# [PD] number to fractions external?

Mike Moser-Booth mmoserbooth at gmail.com
Sat Dec 17 19:19:34 CET 2011

```The one I posted earlier apparently can run into stack overflows. I
think this version fixes it.

.mmb

On Fri, Dec 16, 2011 at 9:30 PM, Mike Moser-Booth <mmoserbooth at gmail.com> wrote:
> I just gave this a go, and here's what I have so far based on the
> Wikipedia link Claude gave. Send the decimal through the left inlet,
> and it outputs the numerator and denominator as a list. The argument
> is the maximum value the denominator is allowed to be, which keeps it
> from going crazy trying to figure out irrational numbers and also
> seems to make up for some floating-points errors. You can change the
> max with the right inlet as well. Right now it defaults to 100, but
> that may be too low. Higher values=more accurate, but potentially more
> computation.
>
> I haven't implemented the rules for decrementing the last value of the
> continuous fractions, so it's not perfect. But it does give 355/113
> for pi. :-)
>
> .mmb
>
> On Fri, Dec 16, 2011 at 2:46 PM, Jonathan Wilkes <jancsika at yahoo.com> wrote:
>>>________________________________
>>> From: i go bananas <hard.off at gmail.com>
>>>To: Ludwig Maes <ludwig.maes at gmail.com>
>>>Cc: pd-list at iem.at
>>>Sent: Friday, December 16, 2011 1:16 PM
>>>Subject: Re: [PD] number to fractions external?
>>>
>>>
>>>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.
>>
>>
>> Wow, how much cpu does that take in Python?  I tried this approach in the form
>>
>> of an abstraction, with a nested until, and worst case it can take as much as a quarter of
>>
>> a second to compute with the constants provided below.
>>
>> (Pentium Dual-core 2.6gHz in WinXP with 0.43 nightly build)
>>
>> -Jonathan
>>
>>
>>>
>>>
>>>
>>>
>>>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 )
>>>>>>
>>>>>>           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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>>>>
>>>
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>>>
>>>
>>
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>
>
>
> --
> Mike Moser-Booth
> mmoserbooth at gmail.com

--
Mike Moser-Booth
mmoserbooth at gmail.com
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