```// ************************************************************************** //
//                                                                            //
//    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-ripple adders both for the intermediate steps and the final step. //
// The depth of the circuit is seen by observing that the evaluation can      //
// proceed diagonally through the array. Thus, the depth of the circuit       //
// is O(M+N) and therefore not optimal.                                       //
// ************************************************************************** //

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 IntMulCRACRA([M]bool ?x,[N]bool ?y,[M+N]bool p) {
event [M-1][N]bool pp;  // digits of partial products
event [M][N-1]bool cp;  // carries for summation
event sM;
// construct M x N multiplier array
for(i=0..M-1) {
// IntAdd/IntSub of pp[i-1][N-1..0] and x[i]&y[N-1..0]
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) : pp[i-1][j]))
let(cin  = (j==0 ? (i==M-1) : cp[i][j-1]))
let(pout = (j==0 | i==M-1 ? p[i+j] : pp[i][j-1]))
let(cout = (j==N-1 ? (i==M-1 ? sM : pp[i][N-1]) : cp[i][j]))