Reference on Opacity variations in merging modes

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I found the algorithms of many merging mode 

BUT all the the formula there do not take opacity into account so as now the blending may be done only at 100% opacity
(btw is for a "blending filter" , that  allow to merge also in mode not available in Gimp 
 obviously the result, the output is the visible from the the merging as new layer )

I'm sure somewhere in the Gimp code or documentation there is the answer:
 how ,mathematically variation of opacity are taken into account, but i am really lost in front of page of codes and doc

could someone ( help me, pointing to a specific page or speciphic doc

Also i need help to find found the algorithms and doc on  modes as "erase" "color erase"" behind" (available for Edit/fade) and "grain extract" "grain merge" ?

Any help or pointer will be really appreciated

thank




      
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