1. Bill Walster June 15, 2006 Computing with Intervals Recent Developments

2. Computing with Intervals: Recent Developments Page 2 Overview Floating-point arithmetic flaws NNSA's “Predictive Science” Intervals solve critical computing problems Intervals are here and are here to stay Sun leads commercial interval development There is still lots to be done Computing with intervals is “big science”

3. Computing with Intervals: Recent Developments Page 3 Floating-point Problem Computational science is “stuck” > Floating-point numbers contain no accuracy information > Impossible to represent and track input data inaccuracies > Impossible to perform rigorous error and sensitivity analyses > Floating-point numbers are a finite set of real numbers > Impossible to numerically “safely” solve important problems – Single and multi-objective (linear and nonlinear) function optimization – Nonlinear systems of equations – Over- and under-determined systems of linear and nonlinear interval equations – Ordinary and partial differential equations Speed kills > The faster machines get, the more chance for silent catastrophic errors

4. Computing with Intervals: Recent Developments Page 4 National Nuclear Security Administration (NNSA) Predictive Science Definition: > “... the application of verified and validated computational simulations to predict reactions within complex systems where routine experimental tests are not feasible.”

5. Computing with Intervals: Recent Developments Page 5 Some Problems Solved with Intervals Proved stability of Tevatron – The world's largest and most powerful particle accelerator htmlhtml Avionics control system design html,html, htmlhtml Solid modeling html and graphics rendering html, htmlhtml Numerical proofs html, html, htmlhtml Robot control html, html, motion planning pdfhtml pdf Measuring physical constants html, htmlhtml

6. Computing with Intervals: Recent Developments Page 6 Large, High-Value Opportunities Enhance software productivity and reliability > Algorithm and code error detection > High abstraction level for application developers > Code transparency Safely reduce product liability in mission-critical applications > Input data uncertainty propagation > Sensitivity analysis Increase speed > Interval bounds minimize unnecessary computing > Important generic interval algorithms scale horizontally > Enhance IC design optimization

7. Computing with Intervals: Recent Developments Page 7 Interval Computing Suppliers Sun Microsystems html, htmlhtml Intel pdfpdf Maple htmlhtml Mathematica htmlhtml MuPad htmlhtml MatLab htmlhtml

8. Computing with Intervals: Recent Developments Page 8 Sun Leads Interval Computing World class consultants: > Ray Moore, Eldon Hansen Foundation for exception-free hardware World class interval compiler support World class interval math library

9. Computing with Intervals: Recent Developments Page 9 Sun Labs Interval Aplications Second order partial differential equations (PDEs) > Elliptic: Laplace's equation > Example: Robot motion planning pdfpdf > Parabolic: Heat diffusion > Hyperbolic: Nonlinear equations leading to shocks Second kind integral equations > Electrostatics and Electrodynamics > Antenna design > Radar cross section Integrated circuit design optimization

10. Computing with Intervals: Recent Developments Page 10 Plans Develop solutions to new problems in key areas > Partial differential and integral equations (PDEs and IEs) > Design optimization examples using PDEs and IEs >Airfoil shape >Radar cross section >Antenna Demonstrate interval benefits relative to alternatives Integrate hardware and software support into existing processors and compilers

11. Computing with Intervals: Recent Developments Page 11 Interval Innovation Opportunities Data-type compiler support alone is insufficient > Additional integrated compiler support > Using dependence to remove unnecessary width > Integrating symbolic and numerical mathematics Interval computing: > Speed and ease-of-use > Interval hardware, tools, solvers, and commercial applications > Successes with demonstrated benefits > Instructional textbooks and software

12. Computing with Intervals: Recent Developments Page 12 Big Science Interval Opportunities Applications, Applications, Applications Given applications, interval speed > Solver library algorithms > Compiler support for speed and narrow width > Hardware for basic interval arithmetic operations

13. bill.walster@sun.com Computing with Intervals Recent Developments