[sdiy] Digital is more analog than analog... and it has 319 dB headroom...

cheater cheater cheater00social at gmail.com
Sun Mar 3 10:11:04 CET 2024

```Also, btw, I thought someone would catch that without it being
mentioned, but 300 dB isn't even the right number, even if we follow
the bizarro logic that the bozo in the video is following.

This is from the second link:

> Let’s forget about the decimal point for now, because that only
> scales a number up or down and has nothing to do with its
> accuracy. It’s the 53-bits that is important, so let’s get a feel for that.
> 53-bits represents a difference of 9,000,000,000,000,000:1. Yeah,
> that’s 9 quadrillion to one, from the smallest to the largest quantity,
> or a whopping, no, staggering, 319db

you heard that right. according to this clown, scaling a number up and
down doesn't have anything to do with how precise of a quantity you
can describe. You can describe a cup of sugar? and you can also
describe 1000 cups of sugar? Doesn't matter - 1000 cups of sugar are
just 1 scaled up by a thousand, so being able to describe 1 cup of
sugar isn't any more precise than being able to describe a sack of
sugar. according to Mark Barton, at least. enjoy your pancakes with a
full burlap sack of sugar dumped into the skillet.

in reality, that's not how floating point numbers work. they have the
ability to scale the significant by an exponent *exactly because* that
improves accuracy by orders of magnitude. specifically by 308 orders
of magnitude up, and 308 orders of magnitude down, so in total 616
orders of magnitude. without using the exponent field, the smallest
positive number you can describe with a float is
1.00000011920928955078125. with using the exponent field, the smallest
positive number you can describe is a 0, then a decimal point, then
307 zeros, then a two, and then some other digits. that's incredibly
more precise. the bozo in this video didn't do his basic research on
floating point numbers and now he's giving talking head interviews
about the topic. this guy can't even get his bullshit straight.

If you wanted to really calculate the "dynamic range" of floating
point numbers you would calculate it this way:

1. what is the smallest number representable as a 64-bit float?
answer: 2.2250738585072014*10^-308 (call that V1)

2. what is the largest number representable as a 64-bit float? answer:
1.7976931348623158*10^308 (call that V2)

3. calculate the ratio: V2 / V1 = 0.80792515178... * 10^616

4. convert to decibels: dB = 20 * log10 (V2 / V1) = 20 * log10
(0.80792515178 * 10^616) = 20 * (log10(0.80792515178) + log10 (10^616))
= 12318 dB.

Twelve thousand decibels of dynamic range. Another ridiculous number.
And that's BEFORE dithering. This shows you how insipid it is to even
think in this manner.

This hopefully brings the point that you shouldn't be talking about
what floating point numbers will or won't do unless you really *do*
know, have checked the technical references, have experience and
check your estimations at every step.

On Sun, Mar 3, 2024 at 8:53 AM cheater cheater
<cheater00social at gmail.com> wrote:
>
> > It DOES keep the noise and distortion from building up and becoming audible after dozens, hundreds, or even billions of MAC-type operations
>
> you're wrong. i can take a full scale 64 bit floating point signal and
> get you that noise and distortion in 1 multiplication, or even one
>
> i thought we were making fun of the disinformation, not stuffing it in
> a pipe and smoking it.
>
>
> On Sun, Mar 3, 2024 at 4:38 AM Ben Bradley via Synth-diy
> <synth-diy at synth-diy.org> wrote:
> >
> > The "300dB" dynamic range of "digital" totally misses the point. It
> > has nothing directly to do with DR. It DOES keep the noise and
> > distortion from building up and becoming audible after dozens,
> > hundreds, or even billions of MAC-type operations on each 64-bit
> > floating-point number. Surely he knows that, but it may be harder to
> > describe and is "less impressive" than the dynamic range of lots of
> > bits.
> >
> > On Sat, 2 Mar 2024 at 14:40, Gordonjcp <gordonjcp at gjcp.net> wrote:
> > >
> > > On Sat, Mar 02, 2024 at 08:19:29PM +0100, cheater cheater via Synth-diy wrote:
> > > > I'll leave this here:
> > > >
> > > > https://www.youtube.com/watch?v=kk-3vXOAtVo
> > > >
> > > > and supplementary material:
> > > >
> > > > https://cherryaudio.com/news/flashback-friday-mark-barton-on-analog-and-modern-digital-synthesis
> > > >
> > > > make sure to hit the bong extra hard before you look at any of that...
> > >
> > > As an exercise for the student, try to work out what sort of signal levels would be involved in "300dB signal to noise ratio".
> > >
> > > --
> > > Gordonjcp
> > >
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