🚀 go-pugleaf

In article <6028@ut-sally.UUCP>, nather@ut-sally.UUCP (Ed Nather) writes:

> long as I sometimes needed.  Then I learned about floating point . . .

>        . . . .  It sounded great until I learned that you give up
> something when you do things that way --simple operations become much
> more complex (and slower) using standard hardware. . . .

For problems appropriate to floating point, the input is already
imprecise.  Planck's constant is not known to more than a dozen
digits at most.  Good floating point software keeps track of
the remaining precision as computations proceed.  Even if the 
results were computed precisely using rational arithmetic,
the results would be more imprecise than the input.  Rounding
in floating point hardware contributes only a minor portion of
the imprecision of the result in properly designed software.

For problems unsuited to floating point, e.g. accounting, yes the
floating point hardware gets in the way.  For accounting one should
use large integers: 48 bits is plenty in practice and no special hardware
is needed.  The 'BCD' baloney often advocated is just that.  Monetary
amounts in accounting are integers.  'BCD' is sometimes used so that
decimal fractions round correctly, but the correct method is to use
integers.

Rational arithmetic is another place for large integers.  Numbers
are represented as the quotient of two large integers.  This is where
special hardware might help.  Symbolic math often uses rational 
arithmetic, but the large integers should be variable length.  Numbers
such as '1' and '2' are far more common than 100 digit monsters.
-- 
Stuart D. Gathman	<..!seismo!{vrdxhq|dgis}!BMS-AT!stuart>