[High Performance Computing] {Udacity} L3: Intro to the Work-Span Model

Posted 2021-12-01 ecoflex

https://s3.amazonaws.com/content.udacity-data.com/courses/gt-cse6220/Course+Notes/Lesson1-1+Introduction+(1).pdf

 

two parts:

 

1, task represented by DAG

 

 

edges << operations => better for parallelism

 

 2, programming model defining DAG

 

 

 

 

 

 

 

 

 

 

 

 

 

work span analysis

 

 

 

 

 

 

 

 

 

 

 https://maths-people.anu.edu.au/~brent/pub/pub022.html

 

 

 

 

 

second condition

 

 

 

 

 

 

 

brent‘s theorem:

 

 

 

 

 

 

 

 

 https://crd-legacy.lbl.gov/~dhbailey/dhbpapers/twelve-ways.pdf

 

 

 

 

 

 

 

 

 

 The correct answer depends on the situation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Holy Grail for span is to find a poly-logarithmic algorithm

 

 

 

 

 

 

 

 

replace par-for with a procedure call

 

 

 

 

 

 

for i loop, the y[i]s are independent from each other

but for j loop, every component depends on y[i] 

 

 

 

 

eg

 

 

 

 

 

 

 

 

 

 

 

 

j loop is linear and executed by n times.

 

 

 

 

 

 

 

 

 

 

 t[:] ← A[i,:] \\cdot x[:]

linear work and logarithmic span (look at the forth slide of this page)

 

 

 

 https://www.cprogramming.com/parallelism.html