// ************************************************************************** // // // // 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 following module implements a multiplication of 2-complement numbers. // // The computation is done by summing up the usual partial products by the use// // of carry-save adders for the intermediate steps and a carry-ripple adder // // for the final step. // // ************************************************************************** // macro M = 5; // number of digits used macro N = 3; // number of digits used macro dval(x,i,k) = (i==k-1 ? -(x[i]?1:0) : (x[i]?1:0)); macro intval(x,k) = sum(i=0..k-1) (dval(x,i,k) * exp(2,i)); module IntMulCSACRA([M]bool ?x,[N]bool ?y,[M+N]bool p) { event [M][N-1]bool pp; // digits of partial products event [M][N]bool cp; // carries for carry-save array event [N]bool cr; // carries for summation in final CRA event pM; // for intermediate value of p[M-1] // construct carry-save array for(i=0..M-1) { for(j=0..N-1) { let(xyin = (i==M-1 xor j==N-1 ? !(x[i]&y[j]) : x[i]&y[j])) let(pin = (i==0 ? (j==N-1) : (j==N-1 ? false : pp[i-1][j]))) let(cin = (i==0 ? false : cp[i-1][j])) let(pout = (j==0 ? (i==M-1 ? pM : p[i]) : pp[i][j-1])) let(cout = cp[i][j]) FullAdd(xyin,pin,cin,cout,pout); } } p[M-1] = !pM; // carry-ripple addition of the last row for(j=0..N-1) let(xin = cp[M-1][j]) let(pin = (j==N-1 ? true : pp[M-1][j])) let(cin = (j==0 ? pM : cr[j-1])) let(sout = p[M+j]) let(cout = cr[j]) FullAdd(xin,pin,cin,cout,sout); // check the result assert(intval(p,M+N) == intval(x,M) * intval(y,N)); }