Parallel Matrix times Vector Solution

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Consider this as an expanded assignment of assignment 2. A Row-wise Block Parallel Mapping I This implementation requires no synchronization K I K = T0 Thread T0 T1 Thread T1 K Y A X A Row-wise Block Parallel Mapping II This implementation requires lots of synchronization A[n X m] s X[0, … , n-1] T00…

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Consider this as an expanded assignment of assignment 2.

A Row-wise Block Parallel Mapping I

This implementation requires no synchronization

K I K

=

T0

Thread T0

T1

Thread T1

K

Y A X

A Row-wise Block Parallel Mapping II

This implementation requires lots of synchronization

A[n X m]

s

X[0, … , n-1]

T00

T01

T0n

T10

T11

T1n

X[0, … , n-1]

Thread Tij

where

Tm0 Tm1 Tmn i = 1 . . . m J = 1 . . .n

A Row-wise Block Parallel Mapping III

This implementation requires lots of synchronization

A[n X m]

s

X[0, … , s-1]

T00

T10

Tm0

T01

T11

Tm1

X[s, … , 2s-1]

T0n

T1n

Tmn

X[n-s-1, … , n-1]

Parallel Matrix times Vector

Give reasons for the differences between mapping I, II and III in terms of spatial- and temporal-locality.

Question: if these mappings are run sequentially, would they have the same performance?

Parallel Matrix times Vector Solution
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