Appendix G, Image.Layer modes

The variables in the expression:

L

The active layer

S

The source layer (the sum of the layers below)

D

The destintion layer (the result)

Xrgb

Layer red (Xr), green (Xg) or blue channel (Xb)

Xhsv

Layer hue (Xh), saturation (Xs) or value channel (Xv) (virtual channels)

aX

Layer alpha, channel in layer alpha

top layer
bottom layer
normal		D=(L*aL+S*(1-aL)*aS) / (aL+(1-aL)*aS), aD=(aL+(1-aL)*aS)
add		D=L+S, apply alpha as "normal" mode
subtract		D=L-S, apply alpha as "normal" mode
multiply		D=L*S, apply alpha as "normal" mode
divide		D=L/S, apply alpha as "normal" mode
modulo		D=L%S, apply alpha as "normal" mode
invsubtract		D=S-L, apply alpha as "normal" mode
invdivide		D=S/L, apply alpha as "normal" mode
invmodulo		D=S%L, apply alpha as "normal" mode
difference		D=abs(L-S), apply alpha as "normal" mode
max		D=max(L,S), apply alpha as "normal" mode
min		D=min(L,S), apply alpha as "normal" mode
bitwise_and		D=L&S, apply alpha as "normal" mode
bitwise_or		D=L|S, apply alpha as "normal" mode
bitwise_xor		D=L^S, apply alpha as "normal" mode
replace		D=(L*aL+S*(1-aL)*aS) / (aL+(1-aL)*aS), aD=aS
red		Dr=(Lr*aLr+Sr*(1-aLr)*aSr) / (aLr+(1-aLr)*aSr), Dgb=Sgb, aD=aS
green		Dg=(Lg*aLg+Sg*(1-aLg)*aSg) / (aLg+(1-aLg)*aSg), Drb=Srb, aD=aS
blue		Db=(Lb*aLb+Sb*(1-aLb)*aSb) / (aLb+(1-aLb)*aSb), Drg=Srg, aD=aS
replace_hsv		Dhsv=(Lhsv*aLrgb+Shsv*(1-aLrgb)*aSrgb) / (aLrgb+(1-aLrgb)*aSrgb), aD=aS
hue		Dh=(Lh*aLr+Sh*(1-aLr)*aSr) / (aLr+(1-aLr)*aSr), Dsv=Lsv, aD=aS
saturation		Ds=(Ls*aLg+Ss*(1-aLg)*aSg) / (aLg+(1-aLg)*aSg), Dhv=Lhv, aD=aS
value		Dv=(Lv*aLb+Sv*(1-aLb)*aSb) / (aLb+(1-aLb)*aSb), Dhs=Lhs, aD=aS
color		Dhs=(Lhs*aLrg+Shs*(1-aLrg)*aSrg) / (aLrg+(1-aLrg)*aSrg), Dv=Lv, aD=aS
darken		Dv=min(Lv,Sv), Dhs=Lhs, aD=aS
lighten		Dv=max(Lv,Sv), Dhs=Lhs, aD=aS
saturate		Ds=max(Ls,Ss), Dhv=Lhv, aD=aS
desaturate		Ds=min(Ls,Ss), Dhv=Lhv, aD=aS
dissolve		i=random 0 or 1, D=i?L:S, aD=i+aS
behind		D=(S*aS+L*(1-aS)*aL) / (aS+(1-aS)*aL), aD=(aS+(1-aS)*aL); simply swap S and L
erase		D=S, aD=aS*(1-aL)
screen		1-(1-S)*(1-L), apply alpha as "normal"
overlay		(1-(1-a)*(1-b)-a*b)*a+a*b, apply alpha as "normal"
burn_alpha		aD=aL+aS, D=L+S; experimental, may change or be removed
equal		each channel D=max if L==S, 0 otherwise, apply with alpha
not_equal		each channel D=max if L!=S, 0 otherwise, apply with alpha
less		each channel D=max if L<S, 0 otherwise, apply with alpha
more		each channel D=max if L>S, 0 otherwise, apply with alpha
less_or_equal		each channel D=max if L<=S, 0 otherwise, apply with alpha
more_or_equal		each channel D=max if L>=S, 0 otherwise, apply with alpha
logic_equal		logic: D=white and opaque if L==S, black and transparent otherwise
logic_not_equal		logic: D=white and opaque if any L!=S, black and transparent otherwise
logic_strict_less		logic: D=white and opaque if all L<S, black and transparent otherwise
logic_strict_more		logic: D=white and opaque if all L>S, black and transparent otherwise
logic_strict_less_equal		logic: D=white and opaque if all L<=L, black and transparent otherwise
logic_strict_more_equal		logic: D=white and opaque if all L>=L, black and transparent otherwise