  Recent advances in selected CI, including the adaptive sampling configuration
interaction (ASCI) algorithm and its heat bath extension, have made the ASCI
approach competitive with the most accurate techniques available, and hence an
increasingly powerful tool in solving quantum Hamiltonians. In this work, we
show that a useful paradigm for generating efficient selected CI/exact
diagonalization algorithms is driven by fast sorting algorithms, much in the
same way iterative diagonalization is based on the paradigm of matrix vector
multiplication. We present several new algorithms for all parts of performing a
selected CI, which includes new ASCI search, dynamic bit masking, fast orbital
rotations, fast diagonal matrix elements, and residue arrays. The algorithms
presented here are fast and scalable, and we find that because they are built
on fast sorting algorithms they are more efficient than all other approaches we
considered. After introducing these techniques we present ASCI results applied
to a large range of systems and basis sets in order to demonstrate the types of
simulations that can be practically treated at the full-CI level with modern
methods and hardware, presenting double- and triple-zeta benchmark data for the
G1 dataset. The largest of these calculations is Si$_{2}$H$_{6}$ which is a
simulation of 34 electrons in 152 orbitals. We also present some preliminary
results for fast deterministic perturbation theory simulations that use hash
functions to maintain high efficiency for treating large basis sets.
