Memory alignment for multidimensional arrays

Multi-dimensional arrays need to be padded in thefastest-moving dimension, to  ensure array sec9ons to be aligned at the desired byte boundaries :

• Fortran: first array dimension 
• C/C++: last array dimension  

npadded= ((n +veclen– 1) /veclen) *veclen

• No alignment requested:veclen= 1
• 16-byte alignment (SSE):veclen= 4 (sp) or 2 (dp)
• 32-byte alignment (AVX2):veclen= 8 (sp) or 4 (dp)
• 64-byte alignment (AVX-512):veclen= 16 (sp) or 8 (dp)

Example:

real, allocatable:: a(:,:), b(:,:), c(:,:)

!dir$ attributes align : 32 :: a,b,c

...

allocate (a(npadded,n))

allocate (b(npadded,n))

allocate (c(npadded,n))

...

do j=1,n

  do k=1,n

    !dir$ vector aligned

    do i=1,npadded

      c(i,j) = c(i,j) &+ a(i,k) * b(k,j)

    end do

  end do

end do

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