Incremental Statistical Timing Analysis for IC Design
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Solution Overview
Problem
Conventional statistical timing analysis methods require re-computation of all input timing data, even when only one input has changed, leading to inefficiency and resource waste during chip timing closure and optimization processes, especially in large designs with multiple input gates.
Innovation Solution
A method for efficient incremental statistical timing analysis that computes the extrema of n random variables by removing the changed variable, using previously computed extrema to incrementally update the new extrema of the remaining (n-1) variables, reducing the need for re-computation of unchanged data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional timing analysis methods re-compute the maximum of all input timing data, then the timing analysis is complete and accurate, but the computational cost is very expensive and machine resources are wasted
Solution Approach 1:
The patent segments the set of n input timing variables into two parts: (n-1) unchanged variables and 1 changed variable. By computing the maximum of the (n-1) unchanged variables once and reusing this result across multiple incremental changes, the method avoids redundant computations while maintaining timing analysis accuracy.
Solution Approach 2:
The patent performs preliminary computation of the maximum of (n-1) unchanged timing variables before the incremental update. This pre-computed maximum is stored and reused when computing new extrema after incremental changes, eliminating the need to re-compute unchanged data and reducing computational overhead.
2Measurement precision
If the timing analysis tool re-computes the extrema of all inputs, then the timing analysis is accurate, but the processing time increases significantly for large designs
Solution Approach 1:
The patent divides the computation into segments: (n-1) unchanged variables processed once to compute their maximum, and 1 changed variable processed incrementally. This segmentation reduces processing time from O(n) to O(1) for each incremental update while preserving accuracy.
Solution Approach 2:
Instead of computing the maximum of all n variables completely each time, the patent performs partial computation only on the changed variable using the pre-computed maximum of unchanged variables. This partial action approach maintains accuracy while significantly reducing processing time.
3Reliability
If conventional methods compute extrema of all n random variables, then the statistical timing analysis is complete, but the computational overhead is very high for million incremental changes
Solution Approach 1:
The patent segments the timing analysis into a one-time computation of (n-1) unchanged variables and incremental updates for changed variables. This enables the tool to handle millions of incremental changes efficiently while maintaining complete and reliable timing analysis coverage.
Solution Approach 2:
The patent establishes continuity by computing the maximum of unchanged variables once and continuously reusing this result across multiple incremental updates. This continuous reuse of pre-computed data maintains analysis completeness while dramatically improving productivity for large-scale optimization.
Data Source
AI summary
In one embodiment, the invention is a method and apparatus for efficient incremental statistical timing analysis and optimization. One embodiment of a method for determining an incremental extrema of n random variables, given a change to at least one of the n random variables, includes obtaining the n random variables, obtaining a first extrema for the n random variables, where the first extrema is an extrema computed prior to the change to the at least one of the n random variables, removing the at least one of the n random variables to form an (n−1) subset, computing a second extrema for the (n−1) subset in accordance with the first extrema and the at least one of the n random variables, and outputting a new extrema of the n random variables incrementally based on the extrema of the (n−1) subset and the at least one of the n random variables that changed.