Re: [boost] [math] floating point classification - testinghelpwanted

From: Matthias Troyer (troyer_at_[hidden])
Date: 2005-12-04 14:44:35

On Dec 3, 2005, at 8:09 PM, John Maddock wrote:

>> ld = hi + low as above is not among the bit patterns he lists as
>> valid. If you apply the definition of epsilon to the "normal" long
>> doubles only, then you get a value like the one Paul Bristow computed
>> for NTL's quad_float.
>
> I agree: that explanation is quite explicit when it says it follows  
> Kahan's
> "double double" and the IEEE spec.  So the low part must be  
> normalised so
> that it's bit's "follow on" from those in the high part.  As it  
> stands,
> 1+numeric_limits<>::epsilon() should evaluate to 1, but we really  
> need to
> check this out.  Does anyone of a numerical inclination, want to  
> run some
> tests on Darwin?

Since i asked the students in my class to write a program calculating  
the machine epsilon as a homework, I just ran our solution (posted at  
http://www.itp.phys.ethz.ch/lectures/PT/Exercises/Uebung1/Solution/ 
eps.cpp). Please overlook that the code is ugly, and does not use any  
templates - they just had one week of C++ training. Anyway, this code:

long double epsilon_long_double() {
   long double eps = 1.;
   long double onepluseps;

   do {
     eps /= 2;
     onepluseps = 1. + eps;
   } while ( onepluseps != 1.);

   return 2*eps;

}

returns 0, hence there is really the problem that numeric_limits<long  
double>::epsilon() == numeric_limits<long double>::min()

Matthias