+ z = w2 / (w1 + w2);
+ }
+
+ // Round to the desired precision. Note that this might take z outside the 0..1 range.
+ *offset = from_fp64<DestFloat>(pos1 + z * (pos2 - pos1));
+ z = (to_fp64(*offset) - pos1) / (pos2 - pos1);
+
+ // 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_fp64<DestFloat>((w1 + z * (w2 - w1)) / (z * z + (1 - z) * (1 - z)));
+
+ if (sum_sq_error != NULL) {
+ float err1 = to_fp64(*total_weight) * (1 - z) - w1;
+ float err2 = to_fp64(*total_weight) * z - w2;
+ *sum_sq_error = err1 * err1 + err2 * err2;
+ }
+}
+
+// Explicit instantiations.
+template
+void combine_two_samples<float>(float w1, float w2, float pos1, float pos2, float num_subtexels, float inv_num_subtexels,
+ float *offset, float *total_weight, float *sum_sq_error);
+
+template
+void combine_two_samples<fp16_int_t>(float w1, float w2, float pos1, float pos2, float num_subtexels, float inv_num_subtexels,
+ fp16_int_t *offset, fp16_int_t *total_weight, float *sum_sq_error);
+
+GLuint fill_vertex_attribute(GLuint glsl_program_num, const string &attribute_name, GLint size, GLenum type, GLsizeiptr data_size, const GLvoid *data)
+{
+ int attrib = glGetAttribLocation(glsl_program_num, attribute_name.c_str());
+ if (attrib == -1) {
+ return -1;
+ }
+
+ GLuint vbo;
+ glGenBuffers(1, &vbo);
+ check_error();
+ glBindBuffer(GL_ARRAY_BUFFER, vbo);
+ check_error();
+ glBufferData(GL_ARRAY_BUFFER, data_size, data, GL_STATIC_DRAW);
+ check_error();
+ glEnableVertexAttribArray(attrib);
+ check_error();
+ glVertexAttribPointer(attrib, size, type, GL_FALSE, 0, BUFFER_OFFSET(0));
+ check_error();
+ glBindBuffer(GL_ARRAY_BUFFER, 0);
+ check_error();
+
+ return vbo;
+}
+
+void cleanup_vertex_attribute(GLuint glsl_program_num, const string &attribute_name, GLuint vbo)
+{
+ int attrib = glGetAttribLocation(glsl_program_num, attribute_name.c_str());
+ if (attrib == -1) {
+ return;