PL - Aula 4

4 de Outubro 2023 - #CP

Ex. 2

a) Limitações vetoriais

A -> consecutive elements in a row -> consecutive access in the vector
C -> same element
B -> consecutive elements in a collumn

Não vai ser vetorizável.

b) Enable vectorization

result of change cycles to i, k , j :
A -> same element
C -> consecutive elements in a row -> consecutive access in the vector
B -> consecutive elements in a row -> consecutive access in the vector

i k j
0 0 1

Vai ser vetorizável.

128b
8B -> 64b
2 elements

Without vectorization:

With vectorization:

Estimated: ( n^3 / 2 )* 8

c)Measure and analyze results

d) Vectorization fine-tuning

Ganhos de 4 vezes mais.

Ex. 3

a) Peak Performance

2 operações em FP
4 elementos de cada vez em cada ciclo
2.5 GHz -> 2.5 billion cycles per second

conclusion: 20 GFlop/s

b)

peak with vectorization: continuous 20 GFlop/s
peak without vectorization: continuous 5 GFlop/s
memory bandwith limitation: see alinea d)
real achievable performance:see alinea c)
measured performance:

d) Memory bandwidth limitation

1 FOP -> 2B

c)

2 FOP (operações vírgula flutuante) -> 2 doubles (16B)
1 operation/8B -> 0.125