Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation,

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Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL SAND C Formal Metrics for Large-Scale Parallel Performance ISC 2015 Kenneth Moreland and Ron Oldfield Sandia National Laboratories

Parallel Algorithm Speedup

Serial time for large problem sizes Cannot be measured in practice

Efficiency

Karp-Flatt Metric

Isoefficiency Metric

Measuring Scalability in Practice  Strong Scaling: Behavior as processing elements are increased and problem size held constant.  Per Amdahl’s Law, strong scaling always has its limits.  Weak Scaling: Behavior as processing elements and job size are increased proportionally.  Per Gustafson-Barsis Law, weak scaling can possibly be increased indefinitely.  Scaling is often demonstrated with absolute run time over different scales.

Demonstrating Strong Scaling

Measuring Strong Scaling O(n/p) O(n/p + log p)O(n/p + p)

Strong Scaling with Log Axes

Measuring Strong Scaling with Log O(n/p) O(n/p + log p)O(n/p + p)

Scaling with More Visual Precision  Our position statement: rate and efficiency better represent scaling behavior.  Although neither rate nor efficiency is a new concept, there is not a lot of consistency in the community.  Through algebra and examples I will show why rate and efficiency are the “right” metrics to use.

Rate

Why Use Rate?

Becomes a constant with n is constant.

Why Use Rate?

Scaling with Rate

Measuring Scaling with Rate O(n/p) O(n/p + log p)O(n/p + p)

Measuring Scaling with Rate O(n/p + log p)O(n/p + p) O(n/p + log p)O(n/p + p)

Efficiency

Measuring Efficiency from Cost

Minimum (best) cost

Scaling with Efficiency

Measuring Scaling with Efficiency O(n/p + log p)O(n/p + p) O(n/p + log p)O(n/p + p)

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Unifying Strong and Weak Scaling

Efficiency Across Data Scales

Unifying Rate Across Data Scales

Rate Across Data Scales

Use Case 1: Gordon Bell Finalist  Measurements of HACC code performance  Excellent Scalability  Measurements across many scales  Lots of data provided in paper

Use Case 1: Gordon Bell Finalist

Use Case 2: Imperfect Scaling  Measures visualization algorithm  A high communication overhead severely limits scalability

Use Case 2: Imperfect Scaling

Final Recommendations  Do not rely on running time for performance analysis. Instead use rate, efficiency, or both.  Avoid using log-log scaling on plot axes, which hides major inefficiencies. If necessary, repeat linear plots at different scales.  Rather than performing them separately, incorporate weak and strong scaling studies in one. Perform several strong scaling studies at different scales of data size. Then find an overall minimal practical cost per unit and plot all the measurements together as demonstrated in the figures in this paper.

Acknowledgements  This material is based in part upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program under Award Number  This material is based in part upon work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing (ASC).