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hard light mode
Description:
Another combination of screen and multiply mode, depending on the blend color (the "opposite" of overlay mode - NOT the "opposite" of soft light mode! - in fact the names of overlay mode and hard light mode should be swapped to be more logical).

Formula:
f(a,b) =  2ab (for b < ½)
1 - 2 * (1 - a) * (1 - b) (else)



Disadvantage:
There is a separate formula for bright and for dark blend colors, so there is a discontinuance for b = ½ (diagram 1 can be sparated into two parts).

Code:
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