> And the mysterious UNITBIT32 number in d_osc.c? Funny you mentioned that! I just wanted to add that instead of approximating trig functions through polynomials one could also read Pd's cosine table ( float * cos_table ) with linear interpolation like it's done in [cos~] and [osc~]. Miller does exactly this in the code for [vcf~] which - I think - is therefore part of d_osc.c and not d_filter.c. I'm wondering which of these methods is more efficient and/or more precise...
> A note on efficiency: coefficients in [hip~] are only recalculated > when cutoff frequency is changed. How important is performance for a > function rarely called? It can be relevant for small blocksizes. Right now I'm working on a project where all audio is done with blocksize 1 + upsampling and that's where some setup code before the actual loop can become a bottleneck. At [block~ 1 0 8] one can get really paranoid of efficiency :-) Christof > Gesendet: Mittwoch, 19. Oktober 2016 um 19:07 Uhr > Von: katja <[email protected]> > An: "Jonathan Wilkes" <[email protected]> > Cc: "[email protected]" <[email protected]> > Betreff: Re: [PD] efficient approximation of trig functions for hi pass > formula (was: could vanilla borrow iemlib's hi pass filter recipe?) > > On Wed, Oct 19, 2016 at 4:25 PM, Jonathan Wilkes <[email protected]> wrote: > > When implemented in C, which approach takes the least amount of time > > to read, reason about, and fully comprehend? > > That is an important question. Pd code is full of clever tricks and > bit hacks for dsp efficiency. What is the origin of q8_rsqrt(), why > and how does it work? What about PD_BIGORSMALL() in m_pd.h? And the > mysterious UNITBIT32 number in d_osc.c? Ideally such code should be > commented not only to denote its function (if necessary) but also to > reference the origin so you may be able to find info. > > An approximation for a trig function should go in an (inline) > function, with a comment if the name can't clarify the function > sufficiently. But to fully comprehend is a different matter. Dsp code > in general takes substantial background to understand. You could > wonder why and how the approximation works, but the same question goes > for the function that it replaces. > > Katja > > > > > -Jonathan > > > > > > > > > > ________________________________ > > From: katja <[email protected]> > > To: "[email protected]" <[email protected]> > > Sent: Wednesday, October 19, 2016 9:06 AM > > Subject: [PD] efficient approximation of trig functions for hi pass formula > > (was: could vanilla borrow iemlib's hi pass filter recipe?) > > > > Changing the thread title to reflect the new approach. Extract of the > > original thread; > > > > - I suggested using iemlib's hi pass filter recipe to improve > > frequency response of [hip~] > > - Christof Ressi pointed to formula in > > http://www.arpchord.com/pdf/coeffs_first_order_filters_0p1.pdf > > - this formula calculates feedback coefficient k = (1 - sin(a)) / > > cos(a) where a = 2 * pi * fc / SR > > - the filter implementation is y[n] = (x[n] - x[n-1]) * (1 + k) / 2 > > + k * y[n-1] > > - following convention in d_filter.c (and pd tilde classes in > > general), trig functions should best be approximated > > - Cyrille provided libre office linear regression result for > > (1-sin(x))/cos(x) > > > > Thanks for the useful infos and discussion. My 'math coach' suggested > > using odd powers of -(x-pi/2) in an approximation polynomial for > > (1-sin(x))/cos(x). The best accuracy/performance balance I could get > > is with this 5th degree polynomial: > > > > (-(x-pi/2))*0.4908 - (x-pi/2)^3*0.04575 - (x-pi/2)^5*0.00541 > > > > Using this approximation in the filter formula, response at cutoff > > frequency is -3 dB with +/-0.06 dB accuracy in the required range 0 < > > x < pi. It can be efficiently implemented in C, analogous to an > > approximation Miller uses in [bp~]. So that is what I'll try next. > > > > Attached patch hip~-models.pd illustrates and compares filter recipes > > using vanilla objects: > > > > - current implementation, most efficient, accuracy +/- 3 dB > > - implementation with trig functions, least efficient, accuracy +/- 0.01 dB > > - implementation with approximation for trig functions, efficient, > > accuracy +/- 0.06 dB > > > > A note on efficiency: coefficients in [hip~] are only recalculated > > when cutoff frequency is changed. How important is performance for a > > function rarely called? I'm much aware of the motto 'never optimize > > early', yet I spent much time on finding a fast approximation, for > > several reasons: it's a nice math challenge, instructive for cases > > where performance matters more, and I want to respect Miller's code > > efficiency when proposing a change. Today pd is even deployed on > > embedded devices so the frugal coding approach is still relevant. > > After 20 years. > > > > Katja > > > > > > On Tue, Oct 18, 2016 at 10:28 AM, cyrille henry <[email protected]> wrote: > >> > >> > >> Le 18/10/2016 à 00:47, katja a écrit : > >>> > >>> The filter recipe that Christof pointed to was easy to plug into the C > >>> code of [hip~] and works perfectly. But when looking further in > >>> d_filter.c I came across an approximation function 'sigbp_qcos()' used > >>> in the bandpass filter. It made me realize once more how passionate > >>> Miller is about efficiency. I'm not going to make a fool of myself by > >>> submitting a 'fix' using two trig functions to calculate a filter > >>> coefficient when a simple approximation could do the job. So that is > >>> what I'm now looking into, with help of a math friend: an efficient > >>> polynomial approximation for (1-sin(x))/cos(x). > >> > >> according to libre office linear regression, for x between 0 and Pi, > >> (1-sin(x))/cos(x) is about : > >> -0.057255x³ + 0.27018x² - 0.9157x + 0.99344 > >> > >> the calc is in attachment, if you want to tune the input source or > >> precision. > >> cheers > >> c > > _______________________________________________ > > [email protected] mailing list > > UNSUBSCRIBE and account-management -> > > https://lists.puredata.info/listinfo/pd-list > > > > > > _______________________________________________ > [email protected] mailing list > UNSUBSCRIBE and account-management -> > https://lists.puredata.info/listinfo/pd-list > _______________________________________________ [email protected] mailing list UNSUBSCRIBE and account-management -> https://lists.puredata.info/listinfo/pd-list
