ME964 High Performance Computing for Engineering Applications

1. ME964High Performance Computing for Engineering Applications Parallel Programming Patterns Oct. 16, 2008

2. Before we get started… • Last Time • CUDA arithmetic support • Performance implications • Accuracy implications • A software design exercise: prefix scan • Preamble to the topic of software design patterns • Today • Parallel programming patterns • Other issues: • HW due on Saturday, 11:59 PM. • I will be in Milwaukee next Th, Mik will be the lecturer - tracing the evolution of the hardware support for the graphics pipeline 2

3. “If you build it, they will come.” “And so we built them. Multiprocessor workstations, massively parallel supercomputers, a cluster in every department … and they haven’t come. Programmers haven’t come to program these wonderful machines. … The computer industry is ready to flood the market with hardware that will only run at full speed with parallel programs. But who will write these programs?” - Mattson, Sanders, Massingill (2005) 3 HK-UIUC

4. Objective • Outline a framework that draws on techniques & best practices used by experienced parallel programmers in order to enable you to • Think about the problem of parallel programming • Address functionality and performance issues in your parallel program design • Discuss your design decisions with others • Select an appropriate implementation platform that will that will facilitate application development 4

5. Fundamentals of Parallel Computing • Parallel computing requires that • The problem can be decomposed into sub-problems that can be safely solved at the same time • The programmer structures the code and data to solve these sub-problems concurrently • The goals of parallel computing are • To solve problems in less time, and/or • To solve bigger problems The problems must be large enough to justify parallel computing and to exhibit exploitable concurrency. 5 HK-UIUC

6. Recommended Reading Mattson, Sanders, Massingill, Patterns for Parallel Programming, Addison Wesley, 2005, ISBN 0-321-22811-1. • Used for this presentation • A good overview of challenges, best practices, and common techniques in all aspects of parallel programming • Book is on reserve at Wendt Library 6 HK-UIUC

7. Parallel Programming: Key Steps • Find the concurrency in the problem • Structure the algorithm so that concurrency can be exploited • Implement the algorithm in a suitable programming environment • Execute and tune the performance of the code on a parallel system NOTE: The reality is that these have not been separated into levels of abstractions that can be dealt with independently. 7 HK-UIUC

8. What’s Next? Focus on thisfor a while From “Patterns for Parallel Programming” 8

9. Challenges of Parallel Programming • Finding and exploiting concurrency often requires looking at the problem from a non-obvious angle • Dependences need to be identified and managed • The order of task execution may change the answers • Obvious: One step feeds result to the next steps • Subtle: numeric accuracy may be affected by ordering steps that are logically parallel with each other 9 HK-UIUC

10. Challenges of Parallel Programming (cont.) • Performance can be drastically reduced by many factors • Overhead of parallel processing • Load imbalance among processor elements • Inefficient data sharing patterns • Saturation of critical resources such as memory bandwidth 10 HK-UIUC

11. Shared Memory vs. Message Passing • We will focus on shared memory parallel programming • This is what CUDA is based on • Future massively parallel microprocessors are expected to support shared memory at the chip level • The programming considerations of message passing model is quite different! 11 HK-UIUC

12. Finding Concurrency in Problems • Identify a decomposition of the problem into sub-problems that can be solved simultaneously • A task decomposition that identifies tasks that can execute concurrently • A data decomposition that identifies data local to each task • A way of grouping tasks and ordering the groups to satisfy temporal constraints • An analysis on the data sharing patterns among the concurrent tasks • A design evaluation that assesses of the quality the choices made in all the steps 12 HK-UIUC

13. Finding Concurrency – The Process Dependence Analysis Decomposition Group Tasks Task Decomposition Design Evaluation Order Tasks Data Decomposition Data Sharing This is typically an iterative process. Opportunities exist for dependence analysis to play earlier role in decomposition. 13 HK-UIUC

14. Find Concr. 1: Decomp. Stage: Task Decomposition • Many large problems have natural independent tasks • The number of tasks used should be adjustable to the execution resources available. • Each task must include sufficient work in order to compensate for the overhead of managing their parallel execution. • Tasks should maximize reuse of sequential program code to minimize design/implementation effort. “In an ideal world, the compiler would find tasks for the programmer. Unfortunately, this almost never happens.” - Mattson, Sanders, Massingill 14 HK-UIUC

15. Example: Task Decomposition Square Matrix Multiplication N • P = M * N of WIDTH ● WIDTH • One natural task (sub-problem) produces one element of P • All tasks can execute in parallel WIDTH M P WIDTH WIDTH WIDTH 15 HK-UIUC

16. Task Decomposition Example: Molecular Dynamics • Simulation of motions of a large molecular system • A natural task is to perform calculations of individual atoms in parallel • For each atom, there are several tasks to complete • Covalent forces acting on the atom • Neighbors that must be considered in non-bonded forces • Non-bonded forces • Update position and velocity • Misc physical properties based on motions • Some of these can go in parallel for an atom It is common that there are multiple ways to decompose any given problem. 16 HK-UIUC

17. Find Concr. 2: Decomp. Stage: Data Decomposition • The most compute intensive parts of many large problems manipulate a large data structure • Similar operations are being applied to different parts of the data structure, in a mostly independent manner. • This is what CUDA is optimized for. • The data decomposition should lead to • Efficient data usage by each UE within the partition • Few dependencies between the UEs that work on different partitions • Adjustable partitions that can be varied according to the hardware characteristics 17 HK-UIUC

18. Data Decomposition Example - Square Matrix Multiplication N • P Row blocks (adjacent full rows) • Computing each partition requires access to entire N array • Square sub-blocks • Only bands of M and N are needed WIDTH • Think how data is stored in the Matrix type • Computing things row-wise or column-wise might actually lead to different performance… M P WIDTH WIDTH WIDTH 18

19. Find Concr. 3: Dependence Analysis - Tasks Grouping • Sometimes natural tasks of a problem can be grouped together to improve efficiency • Reduced synchronization overhead – because when task grouping there is supposedly no need for synchronization • All tasks in the group efficiently share data loaded into a common on-chip, shared storage (Shard Memory) 19 HK-UIUC

20. Task Grouping Example - Square Matrix Multiplication N • Tasks calculating a P sub-block • Extensive input data sharing, reduced memory bandwidth using Shared Memory • All synched in execution WIDTH M P WIDTH WIDTH WIDTH 20 HK-UIUC

21. Find Concr. 4: Dependence Analysis - Task Ordering • Identify the data required by a group of tasks before they can execute • Find the task group that creates it (look upwind) • Determine a temporal order that satisfy all data constraints 21 HK-UIUC

22. Task Ordering Example:Molecular Dynamics Neighbor List Covalent Forces Non-bonded Force Update atomic positions and velocities Next Time Step 22 HK-UIUC

23. Find Concr. 5: Dependence Analysis - Data Sharing • Data sharing can be a double-edged sword • An algorithm that calls for excessive data sharing can drastically reduce advantage of parallel execution • Localized sharing can improve memory bandwidth efficiency • Use the execution of task groups to interleave with (mask) global memory data accesses • Read-only sharing can usually be done at much higher efficiency than read-write sharing, which often requires a higher level of synchronization 23 HK-UIUC

24. Data Sharing Example – Matrix Multiplication • Each task group will finish usage of each sub-block of N and M before moving on • N and M sub-blocks loaded into Shared Memory for use by all threads of a P sub-block • Amount of on-chip Shared Memory strictly limits the number of threads working on a P sub-block • Read-only shared data can be efficiently accessed as Constant or Texture data (on the GPU) • Frees up the shared memory for other uses 24

25. Data Sharing Example – Molecular Dynamics • The atomic coordinates • Read-only access by the neighbor list, bonded force, and non-bonded force task groups • Read-write access for the position update task group • The force array • Read-only access by position update group • Accumulate access by bonded and non-bonded task groups • The neighbor list • Read-only access by non-bonded force task groups • Generated by the neighbor list task group 25 HK-UIUC

26. Find Concr. 6: Design Evaluation • Key questions to ask • How many UE can be used? • How are the data structures shared? • Is there a lot of data dependency that leads to excessive synchronization needs? • Is there enough work in each UE between synchronizations to make parallel execution worthwhile? 26 HK-UIUC

27. Key Parallel Programming Steps • Find the concurrency in the problem • Structure the algorithm so that concurrency can be exploited • Implement the algorithm in a suitable programming environment • Execute and tune the performance of the code on a parallel system 27

28. What’s Next? Focus on thisfor a while From “Patterns for Parallel Programming” 28

29. Algorithm: Definition • A step by step procedure that is guaranteed to terminate, such that each step is precisely stated and can be carried out by a computer • Definiteness – the notion that each step is precisely stated • Effective computability – each step can be carried out by a computer • Finiteness – the procedure terminates • Multiple algorithms can be used to solve the same problem • Some require fewer steps and some exhibit more parallelism 29 HK-UIUC

30. Algorithm Structure - Strategies Organize by Tasks Organize by Data Organize by Flow Task Parallelism Geometric Decomposition Pipeline Divide and Conquer Recursive Data Decomposition Event Condition 30 HK-UIUC

31. Choosing Algorithm Structure Algorithm Design Organize by Task Organize by Data Organize by Data Flow Linear Recursive Linear Recursive Regular Irregular Task Parallelism Divide and Conquer Geometric Decomposition Recursive Data Pipeline Event Driven 31 HK-UIUC

32. Alg. Struct. 1: Organize by StructureLinear Parallel Tasks • Common in the context of distributed memory models • These are the algorithms where the work needed can be represented as a collection of decoupled or loosely coupled tasks that can be executed in parallel • The tasks don’t even have to be identical • Load balancing between UE can be an issue (dynamic load balancing?) • If there is no data dependency involved there is no need for synchronization: the so called “embarrassingly parallel” scenario • Example: ray tracing, a good portion of the N-body problem, Monte Carlo type simulation 32

33. Alg. Struct. 2: Organize by StructureRecursive Parallel Tasks (Divide & Conquer) • Valid when you can break a problem into a set of decoupled or loosely coupled smaller problems, which in turn… • This pattern is applicable when you can solve concurrently and with little synchronization the small problems (the leafs) • Chances are you need synchronization when you have this balanced tree type algorithm • Often required by the merging step (assembling the result from the “subresults”) • Examples: FFT, Linear Algebra problems (see FLAME project), the vector reduce operation 33

34. Computational ordering can have major effects on memory bank conflicts and control flow divergence. 0 1 2 3 … 13 14 15 16 17 18 19 1 2 3 34

35. Alg. Struct. 3: Organize by Data~ Linear (Geometric Decomposition) ~ • This is the case where the UEs gather and work around a big chunk of data with no or little synchronization • Imagine a car that needs to be painted: • One robot paints the front left door, another one the rear left door, another one the hood, etc. • The car is the “data” and it’s parceled up with a collection of UEs acting on these chunks of data • NOTE: this is exactly the algorithmic approach enabled best by the GPU & CUDA • Examples: Matrix multiplication, matrix convolution 35

36. bx 0 1 2 tx bsize-1 0 1 2 N BLOCK_WIDTH WIDTH BLOCK_WIDTH M P 0 0 Psub 1 2 by WIDTH BLOCK_SIZE 1 ty bsize-1 BLOCK_WIDTH BLOCK_WIDTH BLOCK_WIDTH 2 WIDTH WIDTH Tiled (Stenciled) Algorithms are Important for G80 36 HK-UIUC

37. Alg. Struct. 4: Organize by Data~ Recursive Data Scenario ~ • This scenario comes into play when the data that you operate on is structured in a recursive fashion • Balanced Trees • Graphs • Lists • Sometimes you don’t even have to have the data represented as such • See example with prefix scan • You choose to look at data as having a balanced tree structure • Many problems that seem inherently sequential can be approached in this framework • This is typically associated with an net increase in the amount of work you have to do • Work goes up from O(n) to O(n log(n)) (see for instance Hillis and Steele algorithm) • The key question is whether parallelism gained brings you ahead of the sequential alternative 37

38. Example: The prefix scan~ Reduction Step~ for k=0 to M-1 offset = 2k for j=1 to 2M-k-1 in parallel do x[j·2k+1-1] = x[j·2k+1-1] + x[j·2k+1-2k-1] endfor endfor 38

39. Example: The array reduction (the bad choice) Array elements 0 1 2 3 4 5 6 7 8 9 10 11 1 0+1 2+3 4+5 6+7 8+9 10+11 2 0...3 4..7 8..11 3 0..7 8..15 iterations 39 HK-UIUC

40. Alg. Struct. 5: Organize by Data Flow~ Regular: Pipeline ~ • Tasks are parallel, but there is a high degree of synchronization (coordination) between the UEs • The input of one UE is the output of an upwind UE (the “pipeline”) • The time elapsed between two pipeline ticks dictated by the slowest stage of the pipe (the bottleneck) • Commonly employed by sequential chips • For complex problems having a deep pipeline is attractive • At each pipeline tick you output one set of results • Examples: • CPU: instruction fetch, decode, data fetch, instruction execution, data write are pipelined. • The Cray vector architecture drawing heavily on this algorithmic structure when performing linear algebra operations 40

41. Alg. Struct. 6: Organize by Data Flow~ Irregular: Event Driven Scenarios ~ • The furthest away from what the GPU can support today • Well supported by MIMD architectures • You coordinate UEs through asynchronous events • Critical aspects: • Load balancing – should be dynamic • Communication overhead, particularly in real-time application • Suitable for action-reaction type simulations • Examples: computer games, traffic control algorithms 41

42. Key Parallel Programming Steps • Find the concurrency in the problem • Structure the algorithm so that concurrency can be exploited • Implement the algorithm in a suitable programming environment • Execute and tune the performance of the code on a parallel system 42

43. What’s Next? Focus on thisfor a while 43

44. Objective • To understand SPMD and the role of the CUDA supporting structures • How it relates other common parallel programming structures. • What the supporting structures entail for applications development. • How the supporting structures could be used to implement parameterized applications for different levels of efficiency and complexity. 44

45. Parallel Programming Coding Styles - Program and Data Models Program Models Data Models SPMD Shared Data Master/Worker Shared Queue Loop Parallelism Distributed Array Fork/Join These are not necessarily mutually exclusive. 45

46. Program Models • SPMD (Single Program, Multiple Data) • All PE’s (Processor Elements) execute the same program in parallel • Each PE has its own data • Each PE uses a unique ID to access its portion of data • Different PE can follow different paths through the same code • This is essentially the CUDA Grid model • SIMD is a special case - WARP • Master/Worker • Loop Parallelism • Fork/Join 46

47. Program Models • SPMD (Single Program, Multiple Data) • Master/Worker • A Master thread sets up a pool of worker threads and a bag of tasks • Workers execute concurrently, removing tasks until done • Loop Parallelism • Loop iterations execute in parallel • FORTRAN do-all (truly parallel), do-across (with dependence) • Fork/Join • Most general, generic way of creation of threads 47

48. Review: Algorithm Structure Algorithm Design Organize by Task Organize by Data Organize by Data Flow Linear Recursive Linear Recursive Regular Irregular Task Parallelism Divide and Conquer Geometric Decomposition Recursive Data Pipeline Event Driven 48

49. Algorithm Structures vs. Coding Styles(four smiles is best) Source: Mattson, et al. 49

50. Supporting Structures vs. Program Models 50