Rounding on output

[Robert A. Cassels <Cassels%SCRC-TENEX%MIT-MC@SU-DSN>]

    Date: Thu, 16 Jun 1983  20:59 EDT
    From: Scott E. Fahlman <Fahlman@CMU-CS-C>
    Do we really have to lay down complicated rules for rounding of printed
    flonums in the white pages?  I can't believe that all of these marginal
    cases matter.  Why don't we just say that the results are supposed to be
    rounded appropriately and let the implementors worry about overflow
    conditions and how to break ties and what is done with the last bit.

What happens on ties hardly matters, since there is only one value of
exponent for which ties can occur.

In general, I agree that accuracy in printing isn't so important.
But there are enough strange behaviors when you drop a few bits
that I believe it's worth the trouble.  If Common Lisp is to be
used for any sort of serious mathematical work, any rigor we can
introduce will be appreciated down the road.  Why stop with
rational numbers?

I would certainly like the reader to be accurate.  Otherwise it's
a real pain to write approximation routines with nice properties
-- like monotonicity.  Are we to be reduced to writing octal
constants just to be sure that all the bits are right?
How do you write PI (which is supposed to be "the best possible
approximation") in a machine-independent manner?