On Thu, Dec 8, 2011 at 1:06 PM, Eduardo Flores Abad mail@eduardoflores.de wrote:
Hi Katja,
tries to round this way:
100 * (7.1 - 7) / 100 = 0.1
Did you try that, Eduardo? In Pd, you get:
100 * (7.1 - 7) / 100 = 0.0999999
But:
((100 * 7.1) - (100 * 7)) / 100 = 0.1
Or:
((10 * 7.1) - (10 * 7)) / 100 = 0.1
That is:
(71 - 70) / 10 = 0.1
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.
The original quest was to split two digits, which can be done like so:
truncate(71/10) = 7 71 - (truncate(71/10))*10 = 1
Where truncate() is done with the [i ] object. This works for all two-digit ints, for more digits there would be similar solutions.
The main point is: integer subtraction and addition is exact, and floats can represent integers with exactness up to a certain point. A single precision float can represent integers up till 2^24 with exactness, that is 16,777,216, more than 16 million. A 64 bit float ('double') can represent integers up till 2^53, that is 9,007,199,254,740,992 (more than you'll need in dsp).
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.).
Katja
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)
| Mathieu BOUCHARD ----- téléphone : +1.514.383.3801 ----- Montréal, QC
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