine new cavity c.expand();//determine affected triangles c.retriangulate();//re-triangulate region m.update(c);//update mesh wl.add(c.badTriangles()); //add new bad triangles to workset }

28. Observations Application program has a well-defined sequential semantics –No notion of threads/locks/critical sections etc. Set iterators –SETL language was probably first to introduce set iterators –However, SETL set iterators did not permit the sets being iterated on to grow during execution, which is important for our applications

29. Parallel computational model Object-based shared-memory model Computation performed by some number of threads Threads can have their own local memory Threads must invoke methods to access internal state of objects –mesh refinement:shared objects are worklist Mesh –agglomerative clustering priority queue kdTree dendrogram Shared Memory Objects

30. Parallel execution of iterators Master thread and some number of worker threads –master thread begins execution of program and executes code between iterators –when it encounters iterator, worker threads help by executing some iterations concurrently with master –threads synchronize by barrier synchronization at end of iterator Key technical problem –Parallel execution must respect sequential semantics of application program result of parallel execution must appear as though iterations were performed in some interleaved order for poSet iterator, this order must correspond to poSet order –Non-trivial problem each iteration may access mutable shared objects

31. Implementing semantics of iterators 1.Concurrent method invocations that modify object should not step on each other (mutual exclusion) –Library writer uses locks or some other mutex mechanism –Locks acquired during method invocation and released when method invocation ends 2.Uncontrolled interleaving may violate iterator semantics –In (a), contains?(x) must always return false but some interleavings will violate this (e.g., [add(x),contains?(x),remove(x)] –Sometimes, interleaving is OK and is needed for concurrency In (b) (motivated by Delaunay mesh refinement), method invocations can be interleaved provided result of get() is not argument of add()

32. (II) Assertions on methods Concurrent accesses to a mutable object by multiple threads are OK provided method invocations commute Shared Memory Objects get() add() get() add() get() add() get() add() get() add() get() add()

33. Assertions on methods (contd.) Semantic commutativity vs. concrete commutativity –for most implementations of workset, concrete data structure will be different for these two sequences, so commutativity fails –however, at semantic level, these set operations commute provide they operate on different set elements Conclusion: –semantic commutativity is crucial –class implementor must specify this information Commutativity of method invocations, not methods –get() commutes with add() only if element inserted by add() is not the same as the element inserted by get() get() add() get() add() get() add() ?

34. Assertions on methods (contd.) Updates to objects happen before iteration completes (eager commit) So we need a way of undoing the effect of a method invocation Class implementer must provide an ‘inverse’ method As before, semantic inverse is key, not concrete inverse Shared Memory m1 m3 m2

35. Example: set Class SetInterface { void add (Element x); [conflicts] - add(x) - remove(x) - contains?(x) - get() :x [inverse] remove(x) void remove(Element x); [conflicts] - add(x) - remove(x) - contains?(x) - get(): x [inverse] add(x) ……… }

36. Remarks Commutativity information is optional –No commutativity information for a mutable object means only one iteration can manipulate the object at a time Inverse method is more or less essential –for a class w/o commutativity information, inverse methods can be implemented by data copying Difficulty of writing specifications –in our apps, most shared objects are collections (sets, bags, maps) (e.g.), kdTree is simply a set with a nearestNeighbor operation –writing specifications is quite easy Relationship to Abelian group axioms –commutativity, inverse, identity

37. (III) Runtime system: commit pool Maintains iteration record for each ongoing iteration in system Status of iteration –running –ready-to-commit (RTC) –aborted Life-cycle of iteration –thread goes to commit pool for work –commit pool obtains next element from iterator assigns priority to iterator based on priority of element in set creates an iteration record with status running –when iteration completes status of iteration record is set to RTC when that record has highest priority in system, it is allowed to commit –if commutativity conflict is detected commit buffer arbitrates to determine which iteration(s) should be aborted commit buffer executes undo logs of aborted iterations Role of commit pool is similar to that of reorder buffer in out-of-order execution microprocessors

38. (III) Runtime system:conflict logs Each object has a conflict log –Contains sequence of method invocations that have been performed by ongoing iterations Each thread has undo log that contains sequence of inverse method invocations it must execute if it aborts When thread invokes method m on object O –Check if m commutes with method invocations and their inverses in conflict log of object O –If so, add m to conflict log of object O, and m -1 to undo log of thread and execute method –Otherwise, iteration aborts When thread commits iteration –Remove its invocations from conflict logs of all objects it has touched –Zero out its undo log Easy to extend this to support nested method invocations

39. Experiments

40. Experimental Setup Machines –4-processor 1.5 GHz Itanium 2 16 KB L1, 256 KB L2, 3MB L3 cache no shared cache between processors Red Hat Linux –Dual processor, dual core 3.0 GHz Xeon 32 KB L1, 4 MB L2 cache dual cores share L2 Red Hat Linux

41. Delaunay mesh generation Workset: implemented using STL queue Mesh: implemented as a graph –each triangle is a node –edges in graph represent triangle adjacencies –used adjacency list representation of graph Input mesh: –from Shewchuck’s Triangle program –10,156 triangles of which 4,837 were bad

42. Code versions Three versions –reference: sequential version without locks/threads/etc. –FGL: handwritten code that uses fine-grain locks on triangles –meshgen: Galois version Galois work-set implementation –used STL queue first: high abort ratio Sequential code: 21,918 completed+0 aborted Galois(q): 21,736 completed+28,290 aborted –replaced queue with array+random choice Galois(r): 21,908 completed+49 aborted

43. Results

44. Performance Breakdown *4 processor numbers are summed over all processors

45. Agglomerative clustering Two versions –reference: sequential version w/o locks/threads –treebuild: Galois version Data structures –priority queue –kd-tree –dendrogram Data set –from graphics scene with roughly 50,000 light sources

46. Speedups sequential version is best on 1 processor self-relative speed-up of almost 2.75 on 4 processors

47. Abort ratios and CPI Sequential and treebuild perform almost same number of instructions As before, cycles/instruction (CPI) is higher for treebuild mainly because of L3 cache misses –mainly from kdTree Committed iterations Aborted iterations 1 proc57486n/a 4 proc578612528

48. Degree of speculation Measured number of iterations ready to commit (RTC) whenever commit pool creates/aborts/commits an iteration Histogram shown above –X-axis in figure is truncated to show detail near origin –maximum number of RTC iterations is 120 Most of the time, we do not need to speculate too deeply to keep 4 threads busy –but on occasion, we do need to speculate deeply

49. Take-away points Support for ordering speculative computations is very useful for some apps –hard to do agglomerative clustering otherwise May need to speculate deeply in some apps Domain-specific information is very useful for proper scheduling –workset implementation made a huge difference in performance –will probably need to provide hooks for user to specify scheduling policy Reducing cache traffic is important to improve performance further

50. Ongoing work

51. Improving Performance Locality enhancement –Galois approach can expose data-parallelism in irregular applications –Scalable exploitation of parallelism requires attending to locality Specifying scheduling strategies –Delaunay mesh refinement example shows that scheduling of iterations can be critical to lower abort ratios –needed domain knowledge to fix problem

52. Galois methodology How easy is it to specify commutativity of method invocations? –How important is the distinction between semantic and concrete commutativity? How easy is it to write inverse methods? Given a specification of the ADT, can we check commutativity and inverse directives?

53. Benchmarks Existing benchmarks are useless –Wirth: Program = Algorithm + Data structure –current benchmarks are programs –we need algorithms and data structures experience with Delaunay mesh generation & STL queue –variety of input data sets to illustrate range of behavior

54. Irregular programs have data-parallelism –Work-list based iterative algorithms over irregular data structures Data-parallelism may be inherently data-dependent –Pointer/shape analysis cannot work for these apps Optimistic parallelization is essential for such apps –Analysis might be useful to optimize parallel program execution Exploiting abstractions provided by OO is critical –Only CS people still worry about F77 and C anyway…. Exploiting high-level semantic information about programs is critical –Galois knows about sets and ordered sets –Commutativity information is crucial Support for ordering speculative computations important Concurrent access to mutable objects is important Benchmark programs are bad –Programs  –Algorithms+data structures Conclusions

55. Current approaches to parallelization

56. Pessimistic parallelization Use compiler (static) analyses to produce parallel schedule –(e.g.) points-to/shape analysis Problem –Any static technique must produce a parallel schedule that is valid for all inputs to the program –In our applications, parallelism is very dependent on input data Conclusion: static techniques must serialize all iterations –accuracy of analysis is not the issue

57. Semi-static techniques Inspector-executor technique –inspector: small, fast program that uses input data to produce parallel schedule –executor: runs actual program using input data and parallel schedule from inspector Inspector: generated by hand or by compiler Applications: –Parallel sparse matrix factorization –Communication schedules for parallel sparse direct solvers Problem: –data-sets in our problems change as programs execute –Inspector must do all the work of the executor

58. Take-away lessons (contd.) Updates to data structures by one computation must be visible to other computations before first one terminates –(e.g.) worklist thread grabs a bad triangle from worklist before bad triangle processing is done, another thread may want a bad triangle from worklist modifications to worklist made by first thread must be visible to second thread before first thread completes –similar issues arise with priority queue and kdTree But how do we prevent cascading roll-backs?