Vectorizing 3D Arrays Product in Fortran

[Ricardo_F_]

Considering the product of arrays with size nx*ny*nz in Fortran. The given cases will generate the same result:

#1

do k=1,nz
 do j=1,ny
  do i=1,nx
   A(i,j,k)=A(i,j,k)*B(i,j,k)*0.5
  enddo
 enddo
enddo

#2

do ijk=1,nx*ny*nz
 A(ijk,1,1)=A(ijk,1,1)*B(ijk,1,1)*0.5
enddo

#3 

A(:,:,:)=A(:,:,:)*B(:,:,:)*0.5

#4 

A=A*B*0.5

Question: which case (#1, #2, #3 or #4) is the best in terms of vectorization and performance and why?

Someone recommend a literature or website where I can learn more about it?

Thank you,

Ricardo

[jimdempseyatthecove]

#4 "should" be best and equivalent to #1

To improve performance you would want to align the arrays (A and B) to cache line address

!DIR$ ATTRIBUTES ALIGN: 64:: A, B

#2 won't work if array bounds checking is enabled. If array dimensions for aligned allocations do not produce rows (1st index) of multiples of cache line, for the example above #1 can have the loops collapsed (see IVF index)

Jim Dempsey

[TimP]

At full optimization, ifort would perform an optimization equivalent to #2 if possible.  #3 is prone to generation of temporary arrays.  ifort optimization reports should show when either of those happen.

[jimdempseyatthecove]

FWIW I use a similar technique to #2. In a module I have:

    subroutine ArrayDivide6x6(a,d)
        implicit none
        real(i8), intent(inout) :: a(6*6)
        real(i8), intent(in) :: d
        a = a / d
    end subroutine ArrayDivide6x6
...
REAL(i8),DIMENSION(6,6), INTENT(OUT) :: qq_Transpose
...
call ArrayDivide6x6(qq_Transpose, exp(xsi*z))

You should be able to use a similar technique with your example code.
YMMV

I noticed in IVF V17u1 an optimization issue with
  qq_Transpose = qq_Transpose / exp(xsi*z)

Jim Dempsey