```// ************************************************************************** //
//                                                                            //
//    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 procedure for converting signed digit    //
// numbers to equivalent B-complement numbers. The idea is to represent the   //
// given number as the subtraction of two non-negative radix-B numbers pos and//
// neg so that the conversion can be done by a radix-B subtraction. Since the //
// determination of the numbers pos and neg can be done in one step, the time //
// required is essentially the time for radix-B subtraction. The algorithm    //
// below makes use of a simple carry-ripple subtraction requiring O(N) time,  //
// but clearly, this can be reduced to O(log(N)) time by lookahead algorithms.//
// ************************************************************************** //

macro D = 3;     // digit set is -D,...,-1,0,1,...,D
macro B = 5;     // base of the radix numbers
macro N = 4;     // number of digits used for the addition

// macros for signed digit and B-complement numbers
macro alpha(x) = (x<B/2 ? +x : +x-B);
macro gamma(y) = (y<0 ? y+B : y);
macro dval(x,i,k) = (i==k-1 ? alpha(x[i]) : +x[i]);
macro intval(x,k) = sum(i=0..k-1) (dval(x,i,k) * exp(B,i));
macro sgnval(x,k) = sum(i=0..k-1) (x[i] * exp(B,i));

module Sgn2IntPrinciple([N]int{D+1} ?x,[N+1]nat{B} y) {
[N]nat{B} pos,neg;  // positive and negative digits
[N+1]nat{2} c;      // carry

// extract positive and negative digits of given number a
for(i=0..N-1) {
if(x[i]<0) {
pos[i] = 0;
neg[i] = -x[i];
} else {
pos[i] = +x[i];
neg[i] = 0;
}
}
// pos and neg are both signed-digit and radix-B numbers;
// hence, we can perform B-complement subtraction pos-neg for conversion
c[0] = 0;
for(i=0..N-1)
if(pos[i]>=neg[i]+c[i]) {
c[i+1] = 0;
y[i] = (pos[i]-(neg[i]+c[i])) % B;
} else {
c[i+1] = 1;
y[i] = (B+pos[i]-(neg[i]+c[i])) % B;
}
// final digit according to B-complement
y[N] = gamma(-c[N-1]);
// assertion
assert(intval(y,N+1) == sgnval(x,N));
}
```