Why is my program giving me all the non-prime numbers when I ask for prime numbers?

Question

I want to use a bit-array and the Sieve of Eratosthenes algorithm to find all the primes within a certain range. My code compiles, but it prints all the non-prime numbers rather than prime numbers (except for 2 because I ask my Sieve function to print 2). Can someone review my code and give me some hints on how to fix it? Your help is greatly appreciated. Thank you!

Note: The requirement of my homework is to use a bit-array.

#include <stdio.h>
#include <stdlib.h>

//#define MAXBYTES 1000000
#define MAXBYTES 10


void setBit(unsigned int A[], int k);
unsigned getBit(unsigned int A[], int k);
void print_prime (int prime_num);
void sieve_Prime(unsigned int bit_arr[]);

int main (int argc, char** argv)
{
    //int bit_arr[MAXBYTES];      //This is the bit array (32 X MAXBYTES)
    unsigned int bit_arr[MAXBYTES];      //or bit_arr[MAXBYTES]
    int i;

    for (i=0; i < MAXBYTES; i++)
    {
        bit_arr[i] = 0x00;            //initialize all bits to 0s
    }

    setBit(bit_arr, 0);             //0 is not prime, set it to be 1
    setBit(bit_arr, 1);             //1 is not prime, set it to be 1

    sieve_Prime(bit_arr);
    printf("\n");

    return 0;

}

//Set the bit at the k-th position to 1
void setBit(unsigned int A[], int k)
{
    int i = k/32;
    int pos = k % 32;

    unsigned int flag = 1;      //flag = 0000 ..... 00001
    flag = flag << pos;         //flag = 0000...010...000 (shifted k positions)

    A[i] = A[i] | flag;         //Set the bit at the k-th position in A[i];
}

//get the bit at the k-th position
unsigned getBit(unsigned int A[], int k)
{
    int i =k/32;
    int pos = k % 32;

    unsigned int flag = 1;

    flag = flag << pos;

    if (A[i] & flag)
        return 1;
    else
        return 0;
}


void print_prime (int prime_num)
{
    //print a prime number in next of 8 columns
    static int numfound=0;

    if (numfound % 8 == 0)
        printf("\n");
    if (prime_num+1 < MAXBYTES*8)
        printf("%d\t", prime_num);
    numfound++;
}

void sieve_Prime(unsigned int bit_arr[])
{
    int i;
    int k;
    int next_prime = 2;

    print_prime(2);

    while (next_prime+1 < MAXBYTES*8)
    {
        k = next_prime;

        //multiples of next_prime is not primpe
        while(next_prime*k < MAXBYTES*8)
        {
            setBit(bit_arr, next_prime*k);      //set it to be 1
            k++;     
        }

        //find next_prime by skipping non-prime bits marked 1
        while (next_prime + 1 < MAXBYTES*8 && getBit(bit_arr, ++next_prime))
        {
            print_prime(next_prime);
        }
    }
}

Answer 1

The problem is your loop:

while (next_prime + 1 < MAXBYTES*8 && getBit(bit_arr, ++next_prime))
{
    print_prime(next_prime);
}

Your keeping printing things while the bit is set (i.e. while you know it's not a prime). So basically, your loop is "print all the numbers I find while looking for the next prime" rather than "look for the next prime in a loop, then print the next prime".

I suspect you want something like:

next_prime++; // We always want to at least move on once...
while (next_prime + 1 < MAXBYTES*8 && getBit(bit_arr, next_prime))
{
    next_prime++;
}
print_prime(next_prime);

I haven't checked whether that's all that was wrong with the code, but it's certainly an initial thing to fix.

Answer 2

You may init the array with zero values simply by adding the next initialization construct:

unsigned int bit_arr[MAXBYTES] = { };

Then each member of the array will hold zero value. Also, try to avoid the things such as printf("\n");. It is better to use putchar('\n') if you need only to output one symbol at a time.

Additionally, you may add the static keyword to your working function prototypes and definitions except the main function if you'll not use this routines outside this translation unit.