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Fast and accurate depth estimation, or stereo matching, is essential in embedded stereo vision systems, requiring substantial design effort to achieve an appropriate balance among accuracy, speed and hardware cost. To reduce the design effort and achieve the right balance, we propose FP-Stereo for building high-performance stereo matching pipelines on FPGAs automatically. FP-Stereo consists of an open-source hardware-efficient library, allowing designers to obtain the desired implementation instantly. Diverse methods are supported in our library for each stage of the stereo matching pipeline and a series of techniques are developed to exploit the parallelism and reduce the resource overhead. To improve the usability, FP-Stereo can generate synthesizable C code of the FPGA accelerator with our optimized HLS templates automatically. To guide users for the right design choice meeting specific application requirements, detailed comparisons are performed on various configurations of our library to investigate the accuracy/speed/cost trade-off. Experimental results also show that FP-Stereo outperforms the state-of-the-art FPGA design from all aspects, including 6.08% lower error, 2x faster speed, 30% less resource usage and 40% less energy consumption. Compared to GPU designs, FP-Stereo achieves the same accuracy at a competitive speed while consuming much less energy.