Extended Probability Distribution Arithmetic

With shrinking technology dimensions and the demand for low voltage and low power circuits the functional safety margins decrease. This makes the accurate analysis of circuit properties under parameter variations extremely important. Many research has been done in this field for specific problems. Disadvantages of previous approaches are the lack of generality, inefficiency or the absence of methods for general circuit analysis. This paper continues the idea of a general probability distribution arithmetic. We present a method for calculating with random values as simple as with regular numbers. For the first time a method for solving implicit nonlinear equations using this arithmetic is presented. This enables general circuit analysis using the random value arithmetic. Results show that our implementation outperforms the state of the art by orders of magnitudes and allows calculations with 100 independent random values efficiently.