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!!! > > > > > >
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