in glm_quat_from_vecs() - is computation of cos_half_theta correct?

[nirodho]

Maybe I'm missing an optimization here, but the half-angle formula for cosine is:
cos(theta / 2) = sqrt((1 + cos(theta)) / 2)
the code states:
cos(theta / 2) = 1 + cos(theta)

The change results in a different output versor.

void glm_quat_from_vecs(vec3 a, vec3 b, versor dest) {
  CGLM_ALIGN(8) vec3 axis;
  float cos_theta;
  float cos_half_theta;

  cos_theta = glm_vec3_dot(a, b);
  if (cos_theta >= 1.f - GLM_FLT_EPSILON) {  /*  a ∥ b  */
    glm_quat_identity(dest);
    return;
  }
  if (cos_theta < -1.f + GLM_FLT_EPSILON) {  /*  angle(a, b) = π  */
    glm_vec3_ortho(a, axis);
    cos_half_theta = 0.f;                    /*  cos π/2 */
  } else {
    glm_vec3_cross(a, b, axis);
    cos_half_theta = 1.0f + cos_theta;       /*  cos 0 + cos θ  */
   // shouldn't previous line be:
   // cos_half_theta = sqrtf(0.5f * (1.0f + cos_theta));
  }

  glm_quat_init(dest, axis[0], axis[1], axis[2], cos_half_theta);
  glm_quat_normalize(dest);
}

After much head-scratching, I've come to understand that I don't understand quaternions quite as well as I thought I did. I see that there IS a clever optimization here, but have yet to figure it out.

PS: I love this library.