PARALLEL TRANSITION LOCALIZATIONCS 791V COURSE PROJECT VINITHA KHAMBADKAR

Signal Transitions Change from one

significant condition to another in a digital signal ie. High to low or viceversa.

Transition Localization

Measurement analysis in which transition times btwn logic levels for a given digital signal are measured.

L & H are the state boundaries m is the intermediate state ie.

(L+h)/2 For a valid L->H transition,x(i) <m ≤

x(i+1) For a valid H->L transition, x(i+1) ≤

m<x(i)

Complicating Factors

The signal could oscillate over ‘m’ before going to a valid high or low state.

Each signal has dependencies over the previous signal.

Parallel Algorithm

Dr. Lee Barford came up with a parallel Algorithm overcoming the complicating factors including data dependencies.

This Parallel implementation is based on the Parallel Prefix Scan Algorithm.

Dr. Lee implemented this algorithm in C++ on an eight core Intel Xeon server using actual measured data with 262,144 signals .

Parallel Algorithm

1) In Parallel, transform the set S(u[i], p[i]) using map function.

u[i] = 0 , if( l<x(i) <h) = 1 , if( x(i)≤l) = 2 , if( x(i) ≥ h) p[i] = (m - x[i]) / (x[i+1] – x[i]) , if ( x(i)

<m ≤ x(i+1) = (m - x[i+1]) / (x[i] – x[i+1]) ,

if( x(i+1) ≤m<x(i)

2) Parallel scan (u[i],p[i]) ⊕ (u[i+1],p[i+1])

where ⊕1 is given by

⊕2 = min(p[i],p[i+1]) if u[i] ≠ u[i+1]&u[i+1] ≠ 0

= b otherwise Left Identity Element , O = (I,∞)

Sam

ple

Index

Voltage S(u[i],p[i]) Scan(S,⊕)(L, ¥)

(L, ¥)

(L, ¥)

(L, ¥)(I, ¥)

(I,40)

(I, 38)

(I, ¥)

(I,¥)

(H, 41.1)

(H, ¥)

(L, 38)

(L, ¥)

(L, ¥)

(L, 38)

(L, 38)

(H, 38)

(H, ¥)

l hm

My Job

To implement this parallel algorithm in CUDA using the Thrust Library.

Conduct tests on Fermi and other GPU cards available.

Compare timing results with the serial algorithm and the parallel algorithm on eight core CPU.

QUESTIONS