Check equivalence with KLEE

hamming.c

#include "klee/klee.h"
#include <assert.h>
#include <inttypes.h>
#include <stdio.h>
//types and constants used in the functions below

const uint64_t m1  = 0x5555555555555555; //binary: 0101...
const uint64_t m2  = 0x3333333333333333; //binary: 00110011..
const uint64_t m4  = 0x0f0f0f0f0f0f0f0f; //binary:  4 zeros,  4 ones ...
const uint64_t m8  = 0x00ff00ff00ff00ff; //binary:  8 zeros,  8 ones ...
const uint64_t m16 = 0x0000ffff0000ffff; //binary: 16 zeros, 16 ones ...
const uint64_t m32 = 0x00000000ffffffff; //binary: 32 zeros, 32 ones
const uint64_t hff = 0xffffffffffffffff; //binary: all ones
const uint64_t h01 = 0x0101010101010101; //the sum of 256 to the power of 0,1,2,3...

//This is a naive implementation, shown for comparison,
//and to help in understanding the better functions.
//It uses 24 arithmetic operations (shift, add, and).
int popcount_1(uint64_t x) {
    x = (x & m1 ) + ((x >>  1) & m1 ); //put count of each  2 bits into those  2 bits 
    x = (x & m2 ) + ((x >>  2) & m2 ); //put count of each  4 bits into those  4 bits 
    x = (x & m4 ) + ((x >>  4) & m4 ); //put count of each  8 bits into those  8 bits 
    x = (x & m8 ) + ((x >>  8) & m8 ); //put count of each 16 bits into those 16 bits 
    x = (x & m16) + ((x >> 16) & m16); //put count of each 32 bits into those 32 bits 
    x = (x & m32) + ((x >> 32) & m32); //put count of each 64 bits into those 64 bits 
    return x;
}

//This uses fewer arithmetic operations than any other known  
//implementation on machines with slow multiplication.
//It uses 17 arithmetic operations.
int popcount_2(uint64_t x) {
    x -= (x >> 1) & m1;             //put count of each 2 bits into those 2 bits
    x = (x & m2) + ((x >> 2) & m2); //put count of each 4 bits into those 4 bits 
    x = (x + (x >> 4)) & m4;        //put count of each 8 bits into those 8 bits 
    x += x >>  8;  //put count of each 16 bits into their lowest 8 bits
    x += x >> 16;  //put count of each 32 bits into their lowest 8 bits
    x += x >> 32;  //put count of each 64 bits into their lowest 8 bits
    return x & 0x7f;
}

//This uses fewer arithmetic operations than any other known  
//implementation on machines with fast multiplication.
//It uses 12 arithmetic operations, one of which is a multiply.
int popcount_3(uint64_t x) {
    x -= (x >> 1) & m1;             //put count of each 2 bits into those 2 bits
    x = (x & m2) + ((x >> 2) & m2); //put count of each 4 bits into those 4 bits 
    x = (x + (x >> 4)) & m4;        //put count of each 8 bits into those 8 bits 
    return (x * h01)>>56;  //returns left 8 bits of x + (x<<8) + (x<<16) + (x<<24) + ... 
}

int main() {
  uint64_t x = 0;
  uint32_t choice = 0;
  klee_make_symbolic(&x, sizeof(uint64_t), "x");
  klee_make_symbolic(&choice, sizeof(uint32_t), "choice");

  klee_assume(choice < 6);
  
  uint64_t result0 = 0;
  uint64_t result1 = 0;
  // To prove all are equivalent execution is all orders must be tried.
  switch (choice) {
    case 0:
      printf("Trying combination 0\n");
      result0 = popcount_1(x);
      result1 = popcount_2(x);
      break;
    case 1:
      printf("Trying combination 1\n");
      result0 = popcount_1(x);
      result1 = popcount_3(x);
      break;
    case 2:
      printf("Trying combination 2\n");
      result0 = popcount_2(x);
      result1 = popcount_1(x);
      break;
    case 3:
      printf("Trying combination 3\n");
      result0 = popcount_2(x);
      result1 = popcount_3(x);
      break;
    case 4:
      printf("Trying combination 4\n");
      result0 = popcount_3(x);
      result1 = popcount_1(x);
      break;
    case 5:
      printf("Trying combination 5\n");
      result0 = popcount_3(x);
      result1 = popcount_2(x);
      break;
    default:
      assert(0 && "unreachable");
  }

  assert(result0 == result1 && "Not equivalent");
  return 0;
}