Saving custom tone mappings

Question

I'm trying to save custom tone mapping curves for later reference and use.  I can record the "action" of constructing the curve in Image > Adjustments > Curves and applying it to an image.  Unfortunately the "actions" panel does an incomplete job of describing this.  Instead of reporting where all 16 control points were set, it reports the resulting first 72 of the 256 mappings, like so:
  emulate ektachrome
          Curves
          Preset Kind: Custom
          Adjustment: curves adjustment list
          curves adjustment
          Channel: composite channel
          Mapping: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, ...
The ellipsis is Photoshop's, not mine.
How to verify what's in an already created mapping curve "action"?  I can make a tone scale, apply the mapping to it, and then take RGB data off the result. There must be a simpler way than that.  Where are custom "actions" stored?  Can the files be read?  Can they be edited?
Also is there any way to input a tone mapping curve purely numerically and skip the control points business?
Thanks.

Answer 1

Thanks Zeno Bokor.  The hardest part was finding the actions panel menu!
Saving the action set did produce an .atn file, here attached.
It's hardly gibberish. Notepad shows how it works.  BinEditor 2.0 reveals it completely.
Look at what precedes the repeating word "long" (written 6C 6F 6E 67).  After 32 (written 20) comes 34 (written 22), then 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, ...
Note: I had to change the extension of the attachment for the Forum to accept it.  You can knock off the .txt.