Routing FPGAs is a challenging problem because of the relative scarcity of routing resources, both wires and connection points. This can lead either to slow implementations caused by long wiring paths that avoid congestion or a failure to route all signals. This paper presents PathFinder, a router that balances the goals of performance and routability. PathFinder uses an iterative algorithm that converges to a solution in which all signals are routed while achieving close to the optimal performance allowed by the placement. Routability is achieved by forcing signals to negotiate for a resource and thereby determine which signal needs the resource most. Delay is minimized by allowing the more critical signals a greater say in this negotiation. Because PathFinder requires only a directed graph to describe the architecture of routing resources, it adapts readily to a wide variety of FPGA architectures such as Triptych, Xilinx 3000 and mesh-connected arrays of FPGAs. The results of routing ISCAS benchmarks on the Triptych FPGA architecture show an average increase of only 4.5% in critical path delay over the optimum delay for a placement. Routes of ISCAS benchmarks on the Xilinx 3000 architecture show a greater completion rate than commercial tools, as well as 11% faster implementations.
An approach is presented for the evaluation of the tw distinct types of one-electron integrals arising from the ab initio fseudopotentials introduced by Kahn and Goddard. The integrals art shown to reduce to a sum over products of angular and radial integrals, the latter being approximated by power and asymptotic series combined with appropriate recursion relations. The method is valid for arbitt iry angular monvnta of both the pseudopotential and the Cartesian Gd sian basis functions. • 99 f y 9 exp(-p y)dy exp(-x)dx Part 1 (Mapleton House, Brooklyn, N.Y., 1948).
The 1(π,π*) state of ethylene has been thoroughly investigated at the configuration interaction level utilizing an extensive basis set and a configuration selection scheme which emphasizes a correct description of all correlation effects involving the π or π* electrons. The result, contrary to the Hartree–Fock prediction, but in agreement with the general experimental conclusion, is a mostly valence state as indicated by a value for 〈π*‖x2‖π*〉 of 8.8 a.u. using the π* natural orbital. A calculated excitation energy of 7.96 eV is in reasonable agreement with the 7.65 eV experimental absorption maximum. It is found that σ→σ* excitations relative to the ground state are essential to describe the left–right correlation of σ electrons with the π* electron. This in turn compensates for the ionic πA 2–πB 2 nature of the 1(π,π*) state, allowing the SCF state to become contracted at the CI level. The π* orbital in the second 1(π,π*) state appears to be well characterized at a CI level as a 3d orbital constrained to be orthogonal to the mostly valence π* orbital of the lower state. Calculations employing the same configuration selection scheme were done on the 3(π,π*), 1(π,3s), and positive ion states, the characterization of these states being consistent with other theoretical and experimental work.
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