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Field-programmable gate arrays (FPGAs) are an important implementation medium for digital logic. Unfortunately, they currently suffer from poor silicon area utilization due to routing constraints. In this paper we present Triptych, an FPGA architecture designed to achieve improved logic density with competitive performance. This is done by allowing a per-mapping tradeoff between logic and routing resources, and with a routing scheme designed to match the structure of typical circuits. We show that, using manual placement, this architecture yields a logic density improvement of up to a factor of 3.5 over commercial FPGAs, with comparable performance. We also describe Montage, the first FPGA architecture to fully support asynchronous and synchronous interface circuits.