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This paper presents a full hardware implementation of a magnetic tunnel junction based stochastic tunable bitstream generator. It provides highly accurate control of the switching probability, while showing important robustness to process and temperature variations. We propose a new architecture of sensing scheme based on the pre-charged sense amplifier approach that uses an asynchronous digital module to control the internal signals of the sense amplifier with the purpose of improving the reliability against the timing hazards and reducing the power consumption by detecting the end of the reading to stop the required static currents. The circuit also features a digital feedback loop that analyzes the output bitstream and adapt the current in such a way that the bitstream encodes precisely the required probability. This circuit features an important bit generation rate at a low energy cost. Based on an exhaustive characterization of the circuit, we provide a behavioral description in Verilog, with timing and power files to be integrated as a standard cell in the digital design flow for application level evaluation of the performance. Thus, we also provide a design and evaluation flow from device to digital level of abstraction. [ABSTRACT FROM AUTHOR]