[scilab-Users] %eps value can be different than 2.220D-16

[Michaël Baudin]

Hi,

Scilab real values are based on double precision i.e. floating
point values which are stored on 64 bits.
This has nothing to do with the 32/64 bits of the machine, which refer
to the way the memory is addressed.
See the wikipedia page for more details :

http://en.wikipedia.org/wiki/64-bit#32_vs_64_bit

Note that this is a good thing for Scilab users, since it
guarantees that the results are the same, whatever the platform used.
Furthermore, since Scilab 5., the double precision is used whatever
the OS used :

http://www.scilab.org/changes_5/#numerical_precision

"Numerical precision of Scilab under Linux 32 bits has
been switched to double precision (53 bits). Therefore,
the precision on some specific computations is improved
and the consistency between Microsoft Windows & GNU/Linux
enhanced. "

The following is, by the way, a short algorithm to compute eps.
In Scilab, this algorithm is performed by the routine DLAMCH,
from Lapack.
The algorithm requires 53 iterations to perform, because this
is the number of bits (+1) which are required to store the
fractionnal part of a double precision floating point number
(i.e. the size of the mantissa).

eps = 1.0;
done = 0;
i = 0;
while done==0
  eps = eps / 2.0;
  if (1.0+eps==1.0) then
    done = 1;
  end
  i = i + 1;
end
eps = eps * 2;
mprintf("i=%d", i);
mprintf("eps=%e", eps);

The reference for this is the paper by Malcom :

   "Algorithms to Reveal Properties of Floating-Point Arithmetic"
   Michael A. Malcolm
   Stanford University
   Communications of the ACM
   Volume 15 ,  Issue 11  (November 1972)
   Pages: 949 - 951

and its complement :

   "More on Algorithms that Reveal Properties of Floating
   Point Arithmetic Units"
   W. Morven Gentleman, University of Waterloo
   Scott B. Marovich, Purdue University
   Communications of the ACM
   Volume 17 ,  Issue 5  (May 1974)
   Pages: 276 - 277

Best regards,

Michaël Baudin

esmamian a écrit :
> Hi All !
> According to the scilab help, the %eps value is a constrain that 
> represent the machine precision, so i thought it was different between 
> 32 bits machines and the 64 bits ones, but no :-s
>
> I have Scilab 4.0.1 on a 32bits Windows machine and the %eps is 2.220D-16
> My surprise was when i mounted Scilab 5.0.3 over a 64 bits Ubuntu 8.10 
> machine and got the same result :-?
>
> Anyone knows why %eps is the same
> and how i can compute an algorithm with more precision?
>
> Greetings and thanks in advice
>
> --
> Sofia Mamian