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Address Lookup and Classification

Address Lookup and Classification. EE384Y May 23, 2006. Pankaj Gupta Principal Architect and Member of Technical Staff, Netlogic Microsystems pankaj@netlogicmicro.com http://klamath.stanford.edu/~pankaj. Generic Router Architecture (Review from EE384x). Data. Hdr. Data. Hdr.

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Address Lookup and Classification

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  1. Address Lookup and Classification EE384Y May 23, 2006 Pankaj Gupta Principal Architect and Member of Technical Staff, Netlogic Microsystems pankaj@netlogicmicro.com http://klamath.stanford.edu/~pankaj

  2. Generic Router Architecture (Review from EE384x) Data Hdr Data Hdr IP Address Next Hop Address Table Buffer Memory Header Processing Lookup IP Address Update Header Queue Packet ~1M prefixes Off-chip DRAM ~1M packets Off-chip DRAM

  3. Lookups Must be Fast • Lookup mechanism must be simple and easy to implement • Memory access time is the bottleneck • 200Mpps × 2 lookups/pkt = 400 Mlookups/sec → 2.5ns per lookup

  4. Memory Technology (2006) Note: Price, speed and power are manufacturer and market dependent.

  5. Lookup Mechanism is Protocol Dependent

  6. Outline • Routing Lookups • Overview • Exact matching • Direct lookup • Associative lookup • Hashing • Trees and tries • Longest prefix matching • Why LPM? • Tries and compressed tries • Binary search on prefix intervals • References • Packet Classification

  7. Exact Matches in ATM/MPLS Direct Memory Lookup (Outgoing Port, new VCI/label) VCI/MPLS-label Memory Address Data • VCI/Label space is 24 bits • - Maximum 16M addresses. With 64b data, this is 1Gb of memory. • VCI/Label space is private to one link • Therefore, table size can be “negotiated” • Alternately, use a level of indirection

  8. Exact Matches in Ethernet Switches • Layer-2 addresses are usually 48-bits long, • The address is global, not just local to the link, • The range/size of the address is not “negotiable” (like it is with ATM/MPLS) • 248 > 1012, therefore cannot hold all addresses in table and use direct lookup.

  9. Exact Matches in Ethernet Switches (Associative Lookup) “Normal” Memory Port Address Data • Associative memory (aka Content Addressable Memory, CAM) compares all entries in parallel against incoming data. Associative Memory (“CAM”) Network address Location Address Data 48bits Match

  10. Exact MatchesHashing • Use a pseudo-random hash function (relatively insensitive to actual function) • Bucket linearly searched (or could be binary search, etc.) • Leads to unpredictable number of memory references Memory Memory Network Address Hashing Function Pointer 16, say List/Bucket Address Data Data Address 48 List of network addresses in this bucket

  11. Exact Matches Using HashingNumber of memory references

  12. Exact Matches in Ethernet SwitchesPerfect Hashing Network Address Hashing Function Port 16, say Data Address Memory 48 There always exists a perfect hash function. Goal: With a perfect hash function, memory lookup always takes O(1) memory references. Problem: - Finding perfect hash functions (particularly a minimal perfect hash) is complex. - Updates make such a hash function yet more complex - Advanced techniques: multiple hash functions, bloom filters…

  13. Exact Matches in Ethernet SwitchesHashing • Advantages: • Simple to implement • Expected lookup time is small • Updates are fast (except with perfect hash functions) • Disadvantages • Relatively inefficient use of memory • Non-deterministic lookup time (in rare cases) •  Attractive for software-based switches. However, hardware platforms are moving to other techniques (but they can do well with a more sophisticated form of hashing)

  14. Exact Matches in Ethernet Switches Trees and Tries log2N N entries Binary Search Tree Binary Search Trie < > 0 1 < > < > 0 1 0 1 010 111 Lookup time bounded and independent of table size, storage is O(NW) Lookup time dependent on table size, but independent of address length, storage is O(N)

  15. Exact Matches in Ethernet Switches Multiway tries 16-ary Search Trie Ptr=0 means no children 0000, ptr 1111, ptr 1111, ptr 0000, 0 1111, ptr 0000, 0 000011110000 111111111111 Q: Why can’t we just make it a 248-ary trie?

  16. Exact Matches in Ethernet Switches Multiway tries As degree increases, more and more pointers are “0” Table produced from 215 randomly generated 48-bit addresses

  17. Exact Matches in Ethernet SwitchesTrees and Tries • Advantages: • Fixed lookup time • Simple to implement and update • Disadvantages • Inefficient use of memory and/or requires large number of memory references More sophisticated algorithms compress ‘sparse’ nodes.

  18. Outline • Routing Lookups • Overview • Exact matching • Direct lookup • Associative lookup • Hashing • Trees and tries • Longest prefix matching • Why LPM? • Tries and compressed tries • Binary search on prefix intervals • References • Packet Classification

  19. Longest Prefix Matching: IPv4 Addresses • 32-bit addresses • Dotted quad notation: e.g. 12.33.32.1 • Can be represented as integers on the IP number line [0, 232-1]: a.b.c.d denotes the integer: (a*224+b*216+c*28+d) IP Number Line 0.0.0.0 255.255.255.255

  20. Class-based Addressing A B C D E 128.0.0.0 192.0.0.0 0.0.0.0

  21. Lookups with Class-based Addresses netid port# 23 Port 1 Class A 192.33.32.1 Class B 186.21 Port 2 Class C Exact match 192.33.32 Port 3

  22. Problems with Class-based Addressing • Fixed netid-hostid boundaries too inflexible • Caused rapid depletion of address space • Exponential growth in size of routing tables

  23. Early Exponential Growth in Routing Table Sizes Number of BGP routes advertised

  24. Classless Addressing (and CIDR) • Eliminated class boundaries • Introduced the notion of a variable length prefix between 0 and 32 bits long • Prefixes represented by P/l: e.g., 122/8, 212.128/13, 34.43.32/22, 10.32.32.2/32 etc. • An l-bit prefix represents an aggregation of 232-l IP addresses

  25. CIDR:Hierarchical Route Aggregation Backbone routing table 192.2.0/22, R2 Router Backbone R3 R1 R4 R2 R2 ISP, P ISP, Q 192.2.0/22 200.11.0/22 Site, S Site, T 192.2.1/24 192.2.2/24 192.2.1/24 192.2.2/24 192.2.0/22 200.11.0/22 IP Number Line

  26. Source: http://bgp.potaroo.net Post-CIDR Routing Table sizes Optional Exercise: What would this graph look like without CIDR? (Pick any one random AS, and plot the two curves side-by-side) Number of active BGP prefixes

  27. Routing Lookups with CIDR 192.2.2.100 Optional Exercise: Find the ‘nesting distribution’ for routes in your randomly-picked AS 192.2.2/24 192.2.2/24, R3 192.2.0/22 200.11.0/22 192.2.0/22, R2 200.11.0/22, R4 192.2.0.1 200.11.0.33 LPM: Find the most specific route, or the longest matching prefix among all the prefixes matching the destination address of an incoming packet

  28. Longest Prefix Match is Harder than Exact Match • The destination address of an arriving packet does not carry with it the information to determine the length of the longest matching prefix • Hence, one needs to search among the space of all prefix lengths; as well as the space of all prefixes of a given length

  29. LPM in IPv4Use 32 exact match algorithms for LPM! Network Address Exact match against prefixes of length 1 Exact match against prefixes of length 2 Priority Encode and pick Port Exact match against prefixes of length 32

  30. Metrics for Lookup Algorithms • Speed (= number of memory accesses) • Storage requirements (= amount of memory) • Low update time (support >10K updates/s) • Scalability • With length of prefix: IPv4 unicast (32b), Ethernet (48b), IPv4 multicast (64b), IPv6 unicast (128b) • With size of routing table: (sweetspot for today’s designs = 1 million) • Flexibility in implementation • Low preprocessing time

  31. Radix Trie (Recap) Add P5=1110* 0 P5 I Lookup 10111 Trie node A next-hop-ptr (if prefix) 1 B right-ptr left-ptr 1 C D 0 P2 1 1 F E P1 0 G P3 1 H P4

  32. Radix Trie • W-bit prefixes: O(W) lookup, O(NW) storage and O(W) update complexity • Advantages • Simplicity • Extensible to wider fields • Disadvantages • Worst case lookup slow • Wastage of storage space in chains

  33. Leaf-pushed Binary Trie Trie node A left-ptr or next-hop right-ptr or next-hop 1 B 1 C D 0 P1 P2 1 E P2 0 G P3 P4

  34. PATRICIA A Patricia tree internal node 2 0 bit-position 1 B C right-ptr left-ptr P1 3 1 0 E D 5 P2 1 0 F G P3 P4 Lookup 10111 Bitpos 12345

  35. PATRICIA • W-bit prefixes: O(W2) lookup, O(N) storage and O(W) update complexity • Advantages • Decreased storage • Extensible to wider fields • Disadvantages • Worst case lookup slow • Backtracking makes implementation complex

  36. Path-compressed Tree Lookup 10111 A 1, , 2 0 1 C B P1 10,P2,4 0 D 1010,P3,5 1 E P4 Path-compressed tree node structure next-hop (if prefix present) variable-length bitstring bit-position left-ptr right-ptr

  37. Path-compressed Tree • W-bit prefixes: O(W) lookup, O(N) storage and O(W) update complexity • Advantages • Decreased storage • Disadvantages • Worst case lookup slow

  38. Multi-bit Tries Multi-ary trie W/k Depth = W/k Degree = 2k Stride = k bits Binary trie W Depth = W Degree = 2 Stride = 1 bit

  39. Prefix Expansion with Multi-bit Tries If stride = k bits, prefix lengths that are not a multiple of k need to be expanded E.g., k = 2: Maximum number of expanded prefixes corresponding to one non-expanded prefix = 2k-1

  40. Four-ary Trie (k=2) Lookup 10111 A four-ary trie node next-hop-ptr (if prefix) A ptr00 ptr01 ptr10 ptr11 11 10 B C P2 11 10 D E F 10 P3 P11 P12 10 11 H G P41 P42

  41. Prefix Expansion Increases Storage Consumption • Replication of next-hop ptr • Greater number of unused (null) pointers in a node Time ~ W/k Storage ~ NW/k * 2k-1 Optional Exercise: The increase in number of null pointers in LPM is a worse problem than in exact match. Why?

  42. Generalization: Different Strides at Each Trie Level • 16-8-8 split • 4-10-10-8 split • 24-8 split • 21-3-8 split Optional Exercise: Why does this not work well for IPv6?

  43. Choice of Strides: Controlled Prefix Expansion [Sri98] • Advantages • Optimal storage under these constraints • Disadvantages • Updates lead to sub-optimality anyway • Hardware implementation difficult Given a forwarding table and a desired number of memory accesses in the worst case (i.e., maximum tree depth, D) A dynamic programming algorithm to compute the optimal sequence of strides that minimizes the storage requirements: runs in O(W2D) time

  44. Binary Search on Prefix Intervals [Lampson98] P4 P5 P2 P3 P1 I1 I2 I3 I4 I5 I6 1001 0010 0100 0110 1000 1010 1100 1110 1111 0000

  45. 1/8 1/32 1/32 1/2 1/4 1/16 P4 P5 P2 P3 P1 I1 I2 I3 I4 I5 I6 1001 0010 0100 0110 1000 1010 1100 1110 1111 0000 0111 Alphabetic Tree >  0011 1101   > > I3 0001 1100 I6 >   > I1 I2 I4 I5

  46. Another Alphabetic Tree 0001 0011 I1 1/2 0111 I2 1/4 1100 I3 1/8 1101 I4 1/16 I5 I6 1/32 1/32

  47. Multiway Search on Intervals • W-bit N prefixes: O(logN) lookup, • O(N) storage • Advantages • Storage is linear • Can be ‘balanced’ • Lookup time independent of W • Disadvantages • But, lookup time is dependent on N • Incremental updates more complex than tries • Each node is big in size: requires higher memory bandwidth

  48. Routing Lookups: References • [lulea98] A. Brodnik, S. Carlsson, M. Degermark, S. Pink. “Small Forwarding Tables for Fast Routing Lookups”, Sigcomm 1997, pp 3-14. [Example of techniques for decreasing storage consumption] • [gupta98] P. Gupta, S. Lin, N.McKeown. “Routing lookups in hardware at memory access speeds”, Infocom 1998, pp 1241-1248, vol. 3. [Example of hardware-optimized trie with increased storage consumption] • P. Gupta, B. Prabhakar, S. Boyd. “Near-optimal routing lookups with bounded worst case performance,” Proc. Infocom, March 2000 [Example of deliberately skewing alphabetic trees] • P. Gupta, “Algorithms for routing lookups and packet classification”, PhD Thesis, Ch 1 and 2, Dec 2000, available at http://yuba.stanford.edu/ ~pankaj/phd.html [Background and introduction to LPM]

  49. Routing lookups : References (contd) • [lampson98] B. Lampson, V. Srinivasan, G. Varghese. “ IP lookups using multiway and multicolumn search”, Infocom 1998, pp 1248-56, vol. 3. [Multi-way search] • [PerfHash] Y. Lu, B. Prabhakar and F. Bonomi. “Perfect hashing for network applications”, ISIT, July 2006 • [LC-trie] S. Nilsson, G. Karlsson. “Fast address lookup for Internet routers”, IFIP Intl Conf on Broadband Communications, Stuttgart, Germany, April 1-3, 1998. • [sri98] V. Srinivasan, G.Varghese. “Fast IP lookups using controlled prefix expansion”, Sigmetrics, June 1998. • [wald98] M. Waldvogel, G. Varghese, J. Turner, B. Plattner. “Scalable high speed IP routing lookups”, Sigcomm 1997, pp 25-36.

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