+ /*
+ * The formulae are incorrect if the points are equal, in affine coordinates
+ * (X_1, Y_1) == (X_2, Y_2), so we check for this and do doubling if this
+ * happens.
+ *
+ * We use bitwise operations to avoid potential side-channels introduced by
+ * the short-circuiting behaviour of boolean operators.
+ *
+ * The special case of either point being the point at infinity (z1 and/or
+ * z2 are zero), is handled separately later on in this function, so we
+ * avoid jumping to point_double here in those special cases.
+ *
+ * Notice the comment below on the implications of this branching for timing
+ * leaks and why it is considered practically irrelevant.
+ */
+ points_equal = (x_equal & y_equal & (~z1_is_zero) & (~z2_is_zero));
+
+ if (points_equal) {