Ah, when you read Sony Camera documents you often have to put on your
"video engineer" goggles. :)

Which camera are you using? We've done a few Sony camera
characterizations, and may have real data for the camera you're
interested in. F35, perhaps? In my experience, if you have the
luxury of actually running exposure sweeps on a camera you tend to get
much more plausible linearizations than by obeying manufacturer
claims. Sometimes it's a communication issue, but more often the
documentation fails to discriminate between the transform to get to a
scene referred linear (input space) vs an output referred linear
(display space).

Are you referring to this document for the formulas? (SRW_ITG_S-
Log_001_IO_EN.pdf) (google search: sony slog)

Assuming we trust the document for the moment, I think the rule of
thumb is understanding that whenever these guys talk about numbers
that include percentages (such as 0%, or 109%), these are video folks
talking in IRE land. (Ugh!) In the world of broadcast HD television
(rec709 with headroom), a "broadcast safe" black level is at 64/1023,
and safe white is 940/1023. Thus for folks in a broadcast-land
mindset, if you use the full 10-bit code range you're 'over white' by
(1023 / 940) = 1.09.

So when the document says "t has a range of 0 to 1.09", I take this to
mean that you're expected to have input 10-bit codevalues from 64 -
1023.
code 64 = t 0.0
code 1023 = t 1.09

In the later example "S-Log Formula" this is already taken into
account for you.
Y = 379.044 * log10(((x-128)/1752 + 0.037584) + 630
(This assumes 10-bit input, which in practice will only contain values
from 3-1019 due to HD link peculiarities, which you can safely ignore
in this case).

-- Jeremy