Sieve of Eratosthenes in C

sieve.c

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

typedef unsigned long long int t_item;

static t_item all_true = ~0LL;

#define BITS sizeof(t_item)

void init_with_true(t_item *bitset, int maximum) {
    int p = maximum / BITS;
    int i;
    for (i = 0; i <= p; i++) {
        bitset[i] = all_true;
    }
}

t_item contains(t_item *bitset, int i) {
    return !!(bitset[i / BITS] & (1LL << (i % BITS)));
}

void discard(t_item *bitset, int i) {
    bitset[i / BITS] &= ~(1LL << (i % BITS));
}

void primes(t_item *primes_bitset, int maximum) {
    int m, km;
    init_with_true(primes_bitset, maximum);

    discard(primes_bitset, 1);
    for (km = 4; km <= maximum; km += 2) {
        discard(primes_bitset, km);
    }

    for (m = 3; m <= maximum; m += 2) {
        if (contains(primes_bitset, m)) {
            for (km = 2 * m; km <= maximum; km += m) {
               discard(primes_bitset, km);
            }
        }
    }
}

int main(void) {
    int maximum = 100;
    t_item *primes_bitset = (t_item *)malloc(maximum + BITS);
    primes(primes_bitset, maximum);
    int n;
    for (n = 1; n <= maximum; n++) {
        if (contains(primes_bitset, n)) {
            printf("%d\n", n);
        }
    }
    free(primes_bitset);
    return 0;
}

I will leave this as an exercise for the reader.