> I'm not sure I understand what you mean by allocating a delay line for
the sliding mean, but I'll look into it.

Here's an example implementation in Faust.  The "small test" allocates a
length 8 delay line.
The full test takes too long to compile, but you can see the pattern, so
it's easy to just write it.

import("stdfaust.lib");

// Small test:
durSamples = 8;
DUR_SAMPLES_MAX = durSamples*2;

// What we really need (but takes a LONG time to compile):
// DUR_SAMPLES_MAX = 2^16;
// durSamples = int(0.5 + 0.4 * ma.SR);

sliding_mean(durSamples) = _ <:
par(i,DUR_SAMPLES_MAX,ba.if(i<durSamples,@(i),0)) :> /(durSamples);

process = sliding_mean(durSamples);

On Sat, Jul 10, 2021 at 1:12 AM Dario Sanfilippo <sanfilippo.da...@gmail.com>
wrote:

> Dear Julius, thanks for putting it nicely. :)
>
> I'm not sure I understand what you mean by allocating a delay line for the
> sliding mean, but I'll look into it.
>
> A quick improvement to the slidingMean function could be to put the
> integrator after the difference. With a sliding window of .4 sec at 48 kHz,
> we should have about 60 dBs of dynamic range when feeding a full-amp
> constant. It should be even better with close-to-zero-mean signals.
>
> import("stdfaust.lib");
> slidingSum(n) = _ <: _, _@int(max(0,n)) : - : fi.pole(1);
> slidingMean(n) = slidingSum(n)/rint(n);
> t=.4;
> process = ba.if(ba.time < ma.SR * 1, 1.0, .001) <: slidingMean(t*ma.SR) ,
> ba.slidingMean(t*ma.SR) : ba.linear2db , ba.linear2db;
>
> Ciao,
> Dr Dario Sanfilippo
> http://dariosanfilippo.com
>
>
> On Sat, 10 Jul 2021 at 00:27, Julius Smith <julius.sm...@gmail.com> wrote:
>
>> Hi Dario,
>>
>> Ok, I see what you're after now.  (I was considering only the VU meter
>> display issue up to now.)
>>
>> There's only 23 bits of mantissa in 32-bit floating point, and your test
>> counts up to ~100k, which soaks up about 17 bits, and then you hit it with
>> ~1/1024, or 2^(-10), which is then a dynamic range swing of 27 bits.  We
>> can't add numbers separated by 27 bits of dynamic level using a mantissa
>> (or integer) smaller than 27 bits.  Yes, double precision will fix that
>> (52-bit mantissas), but even TIIR methods can't solve this problem.  When
>> adding x and y, the wordlength must be on the order of at least
>> |log2(|x|/|y|)|.
>>
>> The situation is not so dire with a noise input, since it should be zero
>> mean (and if not, a dcblocker will fix it).  However, the variance of
>> integrated squared white noise does grow linearly, so TIIR methods are
>> needed for anything long term, and double-precision allows the TIIR resets
>> to be much farther separated, and maybe not even needed in a given
>> application.
>>
>> Note, by the way (Hey Klaus!), we can simply allocate a 0.4 second delay
>> line for the sliding mean and be done with all this recursive-filter
>> dynamic range management.  It can be a pain, but it also can be managed.
>> That said, 0.4 seconds at 96 kHz is around 15 bits worth
>> (log2(0.4*96000)=15.2), so single-precision seems to me like enough for a
>> simple level meter (e.g., having a 3-digit display), given a TIIR reset
>> every 0.4 seconds.  Since this works out so neatly, I wouldn't be surprised
>> if 0.4 seconds was chosen for the gated-measurement duration for that
>> reason.
>>
>> Cheers,
>> Julius
>>
>>
>> On Fri, Jul 9, 2021 at 1:54 PM Dario Sanfilippo <
>> sanfilippo.da...@gmail.com> wrote:
>>
>>> Thanks, Julius.
>>>
>>> So it appears that the issue I was referring to is in that architecture
>>> too.
>>>
>>> To isolate the problem with ba.slidingMean, we can see that we also get
>>> 0 when transitioning from a constant input of 1 to .001 (see code below).
>>> Double-precision solves the issue. Perhaps we could advise using DP for
>>> this function and the others involving it.
>>>
>>> Ciao,
>>> Dario
>>>
>>> import("stdfaust.lib");
>>> lp1p(cf, x) = fi.pole(b, x * (1 - b))
>>> with {
>>> b = exp(-2 * ma.PI * cf / ma.SR);
>>> };
>>> sig = ba.if(ba.time > ma.SR * 2, .001, 1.0);
>>> t = .4;
>>> process = sig <: ba.slidingMean(t * ma.SR) , lp1p(1.0 / t) , ba.time;
>>>
>>> On Fri, 9 Jul 2021 at 22:40, Julius Smith <julius.sm...@gmail.com>
>>> wrote:
>>>
>>>> I get the zero but not the other:
>>>>
>>>> octave:2> format long
>>>> octave:3> faustout(115200,:)
>>>> ans =
>>>>
>>>>                        0  -2.738748490000000e-02   5.555857930000000e-05
>>>>
>>>>
>>>> On Fri, Jul 9, 2021 at 1:03 PM Dario Sanfilippo <
>>>> sanfilippo.da...@gmail.com> wrote:
>>>>
>>>>> Thanks, Julius.
>>>>>
>>>>> I don't have Octave installed, and I can't see it myself, sorry; if
>>>>> you can inspect the generated values, can you also see if at sample 
>>>>> #115200
>>>>> (48 kHz SR) you get 0 for ms_rec, and, 0.000658808684 for the lowpass?
>>>>>
>>>>> Yes, I might have done something wrong, but the leaky integrator
>>>>> doesn't work well.
>>>>>
>>>>> Ciao,
>>>>> Dario
>>>>>
>>>>> On Fri, 9 Jul 2021 at 21:49, Julius Smith <julius.sm...@gmail.com>
>>>>> wrote:
>>>>>
>>>>>> Here is a longer run that shows Dario's latest test more completely.
>>>>>>   I don't think zi_leaky looks right at the end, but the other two look
>>>>>> reasonable to me.
>>>>>>
>>>>>> Here is the Octave magic for the plot:
>>>>>>
>>>>>>     plot(faustout,'linewidth',2);
>>>>>>     legend('zi','zi\_leaky','zi\_lp','location','southeast');
>>>>>>     grid;
>>>>>>
>>>>>> I had to edit faust2octave to change the process duration, it's
>>>>>> hardwired.  Length option needed!  (Right now no options can take an
>>>>>> argument.)
>>>>>>
>>>>>> Cheers,
>>>>>> - Julius
>>>>>>
>>>>>> On Fri, Jul 9, 2021 at 12:01 PM Julius Smith <julius.sm...@gmail.com>
>>>>>> wrote:
>>>>>>
>>>>>>> Hi Dario,
>>>>>>>
>>>>>>> I tried your latest test and it looks plausible in faust2octave (see
>>>>>>> plot attached).
>>>>>>>
>>>>>>> TIIR filters present a nice, juicy Faust puzzle :-)
>>>>>>> I thought about a TIIR sliding average, but haven't implemented
>>>>>>> anything yet.
>>>>>>> You basically want to switch between two moving-average filters,
>>>>>>> clearing the state of the unused one, and bringing it back to steady 
>>>>>>> state
>>>>>>> before switching it back in.
>>>>>>> In the case of an.ms_envelope_rect, the switching period can be
>>>>>>> anything greater than the rectangular-window length (which is the "warm 
>>>>>>> up
>>>>>>> time" of the moving-average filter).
>>>>>>>
>>>>>>> Cheers,
>>>>>>> - Julius
>>>>>>>
>>>>>>> On Fri, Jul 9, 2021 at 10:49 AM Dario Sanfilippo <
>>>>>>> sanfilippo.da...@gmail.com> wrote:
>>>>>>>
>>>>>>>> Dear Julius, I just pulled and installed Faust 2.33.0.
>>>>>>>>
>>>>>>>> I'm running the test below on caqt and csvplot and I see the same
>>>>>>>> problem: when large inputs are fed in an.ms_envelope_rect, small
>>>>>>>> inputs are truncated to zero afterwards.
>>>>>>>>
>>>>>>>> import("stdfaust.lib");
>>>>>>>> zi = an.ms_envelope_rect(Tg);
>>>>>>>> slidingSum(n) = fi.pole(.999999) <: _, _@int(max(0,n)) :> -;
>>>>>>>> slidingMean(n) = slidingSum(n)/rint(n);
>>>>>>>> zi_leaky(x) = slidingMean(Tg*ma.SR, x * x);
>>>>>>>> lp1p(cf, x) = fi.pole(b, x * (1 - b))
>>>>>>>> with {
>>>>>>>> b = exp(-2 * ma.PI * cf / ma.SR);
>>>>>>>> };
>>>>>>>> zi_lp(x) = lp1p(1 / Tg, x * x);
>>>>>>>> Tg = 0.4;
>>>>>>>> sig = no.noise * ba.if(ba.time > ma.SR * 2, .01, 1.0);
>>>>>>>> process = sig <: zi , zi_leaky , zi_lp , ba.time;
>>>>>>>>
>>>>>>>> I'll look into TIIR filters or have you already implemented those
>>>>>>>> in Faust?
>>>>>>>>
>>>>>>>> Ciao,
>>>>>>>> Dr Dario Sanfilippo
>>>>>>>> http://dariosanfilippo.com
>>>>>>>>
>>>>>>>>
>>>>>>>> On Thu, 8 Jul 2021 at 19:19, Julius Smith <julius.sm...@gmail.com>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>> Hi Dario,
>>>>>>>>>
>>>>>>>>> The problem seems to be architecture-dependent.  I am on a Mac
>>>>>>>>> (latest non-beta software) using faust2caqt.  What are you using?
>>>>>>>>>
>>>>>>>>> I do not see the "strange behavior" you describe.
>>>>>>>>>
>>>>>>>>> Your test looks good for me in faust2octave, with gain set to
>>>>>>>>> 0.01 (-40 dB, which triggers the display bug on my system).  In 
>>>>>>>>> Octave,
>>>>>>>>>  faustout(end,:) shows
>>>>>>>>>
>>>>>>>>>  -44.744  -44.968  -44.708
>>>>>>>>>
>>>>>>>>> which at first glance seems close enough for noise input and
>>>>>>>>> slightly different averaging windows.  Changing the signal to a 
>>>>>>>>> constant
>>>>>>>>> 0.01, I get
>>>>>>>>>
>>>>>>>>>  -39.994  -40.225  -40.000
>>>>>>>>>
>>>>>>>>> which is not too bad, but which should probably be sharpened up.
>>>>>>>>> The third value (zi_lp) is right on, of course.
>>>>>>>>>
>>>>>>>>> gain = 0.01; // hslider("Gain [unit:dB]",-70,-70,0,0.1) :
>>>>>>>>> ba.db2linear;
>>>>>>>>> sig = gain;  //sig = no.noise * gain;
>>>>>>>>>
>>>>>>>>> On Thu, Jul 8, 2021 at 3:53 AM Dario Sanfilippo <
>>>>>>>>> sanfilippo.da...@gmail.com> wrote:
>>>>>>>>>
>>>>>>>>>> Hi, Julius.
>>>>>>>>>>
>>>>>>>>>> I must be missing something, but I couldn't see the behaviour
>>>>>>>>>> that you described, that is, the gating behaviour happening only for 
>>>>>>>>>> the
>>>>>>>>>> display and not for the output.
>>>>>>>>>>
>>>>>>>>>> If a remove the hbargraph altogether, I can still see the
>>>>>>>>>> strange behaviour. Just so we're all on the same page, the strange
>>>>>>>>>> behaviour we're referring to is the fact that, after going back to 
>>>>>>>>>> low
>>>>>>>>>> input gains, the displayed levels are -inf instead of some low,
>>>>>>>>>> quantifiable ones, right?
>>>>>>>>>>
>>>>>>>>>> Using a leaky integrator makes the calculations rather
>>>>>>>>>> inaccurate. I'd say that, if one needs to use single-precision, 
>>>>>>>>>> averaging
>>>>>>>>>> with a one-pole lowpass would be best:
>>>>>>>>>>
>>>>>>>>>> import("stdfaust.lib");
>>>>>>>>>> zi = an.ms_envelope_rect(Tg);
>>>>>>>>>> slidingSum(n) = fi.pole(.999999) <: _, _@int(max(0,n)) :> -;
>>>>>>>>>> slidingMean(n) = slidingSum(n)/rint(n);
>>>>>>>>>> zi_leaky(x) = slidingMean(Tg*ma.SR, x * x);
>>>>>>>>>> lp1p(cf, x) = fi.pole(b, x * (1 - b))
>>>>>>>>>> with {
>>>>>>>>>> b = exp(-2 * ma.PI * cf / ma.SR);
>>>>>>>>>> };
>>>>>>>>>> zi_lp(x) = lp1p(1 / Tg, x * x);
>>>>>>>>>> Tg = 0.4;
>>>>>>>>>> sig = no.noise * gain;
>>>>>>>>>> gain = hslider("Gain [unit:dB]",-70,-70,0,0.1) : ba.db2linear;
>>>>>>>>>> level = ba.linear2db : *(0.5);
>>>>>>>>>> process = sig <: level(zi) , level(zi_leaky) , level(zi_lp);
>>>>>>>>>>
>>>>>>>>>> Ciao,
>>>>>>>>>> Dr Dario Sanfilippo
>>>>>>>>>> http://dariosanfilippo.com
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> On Thu, 8 Jul 2021 at 00:39, Julius Smith <julius.sm...@gmail.com>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>> > I think that the problem is in an.ms_envelope_rect,
>>>>>>>>>>> particularly the fact that it has a non-leaky integrator. I assume 
>>>>>>>>>>> that
>>>>>>>>>>> when large values recirculate in the integrator, the smaller ones, 
>>>>>>>>>>> after
>>>>>>>>>>> pushing the gain down, are truncated to 0 due to single-precision. 
>>>>>>>>>>> As a
>>>>>>>>>>> matter of fact, compiling the code in double precision looks fine 
>>>>>>>>>>> here.
>>>>>>>>>>>
>>>>>>>>>>> I just took a look and see that it's essentially based on + ~ _
>>>>>>>>>>> : (_ - @(rectWindowLenthSamples))
>>>>>>>>>>> This will indeed suffer from a growing roundoff error variance
>>>>>>>>>>> over time (typically linear growth).
>>>>>>>>>>> However, I do not see any noticeable effects of this in my
>>>>>>>>>>> testing thus far.
>>>>>>>>>>> To address this properly, we should be using TIIR filtering
>>>>>>>>>>> principles ("Truncated IIR"), in which two such units pingpong and
>>>>>>>>>>> alternately reset.
>>>>>>>>>>> Alternatively, a small exponential decay can be added: + ~
>>>>>>>>>>> *(0.999999) ... etc.
>>>>>>>>>>>
>>>>>>>>>>> - Julius
>>>>>>>>>>>
>>>>>>>>>>> On Wed, Jul 7, 2021 at 12:32 PM Dario Sanfilippo <
>>>>>>>>>>> sanfilippo.da...@gmail.com> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> I think that the problem is in an.ms_envelope_rect,
>>>>>>>>>>>> particularly the fact that it has a non-leaky integrator. I assume 
>>>>>>>>>>>> that
>>>>>>>>>>>> when large values recirculate in the integrator, the smaller ones, 
>>>>>>>>>>>> after
>>>>>>>>>>>> pushing the gain down, are truncated to 0 due to single-precision. 
>>>>>>>>>>>> As a
>>>>>>>>>>>> matter of fact, compiling the code in double precision looks fine 
>>>>>>>>>>>> here.
>>>>>>>>>>>>
>>>>>>>>>>>> Ciao,
>>>>>>>>>>>> Dr Dario Sanfilippo
>>>>>>>>>>>> http://dariosanfilippo.com
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> On Wed, 7 Jul 2021 at 19:25, Stéphane Letz <l...@grame.fr>
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> « hargraph seems to have some kind of a gate in it that kicks
>>>>>>>>>>>>> in around -35 dB. » humm…. hargraph/vbargrah only keep the last 
>>>>>>>>>>>>> value of
>>>>>>>>>>>>> their written FAUSTFLOAT* zone, so once per block, without any 
>>>>>>>>>>>>> processing
>>>>>>>>>>>>> of course…
>>>>>>>>>>>>>
>>>>>>>>>>>>> Have you looked at the produce C++ code?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Stéphane
>>>>>>>>>>>>>
>>>>>>>>>>>>> > Le 7 juil. 2021 à 18:31, Julius Smith <
>>>>>>>>>>>>> julius.sm...@gmail.com> a écrit :
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > That is strange - hbargraph seems to have some kind of a
>>>>>>>>>>>>> gate in it that kicks in around -35 dB.
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > In this modified version, you can hear that the sound is ok:
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > import("stdfaust.lib");
>>>>>>>>>>>>> > Tg = 0.4;
>>>>>>>>>>>>> > zi = an.ms_envelope_rect(Tg);
>>>>>>>>>>>>> > gain = hslider("Gain [unit:dB]",-10,-70,0,0.1) :
>>>>>>>>>>>>> ba.db2linear;
>>>>>>>>>>>>> > sig = no.noise * gain;
>>>>>>>>>>>>> > process = attach(sig, (sig : zi : ba.linear2db : *(0.5) :
>>>>>>>>>>>>> hbargraph("test",-70,0)));
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > On Wed, Jul 7, 2021 at 12:59 AM Klaus Scheuermann <
>>>>>>>>>>>>> kla...@posteo.de> wrote:
>>>>>>>>>>>>> > Hi all,
>>>>>>>>>>>>> > I did some testing and
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > an.ms_envelope_rect()
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > seems to show some strange behaviour (at least to me). Here
>>>>>>>>>>>>> is a video
>>>>>>>>>>>>> > of the test:
>>>>>>>>>>>>> > https://cloud.4ohm.de/s/64caEPBqxXeRMt5
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > The audio is white noise and the testing code is:
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > import("stdfaust.lib");
>>>>>>>>>>>>> > Tg = 0.4;
>>>>>>>>>>>>> > zi = an.ms_envelope_rect(Tg);
>>>>>>>>>>>>> > process = _ : zi : ba.linear2db : hbargraph("test",-95,0);
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > Could you please verify?
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > Thanks, Klaus
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > On 05.07.21 20:16, Julius Smith wrote:
>>>>>>>>>>>>> > > Hmmm, '!' means "block the signal", but attach should save
>>>>>>>>>>>>> the bargraph
>>>>>>>>>>>>> > > from being optimized away as a result.  Maybe I
>>>>>>>>>>>>> misremembered the
>>>>>>>>>>>>> > > argument order to attach?  While it's very simple in
>>>>>>>>>>>>> concept, it can be
>>>>>>>>>>>>> > > confusing in practice.
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > > I chose not to have a gate at all, but you can grab one
>>>>>>>>>>>>> from
>>>>>>>>>>>>> > > misceffects.lib if you like.  Low volume should not give
>>>>>>>>>>>>> -infinity,
>>>>>>>>>>>>> > > that's a bug, but zero should, and zero should become MIN
>>>>>>>>>>>>> as I mentioned
>>>>>>>>>>>>> > > so -infinity should never happen.
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > > Cheers,
>>>>>>>>>>>>> > > Julius
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > > On Mon, Jul 5, 2021 at 10:39 AM Klaus Scheuermann <
>>>>>>>>>>>>> kla...@posteo.de
>>>>>>>>>>>>> > > <mailto:kla...@posteo.de>> wrote:
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     Cheers Julius,
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     At least I understood the 'attach' primitive now ;)
>>>>>>>>>>>>> Thanks.
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     This does not show any meter here...
>>>>>>>>>>>>> > >     process(x,y) = x,y <: (_,_), attach(x, (Lk2 :
>>>>>>>>>>>>> vbargraph("LUFS",-90,0)))
>>>>>>>>>>>>> > >     : _,_,!;
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     But this does for some reason (although the output is
>>>>>>>>>>>>> 3-channel then):
>>>>>>>>>>>>> > >     process(x,y) = x,y <: (_,_), attach(x, (Lk2 :
>>>>>>>>>>>>> vbargraph("LUFS",-90,0)))
>>>>>>>>>>>>> > >     : _,_,_;
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     What does the '!' do?
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     I still don't quite get the gating topic. In my
>>>>>>>>>>>>> understanding, the meter
>>>>>>>>>>>>> > >     should hold the current value if the input signal
>>>>>>>>>>>>> drops below a
>>>>>>>>>>>>> > >     threshold. In your version, the meter drops to
>>>>>>>>>>>>> -infinity when very low
>>>>>>>>>>>>> > >     volume content is played.
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     Which part of your code does the gating?
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     Many thanks,
>>>>>>>>>>>>> > >     Klaus
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >     On 05.07.21 18:06, Julius Smith wrote:
>>>>>>>>>>>>> > >     > Hi Klaus,
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > Yes, I agree the filters are close enough.  I bet
>>>>>>>>>>>>> that the shelf is
>>>>>>>>>>>>> > >     > exactly correct if we determined the exact
>>>>>>>>>>>>> transition frequency, and
>>>>>>>>>>>>> > >     > that the Butterworth highpass is close enough to the
>>>>>>>>>>>>> > >     Bessel-or-whatever
>>>>>>>>>>>>> > >     > that is inexplicably not specified as a filter type,
>>>>>>>>>>>>> leaving it
>>>>>>>>>>>>> > >     > sample-rate dependent.  I would bet large odds that
>>>>>>>>>>>>> the differences
>>>>>>>>>>>>> > >     > cannot be reliably detected in listening tests.
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > Yes, I just looked again, and there are "gating
>>>>>>>>>>>>> blocks" defined,
>>>>>>>>>>>>> > >     each Tg
>>>>>>>>>>>>> > >     > = 0.4 sec long, so that only ungated blocks are
>>>>>>>>>>>>> averaged to form a
>>>>>>>>>>>>> > >     > longer term level-estimate.  What I wrote gives a
>>>>>>>>>>>>> "sliding gating
>>>>>>>>>>>>> > >     > block", which can be lowpass filtered further,
>>>>>>>>>>>>> and/or gated, etc.
>>>>>>>>>>>>> > >     > Instead of a gate, I would simply replace 0 by
>>>>>>>>>>>>> ma.EPSILON so that the
>>>>>>>>>>>>> > >     > log always works (good for avoiding denormals as
>>>>>>>>>>>>> well).
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > I believe stereo is supposed to be handled like this:
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > Lk2 = _,0,_,0,0 : Lk5;
>>>>>>>>>>>>> > >     > process(x,y) = Lk2(x,y);
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > or
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > Lk2 = Lk(0),Lk(2) :> 10 * log10 : -(0.691);
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > but since the center channel is processed
>>>>>>>>>>>>> identically to left
>>>>>>>>>>>>> > >     and right,
>>>>>>>>>>>>> > >     > your solution also works.
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > Bypassing is normal Faust, e.g.,
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > process(x,y) = x,y <: (_,_), attach(x, (Lk2 :
>>>>>>>>>>>>> > >     vbargraph("LUFS",-90,0)))
>>>>>>>>>>>>> > >     > : _,_,!;
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > Cheers,
>>>>>>>>>>>>> > >     > Julius
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > On Mon, Jul 5, 2021 at 1:56 AM Klaus Scheuermann <
>>>>>>>>>>>>> kla...@posteo.de
>>>>>>>>>>>>> > >     <mailto:kla...@posteo.de>
>>>>>>>>>>>>> > >     > <mailto:kla...@posteo.de <mailto:kla...@posteo.de>>>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     > I can never resist these things!   Faust makes
>>>>>>>>>>>>> it too
>>>>>>>>>>>>> > >     enjoyable :-)
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     Glad you can't ;)
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     I understood you approximate the filters with
>>>>>>>>>>>>> standard faust
>>>>>>>>>>>>> > >     filters.
>>>>>>>>>>>>> > >     >     That is probably close enough for me :)
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     I also get the part with the sliding window
>>>>>>>>>>>>> envelope. If I
>>>>>>>>>>>>> > >     wanted to
>>>>>>>>>>>>> > >     >     make the meter follow slowlier, I would just
>>>>>>>>>>>>> widen the window
>>>>>>>>>>>>> > >     with Tg.
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     The 'gating' part I don't understand for lack of
>>>>>>>>>>>>> mathematical
>>>>>>>>>>>>> > >     knowledge,
>>>>>>>>>>>>> > >     >     but I suppose it is meant differently. When the
>>>>>>>>>>>>> input signal
>>>>>>>>>>>>> > >     falls below
>>>>>>>>>>>>> > >     >     the gate threshold, the meter should stay at the
>>>>>>>>>>>>> current
>>>>>>>>>>>>> > >     value, not drop
>>>>>>>>>>>>> > >     >     to -infinity, right? This is so 'silent' parts
>>>>>>>>>>>>> are not taken into
>>>>>>>>>>>>> > >     >     account.
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     If I wanted to make a stereo version it would be
>>>>>>>>>>>>> something like
>>>>>>>>>>>>> > >     >     this, right?
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     Lk2 = par(i,2, Lk(i)) :> 10 * log10 : -(0.691);
>>>>>>>>>>>>> > >     >     process = _,_ : Lk2 : vbargraph("LUFS",-90,0);
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     Probably very easy, but how do I attach this to
>>>>>>>>>>>>> a stereo
>>>>>>>>>>>>> > >     signal (passing
>>>>>>>>>>>>> > >     >     through the stereo signal)?
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     Thanks again!
>>>>>>>>>>>>> > >     >     Klaus
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > I made a pass, but there is a small scaling
>>>>>>>>>>>>> error.  I think
>>>>>>>>>>>>> > >     it can be
>>>>>>>>>>>>> > >     >     > fixed by reducing boostFreqHz until the
>>>>>>>>>>>>> sine_test is nailed.
>>>>>>>>>>>>> > >     >     > The highpass is close (and not a source of the
>>>>>>>>>>>>> scale error),
>>>>>>>>>>>>> > >     but I'm
>>>>>>>>>>>>> > >     >     > using Butterworth instead of whatever they
>>>>>>>>>>>>> used.
>>>>>>>>>>>>> > >     >     > I glossed over the discussion of "gating" in
>>>>>>>>>>>>> the spec, and
>>>>>>>>>>>>> > >     may have
>>>>>>>>>>>>> > >     >     > missed something important there, but
>>>>>>>>>>>>> > >     >     > I simply tried to make a sliding rectangular
>>>>>>>>>>>>> window, instead
>>>>>>>>>>>>> > >     of 75%
>>>>>>>>>>>>> > >     >     > overlap, etc.
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > If useful, let me know and I'll propose it for
>>>>>>>>>>>>> analyzers.lib!
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > Cheers,
>>>>>>>>>>>>> > >     >     > Julius
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > import("stdfaust.lib");
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > // Highpass:
>>>>>>>>>>>>> > >     >     > // At 48 kHz, this is the right highpass
>>>>>>>>>>>>> filter (maybe a
>>>>>>>>>>>>> > >     Bessel or
>>>>>>>>>>>>> > >     >     > Thiran filter?):
>>>>>>>>>>>>> > >     >     > A48kHz = ( /* 1.0, */ -1.99004745483398,
>>>>>>>>>>>>> 0.99007225036621);
>>>>>>>>>>>>> > >     >     > B48kHz = (1.0, -2.0, 1.0);
>>>>>>>>>>>>> > >     >     > highpass48kHz = fi.iir(B48kHz,A48kHz);
>>>>>>>>>>>>> > >     >     > highpass = fi.highpass(2, 40); // Butterworth
>>>>>>>>>>>>> highpass:
>>>>>>>>>>>>> > >     roll-off is a
>>>>>>>>>>>>> > >     >     > little too sharp
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > // High Shelf:
>>>>>>>>>>>>> > >     >     > boostDB = 4;
>>>>>>>>>>>>> > >     >     > boostFreqHz = 1430; // a little too high -
>>>>>>>>>>>>> they should give
>>>>>>>>>>>>> > >     us this!
>>>>>>>>>>>>> > >     >     > highshelf = fi.high_shelf(boostDB,
>>>>>>>>>>>>> boostFreqHz); // Looks
>>>>>>>>>>>>> > >     very close,
>>>>>>>>>>>>> > >     >     > but 1 kHz gain has to be nailed
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > kfilter = highshelf : highpass;
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > // Power sum:
>>>>>>>>>>>>> > >     >     > Tg = 0.4; // spec calls for 75% overlap of
>>>>>>>>>>>>> successive
>>>>>>>>>>>>> > >     rectangular
>>>>>>>>>>>>> > >     >     > windows - we're overlapping MUCH more (sliding
>>>>>>>>>>>>> window)
>>>>>>>>>>>>> > >     >     > zi = an.ms_envelope_rect(Tg); // mean square:
>>>>>>>>>>>>> average power =
>>>>>>>>>>>>> > >     >     energy/Tg
>>>>>>>>>>>>> > >     >     > = integral of squared signal / Tg
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > // Gain vector Gv = (GL,GR,GC,GLs,GRs):
>>>>>>>>>>>>> > >     >     > N = 5;
>>>>>>>>>>>>> > >     >     > Gv = (1, 1, 1, 1.41, 1.41); // left
>>>>>>>>>>>>> GL(-30deg), right GR
>>>>>>>>>>>>> > >     (30), center
>>>>>>>>>>>>> > >     >     > GC(0), left surround GLs(-110), right surr.
>>>>>>>>>>>>> GRs(110)
>>>>>>>>>>>>> > >     >     > G(i) = *(ba.take(i+1,Gv));
>>>>>>>>>>>>> > >     >     > Lk(i) = kfilter : zi : G(i); // one channel,
>>>>>>>>>>>>> before summing
>>>>>>>>>>>>> > >     and before
>>>>>>>>>>>>> > >     >     > taking dB and offsetting
>>>>>>>>>>>>> > >     >     > LkDB(i) = Lk(i) : 10 * log10 : -(0.691); //
>>>>>>>>>>>>> Use this for a mono
>>>>>>>>>>>>> > >     >     input signal
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > // Five-channel surround input:
>>>>>>>>>>>>> > >     >     > Lk5 = par(i,5,Lk(i)) :> 10 * log10 : -(0.691);
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > // sine_test = os.oscrs(1000); // should give
>>>>>>>>>>>>> –3.01 LKFS, with
>>>>>>>>>>>>> > >     >     > GL=GR=GC=1 (0dB) and GLs=GRs=1.41 (~1.5 dB)
>>>>>>>>>>>>> > >     >     > sine_test = os.osc(1000);
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > process = sine_test : LkDB(0); // should read
>>>>>>>>>>>>> -3.01 LKFS -
>>>>>>>>>>>>> > >     high-shelf
>>>>>>>>>>>>> > >     >     > gain at 1 kHz is critical
>>>>>>>>>>>>> > >     >     > // process = 0,sine_test,0,0,0 : Lk5; //
>>>>>>>>>>>>> should read -3.01
>>>>>>>>>>>>> > >     LKFS for
>>>>>>>>>>>>> > >     >     > left, center, and right
>>>>>>>>>>>>> > >     >     > // Highpass test: process = 1-1' <: highpass,
>>>>>>>>>>>>> highpass48kHz;
>>>>>>>>>>>>> > >     // fft in
>>>>>>>>>>>>> > >     >     > Octave
>>>>>>>>>>>>> > >     >     > // High shelf test: process = 1-1' :
>>>>>>>>>>>>> highshelf; // fft in Octave
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > On Sat, Jul 3, 2021 at 1:08 AM Klaus
>>>>>>>>>>>>> Scheuermann
>>>>>>>>>>>>> > >     <kla...@posteo.de <mailto:kla...@posteo.de>
>>>>>>>>>>>>> > >     >     <mailto:kla...@posteo.de <mailto:
>>>>>>>>>>>>> kla...@posteo.de>>
>>>>>>>>>>>>> > >     >     > <mailto:kla...@posteo.de <mailto:
>>>>>>>>>>>>> kla...@posteo.de>
>>>>>>>>>>>>> > >     <mailto:kla...@posteo.de <mailto:kla...@posteo.de>>>>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Hello everyone :)
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Would someone be up for helping me
>>>>>>>>>>>>> implement an LUFS
>>>>>>>>>>>>> > >     loudness
>>>>>>>>>>>>> > >     >     analyser
>>>>>>>>>>>>> > >     >     >     in faust?
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Or has someone done it already?
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     LUFS (aka LKFS) is becoming more and more
>>>>>>>>>>>>> the standard for
>>>>>>>>>>>>> > >     >     loudness
>>>>>>>>>>>>> > >     >     >     measurement in the audio industry.
>>>>>>>>>>>>> Youtube, Spotify and
>>>>>>>>>>>>> > >     broadcast
>>>>>>>>>>>>> > >     >     >     stations use the concept to normalize
>>>>>>>>>>>>> loudness. A very
>>>>>>>>>>>>> > >     >     positive side
>>>>>>>>>>>>> > >     >     >     effect is, that loudness-wars are
>>>>>>>>>>>>> basically over.
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     I looked into it, but my programming
>>>>>>>>>>>>> skills clearly
>>>>>>>>>>>>> > >     don't match
>>>>>>>>>>>>> > >     >     >     the level for implementing this.
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Here is some resource about the topic:
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     https://en.wikipedia.org/wiki/LKFS
>>>>>>>>>>>>> > >     <https://en.wikipedia.org/wiki/LKFS>
>>>>>>>>>>>>> > >     >     <https://en.wikipedia.org/wiki/LKFS
>>>>>>>>>>>>> > >     <https://en.wikipedia.org/wiki/LKFS>>
>>>>>>>>>>>>> > >     >     <https://en.wikipedia.org/wiki/LKFS
>>>>>>>>>>>>> > >     <https://en.wikipedia.org/wiki/LKFS>
>>>>>>>>>>>>> > >     >     <https://en.wikipedia.org/wiki/LKFS
>>>>>>>>>>>>> > >     <https://en.wikipedia.org/wiki/LKFS>>>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Specifications (in Annex 1):
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >      <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> >>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >       <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >      <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf
>>>>>>>>>>>>> >>>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     An implementation by 'klangfreund' in JUCE
>>>>>>>>>>>>> / C:
>>>>>>>>>>>>> > >     >     >     https://github.com/klangfreund/LUFSMeter
>>>>>>>>>>>>> > >     <https://github.com/klangfreund/LUFSMeter>
>>>>>>>>>>>>> > >     >     <https://github.com/klangfreund/LUFSMeter
>>>>>>>>>>>>> > >     <https://github.com/klangfreund/LUFSMeter>>
>>>>>>>>>>>>> > >     >     >     <https://github.com/klangfreund/LUFSMeter
>>>>>>>>>>>>> > >     <https://github.com/klangfreund/LUFSMeter>
>>>>>>>>>>>>> > >     >     <https://github.com/klangfreund/LUFSMeter
>>>>>>>>>>>>> > >     <https://github.com/klangfreund/LUFSMeter>>>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     There is also a free LUFS Meter in JS /
>>>>>>>>>>>>> Reaper by
>>>>>>>>>>>>> > >     Geraint Luff.
>>>>>>>>>>>>> > >     >     >     (The code can be seen in reaper, but I
>>>>>>>>>>>>> don't know if I
>>>>>>>>>>>>> > >     should
>>>>>>>>>>>>> > >     >     paste it
>>>>>>>>>>>>> > >     >     >     here.)
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Please let me know if you are up for it!
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >     Take care,
>>>>>>>>>>>>> > >     >     >     Klaus
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>>  _______________________________________________
>>>>>>>>>>>>> > >     >     >     Faudiostream-users mailing list
>>>>>>>>>>>>> > >     >     >     Faudiostream-users@lists.sourceforge.net
>>>>>>>>>>>>> > >     <mailto:Faudiostream-users@lists.sourceforge.net>
>>>>>>>>>>>>> > >     >     <mailto:Faudiostream-users@lists.sourceforge.net
>>>>>>>>>>>>> > >     <mailto:Faudiostream-users@lists.sourceforge.net>>
>>>>>>>>>>>>> > >     >     >     <mailto:
>>>>>>>>>>>>> Faudiostream-users@lists.sourceforge.net
>>>>>>>>>>>>> > >     <mailto:Faudiostream-users@lists.sourceforge.net>
>>>>>>>>>>>>> > >     >     <mailto:Faudiostream-users@lists.sourceforge.net
>>>>>>>>>>>>> > >     <mailto:Faudiostream-users@lists.sourceforge.net>>>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >      <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> >>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >       <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >      <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> > >     <
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>> >>>
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     >
>>>>>>>>>>>>> > >     >     > --
>>>>>>>>>>>>> > >     >     > "Anybody who knows all about nothing knows
>>>>>>>>>>>>> everything" --
>>>>>>>>>>>>> > >     Leonard
>>>>>>>>>>>>> > >     >     Susskind
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     >
>>>>>>>>>>>>> > >     > --
>>>>>>>>>>>>> > >     > "Anybody who knows all about nothing knows
>>>>>>>>>>>>> everything" -- Leonard
>>>>>>>>>>>>> > >     Susskind
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > >
>>>>>>>>>>>>> > > --
>>>>>>>>>>>>> > > "Anybody who knows all about nothing knows everything" --
>>>>>>>>>>>>> Leonard Susskind
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> > --
>>>>>>>>>>>>> > "Anybody who knows all about nothing knows everything" --
>>>>>>>>>>>>> Leonard Susskind
>>>>>>>>>>>>> > _______________________________________________
>>>>>>>>>>>>> > Faudiostream-users mailing list
>>>>>>>>>>>>> > Faudiostream-users@lists.sourceforge.net
>>>>>>>>>>>>> >
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>> Faudiostream-users mailing list
>>>>>>>>>>>>> Faudiostream-users@lists.sourceforge.net
>>>>>>>>>>>>> https://lists.sourceforge.net/lists/listinfo/faudiostream-users
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>> "Anybody who knows all about nothing knows everything" --
>>>>>>>>>>> Leonard Susskind
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> "Anybody who knows all about nothing knows everything" -- Leonard
>>>>>>>>> Susskind
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> "Anybody who knows all about nothing knows everything" -- Leonard
>>>>>>> Susskind
>>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> "Anybody who knows all about nothing knows everything" -- Leonard
>>>>>> Susskind
>>>>>>
>>>>>
>>>>
>>>> --
>>>> "Anybody who knows all about nothing knows everything" -- Leonard
>>>> Susskind
>>>>
>>>
>>
>> --
>> "Anybody who knows all about nothing knows everything" -- Leonard Susskind
>>
>

-- 
"Anybody who knows all about nothing knows everything" -- Leonard Susskind
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