Re: OT: definition of "significant figures"

[tmoran@acm.org]

> If you have, say, 100_000 approximately same FP numbers,
> then a naive implementation
> ...
> would perform awfully. Near to the end of the loop you will heavily loose
> accuracy. Because the ratio Sum to X (I) would be around 100_000. To
> cascade it would be a better idea.
  For large N I keep log2(N) partial sums at the various scales.  Is that
what you mean by "cascade"?

> So basically it is difficult to tell in advance how many "right" figures
> you get.
>
> Also you can use interval arithmetic, then you'll exactly know the accuracy
> of the result.
   I presume that for scientific publication one shows standard deviation
or confidence intervals or some appropriate statistic.  "significant
figures" seems more a rough-and-ready approximate way to convey that
information.  My immediate application actually takes a single decimal
latitude or longitude, whose accuracy I can only estimate from its number
of digits, and produces degrees/minutes/seconds, with an appropriate
number of significant fields/digits.