Speedy Gonzales Problem with LongFloat Solver – HPCC Anniversary Conference

Speedy Gonzales, as presented at the HPCC Anniversary Conference, discusses using the HP48G solver and the LongFloat library for extended precision equation solutions. Ph.J. Roussel explores optimal paths, minimal time challenges, and calculations involving incidence angles and beam propagation speeds.

• Speedy Gonzales
• LongFloat library
• HPCC
• Equation solutions
• Incidence angles

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1. Speedy Gonzales Ph.J.Roussel Speedy Gonzales Using the HP48G solver and the LongFLoat library for extended precision equation solutions HPCC anniversary conference 2002.09.21 Imperial College

2. Speedy Gonzales The Speedy Gonzales problem Ph.J.Roussel HPCC anniversary conference 2002.09.21 Imperial College

3. 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 HP48 HPCC anniversary conference 2002.09.21 Imperial College

4. Speedy Gonzales Ph.J.Roussel Observation Analogy with beam travelling through planparallel media with different propagation speeds Relationship between incidence angles: Snell s law ( ) 1 Sin v ( ) v ( ) Sin Sin = = 3 2 v 1 2 3 HPCC anniversary conference 2002.09.21 Imperial College

5. Speedy Gonzales Ph.J.Roussel Constraint: arrive in C Project field lengths using incidence angles ( ) ( ) ( ) + + = DF Tan FH Tan HC Tan AD 1 2 3 Eliminate 1 & 2using Snell s law HPCC anniversary conference 2002.09.21 Imperial College

6. Speedy Gonzales Ph.J.Roussel Solver Equation Using transform variable for computation speed No LongFloat trigonometric function calls! HPCC anniversary conference 2002.09.21 Imperial College

7. Speedy Gonzales Ph.J.Roussel Travelling time Even for non-optimal incidence angles Wide s 3 validity range HPCC anniversary conference 2002.09.21 Imperial College

8. Speedy Gonzales Ph.J.Roussel The LongFLoat library Numbers stored as string objects Specific commands HPCC anniversary conference 2002.09.21 Imperial College

9. Speedy Gonzales Using LongFloats with the Solver Ph.J.Roussel Standard BCD reals for variables Use real component variables with non-overlapping mantissa ranges: HPCC anniversary conference 2002.09.21 Imperial College

10. Speedy Gonzales Using LongFloats with the Solver Function output must be BCD real Ph.J.Roussel Use subtractive cancellation as advantage: HPCC anniversary conference 2002.09.21 Imperial College

11. Speedy Gonzales Using the Multiple Equations Solver Ph.J.Roussel Define set of equations with increasing number of component variables: HPCC anniversary conference 2002.09.21 Imperial College

12. Speedy Gonzales Ph.J.Roussel The MES solution LNGSLVprogram initialises the MES: HPCC anniversary conference 2002.09.21 Imperial College