PWR018

PWR018: Call to recursive function within a loop inhibits vectorization

Issue

Recursive calls within a loop inhibit vectorization.

Actions

Rewrite the loop without the recursive function call to enable vectorization.

Relevance

Many loops can benefit from vectorization. However, loops with calls to recursive functions cannot be vectorized. Recursive functions introduce complex control flow logic which the compilers cannot vectorize automatically.

Note

Whether the loop with a recursive function call is vectorizable or not after de-recursion depends on the property of the original recursive function itself. If the complex control flow logic remains after de-recursion, the loop will remain not vectorizable.

Code example

C

In the following example, the loop is invoking a recursive function computing the Fibonacci number. This recursion inhibits the vectorization of the loop:

double fib(unsigned n) {
  if (n == 0) {
    return 0.0;
  }
  if (n == 1) {
    return 1.0;
  }
  return fib(n - 1) + fib(n - 2);
}

double example(unsigned times) {
  double sum = 0.0;
  for (unsigned i = 0; i < times; i++) {
    sum += fib(i);
  }
  return sum;
}

As an alternative, Fibonacci's sequence can be calculated non-recursively:

double example(unsigned times) {
  double sum = 0.0;
  double fib_0 = 0.0;
  double fib_1 = 1.0;
  for (unsigned i = 2; i < times; i++) {
    double fib = fib_0 + fib_1;
    sum += fib;
    fib_0 = fib_1;
    fib_1 = fib;
  }
  return sum;
}

Fortran

In the following example, the loop is invoking a recursive function computing the Fibonacci number. This recursion inhibits the vectorization of the loop:

module mod_fibonacci
  contains
  recursive function fibonacci(n) result(fibo)
    implicit none
    integer, intent(in) :: n
    integer :: fibo

    if (n == 0) then
      fibo = 0
    else if (n == 1) then
      fibo = 1
    else
      fibo = fibonacci(n - 1) + fibonacci(n - 2)
    end if
  end function fibonacci
end module mod_fibonacci

subroutine example(times)
  use mod_fibonacci, only : fibonacci

  implicit none
  integer, intent(in) :: times
  integer :: i, sum

  sum = 0

  do i = 0, times - 1
    sum = sum + fibonacci(i)
  end do
end subroutine example

As an alternative, Fibonacci's sequence can be calculated non-recursively:

subroutine example(times)
  implicit none
  integer, intent(in) :: times
  integer :: i, sum
  integer :: fib_0, fib_1, fib

  sum = 0
  fib_0 = 0
  fib_1 = 1

  do i = 2, times - 1
    fib = fib_0 + fib_1
    sum = sum + fib
    fib_0 = fib_1
    fib_1 = fib
  end do
end subroutine example

Related resources

• PWR018 examples

References

• Vectorization

• OpenMP canonical form