// textures
SAMPLER_BINDING(8) uniform sampler2D samp8;
SAMPLER_BINDING(9) uniform sampler2D samp9;

const int char_width = 8;
const int char_height = 13;
const int char_count = 95;
const int char_pixels = char_width*char_height;
const vec2 char_dim = vec2(char_width, char_height);
const vec2 font_scale = vec2(1.0/float(char_width)/float(char_count), 1.0/float(char_height));

out vec4 ocol0;
in vec2 uv0;

uniform vec4 resolution;

void main()
{
	vec2 char_pos = floor(uv0*resolution.xy/char_dim);
	vec2 pixel_offset = floor(uv0*resolution.xy) - char_pos*char_dim;

	// just a big number
	float mindiff = float(char_width*char_height) * 100.0;

	float minc = 0.0;
	vec4 mina = vec4(0.0, 0.0, 0.0, 0.0);
	vec4 minb = vec4(0.0, 0.0, 0.0, 0.0);

	for (int i=0; i<char_count; i++)
	{
		vec4 ff = vec4(0.0, 0.0, 0.0, 0.0);
		vec4 f = vec4(0.0, 0.0, 0.0, 0.0);
		vec4 ft = vec4(0.0, 0.0, 0.0, 0.0);
		vec4 t = vec4(0.0, 0.0, 0.0, 0.0);
		vec4 tt = vec4(0.0, 0.0, 0.0, 0.0);

		for (int x=0; x<char_width; x++)
		{
			for (int y=0; y<char_height; y++)
			{
				vec2 tex_pos = char_pos*char_dim + vec2(x,y) + 0.5;
				vec4 tex = texture(samp9, tex_pos * resolution.zw);

				vec2 font_pos = vec2(x+i*char_width, y) + 0.5;
				vec4 font = texture(samp8, font_pos * font_scale);

				// generates sum of texture and font and their squares
				ff += font*font;
				f += font;
				ft += font*tex;
				t += tex;
				tt += tex*tex;
			}
		}

		// The next lines are a bit harder, hf :-)

		// The idea is to find the perfect char with the perfect background color and the perfect font color.
		// As this is an equation with three unknowns, we can't just try all chars and color combinations.

		// As criterion how "perfect" the selection is, we compare the "mean squared error" of the resulted colors of all chars.
		// So, now the big issue: how to calculate the MSE without knowing the two colors ...

		// In the next steps, "a" is the font color, "b" is the background color, "f" is the font value at this pixel, "t" is the texture value

		// So the square error of one pixel is: 
		// e = ( t - a⋅f - b⋅(1-f) ) ^ 2

		// In longer:
		// e = a^2⋅f^2 - 2⋅a⋅b⋅f^2 + 2⋅a⋅b⋅f - 2⋅a⋅f⋅t + b^2⋅f^2 - 2⋅b^2⋅f + b^2 + 2⋅b⋅f⋅t - 2⋅b⋅t + t^2

		// The sum of all errors is: (as shortcut, ff,f,ft,t,tt are now the sums like declared above, sum(1) is the count of pixels)
		// sum(e) = a^2⋅ff - 2⋅a^2⋅ff + 2⋅a⋅b⋅f - 2⋅a⋅ft + b^2⋅ff - 2⋅b^2⋅f + b^2⋅sum(1) + 2⋅b⋅ft - 2⋅b⋅t + tt

		// To find the minimum, we have to derive this by "a" and "b":
		// d/da sum(e) = 2⋅a⋅ff + 2⋅b⋅f - 2⋅b⋅ff - 2⋅ft
		// d/db sum(e) = 2⋅a⋅f - 2⋅a⋅ff - 4⋅b⋅f + 2⋅b⋅ff + 2⋅b⋅sum(1) + 2⋅ft - 2⋅t

		// So, both equations must be zero at minimum and there is only one solution.

		vec4 a = (f*ft - ff*t + f*t - ft*float(char_pixels)) / (f*f  - ff*float(char_pixels));
		vec4 b = (f*ft - ff*t) / (f*f  - ff*float(char_pixels));

		vec4 diff = a*a*ff + 2.0*a*b*f - 2.0*a*b*ff - 2.0*a*ft + b*b *(-2.0*f + ff + float(char_pixels)) + 2.0*b*ft - 2.0*b*t + tt;
		float diff_f = dot(diff, vec4(1.0, 1.0, 1.0, 1.0));

		if (diff_f < mindiff)
		{
			mindiff = diff_f;
			minc = float(i);
			mina = a;
			minb = b;
		}
	}

	vec2 font_pos_res = vec2(minc * float(char_width), 0.0) + pixel_offset + 0.5;

	vec4 col = texture(samp8, font_pos_res * font_scale);
	ocol0 = mina * col + minb * (vec4(1.0,1.0,1.0,1.0) - col);
}