[PD] number to fractions external?
i go bananas
hard.off at gmail.com
Fri Dec 16 19:16:19 CET 2011
if you had read the thread, you would have seen that claude posted a link
to that technique.
now go and make a PD patch that does it, mr smart guy.
On Sat, Dec 17, 2011 at 3:00 AM, Ludwig Maes <ludwig.maes at gmail.com> wrote:
> If you guys 'd done your math, you'd know there is an ancient algorithm
> for approximating numbers by fractions and its called continued fractions.
>
>
> On 16 December 2011 18:38, Lorenzo Sutton <lorenzofsutton at gmail.com>wrote:
>
>> On 16/12/11 16:05, Alexandre Torres Porres wrote:
>>
>>> looks like a job for an external
>>>
>> Not really answering the OP question but something could be done in
>> Python:
>>
>> def find_frac(num):
>> f = float(num)
>> last_error = 1000
>> best = (0,0)
>> for i in xrange(1,1001):
>> for j in xrange(1,i+1):
>> divide = (float(i) / float (j))
>> if divide == f:
>> return ((i,j),0)
>> err = abs(divide - f)
>> if err < last_error:
>> best = (i,j)
>> last_error = err
>> return (best,last_error)
>>
>> This would try to find the exact fraction or the one with the smallest
>> error (trying up to 1000/1000). It would return (numerator, denominator,
>> error). Guess it would work well at least up to 100 but only for positive
>> numbers... and... not for numbers < 1.. and surely it's not optimised etc.
>> etc. :)
>>
>> >>> find_frac(2)
>> ((2, 1), 0)
>> >>> find_frac(1.5)
>> ((3, 2), 0)
>> >>> find_frac(1.**333333333333333333333333333)
>> ((4, 3), 0)
>> >>> find_frac(2.4)
>> ((12, 5), 0)
>> >>> find_frac(2.8)
>> ((14, 5), 0)
>> >>> find_frac(2.987654321)
>> ((242, 81), 1.234568003383174e-11)
>> >>> find_frac(50.32)
>> ((956, 19), 0.004210526315787888)
>> >>> find_frac(50.322)
>> ((956, 19), 0.006210526315790332)
>> >>> find_frac(50.4)
>> ((252, 5), 0)
>> >>> find_frac(10.33)
>> ((971, 94), 0.00021276595744623705)
>> >>> find_frac(10.**33333333333333333333333333)
>> ((31, 3), 0)
>>
>> Lorenzo.
>>
>>>
>>>
>>>
>>> 2011/12/16 i go bananas <hard.off at gmail.com <mailto:hard.off at gmail.com>>
>>>
>>>
>>> actually, i'm not going to do anything more on this.
>>>
>>> i had a look at the articles claude posted, and they went a bit
>>> far over my head.
>>>
>>> my patch will still work for basic things like 1/4 and 7/8, but i
>>> wouldn't depend on it working for a serious application. As you
>>> first suggested, it's not so simple, and if you read claude's
>>> articles, you will see that it isn't.
>>>
>>> it's not brain science though, so maybe someone with a bit more
>>> number understanding can tackle it.
>>>
>>>
>>>
>>> On Sat, Dec 17, 2011 at 12:51 AM, Alexandre Torres Porres
>>> <porres at gmail.com <mailto:porres at gmail.com>> wrote:
>>>
>>> > i had a go at it
>>>
>>> thanks, I kinda had to go too, but no time... :(
>>>
>>> > yeah, my patch only works for rational numbers.
>>>
>>> you know what, I think I asked this before on this list,
>>>
>>> deja'vu
>>>
>>> > will have a look at the article / method you posted, claude.
>>>
>>> are you going at it too? :)
>>>
>>> by the way, I meant something like 1.75 becomes 7/4 and not
>>> 3/4, but that is easy to adapt on your patch
>>>
>>> thanks
>>>
>>> cheers
>>>
>>>
>>>
>>> 2011/12/16 i go bananas <hard.off at gmail.com
>>> <mailto:hard.off at gmail.com>>
>>>
>>>
>>> by the way, here is the method i used:
>>>
>>> first, convert the decimal part to a fraction in the form
>>> of n/100000
>>> next, find the highest common factor of n and 100000
>>> (using the 'division method' like this:
>>> http://easycalculation.com/**what-is-hcf.php<http://easycalculation.com/what-is-hcf.php>)
>>>
>>> then just divide n and 100000 by that factor.
>>>
>>> actually, that means it's accurate to 6 decimal places, i
>>> guess. well...whatever :D
>>>
>>>
>>>
>>>
>>>
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>>
>>
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>
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