32 Bit Float Explained

[antcollinet]

Or six engines of the SpaceX Starship Gaussian explosion generators. I know that sounds completely off topic and irrelevant. Or bottom eight bits of mRNA vaccine side effects unimportant because people are dying and that's the only data that matters. We've moved from GIGO to MAPA--I make up here, on the fly, "Memory Added, Progress Achieved". No one worries as more and more carbon is released into the atmosphere because we'll learn how to program a device with "Quantum Mechanics 1,024 Terabyte Quadra Phase, Duel Linear, Multi-Variate Memory" (or whatever they'll market it as) that will remove C02 digitally from the planet.

I smirk a little when people say we (say my wife) notice a difference between 8-bit and 16-bit audio. I roll my eyes at 24-bit vs 16-bit. At 32-bit--I get scared. When society gets detached from reality people end up burned at the stake. Again, I go off topic. Then again, I don't think I could be any more ON TOPIC for some of us here.

I'm reading that and just blinking with a bemused look on my face.

Sorry - it might just be me - but I have not even a tiny clue what point it is you are trying to make - especially the first paragraph.

 

[AnalogSteph]

Given the discussion in this thread, it seems that it would be good if Amir could use the ASIO drivers to enable 32-bit capture for his testing?

The device is rated at 142 dB(A), so theoretically 24/48 should be just about sufficient, and by 24/96 one should definitely be in the clear. Still, it would be one less worry.

One potential problem I see is that I don't think the AP has low enough output noise to cover the low end accurately... its output impedance is like 600 ohms if memory serves, that's -124.9 dBu at 295 K right there. (As opposed to -128 dBu EIN with a 150 ohm source.)

 

[maxotics]

tiny clue what point it is you are trying to make

Trying to keep is somewhat audio related. I'm 62. When I first started working in audio everything was analog. I understood that you used various materials to register the change in sound pressure to changes in electric currents and from there to changes in magnetic particles (tape) or vinyl grooves--and then back again to listen. Distortion and noise were as big problems then as they are now. But we understood them as problems of MATERIAL, actual physics. That is, you couldn't run a current through a vacuum tube say, at any rate you wanted, without the current losing its original properties--becoming distorted. Or from adding noise due to the electrons from the friction (heat). Etc, etc.

When it was possible to store these changes in a digital format we realized we had to deal with the same problems in the digital space. Problems of quantization. Problems of data transmission errors, etc.

Most people (younger) no longer think about distortion and noise as a limitation of the materials used, the physics. Sure, theoretically, mathematically,128-bit fixed memory has less quantization errors than 16-bit memory. But that doesn't solve the analog problems--which never went away. My rant is based on the general cultural worship of digital technology. A cultural ignorance of analog (physical) constraints. Does that explain it better. Or have I made it worse!

 

[maxotics]

Given the discussion in this thread, it seems that it would be good if Amir could use the ASIO drivers to enable 32-bit capture for his testing?

I just posed a video why I believe Amir would find this a uninformed request. Any comments about the video--especially if I'm WRONG, would be greatly appreciated.

 

[antcollinet]

Trying to keep is somewhat audio related. I'm 62. When I first started working in audio everything was analog. I understood that you used various materials to register the change in sound pressure to changes in electric currents and from there to changes in magnetic particles (tape) or vinyl grooves--and then back again to listen. Distortion and noise were as big problems then as they are now. But we understood them as problems of MATERIAL, actual physics. That is, you couldn't run a current through a vacuum tube say, at any rate you wanted, without the current losing its original properties--becoming distorted. Or from adding noise due to the electrons from the friction (heat). Etc, etc.

When it was possible to store these changes in a digital format we realized we had to deal with the same problems in the digital space. Problems of quantization. Problems of data transmission errors, etc.

Most people (younger) no longer think about distortion and noise as a limitation of the materials used, the physics. Sure, theoretically, mathematically,128-bit fixed memory has less quantization errors than 16-bit memory. But that doesn't solve the analog problems--which never went away. My rant is based on the general cultural worship of digital technology. A cultural ignorance of analog (physical) constraints. Does that explain it better. Or have I made it worse!

Yes, thanks.

Still baffled by your first version though

 

[BeerBear]

I sent my MixPre3-II to @amirm for testing.

Great, I can't wait to see the results!

Given the discussion in this thread, it seems that it would be good if Amir could use the ASIO drivers to enable 32-bit capture for his testing?

If the combined ADCs' output is scaled in such a way that it inevitably hits 0dBFS at high inputs (see this post), then using 32bit floating point is necessary to prevent clipping.
But if the that scaling is user configurable and clipping can be avoided, 24bit integer is probably enough, since the 142db(A) should fit inside 24bit.
Using 32bit float doesn't hurt anyway.

One potential problem I see is that I don't think the AP has low enough output noise to cover the low end accurately... its output impedance is like 600 ohms if memory serves, that's -124.9 dBu at 295 K right there.

Yeah, if some of these devices perform as well as they claim, the AP could become the bottleneck. A good problem to have!

 

[antcollinet]

Great, I can't wait to see the results!

If the combined ADCs' output is scaled in such a way that it inevitably hits 0dBFS at high inputs (see this post), then using 32bit floating point is necessary to prevent clipping.
But if the that scaling is user configurable and clipping can be avoided, 24bit integer is probably enough, since the 142db(A) should fit inside 24bit.
Using 32bit float doesn't hurt anyway.


Yeah, if some of these devices perform as well as they claim, the AP could become the bottleneck. A good problem to have!

That's not going to work. There is no ADC that converts analogue directly to 32 bit float. If you hit clipping in the ADC, then subsequent conversion to float ain't gonna help.

 

[BeerBear]

There is no ADC that converts analogue directly to 32 bit float.

We're not talking about any one ADC here, but of multiple ADCs recording at different gains, combining their outputs into a single stream. Also known as gain-ranging. That's how (almost) all these 32bit float devices work internally. It's been mentioned since the first page.

 

[maxotics]

We're not talking about any one ADC here, but of multiple ADCs recording at different gains, combining their outputs into a single stream. Also known as gain-ranging. That's how (almost) all these 32bit float devices work internally. It's been mentioned since the first page.

I so do not get it. A microphone, for example, will output anywhere from 0 to 500mV. There is only one current. As soon as that current hits any kind of resistance it's going to degrade. In a sense, a pre-amp uses the resistance to modulate another (higher) current of electrons. In a one ADC world that 2nd current would be used to write bits to memory. Again, resistance is used to change the molecular structure of something that it can divert future currents based on it being a "0" or "1".

An ADC can ultimately only have one analog input and one digital output. If you have multiple ADCs you must, if I understand correctly, have multiple currents and if you're creating multiple currents from an original current you must do them in a serial fashion, right? Each time adulterating the source current through resistance. Or is there some quantum method for duplicating a current?

As for 32-bit float. I guess nothing I've said on YouTube or on Medium will convince you that it's only 24-bit rescaled and that rescaling, which is imprecise, provides no benefit if all your measurements of current never need more than 16,777,216 values.

 

[antcollinet]

We're not talking about any one ADC here, but of multiple ADCs recording at different gains, combining their outputs into a single stream. Also known as gain-ranging. That's how (almost) all these 32bit float devices work internally. It's been mentioned since the first page.

Right - but you are still going to be able to clip the ADC in the system with the highest gain. Again FP isn't going to help - or at least is of no benefit compared to a fixed point ADC with input gain control

 

[BeerBear]

I so do not get it.

There are explanations out there about how this works. Some in user manuals, some in patent documents, for example: https://patents.google.com/patent/US20210336629A1/en

As for 32-bit float. I guess nothing I've said on YouTube or on Medium will convince you that it's only 24-bit rescaled and that rescaling, which is imprecise, provides no benefit if all your measurements of current never need more than 16,777,216 values.

It does provide a visual/practical benefit, as I've explained already, also when replying to you.

or at least is of no benefit compared to a fixed point ADC with input gain control

Which is what I said in the previous post you quoted. But there are still at least potential practical benefits. I invite you too to re-read the thread, because it's been mentioned already and we're running in circles now.

 

[AnalogSteph]

Right - but you are still going to be able to clip the ADC in the system with the highest gain.

That is one of the bigger design challenges, aside from the whole DSP algorithms needed to combined both streams of course.

Now the transition tends to be at least 18 dB down. So I suspect that one could fit a limiter of sorts to that higher-gain leg without too much of an impact on distortion. It would have to be something that gives a nice sharp knee (maybe one of these precision clipper circuits or at least something Zener-based), and some RC filtering for the affected opamp's supplies may be advisable so nothing else is affected once it clips.

 

[maxotics]

There are explanations out there about how this works. Some in user manuals, some in patent documents, for example: https://patents.google.com/patent/US20210336629A1/en

Are you trying to wind me up That's a patent for a "measurement system" first of all. There is no mention of "float" anything. I'm not sure if the patent isn't just the work of a nutjob. I'm no expert in this area.

I don't feel you understand the fundamentals. I've already went through some. We can take multiple visual images, say, at different gains, and put them together. This is called HDR photography. The only problem is they are immediately recognized as artificial, not quite right, to most people--if not all. Theoretically, itsounds good. And certainly, I use this technique when I'm doing real estate photography for a friend, but I would never use such a technique in my normal photography. Our phone cameras already do it to an extent, and again, it's a certain "look", just like in audio, it would be a certain "sound."

I get the problem. Highlight roll-off, in videography, remains a real issue. They have dual ISO, etc. All these ways of trying to combine multiple amplifications or "gains". I haven't seen any of them work. That doesn't mean they won't in the future. But I believe, for the reasons I mentioned in the beginning, Mother Nature just won't allow it.

Another effort was the Foveon sensor. It figured out the red, green and blue component of light by detecting how far down the photons pass through a substance. Definitely a different look than Bayer Sensor cameras, But it required a LOT of light. So it failed. Similarly, I believe for any of these "multiple ADC" schemes (whatever that is) to work they would require a strong current to start. So your Shure SM7B or Electro-Voice RE20 (my fav) need not apply.

 

[maxotics]

It does provide a visual/practical benefit, as I've explained already, also when replying to you.

In my field if a software engineer said he picked a data type for the "visual" benefit he would get a big laugh, for sure! Not sure how long he would keep his job though!

 

[AnalogSteph]

Yes, it is an HDR problem. One that was first tackled 30 years ago:

https://worldradiohistory.com/Archive-All-Audio/Archive-Studio-Sound/90s/Studio-Sound-1995-03.pdf

4D goes to third generation
The Deutsche Grammophon Recording Centre has developed a third generation upgrade of the Stage Box system central to the 4D recording chain. All recordings made by the Recording Centre since October 1994 have used the new DG AD III technology, whose convertors feature the new Crystal CS5390 delta-sigma 20-bit A-D convertor ICs to provide 23-bit digital-floating delta-sigma A-D conversion.
The process employs two 20-bit convertors, one handling the input signal at unity gain and the other operated with 18dB gain. A sophisticated DSP algorithm regulates the crossfade between the two convertors, producing three bits of supplementary resolution. The DSP program was modified to allow the DSP chip to handle 20-bit convertors at its inputs and a 24-bit wordlength at its outputs.
Quoted specifications include THD+n of -121dBFs with an input of 997Hz at -30dBFs and linearity errors within 1dB down to -135dBFs, together with a largely flat noise-spectrum.
A further improvement is the development of the Authentic Clock Recovery system, permitting superior reconstruction of the master clock signal under real world operating conditions such as long cable runs and numerous interconnected PLLs, where phase modulation of the clock, jitter, becomes a limiting factor on overall system performance. Because Authentic Clock Recovery uses crystal PLLs driven at 512Fs, as opposed to the current 256Fs standard, A-D conversion at up to 96kHz is possible, with full oversampling capability.
Deutsche Grammophon, Germany. Tel: +49 4044 181115.

Other devices using a composite ADC topology include but are probably not limited to:
Sound Devices MixPre II series recorders
Zoom F6 recorder and UAC-232 audio interface
RØDE NT-1 5th generation XLR/USB microphone
Neumann MT 48 audio interface, and speaking of which,
Merging Technologies ANUBIS audio interface, AKDG8D/AKDG8DP cards for HORUS & HAPI modular audio interfaces
Weiss ADC2 A/D converter

It would be nice to see the measurements of the MT48 at some time.

https://www.neumann.com/globalassets/digizuite/39488-en-studiomagazin_06-2023_mt-48_en.pdf

(BTW - that's a composite ADC for $199.99 US. It's obviously not as clean as the MT48 by far.)

 

[maxotics]

Other devices using a composite ADC topology include but are probably not limited to

My contention is that if Sound Devices and Zoom are reducing high end distortion they're doing it through AGC. Has absolutely nothing to do with 32-bit float. In order to test this we'd have to see if they squish, say, a sine-tonish wave as the amplitudes increase. Since I can't seem to get anyone to learn enough 32-bit float to see why it doesn't increase fidelity what point that test? HAHA! Still, if you've seen something like that done I'd like to see it. Or, if I was going to test, what would you test the Zoom F6 against? Thanks!

PS. I just contacted Zoom, I submitted this support request:

In your audio description on Amazon you claim "32-bit float technology for distortion-free dynamic range" Since 32-bit float, in my understanding, is inherently distorted (imprecise), I'd like to know how this is possible before I buy your unit to test. I don't want to throw money away. Thanks!

 

[AnalogSteph]

 

[KSTR]

That is one of the bigger design challenges, aside from the whole DSP algorithms needed to combined both streams of course.

Now the transition tends to be at least 18 dB down. So I suspect that one could fit a limiter of sorts to that higher-gain leg without too much of an impact on distortion. It would have to be something that gives a nice sharp knee (maybe one of these precision clipper circuits or at least something Zener-based), and some RC filtering for the affected opamp's supplies may be advisable so nothing else is affected once it clips.

As I'm currently thinking about a stacking ADC application for a product, my 2ct.

Clipping control will be essential, you don't want to clip the ADC itself as that would likely give a slow recovery, a precision (low distortion) but very gradual soft clipper would be best, to avoid creating too much out-of-band HF very abruptly because you cannot apply a too aggressive analog low-pass filtering after the clipper.

Another thing is static and dynamic DC offsets. You have differing analog and ADC input offsets for the two (or N) paths that must be handled -- not too hard, though, the zero transitions of the different paths can be exploited for a ongoing runtime DC offset correction/matching. Any ADC internal highpass filters must be turned off because the clipped paths would be thrown off. Analog highpass filter and main anti-aliasing filter must be common and situated before the gain splitting as well, obviously.

Finally, at least 2x oversampling seems to be a good idea to have a steady enough sample stream even for highest target frequencies so that the dynamic crossfade is sufficiently robust, then down-sample the digital output after combination.

 

[KSTR]

My contention is that if Sound Devices and Zoom are reducing high end distortion they're doing it through AGC.

I do know AGC-based range extension is used in medical devices where the AGC control voltage is monitored with the second ADC channel so the original waveform can be reconstructed in the digital domain but I don't know whether this can be implemented well enough for high fidelity audio. It might be feasible for guitar effect pedals and similar where a short overload/clipping transient is tolerable.

 

[kchap]

Is 32 bit FP a technological cul de'sac?

OK, I watched a couple of YouTube videos and read a few web pages. My mathematics and engineering are very basic but I can accept that stacking ADCs can give an additional 2 or 3 bits of resolution and there may be advantages in using 32 bit FP.

Imagine a few years time when it is possible to build an ADC with 23 bits of resolution and by using stacking in conjunction with SOTA amp design, the resolution ban be extened to 25~26 bits. At that point you need to go to 32 bit integers or 64 bit FP.