Use of C99 extra long double math functions after r236148

[Stephen Montgomery-Smith]

On 07/22/2012 01:19 AM, Bruce Evans wrote:

>> 2.  I have thought more about the problem of computing clog(z) when
>> |z| is close to 1.  I now think it might even require precision that
>> is 3 times better than double precision.
>> It is possible that you could, by chance, pick x and y so that |z| = 1
>> + 1e30.  (I wrote a test program, and this did
>                               e-30 here and elsewhere
>> actually happen a few times.)  So when you compute x^2+y^2-1, if you
>> do it using double double precision, you will get 2e30, but only the
>> most significant digits will be accurate.  The ULP will be about
>> 1e15.  You need triple double precision to get ULP's close to 1.
>
> Hmm, I'm not seeing such cases except when |x| or |y| is 1 and the other
> is tiny.

That was my mistake.  I didn't have enough precision in mpfr to use it 
as a proper reference!  Now I tested my code, and I seem to be getting 
ULP's consistently less than 2!

I am attaching my clog code and my test code.  I go in and manually 
change the test code to test around a different range of values.