1. Gaussian Interconnections for On-Chip Networks Ramón Beivide and Enrique Vallejo University of Cantabria, Spain enrique@atc.unican.es

2. R. Beivide, E. Vallejo2 Microgrid Workshop Index Introduction: Why a Topology? Dense Gaussian Networks and other topologies Different layouts Routing:  ideas: Adaptive routing, deadlock avoidance, fault tolerance  Unicast routing  Broadcast Routing Perfect placement of resources Expansibility:  Increasing number of nodes in a Gaussian network  Hierarchical Gaussian networks Some ideas about cache coherence Gaussian Interconnections for On-chip Networks

3. R. Beivide, E. Vallejo3 Microgrid Workshop Introduction Future trends: many PE on a chip Possible interconections: bus, MIN, direct network Bus-based interconnections do not scale – they do not provide a sufficient bandwith when there are many PEs. MIN hard to implement in a chip. Direct networks with a given topology: The way to connect different routers in the chip Gaussian Interconnections for On-chip Networks

4. R. Beivide, E. Vallejo4 Microgrid Workshop Mesh Network Number of Nodes N: N = b x b = b 2 Diameter k: k = (b-1) + (b-1) = 2b-2 Gaussian Interconnections for On-chip Networks

5. R. Beivide, E. Vallejo5 Microgrid Workshop Number of Nodes N: N = (b+1) 2 + b 2 Diameter k= b + b = 2b 0 1 2 -2 3 -3 i 1+i 2+i -1+i -2+i 2i 1+2i -1+2i -i 1-i 2-i -1-i -2-i -2i 1-2i -1-2i 3i -3i 2 b+1 Diamond Network Gaussian Interconnections for On-chip Networks

6. R. Beivide, E. Vallejo6 Microgrid Workshop Torus Network Number of Nodes N: N = b x b = b 2 Diameter k = b -1 b b Gaussian Interconnections for On-chip Networks

7. R. Beivide, E. Vallejo7 Microgrid Workshop 0 1 2 -2 3 -3 i 1+i 2+i 2i 1+2i 2+i -i 2+i -2i 2+i 3i -3i 2b+1 Number of Nodes N: N = (b+1) 2 + b 2 Diameter k = b Dense Gaussian Network Same # links as torus, with peripheral links. Lower mean distance and Diameter. Gaussian Interconnections for On-chip Networks

8. R. Beivide, E. Vallejo8 Microgrid Workshop Topological properties comparative TopologyNodesDiameterAprox. Diam. Average Distance Aprox. Aver. Dist 2-D Mesh 2-D Torus Dense Gaussian Lower average distance and diameter Gaussian Interconnections for On-chip Networks

9. R. Beivide, E. Vallejo9 Microgrid Workshop Area comparative Gaussian Interconnections for On-chip Networks

10. R. Beivide, E. Vallejo10 Microgrid Workshop 3i -2-i -1-i 3 2 -i 1 2i 1+2i 1-2i -1+2i 2-i -2i 1-i i 1+i 2+i -1+i -2+i -3i 1-2i 0 -2 -3 Different Layouts Different layouts for the same network: Mesh-like layout Without peripheral links, bounded link length Gaussian Interconnections for On-chip Networks

11. R. Beivide, E. Vallejo11 Microgrid Workshop Routing ideas Adaptive routing: in-fligh packets can choose their (minimal) path from info in the Routing Record (jumps in each direction), depending on congestion or other parameters. Deadlock avoidance: Bubble routing proposed as a cost-effective deadlock avoidance mechanism (used in IBM’s Blue Gene). Only 2 virtual channels needed per link. Fault-tolerant routing: Inmunet proposed as a fast, efficient mechanism to detect link failures and restore network performance. Gaussian Interconnections for On-chip Networks

12. R. Beivide, E. Vallejo12 Microgrid Workshop Unicast Routing 0 1 2 -2 3 -3 1+i 2+i -1+i -2+i 1+2i -1+2i -i 1-i 2-i -2-i -2i 1-2i -1-2i 3i -3i Route from a to b: Routing record generated From the difference: dest-source (x, y) -1-i i Example: i – (-1-i) = 1+2i (x=1, y=2) 1 jump to the right, 2 jumps up Movement from source node to the origin (node 0) generates routing record. Example 2: The movement makes the arrow fall outside the original network  Peripheral links used Translations from surrounding replicas of the network are considered, to obtain an optimal RR 2i Gaussian Interconnections for On-chip Networks

13. R. Beivide, E. Vallejo13 Microgrid Workshop P 1 2 -2 3 -3 i 1+i 2+i -1+i -2+i 2i -1+2i -i 1-i 2-i -1-i -2-i -2i 1-2i -1-2i 3i -3i 1+2i NW NE SW SE Broadcast Routing Triangle-based broadcast Minimum number of steps The same for any node (due to peripheral links) Balanced use of resources Simple routing based on labels (see abstract) Gaussian Interconnections for On-chip Networks

14. R. Beivide, E. Vallejo14 Microgrid Workshop Perfect placement of resources Resource distribution over the network. All nodes have resources within a given distance (example: distance 1) Resource example: I/O ports Processing elements Memory banks... Gaussian Interconnections for On-chip Networks

15. R. Beivide, E. Vallejo15 Microgrid Workshop Expansibility: Increasing # nodes Increasing Gaussian network: Network can be expanded with the number of nodes necessary to increase diameter in 1 unit: 4k +4. Alternatively, hierarchical Gaussian networks have been proposed, joining several Gaussian networks with another gaussian pattern. Useful for CMPs sceneries, for example (different latency, link length, etc. in each hierarchical level):  Lower level: interconnection between different cores inside a chip. Fast and reliable, with low latency  Higher level: interconnection between different chips. Slower and with higher latency. Gaussian Interconnections for On-chip Networks

16. R. Beivide, E. Vallejo16 Microgrid Workshop Expansibility: Increasing # nodes Gaussian Interconnections for On-chip Networks Lower level (on-chip) with a dense Gaussian pattern. Higher level, with the same pattern. Central routers will have 8 links: 4 internal links 4 external links Route from one node to another: 1) Route to the central router of the same gaussian 2) Route in the higher level to the desired gaussian. 3) Route from the central router of the dest. Gaussian, to the destiny node.

17. R. Beivide, E. Vallejo17 Microgrid Workshop Cache coherence in Gaussian networks Recent proposals based in broadcast, such as TokenB (M. Hill) can beneficiate from a Gaussian interconnection: Broadcast block requests (latency optimized with Gaussian interconection). Unicast response with grants (Tokens) to use memory blocks, between different nodes and main memory. There is no need to maintain a directory for coherence. Broadcast network can work as a bus with a snoopy-like protocol. Gaussian Interconnections for On-chip Networks

18. R. Beivide, E. Vallejo18 Microgrid Workshop

19. R. Beivide, E. Vallejo19 Microgrid Workshop Additional comments (not presented) Dense Gaussian Networks are isomorphic to Dense Midimew Networks. However, these two topologies are not isomorphic in the general case (not dense). In this work, related to Dense Gaussian networks, properties studied for both Gaussian and Midimew topologies are presented. References in the next slide will be thus referred to both Midimew and Gaussian networks

20. R. Beivide, E. Vallejo20 Microgrid Workshop Commented References (I) Midimew networks were first introduced in: R. Beivide, E. Herrada, J.L. Balcázar, Agustín Arruabarrena, “Optimal Distance Networks of Low Degree for Parallel Computers”. IEEE Transactions on Computers, Vol. 40, No 10, Oct 1991, pp. 1109-1124. This paper introduces properties, analysis and some rectangular (mesh-like) layouts. Unicast routing is also proposed, but based on labeling nodes with integer labels (instead of Gaussian numbers). Bounded link-length layouts were introduced in: E. Vallejo, R. Beivide y C. Martínez, “Practicable Layouts for Optimal Circulant Graphs”. Proceedings of the “13th Euromicro Conference on Parallel, Distributed and Network-based Processing”, Lugano, Switzerland, Feb. 2005. A previous work on Midimew folding, which obtained a worse result (maximum link length 4) is the following one: Francis C. M. Lau, Guihai Chen, “Optimal Layouts of Midimew Networks”. IEEE Transactions on Parallel and Distributed Systems, Vol 7, No 9, pp 954-961

21. R. Beivide, E. Vallejo21 Microgrid Workshop Commented References (II) Gaussian Networks will be introduced in: C. Martínez, R. Beivide, J. Gutierrez and E. Gabidulin. "On the Perfect t- Dominating Set Problem in Circulant Graphs and Codes over Gaussian Integers". Accepted for presentation at ISIT’05, September, Australia. This paper also deals with perfect resource placement. Broadcasting in Dense Gaussian Networks will be introduced in: R. Beivide, C. Martínez, E. Vallejo, J. Gutierrez, C. Izu, “Gaussian Interconnection Networks”. Accepted for presentation at the Spanish Parallelism Conferences, Sept. 05, Granada, Spain. This paper also introduces unicast routing in terms of the Gaussian numbers (instead of integer labels) Hierarchical Gaussian Networks will be introduced in: Miquel Moretó, Carmen Martínez, Enrique Vallejo, Ramón Beivide, Mateo Valero, “Hierarchical Topologies for Large-scale Two-level Networks”, Accepted for presentation at the Spanish Parallelism Conferences, Sept. 05, Granada, Spain.

22. R. Beivide, E. Vallejo22 Microgrid Workshop Commented References (III) Bubble routing is described in V. Puente, C. Izu, R. Beivide, J.A. Gregorio, F. Vallejo and J.M. Prellezo, “The Adaptative Bubble Router”, Journal of Parallel and Distributed Computing. Vol 61 - nº 9, September 2001 Inmunnet was introduced in V. Puente, J.A. Gregorio, F. Vallejo and R. Beivide. "Immunet: A Cheap and Robust Fault-Tolerant Packet Routing Mechanism". 31th Annual International Symposium on Computer Architecture (ISCA- 31), pp. 198-209, 2004. Token Coherence was presented in: M. M. K. Martin, M. D. Hill, and D. A. Wood. "Token Coherence: Decoupling Performance and Correctness". 30th Annual International Symposium on Computer Architecture (ISCA-30), pp. 182-193, 2003.