This document summarizes research comparing the performance of single-core and multi-core processors when performing matrix multiplication. It finds that a multi-core processor, the Cell Broad Engine with 8 cores, was about 8 times faster than a single Power Processing Element core. However, performance began to decline for matrices larger than 2048x2048 due to data being swapped to disk. It also compares two multi-core programming models, Sequoia and Cellgen, finding Sequoia more stable but Cellgen having higher performance in other research.

1. Multicore ProcessingWu, Lieh-HaoVMI Class 2010Computer Science

2. What’s Multicore? Multiple cores in a single chipImproving performance by adding coreBecame the main stream in recent years - Examples - Core 2 dual, Core 2 Quad, Core-i3/5/7  Intel - Athlon II X2, Phenom II X4, Opteron AMD - Cell Broad Engine  IBM

3. Why Multicore?The difficulties of single core processor’s development - Overheat - Energy consumption - Electron leakage - Example - Intel abandoned the project of 4GHz processor in fall 2004 Multicore processor resolve these problem and has better performance

4. Research IntroductionPurpose: - To see the performance difference between single core and multicore processorsHow: - Use the PS3 as the host machine - Use the CPU of PS3 to execute a series of matrix multiplication - Execute with single core - Execute with multicore - programming tools are needed for handling cores - Record the time and analysis the performance

5. Play Station 3Physical ComponentsCPU: Cell Broad EngineMemory: 256MBStorage: 80GBSoftware Yellow Dog LinuxCell SDK

6. Cell Broad Engine ProcessorDeveloped by Sony, Toshiba, and IBM jointly.Multicore structure - Power Processing Element x 1 (PPE) - Like a traditional processor - It has its own L1, L2 cache - Synergistic Processing Element x 8 (SPE) - Can be used synchronously - It has 256KB local storage

7. Matrix MultiplicationSimple but time consumingSome assumptions are made for research purpose - Dimension is set to N2 - Data type is set to double - Only even numbers are applied

8. SequoiaAn explicit multicore programming model

9. Mapping a tree structure as a memory hierarchy

10. Basic idea - Consist of three functions - task<inner>: distribute - task<leaf>: compute - task<ext>: connect

11. Programming in SequoiaTo programming in Sequoia, four files are required to run the matrix multiplication. - “Makefile”  for compiling - “matrixmult.sq” Sequoia program - “mapping_ps3.xml”  for mapping - “main.cc”  for starting During the process - Good documentation - Good adaptability for different purposes - Details need to be handled by programmers

12. CellgenAn implicit multicore programming modelC/C++ based programming toolLike OpenMP style - OpenMP APIBasic idea - Starts after “#pragma cell” - Parameters - public: shared by SPEs - private: each SPE has a copyScott SchneiderPh.D. Candidate Virginia Tech

13. Programming in CellgenThere are files needed to run matrix multiplication - Two “Makefile”  for compiling - One “matrixmult.cellgen”  Cellgen code - One “double16b_t.h”  for padding column data - suggested by the author to improve performanceDuring the process - Understandable - C/C++ based; easy to catch up. - Lack of documentation - Only “Readme” file is available.

14. Result in TableThe following is the table for the execution time of PPE only, SPE with Sequoia, and SPE with Cellgen.3 x 8 x 3264x 3264 ≈ 256 MB - Oversize matrix will be swapped between disk and main memory.Can’t get result of Cellgen from size 3072 to 4096. - Either no response or bus error.

15. Result in Graph (1)The following is the line chart generated from thedata of the table.Memory size limitPPE OnlyCellgenSequoia

16. Result in Graph (2)

17. Result AnalysisPerformance of Cellgen - Unexpected overhead or runtime error may occur and throw the performance back.Performance of Sequoia - According to the stable record, it is about 8 times faster than the execution time of PPE. - Although the memory size is 256MB, performance starts dropping down after 2048 2. - The performance becomes the same with PPE after reaching 4096 2 . - Probably the most of the data are swapped with disk, which is out of the Sequoia’s ability.

18. ConclusionMulticore processor has better performance than single core processor, which is about 8 times faster if the memory space is sufficient.Multicore may also have some unexpected overhead or error, which may draw back the performance like what I have in Cellgen. Multicore processing is art. - In the paper “ Programming Multiprocessors With Explicitly Managed Memory Hierarchies,” Cellgen has better performance than Sequoia does. However, Cellgen doesn’t do well like Sequoia in this research.