Accelerated Performance Evaluation of Fixed-Point Systems With Un-Smooth Operations

Abstract

Abstract-The problem of accuracy evaluation is one of the most time consuming tasks during the fixed-point refinement process. Analytical techniques based on perturbation theory have been proposed in order to overcome the need for long fixed-point simulation. However, these techniques are not applicable in the presence of certain operations classified as un-smooth operations. In such circumstances, fixed-point simulation should be used. In this paper, an algorithm detailing the hybrid technique which makes use of an analytical accuracy evaluation technique used to accelerate fixed-point simulation is presented. This technique is applicable to signal processing systems with both feed-forward and feedback interconnect topology between its operations. The acceleration obtained as a result of applications of the proposed technique is consistent with fixed-point simulation, while reducing the time taken for fixed-point simulation by several orders of magnitude.

Error Analysis of the Square Root Operation for the Purpose of Precision Tuning: A Case Study on K-means

“…Efforts have been made to find analytical models in the context of accuracy evaluation of fixedpoint systems. A series of propositions of analytical methods to measure the output noise of signal processing systems were presented in [4], which dealt with smooth operations, then in [5], which catered for decision operators and recently in [8], where a hybrid approach based on both simulation and analytical results was highlighted.…”

“…A plethora of work using simulation-based approaches for the purpose of FLP precision tuning was propounded [3], [6], [7], etc. As for analytical approaches, efforts were made in the context of fixed-point word-length optimization [4], [8] and mainly focused on common arithmetic operations like addition and multiplication. Square root operation is significantly more costly, in terms of energy consumption, than addition or multiplication and requires several iterative cycles to complete.…”

Fixed-point refinement of digital signal processing systems

“…Analytical approaches based on perturbation theory are valid for systems made-up of only smooth operations. For un-smooth operations, hybrid techniques [128] combining simulations and analytical results can used.…”

Analysis of Finite Word-Length Effects in Fixed-Point Systems

“…To handle systems made-up of unsmooth operations, a mixed approach which combines analytical evaluations and simulations has been proposed in [113,114]. The idea is to evaluate directly the application performance metric with fixed-point simulation and to accelerate drastically the simulation with analytical models.…”

“…This technique selectively simulates parts of the system only when an decision error occurs [114]. Given that decision errors are rare event the simulation time is not so important as for classical fixed-point simulations.…”