optimization/9654: extra-precision fp comparisons are less accurate

[Richard Addison-Wood]

It's quite reasonable to assume that

  acos(1-0.5*DBL_EPSILON)

will not be 0.  For a value of d that is
nearly 1:

  acos(d) == sqrt(1-d*d)

is a good approximation (certainly within
representational limits ieee754 double
precision).  The point to notice here is that
if d is distinguishable from 1, d*d will be
even more distinguishable from 1.  All told,
it very reasonable to expect:

  acos(1-0.5*DBL_EPSILON) == sqrt(DBL_EPSILON)

which is a value that is not particularly
close to 0.  However, it is still close
enough to 0 so that:

  sin(sqrt(DBL_EPSILON)) == sqrt(DBL_EPSILON)

is a good approximation.

Of course, this discourse into acos(), sin(),
and sqrt() is beside the point.  With code
like this:

  if (d < 1.0)
  {
    arglessthanone(d);
  }

it should be the case that the arglessthanone()
function should not see an argument value that
is greater than or equal to 1.0.