🚀 go-pugleaf

In article <7806@june.cs.washington.edu> rik@june.cs.washington.edu (Rik Littlefield) writes:
>In article <97749@sun.Eng.Sun.COM>, khb@fatcity.Sun.COM (Keith Bierman Sun Tactical Engineering) writes:
>
><  Tom Lahey's fortran for the pc did this [kept 80-bit vars on the 80x87
><  stack during loop execution]. Example:
><  
><  	sum = 0
><  	do i = 1, n
><  	   sum = x(i)*y(i)
><  	end do

Bug. meant to type sum = sum+ ... i.e. dot product
>
>Perhaps these customers wanted to compare their results against other
>compilers/machines.  Maybe I'm just pessimistic, but when a new compiler
>produces answers that are much different from what I'm used to, "increased
>accuracy" is just about the *last* possibility that comes to mind.
>

Before the ieee standard, this is ALWAYS different. 64-bit math on vax
yields very different answers than IBM or Cray or (new) CDC's , etc.
32-bit math is even "worse". 

Stable algorithms always benefit from improved quality arithmetic. Unstable
algorithms are sensitive (adversely) to _improvement_ in the
arithmetic. The reason one should prefer the extended computation is
that a perfectly stable algorithm may be fed an ill-conditioned
problem. In that event, the extended math can be a godsend.

If you understand FP arithmetic, and your algorithm, the fact that
improved arithmetic quality changes your answer should be no surprise.
If the difference is really significant, it means your algorithm (or
its implementation) sucks. 

This really does happen. I remember porting a FE code once (not to
suns) and getting radically different answers depending on which
compiler I used on the vaxen, and got a totally different answer on
the ieee box I was porting to. Turned out that what they were
computing was a tiny residual, but scaled to be large, and then
printed (and used in suceeding computations). Needless to say, I was
not impressed. Fortunately, it is not a very popular package, so most
bridges and airplanes are probably OK.






Keith H. Bierman
It's Not My Fault ---- I Voted for Bill & Opus