+void combine_two_samples(float w1, float w2, float pos1, float pos1_pos2_diff, float inv_pos1_pos2_diff, float num_subtexels, float inv_num_subtexels,
+ DestFloat *offset, DestFloat *total_weight, float *sum_sq_error)
+{
+ assert(w1 * w2 >= 0.0f); // Should not have differing signs.
+ float z; // Normalized 0..1 between pos1 and pos2.
+ if (fabs(w1 + w2) < 1e-6) {
+ z = 0.5f;
+ } else {
+ z = w2 / (w1 + w2);
+ }
+
+ // Round to the desired precision. Note that this might take z outside the 0..1 range.
+ *offset = from_fp32<DestFloat>(pos1 + z * pos1_pos2_diff);
+ z = (to_fp32(*offset) - pos1) * inv_pos1_pos2_diff;
+
+ // Round to the minimum number of bits we have measured earlier.
+ // The card will do this for us anyway, but if we know what the real z
+ // is, we can pick a better total_weight below.
+ z = lrintf(z * num_subtexels) * inv_num_subtexels;
+
+ // Choose total weight w so that we minimize total squared error
+ // for the effective weights:
+ //
+ // e = (w(1-z) - a)² + (wz - b)²
+ //
+ // Differentiating by w and setting equal to zero:
+ //
+ // 2(w(1-z) - a)(1-z) + 2(wz - b)z = 0
+ // w(1-z)² - a(1-z) + wz² - bz = 0
+ // w((1-z)² + z²) = a(1-z) + bz
+ // w = (a(1-z) + bz) / ((1-z)² + z²)
+ //
+ // If z had infinite precision, this would simply reduce to w = w1 + w2.
+ *total_weight = from_fp32<DestFloat>((w1 + z * (w2 - w1)) / (z * z + (1 - z) * (1 - z)));
+
+ if (sum_sq_error != nullptr) {
+ float err1 = to_fp32(*total_weight) * (1 - z) - w1;
+ float err2 = to_fp32(*total_weight) * z - w2;
+ *sum_sq_error = err1 * err1 + err2 * err2;
+ }
+}
+
+// Create a VBO with the given data. Returns the VBO number.
+GLuint generate_vbo(GLint size, GLenum type, GLsizeiptr data_size, const GLvoid *data);