Statistical Method for Floating-point to Fixed-point Conversion

Changchun Shi, 2002 M.S.
(advisor: Robert W. Brodersen)

    The algorithms used by communication, voice and image processing systems are typically specified as floating point operations. On the other hand, digital ASIC VLSI implementations of these algorithms rely on fixed-point approximations to reduce cost of hardware while increasing throughput rates. The essential design step of floating-point to fixed-point conversion (FFC) proves to be time consuming due to the nonlinear characteristics and the massive design optimization space. In the bid to achieve short product cycles, the execution of FFC is often left to hardware designers, who are familiar with VLSI constraints. The group often has less insight to the algorithm; thus they depend on an ad-hoc approach to evaluate the implications of fixed-point representations. The gap between algorithm and hardware design is aggravated as algorithms continue to become ever more complex. Thus a systematic method for FFC is urgently called for.
    Current methods for FFC employed in industry are lack of theoretical foundation and become intolerably slow when searching space is large. In our research, a solid statistical framework of the problem is established, as needed for a reliable FFC. In this framework, input signals are modeled as random process with parametric PDF; output signals are modeled as PDF with the same input parameters plus the hardware description parameters such as architectures and word lengths; performance specifications are modeled as sufficient statistics of the output random process; and hardware cost is modeled as a function of hardware description parameters. An FFC is then to search the parameter space satisfying the given specification; and an acceptable FFC is to speed up the searching. This speedup requires smart ways to reduce the search steps, fast ways to conduct simulation core, better optimization technique, and fully automation. Several possibilities are suggested for each of the topics. Linear-time-invariant (LTI) systems are then studied; two simulation cores, namely Monte Carlo method and frequency domain method are employed to solve the problem (with light discussion on the limitations of the conventional state-space formulation). Finally, the statistical methods are generalized to any system design level.