[scilab-Users] %eps ?!

[Michaël Baudin]

Hi,

This is a nice one...

To understand the issue, you may run the following lines :

atomsInstall(['floatingpoint','0.2']);
atomsLoad(['floatingpoint','0.2']);
flps = flps_systemnew ( "IEEEdouble" );
flpn = flps_numbernew ( "double" , flps , 0.4 )

This will print the binary decomposition of 0.4 :

Significand = 1001100110011001100110011001100110011001100110011010

You see that the significand makes use of the pattern 1100. This means 
that x=0.4 can be represented in base 2 only with an infinite sequence 
of ones and zeros. You may see the same behaviour with x=0.1. But only 
53 binary digits can be considered, because this is the precision of 
doubles in Scilab. This leads to rounding, i.e. the floating point 
number which is stored is the floating point number which is the closest 
(but not equal) to 0.4.

If you cannot change the test, you may change the condition to :

i = 3;
test = .4*i - 1.2 ;
abs(test)<= %eps

If you can change the test, you can simply use integers, which can be 
safely represented exactly in the range [-2^52,2^52] :

i = 3;
test = 4*i - 12 ;
test==0

Best regards,

Michaël Baudin

PS
A more detailed explanation for x=0.1 is given in "Scilab is not naive", 
Digiteo, Baudin, 2010, provided in the Tutorials section of the site 
scilab.org :

http://www.scilab.org/en/support/documentation/tutorials

See the section A.1, "Why 0.1 is rounded".

Le 15/12/2010 14:47, Frédéric Mabille a écrit :
> Hi,
>
> During the computation of my program, my function "if" produce a 
> strange result.
> I fact, after many investigations, I have observed a very surprising 
> result.
>
> /for i = 1:10/
> /test = .4*i - 1.2 ;/
> /if test == 0 then .../
>
> But when i = 3, scilab give me : test = %eps = -2.220D-16 <> 0 !!!
> It is really awkward.
>
> Could someone have a simple solution ?
> Thx
>
> Frédéric


-- 
Michaël Baudin
Ingénieur de développement
michael.baudin at scilab.org
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94


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