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color burn mode

Description:
This mode is some kind of inverted screen mode (the multiplication is replaced by a division of the "inverse").

Formula:
f(a,b) = 1 - (1 - a) / b

Disadvantage:
The formula can result in values smaller than 0, so some truncation can occur.

Code:

if b = 0 then
  result := 0
else begin
  c := 255 - (((255-a) SHL 8) DIV b);
  if c < 0 then result := 0 else result := c;
end;

inverse color burn mode

Description:
I've never seen this mode anywhere, probably because it is the same than color burn mode, but base color and blend color are swapped (diagram 2 equals "flipped screen mode").

Formula:
f(a,b) = 1 - (1 - b) / a

Disadvantage:
The formula can result in values smaller than 0, so some truncation can occur.

Code:

if a = 0 then
  result := 0
else begin
  c := 255 - (((255-b) SHL 8) DIV a);
  if c < 0 then result := 0 else result := c;
end;

soft burn mode

Description:
This mode is a combination of color burn and inverse color dodge mode, but a lot smoother than both of them. The base image is lightened a bit, but very dark blend colors are "burned" in. I chose this name, because my aim was to make the color burn mode softer.

Formula:

f(a,b) =	½b / (1 - a) (for a + b < 1)
	1 - ½(1 - a) / b (else)

Disadvantages:
The formula can result in values smaller than 0 or greater than 255, so some truncation can occur (but not as extreme as for color burn).
There are two separate formulas (but no real discontinuance).

Code:

if a+b < 256 then begin
  if a = 255 then
    Result := 255
  else begin
    c := (b SHL 7) DIV (255-a);
    if c > 255 then Result := 255 else Result := c;
  end;
end
else begin
  // b cannot be zero here
  c := 255-(((255-a) SHL 7) DIV b);
  if c < 0 then Result := 0 else Result := c;
end;

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