In the last few decades, many attempts have been made to extend CM theory to the setting of real quadratic fields. In this talk I will describe how to turn recent work by Darmon, Pozzi and Vonk into an efficient algorithm for computing p-adic analogues of modular units and Heegner points: Gross--Stark units and Stark--Heegner points. This builds on the framework of Darmon and Vonk's rigid meromorphic cocycles, and involves Hilbert modular forms, overconvergent elliptic modular forms, and Gauss' reduction theory of binary quadratic forms.