bill walster june 15, 2006 computing with intervals recent developments
TRANSCRIPT
Bill Walster
June 15, 2006
Computing
with
Intervals
Recent Developments
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”
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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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.”
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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Interval Computing Suppliers• Sun Microsystems html, html
• Intel pdf
• Maple html
• Mathematica html
• MuPad html
• MatLab html
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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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
Computing with Intervals: Recent Developments
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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
