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/* 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 2012-2013 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;
}