[Gcl-devel] Re: [Maxima] eps in trigi.lisp

[Camm Maguire]

Greetings!  OK the epsilon code still appears a bit non-standard.  The
other constants (least-positive, ...) should have been fixed some time
ago.   I'll try to take a look at this, but I thought I'd post what
gcl does now in case anyone has suggestions for a better approach:

=============================================================================
/* We want the smallest number not satisfying something,
   and so we go quickly down, and then back up.  We have
   to use a function call for test, since in line code may keep
   too much precision, while the usual lisp eql,is not
   in line.
   We use SMALL as a multiple to come back up by.
   We use FMEM(double_negative_epsilon)
   to force the quantity into memory by taking its address
   and then passing it to a function.
*/

#define SMALL 1.05      
        for (float_epsilon = 1.0;
             FMEM(float_epsilon),!SF_EQL((float)(1.0 + 
float_epsilon),(float)1.0);
             float_epsilon /= 2.0)
                ;
        while(SF_EQL((float)(1.0 + float_epsilon),(float)1.0))
          { FMEM(float_epsilon); float_epsilon=float_epsilon*SMALL;}
        for (float_negative_epsilon = 1.0;
            FMEM(float_negative_epsilon), !SF_EQL((float)(1.0 - 
float_negative_epsilon) ,(float)1.0);
             float_negative_epsilon /= 2.0)
                ;
        while(SF_EQL((float)(1.0 - float_negative_epsilon) ,(float)1.0))
          float_negative_epsilon=float_negative_epsilon*SMALL;
        for (double_epsilon = 1.0;
             FMEM(double_epsilon), !(LF_EQL(1.0 + double_epsilon, 1.0));
             double_epsilon /= 2.0)
                ;
        while((LF_EQL(1.0 + double_epsilon, 1.0)))
          double_epsilon=double_epsilon*SMALL;
          ;
        for (double_negative_epsilon = 1.0;
           FMEM(double_negative_epsilon),
               !LF_EQL(1.0 - double_negative_epsilon , 1.0);
             double_negative_epsilon /= 2.0)
                ;
        while(LF_EQL(1.0 - double_negative_epsilon , 1.0))
          double_negative_epsilon=double_negative_epsilon*SMALL;
          ;
        
=============================================================================

"Stavros Macrakis" <address@hidden> writes:

> > long-float-epsilon  value: 1.1102230246251568d-16
> 
> Peculiarly, in Maxima 5.5, gcl 2-3.6, Windows 2000, long-float-epsilon
> is set to 1.1657341758564144E-16, approximately 5% too large; similarly
> for long-float-negative-epsilon.  Probably doesn't matter to many
> people, but....
> 
> By the way, Camm and James, what is the correct way to submit bug
> reports for gcl?

As James said so well, either address@hidden or
http://savannah.gnu.org/projects/gcl.  

Take care,


> 
>       -s
> 
> 
> (setq *print-base* (+ 8 8))
> 
> (integer-decode-float long-float-epsilon)
> 10CCCCCCCCCCCD
> -69
> 1
> 
> (setq lfe 1.1102230246251568d-16)
> (+ 1 lfe -1) => 2.22E-16
> (integer-decode-float lfe)
> 10000000000001
> -69
> 1
> 
> (integer-decode-float long-float-negative-epsilon)
> 10CCCCCCCCCCCD
> -6A
> 1
> 
> (+ 1 (* (- long-float-negative-epsilon) .96))
> 0.99999999999999989
> 
>   So LFNE is not the smallest.
> 
> 
> 

-- 
Camm Maguire                                            address@hidden
==========================================================================
"The earth is but one country, and mankind its citizens."  --  Baha'u'llah