[PD] integer (mis)calculator
Mathieu Bouchard
matju at artengine.ca
Mon Dec 12 07:24:45 CET 2011
Le 20111208 à 14:59:00, katja a écrit :
> Did you try that, Eduardo? In Pd, you get:
> 100 * (7.1  7) / 100 = 0.0999999
[expr 100*(7.17)/100]

[makefilename %.21f]

[print]
0.099999904632568359375
That's actually 209715/2097152. But there aren't so many digits of
precision because once you have 0.09999990 then the rest is guessable (in
some cases you need an extra digit, but not this one).
> ((100 * 7.1)  (100 * 7)) / 100 = 0.1
That's actually exactly 0.100000001490116119385 or 13421773/134217728.
> So this is what Roman already suggested: do subtraction (or addition)
> with integers, to be sure they're exact (up till 2^24), then scale if
> required.
710 is exact ; 100*7.1 is not.
> By the way, many fractions can be represented with exactness in both
> decimal and binary floating point format. This includes values in the
> form 1/2^n (1/2, 1/4, 1/8 etc.).
That's true. But integers also makes it easier for conversions to/from
decimals, because there's a bit less of a headache trying to avoid
rounding while printing things like 3/256 = 0.01171875 rounded to
0.0117188 by [print] (if you don't use [makefilename %.8f] there). As long
as this is not an issue, any nonextreme poweroftwo denominator may be
used. This is also true for poweroftwo multipliers (very large numbers
beyond 2^24 are all even ; beyond 2^25 they're all multiples of 4 ; etc)
______________________________________________________________________
 Mathieu BOUCHARD  téléphone : +1.514.383.3801  Montréal, QC
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