exposure - Is analog gain really actually power-of-two only?

Context

I'm using a Nikon D5200, which features extra ISO values between powers of two, that the Nikon D60 did not offer.

• D60 offers 100, 200, 400, 800, 1600 (1-stop interval).


• D5200 offers two more values (1/3-stop interval) between each of the power-of-two that D60 provided: 100 / 125 / 160 / 200 / 250 / 320 / 400 / 500 / 640 / 800 / 1000 / 1250 / 1600 / 2000 / 2500 / 3200 / 4000 / 5000 / 6400 / 12800 / 25600

(I'm a seasoned StackExchange user and reasonably advanced amateur photographer. To avoid any misunderstanding one might want to see my profile).

ISO usually mean analog gain

As already documented, most of the time the difference between a photograph taken at e.g. ISO 200 and another at ISO 400, all other things being equal, is that an analog amplification gain is applied at the analog-to-digital conversion step. Sources: NX101 -- Capture NX - Understanding Nikon's NEF and How is ISO implemented in digital cameras?

Are all ISO values actual distinct analog gains ?

Recently a friend told me that only power-of-two ISOs are actually implemented with the analog gain, and that other values (like 250, 320) are actually digital post-processing and thus less interesting form a noise and dynamic range point-of-view. For example "shooting at 640 loses some information". There's a similar claim in learning - What is something you learned recently about your gear that you wish you discovered earlier?. It reads:

E.g. In-between stops (640 ISO for example) is a software push above ISO 400.

If only power-of-two ISOs were actual analog gains...

If ISO 640 was a software push above ISO 400, it would mean that ISO 640 does not gain any noise advantage over ISO 400, only possibly (depending on scene) losing by post-processing some highlights that would have been available at ISO 400. Or what else?

It could also be a software reduce from ISO 800, just like ISO 50 in Nikon D800 and D800E was a software reduce from ISO100, couldn't it ? (source: 24 Things You Need to Know About the New Nikon D810).

In that latter case, the noise at ISO 640 would be as good as in ISO 800 (all things being equal, better than ISO 400 as explained on What is "ISO" on a digital camera?) but reduction could just (depending on scene) not reach as much highlights as an actual ISO 800 (analog clipping). Or what else ?

Perhaps the actual processing is only "hinting" the post-processing (base curve, dynamic lighting and the like), producing a picture that actually has the overall exposure requested at 1/3-stop granularity, without actual hard loss. In that case, the RAWs actual exposure might jump only by power-of-two ISOs and not 1/3 steps. Such hypotheses could be corroborated by taking RAWs and JPEGs at all ISOs and see how they behave.

Or perhaps this is all nitpicking?

Question, summarized

• Is it true that analog gains are only power-of-two? In Nikon cameras? In others?


• Should one should prefer shooting with power-of-two ISOs only? Or only in certain cases (JPEG shooting, high dynamic range scenes, ...)?