Decimal arithmetic, with example code

[Bengt Richter]

On 3 Oct 2002 07:08:38 GMT, bokr at oz.net (Bengt Richter) wrote:
[...]
>
>BTW, you probably noticed I wasn't really rounding in my evenround function --
>I was just noodging the value so the subsequent round inside %.f looked like it
>was doing decimal bankers round. I just played a hunch with the BIAS multiply.
>Using FixedPoint as a final formatter for floating point should work better than
>bias-kludging the ordinary round. It's probably about as good an estimate of the
>nearest decimal of a given precision to a given fp number as you can get.
>
[...]
>
>BTW, FWIW, since the denominator is 1L << -e where you round the conversion,
>the following should hold (I think, not very tested):
>
>                exactHalf = 1L << (-e-1)
>                n = top + exactHalf    # ok round except banker's tie with odd no
>                wasTie = not (n & ((exactHalf<<2)-1L))  # odd => even and no 1's below
>                n = (n >> -e) - wasTie # readjust for bad tie result
>
>                assert n == _roundquotient(top, 1L << -e)
>
>Whether it's worth doing depends on speeds which I haven't tested. Depends on divmod and cmp...
>Out of steam for tonight...
>
Not enough steam to get it right ;-/ -- this should work better and faster:

                exactHalf = 1L << (-e-1)
                wasTie = not (top & (exactHalf-1L))  #  no 1's below
                n = top + exactHalf     # ok round except banker's tie => odd
                n = (n >> -e)
                n -= n & wasTie         # readjust for bad tie result
                assert n == _roundquotient(top, 1L << -e)


>BTW2, I wonder if it would be worth while to do a banker's round like round, but guaranteeing
>that the result's magnitude will be the first fp state >= the true decimal value. It would
>be biased minisculely, but it might be helpful for printing non-surprising decimals. str(f)
>seems to be solving part of the problem, but an alternate %f (%F?) to control bankers round
>at a given precision might be nice. A few bits from fixedpoint could be cannibalized.
>

Regards,
Bengt Richter