Use of C99 extra long double math functions after r236148

[Steve Kargl]

On Wed, Jul 18, 2012 at 04:09:06PM -0500, Stephen Montgomery-Smith wrote:
> On 07/18/2012 03:56 PM, Steve Kargl wrote:
> >On Wed, Jul 18, 2012 at 10:07:41AM -0500, Stephen Montgomery-Smith wrote:
> >>
> >>>The most obvious immediate difficulty in translating the above into C is
> >>>that y*y and z*z may overflow when the result shouldn't.
> >>
> >>This will be a lot easier than I originally expected.  When we are in
> >>conditions when overflow might occur, we can simply make the 
> >>approximations
> >>sqrt(y*y-1) = y
> >>csqrt(z*z+1) = signum(x)*z
> >>because in floating point arithmetic, these will not be approximations,
> >>but true exactly.  And I am thinking that the test I will use for when
> >>to use these approximations will be (y==y+1) and (z==z+1) respectively.
> >>  (I would use (z*z==z*z+1) but that test has the overflow problem.)
> >
> >I could be mistaken, but I believe that you need to raise the
> >inexact flag with these approximations because in fact you
> >are doing floating point math.
> >
> 
> Thanks for this observation.  I am looking through the C99 standard, 
> trying to understand the inexact flag.  But I am struggling to interpret it.
> 
> Am I to understand that the inexact flag should be set anytime a 
> floating point operation produces an answer that is not guaranteed 
> exact?  For example, should 1.0/3.0 and sqrt(2.0) raise the inexact flag?

The inexact flag will get raised by the fpu, but you need to
cause the condition.  For your 'sqrt(y*y-1) = y' example, 
you would do something like 'sqrt(y*y-1) = abs(y) - tiny' where
tiny is much less than abs(y).   Search msun/src for inexact
(ie., grep -i inexact msun/src/*.c)

-- 
Steve