PP16 Lec11 IN5 Routing.algo

8/16/2019 PP16 Lec11 IN5 Routing.algo

1/16

1.1

Parallel Processingsp2016

lec# 11

Dr M Shamim Baig


2/16

Routing Algorithms & usageExamples:

1.2


3/16

Static INs:

Routing Algorithms & usageExamples

1.3


4/16

1.4

Self-Routing Algorithm & Usage !ample"2-D/ 3-D/ k-d mesh(non-rap!

Routing-Path (on/ off) multiim-mesh: (a) !-" mesh #ith no #raparoun$

(%) -" mesh #ith no #raparoun


5/16

1.

Self-Routing Algorithm $ Usage !ample"

Path %on/ o""! #$per%ue!'

Routing-Path (on/off net#or') from noe P s () to noe P d ()in a three-imensional h*percu%e using self-routing algorithm

&he 'istance (et)een an* t)o no'es is gi+en (* num(er of (it positions in )hich t)o no'e,s (inar* la(els 'iffer .


6/16

unction (ase' Routing Algorithm $ usagee!ample for *percu(e" Path %on/off net)or

Cube Function: C i (x)=

C i(xd-1 xd-2 … xi ……. x2 x1 x0 )= (xd-1 xd-2 ……xi…. x2 x1 x0 )

where x is d-bit binary node-id for p-node cube, # of dim =d= logp, i is dim index


7/16

"*namic INs:

Routing Algorithms $ usage!amples"

1.


8/161.

5et S (e the (inar* representation of the sourcean' D (e that of the 'estination processor.

&he 'ata tra+erses the lin to the first s)itching

no'e. f the most significant (its of S an' D are

the same7 then the 'ata is route' in pass-throughmo'e (* the s)itch else7 it s)itches to crosso+er.

&his process is repeate' for each of the log p

s)itching stages 'i.

ormal Self-Routing Algorithm for 8mega-9:

$ its usage e!ample ;;;;;;;;

Self-routing approach for +mega-,IN


9/16

Self-routing Algorithm $ Usage Examplein ( x )mega-M*+!

Routing-Paths (on MIN): to route-paths (,,-to- & ,-to-,,! %an e

dran ON the M*+ ith *S.

'2 '1 'o


10/161.10

8mega 9:"

unction %S< $ S= (ase' Routing Approach

5et S (e the (inar* representation of the source

an' D (e that of the 'estination processor.

&he 'ata tra+ersing the lin is 'etermine' (* the

Shuffle S


11/161.11

Shuffle & Exchange unctions

use in +mega-,IN

Shu""le is used as (*S.-0un%tion! & Ex%hange is used as (S1-"un%tion! in )mega M*+

Shuffle Function: S(x)= rotate-left-x

S(xd-1 xd-2 ………. x2 x1 x0 )= (xd-2 xd-3 ………. x1 x0 xd-1 )

Exchange Function: E(x)=

E(xd-1 xd-2 ………. x2 x1 x0 )= (xd-1 xd-2 ………. x2 x1 x0 )

If x is positionID in binary for (p x p), d-stage MI where d= logp !

x= xd-1 xd-2 ………. x2 x1 x0


12/16

examples in ( x )mega-M*+!

1ill 1ork een hen all M*+ links/S1s not

dran

Routing-Paths (on/ off MIN): to route-paths (,,-to- & ,-to-,,! %ane dran ON the M*+ ithout *S. #o aout path OFF the M*+

stage2 stage1 stageo


13/16

Interconnection unctions


14/161.14

Plus-,inus-!i (P,!i) Net#or'

Use' in Prefi!-sum computing %later


15/161.1Butterfl* 9: is use' in & computation

utterfl*-unction

Butterfly Function: B(x)=

B(xd-1 xd-2 ………. x2 x1 x0 )= (x0 xd-2 ………. x2 x1 xd-1 )where x is d-bit binary number where d= logp,

B%110C 011


16/16

Important points for Routing

Di""eren%e eteen Routing in Static s >*namic

interconnection net)or.

Di""eren%e eteen Self-routing s unction

%S< $ S= (ase' routing

Di""eren%e eteen Routing Path identi"i%ation'

D 8: the net)or %static/'*namic

D 8 the net)or (Separate4 not on the netork!

Di""eren%e eteen Appl*%use s =rite %gi+e

Routing Algorithm

1 16

Documents

PP16 Lec11 IN5 Routing.algo