Friday, October 06, 2006

1. Friday, October 06, 2006 Measure twice, cut once. • Carpenter’s Motto

2. Sources of overhead • Inter-process communication • Idling • Replicated computation

3. Sources of overhead • Inter-process communication • Idling • Replicated computation

4. Ts: The original single-processor serial time. • Tis: The additional serial time spent on average for • Inter-processor communications • Setup • Depends on N. • Tp: The original single-processor parallelizable time. • Tip: The additional time spent on average by each processor • Setup • Idle time

5. Simplified expression • S(N) = Ts + Tp Ts+ N*Tis + Tp/N + Tip

6. Straight line reference for linear speedup Ts=10, Tip=1, Tis=0 Communication time negligible compared to computation. What you would expect from Amdahl’s law alone.

7. Ts=10, Tip=1, Tis=10 Adding small serial time. Adding more processors results in lower speedup.

8. Ts=10, Tip=1, Tis=1 Quadratic N dependence, e.g. every processor speaks to all others.

9. Adding processors won’t provide additional speedup unless the problem is scaled up as well. • Should not distribute calculations with small Tp/Tis over a large number of processors.

10. Scaling a problem • Does number of tasks scale with the problem size? • Increase in problem size should increase the number of tasks rather than the size of individual tasks. • Should be able to solve larger problems when more processors are available.

11. What can we tell from our observations? • We implemented an algorithm on parallel computer X and achieved a speedup of 10.8 on 12 processors with problem size N=100 .

12. What can we tell from our observations? • We implemented an algorithm on parallel computer X and achieved a speedup of 10.8 on 12 processors with problem size N=100 . • Region of observation is too narrow. • What if N=10 or N=1000?

13. What can we tell from our observations? • T is the execution time, P is number of processors and N is problem size • T= N + N2/P • T= (N + N2)/P + 100 • T= (N + N2)/P + 0.6 P2 All these algorithms all achieve a speedup of about 10.8 when P=12 and N=100 .

15. Addition example

16. Addition example Speedup : • Ratio of time taken to solve a problem on a single processor to time required to solve it on a parallel computer with p identical processing elements • Speedup for addition example?

17. Speedup : • Comparison with best known serial algorithm

18. Efficiency : Fraction of time which a processor spends doing useful work. E = S/p

19. Cost : Product of parallel runtime and the number of processors. Cost: pTp (Note:Tp here stands to the parallel runtime. The time from the moment the parallel computation starts to the moment last processing element finishes execution)

20. Cost optimal : If cost of solving a problem on a parallel computer has same asymptotic growth as a function of input size as the fastest known sequential algorithm on a single processor. Cost for addition example: O(n logn)

21. Cost optimal : If cost of solving a problem on a parallel computer has same asymptotic growth as a function of input size as the fastest known sequential algorithm on a single processor. Cost for addition example: O(n logn) Not cost optimal.

22. Effect of non-cost-optimality

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26. If overhead increases sub-linearly with respect to problem size. Keep efficiency fixed by increasing both the problem size and number of processors

27. Keep efficiency fixed by increasing both the problem size and number of processors Scalable parallel systems Ability to utilize increasing processing elements effectively

28. Scalability and cost-optimality are related Scalable system can always be made cost-optimal if number of processing elements and size of problem are chosen carefully

29. Scalability and cost-optimality are related Scalable system can always be made cost-optimal if number of processing elements and size of problem are chosen carefully

30. Speedup Anomalies • Speedup that is greater than linear: Super-linear

31. Speedup Anomalies Cache effects. • Each processor has a small amount of cache • When a problem is executed on a greater number of processors, more of its data can be placed in cache and as a result, total computation time will tend to decrease. • If reduction in computation time due to this cache effectoffsets increases in communication and idle time from use of additional processors then super-linearity results. • Similarly, the increased physical memory available in a multiprocessor may reduce the cost of memory accesses by avoiding the need for virtual memory paging.

32. Speedup Anomalies Search anomalies. If a search tree contains solutions at varying depths, then multiple depth-first searches will, on average, explore fewer tree nodes before finding a solution than will a sequential depth-first search.

33. Message Passing • Partitioned address space • Data explicitly decomposed and placed by programmer • Locality of access. • Cooperation for send receive operations. • Structured and static requirements

34. Message Passing • Most message passing programs are written using SPMD

35. Message Passing • The need for a standard.

36. The Message Passing Interface (MPI) standard is the de-facto industry standard for parallel applications. • Designed by leading industry and academic researchers • MPI • Library that is widely used to parallelize scientific and compute-intensive programs

37. LAM (Indiana University),MPICH (Argonne National Laboratory, Chicago) are popular open source implementations of MPI library.

38. Implementations of MPI (such as LAM, MPICH) provide an API of library calls that allow users to pass messages between nodes of a parallel application. • Run on a wide variety of systems, from desktop workstations, clusters to large supercomputers (and everything in between).

39. MPI: the Message Passing Interface The minimal set of MPI routines.

40. Starting and Terminating the MPI Library • MPI_Init is called prior to any calls to other MPI routines. Its purpose is to initialize the MPI environment. • MPI_Finalize is called at the end of the computation, and it performs various clean-up tasks to terminate the MPI environment. • The prototypes of these two functions are: int MPI_Init(int *argc, char ***argv) int MPI_Finalize() • MPI_Init also strips off any MPI related command-line arguments. • All MPI routines, data-types, and constants are prefixed by “MPI_”. The return code for successful completion is MPI_SUCCESS. (mpi.h)

41. Hello World MPI Program #include <stdio.h> #include <mpi.h> int main(int argc, char *argv[]) { int rank, size; MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &rank); MPI_Comm_size(MPI_COMM_WORLD, &size); printf("Hello, world! I am %d of %d\n", rank, size); MPI_Finalize(); return 0; }

42. LAM • Before any MPI programs can be executed, the LAM run-time environment must be launched. This is typically called “booting LAM.”

43. LAM • Before any MPI programs can be executed, the LAM run-time environment must be launched. This is typically called “booting LAM.” • A text file is required that lists the hosts on which to launch the LAM run-time environment. This file is typically referred to as a “boot schema”, “hostfile”, or “machinefile.”

44. Sample machinefile hpcc.lums.edu.pk compute-0-0.local compute-0-1.local compute-0-2.local compute-0-3.local compute-0-4.local compute-0-5.local compute-0-6.local

45. LAM Settings have been done on your accounts and the following files have been copied in your home directory. • ssh_script • machinefile • hellompi.c

46. First time commands (Logout of all old sessions and re-login) source ssh_script

47. First time commands source ssh_script Warning: Permanently added 'compute-0-0.local' (RSA) to the list of known hosts. /bin/bash Warning: Permanently added 'compute-0-1.local' (RSA) to the list of known hosts. /bin/bash Warning: Permanently added 'compute-0-2.local' (RSA) to the list of known hosts. /bin/bash Warning: Permanently added 'compute-0-3.local' (RSA) to the list of known hosts. /bin/bash Warning: Permanently added 'compute-0-4.local' (RSA) to the list of known hosts. /bin/bash Warning: Permanently added 'compute-0-5.local' (RSA) to the list of known hosts. /bin/bash Warning: Permanently added 'compute-0-6.local' (RSA) to the list of known hosts. /bin/bash

48. First time commands source ssh_script /bin/bash /bin/bash /bin/bash /bin/bash /bin/bash /bin/bash /bin/bash

49. First time commands lamboot -v machinefile LAM 7.1.1/MPI 2 C++/ROMIO - Indiana University n-1<13857> ssi:boot:base:linear: booting n0 (hpcc.lums.edu.pk) n-1<13857> ssi:boot:base:linear: booting n1 (compute-0-0.local) n-1<13857> ssi:boot:base:linear: booting n2 (compute-0-1.local) n-1<13857> ssi:boot:base:linear: booting n3 (compute-0-2.local) n-1<13857> ssi:boot:base:linear: booting n4 (compute-0-3.local) n-1<13857> ssi:boot:base:linear: booting n5 (compute-0-4.local) n-1<13857> ssi:boot:base:linear: booting n6 (compute-0-5.local) n-1<13857> ssi:boot:base:linear: booting n7 (compute-0-6.local) n-1<13857> ssi:boot:base:linear: finished

50. First time commands lamnodes n0 hpcc.lums.edu.pk:1:origin,this_node n1 compute-0-0.local:1: n2 compute-0-1.local:1: n3 compute-0-2.local:1: n4 compute-0-3.local:1: n5 compute-0-4.local:1: n6 compute-0-5.local:1: n7 compute-0-6.local:1: