Comparison of 4-class ranks of certain quadratic fields

Let $m$ be a square-free positive integer. Let $r_{4}(K)$ denote the 4-class rank of a quadratic field $K$. This paper examines how likely it is for $r_{4}(\mathbb{Q} (\sqrt {-m}\,)) =r_{4} (\mathbb{Q} (\sqrt {m}\,))$ and for $r_{4} (\mathbb{Q} (\sqrt {-m}\,)) = r_{4} (\mathbb{Q} (\sqrt {m}\,)) +1$.