1. www.clearspeed.comWolfram Technology Conference ENVISION. ACCELERATE.ARRIVE. Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 1 12 October 2006 Accelerating Mathematica®: Vectors for all Simon McIntosh-Smith VP of Applications, ClearSpeed Technology simon@clearspeed.com

2. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 2 Agenda Introduction Accelerators ClearSpeed math acceleration technology Accelerating Mathematica Summary

3. www.clearspeed.comWolfram Technology Conference ENVISION. ACCELERATE.ARRIVE. Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 3 12 October 2006 Introduction

4. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 4 Introduction Mathematica® is being used to solve more and more computationally intensive problems General purpose CPUs keep getting faster, but a new wave of application accelerators are emerging that could give much greater performance –Much as GPUs have done for graphics ClearSpeed has been developing hardware accelerators specifically focused on scientific computing, and which accelerate the low-level math libraries used by Mathematica

5. www.clearspeed.comWolfram Technology Conference ENVISION. ACCELERATE.ARRIVE. Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 5 12 October 2006 Accelerators

6. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 6 Accelerator technologies Visualization and media processing –Good for graphics, video, game physics, speech, … –Graphics Processing Units (GPUs) are well established in the mainstream –But there was a time not too long ago when your PC still did all the graphics in software on the main CPU… –Can be applied to some 32-bit applications, but low accuracy (not IEEE754 floating point), are fairly hard to program, and very power hungry! Embedded content processing –Data mining, encryption, XML, compression –Field Programmable Gate Arrays (FPGAs) are often being used here, mainly to accelerate integer-intensive codes –Poor at floating point, especially 64-bit, and cut corners on precision so don’t get good accuracy –Very hard to program and get good performance

7. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 7 Accelerator technologies continued Math Accelerators –Mostly floating point, 64-bit performance is crucial, high precision, supporting true IEEE754 floating point (“Video game FLOPS” may be fast and cheap, but you get what you pay for, and what’s the wrong answer really worth?) –Can accelerate numerically-intensive applications in Finance Oil and Gas Economics Electromagnetics Bioinformatics And many, many more –This is what ClearSpeed has developed To accelerate Mathematica, a true Math Accelerator is needed…

8. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 8 The other benefit of accelerators – low power Running 1 watt for 1 years costs about $1 Modern CPUs can consume around 100W –$100/year running cost for the CPU alone if used 24/7 Accelerators typically bring significant performance per watt gains –Examples later in this presentation show 1 CPU plus a 25W ClearSpeed board running as fast as a 4 CPU (8 core) machine –This power consumption reduction of around 275W, if applied 24/7, is a $275 energy cost saving –Not to mention how much smaller and quieter the accelerated system can be…

9. www.clearspeed.comWolfram Technology Conference ENVISION. ACCELERATE.ARRIVE. Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 9 12 October 2006 ClearSpeed’s Math Acceleration Technology

10. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 10 What are ClearSpeed’s products? Math accelerator board, The ClearSpeed Advance ™ –Dual ClearSpeed CSX600 coprocessors –R ∞ ≈ 50 GFLOPS for 64-bit matrix multiply (DGEMM) calls Hardware also supports 32-bit floating point –133 MHz PCI-X 2/3 rds length (8”) form factor –1GByte of memory on the board –Linux drivers today for RedHat and Suse Windows coming in a future release –Low power; around 25 Watts Significantly accelerate the low-level math library used by Mathematica (MKL): –Target functions: Level 3 BLAS, LAPACK, FFTs

11. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 11 Which MKL functions can ClearSpeed accelerate? L3 BLAS: DGEMM ZGEMM (upcoming release) Under development – DTRSM and others LAPACK functions for: LU (DGETRF) QR (upcoming release) Cholesky (upcoming release) Under development – Eigenvalues, SVD, … For FFTs: Acceleration for large 2D, 3D to be added in the future Better yet are compound FFT-based functions, such as convolution For trig and other functions: Exploring long vectors of sin, cos, exp, log, sqrt et al

12. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 12 Software development kit (SDK) C compiler with vector extensions (ANSI-C based commercial compiler), assembler, libraries, ddd/gdb- based debugger, newlib-based C-rtl etc. ClearSpeed Advance development boards Available for Linux, Windows

13. www.clearspeed.comWolfram Technology Conference ENVISION. ACCELERATE.ARRIVE. Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 13 12 October 2006 Accelerating Mathematica

14. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 14 Mathematica uses libraries underneath Mathematica BLAS & LAPACK library: Intel’s MKL CPU Software Hardware

15. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 15 Mathematica using accelerated libraries Mathematica BLAS & LAPACK library: Intel’s MKL CPU Software Hardware ClearSpeed’s CSXL Library ClearSpeed Advance TM board

16. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 16 Plug-and-Play – No changes to your notebooks Mathematica defaults to using MKL since v5.2 ClearSpeed provides a modified kernel –Uses a modified “math” script that launches the kernel –Sets the library path to pick up CSXL as well as MKL Functions supported in Mathematica today: –Dot[] –Det[] –LUDecomposition[] –LinearSolve[] –Inverse[] If your notebooks spend a high percentage of your total runtime in these functions, and a lot of time in each call to these functions, then you may have a candidate for ClearSpeed acceleration!

17. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 17 ClearSpeed has been collaborating with ScienceOps to discover what kinds of problems are accelerated –Also see ScienceOps’ own talk here! Early results show a good breadth of applications being accelerated –Performance improvements –Ability to run larger problem sets Initial results show speedup ranging from 2 – 5X What kind of notebooks could be accelerated?

18. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 18 Example notebooks Benchmarked on a fast server for comparison: –4 processors, each dual core (8 cores total), AMD Opteron 870 (2GHz) with 32GBytes of memory running Linux RHE4-64 Comparisons are between: –Using 2 Opteron cores on their own –Using all 8 Opteron cores on their own, and –Using 2 Opteron cores with a single ClearSpeed Advance accelerator board The notebooks are very new and we believe there is more performance to come from the accelerated versions with a bit more tuning

19. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 19 Example notebook descriptions ANOVA –Analysis of variance, a linear least squares minimisation, fitting a curve to sampled data Microarray –Microarray data analysis, determines coexpression networks – sets of genes that are commonly expressed together under different experimental conditions. Calculates a distance – distance metric ImageDecode –Progressive decoding of images using the Haar wavelet transform Spatial Auto Regression (SAR) –Simple regressions iterating on large, dense matrices

20. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 20 Example – ANOVA ANOVA notebook benefits from 2X speedup with 4,000 predictors Two cores with a ClearSpeed accelerator equivalent in performance to an eight core machine!

21. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 21 Example – Microarray Microarray notebook benefits from nearly a 3X speedup with 4,000 inputs Larger problems may receive even more speedup –Data sets with over 6,000 expression levels exist for yeast

22. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 22 Example – ImageDecode ImageDecode notebook speedup ranges from 2-3X depending on the image size When tuned this speedup should also be achieved for images around 960x960 in size (already around 1.6X)

23. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 23 Example – Spatial Auto Regression SAR notebook speedup nearly 2X Larger problems should receive even more speedup –Run-times quite substantial too

24. www.clearspeed.comWolfram Technology Conference ENVISION. ACCELERATE.ARRIVE. Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 24 12 October 2006 Summary

25. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 25 Summary Accelerators can be used to significantly increase performance and performance per watt across a range of interesting applications in Mathematica You need a real 64-bit math accelerator for Mathematica to deliver the precision you depend upon ClearSpeed can accelerate notebooks making intensive use of Dot[], Det[], LUDecomposition[], LinearSolve[] and Inverse[] –More in the future as the libraries are developed Plug-and-play – no changes to your notebooks How fast can you go?

26. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 26 Recent news! ClearSpeed’s accelerators don’t just accelerate your workstation or server, they can be used to build supercomputers too! Announced this Monday: Tokyo Tech have accelerated their Linux supercomputer, TSUBAME, from 38 TFLOPS to 47 TFLOPS with 360 ClearSpeed Advance boards –An increase in performance of 24%, but for just a 1% increase in power consumption Professor Matsuoka standing beside TSUBAME at Tokyo Tech

27. www.clearspeed.comWolfram Technology Conference Copyright © 2006 ClearSpeed Technology plc. All rights reserved. 12 October 2006 27 A special offer at WTC06! If you want to put supercomputer technology in your own machine, ClearSpeed has a special offer at WTC: –37.5% discount available to the first twenty Wolfram Technology Conference attendees purchasing a ClearSpeed Advance accelerator board under the terms of this limited offer –$4,995 plus local sales taxes Talk to a ClearSpeed representative at the conference to find out if your machine is compatible –Launching on x86 for Linux RHE3/4 & SLES9