Floating-point bitwidth analysis via automatic differentiation

• Published in: 2002 IEEE International Conference on Field-Programmable Technology, 2002. (FPT). Proceedings pp. 158 - 165
• Main Authors: Gaffar, A.A., Mencer, O., Luk, W., Cheung, P.Y.K., Shirazi, N.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY IEEE 2002
• Subjects: Applied sciences; Arithmetic; Automatic programming; Circuit properties; Circuits; Computer systems; Data analysis; Design. Technologies. Operation analysis. Testing; Discrete Fourier transforms; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Field programmable gate arrays; Finite impulse response filter; Frequency filters; Hardware; High level synthesis; Integrated circuits; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Sensitivity analysis; Very large scale integration; Performance evaluation; Sensitivity analysis; VLSI circuit; Discrete Fourier transformation; Mathematical method; Field programmable gate array; Implementation; Data flow; Integrated circuit; Finite impulse response filter; Floating point; Arithmetic operation; High level synthesis; Automatic analysis
• ISBN: 0780375742; 9780780375741
• DOI: 10.1109/FPT.2002.1188677

Automatic bitwidth analysis is a key ingredient for highlevel programming of FPGAs and high-level synthesis of VLSI circuits. The objective is to find the minimal number of bits to represent a value in order to minimise the circuit area and to improve efficiency of the respective arithmetic operations, while satisfying user-defined numerical constraints. We present a novel approach to bitwidth- or precision-analysis for floating-point designs. The approach involves analysing the dataflow graph representation of a design to see how sensitive the output of a node is to changes in the outputs of other nodes: higher sensitivity requires higher precision and hence more output bits. We automate such sensitivity analysis by a mathematical method called automatic differentiation, which involves differentiating variables in a design with respect to other variables. We illustrate our approach by optimising the bitwidth for two examples, a discrete Fourier transform (DFT) implementation and a Finite Impulse Response (FIR) filter implementation.