address lookup and classification

1

Address Lookup and Classification

EE384Y

May 23, 2006High PerformanceSwitching and RoutingTelecom Center Workshop: Sept 4, 1997.

Pankaj GuptaPrincipal Architect and Member of Technical

Staff, Netlogic Microsystems

[email protected]://klamath.stanford.edu/~pankaj

2

Generic Router Architecture (Review from EE384x)

LookupIP Address

UpdateHeader

Header ProcessingData Hdr Data Hdr

~1M prefixesOff-chip DRAM

AddressTable

AddressTable

IP Address Next Hop

QueuePacket

BufferMemoryBuffer

Memory~1M packetsOff-chip DRAM

3

Lookups Must be Fast

1. Lookup mechanism must be simple and easy to implement2. Memory access time is the bottleneck

200Mpps × 2 lookups/pkt = 400 Mlookups/sec → 2.5ns per lookup

Year Aggregate Line-rate

Arriving rate of 40B POS packets (Million pkts/sec)

1997 622 Mb/s 1.56

1999 2.5 Gb/s 6.25

2001 10 Gb/s 25

2003 40 Gb/s 100

2006 80 Gb/s 200

4

Memory Technology (2006)

Technology

Max single chip density

$/chip ($/MByte)

Access speed

Watts/chip

Networking DRAM

64 MB $30-$50($0.50-$0.75)

40-80ns 0.5-2W

SRAM 8 MB $50-$60($5-$8)

3-4ns 2-3W

TCAM 2 MB $200-$250($100-$125)

4-8ns 15-30W

Note: Price, speed and power are manufacturer and market dependent.

5

Lookup Mechanism is Protocol Dependent

Networking Protocol

Lookup Mechanism

Techniques we will study

MPLS, ATM, Ethernet

Exact match search

–Direct lookup–Associative lookup–Hashing–Binary/Multi-way Search Trie/Tree

IPv4, IPv6 Longest-prefix match search

-Radix trie and variants-Compressed trie-Binary search on prefix intervals

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Outline

I. 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

II. Packet Classification

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Exact Matches in ATM/MPLS

VCI/MPLS-label

Addre

ss

Memory

Data

(Outgoing Port, new VCI/label)

• 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

Direct Memory Lookup

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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)

• Associative memory (aka Content Addressable Memory, CAM) compares all entries in parallel against incoming data.

Network address Data

AssociativeMemory(“CAM”)

Addre

ss48bitsMatch

Location

Addre

ss“Normal”Memory

Data

Port

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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

HashingFunction

Memory

Addre

ss

Data

NetworkAddress

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16, say Pointer

Memory

Addre

ss

DataList/Bucket

List of network addresses in this bucket

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Exact Matches Using HashingNumber of memory references

Where:

ER Expected number of memory references=

M Number of memory addresses in table=

N Number of linked lists= M N=

M

N)

11(1

12

1

empty)not islist |list oflength Expected(2

1ER

:referencesmemory ofnumber Expected

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Perfect Hashing

HashingFunction

Memory

Addre

ss

Data

NetworkAddress

48

16, say Port

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…

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Hashing• 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)

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Trees and TriesBinary Search Tree

< >

< > < >

log

2 NN entries

Binary Search Trie

0 1

0 1 0 1

111010

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)

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Multiway tries16-ary Search Trie

0000, ptr 1111, ptr

0000, 0 1111, ptr

000011110000

0000, 0 1111, ptr

111111111111

Ptr=0 means no children

Q: Why can’t we just make it a 248-ary trie?

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Multiway tries

Degree ofTree

# MemReferences

# Nodes(x106)

Total Memory(Mbytes)

FractionWasted (%)

2 48 1.09 4.3 494 24 0.53 4.3 738 16 0.35 5.6 8616 12 0.25 8.3 9364 8 0.17 21 98256 6 0.12 64 99.5

Table produced from 215 randomly generated 48-bit addresses

As degree increases, more and more pointers are “0”

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Trees 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.

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Outline

I. 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

II. Packet Classification

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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)

0.0.0.0 255.255.255.255IP Number Line

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Class-based Addressing

A B C D

0.0.0.0

E

128.0.0.0 192.0.0.0

Class Range MS bits netid hostidA 0.0.0.0 –

128.0.0.00 bits 1-7 bits 8-31

B 128.0.0.0 -191.255.255.255

10 bits 2-15 bits 16-31

C 192.0.0.0 -223.255.255.255

110 bits 3-23 bits 24-31

D (multicast)

224.0.0.0 - 239.255.255.255

1110 - -

E (reserved)

240.0.0.0 -255.255.255.255

11110 - -

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Lookups with Class-based Addresses

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186.21

Port 1

Port 2192.33.32.1

Class A

Class B

Class C

192.33.32 Port 3Exact match

netid port#

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Problems with Class-based Addressing

• Fixed netid-hostid boundaries too inflexible– Caused rapid depletion of address

space

• Exponential growth in size of routing tables

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Early Exponential Growth in Routing Table Sizes

Num

ber

of

BG

P r

oute

s advert

ised

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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

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CIDR:Hierarchical Route Aggregation

Backbone

Router

R1R2

R3R4

ISP, P ISP, Q192.2.0/22 200.11.0/22

Site, S

192.2.1/24

Site, T

192.2.2/24 192.2.0/22 200.11.0/22

192.2.1/24 192.2.2/24

192.2.0/22, R2

Backbone routing table

IP Number Line

R2

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Post-CIDR Routing Table sizes

Source: http://bgp.potaroo.net

Nu

mb

er

of

act

ive B

GP p

refixes Optional Exercise: What would this graph

look like without CIDR? (Pick any one random AS, and plot the two curves side-by-side)

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Routing Lookups with CIDR

192.2.0/22, R2

192.2.2/24, R3 192.2.0/22 200.11.0/22

192.2.2/24

200.11.0/22, R4

200.11.0.33192.2.0.1 192.2.2.100

LPM: Find the most specific route, or the longest matching prefix among all the prefixes matching the destination address of an incoming packet

Optional Exercise: Find the ‘nesting distribution’ for routes in your randomly-picked AS

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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

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LPM in IPv4Use 32 exact match algorithms for

LPM!

Exact matchagainst prefixes

of length 1


of length 2


of length 32

Network Address PortPriorityEncodeand pick

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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

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Radix Trie (Recap)

P1 111* H1

P2 10* H2

P3 1010*

H3

P4 10101

H4

P2

P3

P4

P1

A

B

C

G

D

F

H

E

1

0

0

1 1

1

1

Lookup 10111

Add P5=1110*

I

0

P5

next-hop-ptr (if prefix)

left-ptr right-ptr

Trie node

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Radix Trie

• W-bit prefixes: O(W) lookup, O(NW) storage and O(W) update complexity

Advantages

SimplicityExtensible to wider fields

Disadvantages

Worst case lookup slowWastage of storage space in chains

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Leaf-pushed Binary Trie

A

B

C

G

D

E

1

0

0

1

1

left-ptr or next-hop

Trie node

right-ptr or next-hop

P2

P4P3

P2

P1P1 111* H1

P2 10* H2

P3 1010*

H3

P4 10101

H4

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PATRICIA

2A

B C

E

10

1

Patricia tree internal node

3

P3

P2

P4

P110

0F G

D5

bit-position

left-ptr right-ptr

Lookup 10111

P1 111* H1

P2 10* H2

P3 1010*

H3

P4 10101

H4

Bitpos 12345

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• 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 slowBacktracking makes implementation complex

PATRICIA

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Path-compressed Tree

1, , 2A

B C10

10,P2,4

P4

P1

1

0

E

D1010,P3,5

bit-position

left-ptr right-ptr

variable-length bitstring

next-hop (if prefix present)

Path-compressed tree node structure

Lookup 10111

P1 111* H1

P2 10* H2

P3 1010*

H3

P4 10101

H4

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• W-bit prefixes: O(W) lookup, O(N) storage and O(W) update complexity

Advantages

Decreased storage

Disadvantages

Worst case lookup slow

Path-compressed Tree

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Multi-bit Tries

Depth = WDegree = 2Stride = 1 bit

Binary trieW

Depth = W/kDegree = 2k

Stride = k bits

Multi-ary trie

W/k

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Prefix Expansion with Multi-bit Tries

If stride = k bits, prefix lengths that are not a multiple of k need to be expanded

Prefix Expanded prefixes

0* 00*, 01*

11* 11*

E.g., k = 2:

Maximum number of expanded prefixes corresponding to one non-expanded prefix = 2k-

1

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Four-ary Trie (k=2)

P2

P3 P12

A

B

F11

next-hop-ptr (if prefix)

ptr00 ptr01

A four-ary trie node

P11

10

P42

H11

P41

10

10

1110

D

C

E

G

ptr10 ptr11

Lookup 10111

P1 111* H1

P2 10* H2

P3 1010*

H3

P4 10101

H4

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Prefix Expansion Increases Storage Consumption

• Replication of next-hop ptr• Greater number of unused (null)

pointers in a node

Time ~ W/kStorage ~ 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?

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Choice of Strides: Controlled Prefix Expansion [Sri98]

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) timeAdvantages

Optimal storage under these constraints

Disadvantages

Updates lead to sub-optimality anywayHardware implementation difficult

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Binary Search on Prefix Intervals [Lampson98]

0000 11110010 0100 0110 1000 11101010 1100

P1

P4P3

P5P2

Prefix IntervalP1 /0 0000…

1111

P2 00/2 0000…0011

P3 1/1 1000…1111

P4 1101/4 1101…1101

P5 001/3 0010…0011

1001

I1 I3 I4 I5 I6I2

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I1

I3

I2 I4 I5

I6

0111

0011 1101

11000001

>Alphabetic Tree

1/2 1/4

1/8

1/16 1/32

1/32

>

>

>

>

0000 11110010 0100 0110 1000 11101010 1100

P1

P4P3

P5P2

1001

I1 I3 I4 I5 I6I2

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0001

Another Alphabetic Tree

I1

I2

I5

I3

I4

I6

0111

0011

1100

1101

1/2

1/4

1/8

1/16

1/32 1/32

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Advantages

Storage is linearCan be ‘balanced’Lookup time independent of W

Disadvantages

But, lookup time is dependent on NIncremental updates more complex than triesEach node is big in size: requires higher memory bandwidth

•W-bit N prefixes: O(logN) lookup, O(N) storage

Multiway Search on Intervals

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]

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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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