On Thu, 9 Feb 2012, Andrew Haley wrote: > Okay, but the crlibm algorithms could be extended to long > doubles and, presumably, floats. Where's Vincent Lefevre > when you need him? :-)
The crlibm approach, involving exhaustive searches for worst cases for directed rounding, could as I understand it work for functions of one float, double or 80-bit long double argument, but I think the exhaustive searches are still infeasible for binary128 (113-bit mantissa) long double - although you could do functions that are probably (not proven) correctly rounded in that case. For functions of two arguments such as pow, I don't know if it can produce proven correctly rounded versions even for float. IBM long double (double+double) is a special case likely to need its own implementations of many functions. In that case it's not very well-defined what correctly rounded even means (you *can* define it to be the closest representable double+double value, but I doubt that's feasible to implement in libm although it could be done for constant folding with MPFR, and the basic arithmetic operations don't claim to achieve it). Probably the best that's sensible is an output within a few ULP (ULPs defined as if the representation is fixed-width mantissa of 106 or 107 bits except for subnormals) of the mathematical value of the function at an input within a few ULPs of the specified value - this may also be the best that's possible for other floating-point formats for some hard-to-calculate functions. -- Joseph S. Myers jos...@codesourcery.com
