Criticality computation in parameterized statistical timing

Abstract

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.

Decoupling capacitance allocation for timing with statistical noise model and timing analysis

“…To do this, we calculate "criticality" defined as a probability that a gate belongs to the critical path of a circuit. Several methods to compute criticality have been proposed [8], [9]. We adopted the method proposed in Ref.…”

“…The CPU times for adjoint network analysis with a fast linear circuit simulator [10], the convolution in Eq. (9) and SSTA including criticality computation in Eq. (2) are 15.0s, 2.16s and 2.15s (e.g.…”

Fast and Accurate Statistical Criticality Computation Under Process Variations

“…This concept is also extended to edge (node) criticalities in the timing graph of a circuit, i.e., the probability that a path passing through the edge (node) is critical. To this end, works like [2], [8] and [15] attempt to compute the criticality probability of edges in a timing graph, using a canonical first order delay model.…”

“…The cutset-based idea is extended in [15], to compute the criticality of edges by linearly traversing the timing graph. The criticality of an edge in a cutset is computed using a balanced binary partition tree.…”

“…This paper, a preliminary version of which appears in [9], makes the following contributions. First, similar to [15], we propose an algorithm to compute the criticality probability of edges (nodes) in a timing graph using the notion of cutsets. Edges crossing multiple cutsets are dealt with using a zonebased approach, similar to [16], in which old computations are reused to the greatest possible extent.…”