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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/>.
*/
#include "mpn_extras.h"
#include "fmpz_factor.h"
/* P (x : z) = 2 * P1 (x0 : z0) */
/*
Coordinates of P :
x = (x0 + z0)^2 * (x0 - z0)^2 mod n
z = 4 * x0 * z0 * ((x0 - z0)^2 + a24 * 4 * x0 * z0) mod n
*/
void
fmpz_factor_ecm_double(nn_ptr x, nn_ptr z, nn_ptr x0, nn_ptr z0,
nn_ptr n, ecm_t ecm_inf)
{
if (flint_mpn_zero_p(z0, ecm_inf->n_size))
{
flint_mpn_copyi(x, x0, ecm_inf->n_size);
mpn_zero(z, ecm_inf->n_size);
return;
}
/* u = x0 + z0 */
flint_mpn_addmod_n(ecm_inf->u, x0, z0, n, ecm_inf->n_size);
/* u = (x0 + z0)^2 */
flint_mpn_mulmod_preinvn(ecm_inf->u, ecm_inf->u, ecm_inf->u, ecm_inf->n_size, n,
ecm_inf->ninv, ecm_inf->normbits);
/* v = x0 - z0 */
flint_mpn_submod_n(ecm_inf->v, x0, z0, n, ecm_inf->n_size);
/* v = (x0 - z0)^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 = (x0 + z0)^2 * (x0 - z0)^2 */
flint_mpn_mulmod_preinvn(x, ecm_inf->u, ecm_inf->v, ecm_inf->n_size, n,
ecm_inf->ninv, ecm_inf->normbits);
/* w = 4 * x0 * z0 */
flint_mpn_submod_n(ecm_inf->w, ecm_inf->u, ecm_inf->v, n, ecm_inf->n_size);
/* u = a24 * 4 * x0 * z0 */
flint_mpn_mulmod_preinvn(ecm_inf->u, ecm_inf->w, ecm_inf->a24, ecm_inf->n_size, n,
ecm_inf->ninv, ecm_inf->normbits);
/* u = (x0 - z0)^2 + a24 * 4 * x0 * z0 */
flint_mpn_addmod_n(ecm_inf->u, ecm_inf->u, ecm_inf->v, n, ecm_inf->n_size);
/* z = 4 * x0 * z0 * ((x0 - z0)^2 + a24 * 4 * x0 * z0) */
flint_mpn_mulmod_preinvn(z, ecm_inf->w, ecm_inf->u, ecm_inf->n_size, n,
ecm_inf->ninv, ecm_inf->normbits);
}