Re: glibc 2.2: math test failures

[Andreas Jaeger]

>>>>> Michael Deutschmann writes:

 > On 13 Dec 2000, you wrote:
>> The math functions are not specified up to the last bit.  Therefore we
>> allow some errors - but we don't want to make that error range too
>> large.
>> 
>> did you check the manual?  We've got a section on "Known Maximum
>> Errors in Math Functions".

 > Actually I tried -- I was looking for precisely that information, but
 > missed that section.  I grepped on "accuracy", and missed it.  I suggest
 > you add "@cindex accuracy, floating point math" to the section.

 > Still, the information in the section is not very useful.  It's only a
 > look at the accuracy we *seem* to be getting at the moment.  If your
 > policy is to just widen them as you discover new cases, or new problem
 > CPUs, then it's not a trustable long-term guide.

 > What I'd want to know, if I was writing numeric software, is *not* the ULP
 > you are presently getting with the CPU-of-the-month.  I'd want to know the
 > level of ULP that would cause you to take drastic action to correct the
 > problem.  A guaranteed maximum error, if you will.

For a guaranteed maximum error, we would need to either proved the
correctness of our algorithms (some ia64 developers at intel actually
did this with the help of an automatic theorem prover!) or evaluate a
function over a wide range to check our guarantee.  We can't do both
at the moment and nobody volunteered to help here.

 > (By drastic action, I mean publicly declaring that you do not support a
 > problematic CPU, or rewriting the library function do the operation "by
 > hand", just eating the likely ~100x slowdown.)

 > I would think the ANSI/ISO standards should give some maximal error don't
 > they -- to stop a pathological implementor from approximating cos() with
 > a constant function....  You should comment on that, for those trying to 
 > write portable code.
No, they don't give any.

Andreas
-- 
 Andreas Jaeger
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