// One's complement add with register slices.
#include <stdio.h>
#include <stdlib.h>
typedef unsigned int ui;
typedef unsigned char uc;
void ps(uc x[8], char * m){int j=8; while(j--) printf("%01x", 15&x[j]); printf(" %s\n", m);}
ui rn(){return (random()<<4)^random();} // 32 random bits
ui add(ui a, ui b){uc pa[8], pb[8], sl[8], sh[8];
  {int j=8; while(j--) {pa[j] = 15 & (a>>(4*j)); pb[j] = 15 & (b>>(4*j));}}
  if(0){ps(pa, "pb"); printf("%08x\n", a); ps(pb, "pb");  printf("%08x\n", b);}
  // We have divided both of our arguments into 4 bit slices.
  // Next for each slice compute two 4 bit sums:
  {int j=8; while(j--) {sl[j] = pa[j]+pb[j]; sh[j] = pa[j]+pb[j]+1;}}
  if(0) ps(sl, "sl");
  {char P=0, G=0, C=0;
  // Next compute P and G
    {int j=8; while(j--) {P = (P<<1) | sh[j]>>4; G = (G<<1) | sl[j]>>4;}}
  // Now compute C
    {int i=8; while(i--) {char b=0; {int j=8; while(j--) if(i!=j) {
         {char d=(G>>j) & 1; {int k=8; while(k--) {
         if(i<j & j<k | j<k & k<i | k<i & i<j) d &= (P>>k) & 1;}}
       b |= d;}}} C = (C<<1) | b;}}
     if(0) printf("P=%02x G=%02x C=%02x\n", P, G, C);
     {ui ans = 0; {int j = 8; while(j--) ans |= (15&((C&(1<<j))?sh[j]:sl[j]))<<(4*j);}
     return ans;}}}
int main(){int j=100000; while(j--){
  ui a = rn(), b = rn(), s = add(a, b), soc=a+b+(a>~b);
  if(soc != s) printf("%d %08x %08x %08x %08x\n", j, a, b, soc, s);}
 return 0;}