pqc/external/flint-2.4.3/ulong_extras/is_probabprime_lucas.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT 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.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2008 Peter Shrimpton
Copyright (C) 2009 William Hart
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
n_pair_t
lchain_precomp(mp_limb_t m, mp_limb_t a, mp_limb_t n, double npre)
{
n_pair_t current = {0, 0}, old;
int length, i;
mp_limb_t power, xy, xx, yy;
old.x = UWORD(2);
old.y = a;
length = FLINT_BIT_COUNT(m);
power = (UWORD(1) << (length - 1));
for (i = 0; i < length; i++)
{
xy = n_submod(n_mulmod_precomp(old.x, old.y, n, npre), a, n);
if (m & power)
{
yy = n_submod(n_mulmod_precomp(old.y, old.y, n, npre), UWORD(2), n);
current.x = xy;
current.y = yy;
}
else
{
xx = n_submod(n_mulmod_precomp(old.x, old.x, n, npre), UWORD(2), n);
current.x = xx;
current.y = xy;
}
power >>= 1;
old = current;
}
return current;
}
n_pair_t
lchain2_preinv(mp_limb_t m, mp_limb_t a, mp_limb_t n, mp_limb_t ninv)
{
n_pair_t current = {0, 0}, old;
int length, i;
mp_limb_t power, xy, xx, yy;
old.x = UWORD(2);
old.y = a;
length = FLINT_BIT_COUNT(m);
power = (UWORD(1) << (length - 1));
for (i = 0; i < length; i++)
{
xy = n_submod(n_mulmod2_preinv(old.x, old.y, n, ninv), a, n);
if (m & power)
{
yy = n_submod(n_mulmod2_preinv(old.y, old.y, n, ninv), UWORD(2), n);
current.x = xy;
current.y = yy;
}
else
{
xx = n_submod(n_mulmod2_preinv(old.x, old.x, n, ninv), UWORD(2), n);
current.x = xx;
current.y = xy;
}
power >>= 1;
old = current;
}
return current;
}
int
n_is_probabprime_lucas(mp_limb_t n)
{
int i, D, Q;
mp_limb_t A;
mp_limb_t left, right;
n_pair_t V;
D = 0;
Q = 0;
if (((n % 2) == 0) || (FLINT_ABS((mp_limb_signed_t) n) <= 2))
{
return (n == UWORD(2));
}
for (i = 0; i < 100; i++)
{
D = 5 + 2 * i;
if (n_gcd(D, n % D) != UWORD(1))
{
if (n == D)
continue;
else
return 0;
}
if (i % 2 == 1)
D = -D;
if (n_jacobi(D, n) == -1)
break;
}
if (i == 100)
{
return (n_is_square(n) ? -1 : 1);
}
Q = (1 - D) / 4;
if (Q < 0)
{
if (n < UWORD(52))
{
while (Q < 0)
Q += n;
A = n_submod(n_invmod(Q, n), UWORD(2), n);
}
else
A = n_submod(n_invmod(Q + n, n), UWORD(2), n);
}
else
{
if (n < UWORD(52))
{
while (Q >= n)
Q -= n;
A = n_submod(n_invmod(Q, n), UWORD(2), n);
}
else
A = n_submod(n_invmod(Q, n), UWORD(2), n);
}
if (FLINT_BIT_COUNT(n) <= FLINT_D_BITS)
{
double npre = n_precompute_inverse(n);
V = lchain_precomp(n + 1, A, n, npre);
left = n_mulmod_precomp(A, V.x, n, npre);
right = n_mulmod_precomp(2, V.y, n, npre);
}
else
{
mp_limb_t ninv = n_preinvert_limb(n);
V = lchain2_preinv(n + 1, A, n, ninv);
left = n_mulmod_precomp(A, V.x, n, ninv);
right = n_mulmod_precomp(2, V.y, n, ninv);
}
return (left == right);
}