# Loop Constructs

Loops can be formed with the usual `DO...END DO` and `DO WHILE`, or by using an `IF/GOTO` and a label. Loops must have a single entry and a single exit to be vectorized. The following examples illustrate loop constructs that can and cannot be vectorized. The non-vectorizable structure example shows a loop that cannot be vectorized because of the inherent potential for an early exit from the loop.

Vectorizable structure:

    subroutine vec(a, b, c)
      dimension a(100), b(100), c(100)
      integer i
      i = 1
      do while (i .le. 100)
        a(i) = b(i) * c(i)
          if (a(i) .lt. 0.0) a(i) = 0.0
            i = i + 1
      enddo
    end subroutine vec

Non-vectorizable structure:

    subroutine no_vec(a, b, c)
      dimension a(100), b(100), c(100)
      integer i
      i = 1
      do while (i .le. 100)
        a(i) = b(i) * c(i)
    ! The next statement allows early
    !
    exit from the loop and prevents
    ! vectorization of the loop.
        if (a(i) .lt. 0.0) go to 10
        i = i + 1
      enddo
      10 continue
    end subroutine no_vecN
    END

## Loop Exit Conditions

Loop exit conditions determine the number of iterations a loop executes. For example, fixed indexes for loops determine the iterations. The loop iterations must be countable and the number of iterations must be expressed as one of the following:

- A constant.

- A loop invariant term.

- A linear function of outermost loop indices.

In the case where a loops exit depends on computation, the loops are not countable. The examples below show loop constructs that are countable and non-countable. The non-countable loop example demonstrates a loop construct that is non-countable due to dependency loop variant count value.

Countable loop, example one:

    subroutine cnt1 (a, b, c, n, lb)
      dimension a(n), b(n), c(n)
      integer n, lb, i, count
    ! Number of iterations is "n - lb + 1"
      count = n
      do while (count .ge. lb)
        a(i) = b(i) * c(i)
        count = count - 1
        i = i + 1
      enddo ! lb is not defined within loop
    end

Countable loop, example two:

    ! Number of iterations is (n-m+2)/2
    subroutine cnt2 (a, b, c, m, n)
      dimension a(n), b(n), c(n)
      integer i, l, m, n
      i = 1;
      do l = m,n,2
        a(i) = b(i) * c(i)
        i = i + 1
      enddo
    end

Non-countable loop:

    ! Number of iterations is dependent on a(i)
    subroutine foo (a, b, c)
      dimension a(100),b(100),c(100)
      integer i
      i = 1
      do while (a(i) .gt. 0.0)
        a(i) = b(i) * c(i)
        i = i + 1
      enddo
    end

## Strip-mining and Cleanup

Strip-mining, also known as loop sectioning, is a loop transformation technique for enabling SIMD-encoding of loops, as well as a means of improving memory performance. By fragmenting a large loop into smaller segments or strips, this technique transforms the loop structure in two ways:

- By increasing the temporal and spatial locality in the data cache if the data is reusable in different passes of an algorithm.

- By reducing the number of iterations of the loop by a factor of the length of each vector, or number of operations being performed per SIMD operation. With the Intel® Streaming SIMD Extensions (Intel® SSE), the vector or strip-length is reduced by four times: four floating-point data items per single Intel® SSE single-precision floating-point SIMD operation are processed.

First introduced for vectorizers, this technique consists of the generation of code when each vector operation is done for a size less than or equal to the maximum vector length on a given vector machine.

The compiler automatically strip-mines your loop and generates a cleanup loop. For example, assume the compiler attempts to strip-mine the loop before vectorization. After vectorization, the compiler might handle the strip mining and loop cleaning by restructuring the loop.

Before vectorization:

    i = 1
    do while (i<=n)
      a(i) = b(i) + c(i) ! Original loop code
      i = i + 1
    end do

After vectorization:

    !The vectorizer generates the following two loops
    i = 1
    do while (i < (n - mod(n,4)))
    ! Vector strip-mined loop.
      a(i:i+3) = b(i:i+3) + c(i:i+3)
      i = i + 4
    end do
    do while (i <= n)
      a(i) = b(i) + c(i)     !Scalar clean-up loop
      i = i + 1
    end do

Loop Blocking

It is possible to treat loop blocking as strip-mining in two or more dimensions. Loop blocking is a useful technique for memory performance optimization. The main purpose of loop blocking is to eliminate as many cache misses as possible. This technique transforms the memory domain into smaller chunks rather than sequentially traversing through the entire memory domain. Each chunk should be small enough to fit all the data for a given computation into the cache, maximizing data reuse.

Consider the following example. The two-dimensional array A is referenced in the j (column) direction and then in the i (row) direction (column-major order); array B is referenced in the opposite manner (row-major order). Assume that the memory layout is in column-major order; therefore, the access strides of array A and B for the code would be 1 and `MAX`, respectively. `BS = block_size;``MAX` must be evenly divisible by BS.

The arrays could be blocked into smaller chunks so that the total combined size of the two blocked chunks is smaller than the cache size, which can improve data reuse. One way of doing this is shown in the transformed loop after blocking example.

Original loop:

    REAL A(MAX,MAX), B(MAX,MAX)
    DO I =1, MAX
      DO J = 1, MAX
        A(I,J) = A(I,J) + B(J,I)
      ENDDO
    ENDDO

Transformed loop after blocking:

    REAL A(MAX,MAX), B(MAX,MAX)
    DO I =1, MAX, BS
      DO J = 1, MAX, BS
       DO II = I, I+MAX, BS-1
        DO J = J, J+MAX, BS-1
         A(II,JJ) = A(II,JJ) + B(JJ,II)
        ENDDO
       ENDDO
      ENDDO
    ENDDO

## Loop Interchange and Subscripts with Matrix Multiply

Loop interchange is often used for improving memory access patterns. Matrix multiplication is commonly written as shown in the typical matrix multiplication example.

The use of B(K,J) is not a stride-1 reference and therefore will not be vectorized efficiently.

If the loops are interchanged, all the references become stride-1 as shown in the matrix multiplication with stride-1 example.

Typical matrix multiplication:

    subroutine matmul_slow(a, b, c)
      integer :: i, j, k
      real :: a(100,100), b(100,100), c(100,100)
      do i = 1, n
        do j = 1, n
          do k = 1, n
            c(i,j) = c(i,j) + a(i,k)*b(k,j)
          end do
        end do
      end do
    end subroutine matmul_slow

Matrix multiplication with stride-1:

    subroutine matmul_fast(a, b, c)
      integer :: i, j, k
      real :: a(100,100), b(100,100), c(100,100)
      do j = 1, n
        do k = 1, n
          do i = 1, n
            c(i,j) = c(i,j) + a(i,k)*b(k,j)
          enddo
        enddo
      enddo
    end subroutine matmul_fast

Interchanging is not always possible because of dependencies, which can lead to different results.

Parent topic: Automatic Vectorization