On Wed, Apr 11, 2007 at 12:48:34PM -0500, Jay Belanger wrote:
> But computer programs could use any base they want, at the cost of
> some efficiency. I would (perhaps foolishly) expect a computer
> algebra system to do numerics better than, say, a simple C program.
Your metric for "better" is the issue. The agreed upon standard metric
for good floating point arithmetic is the IEEE specification. It has
all sorts of nice properties such as gracefully handling degraded
precision, and a statistically unbiased rounding, sign bits for zero,
and all sorts of goodies. It's specifically designed so that iterative
computations in floating point will converge consistently when
designed in a reasonable manner and implemented on various different
hardware.
A system designed to satisfy 5th graders will not have any of these
nice properties. I personally believe that we should change the way we
teach 5th graders rather than change the way we write computer
programs. :-)
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan