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This stems from different HDR workflows that I know.

In Photoshop for example, you can merge multiple images to a single HDR file. As far as I remember, when you go for a 16-bit file you also pick one of the processes that makes everything look funky and colorful, i.e., tone mapping. In contrast to that, when you choose 32-bit, it just merges the images into a 32-bit file.

To me, that 32-bit workflow is what HDR is all about: creating one image that has a higher dynamic range. Getting that back into 8-bit files for display is a different story.

Why is there no such workflow available for 16-bit files? Is that just the way Photoshop is?

If there was an option to merge to 16-bit HDR, would that be the better choice? (Given the possibly smaller file size) When/why should one bit depth be chosen over the other?

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I happen to agree with you that the compositing of the High Range step of the image and tonemapping should be separate considerations and given separate terminology. Unfortunately that is not a definition that has fallen into common parlance and as such HDR is to most photographers a synonym for (frequently garish) tonemapping.

In adobe's way of thinking, it is compositing multiple 16-bit raw originals (even if in reality they are frequently only 12/14 bit depending on the camera) to make the HR composite which has to be higher than 16-bits in range. To save out back to 16 bit, the choice is data loss either by tonemapping or clipping.

For the 32 bit HDR format the Dynamic Range available in the output format exceeds the input format and so there is no need to tonemap to preserve detail.

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There's an important difference in 32 bit vs. 16 bit images (as applies to PS): A 32 bit HDR uses 32 bit floating point numbers for each colour channel, 16 and 8 bit image formats use integers. That has a huge impact on available dynamic range, HDR formats trade practically unlimited DR for precision. It's not just "2^16 vs 2^32 colours".

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    Photoshop also uses a linear gamma curve in 32-bit mode so you get more accurate blending.
    – Matt Grum
    Apr 22, 2015 at 13:03
  • A bit is a bit, you can still only represent 2^32 values in floating point because only 2^32 states can be represented...
    – James Snell
    Jun 27, 2018 at 21:16
  • @JamesSnell but they are not evenly spaced. they range from 2^-126 to 2^127. that defines the DR of the format. (i don't know if negative values are used)
    – ths
    Jun 28, 2018 at 6:29
  • @ths - If your storage is 32bit per colour then that's your DR. It's still only 2^32 as that is how many different values an IEEE754 float holds, that is true irrespective of the wider bounds that a float holds in decimal. 01110010 10100011 10110000 00100001 in memory is 6.48434987305284552130299533722 E30 as float or 1923330081 as unsigned integer - that's just how things are. You cannot magically invent representations where that are none.
    – James Snell
    Jun 30, 2018 at 23:41
  • DR is the ratio of highest to lowest value.
    – ths
    Jul 1, 2018 at 11:55
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You should choose a higher dynamic range (e.g. 32 vs 16 vs 8 bit) to maintain smooth variation in data. When you come to downsampling the data, you have control over how the values are filtered.

For photos, this generally means gradients. If you compress the data into 8 bits, there generally won't be enough "steps" in channel values to smoothly combine the tone gradients from the original images.

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