Overview of Parallel Programming Paradigms

1. Lecture 29: Parallel Programming Overview

2. Parallel Programming Paradigms --Various Methods • There are many methods of programming parallel computers. Two of the most common are message passing and data parallel. • Message Passing - the user makes calls to libraries to explicitly share information between processors. • Data Parallel - data partitioning determines parallelism • Shared Memory - multiple processes sharing common memory space • Remote Memory Operation - set of processes in which a process can access the memory of another process without its participation • Threads - a single process having multiple (concurrent) execution paths • Combined Models - composed of two or more of the above. • Note: these models are machine/architecture independent, any of the models can be implemented on any hardware given appropriate operating system support. An effective implementation is one which closely matches its target hardware and provides the user ease in programming.

3. Parallel Programming Paradigms: Message Passing The message passing model is defined as: • set of processes using only local memory • processes communicate by sending and receiving messages • data transfer requires cooperative operations to be performed by each process (a send operation must have a matching receive) • Programming with message passing is done by linking with and making calls to libraries which manage the data exchange between processors. Message passing libraries are available for most modern programming languages.

4. Parallel Programming Paradigms: Data Parallel • The data parallel model is defined as: • Each process works on a different part of the same data structure • Commonly a Single Program Multiple Data (SPMD) approach • Data is distributed across processors • All message passing is done invisibly to the programmer • Commonly built "on top of" one of the common message passing libraries • Programming with data parallel model is accomplished by writing a program with data parallel constructs and compiling it with a data parallel compiler. • The compiler converts the program into standard code and calls to a message passing library to distribute the data to all the processes.

5. Implementation of Message Passing: MPI • Message Passing Interface often called MPI. • A standard portable message-passing library definition developed in 1993 by a group of parallel computer vendors, software writers, and application scientists. • Available to both Fortran and C programs. • Available on a wide variety of parallel machines. • Target platform is a distributed memory system • All inter-task communication is by message passing. • All parallelism is explicit: the programmer is responsible for parallelism the program and implementing the MPI constructs. • Programming model is SPMD (Single Program Multiple Data)

6. Implementations: F90 / High Performance Fortran (HPF) • Fortran 90 (F90) - (ISO / ANSI standard extensions to Fortran 77). • High Performance Fortran (HPF) - extensions to F90 to support data parallel programming. • Compiler directives allow programmer specification of data distribution and alignment. • New compiler constructs and intrinsics allow the programmer to do computations and manipulations on data with different distributions.

7. Steps for Creating a Parallel Program • If you are starting with an existing serial program, debug the serial code completely • Identify the parts of the program that can be executed concurrently: • Requires a thorough understanding of the algorithm • Exploit any inherent parallelism which may exist. • May require restructuring of the program and/or algorithm. May require an entirely new algorithm. • Decompose the program: • Functional Parallelism • Data Parallelism • Combination of both • Code development • Code may be influenced/determined by machine architecture • Choose a programming paradigm • Determine communication • Add code to accomplish task control and communications • Compile, Test, Debug • Optimization • Measure Performance • Locate Problem Areas • Improve them

8. Exec time w/o E Speedup w/ E = ---------------------- Exec time w/ E Amdahl’s Law • Speedup due to enhancement E is • Suppose that enhancement E accelerates a fraction F (F <1) of the task by a factor S (S>1) and the remainder of the task is unaffected ExTime w/ E = ExTime w/o E  ((1-F) + F/S) Speedup w/ E = 1 / ((1-F) + F/S)

9. Examples: Amdahl’s Law • Amdahl’s Law tells us that to achieve linear speedup with 100 processors (e.g., speedup of 100), none of the original computation can be scalar! • To get a speedup of 99 from 100 processors, the percentage of the original program that could be scalar would have to be 0.01% or less • What speedup could we achieve from 100 processors if 30% of the original program is scalar? Speedup w/ E = 1 / ((1-F) + F/S) = 1 / (0.7 + 0.7/100) = 1.4 • Serial program/algorithm might need to be restructuring to allow for efficient parallelization.

10. Decomposing the Program • There are three methods for decomposing a problem into smaller tasks to be performed in parallel: Functional Decomposition, Domain Decomposition, or a combination of both • Functional Decomposition (Functional Parallelism) • Decomposing the problem into different tasks which can be distributed to multiple processors for simultaneous execution • Good to use when there is not static structure or fixed determination of number of calculations to be performed • Domain Decomposition (Data Parallelism) • Partitioning the problem's data domain and distributing portions to multiple processors for simultaneous execution • Good to use for problems where: • data is static (factoring and solving large matrix or finite difference calculations) • dynamic data structure tied to single entity where entity can be subsetted (large multi-body problems) • domain is fixed but computation within various regions of the domain is dynamic (fluid vortices models) • There are many ways to decompose data into partitions to be distributed: • One Dimensional Data Distribution • Block Distribution • Cyclic Distribution • Two Dimensional Data Distribution • Block Block Distribution • Block Cyclic Distribution • Cyclic Block Distribution

11. Functional Decomposing of a Program • Decomposing the problem into different tasks which can be distributed to multiple processors for simultaneous execution • Good to use when there is not static structure or fixed determination of number of calculations to be performed

12. Functional Decomposing of a Program

13. Domain Decomposition (Data Parallelism) • Partitioning the problem's data domain and distributing portions to multiple processors for simultaneous execution • There are many ways to decompose data into partitions to be distributed:

14. Summing 100,000 Numbers on 100 Processors • Start by distributing 1000 elements of vector A to each of the local memories and summing each subset in parallel sum = 0; for (i = 0; i<1000; i = i + 1) sum = sum + Al[i]; /* sum local array subset • The processors then coordinate in adding together the sub sums (Pn is the number of the processor, send(x,y) sends value y to processor x, and receive() receives a value) half = 100; limit = 100; repeat half = (half+1)/2; /*dividing line if (Pn>= half && Pn<limit) send(Pn-half,sum); if (Pn<(limit/2)) sum = sum + receive(); limit = half; until (half == 1); /*final sum in P0’s sum

15. sum sum sum sum sum sum sum sum sum sum P0 P1 P2 P3 P4 P5 P6 P7 P8 P9 An Example with 10 Processors half = 10

16. Domain Decomposition (Data Parallelism) • Partitioning the problem's data domain and distributing portions to multiple processors for simultaneous execution • There are many ways to decompose data into partitions to be distributed:

17. Cannon's Matrix Multiplication

18. Review: Multiprocessor Basics • Q1 – How do they share data? • Q2 – How do they coordinate? • Q3 – How scalable is the architecture? How many processors?

19. Review: Bus Connected SMPs (UMAs) • Caches are used to reduce latency and to lower bus traffic • Must provide hardware for cache coherence and process synchronization • Bus traffic and bandwidth limits scalability (<~ 36 processors) Processor Processor Processor Processor Cache Cache Cache Cache Single Bus Memory I/O

20. Processor Processor Processor Cache Cache Cache Memory Memory Memory Interconnection Network (IN) Network Connected Multiprocessors • Either a single address space (NUMA and ccNUMA) with implicit processor communication via loads and stores ormultiple private memories with message passing communication with sends and receives • Interconnection network supports interprocessor communication

21. Communication in Network Connected Multi’s • Implicit communication via loads and stores • hardware designers have to provide coherent caches and process synchronization primitive • lower communication overhead • harder to overlap computation with communication • more efficient to use an address to remote data when demanded rather than to send for it in case it might be used (such a machine has distributed shared memory (DSM)) • Explicit communication via sends and receives • simplest solution for hardware designers • higher communication overhead • easier to overlap computation with communication • easier for the programmer to optimize communication

22. Cache Coherency in NUMAs • For performance reasons we want to allow the shared data to be stored in caches • Once again have multiple copies of the same data with the same address in different processors • bus snooping won’t work, since there is no single bus on which all memory references are broadcast • Directory-base protocols • keep a directory that is a repository for the state of every block in main memory (which caches have copies, whether it is dirty, etc.) • directory entries can be distributed (sharing status of a block always in a single known location) to reduce contention • directory controller sends explicit commands over the IN to each processor that has a copy of the data

23. IN Performance Metrics • Network cost • number of switches • number of (bidirectional) links on a switch to connect to the network (plus one link to connect to the processor) • width in bits per link, length of link • Network bandwidth (NB) – represents the best case • bandwidth of each link * number of links • Bisection bandwidth (BB) – represents the worst case • divide the machine in two parts, each with half the nodes and sum the bandwidth of the links that cross the dividing line • Other IN performance issues • latency on an unloaded network to send and receive messages • throughput – maximum # of messages transmitted per unit time • # routing hops worst case, congestion control and delay

24. Bus IN • N processors, 1 switch ( ), 1 link (the bus) • Only 1 simultaneous transfer at a time • NB = link (bus) bandwidth * 1 • BB = link (bus) bandwidth * 1 Bidirectional network switch Processor node

25. Ring IN • If a link is as fast as a bus, the ring is only twice as fast as a bus in the worst case, but is N times faster in the best case • N processors, N switches, 2 links/switch, N links • N simultaneous transfers • NB = link bandwidth * N • BB = link bandwidth * 2

26. Fully Connected IN • N processors, N switches, N-1 links/switch, (N*(N-1))/2 links • N simultaneous transfers • NB = link bandwidth * (N*(N-1))/2 • BB = link bandwidth * (N/2)2

27. Crossbar (Xbar) Connected IN • N processors, N2 switches (unidirectional),2 links/switch, N2 links • N simultaneous transfers • NB = link bandwidth * N • BB = link bandwidth * N/2

28. 3-cube Hypercube (Binary N-cube) Connected IN • N processors, N switches, logN links/switch, (NlogN)/2 links • N simultaneous transfers • NB = link bandwidth * (NlogN)/2 • BB = link bandwidth * N/2 2-cube

29. 2D and 3D Mesh/Torus Connected IN • N simultaneous transfers • NB = link bandwidth * 4N or link bandwidth * 6N • BB = link bandwidth * 2 N1/2 or link bandwidth * 2 N2/3 • N processors, N switches, 2, 3, 4 (2D torus) or 6 (3D torus) links/switch, 4N/2 links or 6N/2 links

30. Fat Tree • Trees are good structures. People in CS use them all the time. Suppose we wanted to make a tree network. A B C D • Any time A wants to send to C, it ties up the upper links, so that B can't send to D. • The bisection bandwidth on a tree is horrible - 1 link, at all times • The solution is to 'thicken' the upper links. • More links as the tree gets thicker increases the bisection • Rather than design a bunch of N-port switches, use pairs

31. Fat Tree • N processors, log(N-1)*logN switches, 2 up + 4 down = 6 links/switch, N*logN links • N simultaneous transfers • NB = link bandwidth * NlogN • BB = link bandwidth * 4

32. SGI NUMAlink Fat Tree www.embedded-computing.com/articles/woodacre

33. IN Comparison • For a 64 processor system

34. Network Connected Multiprocessors

35. IBM BlueGene

36. A BlueGene/L Chip 11GB/s 32K/32K L1 440 CPU Double FPU 2KB L2 4MB L3 ECC eDRAM 128B line 8-way assoc 128 256 5.5 GB/s 16KB Multiport SRAM buffer 256 700 MHz 256 32K/32K L1 440 CPU Double FPU 2KB L2 128 256 5.5 GB/s 11GB/s Gbit ethernet DDR control 3D torus Fat tree Barrier 1 8 6 in, 6 out 1.6GHz1.4Gb/s link 3 in, 3 out 350MHz 2.8Gb/s link 4 global barriers 144b DDR 256MB 5.5GB/s

37. Networks of Workstations (NOWs) Clusters • Clusters of off-the-shelf, whole computers with multiple private address spaces • Clusters are connected using the I/O bus of the computers • lower bandwidth that multiprocessor that use the memory bus • lower speed network links • more conflicts with I/O traffic • Clusters of N processors have N copies of the OS limiting the memory available for applications • Improved system availability and expandability • easier to replace a machine without bringing down the whole system • allows rapid, incremental expandability • Economy-of-scale advantages with respect to costs

38. Commercial (NOW) Clusters

39. Summary • Flynn’s classification of processors - SISD, SIMD, MIMD • Q1 – How do processors share data? • Q2 – How do processors coordinate their activity? • Q3 – How scalable is the architecture (what is the maximum number of processors)? • Shared address multis – UMAs and NUMAs • Scalability of bus connected UMAs limited (< ~ 36 processors) • Network connected NUMAs more scalable • Interconnection Networks (INs) • fully connected, xbar • ring • mesh • n-cube, fat tree • Message passing multis • Cluster connected (NOWs) multis