On Tue, 5 Mar 2019, Jonathan Wakely wrote: > The midpoint and lerp functions for floating point types come straight > from the P0811R3 proposal, with no attempt at optimization.
I don't know whether P0811R3 states different requirements from the public P0811R2, but the implementation of midpoint using isnormal does *not* satisfy "at most one inexact operation occurs" and is *not* correctly rounded, contrary to the claims made in P0811R2. Consider e.g. midpoint(DBL_MIN + DBL_TRUE_MIN, DBL_MIN + DBL_TRUE_MIN). The value DBL_MIN + DBL_TRUE_MIN is normal, but dividing it by 2 is inexact (and so that midpoint implementation would produce DBL_MIN as result, so failing to satisfy midpoint(x, x) == x). Replacing isnormal(x) by something like isgreaterequal(fabs(x), MIN*2) would avoid those inexact divisions, but there would still be spurious overflows in non-default rounding modes for e.g. midpoint(DBL_MAX, DBL_TRUE_MIN) in FE_UPWARD mode, so failing "No overflow occurs" if that's meant to apply in all rounding modes. -- Joseph S. Myers jos...@codesourcery.com
