Re: accuracy of intrinsic SUM function

[Steve Kargl <sgk at troutmask dot apl dot washington dot edu>]

On Mon, Aug 27, 2012 at 05:45:38PM +0200, Schorsch MCMLX wrote:
> Meanwhile, I've slightly modifed code posted by Paul van Delst to 
> comp.lang.fortran in 2009 in order to measure performance:
> 
> variable
>     SUBROUTINE Begin_Timing( Timing )  ! In/Output
>     TYPE(Timing_type), INTENT(IN OUT) :: Timing
>     CALL SYSTEM_CLOCK(COUNT_RATE=Timing%Hertz,COUNT=Timing%Begin_Clock)

If you are on a UNIX or UNIX-like system (e.g., linux or FreeBSD)
that includes getrusage(), then use cpu_time().  cpu_time() will 
have microsecond resolution.

> Here's my new pairwise and double-double (referred to as hiDD in the 
> figures) code. The pairwise code can be speeded up a little bit by 
> using selects instead of ifs...:
> 

Thanks for the code example.  I've simply removed it to
keep this brief.

> P.S.: if the list does not receive attachments, please let me know, 
> then I'll copy the raw data in here...

I've looked at your graphs, and don't understand the errors
that you measured.  In SUMS_ND-MN48-SD4_GF471W7x64.png, you
show SUMrecu with an error within +-40 ULP.  This makes no sense
to me in that one normally measures errors in the significand.
If you have a result that matches the exact result to the last
bit, then you have 0 ULP in your result.  Any deviation in your
result from the exact result is some positive number of ULP.
See, for example, 
http://ljk.imag.fr/membres/Carine.Lucas/TPScilab/JMMuller/ulp-toms.pdf
for various definitions of ULP.





-- 
Steve