Mon, 07 Jul 2003 12:01:09 +0200
Jon Fairbairn comments //Steffen Mazanek//:
>>13421773 % 134217728
>>I do not know how this fraction is calculated, but
>>it does not fit my expectations :-)
> Remember that internally arithmetic is binary, and that 0.1
> can't be expressed exactly as a floating point number. I
> think that's the explanation.
>>Ok, ok, it is no bug...
> No, I think it is a bug: 0.1 ought to be equivalent to
> fromRational (1%10), but Hugs isn't intended for numerical
> work. GHCi gets the right answer.
This is less a bug than a Nessie monster which haunts Hugs
some centuries already, and on Internet the issue has been
discussed at least 4 times. The old, experimental Gofer
Prelude numeric functions were sometimes abominable, since
Mark Jones concentrated on other things, and nobody really
complained, people were busy with other stuff as well.
But I can't understand why this continues until now. The
obvious technique to convert floats to rationals is the
continued fraction expansion which gives the simplified
I don't understand the remark that the internal arithmetic is
binary. Sure, it is, so what? Why Ross Paterson underlies
this as well? He concludes:
> The real fix would be to keep the literals as Rationals, but
> this would be too expensive in the Hugs setting.
Andrew Bromage says some words about errors and representation.
I think that the problem can (perhaps should) be dealt with at
a higher level. What's wrong with conversion functions like
those below. First, convert a float to a lazy list of coeffs.
of a regular continued fraction:
tocfrac x =
let n = floor x
y = x-fromInteger n
in n : if y==0.0 then  else tocfrac (recip y)
and then reconstruct using Euler sequences as described in
Knuth or perhaps an optimized method, the one I cite is not
very efficient. It gives a list of (N,D) -- *all* rational
approximants of the original float.
continuant l@(_:ql) = zip (tail (euseq l)) (euseq ql)
euseq  = 
euseq (x:q) = eus 1 x q
eus p0 p1 (a:cq) = p0 : eus p1 (a*p1+p0) cq
eus p0 p1  = [p0,p1]
Now, test it:
r=take 10 (continuant (tocfrac pp))
You should get
etc;, anyway all that is already inexact...
For 0.1 one gets [(0,1),(1,10)]