Re: Floating Point comparisons

From: rogeeff (rogeeff_at_[hidden])
Date: 2001-12-22 13:40:04

--- In boost_at_y..., "Paul A. Bristow" <boost_at_h...> wrote:
> Is it simply that the calculation
> 
> |d3 - 11| / 11
> 
> also has some roundoff opportunities?
> 
> Or is this too naive a suggestion?

Even with 2 more rounding errors we would have 3. But result is 4.

> 
> Paul
> 
> Dr Paul A Bristow, hetp Chromatography
> Prizet Farmhouse
> Kendal, Cumbria
> LA8 8AB      UK
> [phone]
> Mobile [phone]
> mailto:pbristow_at_h...

Gennadiy.

> 
> 
> > -----Original Message-----
> > From: rogeeff [mailto:rogeeff_at_m...]
> > Sent: Wednesday, December 19, 2001 8:53 AM
> > To: boost_at_y...
> > Subject: [boost] Re: Floating Point comparisons
> >
> >
> > Hi,
> >
> > After some clarification I still got one confusing example:
> >
> > #include <iostream>
> > #include <limits>
> >
> >
> > int main()
> > {
> >     double d = 11;
> >     d /= 10;
> >     d = d*d - d;
> >
> >     d *= 100;
> >
> >     std::cout << ((d - 11)/ d / 
std::numeric_limits<double>::epsilon
> > () ) << std::endl;
> >
> >     return 0;
> > }
> >
> > Intent is to calculate some value and comapre it with the real 
value.
> >
> > so I did:
> >
> > d1 = 11/10          - 1 rounding error
> > d2 = d1*d1 - d1     - 2 rounding errors
> > d3 = d2 * 100       - 1 rounding error
> >
> > The resulting value should be again 11. Now I calculate relative
> > rounding error between resulting value and real value. It expected
> > do not exceed (1+2+1)*1/2 * epsilon = 2 * epsilon. So expected 
that:
> >
> > |d3 - 11| / 11 <= 2* epsilon
> >
> > or
> >
> > |d3 - 11| / 11 / epsilon <= 2
> >
> > While I am getting from MSVC is ~4.
> >
> > What could it be?
> >
> > Gennadiy.
> >
> >
> >
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> >
> >