besides the cases already covered with gamut mapping etc, you can also
get "negative" values due to uncertainty of where black is. Take for
example the case of a digital sensor in a camera, if you capture with
the lens cap on, noise will mean you will get a range of values about
a mean value, if this is value considered as 0 then there will be some
pixels where the value is less than zero, throwing away this by
clipping degrades the quality of the images.

on the subject of extending/extrapolating trc, one approach is to
mirror the function similar to Elle's suggestion using

temp = pow(abs(x))
out = copysign(temp, x)

this tends to be reasonable as it gives a continuous gradient.

Kevin

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