Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
A generalized discrepancy and quadrature error bound
Mathematics of Computation
Analysis and Design of Analog Integrated Circuits
Analysis and Design of Analog Integrated Circuits
Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature
SIAM Journal on Scientific Computing
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
First-order incremental block-based statistical timing analysis
Proceedings of the 41st annual Design Automation Conference
An efficient algorithm for statistical minimization of total power under timing yield constraints
Proceedings of the 42nd annual Design Automation Conference
Projection-based performance modeling for inter/intra-die variations
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
ISQED '07 Proceedings of the 8th International Symposium on Quality Electronic Design
Proceedings of the 44th annual Design Automation Conference
Low discrepancy sequences in high dimensions: How well are their projections distributed?
Journal of Computational and Applied Mathematics
Novel algorithms for fast statistical analysis of scaled circuits
Novel algorithms for fast statistical analysis of scaled circuits
Efficient Monte Carlo based incremental statistical timing analysis
Proceedings of the 45th annual Design Automation Conference
Practical, fast Monte Carlo statistical static timing analysis: why and how
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
On efficient Monte Carlo-based statistical static timing analysis of digital circuits
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Efficient trimmed-sample Monte Carlo methodology and yield-aware design flow for analog circuits
Proceedings of the 49th Annual Design Automation Conference
Scalable sampling methodology for logic simulation: reduced-ordered Monte Carlo
Proceedings of the International Conference on Computer-Aided Design
A fast analog circuit yield estimation method for medium and high dimensional problems
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Generation of surrogate models of Pareto-optimal performance trade-offs of planar inductors
Analog Integrated Circuits and Signal Processing
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
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At the nanoscale, no circuit parameters are truly deterministic; most quantities of practical interest present themselves as probability distributions. Thus, Monte Carlo techniques comprise the strategy of choice for statistical circuit analysis. There are many challenges in applying these techniques efficiently: circuit size, nonlinearity, simulation time, and required accuracy often conspire to make Monte Carlo analysis expensive and slow. Are we--the integrated circuit community-- alone in facing such problems? As it turns out, the answer is "no." Problems in computational finance share many of these characteristics: high dimensionality, profound nonlinearity, stringent accuracy requirements, and expensive sample evaluation. We perform a detailed experimental study of how one celebrated technique from that domain--quasi-Monte Carlo (QMC) simulation--can be adapted effectively for fast statistical circuit analysis. In contrast to traditional pseudorandom Monte Carlo sampling, QMC uses a (shorter) sequence of deterministically chosen sample points. We perform rigorous comparisons with both Monte Carlo and Latin hypercube sampling across a set of digital and analog circuits, in 90 and 45nm technologies, varying in size from 30 to 400 devices. We consistently see superior performance from QMC, giving 2× to 8× speedup over conventional Monte Carlo for roughly 1% accuracy levels. We present rigorous theoretical arguments that support and explain this superior performance of QMC. The arguments also reveal insights regarding the (low) latent dimensionality of these circuit problems; for example, we observe that over half of the variance in our test circuits is from unidimensional behavior. This analysis provides quantitative support for recent enthusiasm in dimensionality reduction of circuit problems.