The successive cancellation list decoding algorithm for polar codes yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar decoding performance at a much lower computational complexity, but software implementations report a sub-par T/P performance. In this technical report, the benefits of the fast simplified successive cancellation list decoder are extended to the stack algorithm, resulting in a throughput increase by two orders of magnitude over the traditional stack decoder.