From: Markus <markus@...>
Date: 2004-10-29T01:13:55+09:00
Subject: Re: Rounding error, (100.0 * 9.95).to_i == 994

On Wed, 2004-10-27 at 17:40, trans. (T. Onoma) wrote:
> On Wednesday 27 October 2004 08:22 pm, markus@reality.com wrote:
> | My favorite trick is storing a "repeat length" that works like the
> | bar you use when dealing with repeated decimals on paper.  I once saw a
> | very clever description of how to make that work.  But (so far as I know),
> | no FPU designers read the same paper.
> 
> That was I was thinking. Do you know where your read it?

     No.  I think it was an ACM or IEEE paper from the early eighties. 
But I can't even swear to that.  The basic idea was that:

     1. You don't have to worry about repeat lengths greater than your
        mantissa length
     2. Repeats automatically "end align"
     3. Non-repeating decimals can be thought of as having a repeat
        length of one on the terminal bit
     4. Repeats combine with an LCM rule, which can be computed in
        hardware comparable in complexity to the exponent logic or
        stored if you accept some limitations
     5. Detecting reductions in repeat length could be done by using
        some sort of shift xor thing that was described (IIRC) as being
        simple but seemed complex to me
     6. It doesn't matter if it ever get implemented as long as the
        author can add the paper about how it could be done to his
        publications list

    -- Markus