  We compute on all quantum states several measures that characterise
asymptotic quantum coherence manipulation under restricted classes of
operations. We focus on the distillable coherence, i.e. the maximum rate of
production of approximate pure bits of coherence starting from independent
copies of an input state $\rho$, and on the coherence cost, i.e. the minimum
rate of consumption of pure coherence bits that is needed to generate many
copies of $\rho$ with vanishing error. We obtain the first closed-form
expression for the distillable coherence under strictly incoherent operations
(SIO), proving that it coincides with that obtained via physically incoherent
operations (PIO). This shows that SIO and PIO are equally weak at distilling
coherence, sheds light on the recently discovered phenomenon of generic bound
coherence, and provides us with an explicit optimal distillation protocol that
is amenable to practical implementations. We give a single-letter formula for
the coherence cost under PIO, showing that it is finite on a set of states with
nonzero volume. Since PIO can be realised in a laboratory with incoherent
ancillae, unitaries, and measurements, our result puts fundamental limitations
on coherence manipulation in an experimentally relevant setting. We find
examples of 'abyssally bound' states with vanishing PIO distillable coherence
yet infinite PIO coherence cost. Our findings complete the picture of
asymptotic coherence manipulation under all the main classes of incoherent
operations.
