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$\begingroup$If you wanted to set P to the Ed25519 base point, what 4 component values would you use for P? I'm guessing the problem is related to confusion between coordinate systems. When you add, normally the Augend is in P3 coordinate space, and the Addend is converted to "cached" coordinate space first, where the conversion is (X,Y,Z,T)->(Y + X, Y - X, Z, 2*d*T).$\endgroup$
$\begingroup$Sorry, my fault. It's neither the addition nor the doubling that's incorrect. It's that I'm generating points with random coordinates which are not valid curve points$\endgroup$
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