// ************************************************************************** // // // // 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 opposite directions, so only every other step can be used to pipe // // in element of an input stream (see [Kung82]). This is due to the fact that // // the relative speed of both streams is double the cycle frequency. Thus, // // the performance of the module is only half of that of ConvArray01 and // // ConvArray02. However, the array can perform two convolutions of two input // // streams that must then be piped in in an interleaved way in the unique // // input x_in. 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). // // // // 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(x[0]) = x_in // // next(x[1]) = x[0] // // next(x[2]) = x[1] // // next(x[3]) = x[2] // // next(x[4]) = x[3] // // next(y[0]) = w[4]*x[4] // // next(y[1]) = w[3]*x[3]+y[0] // // next(y[2]) = w[2]*x[2]+y[1] // // next(y[3]) = w[1]*x[1]+y[2] // // next(y[4]) = w[0]*x[0]+y[3] // // y_out = y[4] // // // // Thus, we have // // x[k](t+k+1) = x(t) and // // y_out(t+N) = sum(k=0..N-1) (w[k] * x[k](N-1-k)) // // so that the output stream is computed as desired above. // // 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(15) = y_out(16) = 10*1 + 8*2 + 6*3 + 4*4 + 2*5 = 70 // // y_out(17) = y_out(18) = 10*2 + 8*3 + 6*4 + 4*5 + 2*6 = 100 // // y_out(19) = y_out(20) = 10*3 + 8*4 + 6*5 + 4*6 + 2*7 = 130 // // y_out(21) = y_out(22) = 10*4 + 8*5 + 6*6 + 4*7 + 2*8 = 160 // // y_out(23) = y_out(24) = 10*5 + 8*6 + 6*7 + 4*8 + 2*9 = 190 // // // // ************************************************************************** // macro N = 5; module ConvArray03(int ?x_in,!y_out,bool ?lw) { [N]int 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(x[j]) = (j==0 ? x_in : x[j-1]); next(y[j]) = (j==0 ? 0 : y[j-1]) + w[N-1-j] * x[N-1-j]; } pause; } } drivenby { [N]int dx,dw; // local stores for x and w in driver // first load weights 2,4,6,8 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..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[k])); pause; pause; } }