Following up on my action item from the previous meeting, here is a proposal for adding a Log operator to CLF that could be used for a variety of lin-to-log type transforms.

There are three classes of these transforms that I think we should support. First there is the basic logarithm. OCIO has this and it is regularly used (along with an affine transform) to create shaper transforms when needing to apply linear values to LUTs. Second, there is the classic Cineon type lin-to-log transform and the related Josh Pines type transform (the latter being similar to Cineon but is more fun at parties, also it handles blacks better!). These can be implemented as an affine transform (a multiply and add), followed by a logarithm, followed by another affine transform. Third, there is a Cineon type curve with the addition of a linear section near black. This handles most of the digital camera log curves including Alexa LogC (for typical EIs), Sony SLog3, Panasonic VLog, and Red Log3G10, as well as ACEScct.

So here is a rough proposal for an XML syntax that could represent these three types of log curves.

Basic logarithm examples (base 10 and 2 allowed):

```
<Log inBitDepth="16f" outBitDepth="12i" style="log10" />
<Log inBitDepth="12i" outBitDepth="16f" style="antiLog10" />
<Log inBitDepth="16f" outBitDepth="12i" style="log2" />
<Log inBitDepth="12i" outBitDepth="16f" style="antiLog2" />
```

Cineon style logarithm examples:

```
> <Log inBitDepth="32f" outBitDepth="10i" style="linToLog">
<LogParams gamma="0.6" refBlack=" 95." refWhite="685." highlight="1.0" shadow="0.0" />
</Log>
<Log inBitDepth="10i" outBitDepth="32f" style="logToLin">
<LogParams gamma="0.6" refBlack=" 95." refWhite="685." highlight="1.0" shadow="0.0" />
</Log>
```

If the parameters are different per channel, they may be expressed this way:

```
<LogParams channel="R" gamma="0.5" refWhite="681" refBlack="95" highlight="0.9" shadow="0.0045" />
<LogParams channel="G" gamma="0.6" refWhite="682" refBlack="94" highlight="1" shadow="0.0025" />
<LogParams channel="B" gamma="0.65" refWhite="683" refBlack="93" highlight="0.8" shadow="0.0035" />
```

In order to be more in line with OCIO, we should also allow specifying the LogParams as follows:

```
<Log inBitDepth="32f" outBitDepth="10i" style="linToLog">
<LogParams linSideSlope="1.0" linSideOffset="0.0" logSideSlope="1.0" logSideOffset="0.0" base="10.0" />
</Log>
```

The implied lin-to-log equation is:

`y = logSideSlope * log( linSideSlope * x + linSideOffset, base ) + logSideOffset;`

(If the traditional refBlack/refWhite/gamma syntax above is used, those parameters may be converted to utilize this same equation too.)

Finally, the Camera Log style transforms would be written as follows:

```
<Log inBitDepth="32f" outBitDepth="10i" style="cameraLinToLog">
<LogParams linSideSlope="1.0" linSideOffset="0.0" logSideSlope="1.0" logSideOffset="0.0" linSideBreak="0.0" linearGain="1.0" base="10.0" />
</Log>
<Log inBitDepth="10i" outBitDepth="32f" style="cameraLogToLin">
<LogParams linSideSlope="1.0" linSideOffset="0.0" logSideSlope="1.0" logSideOffset="0.0" linSideBreak="0.0" linearGain="1.0" base="10.0" />
</Log>
```

The implied lin-to-log equation is:

```
if (x <= linSideBreak)
y = x * linearGain + k;
else
y = logSideSlope * log( linSideSlope * x + linSideOffset, base ) + logSideOffset;
```

And where k is calculated so the two pieces are continuous at the break point. The linearGain parameter is optional. If it is missing, the default is to calculate it so that the two pieces are also continuous in slope (e.g., like ACEScct).

There are some details to be filled in such as more detailed pseudo-code and the details around bit-depth, and I could add these in a more formal proposal later if there is interest in proceeding. Also, there are some other log-like curves such as PQ and HLG that are not covered here. That said, hopefully the above will at least serve as a good strawman to continue the discussion.