S-Log does not compress highlights more than regular gammas. Easily testable in Resolve. I use it to my advantage everyday.

Of course the scale is logarithmic, that's why it can allocate the bits evenly. Seriously, that is the only reason log gammas exist, to allow even bit distribution rather than reducing bit distribution in the highlights.
Regardless of what the numbers may tell you, I get more out of the highlights than I can get out the shadows.
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S-Log does not compress highlights more than regular gammas.

Then please explain how exactly do you fit an additional 3 stops of dynamic range into the same size file?

You only have to look at an ungraded S-Log scene to see the compression. S-Log looks flat because something that might be twice as bright as something else in the real world, only looks a little brighter after recording with S-Log because fewer bits are being used to differentiate one stop from the next compared to a standard gamma as a result the brighter stops are brought closer together, the contrast is reduced and the image looks flat. That is an effect of log compression.

The file size for an S-Log is exactly the same as it is with standard gammas (assuming the same codec/bit depth is used). Standard gammas give 9 stops, cinegammas 11.5 stops and S-Log 13 stops. In all cases there is no surplus or spare data, the file size does not change, so how do you think the engineers managed to squeeze 13 stops instead of the original 9 stops of a standard gamma into the same sized file? Answer: More compression. Do you compress the important mid range and skin tones or do you compress the highlights where people tend not to notice issues? Answer: Highlights. It turns out that if you use log based compression this works well as it follows the log response of the human visual system. But you MUST remember that the camera and the TV/Monitor are linear devices, it is only the bit in between that is log. So you record using log, but then have to convert that log back to linear (or at least a near linear standard power law gamma) in post to make it look right. So now what's going on with your brighter stops? Your taking your log sized 70ish bits per stop and expanding that to the required 200ish bits for the brightest stops. There's a shortfall of 130ish bits of data, data discarded during capture, lost picture information, but provided it's in the highlights it doesn't really matter as our own visual system won't notice highlight issues. Over expose while shooting however and then you can run into issues such as plastic looking skin etc.

If as you assert, log is not adding compression then there would be no need for linear raw. But if you have ever worked with linear data you will know exactly how much more picture information there is in the highlights in linear data than there is in log. You will know that with linear you can expose a face anywhere in the exposure range and provided it isn't clipped it will grade perfectly. This is definitely not the case with log and we have seen plenty of examples on this board of exactly this. Over expose a face and it can be very difficult to make it look nice. While you can grade the face to a normal levels, the skin looks odd if it's been over exposed, why? Because the extra compression in the higher stops means that you loose the subtle textures that make a face look real and not like plastic.

If you still think I'm wrong then you might want to read through Adam Wilts article on log http://provideocoalition.com/aadams/story/the_not_so_technical_guide_to_s_log_and_log_gamma_curves/P3

If you look at the plots in the Abel cine videos http://blog.abelcine.com/2011/08/04/f3-s-log-part-1-on-the-charts/ you will see that between 40ire and 104ire with Cinegamma one there are 4 stops, with S-Log there are 5.5 stops, so an extra 200% of dynamic range has been squeezed into the same space, the highlights must be more compressed to do this. Consider that compared to Rec-709, Cinegamma one already uses a lot of additional highlight compression and it should be plain to see that the S-log does use a lot of highlight compression. If you compare the gaps between the steps for a standard gamma plot (with the knee off) and S-log you will see the gaps between the brighter exposure steps are much much bigger with the standard gammas than S-log, because the S-log highlights are compressed, the compression bringing the steps closer together. It's only by bringing the steps closer together that you can make space for the additional stops of dynamic range.

Just a small aside, I recently bought one of these middle grey/ white flex cards and now it is easy to meter both grey and white by flipping the thing over. Folds up to about the size of an iPad mini.

Lastolite EzyBalance Gray Card LL LR1250 B&H Photo Video (http://www.bhphotovideo.com/bnh/controller/home?O=orderHistory&A=details&Q=&sku=330874&is=REG)