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/*
Copyright (C) 2015 Kushagra Singh
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
/* Outer wrapper for ECM
makes calls to stage I and stage II (two) */
#include "mpn_extras.h"
#include "fmpz_factor.h"
/* P (x : z) = P1 (x1 : z1) + P2 (x2 : z2) where P0 (x0 : zo) is P - Q */
/* Coordinates of P :
x = 4 * z0 * (x1 * x2 - z1 * z2)^2 mod n
z = 4 * x0 * (x2 * z1 - x1 * z2)^2 mod n
*/
void
fmpz_factor_ecm_add(nn_ptr x, nn_ptr z, nn_ptr x1, nn_ptr z1, nn_ptr x2,
nn_ptr z2, nn_ptr x0, nn_ptr z0, nn_ptr n, ecm_t ecm_inf)
{
if (flint_mpn_zero_p(z1, ecm_inf->n_size))
{
flint_mpn_copyi(x, x2, ecm_inf->n_size);
flint_mpn_copyi(z, z2, ecm_inf->n_size);
return;
}
if (flint_mpn_zero_p(z2, ecm_inf->n_size))
{
flint_mpn_copyi(x, x1, ecm_inf->n_size);
flint_mpn_copyi(z, z1, ecm_inf->n_size);
return;
}
if (flint_mpn_zero_p(z0, ecm_inf->n_size))
{
fmpz_factor_ecm_double(x, z, x1, z1, n, ecm_inf);
return;
}
/* u = (x2 - z2) */
flint_mpn_submod_n(ecm_inf->u, x2, z2, n, ecm_inf->n_size);
/* v = (x1 + z1) */
flint_mpn_addmod_n(ecm_inf->v, x1, z1, n, ecm_inf->n_size);
/* u = (x2 - z2) * (x1 + z1) */
flint_mpn_mulmod_preinvn(ecm_inf->u, ecm_inf->u, ecm_inf->v, ecm_inf->n_size,
n, ecm_inf->ninv, ecm_inf->normbits);
/* v = (x1 - z1) */
flint_mpn_submod_n(ecm_inf->v, x1, z1, n, ecm_inf->n_size);
/* w = (x2 + z2) */
flint_mpn_addmod_n(ecm_inf->w, x2, z2, n, ecm_inf->n_size);
/* v = (x1 - z1) * (x2 + z2) */
flint_mpn_mulmod_preinvn(ecm_inf->v, ecm_inf->v, ecm_inf->w, ecm_inf->n_size,
n, ecm_inf->ninv, ecm_inf->normbits);
/* w = 2 * (x1 * x2 - z1 * z2) */
flint_mpn_addmod_n(ecm_inf->w, ecm_inf->u, ecm_inf->v, n, ecm_inf->n_size);
/* v = 2 * (x2 * z1 - x1 * z2) */
flint_mpn_submod_n(ecm_inf->v, ecm_inf->v, ecm_inf->u, n, ecm_inf->n_size);
/* w = 4 * (x1 * x2 - z1 * z2)^2 */
flint_mpn_mulmod_preinvn(ecm_inf->w, ecm_inf->w, ecm_inf->w, ecm_inf->n_size,
n, ecm_inf->ninv, ecm_inf->normbits);
/* v = 4 * (x2 * z1 - x1 * z2)^2 */
flint_mpn_mulmod_preinvn(ecm_inf->v, ecm_inf->v, ecm_inf->v, ecm_inf->n_size,
n, ecm_inf->ninv, ecm_inf->normbits);
/* x = 4 * z0 * (x1 * x2 - z1 * z2)^2 */
flint_mpn_mulmod_preinvn(x, z0, ecm_inf->w, ecm_inf->n_size, n, ecm_inf->ninv,
ecm_inf->normbits);
/* z = 4 * x0 * (x2 * z1 - x1 * z2)^2 */
flint_mpn_mulmod_preinvn(z, x0, ecm_inf->v, ecm_inf->n_size, n, ecm_inf->ninv,
ecm_inf->normbits);
}