[ars]

When you store 19999999999...9999999999 as a float you round it, not truncate it.

19999999999...9999999999 = 20.....00 when rounded to 15 significant digits.

You can even truncate it to 15 digits just to get it in there, and then round it to 14 digits.

[extension]

Rounding can just as easily give you the wrong answer as truncating e.g:

  100000...000000
  199999...999999

[ars]

Good point.

Hmm, I guess I would split the numbers in half, and sum each set of half's (making sure to set the exponent correctly).

Then add the less significant half to the more significant half.

i.e. basically add the numbers in order of magnitude. It doesn't have to be just two half's.

Did anyone post this as a solution?

I do remember learning this somewhere - it was a warning about loss of precision when adding lots of small numbers to a few large ones. And the solution was to do all the small numbers first.

Seems like this would be a perfect place to teach this lesson. Do you know if this site does that?