From: jmichel@...3.institut.math.jussieu.fr (Jean Michel)
Date: 2001-07-30T04:09:56+09:00
Subject: [ruby-talk:18755] Re: Numbers classes.. Rational number? [was: Ruby as opposed to Python?]

In article <3b645247$0$51737$edfadb0f@dspool01.news.tele.dk>,
MikkelFJ <mikkelj-anti-spam@post1.dknet.dk> wrote:
>
>A different pretty cool number class is interval arithmetic.
>Given the topic of the discussion I thought I'd mention it.
>Interval arithmetic is not just a gimmick. It is possible to do exact
>calculations and reason about the accuracy of the result.

Unfortunately, interval arithmetic is a nice idea which does not work in
practice, as  you will discover  asking anybody  who has looked  hard at
it  (usually  in  order  to  try  to  make  provably  correct  numerical
computations). The problem is that  interval arithmetic, while trying to
guarantee error  bounds, is  *much* too  pessimistic. The  actual errors
grow  exponentially  less than  the  errors  predicted by  the  interval
arithmetic, because  in practice errors  do not  have all the  same sign
thus tend  to cancel out.  As a  result most computations,  even trivial
ones, become impossible with interval arithmetic, requiring huge initial
precision to get any significant digits at the end.

  Best regards,
    Jean MICHEL