Natesan Venkateswaran

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

Criticality computation in parameterized statistical timing

Chips manufactured in 90 nm technology have shown large parametric variations, and a worsening trend is predicted. These parametric variations make circuit optimization difficult since different paths are frequency-limiting in different parts of the multi-dimensional process space. Therefore, it is desirable to have a new diagnostic metric for robust circuit optimization. This paper presents a novel algorithm to compute the criticality probability of every edge in the timing graph of a design with linear complexity in the circuit size. Using industrial benchmarks, we verify the correctness of our criticality computation via Monte Carlo simulation. We also show that for large industrial designs with 442,000 gates, our algorithm computes all edge criticalities in less than 160 seconds

Clock-skew constrained placement for row based designs

In this paper we address the problem of placement of standard cells under the constraints of minimizing the clock-skew. We propose a quadratic programming based methodology for placement that not only results in an area and timing wise good placement but also a supporting zero-skew clock routing tree. Under the clock-skew constraints, our method produces significant reduction in the cost of zero-skew clock routing tree. During placement, we are able to obtain significant speed-up due to variable reduction and constraint modification.

Optimization objectives and models of variation for statistical gate sizing

This paper approaches statistical optimization by examining gate delay variation models and optimization objectives. Most previous work on statistical optimization has focused exclusively on the optimization algorithms without considering the effects of the variation models and objective functions. This work empirically derives a simple variation model that is then used to optimize for robustness. Optimal results from example circuits used to study the effect of the statistical objective function on parametric yield.

Reversible statistical max/min operation: concept and applications to timing

The increasing significance of variability in modern sub-micron manufacturing process has led to the development and use of statistical techniques for chip timing analysis and optimization. Statistical timing involves fundamental operations like statistical-add, sub, max and min to propagate timing information (modeled as random variables with known probability distributions) through a timing graph model of a chip design. Although incremental timing during optimization updates timing information of only certain parts of the timing-graph, lack of established reversible statistical max or min techniques forces more-than-required computations. This paper describes the concept of reversible statistical max and min for correlated Gaussian random variables, and suggests potential applications to statistical timing. A formal proof is presented to establish the uniqueness of reversible statistical max. Experimental results show run-time savings when using the presented technique in the context of chipslack computation during incremental timing optimization.

Timing analysis with nonseparable statistical and deterministic variations

Statistical static timing analysis (SSTA) is ideal for random variations but is not suitable for environmental variations like Vdd and temperature. SSTA uses statistical approximation, according to which circuit timing is predicted accurately only for highly probable combinations of variational parameters. SSTA is not able to handle accurately deterministic sources of variation like supply voltage. This paper presents a novel technique for modeling nonseparable deterministic and statistical variations in single timing run.

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.

Sharing and Re-use of Statistical Timing Macro-Models across Multiple Voltage Domains

This paper presents an approach to solving the problem of generating a single statistical timing macro-model or abstract for a chip component, and subsequently applying it smartly at multiple voltage domain conditions at a parent level of hierarchy during hierarchical timing. This approach avoids overheads in a traditional approach of having either multiple abstracts for the same component corresponding to different voltage domains, or having excessive guard-bands in a single common abstract. Results are presented for a set of test cases including industrial microprocessor units. The results exhibit more than 200 picoseconds of improved accuracy (both pessimism reduction and optimism avoidance) when using the proposed solution in comparison to an approach that assumes a single voltage domain compatible abstract.