SimPL: An effective placement algorithm

Abstract

Abstract-We propose a self-contained, flat, forcedirected algorithm for global placement that is simpler than existing placers and easier to integrate into timingclosure flows. It maintains lower-bound and upper-bound placements that converge to a final solution. The upperbound placement is produced by a novel rough legalization algorithm. Our placer SimPL outperforms mPL6, NTUPlace3, FastPlace3, APlace2 and Capo simultaneously in runtime and solution quality, running 6.4 times faster than mPL6 and reducing wirelength by 2% on the ISPD 2005 benchmark suite. I. INTRODUCTIONGlobal placement currently remains at the core of physical design and is a gating factor for downstream optimizations during timing closure [2]. Despite impressive improvements reported by researchers [15] and industry software in the last five years, state-ofthe-art algorithms and tools for placement suffer several key shortcomings which are becoming more pronounced at recent technology nodes. These shortcomings fall into four categories: (i) speed, (ii) solution quality, (iii) simplicity and integration with other optimizations, (iv) support for multithreaded execution. We propose the SimPL algorithm that simultaneously improves results in the first three categories and lends itself naturally to parallelism on multicore CPUs. [6]. Forcedirected algorithms model total net length by a quadratic function of cell locations and minimize it by solving a large sparse system of linear equations. To discourage cell overlap, forces are added pulling cells away from high-density areas. These forces are modeled by pseudopins and pseudonets, which extend the original quadratic function [11]. They are updated after each linear-system solve until iterations converge. Non-linear optimization models net length by more sophisticated differentiable functions with linear asymptotic behavior which are then minimized by advanced numerical analysis techniques [12]. Cell density is modeled by functional terms, which are more accurate than forces, but also require updates after each change to placement [7], [12]. Algorithms in both categories are directly used in the industry or closely resemble those in industry placers.

Placement: From Wirelength to Detailed Routability

“…SimPLR [52] also considers the amount of routing congestion in the inflation function. Cells in the GCell with serious routing congestion will be inflated more than those in GCell with lower routing demand overflow.…”

ePlace-MS: Electrostatics-Based Placement for Mixed-Size Circuits

“…Due to the function order restriction in the quadratic placement infrastructure, the density cost is degraded from exponential to linear, which helps achieve convexity and efficiency but loses quality. SimPL [16] and ComPLx [17] determine the anchor position via recursive bipartitioning, while convergence is theoretically promised via the primal-dual framework. Nevertheless, the solution quality is sensitive towards the initial solution.…”

POLAR: Placement based on novel rough legalization and refinement

“…In recent years, the placers [7], [8], [9], [10], [11] adopt a new technique called rough legalization. The key idea of rough legalization is that almost legal placement is used to guide the spreading force generation.…”

“…The key idea of rough legalization is that almost legal placement is used to guide the spreading force generation. In SimPL [7], the rough legalization is implemented by top-down geometric partitioning and non-linear scaling. In ComPLx [8], the entire placement process is modelled by subgradient primal-dual Lagrange optimization, and LAL is modelled by a feasibility projection.…”

“…In this paper, we propose a new quadratic placer called POLAR inspired by SimPL [7] and based upon a novel rough legalization and refinement approach. We notice that while the placement solution by quadratic based wirelength minimization may have considerable overlaps, the relative positions of cells can be trusted in producing a legal placement with good wirelength.…”