Adaptive Function Segmentation Methodology for Resources Optimization of Hardware-Based Function Evaluators
Trejo-Arellano, Juan M.
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DescriptionThis thesis presents a new adaptive function segmentation methodology (AFSM), for the evaluation of mathematical functions through piecewise polynomial approximation (PPA) methods. This methodology is planned to be employed for the development of an efficient hardware-based channel emulator in future development steps of the current project. In contrast to state-of-art segmentation methodologies, which applicability is limited because these are highly dependent on the function shape and require significant intervention from the user to setup appropriately the algorithm, the proposed segmentation methodology is flexible and applicable to any continuous function within an evaluation interval. Through the analysis of the first and second order derivatives, the methodology becomes aware of the function shape and adapts the algorithm behavior accordingly. The proposed segmentation methodology aims towards hardware architectures of limited resources that resort to fixed-point numeric representation where hardware designer should make a compromise between resources consumption and output accuracy. An optimization algorithm is implemented to assist the user in searching the best segmentation parameters that maximize the outcome of the design trade-offs for a given signal-to-quantization-noise ratio requirement. When compared to state-of-the-art segmentation methodologies, the proposed AFSM delivers better performance of approximation for the hardware-based evaluation of transcendental functions given that fewer segments and consequently fewer hardware resources are required.
Consejo Nacional de Ciencia y Tecnología