clicliclic@freenet.de  wrote:   
   >   
   > antispam@math.uni.wroc.pl schrieb:   
   > >   
   > > Richard Fateman  wrote:   
   > > >   
   > > > The rationale for particular sizes of exponent and mantissa was a   
   subject for discussion in the   
   > > > IEEE floating-point committee.  As I recall, the number of electrons in   
   the universe is   
   > > > not so relevant.  I forget the details.  certainly 32 bits for the sign   
   is excessive. Dunno   
   > > > about the exponent.  It would be nice if you also allowed for IEEE   
   special items like   
   > > > NaN,  infinity, signed zero. etc.   
   > > >   
   > > > If you are doing a sequence of floating-point computations in which each   
   operation loses   
   > > > some information to round-off, the usefulness of a particular length   
   mantissa   
   > > >  depends on how long a sequence you have.   
   > > >   
   > > >  I have repeatedly posted one-line programs in Mathematica that lose   
   > > > a decimal digit about every 3 times through a loop.  The computation,   
   repeated, is   
   > > > x= 2*x-x   
   > >   
   > > This is very artifical example.  AFAICS x = 4*x(1 - 1) would be   
   > > a bit closer to real life.  It naturaly looses 1 bit of   
   > > accuracy every iteration and with Mathematica probably 2 bits   
   > > per iteration.   
   > >   
   >   
   > I suspect a typo somewhere:   
   >   
   >   ITERATES(4*x*(1 - 1), x, 1, 10)   
   >   
   >   [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]   
   >   
      
   Should be: x = 4*x(1 - x) considered as mapping from interval   
   [0, 1] to itself.   
      
   Extra info: there is countable set of value for which in exact   
   arithmetic you eventually get zero.  Most ot them are irrational,   
   but 0, 1/2, 1 are rational, so if you want to see loss of   
   precision, then x should be different from those rational   
   values.   
      
   BTW.  Case with coefficient 4 is easy for theoretical analysis.   
   People did a lot of experiments studying what happens if   
   you replace 4 by something slightly smaller.  When coefficient   
   is small enough then resulting sequence converges to 0   
   regardless of starting value.   
      
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