Advanced blend mode fallback shaders are wrong once < 1 alphas are involved

overlay

uniform sampler2D base_layer;
uniform sampler2D blend_layer;
void main() {
    vec4 base = texture2D( base_layer, uv_coords );
    if (base.a != 0.0) base.rgb /= base.a; else base = vec4(0.0);
    vec4 blend = texture2D( blend_layer, uv_coords );
    if (blend.a != 0.0) blend.rgb /= blend.a; else blend = vec4(0.0);
    vec4 res = vec4(0.0);
    float p0 = base.a * blend.a; float p1 = base.a * (1 - blend.a); float p2 = blend.a * (1 - base.a);
    res.a = p0 + p1 + p2;
    // overlay = 2 * bottom * top if bottom < 0.5, 1 - 2 * (1 - bottom) * (1 - top) otherwise
    float f_rs_rd = (base.r < 0.5 ? (2.0 * base.r * blend.r) : (1.0 - 2.0 * (1.0 - base.r) * (1.0 - blend.r)));
    float f_gs_gd = (base.g < 0.5 ? (2.0 * base.g * blend.g) : (1.0 - 2.0 * (1.0 - base.g) * (1.0 - blend.g)));
    float f_bs_bd = (base.b < 0.5 ? (2.0 * base.b * blend.b) : (1.0 - 2.0 * (1.0 - base.b) * (1.0 - blend.b)));
    res.r = f_rs_rd * p0 + base.r * p1 + blend.r * p2;
    res.g = f_gs_gd * p0 + base.g * p1 + blend.g * p2;
    res.b = f_bs_bd * p0 + base.b * p1 + blend.b * p2;
    fragOutput = vec4(res.rgb * res.a, res.a);
}

color burn

uniform sampler2D base_layer;
uniform sampler2D blend_layer;
void main() {
    vec4 base = texture2D( base_layer, uv_coords );
    if (base.a != 0.0) base.rgb /= base.a; else base = vec4(0.0);
    vec4 blend = texture2D( blend_layer, uv_coords );
    if (blend.a != 0.0) blend.rgb /= blend.a; else blend = vec4(0.0);
    vec4 res = vec4(0.0);
    float p0 = base.a * blend.a; float p1 = base.a * (1 - blend.a); float p2 = blend.a * (1 - base.a);
    res.a = p0 + p1 + p2;
    // color burn = invert the bottom layer, divide it by the top layer, then invert
    float f_rs_rd = ((base.r == 1.0) ? 1.0 : (blend.r == 0.0) ? 0.0 : 1.0 - min(1.0, ((1.0 - base.r) / blend.r)));
    float f_gs_gd = ((base.g == 1.0) ? 1.0 : (blend.g == 0.0) ? 0.0 : 1.0 - min(1.0, ((1.0 - base.g) / blend.g)));
    float f_bs_bd = ((base.b == 1.0) ? 1.0 : (blend.b == 0.0) ? 0.0 : 1.0 - min(1.0, ((1.0 - base.b) / blend.b)));
    res.r = f_rs_rd * p0 + base.r * p1 + blend.r * p2;
    res.g = f_gs_gd * p0 + base.g * p1 + blend.g * p2;
    res.b = f_bs_bd * p0 + base.b * p1 + blend.b * p2;
    fragOutput = vec4(res.rgb * res.a, res.a);
}

color dodge

uniform sampler2D base_layer;
uniform sampler2D blend_layer;
void main() {
    vec4 base = texture2D( base_layer, uv_coords );
    if (base.a != 0.0) base.rgb /= base.a; else base = vec4(0.0);
    vec4 blend = texture2D( blend_layer, uv_coords );
    if (blend.a != 0.0) blend.rgb /= blend.a; else blend = vec4(0.0);
    vec4 res = vec4(0.0);
    float p0 = base.a * blend.a; float p1 = base.a * (1 - blend.a); float p2 = blend.a * (1 - base.a);
    res.a = p0 + p1 + p2;
    // color dodge = divide bottom layer by inverted top layer
    float f_rs_rd = ((base.r == 0.0) ? 0.0 : (blend.r == 1.0) ? 1.0 : min(base.r / (1.0 - blend.r), 1.0));
    float f_gs_gd = ((base.g == 0.0) ? 0.0 : (blend.g == 1.0) ? 1.0 : min(base.g / (1.0 - blend.g), 1.0));
    float f_bs_bd = ((base.b == 0.0) ? 0.0 : (blend.b == 1.0) ? 1.0 : min(base.b / (1.0 - blend.b), 1.0));
    res.r = f_rs_rd * p0 + base.r * p1 + blend.r * p2;
    res.g = f_gs_gd * p0 + base.g * p1 + blend.g * p2;
    res.b = f_bs_bd * p0 + base.b * p1 + blend.b * p2;
    fragOutput = vec4(res.rgb * res.a, res.a);
}