rand(5) -> rand(7)

int rand7() //random number from 1 - 7
{
    int r = 0;
    do
    {
       int a = rand(5) - 1; //uniformly at random from 0 to 4
       int b = rand(5) - 1;  //uniformly at random from 0 to 4
       r = 5*b + a;  //uniformly at random from 0 to 24
    }
    while (r >= 21); // in this event, we have to roll again
   //postcondition of loop: we have a number uniformly at random between 0 and 20

  return r % 7 + 1; 
  
  //there are 3 numbers in [0, 20] for each possible return value
  //so each has equal probability.      
}

 

确保每一步都是distribution uniformly.