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Amber is a system-on-chip (SoC) with a coarse-grained reconfigurable array (CGRA) for acceleration of dense linear algebra applications, such as machine learning (ML), image processing, and computer vision. It is designed using an agile accelerator-compiler co-design flow; the compiler updates automatically with hardware changes, enabling continuous application-level evaluation of the hardware-software system. To increase hardware utilization and minimize reconfigurability overhead, Amber features the following: 1) dynamic partial reconfiguration (DPR) of the CGRA for higher resource utilization by allowing fast switching between applications and partitioning resources between simultaneous applications; 2) streaming memory controllers supporting affine access patterns for efficient mapping of dense linear algebra; and 3) low-overhead transcendental and complex arithmetic operations. The physical design of Amber features a unique clock distribution method and timing methodology to efficiently layout its hierarchical and tile-based design. Amber achieves a peak energy efficiency of 538 INT16 GOPS/W and 483 BFloat16 GFLOPS/W. Compared with a CPU, a GPU, and a field-programmable gate array (FPGA), Amber has up to 3902x, 152x, and 107x better energy-delay product (EDP), respectively.