Quantum phase estimation

Given access to the controlled version of an $n$-qubit unitary $U$ and its eigenstate $\ket{\psi}$ such that $U\ket{\psi}=e^{2\pi i\theta}\ket{\psi}$, for every integer $n_a\geq1$, there exists a quantum algorithm that estimates $\theta$ modulo $1$ up to precision $2^{-n_a}$ and failure probability at most $1-4/\pi^2$, using at most $n_a$ ancilla qubits, $2^{n_a}-1$ queries to controlled-$U$, $n_a(n_a-1)+3\lfloor n_a/2\rfloor$ CNOT gates, and $n_a(3n_a+1)/2$ single-qubit gates.