A Fast and Fuzzy Functional Simulator of Inexact Arithmetic Operators for Approximate Computing Systems

Abstract

Inexact operators are developed to exploit the tolerance of an application to imprecisions. These operators aim at reducing system energy consumption and memory footprint. In order to integrate the appropriate inexact operators in a complex system, the Quality of Service of the approximate system must be thoroughly studied through simulation. However, when simulating on a PC or workstation, the custom bit-level structures of inexact operators are not implemented in the instruction set of the simulating architecture. Consequently, the simulation requires a costly emulation, leading to expensive bit-level simulations. This paper proposes a new "Fast and Fuzzy" functional simulation method for inexact operators whose probabilistic behavior is correlated with the Most Significant Bits of the input operands. The proposed method processes real signal data and simplifies the error model for inexact operators, accelerating the simulation of the system. The modelization accuracy of the error can be controlled by a parameter called fuzzyness degree F. Using the proposed method, the bit-accurate logic-level simulation of inexact operators is replaced by an exact operator to which a pseudo-random error variable is added. Experiments on 16-bit operators show that the proposed simulation method, when compared to a bit-accurate logic level simulation, is up to 44 times faster.