Metrics, Noise Propagation Models, and Design Framework for Floating-Point Approximate Computing

Approximate computing has emerged as an efficient solution for energy saving at the expense of calculation accuracy, especially for floating-point operation intensive applications, which have urgent demands for some uniform design frameworks for floating-point approximate computing combining the approximate computing techniques with the metrics of applications. In this paper, a simple approximate method with a zero-mean noise for the mantissa was introduced firstly, called PAM. Secondly, based on the proposed approximate method, the corresponding noise propagation models for floating-point operations were built, including floating-point addition, subtraction, and multiplication. Thirdly, a uniform design framework, which is only related to the operational-level topology of applications, was presented. The presented design framework can be used to evaluate the quality of data produced by applications before the circuit design is completed, and the efficient bit width of the mantissa can be obtained under specific requirements, which is also suitable for truncation. Finally, we studied the feasibility of the proposed design framework through two typical applications of image processing, edge detection and Gaussian filtering. The experimental results of edge detection have shown that our proposed design framework could effectively predict efficient bit width under the specific peak signal-to-noise ratio, with a difference of 1–2 bits in extreme situations. The Gaussian filtering experiment has demonstrated that the proposed design framework could apply to applications with complex calculations and structures.