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!!!
>
