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PWR020: Consider loop fission to enable vectorization

Issue​

The loop can be partially vectorized straightforwardly by moving the non-vectorizable statements of the loop body to a separate loop.

Actions​

Rewrite the loop to enable partial vectorization by separating the vectorizable statements in a first loop and the non-vectorizable statements in a second loop.

Relevance​

vectorization is one of the most important ways to speed up the computation of a loop. In practice, loops may contain a mix of computations where only a part of the loop body introduces loop-carrie dependencies that prevent vectorization. Different types of compute patterns make explicit the loop-carried dependencies present in the loop. On the one hand, the forall compute pattern is free of loop-carried dependencies and can be vectorized. On the other hand, the following compute patterns have loop-carried-dependencies and cannot be vectorized:

  • The sparse reduction compute pattern - e.g. the reduction variable has an read-write indirect memory access pattern which does not allow to determine the dependencies between the loop iterations at compile-time.

  • The recurrence compute pattern - e.g. typically computes the value of an array element using the value of another array element calculated in a previous loop iteration.

note

The scalar reduction compute pattern is kind of an edge case, it introduces loop-carried dependencies, but processors often support vector instructions for reductions by hardware. However, there are situations where it may be preferable to execute reduction operations with scalar instructions. An example is a hardware processor that lacks vector instructions for specific reduction operations. Another example is a code where it is key to find a trade-off between performance and precision control, avoiding round-off errors in floating point operations. Note loop fission is a solution that still enables the partial vectorization of part of the loop.

Thus, loop fission enables the partial vectorization by moving the non-vectorizable statements of the sparse reduction and recurrence compute patterns to a separate loop. Frequently, loop fission can be implemented in a straightforward manner because there are not any temporary scalar variables in the loop body.

Code examples​

C​

The second loop in the following example exhibits a forall and a sparse reduction compute pattern for arrays A and B, respectively. The sparse reduction introduces loop-carried dependencies that inhibit loop vectorization.

void example() {
  int A[1000], B[1000], C[1000];

  for (int i = 0; i < 1000; i++) {
    A[i] = B[i] = C[i] = i;
  }

  for (int i = 0; i < 1000; i++) {
    A[i] += i;
    B[C[i]] += i;
  }
}

After applying loop fission, the original loop is split into two loops: first loop computes the vectorizable part of the loop body (the forall pattern), and second loop computes the non-vectorizable part in scalar mode (the sparse reduction).

void example() {
  int A[1000], B[1000], C[1000];

  for (int i = 0; i < 1000; i++) {
    A[i] = B[i] = C[i] = i;
  }

  for (int i = 0; i < 1000; i++) {
    A[i] += i;
  }

  for (int i = 0; i < 1000; i++) {
    B[C[i]] += i;
  }
}

Fortran​

The second loop in the following example exhibits a forall and a sparse reduction compute pattern for arrays a and b, respectively. The sparse reduction introduces loop-carried dependencies that inhibit loop vectorization.

subroutine example()
  implicit none
  integer :: a(100), b(100), c(100), i

  do i = 1, 100
    a(i) = i
    b(i) = i
    c(i) = i
  end do

  do i = 1, 100
    a(i) = a(i) + i
    b(c(i)) = b(c(i)) + i
  end do
end subroutine example

After applying loop fission, the original loop is split into two loops: first loop computes the vectorizable part of the loop body (the forall pattern), and second loop computes the non-vectorizable part in scalar mode (the sparse reduction).

subroutine example()
  implicit none
  integer :: a(100), b(100), c(100), i

  do i = 1, 100
    a(i) = i
    b(i) = i
    c(i) = i
  end do

  do i = 1, 100
    a(i) = a(i) + i
  end do

  do i = 1, 100
    b(c(i)) = b(c(i)) + i
  end do
end subroutine example

References​