On 07/08/2012 06:58 PM, Steve Kargl wrote:
On Sun, Jul 08, 2012 at 02:06:46PM -0500, Stephen Montgomery-Smith wrote:
So do people really work hard to get that last drop of ulp out of their
calculations?
I know very few scientist who work hard to reduce the ULP. Most
have little understanding of floating point.
Would a ulp=10 be considered unacceptable?
Yes, it is unacceptable for the math library. Remember ULPs
propagate and can quickly grow if the initial ulp for a
result is large.
OK. But suppose I wanted ld80 precision. What would be the advantage
of using an ld80 expl function with a ulp of 1 over an ld128 expl
function with a ulp of 10? The error propagation in the latter case
could not be worse than the error propagation in the latter case.
In other words, if I were asked to write a super-fantastic expl
function, where run time was not a problem, I would use mpfr, use
Taylor's series with a floating point precision that had way more digits
than I needed, and then just truncate away the last digits when
returning the answer. And this would be guaranteed to give the correct
answer to just above 0.5 ulp (which I assume is best possible).
From a scientist's point of view, I would think ulp is a rather
unimportant concept. The concepts of absolute and relative error are
much more important to them.
The only way I can see ULP errors greatly propagating is if one is
performing iteration type calculations (like f(f(f(f(x))))). This sort
of thing is done when computing Julia sets and such like. And in that
case, as far as I can see, a slightly better ulp is not going to
drastically change the limitations of whatever floating point precision
you are using.
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