Ilya Zakharevich on Tue, 1 Oct 2002 12:22:04 -0700

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Re: bug in addrr

On Tue, Oct 01, 2002 at 05:05:27PM +0200, Karim BELABAS wrote:
> * So the number of significant bits remaining in the extra word we added is
> at most m - sh. If this is <= 2, I cancel the extra word and round
> appropriately.
> '2' is arbitrary. '0' is completely safe (we cancel nothing but bogus bits).
> Could make it 1, 2, 3 ... [ here we do cancel a few correct bits ].
> As it stands, some routines lose precision (a little bit) faster. But it
> doesn't seem to break anything, and it fixes a few problems like the above.

What IEEE teaches us is that it is vital to have *exact* answers for
the elementary operations.  This algorithm breaks this principle; we
know that it will lead to *significant* errors near the "critical" points.

What IEEE does not have is a possibility to increase the precision and
redo the calculations; so in the PARI situation this is a little bit
less critical.  But still...