subroutine MXM(a, m, b, k, c, n)
c
c matrix multiply with a 4x4 pencil 
c
      real a(m,k), b(k,n), c(m,n)
      real s11, s12, s13, s14, s21, s22, s23, s24
      real s31, s32, s33, s34, s41, s42, s43, s44

      mresid = MODULO(m,4) 
      nresid = MODULO(n,4) 
      m1 = m - mresid + 1
      n1 = n - nresid + 1

      do i=1,m-mresid,4
        do j=1,n-nresid,4
          s11 = 0.0d0
          s21 = 0.0d0
          s31 = 0.0d0
          s41 = 0.0d0
          s12 = 0.0d0
          s22 = 0.0d0
          s32 = 0.0d0
          s42 = 0.0d0
          s13 = 0.0d0
          s23 = 0.0d0
          s33 = 0.0d0
          s43 = 0.0d0
          s14 = 0.0d0
          s24 = 0.0d0
          s34 = 0.0d0
          s44 = 0.0d0
          do l=1,k
            s11 = s11 + a(i,l)*b(l,j)
            s12 = s12 + a(i,l)*b(l,j+1)
            s13 = s13 + a(i,l)*b(l,j+2)
            s14 = s14 + a(i,l)*b(l,j+3)

            s21 = s21 + a(i+1,l)*b(l,j)
            s22 = s22 + a(i+1,l)*b(l,j+1)
            s23 = s23 + a(i+1,l)*b(l,j+2)
            s24 = s24 + a(i+1,l)*b(l,j+3)

            s31 = s31 + a(i+2,l)*b(l,j)
            s32 = s32 + a(i+2,l)*b(l,j+1)
            s33 = s33 + a(i+2,l)*b(l,j+2)
            s34 = s34 + a(i+2,l)*b(l,j+3)

            s41 = s41 + a(i+3,l)*b(l,j)
            s42 = s42 + a(i+3,l)*b(l,j+1)
            s43 = s43 + a(i+3,l)*b(l,j+2)
            s44 = s44 + a(i+3,l)*b(l,j+3)
          enddo
          c(i,j)     = s11 
          c(i,j+1)   = s12 
          c(i,j+2)   = s13
          c(i,j+3)   = s14

          c(i+1,j)   = s21 
          c(i+2,j)   = s31 
          c(i+3,j)   = s41 

          c(i+1,j+1) = s22
          c(i+2,j+1) = s32
          c(i+3,j+1) = s42

          c(i+1,j+2) = s23
          c(i+2,j+2) = s33
          c(i+3,j+2) = s43

          c(i+1,j+3) = s24
          c(i+2,j+3) = s34
          c(i+3,j+3) = s44
        enddo
* Residual when n is not multiple of 4
        if (nresid .ne. 0) then
          if (nresid .eq. 1) then
            s11 = 0.0d0
            s21 = 0.0d0
            s31 = 0.0d0
            s41 = 0.0d0
            do l=1,k
              s11 = s11 + a(i,l)*b(l,n)
              s21 = s21 + a(i+1,l)*b(l,n)
              s31 = s31 + a(i+2,l)*b(l,n)
              s41 = s41 + a(i+3,l)*b(l,n)
            enddo
            c(i,n)     = s11 
            c(i+1,n)   = s21 
            c(i+2,n)   = s31 
            c(i+3,n)   = s41 
          elseif (nresid .eq. 2) then
            s11 = 0.0d0
            s21 = 0.0d0
            s31 = 0.0d0
            s41 = 0.0d0
            s12 = 0.0d0
            s22 = 0.0d0
            s32 = 0.0d0
            s42 = 0.0d0
            do l=1,k
              s11 = s11 + a(i,l)*b(l,j)
              s12 = s12 + a(i,l)*b(l,j+1)

              s21 = s21 + a(i+1,l)*b(l,j)
              s22 = s22 + a(i+1,l)*b(l,j+1)

              s31 = s31 + a(i+2,l)*b(l,j)
              s32 = s32 + a(i+2,l)*b(l,j+1)

              s41 = s41 + a(i+3,l)*b(l,j)
              s42 = s42 + a(i+3,l)*b(l,j+1)
            enddo
            c(i,j)     = s11 
            c(i,j+1)   = s12

            c(i+1,j)   = s21 
            c(i+2,j)   = s31 
            c(i+3,j)   = s41 

            c(i+1,j+1) = s22
            c(i+2,j+1) = s32
            c(i+3,j+1) = s42
          else
            s11 = 0.0d0
            s21 = 0.0d0
            s31 = 0.0d0
            s41 = 0.0d0
            s12 = 0.0d0
            s22 = 0.0d0
            s32 = 0.0d0
            s42 = 0.0d0
            s13 = 0.0d0
            s23 = 0.0d0
            s33 = 0.0d0
            s43 = 0.0d0
            do l=1,k
              s11 = s11 + a(i,l)*b(l,j)
              s12 = s12 + a(i,l)*b(l,j+1)
              s13 = s13 + a(i,l)*b(l,j+2)

              s21 = s21 + a(i+1,l)*b(l,j)
              s22 = s22 + a(i+1,l)*b(l,j+1)
              s23 = s23 + a(i+1,l)*b(l,j+2)

              s31 = s31 + a(i+2,l)*b(l,j)
              s32 = s32 + a(i+2,l)*b(l,j+1)
              s33 = s33 + a(i+2,l)*b(l,j+2)

              s41 = s41 + a(i+3,l)*b(l,j)
              s42 = s42 + a(i+3,l)*b(l,j+1)
              s43 = s43 + a(i+3,l)*b(l,j+2)
            enddo
            c(i,j)     = s11 
            c(i+1,j)   = s21 
            c(i+2,j)   = s31 
            c(i+3,j)   = s41 
            c(i,j+1)   = s12 
            c(i+1,j+1) = s22
            c(i+2,j+1) = s32
            c(i+3,j+1) = s42
            c(i,j+2)   = s13
            c(i+1,j+2) = s23
            c(i+2,j+2) = s33
            c(i+3,j+2) = s43
          endif
        endif
      enddo

* Residual when m is not multiple of 4
      if (mresid .eq. 0) then
        return
      elseif (mresid .eq. 1) then
        do j=1,n-nresid,4
          s11 = 0.0d0
          s12 = 0.0d0
          s13 = 0.0d0
          s14 = 0.0d0
          do l=1,k
            s11 = s11 + a(m,l)*b(l,j)
            s12 = s12 + a(m,l)*b(l,j+1)
            s13 = s13 + a(m,l)*b(l,j+2)
            s14 = s14 + a(m,l)*b(l,j+3)
          enddo
          c(m,j)     = s11 
          c(m,j+1)   = s12 
          c(m,j+2)   = s13
          c(m,j+3)   = s14
        enddo
* mresid is 1, check nresid
        if (nresid .eq. 0) then
          return
        elseif (nresid .eq. 1) then
          s11 = 0.0d0
          do l=1,k
            s11 = s11 + a(m,l)*b(l,n)
          enddo
          c(m,n) = s11
          return
        elseif (nresid .eq. 2) then
          s11 = 0.0d0
          s12 = 0.0d0
          do l=1,k
            s11 = s11 + a(m,l)*b(l,n-1)
            s12 = s12 + a(m,l)*b(l,n)
          enddo
          c(m,n-1) = s11
          c(m,n) = s12
          return
        else
          s11 = 0.0d0
          s12 = 0.0d0
          s13 = 0.0d0
          do l=1,k
            s11 = s11 + a(m,l)*b(l,n-2)
            s12 = s12 + a(m,l)*b(l,n-1)
            s13 = s13 + a(m,l)*b(l,n)
          enddo
          c(m,n-2) = s11
          c(m,n-1) = s12
          c(m,n) = s13
          return
        endif          
      elseif (mresid .eq. 2) then
        do j=1,n-nresid,4
          s11 = 0.0d0
          s12 = 0.0d0
          s13 = 0.0d0
          s14 = 0.0d0
          s21 = 0.0d0
          s22 = 0.0d0
          s23 = 0.0d0
          s24 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-1,l)*b(l,j)
            s12 = s12 + a(m-1,l)*b(l,j+1)
            s13 = s13 + a(m-1,l)*b(l,j+2)
            s14 = s14 + a(m-1,l)*b(l,j+3)

            s21 = s21 + a(m,l)*b(l,j)
            s22 = s22 + a(m,l)*b(l,j+1)
            s23 = s23 + a(m,l)*b(l,j+2)
            s24 = s24 + a(m,l)*b(l,j+3)
          enddo
          c(m-1,j)   = s11 
          c(m-1,j+1) = s12 
          c(m-1,j+2) = s13
          c(m-1,j+3) = s14
          c(m,j)     = s21
          c(m,j+1)   = s22 
          c(m,j+2)   = s23
          c(m,j+3)   = s24
        enddo
* mresid is 2, check nresid
        if (nresid .eq. 0) then
          return
        elseif (nresid .eq. 1) then
          s11 = 0.0d0
          s21 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-1,l)*b(l,n)
            s21 = s21 + a(m,l)*b(l,n)
          enddo
          c(m-1,n) = s11
          c(m,n) = s21
          return
        elseif (nresid .eq. 2) then
          s11 = 0.0d0
          s21 = 0.0d0
          s12 = 0.0d0
          s22 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-1,l)*b(l,n-1)
            s12 = s12 + a(m-1,l)*b(l,n)
            s21 = s21 + a(m,l)*b(l,n-1)
            s22 = s22 + a(m,l)*b(l,n)
          enddo
          c(m-1,n-1) = s11
          c(m-1,n)   = s12
          c(m,n-1)   = s21
          c(m,n)     = s22
          return
        else
          s11 = 0.0d0
          s21 = 0.0d0
          s12 = 0.0d0
          s22 = 0.0d0
          s13 = 0.0d0
          s23 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-1,l)*b(l,n-2)
            s12 = s12 + a(m-1,l)*b(l,n-1)
            s13 = s13 + a(m-1,l)*b(l,n)
            s21 = s21 + a(m,l)*b(l,n-2)
            s22 = s22 + a(m,l)*b(l,n-1)
            s23 = s23 + a(m,l)*b(l,n)
          enddo
          c(m-1,n-2) = s11
          c(m-1,n-1) = s12
          c(m-1,n)   = s13
          c(m,n-2)   = s21
          c(m,n-1)   = s22
          c(m,n)     = s23
          return
        endif
      else
* mresid is 3
        do j=1,n-nresid,4
          s11 = 0.0d0
          s21 = 0.0d0
          s31 = 0.0d0

          s12 = 0.0d0
          s22 = 0.0d0
          s32 = 0.0d0

          s13 = 0.0d0
          s23 = 0.0d0
          s33 = 0.0d0

          s14 = 0.0d0
          s24 = 0.0d0
          s34 = 0.0d0

          do l=1,k
            s11 = s11 + a(m-2,l)*b(l,j)
            s12 = s12 + a(m-2,l)*b(l,j+1)
            s13 = s13 + a(m-2,l)*b(l,j+2)
            s14 = s14 + a(m-2,l)*b(l,j+3)

            s21 = s21 + a(m-1,l)*b(l,j)
            s22 = s22 + a(m-1,l)*b(l,j+1)
            s23 = s23 + a(m-1,l)*b(l,j+2)
            s24 = s24 + a(m-1,l)*b(l,j+3)

            s31 = s31 + a(m,l)*b(l,j)
            s32 = s32 + a(m,l)*b(l,j+1)
            s33 = s33 + a(m,l)*b(l,j+2)
            s34 = s34 + a(m,l)*b(l,j+3)
          enddo
          c(m-2,j)   = s11 
          c(m-2,j+1) = s12 
          c(m-2,j+2) = s13
          c(m-2,j+3) = s14

          c(m-1,j)   = s21 
          c(m-1,j+1) = s22
          c(m-1,j+2) = s23
          c(m-1,j+3) = s24

          c(m,j)     = s31 
          c(m,j+1)   = s32
          c(m,j+2)   = s33
          c(m,j+3)   = s34
        enddo
* mresid is 3, check nresid
        if (nresid .eq. 0) then
          return
        elseif (nresid .eq. 1) then
          s11 = 0.0d0
          s21 = 0.0d0
          s31 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-2,l)*b(l,n)
            s21 = s21 + a(m-1,l)*b(l,n)
            s31 = s31 + a(m,l)*b(l,n)
          enddo
          c(m-2,n) = s11
          c(m-1,n) = s21
          c(m,n) = s31
          return
        elseif (nresid .eq. 2) then
          s11 = 0.0d0
          s21 = 0.0d0
          s31 = 0.0d0
          s12 = 0.0d0
          s22 = 0.0d0
          s32 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-2,l)*b(l,n-1)
            s12 = s12 + a(m-2,l)*b(l,n)
            s21 = s21 + a(m-1,l)*b(l,n-1)
            s22 = s22 + a(m-1,l)*b(l,n)
            s31 = s31 + a(m,l)*b(l,n-1)
            s32 = s32 + a(m,l)*b(l,n)
          enddo
          c(m-2,n-1) = s11
          c(m-2,n)   = s12
          c(m-1,n-1) = s21
          c(m-1,n)   = s22
          c(m,n-1)   = s31
          c(m,n)     = s32
          return
        else
          s11 = 0.0d0
          s21 = 0.0d0
          s31 = 0.0d0
          s12 = 0.0d0
          s22 = 0.0d0
          s32 = 0.0d0
          s13 = 0.0d0
          s23 = 0.0d0
          s33 = 0.0d0
          do l=1,k
            s11 = s11 + a(m-2,l)*b(l,n-2)
            s12 = s12 + a(m-2,l)*b(l,n-1)
            s13 = s13 + a(m-2,l)*b(l,n)
            s21 = s21 + a(m-1,l)*b(l,n-2)
            s22 = s22 + a(m-1,l)*b(l,n-1)
            s23 = s23 + a(m-1,l)*b(l,n)
            s31 = s31 + a(m,l)*b(l,n-2)
            s32 = s32 + a(m,l)*b(l,n-1)
            s33 = s33 + a(m,l)*b(l,n)
          enddo
          c(m-2,n-2) = s11
          c(m-2,n-1) = s12
          c(m-2,n)   = s13
          c(m-1,n-2) = s21
          c(m-1,n-1) = s22
          c(m-1,n)   = s23
          c(m,n-2)   = s31
          c(m,n-1)   = s32
          c(m,n)     = s33
          return
        endif
      endif
      end