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Computer Science 320

Computer Science 320. Measuring Speedup. What Is Running Time?. T ( N , K ) says that the running time T is a function of the problem size N and the number of processors K

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Computer Science 320

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  1. Computer Science 320 Measuring Speedup

  2. What Is Running Time? • T(N, K) says that the running time T is a function of the problem size N and the number of processors K • To determine speedup, we’ll always determine both Tseq(N, K) and Tpar(N, K), where K = 1 and K > 1, respectively

  3. What Is Speed? • Speed is the rate at which program runs can be done • S(N, K) = 1 / T(N, K) • Measured in program runs per second, rather than seconds per run

  4. What Is Speedup? • Speedup is the speed of a parallel version running on K processors relative to a sequential version running on one processor • Speedup(N, K) = Spar(N, K) / Sseq(N, 1) • Why seq in the denominator?

  5. Speedupin Terms of Running Time Speedup(N, K) = Tseq(N, K) / Tpar(N, K) Ideally, the speedup should equal K, or a linear speedup The real speedup of most algorithms is sublinear

  6. What Is Efficiency? Eff(N, K) = Speedup(N, K) / K Usually a fraction < 1

  7. Amdahl’s Law • The sequential portion of a parallel program puts an upper bound on the efficiency it can achieve • The sequential parts are usually run at startup and cleanup

  8. What Is the Sequential Fraction? • The sequential fraction F is the fraction of the code that must be run sequentially • F * T(N, 1) is the running time of the sequential part on a single processor • (1 – F) * T(N, 1) is the running time of the parallel part on a single processor

  9. Amdahl’s Law T(N, K) = F * T(N, K) + 1/K * (1 – F) * T(N, K) Running time when the parallel part is equally divided among K processors

  10. Speedup and Efficiency in Terms of Sequential Fraction Speedup(N, K) = 1 /(F + (1 – F) / K) Eff(N, K) = 1 / (K * F + 1 – F)

  11. Consequences of Amdahl • As K increases, the speedup approaches 1 / F • As K goes to infinity, the efficiency approaches 0

  12. Predicted Speedups

  13. Predicted Efficiencies

  14. A Normal Plot for up to 8 Processors

  15. Experimentally Determining F To calculate the sequntial fraction F from the running time measurements, we rearrange Amdahl’s Law to get F = (K * T(N, K) - T(N, 1)) / (K * T(N, 1) - T(N, 1)) Called EDSF If F is not a constant or EDSF versus K is not a horizontal line, something’s not right with the program

  16. Measuring Running Times • Not the same on each run with the same data set • Take the minimum time of several runs, not the average time. Why?

  17. Experimental Situation • Close all unnecessary apps and prevent remote logins • Tseq(N, 1) must be at least 60 seconds • Run the sequential program 7 times on each data size N, and take the minimum time

  18. Experimental Situation • For each data size N and for each K from 1 up to the number of available processors, run Tpar(N, K) 7 times and take each minimum time

  19. Running Time of Key Search

  20. Speedup of Key Search

  21. Efficiency of Key Search

  22. EDSF of Key Search

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