Re: WIP: rewrite numeric division

Because this has not been applied, this has been saved for the 8.4 release:

    http://momjian.postgresql.org/cgi-bin/pgpatches_hold

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Tom Lane wrote:
> I wrote:
> > I just blew the dust off my old copy of Knuth vol 2, and see that his
> > algorithm for multi-precision division generates output digits that are
> > correct to start with (or at least he never needs to revisit a digit
> > after moving on to the next).  ISTM we should go over to an approach
> > like that.
>
> The attached proposed patch rewrites div_var() using Knuth's algorithm,
> meaning that division should always produce an exact truncated output
> when asked to truncate at X number of places.  This passes regression
> tests and fixes both of the cases previously exhibited:
> http://archives.postgresql.org/pgsql-bugs/2007-06/msg00068.php
> http://archives.postgresql.org/pgsql-general/2005-05/msg01109.php
>
> The bad news is that it's significantly slower than the CVS-HEAD code;
> it appears that for long inputs, div_var is something like 4X slower
> than before, depending on platform.  The numeric_big regression test
> takes about twice as long as before on one of my machines, and 50%
> longer on another.  This is because the innermost loop now involves
> integer division, which it didn't before.  (According to oprofile,
> just about all the time goes into the loop that subtracts qhat * divisor
> from the working dividend, which is what you'd expect.)
>
> Now it's unlikely that real-world applications are going to be as
> dependent on the speed of div_var for long inputs as numeric_big is.
> And getting the right answer has to take priority over speed anyway.
> Still this is a bit annoying.  Anyone see a way to speed it up, or
> have another approach?
>
>             regards, tom lane
>

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