Cosmic reionization starts when the first generation of stars begin to photoionize beyond the interstellar medium and into the intergalactic medium. The HII regions will grow in size and number with time, merge with one another, and when there is complete overlap, then reionization is complete and the universe becomes transparent to UV photons. Updated observations from SDSS and WMAP are consistent with a generic model of patchy reionization beginning as early as z ~ 20 and ending about z ~ 6. In order to study patchy reionization for different star formation histories, we have run several high-resolution N-body + radiative transfer simulations with up to 24 billion particles and 360^3 RT grid cells. The RT calculations utilize a new ray tracing algorithm in which the initially O(N^2) scaling is converted to O(N) as the radiation filling factor approaches unity in the limit of complete reionization. We demonstrate that the current observational constraints require a star formation history where both Pop III and Pop II stars are significant sources of photoionizing radiation.