Re: erfc() behavior change

[Walter Neumann <neumann@math.columbia.edu>]

Thanks for the clarification. I think you are saying that for a zero real 
only the precision is relevant. But the following is then still confusing:

? 0.e-10
%1 = 0.E-38
? precision(%)
%2 = 48
? %1*10^40
%3 = 0.E1
? precision(%)
%4 = 0

I would expect the answers to be 0.E-48, 48, 0.E-10, 10 respectively.

--walter

On Thu, 12 May 2005, Karim Belabas wrote:

> * Walter Neumann [2005-05-12 17:15]:
> > There does seem to be a related incosistency however:
> >
> > ? erfc(-2^11)
> > %1 = 2.000000000000000000000000000
> > ? 2-%1
> > %2 = 0.E-1821573
> > ? precision(%2)
> > %3 = 1821573
> >
> > ...
> >
> > ? 0.0
> > %10 = 0.E-28
> > ? precision(%)
> > %11 = 28
> > ? 0.0e-90
> > %12 = 0.E-91
> > ? precision(%)
> > %13 = 96
> > ? 1.e-90
> > %14 = 1.000000000000000000000000000 E-90
> > ? precision(%)
> > %15 = 28
> >
> > Shouldn't precision in %3 and %13 be something like 28?
>
> 'precision' is not really defined in the documentation (should be...).
>
> * For a basic type not involving floating point components, precision(x)
> is +oo [ well, an absurdly large number, strictly larger than the precision
> of any inexact object. ]
>
> * For a _non_zero_ t_REAL x, precision(x) is the number of significant digits
> for _non_zero_ x.  This is only approximately true: various radix
> conversions and assorted roundings are involved.
>
> * For a _zero_ t_REAL x, precision(x) is max(- expo_10(x), 0).
> There are no significant digits in this case.
>
> * For a t_COMPLEX, precision(x + I*y) is (roughly) precision(|x| + |y|).
>
> * For another recursive object, precision(x) is the min of all involved
> precisions.
>
>
> The precision of
>
>  X*(1. to 100 significant digits) + 0.e-1000
>
> is 100.
>
>  X*(1. to 100 significant digits) + 0.e+1000
>
> is 0.
>
> Hope this helps,
>
>    Karim.