Kerim Kalafala

First-order incremental block-based statistical timing analysis

Variability in digital integrated circuits makes timing verification an extremely challenging task. In this paper, a canonical first-order delay model that takes into account both correlated and independent randomness is proposed. A novel linear-time block-based statistical timing algorithm is employed to propagate timing quantities like arrival times and required arrival times through the timing graph in this canonical form. At the end of the statistical timing, the sensitivity of all timing quantities to each of the sources of variation is available. Excessive sensitivities can then be targeted by manual or automatic optimization methods to improve the robustness of the design. This paper also reports the first incremental statistical timer in the literature, which is suitable for use in the inner loop of physical synthesis or other optimization programs. The third novel contribution of this paper is the computation of local and global criticality probabilities. For a very small cost in computer time, the probability of each edge or node of the timing graph being critical is computed. Numerical results are presented on industrial application-specified integrated circuit (ASIC) chips with over two million logic gates, and statistical timing results are compared to exhaustive corner analysis on a chip design whose hardware showed early mode timing violations

First-Order Incremental Block-Based Statistical Timing Analysis

Variability in digital integrated circuits makes timing verification an extremely challenging task. In this paper, a canonical first-order delay model that takes into account both correlated and independent randomness is proposed. A novel linear-time block-based statistical timing algorithm is employed to propagate timing quantities like arrival times and required arrival times through the timing graph in this canonical form. At the end of the statistical timing, the sensitivity of all timing quantities to each of the sources of variation is available. Excessive sensitivities can then be targeted by manual or automatic optimization methods to improve the robustness of the design. This paper also reports the first incremental statistical timer in the literature, which is suitable for use in the inner loop of physical synthesis or other optimization programs. The third novel contribution of this paper is the computation of local and global criticality probabilities. For a very small cost in computer time, the probability of each edge or node of the timing graph being critical is computed. Numerical results are presented on industrial application-specified integrated circuit (ASIC) chips with over two million logic gates, and statistical timing results are compared to exhaustive corner analysis on a chip design whose hardware showed early mode timing violations

Statistical timing for parametric yield prediction of digital integrated circuits

Uncertainty in circuit performance due to manufacturing and environmental variations is increasing with each new generation of technology. It is therefore important to predict the performance of a chip as a probabilistic quantity. This paper proposes three novel path-based algorithms for statistical timing analysis and parametric yield prediction of digital integrated circuits. The methods have been implemented in the context of the EinsTimer static timing analyzer. The three methods are complementary in that they are designed to target different process variation conditions that occur in practice. Numerical results are presented to study the strengths and weaknesses of these complementary approaches. Timing analysis results in the face of statistical temperature and Vdd variations are presented on an industrial ASIC part on which a bounded timing methodology leads to surprisingly wrong results

Statistical Timing for Parametric Yield Prediction of Digital Integrated Circuits

Uncertainty in circuit performance due to manufacturing and environmental variations is increasing with each new generation of technology. It is therefore important to predict the performance of a chip as a probabilistic quantity. This paper proposes three novel path-based algorithms for statistical timing analysis and parametric yield prediction of digital integrated circuits. The methods have been implemented in the context of the EinsTimer static timing analyzer. The three methods are complementary in that they are designed to target different process variation conditions that occur in practice. Numerical results are presented to study the strengths and weaknesses of these complementary approaches. Timing analysis results in the face of statistical temperature and Vdd variations are presented on an industrial ASIC part on which a bounded timing methodology leads to surprisingly wrong results

A distributed timing analysis framework for large designs

Given ever-increasing circuit complexities, recent trends are driving the requirement for distributed timing analysis (DTA) in electronic design automation (EDA) tools. However, DTA has received little research attention so far and remains a critical problem. In this paper, we introduce a DTA framework for large designs. Our framework supports (1) general design partitions in distributed file systems, (2) non-blocking IO with event-driven loop for effective communication and computation overlap, and (3) an efficient messaging interface between application and network layers. The effectiveness and scalability of our framework has been evaluated on large hierarchical industry designs over a cluster with hundreds of machines.

Prototype for a large-scale static timing analyzer running on an IBM Blue Gene

This paper focuses on parallelization of the classic static timing analysis (STA) algorithm for verifying timing characteristics of digital integrated circuits. Given ever-increasing circuit complexities, including the need to analyze circuits with billions of transistors, across potentially thousands of process corners, with accuracy tolerances down to the picosecond range, sequential execution of STA algorithms is quickly becoming a bottleneck to the overall chip design closure process. A message passing based parallel processing technique for performing STA leveraging an IBM Blue Gene/L supercomputing platform is presented. Results are collected for a small industrial 65 nm benchmarking design, where the algorithm demonstrates speedup of nearly 39 times on 64 processors and a peak of 119 times (without partitioning costs, speedup is 263 times) on 1024 processors. With an idealized synthetic circuit, the algorithm demonstrated 259 times speedup, 925 times speedup without partitioning overhead, on 1024 processors. To the best of our knowledge, this is the first result demonstrating scalable STA on the IBM Blue Gene.

Practical statistical static timing analysis with current source models

This paper considers the practical nuances of using current source gate models in an industrial statistical timing analysis environment. Specifically, the memory overhead of a naive implementation combining statistical and current source models to obtain and store gate output waveforms is found to be impractical for large microprocessor designs. A study is performed to observe variational gate output waveforms, and a technique is presented to store the waveforms in a memory efficient manner with minimal accuracy impact. The presented technique is validated over a set of 14 nanometer designs, and has enabled the usage of current source models in our industrial statistical timing analysis flow. Results demonstrate slack accuracy improvements of up to 17 picoseconds with a 1.15X run-time overhead and 1.1 gigabytes per million-gates memory overhead in comparison to an existing flow.