Reductions

Objectives

1. Understand reductions

Notes

• variables declared outside the parallel block are shared
• Variables inside the block are per thread.
• Reading and writing to shared variables can be problematic
  • you can do this in a critical region
  • #pragma omp critical
• You can do like we did and declare a variable for each thread (vector)
• Or you can use a reduction
  • #pragma omp parallel for reduction(operator:variable)
    • The variable becomes a per-thread variable
    • The variable is initialized to the operators default value.
    • Each thread reduces the value into the local variable
    • At the end of the parallel region, the reduction operator will be performed in a critical region.
  • Reduction operators: reference.
    • +, -, |, ^, || initialized to 0.
    • *, && initialized to 1.
    • max - smallest value of the type.
    • min - largest value of the type.
• It is most likely that reductions are done in a tree like manner.
  • Consider 8 threads doing a sum.
  • Step 1: on threads 0 through 3: s_i = s_i + sum_i+4
  • Step 2: on threads 0 through 1: s_i = s_i + sum_i+2
  • Step 3: on threads 0 : s_i = s_i + sum_i+1
• I just used these pairings because it was easy to write the notation.
  • It is likely that this is performed in some other way.
• You can make your own reductions.
  • See reductions.cpp for an example.
  • But these can be functions as well.