I believe the relative error in our basic operations is *less than* or equal to one ULP. However, in portable C++, we can not hack the floating-point type---never. One of our back ends has base-10. The other two have an intriguing combinations of base-2. The hacks of the internal details of these representations would not be portable.
I guess my statement was too ambiguous. I don't ask this functionality to be accessible through generic mp_number interface, but via backend interface of cpp_dec_float. To test for relative (in)-equality within one ULP, you need to take the
ratio of two quantities, subtract this ratio from 1 and subsequently take the absolute value of the result to obtain a basis for comparison with 1 ULP.
Approach you mentioned requires division and would be quite slow. It is a lot faster to compare internal integer representations. This is the normal way for any floating-point type. It is a lot to take at
first. But no portable code can rely on the internal representation of the floating-point type. You can only use library functions, limits and/or comparison.
Ok, that's another way to go. It would be great to have ulp comparison functionality as part of the library. Particularly I am interested in the following prototype: bool ulp_equal(const mp_number<fpt_type> &a, const mp_number<fpt_type> &b, unsigned int ulps); Thanks, Andrii Unsubscribe & other changes: http://lists.boost.org/** mailman/listinfo.cgi/boost<http://lists.boost.org/mailman/listinfo.cgi/boost>