```// ************************************************************************** //
//                                                                            //
//    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, x(t) is broadcast to all elements, and the w[k] stay //
// in the cells, while y(t) is piped through the array (see [Kung82]).        //
//                                                                            //
// 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(y[0]) = x_in*w[0]                                          //
//            next(y[1]) = x_in*w[1]+y[0]                                     //
//            next(y[2]) = x_in*w[2]+y[1]                                     //
//            next(y[3]) = x_in*w[3]+y[2]                                     //
//            next(y[4]) = x_in*w[4]+y[3]                                     //
//            y_out = y[4]                                                    //
//                                                                            //
// Thus, the output stream y_out is computed as desired above.                //
// For weights w[4..0] = [2,4,6,8,10] and inputs x_in = 0,1,2,3,4,5,...,      //
// we therefore obtain:                                                       //
//                                                                            //
//    y_out(10) = 10*1 + 8*2 + 6*3 + 4*4 + 2*5 =  70                          //
//    y_out(11) = 10*2 + 8*3 + 6*4 + 4*5 + 2*6 = 100                          //
//    y_out(12) = 10*3 + 8*4 + 6*5 + 4*6 + 2*7 = 130                          //
//    y_out(13) = 10*4 + 8*5 + 6*6 + 4*7 + 2*8 = 160                          //
//    y_out(14) = 10*5 + 8*6 + 6*7 + 4*8 + 2*9 = 190                          //
//                                                                            //
// ************************************************************************** //

macro N = 5;

module ConvArray01(int ?x_in,!y_out,bool ?lw) {
[N]int w,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(y[j]) = (j==0 ? w[j] * x_in : y[j-1] + w[j] * x_in);
}
pause;
}
}
drivenby {
[N]int dx,dw; // local stores for x and w in driver

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