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We calculate the total galactic Shapiro delay to the Crab pulsar by includingthe contributions from the dark matter as well as baryonic matter along theline of sight. The total delay due to dark matter potential is about 3.4 days.For baryonic matter, we included the contributions from both the bulge and thedisk, which are approximately 0.12 and 0.32 days respectively. The total delayfrom all the matter distribution is therefore 3.84 days. We also calculate thelimit on violations of Einstein's equivalence principle by using observationsof "nano-shot" giant pulses from the Crab pulsar with time-delay $<0.4$~ns aswell as using time differences between radio and optical photons observed fromthis pulsar. Using the former, we obtain a limit on violation of Einstein'sequivalence principle in terms of the PPN parameter $\Delta \gamma < 2.41\times10^{-15}$. From the time-difference between simultaneous optical and radioobservations, we get $\Delta \gamma < 1.54\times 10^{-9}$. We also point outdifferences in our calculation of Shapiro delay and that from two recent papers(arXiv:1612.00717 and arXiv:1608.07657), which used the same observations toobtain a corresponding limit on $\Delta \gamma$.

Galactic Shapiro Delay to the Crab Pulsar and limit on Einstein's Equivalence Principle Violation