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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 2012-2020 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 https://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 / %u)\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 * _GL_ATTRIBUTE_MALLOC
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)
return 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);
free (sieve);
free (prime_list);
if (ferror (stdout) + fclose (stdout))
{
fprintf (stderr, "write error: %s\n", strerror (errno));
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
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