high precision mathematics

[Carl Banks]

Tim Roberts wrote:
> And the original poster should understand that this is true because such
> systems are of little practical use.  There are very, very few physical
> processes where floating point is useful AND precision of more than 6
> significant digits is really required.  Large integers can be useful (and
> Python supports them), but a requirement for high precision floats is
> usually a sign that the requirer does not understand his problem space.


Incredibly untrue.

Many physical and nonphysical systems require high precision, usually
because they involve calculating small differences between large
numbers.  Some examples off the top of my head:

Fractals: deep zooming.

Flight simulation: The earth's radius is about 20 million feet (about
7 million meters for my SI using friends), and the simulator must
resolve, at a minimum, distances of about 0.1 feet.  That's a
difference of 9 decimal places.  We then need several more places for
numerical robustness.

Optimization: Many optimization algorithms, especially in linear
programming, have numerical problems with single precision.

Differential equation solving: Certain differential equations have an
undesirable property called stiffness.  This happens a lot in fluid
mechanics.  High precision and other tricks are used to solve such
problems.


-- 
CARL BANKS                                http://www.aerojockey.com
"Nullum mihi placet tamquam provocatio magna.  Hoc ex eis non est."