Waveshaper :: Gloubi-boulga

References : Laurent de Soras on IRC
Notes :
Multiply input by gain before processing
Code :
const double x = input * 0.686306;
const double a = 1 + exp (sqrt (fabs (x)) * -0.75);
output = (exp (x) - exp (-x * a)) / (exp (x) + exp (-x));

Comments
from : theo[DOT]burt[[AT][AT][AT]T]virgin[dot]net
comment : Just tried this out, sound is incredible, but is horrifically expensive... Can anyone think of any realistic ways to optimize/approximate this?

from : mailthing[AT]trilete[DOT]net
comment : you can use a taylor series approximation for the exp , save time by realizing that exp(-x) = 1/exp(x), use newton's method to calculate the sqrt with less precision... and if you use SIMD instructions, you can calculate several values in parallel. dunno what the savings would be like, but it would surely be faster.

from : Christian[AT]savioursofsoul[DOT]de
comment : Maybe something like this: function GloubiBoulga(x:Single):Single; var a,b:Single; begin x:=x*0.686306; a:=1+exp(sqrt(f_abs(x))*-0.75); b:=exp(x); Result:=(b-exp(-x*a))*b/(b*b+1); end; still expensive, but...

from : Christian[AT]savioursofsoul[DOT]de
comment : A Taylor series doesn't work very well, because the approximation effects the result very early due to a) numerical critical additions & subtractions of approximations b) approximating approximated "a" makes the result evene more worse. The above version has already been improved, by removing 2 of 5 exp() functions. You can also try to express the exp(x)+exp(-x) as cosh(x) with its approximation. So: b:=exp(x); Result:=(b-exp(-x*a))*b/(b*b+1); would be: Result:=(exp(x)-exp(-x*a))*20160/40320+x*x*(20160+ x*x*(1680+x*x*(56+x*x))); but this is again more worse. Anyone else?

from : ShadowHugger[AT]dev[DOT]null
comment : Use table lookup with interpolation.

from : decil[AT]gtlab[DOT]net
comment : IMHO, you can use x-0.15*x^2-0.15*x^3 instead of this scary formula. I try to explain my position with this small graph: http://liteprint.com/download/replacment.png This is only first step, if you want to get more correct result you can use interpolation method called method of minimal squares (this is translation from russian, maybe in england it has another name)

from : musicdsp[AT]dsparsons[DOT]co[DOT]uk
comment : That's much better decil - thx for that! DSP

from : decil[AT]gtlab[DOT]net
comment : You are welcome :) Now I've working under plugin with wapeshapping processing like this. I've put a link to it here, when I've done it.

from : decil[AT]gtlab[DOT]net
comment : You can check my version: http://liteprint.com/download/SweetyVST.zip Please, send comments and suggestions to my email. Dmitry.

from : jayman_21[AT]hotmail[DOT]com
comment : Which formula exactly did you use decil, for your plugin? How do you get different harmonics from this algo. thanx jay

from : mail[AT]trilete[DOT]net
comment : wow, blast from the past seeing this turn up on kvraudio. christian - i'd have thought that an advantage of using a taylor series approximation would be that it limits the order of the polynomial (and the resulting bandwidth) somewhat. it's been ages since i tested, but i thought i got some reasonable sounding results using the taylor series approximation. maybe not. decil - isn't that a completely unrelated polynomial (similar to the common and cheap x - a x^3 ?). i'd think you'd have to do something about the dc from the x^2 term, too (or do a sign(x)*x^2). anyway, your plugin sounds to be popular so i look forward to checking it out later at home.

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