Clock-Tree-Aware Incremental Timing-Driven Placement

Abstract

The increasing impact of interconnections on overall circuit performance makes timing-driven placement (TDP) a crucial step toward timing closure. Current TDP techniques improve critical paths but overlook the impact of register placement on clock tree quality. On the other hand, register placement techniques found in the literature mainly focus on power consumption, disregarding timing and routabilty. Indeed, postponing register placement may undermine the optimization achieved by TDP, since the wiring between sequential and combinational elements would be touched. This work proposes a new approach for an effective coupling between register placement and TDP that relies on two key aspects to handle sequential and combinational elements separately: only the registers in the critical paths are touched by TDP (in practice they represent a small percentage of the total number of registers), and the shortening of clock tree wirelength can be obtained with limited variation in signal wirelength and placement density. The approach consists of two steps: (1) incremental register placement guided by a virtual clock tree to reduce clock wiring capacitance while preserving signal wirelength and density, and (2) incremental TDP to minimize the total negative slack. For the first step, we propose a novel technique that combines clock-net contraction and register clustering forces to reduce the clock wirelength. For the second step, we propose a novel Lagrangian Relaxation formulation that minimizes total negative slack for both setup and hold timing violations. To solve the formulation, we propose a TDP technique using a novel discrete search that employs a Euclidean distance to define a proper neighborhood. For the experimental evaluation of the proposed approach, we relied on the ICCAD 2014 TDP contest infrastructure and compared our results with the best results obtained from that contest in terms of timing closure, clock tree compactness, signal wirelength, and density. Assuming a long displacement constraint, our technique achieves worst and total negative slack reductions of around 24% and 26%, respectively. In addition, our approach leads to 44% shorter clock tree wirelength with negligible impact on signal wirelength and placement density. In the face of such results, the proposed coupling seems a useful approach to handle the challenges faced by contemporary physical synthesis.