Here's the demonstration. While the symmetric table will eventually drift a little, it stays stable for far longer than osc~ or cosinesum. Although, to be fair, the real test in building a cosine table from scratch in Pd would be to fill the table using [cos], walking through indices and dividing by table size to get phase.
Matt On Thu, Jun 6, 2024 at 1:39 PM Matt Barber <[email protected]> wrote: > The main reason for symmetry was stable FM synthesis – when you modulate > frequency, any overall differences in the shape of the cosine wave shape > accumulate quickly as an error in the osc~'s phase increment, causing > significant drift in the spectrum. It's not a problem when you modulate > phase directly since the modulator is decoupled from the phasor. > > MB > > On Thu, Jun 6, 2024, 1:24 PM Miller Puckette <[email protected]> > wrote: > >> Precisely that: cache pollution in general. At some point the overall >> speed of the program will suffer, depending on CPU design, cache size, >> and probable other factors. >> >> If the input to a cos~ object (for example) is between 1 and 2 you'll >> get the same loss of accuracy but still there will be rounding behavior >> that will (probably) give unsymmetric behavior. >> >> Anyway, I don't remember hearing any reason why symmetry should be >> important in itself. >> >> cheers >> >> M >> >> On 6/6/24 6:51 PM, Matt Barber wrote: >> > Since cos~ wraps, one could theoretically take advantage of the equal >> > distribution of float values between 1.0 and 2.0. >> > >> > Profiling a larger table would be useful – I prefer accuracy over >> > performance in general, but I wonder where the performance hit would >> > come from, outside of unpredictable cache misses. >> > >> > >> > >> > On Thu, Jun 6, 2024, 11:25 AM Miller Puckette >> > <[email protected]> wrote: >> > >> > Well, as far as I can tell making the table "symmetric" won't >> > matter at >> > all since, for instance, 0.1 and 0.9 won't give the same lookup >> > values >> > anyway because they can't themselves be represented exactly and >> > will be >> > truncated differently (0.1 will be more accurately represented than >> > 0.9). On the other hand, values like 0.25 or -0.5 can be >> represented >> > exactly so it might be worthwhile to bash true 1s, -1,s, and 0s >> where >> > they belong in the table. >> > >> > Hearing that Max defaults to a ridiculously big table makes me >> wonder >> > though... first, is 2048 really enough (and at what point is there a >> > real performance penalty for bigger tables). And: not for this >> > release >> > but later perhaps, should 64-bit Pd use a bigger table? >> > >> > As I figure it, the 2048-point table differs from the true cosine, >> > absolute worst case, by (2pi/2048)^2 / 8, or about 2(-19.7) - >> > i.e., 19.7 >> > bit accuracy. But the error is dominated by an amplitude change >> (the >> > best-matching cosine to the line-segment approximation has amplitude >> > less than 1). Accounting for that and taking RMS error instead of >> > worst-case gives an error estimate 2.7 bits more optimistic: 22.4 >> > bits, >> > which is close to the accuracy of a 32-bit number. >> > >> > I don't have my RPI3 handy (I'm on the road) but I'm now wondering >> if >> > the default shouldn't be 4096, which would give us an additional 2 >> > bits >> > of goodness. Any opinions? >> > >> > cheers >> > >> > M >> > >> > On 6/5/24 9:35 PM, Matt Barber wrote: >> > > A couple of things: >> > > >> > > 1. I'm pretty sure any error in cos at pi and 2pi will be >> > smaller in >> > > double precision than float's epsilon, so I don't think that >> > there's >> > > any need to set -1.0 and 1.0 explicitly after all except to be >> > extra >> > > safe. However, at pi/2 and 3pi/2 the error is still larger than >> the >> > > minimum normal number, so it is worth setting the zero crossings >> > to 0.0. >> > > >> > > 2. For garray_dofo() there isn't a great way of using explicit >> > 0.0 at >> > > zero crossings without incurring an extra check, like don't add >> > to the >> > > sum if absolute value is less than e.g. 1.0e-10. For this, >> probably >> > > just using M_PI and incrementing integer phase like for the cosine >> > > table is enough. >> > > >> > > MB >> > > >> > > >> > > On Wed, Jun 5, 2024 at 2:20 PM Alexandre Torres Porres >> > > <[email protected]> wrote: >> > > >> > > Em qua., 5 de jun. de 2024 às 14:31, Matt Barber >> > > <[email protected]> escreveu: >> > > >> > > While we're at it, I think it would be worth tuning >> > > garray_dofo() to use the same so that sinesum and >> > > cosinesum have the same level of accuracy, guarantees of >> > > symmetry, etc. >> > > >> > > MB >> > > >> > > >> > > Good catch! In fact, I think this is a great opportunity to >> also >> > > fix this bug >> https://github.com/pure-data/pure-data/issues/371 >> > > >> > < >> https://urldefense.com/v3/__https://github.com/pure-data/pure-data/issues/371__;!!Mih3wA!Gx7B-gwSgjsuIXmREh2__bBbYdt1d6pi29crpkLOOyltinVweZR3u6Q6vl9ItouugFy2oefgYhPlew$ >> > >> > > which is totally related. I just reopened >> > > https://github.com/pure-data/pure-data/issues/105 >> > > >> > < >> https://urldefense.com/v3/__https://github.com/pure-data/pure-data/issues/105__;!!Mih3wA!Gx7B-gwSgjsuIXmREh2__bBbYdt1d6pi29crpkLOOyltinVweZR3u6Q6vl9ItouugFy2oedw4qUPfQ$ >> > >> > > as well as I'm still considering the table could/should be >> still >> > > "perfectly symmetric" considering 0 crossings and the >> start/end >> > > points. >> > > >> > > >> > > On Wed, Jun 5, 2024 at 12:52 PM Alexandre Torres Porres >> > > <[email protected]> wrote: >> > > >> > > For the record and sake of comparison, Cyclone uses >> > > a 16384 points table, and linear interpolation, >> > calculated >> > > with double precision. We did this because MAX >> documents >> > > it uses such a table, and we made it (well, Matt did) >> > > simetric. >> > > >> > > I see Pd is doing kind of the same, huh? linear >> > > interpolation on a table calculated with double >> > precision. >> > > >> > > I see SuperCollider mentions it uses 8192 points and >> > > linear interpolation on its oscillator. >> > > >> > > I guess MAX is exaggerating its table size a bit :) >> > but I >> > > wonder why Pd is still about to use a relatively >> smaller >> > > table size. I'm curious to know how much an increase >> in >> > > table size actually offers a better resolution and how >> > > much it ruins performance. For instance, I'm using the >> > > same as Cyclone in ELSE oscillators, could I just >> reduce >> > > it at least to 8192 points or even less and down to >> Pd's >> > > 2048 size worry free? >> > > >> > > Thanks >> > > >> > > >> > > >> > > Em qua., 5 de jun. de 2024 às 13:28, Alexandre Torres >> > > Porres <[email protected]> escreveu: >> > > >> > > Nice one Matt! >> > > >> > > Em qua., 5 de jun. de 2024 às 08:13, Christof >> Ressi >> > > <[email protected]> escreveu: >> > > >> > >> @Miller: what do you think? IMO we should >> > >> make the cos table as good as we can, so >> we >> > >> won't have any regrets :) >> > >> >> > > +1000!!! >> > > >> > >> >
FM-instability.pd
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