BİL 542 Parallel Computing

Transcription

1 BİL 542 Parallel Computing 1

2 Chapter 1 Parallel Programming 2

3 Why Use Parallel Computing? Main Reasons: Save time and/or money: In theory, throwing more resources at a task will shorten its time to completion, with potential cost savings. Parallel clusters can be built from cheap, commodity components. Solve larger problems: Many problems are so large and/or complex that it is impractical or impossible to solve them on a single computer, especially given limited computer memory. For example: Web search engines/databases processing millions of transactions per second 3

4 Demand for Computational Speed Continual demand for greater computational speed from a computer system than is currently possible Areas requiring great computational speed include numerical modeling and simulation of scientific and engineering problems. Computations must be completed within a reasonable time period. 4

5 Grand Challenge Problems One that cannot be solved in a reasonable amount of time with today s computers. Obviously, an execution time of 10 years is always unreasonable. Examples Databases, data mining Oil exploration Web search engines, web based business services Medical imaging and diagnosis Pharmaceutical design Management of national and multi-national corporations Financial and economic modeling Advanced graphics and virtual reality, particularly in the entertainment industry Networked video and multi-media technologies Collaborative work environments Modeling large DNA structures Global weather forecasting Modeling motion of astronomical bodies. 5

6 Weather Forecasting Atmosphere modeled by dividing it into 3- dimensional cells. Calculations of each cell repeated many times to model passage of time. 6

7 Global Weather Forecasting Example Suppose whole global atmosphere divided into cells of size 1 mile 1 mile 1 mile to a height of 10 miles (10 cells high) - about cells. Suppose each calculation requires 200 floating point operations. In one time step, floating point operations necessary. To forecast the weather over 7 days using 1-minute intervals, a computer operating at 1Gflops (10 9 floating point operations/s) takes 10 6 seconds or over 10 days. To perform calculation in 5 minutes requires computer operating at 3.4 Tflops ( floating point operations/sec). 7

8 Modeling Motion of Astronomical Bodies Each body attracted to each other body by gravitational forces. Movement of each body predicted by calculating total force on each body. With N bodies, N - 1 forces to calculate for each body, or approx. N 2 calculations. (N log 2 N for an efficient approx. algorithm.) After determining new positions of bodies, calculations repeated. 8

9 Modeling Motion of Astronomical Bodies A galaxy might have, say, stars. Even if each calculation done in 1 ms (extremely optimistic figure), it takes 10 9 years for one iteration using N 2 algorithm and almost a year for one iteration using an efficient N log 2 N approximate algorithm. 9

10 Astrophysical N-body simulation by Scott Linssen (undergraduate UNC-Charlotte student). 10

11 Parallel Computing Using more than one computer, or a computer with more than one processor, to solve a problem. Motives Usually faster computation - very simple idea - that n computers operating simultaneously can achieve the result n times faster - it will not be n times faster for various reasons. Other motives include: fault tolerance, larger amount of memory available,... 11

12 Parallel Computing vs Traditional Computing 12

13 Background Parallel computers - computers with more than one processor - and their programming - parallel programming - has been around for more than 40 years. 13

14 14

15 Speedup Factor S(p) = Execution time using one processor (best sequential algorithm) Execution time using a multiprocessor with p processors = t s t p where t s is execution time on a single processor and t p is execution time on a multiprocessor. S(p) gives increase in speed by using multiprocessor. Use best sequential algorithm with single processor system. Underlying algorithm for parallel implementation might be (and is usually) different. 15

16 Speedup factor can also be cast in terms of computational steps: S(p) = Number of computational steps using one processor Number of parallel computational steps with p processors Can also extend time complexity to parallel computations. 16

17 Maximum Speedup Maximum speedup is usually p with p processors (linear speedup). Possible to get superlinear speedup (greater than p) but usually a specific reason such as: Extra memory in multiprocessor system 17

18 Speedup against number of processors 20 f = 0% f = 5% f = 10% f = 20% Number of processors, p COMPE472 Parallel Computing 18

19 Maximum Speedup Factors limiting speedup Communication time Extra computations in the parallel algorithm (reevaluation of constants locally) Idle time of some processors COMPE472 Parallel Computing 19

20 Maximum Speedup Amdahl s law t s (a) One processor ft s Serial section (1 - f ) t s Parallelizable sections (b) Multiple processors p processors t p (1 - f ) t s / p 20

21 Amdahl s Law Speedup factor is given by: S(p) t s p ft s (1 f )t s /p 1 (p 1)f This equation is known as Amdahl s law COMPE472 Parallel Computing 21

22 Amdahl s law Even with infinite number of processors, maximum speedup is limited : Example With only 5% of computation being serial, maximum speedup is 20, irrespective of number of processors. 22

23 Superlinear Speedup example - Searching (a) Searching each sub-space sequentially Start Time Sub-space search t s /p t s D t x t s /p Solution found x indeterminate 23

24 (b) Searching each sub-space in parallel D t Solution found 24

25 Speed-up then given by S(p) = x t s p D t + D t COMPE472 Parallel Computing 25

26 Worst case for sequential search when solution found in last sub-space search. Then parallel version offers greatest benefit. 26

27 Least advantage for parallel version when solution found in first sub-space search of the sequential search, i.e. S(p) = D t D t = 1 Actual speed-up depends upon which subspace holds solution but could be extremely large. 27

28 Scalability Architecturally scalable system Increase in number of processors leading to increase in speedup Architectural/Algorithmic scalability Increase in data size can be accomodated by the increase in number of processors 28

29 Message-Passing Computations In a message passing environment, computation time consists of two parts: t p t comp t comm The ratio below can be used as a metric: comp comm time time t t comp comm 29

30 Types of Parallel Computers Two principal types: Shared memory multiprocessor Distributed memory multicomputer 30

31 Type of parallel systems Shared-memory Distributed-memory 31

32 Shared Memory Multiprocessor 32

33 Conventional Computer Consists of a processor executing a program stored in a (main) memory: Main memory Instr uctions (to processor) Data (to or from processor) Processor Each main memory location located by its address. Addresses start at 0 and extend to 2 b - 1 when there are b bits (binary digits) in address. 33

34 Shared Memory Multiprocessor System Natural way to extend single processor model - have multiple processors connected to multiple memory modules, such that each processor can access any memory module : One address space Memory module Interconnection network Processors 34

35 Simplistic view of a small shared memory multiprocessor Processors Shared memory Bus Dual Pentiums Quad Pentiums Examples: 35

36 Quad Pentium Shared Memory Multiprocessor Processor Processor Processor Processor L1 cache L1 cache L1 cache L1 cache L2 Cache L2 Cache L2 Cache L2 Cache Bus interface Bus interface Bus interface Bus interface Processor/ memory b us I/O interf ace Memory controller I/O b us Shared memory Memory 36

37 Programming Shared Memory Multiprocessors Threads - programmer decomposes program into individual parallel sequences, (threads), each being able to access variables declared outside threads. Example: Pthreads (unix) Sequential programming language with preprocessor compiler directives to declare shared variables and specify parallelism. Example: OpenMP (needs OpenMP compiler) 37

38 Sequential programming language with added syntax to declare shared variables and specify parallelism. Example UPC (Unified Parallel C) - needs a UPC compiler. Parallel programming language with syntax to express parallelism - compiler creates executable code for each processor (not now common) Sequential programming language and ask parallelizing compiler to convert it into parallel executable code. (not now common) 38

39 Message-Passing Multicomputer Complete computers connected through an interconnection network: Messages Processor Interconnection network Local memory Computers 39

40 Interconnection Networks Limited and exhaustive interconnections 2- and 3-dimensional meshes Hypercube (not now common) Using Switches: Crossbar Trees Multistage interconnection networks Peer-to-peer 40

41 Two-dimensional array (mesh) Computer/ processor Links 41

42 Three-dimensional hypercube In a d-dim hypercube, each node connects to one node in each dimension. Above a 3-d hypercube is shown. Each node is assigned a 3 bit address. Address difference between nodes is only 1 bit. 42

43 Crossbar switch Provides exhaustive connections using one switch for each connection. Used in shared memory systems. 43

44 Tree Root Links Switch element Processors 44

45 Multistage Interconnection Network Example: Omega network 45

46 Communication Methods Circuit switching Establish the path Maintain/Reserve links for message passing Simple telephone system is an example Used in early multicomputers (INTEL IPSC-2) Packet switching Divide message into packets Packet = Source/Dest addresses + Data Packet max size is known Mail system is an example 46

47 Flynn s Classifications Flynn (1966) created a classification for computers based upon instruction streams and data streams: Single instruction -single data (SISD) computer Single processor computer - single stream of instructions generated from program. Instructions operate upon a single stream of data items. 47

48 Single Instruction, Single Data (SISD): A Single Single Deterministic This Examples: serial (non-parallel) computer instruction: only one instruction stream is being acted on by the CPU during any one clock cycle data: only one data stream is being used as input during any one clock cycle execution is the oldest and until recently, the most prevalent form of computer most PCs, single CPU workstations and mainframes 48

49 SISD 49

50 Multiple Instruction Stream-Multiple Data Stream (MIMD) Computer General-purpose multiprocessor system - each processor has a separate program and one instruction stream is generated from each program for each processor. Each instruction operates upon different data. Both the shared memory and the messagepassing multiprocessors so far described are in the MIMD classification. 50

51 MIMD Multiple Instruction, Multiple Data (MIMD): Currently, the most common type of parallel computer. Most modern computers fall into this category. Multiple Instruction: every processor may be executing a different instruction stream Multiple Data: every processor may be working with a different data stream Examples: most current supercomputers, networked parallel computer "grids" and multi-processor SMP computers - including some types of PCs. 51

52 MIMD 52

53 Single Instruction Stream-Multiple Data Stream (SIMD) Computer A specially designed computer - a single instruction stream from a single program, but multiple data streams exist. Instructions from program broadcast to more than one processor. Each processor executes same instruction in synchronism, but using different data. Developed because a number of important applications that mostly operate upon arrays of data. 53

54 SIMD Single Instruction, Multiple Data (SIMD): A type of parallel computer Single instruction: All processing units execute the same instruction at any given clock cycle Multiple data: Each processing unit can operate on a different data element This type of machine typically has an instruction dispatcher, a very highbandwidth internal network, and a very large array of very small-capacity instruction units. Best suited for specialized problems characterized by a high degree of regularity,such as image processing. COMPE472 Parallel Computing 54

55 SIMD COMPE472 Parallel Computing 55

56 Networked Computers as a Computing Platform A network of computers became a very attractive alternative to expensive supercomputers and parallel computer systems for high-performance computing in early 1990 s. Several early projects. Notable: Berkeley NOW (network of workstations) project. NASA Beowulf project. 56

57 Key advantages: Very high performance workstations and PCs readily available at low cost. The latest processors can easily be incorporated into the system as they become available. Existing software can be used or modified. COMPE472 Parallel Computing 57

58 Software Tools for Clusters Based upon Message Passing Parallel Programming: Parallel Virtual Machine (PVM) - developed in late 1980 s. Became very popular. Message-Passing Interface (MPI) - standard defined in 1990s. Both provide a set of user-level libraries for message passing. Use with regular programming languages (C, C++,...). 58

59 Beowulf Clusters* A group of interconnected commodity computers achieving high performance with low cost. Typically using commodity interconnects - high speed Ethernet, and Linux OS. * Beowulf comes from name given by NASA Goddard Space Flight Center cluster project. 59

60 Cluster Interconnects Originally fast Ethernet on low cost clusters Gigabit Ethernet - easy upgrade path More Specialized/Higher Performance Myrinet Gbits/sec - disadvantage: single vendor clan SCI (Scalable Coherent Interface) QNet Infiniband - may be important as infininband interfaces may be integrated on next generation PCs 60