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
Speedy Gonzales
Ph.J.Roussel
The Speedy Gonzales problem
HPCC anniversary conference 2002.09.21
Imperial College
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
Speedy Gonzales
Ph.J.Roussel
Observation
• Analogy with beam travelling
through planparallel media
with different propagation speeds
 Relationship between incidence angles:
Snell’s law
Sin 1  Sin  2  Sin  3 


v1
v2
v3
HPCC anniversary conference 2002.09.21
Imperial College
Speedy Gonzales
Ph.J.Roussel
Constraint: arrive in C
• Project field lengths using incidence angles
DF  Tan 1   FH  Tan  2   HC  Tan 3   AD
• Eliminate 1 & 2 using Snell’s law
HPCC anniversary conference 2002.09.21
Imperial College
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
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
Speedy Gonzales
Ph.J.Roussel
The LongFLoat library
• Numbers stored as string objects
• Specific commands
HPCC anniversary conference 2002.09.21
Imperial College
Speedy Gonzales
Ph.J.Roussel
Using LongFloats with the Solver
• Standard BCD reals for variables
 Use real component variables
with non-overlapping mantissa ranges:
HPCC anniversary conference 2002.09.21
Imperial College
Speedy Gonzales
Ph.J.Roussel
Using LongFloats with the Solver
• Function output must be BCD real
 Use subtractive cancellation as advantage:
HPCC anniversary conference 2002.09.21
Imperial College
Speedy Gonzales
Ph.J.Roussel
Using the Multiple Equations Solver
• Define set of equations with increasing
number of component variables:
HPCC anniversary conference 2002.09.21
Imperial College
Speedy Gonzales
Ph.J.Roussel
The MES solution
•
LNGSLV
program initialises the MES:
HPCC anniversary conference 2002.09.21
Imperial College