Re: [PD] number to fractions external?
Le 2011-12-18 à 12:51:00, Alexandre Torres Porres a écrit : I will take care of that after february, when I finish up my thesis. Can I count on you to help me revise it? Sorry, I meant to say : « Yes ». __ | Mathieu BOUCHARD - téléphone : +1.514.383.3801 - Montréal, QC___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
I will take care of that after february, when I finish up my thesis. Can I count on you to help me revise it? thanks alex 2011/12/18 Mathieu Bouchard ma...@artengine.ca Le 2011-12-18 à 02:42:00, Alexandre Torres Porres a écrit : by the way, you guys rock :-) So, btw, where can people download the psprofile externals ? __**__** __ | Mathieu BOUCHARD - téléphone : +1.514.383.3801 - Montréal, QC ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
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 mmoserbo...@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 jancs...@yahoo.com wrote: From: i go bananas hard@gmail.com To: Ludwig Maes ludwig.m...@gmail.com Cc: pd-list@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.m...@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 lorenzofsut...@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(1.333) ((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(10.33) ((31, 3), 0) Lorenzo. 2011/12/16 i go bananas hard@gmail.com mailto:hard@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 por...@gmail.com mailto:por...@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@gmail.com mailto:hard@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6
Re: [PD] number to fractions external?
Le 2011-12-16 à 00:52:00, Alexandre Torres Porres a écrit : Is there an external that converts decimal numbers to fractions, like 1.5 = 3 / 2 ? I bet it's complicated to do it as a vanilla patch, right? Take the number, subtract its whole part to get something less than 1, then invert it to get something bigger than 1, and repeat. You will get a list of characteristic numbers that can be used to make good approximations real quick by doing a+1/(b+1/(c+1/(d+1/(e+etc... But unlike what this latter formula looks like, you don't even need to keep a list containing values a b c d e etc... because there's a simple shortcut so that you don't have to start with the innermost parentheses. http://pt.wikipedia.org/wiki/Fra%C3%A7%C3%A3o_cont%C3%ADnua __ | Mathieu BOUCHARD - téléphone : +1.514.383.3801 - Montréal, QC___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
Le 2011-12-17 à 03:44:00, i go bananas a écrit : how do you get from a continued fraction in the form like this: [0;1,5,2,2] to a fraction in the form like this: 27/32 this patch gets as far as that [0; 1,5,2,2] form. but i'm still not sure how to get further keep track of the last two fractions and feed that to something like expr. e.g. $f1 = element of the list $f2 = last numerator $f3 = last denominator $f4 = next-to-last numerator $f5 = next-to-last denominator the number before the semicolon should go with the values 1 0 0 1 to start the algorithm (yes, you have to pretend that a denominator is zero, but don't worry) then it would be something like : [expr $f1*$f2+$f4; $f1*$f3+$f5; $f2; $f3] and then you take the four outputs and feed them back into expr together with the next number in the continued fraction... the advantage of this, is that you can go left-to-right. With the more obvious method, you have to go right-to-left, because the innermost terms (inside many parentheses) are at the right. The left-to-right formula is something I learned in Number Theory course in fév.2003, but naturally, I had to look it up in Wikipédia in order to remember, as I don't use this very often... Let's try the formula with [0;1,5,2,2] : 0 1 0 0 1 gives 0 1 1 0 1 0 1 1 0 gives 1 1 0 1 5 1 1 0 1 gives 5 6 1 1 2 5 6 1 1 gives 11 13 5 6 2 11 13 5 6 gives 27 32 11 13 looks like it works ! 27 32 appear in the 2nd and 1st outlets. __ | Mathieu BOUCHARD - téléphone : +1.514.383.3801 - Montréal, QC___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
when I change the maximum denominator value results are weird and Pd freezes. cheers 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com I just added it to my library on GitHub: https://github.com/dotmmb/mmb But, yeah, feel free to use it however you want. .mmb On Sat, Dec 17, 2011 at 2:07 PM, Alexandre Torres Porres por...@gmail.com wrote: this looks great huh? I have this pd examples that deal with tuning theory, are you releasing this somewhere so i can use it? thanks alex 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com They're not working? Huh... Well, here's the text versions: dec2frac.mmb.pd: #N canvas 60 22 908 750 10; #X obj 298 36 inlet; #X obj 573 359 t l; #X obj 240 574 list; #X obj 198 415 sel 0; #X obj 207 168 expr 1/$f1; #X obj 478 359 list append; #N canvas 203 22 687 744 simplify 0; #X obj 144 28 inlet; #X obj 198 155 list length; #X obj 145 132 t l l; #X obj 165 214 spigot; #X obj 51 239 spigot; #X obj 84 213 == 1; #X obj 205 275 list split 2; #X obj 98 423 pack f f; #X obj 272 371 list split 1; #X obj 237 340 list; #X obj 198 188 1; #X obj 98 377 expr $f2*$f1+1 \; $f1; #X obj 305 513 list append; #X obj 305 541 expr $f1*$f2+$f3 \; $f2; #X obj 307 589 pack f f; #X obj 229 423 t b l; #X obj 226 631 list; #X obj 97 448 t l l; #X obj 102 687 outlet; #X text 206 80 converts the continued fraction form into a simple fraction ; #X connect 0 0 2 0; #X connect 1 0 5 0; #X connect 1 0 10 0; #X connect 2 0 3 0; #X connect 2 0 4 0; #X connect 2 1 1 0; #X connect 3 0 6 0; #X connect 4 0 18 0; #X connect 5 0 4 1; #X connect 6 0 11 0; #X connect 6 1 9 1; #X connect 7 0 17 0; #X connect 8 0 12 0; #X connect 8 1 9 1; #X connect 8 2 16 0; #X connect 9 0 8 0; #X connect 10 0 3 1; #X connect 11 0 7 0; #X connect 11 1 7 1; #X connect 12 0 13 0; #X connect 13 0 14 0; #X connect 13 1 14 1; #X connect 14 0 15 0; #X connect 15 0 9 0; #X connect 15 1 16 1; #X connect 15 1 12 1; #X connect 16 0 18 0; #X connect 17 0 15 0; #X connect 17 1 12 1; #X restore 478 385 pd simplify; #X obj 325 713 outlet; #X obj 368 630 list; #X obj 479 411 t l l; #X obj 596 577 sel 1; #X obj 281 348 spigot; #X msg 336 349 0; #X obj 281 372 t f b; #X obj 505 438 list split 1; #X obj 535 469 route bang; #X msg 333 382 1; #X text 41 573 This is just here for debugging; #X obj 634 406 loadbang; #X obj 634 427 f \$1; #X text 612 683 .mmb; #X text 638 625 TODO: implement decrementing rules; #X obj 102 674 prepend set; #X obj 300 210 expr if($f10 \, int($f1-1) \, int($f1)) \; $f1; #X obj 310 268 expr $f2-$f1 \; $f1; #X text 533 211 floor; #X obj 628 36 inlet; #X obj 628 123 max 1; #X obj 596 556 1000; #X obj 298 100 t b b f b; #N canvas 0 22 450 300 test.if.integer 0; #X obj 206 117 expr int($f1)==$f1; #X obj 151 28 inlet; #X obj 151 64 t f f; #X obj 129 186 spigot; #X obj 179 186 spigot; #X obj 164 160 != 1; #X obj 129 242 outlet; #X obj 179 242 outlet; #X msg 179 214 \$1 1; #X connect 0 0 4 1; #X connect 0 0 5 0; #X connect 1 0 2 0; #X connect 2 0 3 0; #X connect 2 0 4 0; #X connect 2 1 0 0; #X connect 3 0 6 0; #X connect 4 0 8 0; #X connect 5 0 3 1; #X connect 8 0 7 0; #X restore 298 76 pd test.if.integer; #X obj 403 111 s \$0-to.outlet; #X obj 395 671 r \$0-to.outlet; #X msg 101 698; #X obj 634 452 max 1; #X obj 306 157 until; #X obj 335 134 r \$0-stop.until; #X obj 306 183 f; #X obj 127 483 s \$0-stop.until; #X obj 595 604 s \$0-stop.until; #X connect 0 0 30 0; #X connect 1 0 5 1; #X connect 2 0 22 0; #X connect 3 0 8 0; #X connect 3 0 38 0; #X connect 3 1 4 0; #X connect 4 0 23 0; #X connect 5 0 1 0; #X connect 5 0 2 1; #X connect 5 0 6 0; #X connect 6 0 9 0; #X connect 8 0 7 0; #X connect 9 0 8 1; #X connect 9 1 14 0; #X connect 10 0 8 0; #X connect 10 0 39 0; #X connect 10 1 16 0; #X connect 11 0 13 0; #X connect 12 0 11 1; #X connect 13 0 3 0; #X connect 13 1 12 0; #X connect 14 1 15 0; #X connect 15 0 16 0; #X connect 15 1 28 0; #X connect 16 0 11 1; #X connect 18 0 19 0; #X connect 19 0 34 0; #X connect 22 0 33 0; #X connect 23 0 24 0; #X connect 23 1 24 1; #X connect 24 0 11 0; #X connect 24 1 5 0; #X connect 26 0 27 0; #X connect 27 0 10 1; #X connect 28 0 10 0; #X connect 29 0 2 0; #X connect 29 1 35 0; #X connect 29 2 37 1; #X connect 29 3 5 1; #X connect 29 3 8 1; #X connect 30 0 29 0; #X connect 30 1 31 0; #X connect 32 0 7 0; #X connect 34 0 28 1; #X connect 35 0 37 0; #X connect 36 0 35 1; #X connect 37 0 23 0; dec2frac.mmb-help.pd: #N canvas 431 22 944 500 10; #X obj 25 12 cnv 15 400 35 empty empty dec2frac.mmb 20 12 0 14 -4160 -203904 0; #X obj 25 48 cnv 15 400 70 empty empty empty 20 12 0 14 -203904 -66577 0; #X text 812 417 .mmb; #X
Re: [PD] number to fractions external?
Oops, the right inlet was connected to a [sel] when it should have been connected to [ 1000]. I'll upload the fix here and on GitHub. .mmb On Sat, Dec 17, 2011 at 7:57 PM, Alexandre Torres Porres por...@gmail.com wrote: when I change the maximum denominator value results are weird and Pd freezes. cheers 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com I just added it to my library on GitHub: https://github.com/dotmmb/mmb But, yeah, feel free to use it however you want. .mmb On Sat, Dec 17, 2011 at 2:07 PM, Alexandre Torres Porres por...@gmail.com wrote: this looks great huh? I have this pd examples that deal with tuning theory, are you releasing this somewhere so i can use it? thanks alex 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com They're not working? Huh... Well, here's the text versions: dec2frac.mmb.pd: #N canvas 60 22 908 750 10; #X obj 298 36 inlet; #X obj 573 359 t l; #X obj 240 574 list; #X obj 198 415 sel 0; #X obj 207 168 expr 1/$f1; #X obj 478 359 list append; #N canvas 203 22 687 744 simplify 0; #X obj 144 28 inlet; #X obj 198 155 list length; #X obj 145 132 t l l; #X obj 165 214 spigot; #X obj 51 239 spigot; #X obj 84 213 == 1; #X obj 205 275 list split 2; #X obj 98 423 pack f f; #X obj 272 371 list split 1; #X obj 237 340 list; #X obj 198 188 1; #X obj 98 377 expr $f2*$f1+1 \; $f1; #X obj 305 513 list append; #X obj 305 541 expr $f1*$f2+$f3 \; $f2; #X obj 307 589 pack f f; #X obj 229 423 t b l; #X obj 226 631 list; #X obj 97 448 t l l; #X obj 102 687 outlet; #X text 206 80 converts the continued fraction form into a simple fraction ; #X connect 0 0 2 0; #X connect 1 0 5 0; #X connect 1 0 10 0; #X connect 2 0 3 0; #X connect 2 0 4 0; #X connect 2 1 1 0; #X connect 3 0 6 0; #X connect 4 0 18 0; #X connect 5 0 4 1; #X connect 6 0 11 0; #X connect 6 1 9 1; #X connect 7 0 17 0; #X connect 8 0 12 0; #X connect 8 1 9 1; #X connect 8 2 16 0; #X connect 9 0 8 0; #X connect 10 0 3 1; #X connect 11 0 7 0; #X connect 11 1 7 1; #X connect 12 0 13 0; #X connect 13 0 14 0; #X connect 13 1 14 1; #X connect 14 0 15 0; #X connect 15 0 9 0; #X connect 15 1 16 1; #X connect 15 1 12 1; #X connect 16 0 18 0; #X connect 17 0 15 0; #X connect 17 1 12 1; #X restore 478 385 pd simplify; #X obj 325 713 outlet; #X obj 368 630 list; #X obj 479 411 t l l; #X obj 596 577 sel 1; #X obj 281 348 spigot; #X msg 336 349 0; #X obj 281 372 t f b; #X obj 505 438 list split 1; #X obj 535 469 route bang; #X msg 333 382 1; #X text 41 573 This is just here for debugging; #X obj 634 406 loadbang; #X obj 634 427 f \$1; #X text 612 683 .mmb; #X text 638 625 TODO: implement decrementing rules; #X obj 102 674 prepend set; #X obj 300 210 expr if($f10 \, int($f1-1) \, int($f1)) \; $f1; #X obj 310 268 expr $f2-$f1 \; $f1; #X text 533 211 floor; #X obj 628 36 inlet; #X obj 628 123 max 1; #X obj 596 556 1000; #X obj 298 100 t b b f b; #N canvas 0 22 450 300 test.if.integer 0; #X obj 206 117 expr int($f1)==$f1; #X obj 151 28 inlet; #X obj 151 64 t f f; #X obj 129 186 spigot; #X obj 179 186 spigot; #X obj 164 160 != 1; #X obj 129 242 outlet; #X obj 179 242 outlet; #X msg 179 214 \$1 1; #X connect 0 0 4 1; #X connect 0 0 5 0; #X connect 1 0 2 0; #X connect 2 0 3 0; #X connect 2 0 4 0; #X connect 2 1 0 0; #X connect 3 0 6 0; #X connect 4 0 8 0; #X connect 5 0 3 1; #X connect 8 0 7 0; #X restore 298 76 pd test.if.integer; #X obj 403 111 s \$0-to.outlet; #X obj 395 671 r \$0-to.outlet; #X msg 101 698; #X obj 634 452 max 1; #X obj 306 157 until; #X obj 335 134 r \$0-stop.until; #X obj 306 183 f; #X obj 127 483 s \$0-stop.until; #X obj 595 604 s \$0-stop.until; #X connect 0 0 30 0; #X connect 1 0 5 1; #X connect 2 0 22 0; #X connect 3 0 8 0; #X connect 3 0 38 0; #X connect 3 1 4 0; #X connect 4 0 23 0; #X connect 5 0 1 0; #X connect 5 0 2 1; #X connect 5 0 6 0; #X connect 6 0 9 0; #X connect 8 0 7 0; #X connect 9 0 8 1; #X connect 9 1 14 0; #X connect 10 0 8 0; #X connect 10 0 39 0; #X connect 10 1 16 0; #X connect 11 0 13 0; #X connect 12 0 11 1; #X connect 13 0 3 0; #X connect 13 1 12 0; #X connect 14 1 15 0; #X connect 15 0 16 0; #X connect 15 1 28 0; #X connect 16 0 11 1; #X connect 18 0 19 0; #X connect 19 0 34 0; #X connect 22 0 33 0; #X connect 23 0 24 0; #X connect 23 1 24 1; #X connect 24 0 11 0; #X connect 24 1 5 0; #X connect 26 0 27 0; #X connect 27 0 10 1; #X connect 28 0 10 0; #X connect 29 0 2 0; #X connect 29 1 35 0; #X connect 29 2 37 1; #X connect 29 3 5 1; #X connect 29 3 8 1; #X connect 30 0 29 0; #X connect 30 1 31 0; #X connect 32 0 7 0; #X connect 34 0 28 1; #X connect 35 0 37 0; #X connect 36 0 35 1; #X connect 37 0 23 0; dec2frac.mmb-help.pd:
Re: [PD] number to fractions external?
i kinda figured that 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com Oops, the right inlet was connected to a [sel] when it should have been connected to [ 1000]. I'll upload the fix here and on GitHub. .mmb On Sat, Dec 17, 2011 at 7:57 PM, Alexandre Torres Porres por...@gmail.com wrote: when I change the maximum denominator value results are weird and Pd freezes. cheers 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com I just added it to my library on GitHub: https://github.com/dotmmb/mmb But, yeah, feel free to use it however you want. .mmb On Sat, Dec 17, 2011 at 2:07 PM, Alexandre Torres Porres por...@gmail.com wrote: this looks great huh? I have this pd examples that deal with tuning theory, are you releasing this somewhere so i can use it? thanks alex 2011/12/17 Mike Moser-Booth mmoserbo...@gmail.com They're not working? Huh... Well, here's the text versions: dec2frac.mmb.pd: #N canvas 60 22 908 750 10; #X obj 298 36 inlet; #X obj 573 359 t l; #X obj 240 574 list; #X obj 198 415 sel 0; #X obj 207 168 expr 1/$f1; #X obj 478 359 list append; #N canvas 203 22 687 744 simplify 0; #X obj 144 28 inlet; #X obj 198 155 list length; #X obj 145 132 t l l; #X obj 165 214 spigot; #X obj 51 239 spigot; #X obj 84 213 == 1; #X obj 205 275 list split 2; #X obj 98 423 pack f f; #X obj 272 371 list split 1; #X obj 237 340 list; #X obj 198 188 1; #X obj 98 377 expr $f2*$f1+1 \; $f1; #X obj 305 513 list append; #X obj 305 541 expr $f1*$f2+$f3 \; $f2; #X obj 307 589 pack f f; #X obj 229 423 t b l; #X obj 226 631 list; #X obj 97 448 t l l; #X obj 102 687 outlet; #X text 206 80 converts the continued fraction form into a simple fraction ; #X connect 0 0 2 0; #X connect 1 0 5 0; #X connect 1 0 10 0; #X connect 2 0 3 0; #X connect 2 0 4 0; #X connect 2 1 1 0; #X connect 3 0 6 0; #X connect 4 0 18 0; #X connect 5 0 4 1; #X connect 6 0 11 0; #X connect 6 1 9 1; #X connect 7 0 17 0; #X connect 8 0 12 0; #X connect 8 1 9 1; #X connect 8 2 16 0; #X connect 9 0 8 0; #X connect 10 0 3 1; #X connect 11 0 7 0; #X connect 11 1 7 1; #X connect 12 0 13 0; #X connect 13 0 14 0; #X connect 13 1 14 1; #X connect 14 0 15 0; #X connect 15 0 9 0; #X connect 15 1 16 1; #X connect 15 1 12 1; #X connect 16 0 18 0; #X connect 17 0 15 0; #X connect 17 1 12 1; #X restore 478 385 pd simplify; #X obj 325 713 outlet; #X obj 368 630 list; #X obj 479 411 t l l; #X obj 596 577 sel 1; #X obj 281 348 spigot; #X msg 336 349 0; #X obj 281 372 t f b; #X obj 505 438 list split 1; #X obj 535 469 route bang; #X msg 333 382 1; #X text 41 573 This is just here for debugging; #X obj 634 406 loadbang; #X obj 634 427 f \$1; #X text 612 683 .mmb; #X text 638 625 TODO: implement decrementing rules; #X obj 102 674 prepend set; #X obj 300 210 expr if($f10 \, int($f1-1) \, int($f1)) \; $f1; #X obj 310 268 expr $f2-$f1 \; $f1; #X text 533 211 floor; #X obj 628 36 inlet; #X obj 628 123 max 1; #X obj 596 556 1000; #X obj 298 100 t b b f b; #N canvas 0 22 450 300 test.if.integer 0; #X obj 206 117 expr int($f1)==$f1; #X obj 151 28 inlet; #X obj 151 64 t f f; #X obj 129 186 spigot; #X obj 179 186 spigot; #X obj 164 160 != 1; #X obj 129 242 outlet; #X obj 179 242 outlet; #X msg 179 214 \$1 1; #X connect 0 0 4 1; #X connect 0 0 5 0; #X connect 1 0 2 0; #X connect 2 0 3 0; #X connect 2 0 4 0; #X connect 2 1 0 0; #X connect 3 0 6 0; #X connect 4 0 8 0; #X connect 5 0 3 1; #X connect 8 0 7 0; #X restore 298 76 pd test.if.integer; #X obj 403 111 s \$0-to.outlet; #X obj 395 671 r \$0-to.outlet; #X msg 101 698; #X obj 634 452 max 1; #X obj 306 157 until; #X obj 335 134 r \$0-stop.until; #X obj 306 183 f; #X obj 127 483 s \$0-stop.until; #X obj 595 604 s \$0-stop.until; #X connect 0 0 30 0; #X connect 1 0 5 1; #X connect 2 0 22 0; #X connect 3 0 8 0; #X connect 3 0 38 0; #X connect 3 1 4 0; #X connect 4 0 23 0; #X connect 5 0 1 0; #X connect 5 0 2 1; #X connect 5 0 6 0; #X connect 6 0 9 0; #X connect 8 0 7 0; #X connect 9 0 8 1; #X connect 9 1 14 0; #X connect 10 0 8 0; #X connect 10 0 39 0; #X connect 10 1 16 0; #X connect 11 0 13 0; #X connect 12 0 11 1; #X connect 13 0 3 0; #X connect 13 1 12 0; #X connect 14 1 15 0; #X connect 15 0 16 0; #X connect 15 1 28 0; #X connect 16 0 11 1; #X connect 18 0 19 0; #X connect 19 0 34 0; #X connect 22 0 33 0; #X connect 23 0 24 0; #X connect 23 1 24 1; #X connect 24 0 11 0; #X connect 24 1 5 0; #X connect 26 0 27 0; #X connect 27 0 10 1; #X connect 28 0 10 0; #X connect 29 0 2 0; #X connect 29 1 35 0;
Re: [PD] number to fractions external?
thanks mattieu! i got it working, thanks to your great help! you have no idea how bummed out i was that i couldn't make this work the other day. dec-to-frac-help.pd Description: Binary data dec-to-frac.pd Description: Binary data ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
cool, but now we have two patches that behave and work the same way? thanks Alex 2011/12/18 i go bananas hard@gmail.com thanks mattieu! i got it working, thanks to your great help! you have no idea how bummed out i was that i couldn't make this work the other day. ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
I mean one from bananas and another from mike, i guess it was clear 2011/12/18 Alexandre Torres Porres por...@gmail.com cool, but now we have two patches that behave and work the same way? thanks Alex 2011/12/18 i go bananas hard@gmail.com thanks mattieu! i got it working, thanks to your great help! you have no idea how bummed out i was that i couldn't make this work the other day. ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
by the way, you guys rock :-) 2011/12/18 Alexandre Torres Porres por...@gmail.com I mean one from bananas and another from mike, i guess it was clear 2011/12/18 Alexandre Torres Porres por...@gmail.com cool, but now we have two patches that behave and work the same way? thanks Alex 2011/12/18 i go bananas hard@gmail.com thanks mattieu! i got it working, thanks to your great help! you have no idea how bummed out i was that i couldn't make this work the other day. ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
Le 2011-12-16 à 15:51:00, i go bananas a écrit : (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) The division method is much more known as Euclid's Algorithm... And I never saw it named HCF before. Always PGCD in French and GCD in English. By the way, GridFlow has an operator for computing one or many GCD at once : [# gcd]. Here's a visualisation of the GCD of all combinations of numbers from 0 to 255 : http://gridflow.ca/gallery/gcd.gif I made it in fév.2003... it's one of the oldest GridFlow patches ever. then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D 10 means 5 decimal places. A million is 6 decimal places. You can see that by looking at how 10, 100, 1000, etc. multiply with each other, and also, logarithms in base 10. __ | Mathieu BOUCHARD - téléphone : +1.514.383.3801 - Montréal, QC___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
Le 2011-12-18 à 02:42:00, Alexandre Torres Porres a écrit : by the way, you guys rock :-) So, btw, where can people download the psprofile externals ? __ | Mathieu BOUCHARD - téléphone : +1.514.383.3801 - Montréal, QC___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
On 16/12/11 06:51, i go bananas wrote: by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. I don't think that method will give happy results for most simple fractions. Plus it's useful to get approximations that are simpler or more accurate, like 3 or 22/7 or 355/113 for pi.. Your patch doesn't work very well for me: input: 1/7 fraction: 2857/2 input: 8/9 fraction: 1/12500 input: 7/11 fraction: 15909/25000 input: 11/17 fraction: 4313.67/.67 (input is $1 $2--[/], so as accurate as floating point is...) actually, that means it's accurate to 6 decimal places, i guess. There's a way to get a simple fraction like 1/7 instead of 143/1000 or whatever, could be possible to implement in Pd? (I've not tried.) [0] http://hackage.haskell.org/packages/archive/base/latest/doc/html/src/Data-Ratio.html#approxRational [1] http://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations well...whatever :D Claude ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
yeah, my patch only works for rational numbers. will have a look at the article / method you posted, claude. On Fri, Dec 16, 2011 at 7:49 PM, Claude Heiland-Allen cla...@goto10.orgwrote: On 16/12/11 06:51, i go bananas wrote: by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/**what-is-hcf.phphttp://easycalculation.com/what-is-hcf.php) then just divide n and 10 by that factor. I don't think that method will give happy results for most simple fractions. Plus it's useful to get approximations that are simpler or more accurate, like 3 or 22/7 or 355/113 for pi.. Your patch doesn't work very well for me: input: 1/7 fraction: 2857/2 input: 8/9 fraction: 1/12500 input: 7/11 fraction: 15909/25000 input: 11/17 fraction: 4313.67/.67 (input is $1 $2--[/], so as accurate as floating point is...) actually, that means it's accurate to 6 decimal places, i guess. There's a way to get a simple fraction like 1/7 instead of 143/1000 or whatever, could be possible to implement in Pd? (I've not tried.) [0] http://hackage.haskell.org/**packages/archive/base/latest/** doc/html/src/Data-Ratio.html#**approxRationalhttp://hackage.haskell.org/packages/archive/base/latest/doc/html/src/Data-Ratio.html#approxRational [1] http://en.wikipedia.org/wiki/**Continued_fraction#Best_** rational_approximationshttp://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations well...whatever :D Claude __**_ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/** listinfo/pd-list http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
sorry, should have said 'finite' numbers. ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
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@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
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 por...@gmail.comwrote: 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@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
looks like a job for an external 2011/12/16 i go bananas hard@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 por...@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@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
it's possible in vanilla, but the mathematics goes over my head On Sat, Dec 17, 2011 at 1:05 AM, Alexandre Torres Porres por...@gmail.comwrote: looks like a job for an external 2011/12/16 i go bananas hard@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 por...@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@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
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(1.333) ((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(10.33) ((31, 3), 0) Lorenzo. 2011/12/16 i go bananas hard@gmail.com mailto:hard@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 por...@gmail.com mailto:por...@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@gmail.com mailto:hard@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
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 lorenzofsut...@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.**333) ((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.**33) ((31, 3), 0) Lorenzo. 2011/12/16 i go bananas hard@gmail.com mailto:hard@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 por...@gmail.com mailto:por...@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@gmail.com mailto:hard@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/**what-is-hcf.phphttp://easycalculation.com/what-is-hcf.php) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D __**_ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/** listinfo/pd-list http://lists.puredata.info/listinfo/pd-list __**_ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/** listinfo/pd-list http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
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. On Sat, Dec 17, 2011 at 3:00 AM, Ludwig Maes ludwig.m...@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 lorenzofsut...@gmail.comwrote: 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.**333) ((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.**33) ((31, 3), 0) Lorenzo. 2011/12/16 i go bananas hard@gmail.com mailto:hard@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 por...@gmail.com mailto:por...@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@gmail.com mailto:hard@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/**what-is-hcf.phphttp://easycalculation.com/what-is-hcf.php) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D __**_ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/** listinfo/pd-list http://lists.puredata.info/listinfo/pd-list __**_ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/** listinfo/pd-list http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
how do you get from a continued fraction in the form like this: [0;1,5,2,2] to a fraction in the form like this: 27/32 this patch gets as far as that [0; 1,5,2,2] form. but i'm still not sure how to get further continued.pd Description: Binary data ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
online calculator http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
yes, but it's difficult to embed that in a pd patch, yeah? On Sat, Dec 17, 2011 at 4:05 AM, Alexandre Torres Porres por...@gmail.comwrote: online calculator http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
From: i go bananas hard@gmail.com To: Ludwig Maes ludwig.m...@gmail.com Cc: pd-list@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.m...@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 lorenzofsut...@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(1.333) ((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(10.33) ((31, 3), 0) Lorenzo. 2011/12/16 i go bananas hard@gmail.com mailto:hard@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 por...@gmail.com mailto:por...@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@gmail.com mailto:hard@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
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 jancs...@yahoo.com wrote: From: i go bananas hard@gmail.com To: Ludwig Maes ludwig.m...@gmail.com Cc: pd-list@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.m...@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 lorenzofsut...@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(1.333) ((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(10.33) ((31, 3), 0) Lorenzo. 2011/12/16 i go bananas hard@gmail.com mailto:hard@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 por...@gmail.com mailto:por...@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@gmail.com mailto:hard@gmail.com by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info
[PD] number to fractions external?
hi there, Is there an external that converts decimal numbers to fractions, like 1.5 = 3 / 2 ? I bet it's complicated to do it as a vanilla patch, right? thanks alex ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
i had a go at it. This one converts up to 5 decimal places (you could probably mod it to do more, but then you get pretty close to the limits of float-based arithmetic, i think). i was getting glitches, because of the known issue where 58/1000 comes out as 57.9.. , so i have just added a tiny amount to each number to stop this. also, the one i have done here splits a number into whole and fractional parts, but it would be trivial to multiply the whole by the denominator to express the number as a vulgar fraction (3/2, etc) On Fri, Dec 16, 2011 at 11:52 AM, Alexandre Torres Porres por...@gmail.comwrote: hi there, Is there an external that converts decimal numbers to fractions, like 1.5 = 3 / 2 ? I bet it's complicated to do it as a vanilla patch, right? thanks alex ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list dec2frac.pd Description: Binary data dec2frac-help.pd Description: Binary data ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
Re: [PD] number to fractions external?
by the way, here is the method i used: first, convert the decimal part to a fraction in the form of n/10 next, find the highest common factor of n and 10 (using the 'division method' like this: http://easycalculation.com/what-is-hcf.php ) then just divide n and 10 by that factor. actually, that means it's accurate to 6 decimal places, i guess. well...whatever :D ___ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management - http://lists.puredata.info/listinfo/pd-list
