CS 184 a Computer Architecture Structure and Organization

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CS 184 a: Computer Architecture (Structure and Organization) Day 16: February 14, 2003 Interconnect

CS 184 a: Computer Architecture (Structure and Organization) Day 16: February 14, 2003 Interconnect 6: Mo. T Caltech CS 184 Winter 2003 -- De. Hon 1

Previously • HSRA/BFT – natural hierarchical network – Switches scale O(N) • Mesh –

Previously • HSRA/BFT – natural hierarchical network – Switches scale O(N) • Mesh – natural 2 D network – Switches scale W(Np+0. 5) Caltech CS 184 Winter 2003 -- De. Hon 2

Today • • Good Mesh properties HSRA vs. Mesh Mo. T Grand unified network

Today • • Good Mesh properties HSRA vs. Mesh Mo. T Grand unified network theory – Mo. T vs. HSRA – Mo. T vs. Mesh Caltech CS 184 Winter 2003 -- De. Hon 3

Mesh 1. Wire delay can be Manhattan Distance 2. Network provides Manhattan Distance route

Mesh 1. Wire delay can be Manhattan Distance 2. Network provides Manhattan Distance route from source to sink Caltech CS 184 Winter 2003 -- De. Hon 4

HSRA/BFT • Physical locality does not imply logical closeness Caltech CS 184 Winter 2003

HSRA/BFT • Physical locality does not imply logical closeness Caltech CS 184 Winter 2003 -- De. Hon 5

HSRA/BFT • Physical locality does not imply logical closeness • May have to route

HSRA/BFT • Physical locality does not imply logical closeness • May have to route twice the Manhattan distance Caltech CS 184 Winter 2003 -- De. Hon 6

Tree Shortcuts • Add to make physically local things also logically local • Now

Tree Shortcuts • Add to make physically local things also logically local • Now wire delay always proportional to Manhattan distance • May still be 2 longer wires Caltech CS 184 Winter 2003 -- De. Hon 7

BFT/HSRA ~ 1 D • Essentially onedimensional tree – Laid out well in 2

BFT/HSRA ~ 1 D • Essentially onedimensional tree – Laid out well in 2 D Caltech CS 184 Winter 2003 -- De. Hon 8

Consider Full Population Tree To. M Tree of Meshes Caltech CS 184 Winter 2003

Consider Full Population Tree To. M Tree of Meshes Caltech CS 184 Winter 2003 -- De. Hon 9

Can Fold Up Caltech CS 184 Winter 2003 -- De. Hon 10

Can Fold Up Caltech CS 184 Winter 2003 -- De. Hon 10

Gives Uniform Channels Works nicely p=0. 5 Channels log(N) [Greenberg and Leiserson, Appl. Math

Gives Uniform Channels Works nicely p=0. 5 Channels log(N) [Greenberg and Leiserson, Appl. Math Lett. v 1 n 2 p 171, 1988] Caltech CS 184 Winter 2003 -- De. Hon 11

Gives Uniform Channels (and add shortcuts) Caltech CS 184 Winter 2003 -- De. Hon

Gives Uniform Channels (and add shortcuts) Caltech CS 184 Winter 2003 -- De. Hon 12

How wide are channels? Caltech CS 184 Winter 2003 -- De. Hon 13

How wide are channels? Caltech CS 184 Winter 2003 -- De. Hon 13

How wide are channels? Caltech CS 184 Winter 2003 -- De. Hon 14

How wide are channels? Caltech CS 184 Winter 2003 -- De. Hon 14

How wide are channels? • A constant factor wider than lower bound! • P=2/3

How wide are channels? • A constant factor wider than lower bound! • P=2/3 ~8 • P=3/4 ~5. 5 Caltech CS 184 Winter 2003 -- De. Hon 15

Implications • Tree never requires more than constant factor more wires than mesh –

Implications • Tree never requires more than constant factor more wires than mesh – Even w/ the non-minimal length routes – Even w/out shortcuts • Mesh global route upper bound channel width is O(Np-0. 5) – Can always use foldsquash tree as the route Caltech CS 184 Winter 2003 -- De. Hon 16

Mo. T Caltech CS 184 Winter 2003 -- De. Hon 17

Mo. T Caltech CS 184 Winter 2003 -- De. Hon 17

Recall: Mesh Switches • Switches per switchbox: – 6 w/Lseg • Switches into network:

Recall: Mesh Switches • Switches per switchbox: – 6 w/Lseg • Switches into network: – (K+1) w • Switches per PE: – 6 w/Lseg + Fc (K+1) w – w = c. Np-0. 5 – Total Np-0. 5 • Total Switches: N*(Sw/PE) Np+0. 5 > N Caltech CS 184 Winter 2003 -- De. Hon 18

Recall: Mesh Switches • Switches per PE: – 6 w/Lseg + Fc (K+1) w

Recall: Mesh Switches • Switches per PE: – 6 w/Lseg + Fc (K+1) w – w = c. Np-0. 5 – Total Np-0. 5 • Not change for – Any constant Fc – Any constant Lseg Caltech CS 184 Winter 2003 -- De. Hon 19

Mesh of Trees • Hierarchical Mesh • Build Tree in each column [Leighton/FOCS 1981]

Mesh of Trees • Hierarchical Mesh • Build Tree in each column [Leighton/FOCS 1981] Caltech CS 184 Winter 2003 -- De. Hon 20

Mesh of Trees • Hierarchical Mesh • Build Tree in each column • …and

Mesh of Trees • Hierarchical Mesh • Build Tree in each column • …and each row [Leighton/FOCS 1981] Caltech CS 184 Winter 2003 -- De. Hon 21

Mesh of Trees • More natural 2 D structure • Maybe match 2 D

Mesh of Trees • More natural 2 D structure • Maybe match 2 D structure better? – Don’t have to route out of way Caltech CS 184 Winter 2003 -- De. Hon 22

Support P P=0. 5 Caltech CS 184 Winter 2003 -- De. Hon P=0. 75

Support P P=0. 5 Caltech CS 184 Winter 2003 -- De. Hon P=0. 75 23

Mo. T Parameterization • Support C with additional trees C=1 C=2 Caltech CS 184

Mo. T Parameterization • Support C with additional trees C=1 C=2 Caltech CS 184 Winter 2003 -- De. Hon 24

Mesh of Trees • Logic Blocks – Only connect at leaves of tree •

Mesh of Trees • Logic Blocks – Only connect at leaves of tree • Connect to the C trees (4 C) Caltech CS 184 Winter 2003 -- De. Hon 25

Switches • Total Tree switches – 2 C (switches/tree) • Sw/Tree: Caltech CS 184

Switches • Total Tree switches – 2 C (switches/tree) • Sw/Tree: Caltech CS 184 Winter 2003 -- De. Hon 26

Switches • Total Tree switches – 2 C (switches/tree) • Sw/Tree: Caltech CS 184

Switches • Total Tree switches – 2 C (switches/tree) • Sw/Tree: Caltech CS 184 Winter 2003 -- De. Hon 27

Switches • Only connect to leaves of tree • C (K+1) switches per leaf

Switches • Only connect to leaves of tree • C (K+1) switches per leaf • Total switches § Leaf + Tree § O(N) Caltech CS 184 Winter 2003 -- De. Hon 28

Wires • Design: O(Np) in top level • Total wire width of channels: O(Np)

Wires • Design: O(Np) in top level • Total wire width of channels: O(Np) – Another geometric sum • No detail route guarantee (at present) Caltech CS 184 Winter 2003 -- De. Hon 29

Empirical Results • Benchmark: Toronto 20 • Compare to Lseg=1, Lseg=4 – CLMA ~

Empirical Results • Benchmark: Toronto 20 • Compare to Lseg=1, Lseg=4 – CLMA ~ 8 K LUTs • Mesh(Lseg=4): w=14 122 switches • Mo. T(p=0. 67): C=4 89 switches – Benchmark wide: 10% less • CLMA largest • Asymptotic advantage Caltech CS 184 Winter 2003 -- De. Hon 30

Shortcuts • Strict Tree – Same problem with physically far, logically close Caltech CS

Shortcuts • Strict Tree – Same problem with physically far, logically close Caltech CS 184 Winter 2003 -- De. Hon 31

Shortcuts • Empirical – Shortcuts reduce C – But net increase in total switches

Shortcuts • Empirical – Shortcuts reduce C – But net increase in total switches Caltech CS 184 Winter 2003 -- De. Hon 32

Staggering • With multiple Trees – Offset relative to each other – Avoids worst-case

Staggering • With multiple Trees – Offset relative to each other – Avoids worst-case discrete breaks – One reason don’t benefit from shortcuts Caltech CS 184 Winter 2003 -- De. Hon 33

Flattening • Can use arity other than two Caltech CS 184 Winter 2003 --

Flattening • Can use arity other than two Caltech CS 184 Winter 2003 -- De. Hon 34

Mo. T Parameters • • • Shortcuts Staggering Corner Turns Arity Flattening Caltech CS

Mo. T Parameters • • • Shortcuts Staggering Corner Turns Arity Flattening Caltech CS 184 Winter 2003 -- De. Hon 35

Mo. T Layout Main issue is layout 1 D trees in multilayer metal Caltech

Mo. T Layout Main issue is layout 1 D trees in multilayer metal Caltech CS 184 Winter 2003 -- De. Hon 36

Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 37

Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 37

Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 38

Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 38

Composite Logic Block Tile Caltech CS 184 Winter 2003 -- De. Hon 39

Composite Logic Block Tile Caltech CS 184 Winter 2003 -- De. Hon 39

P=0. 75 Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 40

P=0. 75 Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 40

P=0. 75 Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 41

P=0. 75 Row/Column Layout Caltech CS 184 Winter 2003 -- De. Hon 41

Mo. T Layout • Easily laid out in Multiple metal layers – Minimal O(Np-0.

Mo. T Layout • Easily laid out in Multiple metal layers – Minimal O(Np-0. 5) layers • Contain constant switching area per LB – Even with p>0. 5 Caltech CS 184 Winter 2003 -- De. Hon 42

Relation? Caltech CS 184 Winter 2003 -- De. Hon 43

Relation? Caltech CS 184 Winter 2003 -- De. Hon 43

How Related? • What lessons translate amongst networks? • Once understand design space –

How Related? • What lessons translate amongst networks? • Once understand design space – Get closer together • Ideally – One big network design we can parameterize Caltech CS 184 Winter 2003 -- De. Hon 44

Mo. T HSRA (P=0. 5) Caltech CS 184 Winter 2003 -- De. Hon 45

Mo. T HSRA (P=0. 5) Caltech CS 184 Winter 2003 -- De. Hon 45

Mo. T HSRA (p=0. 75) Caltech CS 184 Winter 2003 -- De. Hon 46

Mo. T HSRA (p=0. 75) Caltech CS 184 Winter 2003 -- De. Hon 46

Mo. T HSRA • A C Mo. T maps directly onto a 2 C

Mo. T HSRA • A C Mo. T maps directly onto a 2 C HSRA – Same p’s • HSRA can route anything Mo. T can Caltech CS 184 Winter 2003 -- De. Hon 47

HSRA Mo. T • Decompose and look at rows • Add homogeneous, upper-level corner

HSRA Mo. T • Decompose and look at rows • Add homogeneous, upper-level corner turns Caltech CS 184 Winter 2003 -- De. Hon 48

HSRA Mo. T Caltech CS 184 Winter 2003 -- De. Hon 49

HSRA Mo. T Caltech CS 184 Winter 2003 -- De. Hon 49

HSRA Mo. T Caltech CS 184 Winter 2003 -- De. Hon 50

HSRA Mo. T Caltech CS 184 Winter 2003 -- De. Hon 50

HSRA Mo. T Caltech CS 184 Winter 2003 -- De. Hon 51

HSRA Mo. T Caltech CS 184 Winter 2003 -- De. Hon 51

HSRA Mo. T • HSRA + HSRAT = Mo. T w/ H-UL-CT – Same

HSRA Mo. T • HSRA + HSRAT = Mo. T w/ H-UL-CT – Same C, P – H-UL-CT: Homogeneous, Upper-Level, Corner Turns Caltech CS 184 Winter 2003 -- De. Hon 52

HSRA Mo. T (p=0. 75) Caltech CS 184 Winter 2003 -- De. Hon 53

HSRA Mo. T (p=0. 75) Caltech CS 184 Winter 2003 -- De. Hon 53

HSRA Mo. T (p=0. 75) • Can organize HSRA as Mo. T • P>0.

HSRA Mo. T (p=0. 75) • Can organize HSRA as Mo. T • P>0. 5 Mo. T layout – Tells us how to layout p>0. 5 HSRA Caltech CS 184 Winter 2003 -- De. Hon 54

Mo. T vs. Mesh • Mo. T has Geometric Segment Lengths • Mesh has

Mo. T vs. Mesh • Mo. T has Geometric Segment Lengths • Mesh has flat connections • Mo. T must climb tree – Parameterize w/ flattening • Mo. T has O(Np-0. 5) less switches Caltech CS 184 Winter 2003 -- De. Hon 55

Mo. T vs. Mesh • Wires – Asymptotically the same (p>0. 5) – Cases

Mo. T vs. Mesh • Wires – Asymptotically the same (p>0. 5) – Cases where Mesh requires constant less – Cases where require same number Caltech CS 184 Winter 2003 -- De. Hon 56

Admin • Monday = President’s Day Holiday – No Class – (CS Systems down

Admin • Monday = President’s Day Holiday – No Class – (CS Systems down for Maintenance) – Assignment due Wed. as a result Caltech CS 184 Winter 2003 -- De. Hon 57

Big Ideas • Networks driven by same wiring requirements – Have similar wiring asymptotes

Big Ideas • Networks driven by same wiring requirements – Have similar wiring asymptotes • Can bound – Network differences – Worst-case mesh global routing • Hierarchy structure allows to save switches – O(N) vs. W(Np+0. 5) Caltech CS 184 Winter 2003 -- De. Hon 58