[PD] integer (mis)calculator

[Mathieu Bouchard]

Le 2011-12-08 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*(7.1-7)/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 non-extreme power-of-two denominator may be 
used. This is also true for power-of-two multipliers (very large numbers 
beyond 2^24 are all even ; beyond 2^25 they're all multiples of 4 ; etc)

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