Understanding brightness, contrast and saturation in Photoshop

In addition to all of the above, range analysis may not be straightforward if you left the Legacy option disabled in Brightness/Contrast. With Legacy off, those controls roll off near the ends of the ranges to avoid hard clipping, so some kind of curve is probably involved. With Legacy on, they work like the earliest versions of Photoshop where the transformation is (I think...) linear and will clip if overdriven.

The Camera Raw sliders have even more non-linear "smarts" built into them. In general you'll get the best answer if you can ask the engineers directly, but this is only a user-to-user forum.

I suggest you create control colour samples over a range, and apply Photoshop. By analysis and interpolation you may be able to get an approximation of what Photoshop does.

Adobe do do not give the info for you to create rival or compatible software so easily.

What are you talking about exactly – Adjustments, Camera Raw, …?

Only the developers will be able to tell you how those exact values "under the hood" and are applied to images in each colour mode and colour space. This is a user forum so is not monitored by developers.

Dave