Directory Based Systems-Parallel Processing-Lecture Slides, Slides of Parallel Computing and Programming

Prof. Bhairav Gupta delivered this lecture at Ankit Institute of Technology and Science for Parallel Processing course. It includes: Directory, Based, Systems, Snoopy, Caches, Coherence, IN, Processor, Interconnection, Network

Typology: Slides

2011/2012

Uploaded on 07/23/2012

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Directory Based Systems
In snoopy caches, each coherence operation is sent to
all processors. This is an inherent limitation.
Why not send coherence requests to only those
processors that need to be notified?
This is done using a directory, which maintains a
presence vector for each data item (cache line) along
with its global state.
When IN is not a bus(like MIN etc), broadcast in not
implicit & requires additional hadware & time delay to
configure. A point to point comm is favoured.
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Directory Based Systems

•^

In snoopy caches, each coherence operation is sent toall processors. This is an inherent limitation.

•^

Why not send coherence requests to only thoseprocessors that need to be notified?

•^

This is done using a directory, which maintains apresence vector for each data item (cache line) alongwith its global state.

•^

When IN is not a bus(like MIN etc), broadcast in notimplicit & requires additional hadware & time delay toconfigure. A point to point comm is favoured.

Directory Based Systems

Architecture of typical directory based systems:(a) a centralized directory (b) a distributed directory.

(a)^

(b)

Directory

Data

State

PresenceBits

ProcessorCache ProcessorCache

ProcessorCache

ProcessorCache

Interconnection Network

Interconnection Network

Memory

Presence bits / State

ProcessorCache Memory

Presence bits / State

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Directory Entries in the Multiprocessors

Topology Embedding

Topologies Embedding Issues

•^

Performance Metric– Dilation– Congestion

•^

Embedding Sparser networks in Denser Networks– Linear Array into a Mesh– Linear Array into a Hypercube– Mesh into a Hypercube

•^

Embedding Denser Networks in Sparser Networks– Mesh into a Linear Array– Hypercube into a Mesh

Mapping Techniques for Graphs: Metrics •^

When mapping a graph

G(V,E)

into

G’(V’,E’),

the

following metrics are important:

•^

The maximum number of edges mapped onto any edgein^

E’

is called the

congestion

of the mapping.

•^

The maximum number of links in

E’

that any edge in

E

is

mapped onto is called the

dilation

of the mapping.

•^

The ratio of the number of nodes in the set

V’

to that in

set

V

is called the

expansion

of the mapping.

Embedding a Linear Arrayinto a Hypercube: Example

(^ a) A three-bit reflected Gray code ring; and (b) its embedding into a

three-dimensional hypercube.

1−bit Gray code
2−bit Gray code
3−bit Gray code
3−D hypercube
8−processor ring
Reflectalong thisline

(a) 110

010 000

011 001

111 101

(b) 100

Embedding a Mesh into a Hypercube

(a) A 4

×^ 4 mesh illustrating the mapping of mesh nodes to the nodes in a four-dimensionalhypercube; and (b) a 2

×^ 4 mesh embedded into a three-dimensional hypercube.

Once again, the congestion, dilation, and expansion of the mapping is 1.

Processors in a column haveidentical two least−significant bits
Processors in a row have identicaltwo most−significant bits

(a)

(b)

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