Unifying Bit-width Optimisation for Fixed-point and Floating-point Designs
[IEEE Symposium on Field Programmable Custom Computing Machines, Napa Valley, 2004]
by Altaf A. Gaffar, Oskar Mencer, Wayne Luk, Peter Y.K. Cheung 

abstract. 
This paper presents a method that offers a uniform treatment for bit-width optimisation 
of both fixed-point and floating-point designs. Our work utilises automatic 
differentiation to compute the sensitivities of outputs to the bitwidth of the various 
operands in the design. This sensitivity analysis enables us to explore and compare 
fixed-point and floating-point implementation for a particular design. As a result we 
can automate the selection of the optimal number representation for each variable in 
a design to optimize area and performance. We implement our method in the BitSize tool 
targeting reconfigurable architectures, which takes user-defined constraints to direct 
the optimisation procedure. We illustrate our approach using applications such as 
ray-tracing and function approximation.