1. Performance Models for Application Optimization
Walid Abu-Sufah
Visiting Scholar, University of Illinois
Associate Professor, University of Jordan

2. Outline Objective Overview Relate roofline/capacity Open Issues
Roofline model
Capacity model
Relate roofline/capacity
Open Issues
Discussion: How could PMUs help

3. 1. Objective
Explore how a model for a target architecture could be used for application tuning (may be in a compiler?).
All approaches, including autotuning, have involved running experiments.
Library guys may be willing to do that but compiler guys don't want to make a compiler that 'searches'. 99% of developers wouldn't use it.

4. 2.1 Roofline Model
For applications where off-chip memory bandwidth is the constraining resource (limit) in system performance.
Relates processor performance to off-chip memory traffic.
Bound and Bottleneck Model
good enough to understand which optimizations to try to get next level of performance
So far, demonstrated for several HPC dwarfs and multicore systems.

5. Bounds = Peak Processing Bandwidth; MFLOP/sec
= Peak DRAM Bandwidth; Mbytes/sec
“Operational Intensity”:
Average number of Floating Point Operations per Byte to DRAM, FLOPs/Byte
Varies by multicore design (cache org.) and dwarf
Characterize dwarf for a particular multicore design

6. Performance Model Graph
Y axis is GFLOPs/sec
X-axis is FLOPs/Byte
(i.e. Operational Intensity)
Can plot peak DRAM BW, since
(GFLOPs/sec)
(FLOPs/Byte)
“Roofline”
= GBytes/sec

7. Roofline Visual Performance Model
“Ridge Point”: minimum Operational Intensity to get Peak Performance
Compute Bound
Memory Bound
Ridge Point

8. Roofline model for AMD Opteron X2

9. Roofline model for Opteron X2 vs. Opteron X4

10. Roofline model with ceilings for Opteron X2

11. Roofline model with ceilings for Opteron X2.

12. Roofline model with ceilings for Opteron X2

13. What is next for Roofline
Non-floating point kernels would be interesting
e.g., Sort (potential exchanges/sec vs GB/s), Graph Traversal (nodes traversed/sec vs. GB/s)
Opportunities for others to help investigate: many kernels, multicores, metrics, …
For example, Jike Chong ported two financial PDE solvers to four other multicore computers: the Intel Penryn and Larrabee and NVIDIA G80 and GTX280.[9] He used the Roofline model to keep track the platforms' peak arithmetic throughput and L1, L2, and DRAM bandwidths. By analyzing an algorithm's working set and operational intensity, he was able to use the Roofline model to quickly estimate the needs for algorithmic improvements. Specifically, for the option-pricing problem with an implicit PDE solver, the working set is small enough to fit into L1 and the L1 bandwidth is sufficient to support peak arithmetic throughput, so the Roofline model indicates that no optimization is necessary. For option pricing with an explicit PDE formulation, the working set is too large to fit into cache, and the Roofline model helps to indicate the extent to which cache blocking is necessary to extract peak arithmetic performance

14. 2.2 Capacity Model HW represented as nodes with “peak” BW
In this talk & for illustration purposes, we assume only two nodes, a memory and a processing node with BWs:
System is represented as graph of HW nodes

15. Performance Depends on:
System Characteristics
Peak BWs of nodes
Memory hierarchy (cache) organization/ size
Operational overlap
Application Characteristics
Relative demands on BWs
Overheads

16. Definitions Ration of peak BWs, BW-used per node: , Ratio of BWs-used
Ratio of BW-used per node to system bandwidth-used:

17. Capacity of A Node Average node BW utilized by an application
A function of
Application characteristics
Node BW

18. Saturated Node Capacity
Assume that at least one of the nodes is saturated, then processor capacity, , is given by
A similar expression applies for memory capacity,
System capacity,
Similar argument holds for unsaturated node pair

19. Saturated Node Capacity Expression – Example
For αp,m = ½

20. Processor, Memory, and System Capacity Curves ( )

21. 3. Relating Roofline/ Capacity
A processing optimization ceiling, x , in Roofline corresponds to a used processing BW
A memory optimization ceiling , y, in Roofline corresponds to a used memory BW,
If an application is optimized using optimizations x and y then

22. Roofline model with ceilings for Opteron X2

23. 4. Open Issues Modeling with different performance limiting factors
Cache resident client applications (i.e. memory BW is not the limit)
Introduce additional bounds: Network BW and IO BW
Development of tools based on models for use in application optimization

24. 5. Discussion: How could PMUs help

25. References: Roofline Model
S. Williams, A. Waterman, D. Patterson, "Roofline: an insightful visual performance model for multicore architectures,” Communications of the ACM, Volume 52 , Issue 4 (April 2009), Pages
David Patterson,” The Parallel Revolution Has Started: Are You Part of the Solution or Part of the Problem?“, April 8, 2009 lecture in the Distinguished Lecture Series ( )

26. References: Capacity Model
D. J. Kuck, "Computer System Capacity Fundamentals,” National Bureau of Standards, Technical Note 851, Oct
D. J. Kuck, B. Kumar, A system model for computer performance evaluation, March 1976 SIGMETRICS 76: Proceedings of the 1976 ACM SIGMETRICS Conference on computer performance modeling measurement and evaluation.
D.J. Kuck, The Structure of Computers and Computations, Vol. I, John Wiley & Sons, Inc., 1978.

27. David J. Kuck “Capacity-based Codesign of Computer HW and SW“, January 26, 2009 lecture in the Distinguished Lecture Series ( )