Sebastian Macke wrote: [Please keep cln-list in CC. If you write to me privately, the probability that you get a response is less than 0.3.]

I used your library with a template class. template <class T> Here I define one and zero as T(1.) T(0.)

Please read again the essential, central chapter "Ordinary number types" of the CLN documentation. From it, it follows that - Numbers such as 1.0 or 0.0 are floating-points and thus are approximate. - If you want a "one" and "zero" in a ring, you should take exact numbers, (cl_I)1 or (cl_I)0. - You don't need templates, because the cl_F, cl_R, cl_N types already comprise 'float' and 'double' (and longer) precisions.

This works without problem with float, double and long double But with your implementation I can lose precision.

In the previous mail I explained to you that when you combine two floating- point numbers with different precision, the result will have an accuracy that approximately equals the minimum of the two precisions. This is a mathematical property of the definition of accuracy. (You can verify it with interval arithmetic or with statistics, if you like.) You then have the choice: - Return a result with a precision approximately equal to its accuracy. This is what CLN does. Or - Return a result whose precision is the *maximum* of the two precisions. If you do this, you are betraying the user of your program. Bruno