```// ************************************************************************** //
//                                                                            //
//    eses                   eses                                             //
//   eses                     eses                                            //
//  eses    eseses  esesese    eses   Embedded Systems Group                  //
//  ese    ese  ese ese         ese                                           //
//  ese    eseseses eseseses    ese   Department of Computer Science          //
//  eses   eses          ese   eses                                           //
//   eses   eseses  eseseses  eses    University of Kaiserslautern            //
//    eses                   eses                                             //
//                                                                            //
// ************************************************************************** //
// The module below computes the discrete convolution of an input stream x(t) //
// with respect to given weights w[0],...w[N-1], i.e., it computes an output  //
// stream y(t) defined as                                                     //
//                                                                            //
//        y_out(t+N-1) = sum(k=0..N-1) w[k] * x_in(t+k)                       //
//                                                                            //
// The weights w[i] can be loaded into the module by piping them in via the   //
// input while setting input lw=True until all weights have arrived at the    //
// right places. Having N cells, the module can compute the products and their//
// sums in one step, and in each step one convolution is obtained.            //
// In the version below, the w[k] stay in the cells, while both x(t) and y(t) //
// are piped through the array. In contrast to ConvArray03, however, x and y  //
// flow in the same direction, but x has only half the speed of y.            //
// Note also that the weights have to be piped in in the reverse ordering when//
// the results should be the same as for ConvArray01 (and thus in the same    //
// ordering as in ConvArray02 and in ConvArray03).                            //
//                                                                            //
// For N=5, the array implements the equations:                               //
//                                                                            //
//            next(w[0]) = lw?x_in:w[0]                                       //
//            next(w[1]) = lw?w[0]:w[1]                                       //
//            next(w[2]) = lw?w[1]:w[2]                                       //
//            next(w[3]) = lw?w[2]:w[3]                                       //
//            next(w[4]) = lw?w[3]:w[4]                                       //
//            next(v[0]) = x_in                                               //
//            next(x[0]) = v[0]                                               //
//            next(v[1]) = x[0]                                               //
//            next(x[1]) = v[1]                                               //
//            next(v[2]) = x[1]                                               //
//            next(x[2]) = v[2]                                               //
//            next(v[3]) = x[2]                                               //
//            next(x[3]) = v[3]                                               //
//            next(v[4]) = x[3]                                               //
//            next(x[4]) = v[4]                                               //
//            next(y[0]) = w[0]*x[0]                                          //
//            next(y[1]) = w[1]*x[1]+y[0]                                     //
//            next(y[2]) = w[2]*x[2]+y[1]                                     //
//            next(y[3]) = w[3]*x[3]+y[2]                                     //
//            next(y[4]) = w[4]*x[4]+y[3]                                     //
//            y_out = y[4]                                                    //
//                                                                            //
// Thus, we have y_out(t+N-1) = sum(k=0..N-1) (w[k] * x[k](t+k)) and          //
// x[k](t) = x(t-2*k-2), so that the output stream is computed as desired.    //
// For weights w[4..0] = [10,8,6,4,2] and inputs x_in = 0,1,2,3,4,5,...,      //
// we therefore obtain:                                                       //
//                                                                            //
//    y_out(16) = 10*1 + 8*2 + 6*3 + 4*4 + 2*5 =  70                          //
//    y_out(17) = 10*2 + 8*3 + 6*4 + 4*5 + 2*6 = 100                          //
//    y_out(18) = 10*3 + 8*4 + 6*5 + 4*6 + 2*7 = 130                          //
//    y_out(19) = 10*4 + 8*5 + 6*6 + 4*7 + 2*8 = 160                          //
//    y_out(20) = 10*5 + 8*6 + 6*7 + 4*8 + 2*9 = 190                          //
//                                                                            //
// ************************************************************************** //

macro N = 6;

module ConvArray04(int ?x_in,!y_out,bool ?lw) {
[N]int v,w,x,y;

loop {
y_out = y[N-1];
for(j=0..N-1) {
next(w[j]) = (lw ? (j==0 ? x_in : w[j-1]) : w[j]);
next(v[j]) = (j==0 ? x_in : x[j-1]);
next(x[j]) = v[j];
next(y[j]) = (j==0 ? 0 : y[j-1]) + w[j] * x[j];
}
pause;
}
}
drivenby {
[N]int dx,dw; // local stores for x and w in driver

for(i=0..N-1) {
x_in = 2*(N-1-i)+2;
dw[i] = 2*i+2;
lw = true;
pause;
}
// now do some computation
for(i=0..3*N-1) {
x_in = i+1;
lw = false;
if(i>3*N)
assert(y_out == sum(k=0..N-1) (dw[k] * dx[k]));
pause;
}
}
```