SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction

TL;DR

This paper introduces SWATI, an automated method combining testing and induction to synthesize optimal fixed-point implementations of numerical routines, balancing accuracy and implementation cost.

Contribution

The paper presents a novel technique that automatically generates fixed-point code from floating-point designs, optimizing for accuracy and cost using testing and induction.

Findings

Effectively synthesizes fixed-point implementations with minimal word-width.

Balances accuracy requirements with implementation cost.

Demonstrated on control, robotics, and signal processing examples.

Abstract

In this paper, we present an automated technique SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction, which uses a combination of Nelder-Mead optimization based testing, and induction from examples to automatically synthesize optimal fixedpoint implementation of numerical routines. The design of numerical software is commonly done using floating-point arithmetic in design-environments such as Matlab. However, these designs are often implemented using fixed-point arithmetic for speed and efficiency reasons especially in embedded systems. The fixed-point implementation reduces implementation cost, provides better performance, and reduces power consumption. The conversion from floating-point designs to fixed-point code is subject to two opposing constraints: (i) the word-width of fixed-point types must be minimized, and (ii) the outputs of the fixed-point program must be accurate. In this paper, we propose a new solution to this problem. Our technique takes the floating-point program, specified accuracy and an implementation cost model and provides the fixed-point program with specified accuracy and optimal implementation cost. We demonstrate the effectiveness of our approach on a set of examples from the domain of automated control, robotics and digital signal processing.