Dual-V_TH optimization script with gate resizing

This project, developed in the context of the Synthesis and Optimization of Digital Systems course (Prof. Andrea Calimera, Politecnico di Torino, A.Y. 2018/'19), consists in a Tcl procedure to be used within Synopsys PrimeTime for a constrained multi-objective post-synthesis optimization of a netlist of standard cells. This algorithm has been awarded with the first place in the course contest, among the other projects of the 2019 SODS course.

Given an input savings parameter, the dualVth procedure performs a dual-V_TH cell assignment with gate resizing of the loaded netlist, with the aim to meet the constraint on the leakage power while looking for a tradeoff between dynamic power consumption and worst case slack in the smallest possible time. The implementation of the algorithm is based on the ST CMOS 65nm technology library.

The backbone of the algorithm is a while loop divided into three main parts, described in the following.

1. Dynamic power - slack tradeoff

Firstly, a transformation aimed to improve the tradeoff between dynamic power and worst case slack is performed. A good approach proved to be to define two parameters, and : the algorithm resizes to smaller all cells with max_slack > , to save dynamic (and leakage) power with non-critical cells, and to bigger the ones with max_slack < , to try to improve the worst case slack. What remains defined is a safe zone between and , from which cells are not moved unless global changes affect them.

Note that cells are swapped to smaller or bigger only of one size at a time: this allows to explore more in detail the cost function; if a cell can be further resized it will indeed remain outside the safe zone, being subject to resizing in following iterations. The parameter is recomputed at each iteration as a function of the worst case slack; such dependency has been modeled empirically to try not to swap to bigger too much cells, which has negative outcomes. As far as is concerned, a good value turned out to be 0: since in most cases the worst case slack becomes negative, such transformation will not lead to further damages, while exploiting the higher possibility of size decreasing; also, if needed, cells with smallest slack will be anyway enlarged in following iterations if the cost function improves, and brought back to a positive slack.

2. Leakage constraint

In this phase, the leakage power constraint is enforced; the algorithm needs to repeat this step at each iteration since swaps in size of cells affect the design leakage. Since leakage power is a local property, a quick approach, which needs only two update_power calls, can be exploited. The cells to swap to HVT alternatives are selected basing on a priority index, the product cellLVT_slack · leak_diff, as a tradeoff between HVT cells number and timing deterioration. Only LVT cells (and not cells previously swapped to HVT) are affected in this step.

3. Cost function evaluation

In this phase the current cost function is computed, and compared to the cost function of the previous iteration. If currentCF > previousCF, the loop is broken, supposing that the algorithm reached a local minimum. This might not be true, but this is a form of tradeoff between the quality of the result and the execution time. When a local minimum is found, the last performed iteration needs to be undone; dictionaries to quickly revert the changes are used for this purpose. The cost function is computed as:

The loop is also broken if the number of iterations exceeds 6: this is another form of tradeoff to bound the execution time.