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This paper presents a novel approach to fractional bit-width optimization of fixed-point designs. We first propose a divide-and-conquer algorithm that can assign optimal fractional bit-widths to a special class of designs that does not have re-convergent paths starting from an internal signal. General designs are partitioned into designs of that special class and our algorithm is applied to each design. The algorithm recursively breaks down a given design into sub-designs and finds Pareto optimal solutions to each sub-design. Those solutions are merged to form Pareto optimal solutions to a larger design. In addition, two pruning methods based on area and error, respectively, are proposed, speeding up the algorithm. The optimization process is guided by static maximum absolute error analysis, and functional correctness is guaranteed for all possible input stimuli. Our approach is demonstrated in five case studies including polynomial approximation and RGB-to-YCbCr conversion, for which the divide-and-conquer algorithm produces the optimal solutions. [ABSTRACT FROM PUBLISHER]

We propose simple and efficient optimization-based untangling strategies for 2D polygonal and 3D polyhedral meshes. The first approach uses a size-based mesh metric, which eliminates inverted elements by averaging element size over the entire mesh. The second method uses a hybrid quality metric, which untangles inverted elements by simultaneously averaging element size and improving element shape. The last method using a variant of the hybrid quality metric gives a high penalty for inverted elements and employs an adaptive sigmoid function for handling various mesh sizes. Numerical experiments are presented to show the effectiveness of the proposed untangling strategies for various 2D polygonal and 3D polyhedral meshes. [ABSTRACT FROM AUTHOR]

In the face of large-scale process variations, statistical timing methodology has advanced significantly over the last few years, and statistical path selection takes advantage of it in at-speed testing. In deterministic path selection, the separation of path selection and test generation is known to require time consuming iteration between the two processes. This paper shows that in statistical path selection, this is not only the case, but also the quality of results can be severely degraded even after the iteration. To deal with this issue, we consider testability in the first place by integrating a satisfiability (SAT) solver, and this necessitates a new statistical path selection method. We integrate the SAT solver in a novel way that leverages the conflict analysis of modern SAT solvers, which provides more than 4X speedup without special optimizations of the SAT solver for this particular application. Our proposed method is based on a generalized path criticality metric whose properties allow efficient pruning. Our experimental results show that the proposed method achieves 47% better quality of results on average, and up to 361X speedup compared to statistical path selection followed by test generation. [ABSTRACT FROM AUTHOR]