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/*
* Copyright (c) 2003 Matteo Frigo
* Copyright (c) 2003 Massachusetts Institute of Technology
*
* 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 2 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, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
/* $Id: primes.c,v 1.1 2008/10/17 06:11:29 scuri Exp $ */
#include "ifftw.h"
/***************************************************************************/
/* Rader's algorithm requires lots of modular arithmetic, and if we
aren't careful we can have errors due to integer overflows. */
#ifdef SAFE_MULMOD
# include <limits.h>
/* compute (x * y) mod p, but watch out for integer overflows; we must
have x, y >= 0, p > 0. This routine is slow. */
int X(safe_mulmod)(int x, int y, int p)
{
if (y == 0 || x <= INT_MAX / y)
return((x * y) % p);
else {
int y2 = y/2;
return((X(safe_mulmod)(x, y2, p) +
X(safe_mulmod)(x, y - y2, p)) % p);
}
}
#endif /* safe_mulmod ('long long' unavailable) */
/***************************************************************************/
/* Compute n^m mod p, where m >= 0 and p > 0. If we really cared, we
could make this tail-recursive. */
int X(power_mod)(int n, int m, int p)
{
A(p > 0);
if (m == 0)
return 1;
else if (m % 2 == 0) {
int x = X(power_mod)(n, m / 2, p);
return MULMOD(x, x, p);
}
else
return MULMOD(n, X(power_mod)(n, m - 1, p), p);
}
/* the following two routines were contributed by Greg Dionne. */
static int get_prime_factors(int n, int *primef)
{
int i;
int size = 0;
primef[size++] = 2;
do
n >>= 1;
while ((n & 1) == 0);
if (n == 1)
return size;
for (i = 3; i * i <= n; i += 2)
if (!(n % i)) {
primef[size++] = i;
do
n /= i;
while (!(n % i));
}
if (n == 1)
return size;
primef[size++] = n;
return size;
}
int X(find_generator)(int p)
{
int n, i, size;
int primef[16]; /* smallest number = 32589158477190044730 > 2^64 */
int pm1 = p - 1;
if (p == 2)
return 1;
size = get_prime_factors(pm1, primef);
n = 2;
for (i = 0; i < size; i++)
if (X(power_mod)(n, pm1 / primef[i], p) == 1) {
i = -1;
n++;
}
return n;
}
/* Return first prime divisor of n (It would be at best slightly faster to
search a static table of primes; there are 6542 primes < 2^16.) */
int X(first_divisor)(int n)
{
int i;
if (n <= 1)
return n;
if (n % 2 == 0)
return 2;
for (i = 3; i*i <= n; i += 2)
if (n % i == 0)
return i;
return n;
}
int X(is_prime)(int n)
{
return(n > 1 && X(first_divisor)(n) == n);
}
int X(next_prime)(int n)
{
while (!X(is_prime)(n)) ++n;
return n;
}
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