Placement is an essential step in electronic design automation — the portion of the physical design flow that assigns exact locations for various circuit components within the chip's core area. An inferior placement assignment will not only affect the chip's performance but might also make it non-manufacturable by producing excessive wire-length, which is beyond available routing resources. Consequently, a placer must perform the assignment while optimizing a number of objectives to ensure that a circuit meets its performance demands. Together, the placement and routing steps of IC design are known as place and route.

A placer takes a given synthesized circuit netlist together with a technology library and produces a valid placement layout. The layout is optimized according to the aforementioned objectives and ready for cell resizing and buffering — a step essential for timing and signal integrity satisfaction. Clock-tree synthesis and Routing follow, completing the physical design process. In many cases, parts of, or the entire, physical design flow are iterated a number of times until design closure is achieved.

Application specifics

In the case of application-specific integrated circuits, or ASICs, the chip's core layout area comprises a number of fixed height rows, with either some or no space between them. Each row consists of a number of sites which can be occupied by the circuit components. A free site is a site that is not occupied by any component. Circuit components are either standard cells, macro blocks, or I/O pads.[1] Standard cells have a fixed height equal to a row's height, but have variable widths. The width of a cell is an integral number of sites.

On the other hand, blocks are typically larger than cells and have variable heights that can stretch a multiple number of rows.[1] Some blocks can have preassigned locations — say from a previous floorplanning process — which limit the placer's task to assigning locations for just the cells. In this case, the blocks are typically referred to by fixed blocks. Alternatively, some or all of the blocks may not have preassigned locations. In this case, they have to be placed with the cells in what is commonly referred to as mixed-mode placement.

In addition to ASICs, placement retains its prime importance in gate array structures such as field-programmable gate arrays (FPGAs). Here, prefabricated transistors are typically arranged in rows (or “arrays”) that are separated by routing channels.[2] Placement maps the circuit's subcircuits into programmable FPGA logic blocks in a manner that guarantees the completion of the subsequent stage of routing.

Objectives and constraints

Placement is formulated as constrained optimization. In particular, the clock cycle of a chip is determined by the delay of its longest path, usually referred to as the critical path. Given a performance specification, a placer must ensure that no path exists with delay exceeding the maximum specified delay.

Other key constraints include

There are usually multiple optimization objectives, including:

Additionally, it is desirable to finish the placement process quickly.

Total wirelength is typically the primary objective of most existing placers and serves as a precursor to other optimizations because, e.g., power and delay tend to grow with wire length. Total wire length determines the routing demand and whether it can be satisfied by the routing supply defined by available routing tracks. However, making wires very short sometimes leads to local routing demand exceeding local routing supply. Such situations often require routing detours, which increase wire lengths and signal delays. Therefore, after preliminary optimization of total wirelength, it is also important to handle routing congestion.

Power minimization typically notes wires with greater switching activity factors and assigns greater priority to making them shorter. When many "hot" components are placed nearby, a hot spot may arise and lead to harmful temperature gradients. In such cases, components can be spread out.

Basic techniques

Placement is divided into global placement and detailed placement. Global placement introduces dramatic changes by distributing all the instances to appropriate locations in the global scale with minor overlaps allowed. Detailed placement shifts each instance to nearby legal location with very moderate layout change. Placement and overall design quality is most dependent on the global placement performance.

Early techniques for placement of integrated circuits can be categorized as combinatorial optimization. For IC designs with thousands or tens of thousands of components, simulated annealing[3] methodologies such as TimberWolf[4] exhibits the best results. When IC designs grew to millions of components, placement leveraged hypergraph partitioning[5] using nested-partitioning frameworks such as Capo.[6] Combinatorial methods directly prevent component overlaps but struggle with interconnect optimization at large scale. They are typically stochastic and can produce very different results for the same input when launched multiple times.

Analytical methods for global placement model interconnect length by a continuous function and minimize this function directly subject to component density constraints. These methods run faster and scale better than combinatorial methods, but do not prevent component overlaps and must be postprocessed by combinatorial methods for detailed placement. Quadratic placement is an early analytical method that models interconnect length by a quadratic function and uses high-performance quadratic optimization techniques. When it was developed, it demonstrated competitive quality of results and also stability, unlike combinatorial methods. GORDIAN[7] formulates the wirelength cost as a quadratic function while still spreading cells apart through recursive partitioning. The algorithm[8] models placement density as a linear term into the quadratic cost function and solves the placement problem by pure quadratic programming. A common enhancement is weighting each net by the inverse of its length on the previous iteration. Provided the process converges, this minimizes an objective linear in the wirelength.[9] The majority of modern quadratic placers (KraftWerk,[10] FastPlace,[11] SimPL[12]) follow this framework, each with different heuristics on how to determine the linear density force.

Nonlinear placement models wirelength by exponential (nonlinear) functions and density by local piece-wise quadratic functions, in order to achieve better accuracy thus quality improvement.[13] Follow-up academic work includes APlace[14] and NTUplace.[15]

ePlace[16] is a state of the art global placement algorithm. It spreads instances apart by simulating an electrostatic field, which minimizes quality overhead thus achieves good performance.

In 2021, Google Brain reported good results from the use of AI techniques (in particular reinforcement learning) for the placement problem.[17] However, this result is quite controversial,[18][19][20] as the paper does not contain head-to-head comparisons to existing placers, and is difficult to replicate due to proprietary content. At least one initially favorable commentary has been retracted upon further review.[21]

See also


  1. ^ a b A. Kahng, J. Lienig, I. Markov, J. Hu: "VLSI Physical Design: From Graph Partitioning to Timing Closure", Springer (2022), doi:10.1007/978-90-481-9591-6, ISBN 978-3-030-96414-6, pp. 10-13.
  2. ^ A. Kahng, J. Lienig, I. Markov, J. Hu: "VLSI Physical Design: From Graph Partitioning to Timing Closure", Springer (2022), doi:10.1007/978-90-481-9591-6, ISBN 978-3-030-96414-6, pp. 14-15.
  3. ^ S. Kirkpatrick, C. D. G. Jr., and M. P. Vecchi (1983). "Optimization by Simulated Annealing". Science. 220 (4598): 671–680. Bibcode:1983Sci...220..671K. doi:10.1126/science.220.4598.671. PMID 17813860.((cite journal)): CS1 maint: multiple names: authors list (link)
  4. ^ C. Sechen and A. Sangiovanni-Vincentelli (1986). "TimberWolf3.2: A New Standard Cell Placement and Global Routing Package.". Proceedings of the Design Automation Conference. ACM. pp. 432–439.
  5. ^ George Karypis, Rajat Aggarwal, Vipin Kumar, and Shashi Shekhar (1997). "Multilevel Hypergraph Partitioning: Applications in VLSI Domain". Proceedings of the Design Automation Conference. ACM. pp. 526–529.((cite conference)): CS1 maint: multiple names: authors list (link)
  6. ^ Caldwell, A.E.; Kahng, A.B.; Markov, I.L. (June 2000). "Can recursive bisection alone produce routable placements?". Proceedings of the 37th Design Automation Conference. pp. 477–482. doi:10.1109/DAC.2000.855358.
  7. ^ Kleinhans, J.M.; Sigl, G.; Johannes, F.M.; Antreich, K.J. (March 1991). "GORDIAN: VLSI placement by quadratic programming and slicing optimization". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 10 (3): 356–365. doi:10.1109/43.67789. S2CID 15274014.
  8. ^ H. Eisenmann and F. M. Johannes (1998). "Generic Global Placement and Floorplanning". Proceedings of the Design Automation Conference. ACM. pp. 269–274.
  9. ^ Sigl, Georg, Konrad Doll, and Frank M. Johannes (1991). "Analytical placement: A linear or a quadratic objective function?". Proceedings of the 28th ACM/IEEE design automation conference. ACM. pp. 427–432.((cite conference)): CS1 maint: multiple names: authors list (link)
  10. ^ P. Spindler, U. Schlichtmann, and F. M. Johannes (2008). "Kraftwerk2 - A Fast Force-Directed Quadratic Placement Approach Using an Accurate Net Model". IEEE Transactions on Computer-Aided Design. 27 (8): 1398–1411. doi:10.1109/TCAD.2008.925783. S2CID 16054185.((cite journal)): CS1 maint: multiple names: authors list (link)
  11. ^ N. Viswanathan, M. Pan, and C. Chu (2007). "FastPlace3.0: A Fast Multilevel Quadratic Placement Algorithm with Placement Congestion Control". Proceedings of the Asia-South Pacific Design Automation Conference. pp. 135–140.((cite conference)): CS1 maint: multiple names: authors list (link)
  12. ^ Kim, M.-C.; Lee D.-J.; Markov I.L. (January 2011). "SimPL: An Effective Placement Algorithm". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 31 (1): 50–60. CiteSeerX doi:10.1109/TCAD.2011.2170567. S2CID 47293399.
  13. ^ USA 6301693, W. C. Naylor, R. Donelly, and L. Sha, "Non-Linear Optimization System and Method for Wire Length and Delay Optimization for an Automatic Electric Circuit Placer" 
  14. ^ A. B. Kahng, S. Reda and Q. Wang (2005). "Architecture and Details of a High Quality, Large-Scale Analytical Placer". Proceedings of the International Conference on Computer-Aided Design. pp. 891–898.
  15. ^ T.-C. Chen, Z.-W. Jiang, T.-C. Hsu, H.-C. Chen, and Y.-W. Chang (2008). "NTUPlace3: An Analytical Placer for Large-Scale Mixed-Size Designs with Preplaced Blocks and Density Constraint" (PDF). IEEE Transactions on Computer-Aided Design. 27 (7): 1228–1240. doi:10.1109/TCAD.2008.923063. S2CID 11912537.((cite journal)): CS1 maint: multiple names: authors list (link)
  16. ^ J. Lu, P. Chen, C.-C. Chang, L. Sha, D. J.-S. Huang, C.-C. Teng and C.-K. Cheng (2014). "ePlace: Electrostatics Based Placement Using Nesterov's Method". Proceedings of the Design Automation Conference. ACM. pp. 1–6.((cite conference)): CS1 maint: multiple names: authors list (link)
  17. ^ Azalia Mirhoseini, Anna Goldie, Mustafa Yazgan (2021). "A Graph Placement Methodology for Fast Chip Design". Nature. 594 (7862): 207–212. arXiv:2004.10746. Bibcode:2021Natur.594..207M. doi:10.1038/s41586-021-03544-w. PMID 34108699. S2CID 235395490.((cite journal)): CS1 maint: multiple names: authors list (link)
  18. ^ Cheng, Chung-Kuan, Andrew B. Kahng, Sayak Kundu, Yucheng Wang, and Zhiang Wang (Mar 2023). "Assessment of Reinforcement Learning for Macro Placement". Proceedings of the 2023 International Symposium on Physical Design. pp. 158–166. arXiv:2302.11014. doi:10.1145/3569052.3578926. ISBN 978-1-4503-9978-4.((cite book)): CS1 maint: multiple names: authors list (link)
  19. ^ Igor L. Markov. "The False Dawn: Reevaluating Google's Reinforcement Learning for Chip Macro Placement". arXiv:2306.09633.
  20. ^ Agam Shah (October 3, 2023). "Google's Controversial AI Chip Paper Under Scrutiny Again".
  21. ^ Kahng, Andrew B. (2021). "RETRACTED ARTICLE: AI system outperforms humans in designing floorplans for microchips". Nature. 594 (7862): 183–185. Bibcode:2021Natur.594..183K. doi:10.1038/d41586-021-01515-9. PMID 34108693. S2CID 235394411.

Further reading/External links