Trigonometric method to handle realistic error probabilities in logic circuits

We present a novel trigonometry-based probability calculation (TPC) method for analyzing circuit behavior and reliability in the presence of errors that occur with extremely low probability. Signal and error probabilities are represented by trigonometric functions controlled by their corresponding angles. By combining trigonometric identities and Taylor expansions, the effect of an error at a particular gate is simulated as a rotation. In addition, the correlations among signals caused by reconvergence are carefully handled. The TPC method is shown to be more scalable and accurate than prior approaches, especially for very low-probability errors. We measure the performance of TPC by applying it to the ISCAS and LGSyn-91 benchmark circuits. Experimental results show that TPC achieves near-linear runtime complexity even with the largest circuits, while the accuracy gradually increases with decreasing error probabilities.