Speedy Gonzales Ph J Roussel Speedy Gonzales Using

Speedy Gonzales Ph. J. Roussel The Speedy Gonzales problem HPCC anniversary conference College 2002.

Speedy Gonzales Ph. J. Roussel • Speedy Gonzales wants to get from A to

Speedy Gonzales Ph. J. Roussel Observation • Analogy with beam travelling through planparallel media

Speedy Gonzales Ph. J. Roussel Constraint: arrive in C • Project field lengths using

Speedy Gonzales Ph. J. Roussel Solver Equation • Using transform variable for computation speed

Speedy Gonzales Ph. J. Roussel Travelling time • Even for non-optimal incidence angles •

Speedy Gonzales Ph. J. Roussel The Long. FLoat library • Numbers stored as string

Speedy Gonzales Ph. J. Roussel Using Long. Floats with the Solver • Standard BCD

Speedy Gonzales Ph. J. Roussel Using Long. Floats with the Solver • Function output

Speedy Gonzales Ph. J. Roussel Using the Multiple Equations Solver • Define set of

Speedy Gonzales Ph. J. Roussel The MES solution • LNGSLV program initialises the MES:

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Speedy Gonzales Ph. J. Roussel Speedy Gonzales Using the HP 48 G solver and the Long. FLoat library for extended precision equation solutions HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel The Speedy Gonzales problem HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel • Speedy Gonzales wants to get from A to C as fast as possible. Problem: · optimal path? · minimal time? Challenge: · 48 digits accuracy · solve on an HP 48 HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Observation • Analogy with beam travelling through planparallel media with different propagation speeds Þ Relationship between incidence angles: Snell’s law HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Constraint: arrive in C • Project field lengths using incidence angles • Eliminate a 1 & a 2 using Snell’s law HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Solver Equation • Using transform variable for computation speed Þ No Long. Float trigonometric function calls! HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Travelling time • Even for non-optimal incidence angles • Wide sa 3 validity range HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel The Long. FLoat library • Numbers stored as string objects • Specific commands HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Using Long. Floats with the Solver • Standard BCD reals for variables ® Use real component variables with non-overlapping mantissa ranges: HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Using Long. Floats with the Solver • Function output must be BCD real ® Use subtractive cancellation as advantage: HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel Using the Multiple Equations Solver • Define set of equations with increasing number of component variables: HPCC anniversary conference College 2002. 09. 21 Imperial

Speedy Gonzales Ph. J. Roussel The MES solution • LNGSLV program initialises the MES: HPCC anniversary conference College 2002. 09. 21 Imperial