http://gcc.gnu.org/bugzilla/show_bug.cgi?id=48738
--- Comment #3 from Richard Guenther <rguenth at gcc dot gnu.org> 2011-04-23
16:24:08 UTC ---
(In reply to comment #2)
> (In reply to comment #1)
> > Integer exponent powers are computed using
> >
> > TYPE
> > NAME (TYPE x, int m)
> > {
> > unsigned int n = m < 0 ? -m : m;
> > TYPE y = n % 2 ? x : 1;
> > while (n >>= 1)
> > {
> > x = x * x;
> > if (n % 2)
> > y = y * x;
> > }
> > return m < 0 ? 1/y : y;
> > }
> >
> > or optimal power series expansion for constant exponents starting with
> > GCC 4.5.
> >
> > ISTR the standard allows this. You should use a double exponent to
> > use the real power function, pow (2., -1024.)
>
> I have no objection to using such optimizations for integer exponents, and I
> am
> aware that it . But perhaps it could be improved further, by widening the
> range over which the result for an integer exponent will be consistent with
> the
> corresponding double (or whatever) exponent.
>
> If the code above was changed to something like what goes below, would it be
> worse?
>
> TYPE
> NAME (TYPE x, int m)
> {
> unsigned int n;
> if(m < 0){
> n = -m;
> x = TYPE(1) / x;
> }
> TYPE y = n % 2 ? x : 1;
> while (n >>= 1)
> {
> x = x * x;
> if (n % 2)
> y = y * x;
> }
> return y;
> }
I'm sure you can create a similar issue for this variant. Fact is that
there are multiple roundings involved in computing integer powers.
