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This work discusses CHARM, a Composable Heterogeneous Accelerator-Rich Microprocessor design that provides scalability, flexibility, and design reuse in the space of accelerator-rich CMPs. CHARM features a hardware structure called the accelerator block composer (ABC), which can dynamically compose a set of accelerator building blocks (ABBs) into a loosely coupled accelerator (LCA) to provide orders of magnitude improvement in performance and power efficiency. Our software infrastructure provides a data flow graph to describe the composition, and our hardware components dynamically map available resources to the data flow graph to compose the accelerator from components that may be physically distributed across the CMP. Our ABC is also capable of providing load balancing among available compute resources to increase accelerator utilization. Running medical imaging benchmarks, our experimental results show an average speedup of 2.1X (best case 3.7X) compared to approaches that use LCAs together with a hardware resource manager. We also gain in terms of energy consumption (average 2.4X; best case 4.7X).