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

Bill Walster

June 15, 2006

Computing

with

Intervals

Recent Developments

Computing with Intervals: Recent Developments

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”


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


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.”


Some Problems Solved with Intervals • Proved stability of Tevatron – The world's largest

and most powerful particle accelerator html

• Avionics control system design html ,html, html

• Solid modeling html and graphics rendering html, html

• Numerical proofs html , html , html

• Robot control html, html , motion planning pdf

• Measuring physical constants html, html


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


Interval Computing Suppliers• Sun Microsystems html, html

• Intel pdf

• Maple html

• Mathematica html

• MuPad html

• MatLab html


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


Sun Labs Interval Aplications

• Second order partial differential equations (PDEs)

> Elliptic: Laplace's equation> Example: Robot motion planning pdf

> 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


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


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


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

[email protected]

Computing

with

Intervals

Recent Developments

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

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