Outline 0024 Spring 2010 2 :: 2 Programming problem 2 0024 - PowerPoint PPT Presentation

Outline �� 0024 Spring 2010 � – 2 :: 2 – �

Programming problem 2 � 0024 Spring 2010 � – 2 :: 3 – �

Parallel solution � Given a vector X of length N, N = 2 k for some k � Given P = N processors (execution units) � Distribute X so that X i is stored on processor P i (for 0 <= i < N). � Compute T j = X 2*j + X 2*j+1 on P j � Rename T to X, renumber the processors so that P new i = P old 2*i and repeat until T 0 contains the result. � Note: some processors idle after fi rst step. Number of steps proportional to log N. � 0024 Spring 2010 � – 2 :: 4 – �

Comments � 0024 Spring 2010 � – 2 :: 5 – �

Programming problem 2a � 0024 Spring 2010 � – 2 :: 6 – �

Parallel solution � Given a vector X of length N, N = 2 k for some k � Given P = N processors (execution units) � Phase 1 (like for Problem 1) � Distribute X so that X i is stored on processor P i (for 0 <= i < N). � Compute T j = X 2*j + X 2*j+1 on P j � Rename T to X, renumber the processors so that P new i = P old 2*i and repeat until T 0 contains the result. � 0024 Spring 2010 � – 2 :: 7 – �

Phase 2 � Imagine the root of the tree (here P 0 ) to receive a “0” from its “parent” (which does not exist). � All non-leaf nodes receive a value from their parent. Each node relays to its left child the received value. Each node sends to its right child the sum of the (received) parent value and the value computed by the left child in Phase 1. � Leaf nodes add the value received from the parent and add it to the saved input value. � 0024 Spring 2010 � – 2 :: 8 – �

Example � 55 � 25 � 30 � 7 � 18 � 10 � 20 � 4 � 3 � 7 � 11 � 9 � 1 � 12 � 8 � 0024 Spring 2010 � – 2 :: 9 – �

Example � 0 � 55 � 25 � 30 � 7 � 18 � 10 � 20 � 4 � 3 � 7 � 11 � 9 � 1 � 12 � 8 � 0024 Spring 2010 � – 2 :: 10 – �

Example � 55 � 0 � 25 � 25 � 30 � 7 � 18 � 10 � 20 � 4 � 3 � 7 � 11 � 9 � 1 � 12 � 8 � 0024 Spring 2010 � – 2 :: 11 – �

Example � 55 � 25 � 30 � 0 � 7 � 25 � 35 � 7 � 18 � 10 � 20 � 4 � 3 � 7 � 11 � 9 � 1 � 12 � 8 � 0024 Spring 2010 � – 2 :: 12 – �

Example � 55 � 25 � 30 � 7 � 18 � 10 � 20 � 35 � 47 � 4 � 3 � 7 � 11 � 9 � 1 � 12 � 8 � 0 � 4 � 7 � 14 � 25 � 34 � 0024 Spring 2010 � – 2 :: 13 – �

Example � 55 � 25 � 30 � 7 � 18 � 10 � 20 � 4 � 3 � 7 � 11 � 9 � 1 � 12 � 8 � 4 � 7 � 14 � 25 � 34 � 35 � 47 � 55 � 0024 Spring 2010 � – 2 :: 14 – �

Programming problem 3 � 0024 Spring 2010 � – 2 :: 15 – �