1 / 48

ME964 High Performance Computing for Engineering Applications

ME964 High Performance Computing for Engineering Applications. Parallel Programming Patterns Discussion of Midterm Project Oct. 21, 2008. Before we get started…. Last Time Parallel Programming patterns The “Finding Concurrency Design Space” The “Algorithm Structure Design Space” Today

cicero
Download Presentation

ME964 High Performance Computing for Engineering Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ME964High Performance Computing for Engineering Applications Parallel Programming Patterns Discussion of Midterm Project Oct. 21, 2008

  2. Before we get started… • Last Time • Parallel Programming patterns • The “Finding Concurrency Design Space” • The “Algorithm Structure Design Space” • Today • Parallel Programming patterns • Discuss the “Supporting Structures Design Space” • Discussion of the Midterm Project • Assigned today, due on 11/18 or 11/09 (based on level of difficulty) • Other issues: • I will be in Milwaukee on Th, Mik will be the lecturer - tracing the evolution of the hardware support for the graphics pipeline 2

  3. 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 3

  4. What’s Comes Next? Focus on thisfor a while 4

  5. Before We Dive In… • You hover in this design space when you ponder whether an MPI or an SPMD or a event driven simulation environment is what it takes to optimally design your algorithm • We are not going to focus on this process too much since it’s clear that we are stuck with SPMD • All that we’ll be doing is to compare SPMD with other parallel programming paradigms to understand when SPMD is good and when it is bad • Also, we will not cover the “Implementation Mechanisms” design space since we don’t need to wrestle with how to spawn and join threads, how to do synchronization, etc. • This would be Chapter 6 of the book 5

  6. Supporting Structures ~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. 6

  7. Program Structuring Patterns • 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 • Master/Worker • Loop Parallelism • Fork/Join 7

  8. Program Structuring Patterns(the rest of the pack) • 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) • Very common in OpenMP • Fork/Join • Most general way of creation of threads (the POSIX standard) • Can be regarded as a very low level approach in which you use the OS to manage parallelism 8

  9. 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 9

  10. Algorithm Structures vs. Supporting Structures Four smilies is the best (Source: Mattson, et al.) 10

  11. Supporting Structures vs. Program Models 11

  12. More on SPMD • Dominant coding style of scalable parallel computing • MPI code is mostly developed in SPMD style • Many OpenMP code is also in SPMD (next to loop parallelism) • Particularly suitable for algorithms based on data parallelism, geometric decomposition, divide and conquer. • Main advantage • Tasks and their interactions visible in one piece of source code, no need to correlated multiple sources SPMD is by far the most commonly used pattern for structuring parallel programs. 12

  13. Typical SPMD Program Phases • Initialize • Establish localized data structure and communication channels • Obtain a unique identifier • Each thread acquires a unique identifier, typically in the range from 0 to N-1, where N is the number of threads. • Both OpenMP and CUDA have built-in support for this. • Distribute Data • Decompose global data into chunks and localize them, or • Sharing/replicating major data structure using thread ID to associate subset of the data to threads • Run the core computation • More details in next slide… • Finalize • Reconcile global data structure, prepare for the next major iteration 13

  14. Core Computation Phase • Thread IDs are used to differentiate behavior of threads • Use thread ID in loop index calculations to split loop iterations among threads • Use conditions based on thread ID to branch to their specific actions Both can have very different performance results and code complexity depending on the way they are done. 14

  15. A Simple Example • Assume • The computation being parallelized has 1,000,000 iterations. • Sequential code: Num_steps = 1000000; for (i=0; i< num_steps, i++) { … } 15

  16. SPMD Code Version 1 • Assign a chunk of iterations to each thread • The last thread also finishes up the remainder iterations num_steps = 1000000; i_start = my_id * (num_steps/num_threads); i_end = i_start + (num_steps/num_threads); if (my_id == (num_threads-1)) i_end = num_steps; for (i = i_start; i < i_end; i++) { …. } Reconciliation of results across threads if necessary. 16

  17. Problems with Version 1 • The last thread executes more iterations than others • The number of extra iterations is up to the total number of threads – 1 • This is not a big problem when the number of threads is small • When there are thousands of threads, this can create serious load imbalance problems. • Also, the extra if statement is a typical source of “branch divergence” in CUDA programs. 17

  18. SPMD Code Version 2 • Assign one more iterations to some of the threads int rem = num_steps % num_threads; i_start = my_id * (num_steps/num_threads); i_end = i_start + (num_steps/num_threads); if (rem != 0) { if (my_id < rem) { i_start += my_id; i_end += (my_id +1); } else { i_start += rem; i_end += rem; } . Less load imbalance More branch divergence. 18

  19. SPMD Code Version 3 • Use cyclic distribution of iteration num_steps = 1000000; for (i = my_id; i < num_steps; i+= num_threads) { …. } Less load imbalance Loop branch divergence in the last Warp Data padding further eliminates divergence. 19

  20. Comparing the Three Versions Version 1 ID=0 ID=1 ID=2 ID=3 Version 2 ID=0 ID=1 ID=2 ID=3 Version 3 ID=0 ID=1 ID=2 ID=3 Padded version1 1 may be best for some data access patterns. 20

  21. Data Styles • Shared Data • All threads share a major data structure • This is what CUDA supports • Shared Queue • All threads see a “thread safe” queue that maintains ordering of data communication • Very relevant in conjunction with the Master/Worker scenarios • Distributed Array • Decomposed and distributed among threads • Limited support in CUDA Shared Memory • Typically an issue in NUMA layouts 21

  22. End: Parallel Programming Patterns Begin: Overview Reminder of Semester 22

  23. The Reminder of the Semester • There will be one more lecture on CUDA (in November) • There will be three lectures on MPI • There will be about four to five guest lectures • On massively parallel hardware design • On grid computing (the Condor project) • On the N-body problem • Midterm exam on 11/20 • Midterm Project (assigned today, due on 11/17 or sooner) • I’ll explain why “sooner” shortly • Final Project (due on last Friday, Dec. 19, at 11:59 PM) 23

  24. Midterm Project • The topic: Produce a Collision Detection “engine” • Deal with spheres or ellipsoids • There will be two levels of difficulty: • The entry level • You implement a simple “brute force” approach • Deal only with spheres of various radii • Due Date: November 9, 11:59 PM • The advanced level • Apply a sophisticated design to produce a parallel algorithm that is very efficient • Deal with ellipsoids • Note that spheres are a particular case of ellipsoids • Due Date: November 17, 11:59 PM • Most likely make this engine a part of your Final Project • Independent of the level embraced, you’ll be presenting your work on November 18, during regular class hours • You’ll have 10 minutes to make a PowerPoint presentation. The presentations are part of the project (to be submitted for grading) • Please observe the Nov. 17 deadline for presentations for both levels 24

  25. Final Project • Work on something related to your research • I can assist you with selecting a topic • I will help you with the design • There is a “default” Final Project, in case you can’t choose

  26. The Final Project: Further Comments • There is a connection between the Midterm and Final Projects: • It is up to you to decide what you want to work on for the Final Project • However, if you don’t know what to work on, I’ll assign you a Granular Dynamics problem (this is the “default” Final Project) • An important part of this problem is the collision detection stage Granular Dynamics Problem 26

  27. The Final Project: Concluding Remarks • To conclude, the default Final Project will look like this: Final Project = Midterm Project + Some Extra Headache Granular Material Dynamics • Keep in mind: • If you plan to do the default final project, think ahead and implement a collision detection engine that is suitable to a scenario where the bodies slightly change their location each time you have to do the contact detection • This is because in granular flow the particles move in space • Maybe you can run a “cheaper” collision detection after an initial “exhaustive” one • You’ll need to look at problems with millions of colliding bodies 27

  28. End: Overview Reminder of Semester Begin: Midterm Project 28

  29. The Collision Problem(The Midterm Project) • Problem Statement: • A large set of spheres or ellipsoids is given to you • Provide collision state information for each pair of bodies that are colliding • The bodies that you are dealing with are of spherical shape • Spheres are of arbitrary radius R, where Rlow < R < Rhigh • The bound values Rlow and Rhigh are given to you • Their location is given to you • NOTE: The ellipsoid case is similar (skipped here the discussion) • You will have to validate your results against “Bullet”, which is an open source game development tool. 29

  30. Proposed Workflow The proposed workflow below will be captured in a Visual Studio Solution (with three Projects) that will be provided to you (zipped file). You are responsible for the part in red font below. • Generate an initial distribution of the spheres (part of Project 1) • Load data (part of Project 2) • Run collision detection on the device (part of Project 2) • Save results in a file (part of Project 2) • Run collision detection using the Bullet library (part of Project 3) • The utility will tell you if you “passed” or “failed” (part of Project 3) 30

  31. Project template • Solution contains three projects • First project is used to generate the input data (distribution of the spheres along with their radius) • Second project loads input data and checks for collisions • This is the project you modify • The main driver calls a function that invokes the collision detection kernel • Pretty much like you’ve had to do in your HW • Third project does the Bullet part followed up by the validation • Uses ‘C’ function notation • Main file uses C++ classes and objects • Allows C++ and C code to work together 31

  32. Spheres: Possible Contact Cases A B A B • Convention: • Color code for object A: bluish • Color code for object B: greenish • Sphere contacts sphere • One contact point • Normal - from center of B to center of A • Sphere interpenetrates sphere • Two contact points • Points on objects furthest in • Normal - from center of B to center of A 32

  33. Possible Contact Cases (Contd.) B A A B A B • Sphere exactly on top of sphere • Two points returned • Points on surface that intersect the x-axis • Normal is on +x axis • Sphere inside sphere • Two points returned • Points on surface that intersect the x-axis • Normal is on +x axis • Spheres are not in contact • Nothing to report, ignore 33

  34. Bullet Physics Library • Bullet is a cross platform open source physics library. • Can simulate many types of objects • Rigid bodies (concave, convex, triangular mesh, etc.) • Cloth, soft bodies • Supports joints and constraints • Geared towards game development. • Speed vs. accuracy: comes on the side of speed • Bullet’s collision detection will be used to verify your results 34

  35. Screenshot, Bullet 35

  36. Relevant Variables Variables you need to return and calculate btVector3 positionWorldOnA btVector3 positionWorldOnB btVector3 normalWorldOnB int objectIdA (note: this is the Id associated with A) int objectIdB (note: this is the Id associated with B) Additional parameters for Final Project*: localPointA localPointB btVector3 lateralFrictionDir1 btVector3 lateralFrictionDir2 distance1 All variables retuned per contact by Bullet btVector3 localPointA btVector3 localPointB btVector3 positionWorldOnB btVector3 positionWorldOnA   btVector3 normalWorldOnB btScalar distance1 btVector3 lateralFrictionDir1 btVector3 lateralFrictionDir2 int partId0 int partId1 int index0 int index1 btScalar combinedFriction btScalar combinedRestitution void * userPersistentData btScalar appliedImpulse bool lateralFrictionInitialized int lifeTime btScalar appliedImpulseLateral1 btScalar appliedImpulseLateral2 36

  37. Variable Description positionWorldOnB (float3) Absolute Collision location on object A positionWorldOnA (float3) Absolute Collision location on object B normalWorldOnB (float3) Collision Normal Vector from B to A objectIdA (int) Object A ID objectIdB (int) Object B ID (Id starts from 0) Other parameters that need to be implemented for Final Project (if you take this route): localPointA (float3) Collision point w/ respect to center of object A localPointB (float3) Collision point w/ respect to center of object B distance1 (float) Distance between collision points lateralFrictionDir1 (float3) Vector orthogonal to normal and Dir2 lateralFrictionDir2 (float3) Vector orthogonal to normal and Dir1 37

  38. The Passed/Failed Issue • The comparison is going to be made based on • The contact location expressed in global reference frame • There will be an epsilon value that controls this test • The contact normal • Your normal and Bullet’s normal should be within 10± • For comparison purposes, your contacts should be ordered such that • I still owe you two things: • How are body A and body B chosen? • What to do with this collision case: 38

  39. Common Sense Advice • Donald Knuth (1974): Premature optimization is the root of all evil • Get it to run first, add the bells and whistles later on… • Embrace a Crawl – Walk – Run approach 39

  40. Collision Detection ~ Some Possible Approaches ~ Brute force – simplest and slowest Ok to implement, unless you want to make this your final project, in which case you’ll have to implement one of the other three methods below It relies on an exhaustive search: N(N-1)/2 tests (given N bodies) Baraff – sorting based (the method is sometimes called “culling” Harada – rely on voxel and texture, not recommended Scott Le Grand – spatial subdivision method 40

  41. References • The methods of Scott Le Grand and Harada are explained in great detail in GPU Gems 3 (you can borrow it from me) • I also have the following references (found them on the web, contact me if you need them): Naga, K. G., R. Stephane, C. L. Ming, and M. Dinesh, 2003: CULLIDE: interactive collision detection between complex models in large environments using graphics hardware. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware, Eurographics Association. Baraff, D., 1997: An Introduction to Physically Based Modeling: Rigid Body Simulation II—Nonpenetration Constraints. SIGGRAPH Course Notes. 41

  42. Brute Force Iterate over all combinations of object pairs and perform distance checks on them Store pairs that are colliding into list and compute required information Iterate over each pair and calculate additional contact data. 42

  43. Baraff – Sorting axis p6 p5 p3 p4 p1 p2 b3 b6 b1 e6 e1 b5 b2 e3 b4 e5 e4 e2 • Every time an object p begins on the axis add p to stack • Every time an object p ends on the axis remove p from stack • Each time an object is added to stack compare it to those still on stack • p1 check with p3 and p6 • p5 check with p3 • An object is colliding with another if they overlap on all three axes. • Multi GPU relevant: yes, it can speed up the problem by simultaneously culling based on more axes 43

  44. Example: Why this is tricky at times (The issue of false positives) 44

  45. Harada , GPU Gems 3 • Mostly meant to deal with spheres, and of the same radii • “Voxel” collision method • Voxel ´ 3d pixel • Spheres are used to represent other objects • Fill object’s space using spheres • Use many 2D textures to store data. • Textures make up 3d grid • Optimize by using texture memory • Easier to coalesce reads and writes 45

  46. Harada (Contd.) • Each voxel in texture contains up to 4 object id’s • Stored in RGBA values • Objects and cells need to be sized so that this is true • Constant radius is preferred but some variation can exist • Too much variation could cause instances with >4 objects in one cell’s space • Test each cell with its 26 neighbors • Iterate over all cells in this way 46

  47. Scott Le Grand, GPU Gems 3 • Spatial subdivision method • Divide space into three dimensional grid • Collision state of spheres cannot be modified by different threads • Cells numbered by processing order (1, 2,…) • First all #1 cells are processed, then #2 cells and so on • Insures that two threads do not overwrite collision data for one sphere • Spheres get assigned a home cell id and overlapping “phantom” cell id’s • Array gets sorted by cell number and type 47

  48. Scott Le Grand (Contd.) • From this list determine which cells have multiple objects inside • These cells will be checked for collisions • Task is simplified because cell id list is already sorted by cell number • By checking for a change in cell id the number of objects in that cell can be determined. • If cell only has phantom objects it will not be checked • Phantom objects - objects whose centroid is not in that cell but still intersects it • Cell id must have at least one home id and >1 objects to be checked • Multi GPU relevant: yes, it can increase the size of the problem being addressed 48

More Related