Parallel and Distributed Processing CSE 8380

1. Parallel and Distributed ProcessingCSE 8380 January 27 2005 Session 5

2. Contents • Dynamic Networks • Bus based systems • Switch based systems

3. Interconnection Network Dynamic Static Bus-based Switch-based 1-D 2-D HC Crossbar Single Multiple SS MS

4. Dynamic Network Analysis Parameters: • Cost • Delay: latency • Blocking characteristics • Fault tolerance

5. C C C P P P P P P Bus Based IN Global Memory Global Memory

6. Dynamic Interconnection Networks • Communication patterns are based on program demands • Connections are established on the fly during program execution • Multistage Interconnection Network (MIN) and Crossbar

7. Switch Modules • A x B switch module • A inputs and B outputs • In practice, A = B = power of 2 • Each input is connected to one or more outputs (conflicts must be avoided) • One-to-one (permutation) and one-to-many are allowed

8. 2x2 Switch Binary Switch Legitimate States = 4 Permutation Connections = 2

9. Straight Exchange Upper-broadcast Lower-broadcast The different setting of the 2X2 SE Legitimate Connections

10. Group Work General Case ??

11. Multistage Interconnection Networks ISC  Inter-stage Connection Patterns ISC1 ISC2 ISCn switches switches switches

12. Perfect-Shuffle Routing Function • Given x = {an, an-1, …, a2, a1} • P(x) = {an-1, …, a2, a1 , an} X =110001 P(x) = 100011

13. Perfect Shuffle Example 000  000 001  010 010  100 011  110 100  001 101  011 110  101 111  111

14. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Perfect-Shuffle

15. Exchange Routing Function • Given x = {an, an-1, …, a2, a1} • Ei(x) = {an, an-1, …, ai, …, a2, a1} X = 0000000 E3(x) = 0000100

16. Exchange E1 000 001 001 000 010 011 011 010 100 101 101 100 110 111 111 110

17. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Exchange E1

18. Butterfly Routing Function • Given x = {an, an-1, …, a2, a1} • B(x) = {a1 , an-1, …, a2, an} X =010001 P(x) = 110000

19. Butterfly Example 000  000 001  100 010  010 011  110 100  001 101  101 110  011 111  111

20. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Butterfly

21. Multi-stage network 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111

22. MIN (cont.) An 8X8 Banyan network

23. Min Implementation Control (X) Source (S) Destination (D) X = f(S,D)

24. A C A C B D B D X = 0 X = 1 ( ) ) crossed (straight Example

25. stage 2 stage 1 stage 3 Consider this MIN D1 S1 D2 S2 S3 D3 D4 S4 D5 S5 D6 S6 D7 S7 S8 D8

26. Example (Cont.) • Let control variable be X1, X2, X3 • Find the values of X1, X2, X3 to connect: • S1  D6 • S7  D5 • S4  D1

27. The 3 connections stage 2 stage 1 stage 3 D1 S1 D2 S2 S3 D3 D4 S4 D5 S5 D6 S6 D7 S7 S8 D8

28. Boolean Functions • X = x1, x2, x3 • S = s2, s2, s3 • D = d1, d2, d3 • Find X = f(S,D)

29. M1 M2 M3 M4 M5 M6 M7 M8 P1 P2 P3 P4 P5 P6 P7 P8 Crossbar Switch

30. Analysis and performance metricsdynamic networks