1. Raspberry Pi Performance Benchmarking
Justin Moore
Salish Kootenai College

2. Overview Raspberry Pi Cluster Build Performance
Performance Benchmark Tools
Tuning
Analysis
Conclusion

3. Raspberry Pi Cluster – Model B
CPU – Broadcom ARM11 76JZF-S 700MHz
Can overclock to 1000MHz
RAM – 512MB
448MB/64MB – CPU/GPU
Linux OS
10/100 BaseT Ethernet port
Size of a credit card
Price - $35
Image:

4. Raspberry Pi Cluster - Setup
Router – Western Digital N750
NFS mounted external hard drive – 500GB Buffalo Inc.
4 Pi cluster
USB hub – Manhattan 7 port USB 2.0
SD card – Kodak 8GB
~$200
Transition to next slide with “After the cluster was set up, we wanted to measure performance”

5. Performance – Floating Point Operations
How we measure performance
Busy CPU? Speed?
What is a floating point operation (FLOP)?
Arithmetic operation
Formats
Single
Double
Performance measurement by FLOPS
How do we measure FLOPS?
General Matrix Multiplication (GEMM)
High computational intensity with an increase in matrix size

6. Performance Benchmarking
Single Raspberry Pi
BLAS - Basic Linear Algebra Subprograms
ATLAS - Automatically Tuned Linear Algebra Software
Auto tunes BLAS for any system
Raspberry Pi Cluster
MPI - Message Passing Interface
Standard API for inter-process communication
Facilitates parallel programming
MPICH p1
HPL - High Performance LINPACK
Tuned MPI
Combined with ATLAS
Wrote Custom code
ATLAS
Added parallel capability
Compared with HPL

7. MyGEMM – Naïve Implementation= *
C (i,j)
A(i,k)
B (k,j)
Where N = Matrix Size
For i = 1 to N
For j = 1 to N
For k = 1 to N
C(i,j)=C(i,j)+A(i,k)*B(k,j)
striding bad!
----- Meeting Notes (7/30/14 13:38) -----
Transistion to benchmarking slide

8. MyGEMM – Naïve Pitfalls
GEMM – Naïve method inefficient
Two whole matrices are loaded in to memory
Cache is not used efficiently
Strides through the matrix
If not Naïve, then what?
Naïve

9. MyGEMM – Software Tuning
What is block matrix multiplication
Matrix is split into smaller matrices/blocks
Shrinks matrix size to allow both A & B into fast memory
A11
A12
A13
A14
A21
A22
A23
A24
Reduces striding by fully utilizing memory hierarchy
Transistion
After we tuned for a single node we scaled it to our cluster
a11
a12
A11
A31
A32
A33
A34
a21
a22
A41
A42
A43
A44

10. MyGEMM – Cluster Software Tuning
How do we distribute the matrix multiplication?
MPI used to distribute blocks to nodes
MyGEMM allows for experimentation on block size
A11
A12
A13
A14
Node 1
A21
A22
A23
A24
Node 2
A31
A32
A33
A34
Start with further division of matrix
Why to divide matrix?
How do I reduce matrix size?
Divided by number of nodes in the cluster
allows matrix multiplication on higher sizes
What is cache blocking?
reduce the matrix to the exact size of my cache
Why blocks?
Row/Column wise multiplication
Loop unrolling
----- Meeting Notes (7/28/14 13:54) -----
reduces matrix to fit the cache
block size is reduced to fit in cache
----- Meeting Notes (7/30/14 08:29) -----
remove bullet 1
add mygemm parallel talk
how to distribute the matrix
A41
Node 3
A42
A43
A44
Node 4

11. Hardware Tuning
Raspberry Pi allows CPU overclocking and memory sharing between CPU and GPU
Memory
Memory is shared between CPU and GPU
512MB total onboard memory
Up to 496MB can be used for CPU
More memory = larger matrices
CPU Clock
Up to 1000 MHz from 700MHz

18. Conclusion Performance is dependent on key factors Top 500 – 1993
Matrix Size
Block Size
RAM size
CPU speed
Top 500 – 1993
T#292
Tied with General Motors
----- Meeting Notes (7/30/14 16:07) -----
move after yellowstone

19. Conclusion – Pi Cluster vs. Yellowstone
ARM11, 32 bit, Double Precision
Yellowstone
Sandy Bridge Xeon, 64 bit, Double Precision
Power
15.6 Watts
1.4 MWatts
Performance
836 MFLOPS
1.2 PFLOPS
Price
$250.00
$22,500,000.00
MFLOPS/W
54.8
875.3
MFLOPS/$
3.4
57.2

20. Thank You Dr. Richard Loft Raghu Raj Prasanna Kumar Amogh Simha
Stephanie Barr

21. Questions?