On Sat, Oct 3, 2009 at 12:58 AM, rjf <fate...@gmail.com> wrote:
>
> Reading the bug report it seemed to me that the code was determining
> in some way that terms could be dropped off the sum because they were
> too small to contribute, and then
> stopped adding them in. Is that the "simple implementation bug"? Or is
> that an additional bad idea?

The summation code basically adds terms that are close together
exactly (using a big integer mantissa) and discards terms that are
much smaller. If the first pass over the terms results in a large
cancellation, the summation is restarted at higher precision and
eventually (if necessary) the smaller terms will be included as well.

The bug was due to a basic, dumb error in the formula used to
determine "much smaller", and the reason the bug wasn't detected
before by any tests is that it only triggered in some cases (indeed,
in a platform dependent way) and with precisions or numbers around 40
digits or larger.

Fredrik

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