One Method - All Error-Metrics: A Three-Stage Approach for Error-Metric Evaluation in Approximate Computing

Approximate Computing (AC) is a design paradigm that makes use of the error tolerance inherited by many applications. The goal of AC is to trade off accuracy for performance in terms of computation time, energy consumption and/or hardware complexity.In the field of circuit design for AC, error-metrics are used to express the degree of approximation. Evaluating these error-metrics is a key challenge. Several approaches exist, however, to this day not all relevant metrics can be evaluated with formal methods. Recently, Symbolic Computer Algebra (SCA) has been used to evaluate error-metrics during approximate hardware generation. In this paper, we generalize the idea to use SCA and propose a methodology which is suitable for formal evaluation of all established error-metrics. This approach can be divided into three stages: 1) Determine the remainder of the AC circuit wrt. the specification using SCA, 2) build an Algebraic Decision Diagram (ADD) to represent the remainder and 3) evaluate each error-metric by a tailored ADD traversal algorithm. In the experiments, we apply our algorithms to a large and well-known benchmark set.