/* Factoring of uintmax_t numbers. Generation of needed tables.

   Contributed to the GNU project by Torbjörn Granlund and Niels Möller
   Contains code from GNU MP.

Copyright 2012 Free Software Foundation, Inc.

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; either version 3 of the License, or (at your option) any later
version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE.  See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with
this program.  If not, see http://www.gnu.org/licenses/.  */

#include <config.h>

#include <limits.h>
#include <stdint.h>
#include <inttypes.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <errno.h>

/* Deactivate config.h's "rpl_"-prefixed definitions of these symbols.  */
#undef fclose
#undef malloc
#undef strerror

/* An unsigned type that is no narrower than 32 bits and no narrower
   than unsigned int.  It's best to make it as wide as possible.
   For GCC 4.6 and later, use a heuristic to guess whether unsigned
   __int128 works on your platform.  If this heuristic does not work
   for you, please report a bug; in the meantime compile with, e.g.,
   -Dwide_uint='unsigned __int128' to override the heuristic.  */
#ifndef wide_uint
# if 4 < __GNUC__ + (6 <= __GNUC_MINOR__) && ULONG_MAX >> 31 >> 31 >> 1 != 0
typedef unsigned __int128 wide_uint;
# else
typedef uintmax_t wide_uint;
# endif
#endif

struct prime
{
  unsigned p;
  wide_uint pinv; /* Inverse mod b = 2^{bitsize of wide_uint} */
  wide_uint lim; /* floor ((wide_uint) -1 / p) */
};

static wide_uint _GL_ATTRIBUTE_CONST
binvert (wide_uint a)
{
  wide_uint x = 0xf5397db1 >> (4*((a/2) & 0x7));
  for (;;)
    {
      wide_uint y = 2*x - x*x*a;
      if (y == x)
        return x;
      x = y;
    }
}

static void
process_prime (struct prime *info, unsigned p)
{
  wide_uint max = -1;
  info->p = p;
  info->pinv = binvert (p);
  info->lim = max / p;
}

static void
print_wide_uint (wide_uint n, int nesting, unsigned wide_uint_bits)
{
  /* Number of bits per integer literal.  8 is too many, because
     uintmax_t is 32 bits on some machines so we cannot shift by 32 bits.
     So use 7.  */
  int hex_digits_per_literal = 7;
  int bits_per_literal = hex_digits_per_literal * 4;

  unsigned remainder = n & ((1 << bits_per_literal) - 1);

  if (n != remainder)
    {
      int needs_parentheses = n >> bits_per_literal >> bits_per_literal != 0;
      if (needs_parentheses)
        printf ("(");
      print_wide_uint (n >> bits_per_literal, nesting + 1, wide_uint_bits);
      if (needs_parentheses)
        printf (")\n%*s", nesting + 3, "");
      printf (" << %d | ", bits_per_literal);
    }
  else if (nesting)
    {
      printf ("(uintmax_t) ");
      hex_digits_per_literal
        = ((wide_uint_bits - 1) % bits_per_literal) % 4 + 1;
    }

  printf ("0x%0*xU", hex_digits_per_literal, remainder);
}

static void
output_primes (const struct prime *primes, unsigned nprimes)
{
  unsigned i;
  unsigned p;
  int is_prime;

  /* Compute wide_uint_bits by repeated shifting, rather than by
     multiplying sizeof by CHAR_BIT, as this works even if the
     wide_uint representation has holes.  */
  unsigned wide_uint_bits = 0;
  wide_uint mask = -1;
  for (wide_uint_bits = 0; mask; wide_uint_bits++)
    mask >>= 1;

  puts ("/* Generated file -- DO NOT EDIT */\n");
  printf ("#define WIDE_UINT_BITS %u\n", wide_uint_bits);

  for (i = 0, p = 2; i < nprimes; i++)
    {
      unsigned int d8 = i + 8 < nprimes ? primes[i + 8].p - primes[i].p : 0xff;
      if (255 < d8) /* this happens at 668221 */
        abort ();
      printf ("P (%u, %u,\n   (", primes[i].p - p, d8);
      print_wide_uint (primes[i].pinv, 0, wide_uint_bits);
      printf ("),\n   UINTMAX_MAX / %d)\n", primes[i].p);
      p = primes[i].p;
    }

  printf ("\n#undef FIRST_OMITTED_PRIME\n");

  /* Find next prime */
  do
    {
      p += 2;
      for (i = 0, is_prime = 1; is_prime; i++)
        {
          if (primes[i].p * primes[i].p > p)
            break;
          if (p * primes[i].pinv <= primes[i].lim)
            {
              is_prime = 0;
              break;
            }
        }
    }
  while (!is_prime);

  printf ("#define FIRST_OMITTED_PRIME %u\n", p);
}

static void *
xalloc (size_t s)
{
  void *p = malloc (s);
  if (p)
    return p;

  fprintf (stderr, "Virtual memory exhausted.\n");
  exit (EXIT_FAILURE);
}

int
main (int argc, char **argv)
{
  int limit;

  char *sieve;
  size_t size, i;

  struct prime *prime_list;
  unsigned nprimes;

  if (argc != 2)
    {
      fprintf (stderr, "Usage: %s LIMIT\n"
               "Produces a list of odd primes <= LIMIT\n", argv[0]);
      return EXIT_FAILURE;
    }
  limit = atoi (argv[1]);
  if (limit < 3)
    exit (EXIT_SUCCESS);

  /* Make limit odd */
  if ( !(limit & 1))
    limit--;

  size = (limit-1)/2;
  /* sieve[i] represents 3+2*i */
  sieve = xalloc (size);
  memset (sieve, 1, size);

  prime_list = xalloc (size * sizeof (*prime_list));
  nprimes = 0;

  for (i = 0; i < size;)
    {
      unsigned p = 3+2*i;
      unsigned j;

      process_prime (&prime_list[nprimes++], p);

      for (j = (p*p - 3)/2; j < size; j+= p)
        sieve[j] = 0;

      while (i < size && sieve[++i] == 0)
        ;
    }

  output_primes (prime_list, nprimes);

  if (ferror (stdout) + fclose (stdout))
    {
      fprintf (stderr, "write error: %s\n", strerror (errno));
      return EXIT_FAILURE;
    }

  return EXIT_SUCCESS;
}