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Speedy Gonzales

Speedy Gonzales Using the HP48G solver and the LongFLoat library for extended precision equation solutions. The Speedy Gonzales problem. 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 HP48.

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Speedy Gonzales

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  1. Speedy Gonzales Using the HP48G solverand the LongFLoat libraryfor extended precisionequation solutions

  2. The Speedy Gonzales problem

  3. 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 HP48

  4. Observation • Analogy with beam travelling through planparallel media with different propagation speeds • Relationship between incidence angles: Snell’s law

  5. Constraint: arrive in C • Project field lengths using incidence angles • Eliminate a1 & a2 using Snell’s law

  6. Solver Equation • Using transform variable for computation speed • No LongFloat trigonometric function calls!

  7. Travelling time • Even for non-optimal incidence angles • Wide sa3 validity range

  8. The LongFLoat library • Numbers stored as string objects • Specific commands

  9. Using LongFloats with the Solver • Standard BCD reals for variables • Use real component variableswith non-overlapping mantissa ranges:

  10. Using LongFloats with the Solver • Function output must be BCD real • Use subtractive cancellation as advantage:

  11. Using the Multiple Equations Solver • Define set of equations with increasing number of component variables:

  12. The MES solution • LNGSLVprogram initialises the MES:

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