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:

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

Attachment: binZ6bTIGGXbC.bin
Description: numeric-div.patch.gz

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