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

typedef unsigned int hashval_t;

struct prime_ent
{
  hashval_t prime;
  hashval_t inv;
  hashval_t inv_m2;     /* inverse of prime-2 */
  hashval_t shift;
};

static struct prime_ent const prime_tab[] = {
  {          7, 0x24924925, 0x9999999b, 2 },
  {         13, 0x3b13b13c, 0x745d1747, 3 },
  {         31, 0x08421085, 0x1a7b9612, 4 },
  {         61, 0x0c9714fc, 0x15b1e5f8, 5 },
  {        127, 0x02040811, 0x0624dd30, 6 },
  {        251, 0x05197f7e, 0x073260a5, 7 },
  {        509, 0x01824366, 0x02864fc8, 8 },
  {       1021, 0x00c0906d, 0x014191f7, 9 },
  {       2039, 0x0121456f, 0x0161e69e, 10 },
  {       4093, 0x00300902, 0x00501908, 11 },
  {       8191, 0x00080041, 0x00180241, 12 },
  {      16381, 0x000c0091, 0x00140191, 13 },
  {      32749, 0x002605a5, 0x002a06e6, 14 },
  {      65521, 0x000f00e2, 0x00110122, 15 },
  {     131071, 0x00008001, 0x00018003, 16 },
  {     262139, 0x00014002, 0x0001c004, 17 },
  {     524287, 0x00002001, 0x00006001, 18 },
  {    1048573, 0x00003001, 0x00005001, 19 },
  {    2097143, 0x00004801, 0x00005801, 20 },
  {    4194301, 0x00000c01, 0x00001401, 21 },
  {    8388593, 0x00001e01, 0x00002201, 22 },
  {   16777213, 0x00000301, 0x00000501, 23 },
  {   33554393, 0x00001381, 0x00001481, 24 },
  {   67108859, 0x00000141, 0x000001c1, 25 },
  {  134217689, 0x000004e1, 0x00000521, 26 },
  {  268435399, 0x00000391, 0x000003b1, 27 },
  {  536870909, 0x00000019, 0x00000029, 28 },
  { 1073741789, 0x0000008d, 0x00000095, 29 },
  { 2147483647, 0x00000003, 0x00000007, 30 },
  /* Avoid "decimal constant so large it is unsigned" for 4294967291.  */
  { 0xfffffffb, 0x00000006, 0x00000008, 31 }
};

static unsigned int
higher_prime_index (unsigned long n)
{
  unsigned int low = 0;
  unsigned int high = sizeof(prime_tab) / sizeof(prime_tab[0]);

  while (low != high)
    {
      unsigned int mid = low + (high - low) / 2;
      if (n > prime_tab[mid].prime)
        low = mid + 1;
      else
        high = mid;
    }

  /* If we've run out of primes, abort.  */
  if (n > prime_tab[low].prime)
    {
      fprintf (stderr, "Cannot find prime bigger than %lu\n", n);
      abort ();
    }

  return low;
}


int
main (int argc, char **argv)
{
  if (argc < 2)
    {
      fprintf (stderr, "Usage: hash <number>\n");
      return 1;
    }

  printf ("Answer: %d\n", higher_prime_index (strtoul (argv[1], NULL, 0)));
  return 0;
}