/// ColorBurn (a/aa, b/ba) =
/// 1. if (a==0 && b==ba): 1.
/// 2. if (a==0 && b!=ba): 0.
/// 3. if (a!=0): 1 - min (1, (1-b/ba) * (aa/a)).
///
/// color = a*(1-ba) + b*(1-aa) + aa*ba*ColorBurn(a/aa, b/ba) =
/// 1. a*(1-ba) + b*(1-aa) + aa*ba*1 = aa*(ba-b) + b.
/// 2. a*(1-ba) + b*(1-aa) + aa*ba*0 = b*(1-aa).
/// 3. a*(1-ba) + b*(1-aa) + aa*ba*(1 - min (1, (1-b/ba) * (aa/a))).
float
bm_color_burn (float a, float aa, float b, float ba)
{
    if (a==0) {
        if (b==ba)
            return aa*(ba-b) + b;
        else
            return b*(1-aa);
    } else
        return a*(1-ba) + b*(1-aa) +
               aa*ba * (1 - std::min (1.0f, (1 - b/ba)*(aa/a)));
}

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