Several advanced algorithms in defense and security objectives require high-speed computation of nonlinear functions. These include detection, localization, and identification. Increasingly, such computations must be performed in double precision accuracy in real time. In this paper, we develop a significance-based interpolative approach to such evaluations for double precision arguments. It is shown that our approach requires only one major multiplication, which leads to a unified and fast, two-cycle, VLSI architecture for mantissa computations. In contrast, the traditional iterative computations require several cycles to converge and typically these computations vary a lot from one function to another. Moreover, when the evaluation pertains to a compound or concatenated function, the overall time required becomes the sum of the times required by the individual operations. For our approach, the time required remains two cycles even for such compound or concatenated functions. Very importantly, the paper develops a key formula for predicting and bounding the worst case arithmetic error. This new result enables the designer to quickly select the architectural parameters without the expensive and intolerably long simulations, while guaranteeing the desired accuracy. The specific application focus is the mapping of the Independent Component Analysis (ICA) technique to a coarse-grain parallel-processing architecture.