Yep, this one, with a one-shot [until] through the indices into $0-cos-BAD is better than cosinesum in the previous patch, but it still drifts visibly/audibly after a couple minutes; obviously wouldn't be as much of a problem in double precision, though.
On Thu, Jun 6, 2024 at 1:53 PM Matt Barber <[email protected]> wrote: > 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-2.pd
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