Copyright 1995, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2005, 2009
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 <stdlib.h>
#include <stdio.h>
#include <string.h>
#include "gmp.h"
int flag_verbose = 0;
static unsigned add[] = {4, 2, 4, 2, 4, 6, 2, 6};
void
factor_using_division (mpz_t t, unsigned int limit)
{
mpz_t q, r;
unsigned long int f;
int ai;
unsigned *addv = add;
unsigned int failures;
if (flag_verbose > 0)
{
printf ("[trial division (%u)] ", limit);
fflush (stdout);
}
mpz_init (q);
mpz_init (r);
f = mpz_scan1 (t, 0);
mpz_div_2exp (t, t, f);
while (f)
{
printf ("2 ");
fflush (stdout);
--f;
}
for (;;)
{
mpz_tdiv_qr_ui (q, r, t, 3);
if (mpz_cmp_ui (r, 0) != 0)
break;
mpz_set (t, q);
printf ("3 ");
fflush (stdout);
}
for (;;)
{
mpz_tdiv_qr_ui (q, r, t, 5);
if (mpz_cmp_ui (r, 0) != 0)
break;
mpz_set (t, q);
printf ("5 ");
fflush (stdout);
}
failures = 0;
f = 7;
ai = 0;
while (mpz_cmp_ui (t, 1) != 0)
{
mpz_tdiv_qr_ui (q, r, t, f);
if (mpz_cmp_ui (r, 0) != 0)
{
f += addv[ai];
if (mpz_cmp_ui (q, f) < 0)
break;
ai = (ai + 1) & 7;
failures++;
if (failures > limit)
break;
}
else
{
mpz_swap (t, q);
printf ("%lu ", f);
fflush (stdout);
failures = 0;
}
}
mpz_clears (q, r, NULL);
}
void
factor_using_division_2kp (mpz_t t, unsigned int limit, unsigned long p)
{
mpz_t r;
mpz_t f;
unsigned int k;
if (flag_verbose > 0)
{
printf ("[trial division (%u)] ", limit);
fflush (stdout);
}
mpz_init (r);
mpz_init_set_ui (f, 2 * p);
mpz_add_ui (f, f, 1);
for (k = 1; k < limit; k++)
{
mpz_tdiv_r (r, t, f);
while (mpz_cmp_ui (r, 0) == 0)
{
mpz_tdiv_q (t, t, f);
mpz_tdiv_r (r, t, f);
mpz_out_str (stdout, 10, f);
fflush (stdout);
fputc (' ', stdout);
}
mpz_add_ui (f, f, 2 * p);
}
mpz_clears (f, r, NULL);
}
void
factor_using_pollard_rho (mpz_t n, unsigned long a, unsigned long p)
{
mpz_t x, x1, y, P;
mpz_t t1, t2;
unsigned long long k, l, i;
if (flag_verbose > 0)
{
printf ("[pollard-rho (%lu)] ", a);
fflush (stdout);
}
mpz_inits (t1, t2, NULL);
mpz_init_set_si (y, 2);
mpz_init_set_si (x, 2);
mpz_init_set_si (x1, 2);
mpz_init_set_ui (P, 1);
k = 1;
l = 1;
while (mpz_cmp_ui (n, 1) != 0)
{
for (;;)
{
do
{
if (p != 0)
{
mpz_powm_ui (x, x, p, n);
mpz_add_ui (x, x, a);
}
else
{
mpz_mul (t1, x, x);
mpz_mod (x, t1, n);
mpz_add_ui (x, x, a);
}
mpz_sub (t1, x1, x);
mpz_mul (t2, P, t1);
mpz_mod (P, t2, n);
if (k % 32 == 1)
{
mpz_gcd (t1, P, n);
if (mpz_cmp_ui (t1, 1) != 0)
goto factor_found;
mpz_set (y, x);
}
}
while (--k != 0);
mpz_gcd (t1, P, n);
if (mpz_cmp_ui (t1, 1) != 0)
goto factor_found;
mpz_set (x1, x);
k = l;
l = 2 * l;
for (i = 0; i < k; i++)
{
if (p != 0)
{
mpz_powm_ui (x, x, p, n);
mpz_add_ui (x, x, a);
}
else
{
mpz_mul (t1, x, x);
mpz_mod (x, t1, n);
mpz_add_ui (x, x, a);
}
}
mpz_set (y, x);
}
factor_found:
do
{
if (p != 0)
{
mpz_powm_ui (y, y, p, n); mpz_add_ui (y, y, a);
}
else
{
mpz_mul (t1, y, y);
mpz_mod (y, t1, n);
mpz_add_ui (y, y, a);
}
mpz_sub (t1, x1, y);
mpz_gcd (t1, t1, n);
}
while (mpz_cmp_ui (t1, 1) == 0);
mpz_divexact (n, n, t1);
if (!mpz_probab_prime_p (t1, 10))
{
do
{
mp_limb_t a_limb;
mpn_random (&a_limb, (mp_size_t) 1);
a = a_limb;
}
while (a == 0);
if (flag_verbose > 0)
{
printf ("[composite factor--restarting pollard-rho] ");
fflush (stdout);
}
factor_using_pollard_rho (t1, a, p);
}
else
{
mpz_out_str (stdout, 10, t1);
fflush (stdout);
fputc (' ', stdout);
}
mpz_mod (x, x, n);
mpz_mod (x1, x1, n);
mpz_mod (y, y, n);
if (mpz_probab_prime_p (n, 10))
{
mpz_out_str (stdout, 10, n);
fflush (stdout);
fputc (' ', stdout);
break;
}
}
mpz_clears (P, t2, t1, x1, x, y, NULL);
}
void
factor (mpz_t t, unsigned long p)
{
unsigned int division_limit;
if (mpz_sgn (t) == 0)
return;
division_limit = mpz_sizeinbase (t, 2);
if (division_limit > 1000)
division_limit = 1000 * 1000;
else
division_limit = division_limit * division_limit;
if (p != 0)
factor_using_division_2kp (t, division_limit / 10, p);
else
factor_using_division (t, division_limit);
if (mpz_cmp_ui (t, 1) != 0)
{
if (flag_verbose > 0)
{
printf ("[is number prime?] ");
fflush (stdout);
}
if (mpz_probab_prime_p (t, 10))
mpz_out_str (stdout, 10, t);
else
factor_using_pollard_rho (t, 1L, p);
}
}
int
main (int argc, char *argv[])
{
mpz_t t;
unsigned long p;
int i;
if (argc > 1 && !strcmp (argv[1], "-v"))
{
flag_verbose = 1;
argv++;
argc--;
}
if (argc > 1 && !strcmp (argv[1], "-q"))
{
flag_verbose = -1;
argv++;
argc--;
}
mpz_init (t);
if (argc > 1)
{
p = 0;
for (i = 1; i < argc; i++)
{
if (!strncmp (argv[i], "-Mp", 3))
{
p = atoi (argv[i] + 3);
mpz_set_ui (t, 1);
mpz_mul_2exp (t, t, p);
mpz_sub_ui (t, t, 1);
}
else if (!strncmp (argv[i], "-2kp", 4))
{
p = atoi (argv[i] + 4);
continue;
}
else
{
mpz_set_str (t, argv[i], 0);
}
if (mpz_cmp_ui (t, 0) == 0)
puts ("-");
else
{
factor (t, p);
puts ("");
}
}
}
else
{
for (;;)
{
mpz_inp_str (t, stdin, 0);
if (feof (stdin))
break;
if (flag_verbose >= 0)
{
mpz_out_str (stdout, 10, t); printf (" = ");
}
factor (t, 0);
puts ("");
}
}
exit (0);
}
