1 /*
2     Copyright (C) 2015 Kushagra Singh
3 
4     This file is part of FLINT.
5 
6     FLINT is free software: you can redistribute it and/or modify it under
7     the terms of the GNU Lesser General Public License (LGPL) as published
8     by the Free Software Foundation; either version 2.1 of the License, or
9     (at your option) any later version.  See <https://www.gnu.org/licenses/>.
10 */
11 
12 #include <gmp.h>
13 #include "flint.h"
14 #include "fmpz.h"
15 #include "mpn_extras.h"
16 
17 /* P (x : z) = 2 * P1 (x0 : z0)  */
18 
19 /*
20     Coordinates of P :
21 
22         x = (x0 + z0)^2 * (x0 - z0)^2 mod n
23         z = 4 * x0 * z0 * ((x0 - z0)^2 + a24 * 4 * x0 * z0) mod n
24 */
25 
26 void
fmpz_factor_ecm_double(mp_ptr x,mp_ptr z,mp_ptr x0,mp_ptr z0,mp_ptr n,ecm_t ecm_inf)27 fmpz_factor_ecm_double(mp_ptr x, mp_ptr z, mp_ptr x0, mp_ptr z0,
28                        mp_ptr n, ecm_t ecm_inf)
29 {
30     if (flint_mpn_zero_p(z0, ecm_inf->n_size))
31     {
32         flint_mpn_copyi(x, x0, ecm_inf->n_size);
33         mpn_zero(z, ecm_inf->n_size);
34         return;
35     }
36 
37     /* u = x0 + z0 */
38     fmpz_factor_ecm_addmod(ecm_inf->u, x0, z0, n, ecm_inf->n_size);
39 
40     /* u = (x0 + z0)^2 */
41     flint_mpn_mulmod_preinvn(ecm_inf->u, ecm_inf->u, ecm_inf->u, ecm_inf->n_size, n,
42                              ecm_inf->ninv, ecm_inf->normbits);
43 
44     /* v = x0 - z0 */
45     fmpz_factor_ecm_submod(ecm_inf->v, x0, z0, n, ecm_inf->n_size);
46 
47     /* v = (x0 - z0)^2 */
48     flint_mpn_mulmod_preinvn(ecm_inf->v, ecm_inf->v, ecm_inf->v, ecm_inf->n_size, n,
49                              ecm_inf->ninv, ecm_inf->normbits);
50 
51     /* x = (x0 + z0)^2 * (x0 - z0)^2 */
52     flint_mpn_mulmod_preinvn(x, ecm_inf->u, ecm_inf->v, ecm_inf->n_size, n,
53                              ecm_inf->ninv, ecm_inf->normbits);
54     /* w = 4 * x0 * z0 */
55     fmpz_factor_ecm_submod(ecm_inf->w, ecm_inf->u, ecm_inf->v, n, ecm_inf->n_size);
56 
57     /* u = a24 * 4 * x0 * z0 */
58     flint_mpn_mulmod_preinvn(ecm_inf->u, ecm_inf->w, ecm_inf->a24, ecm_inf->n_size, n,
59                              ecm_inf->ninv, ecm_inf->normbits);
60 
61     /* u = (x0 - z0)^2 + a24 * 4 * x0 * z0 */
62     fmpz_factor_ecm_addmod(ecm_inf->u, ecm_inf->u, ecm_inf->v, n, ecm_inf->n_size);
63 
64     /* z = 4 * x0 * z0 * ((x0 - z0)^2 + a24 * 4 * x0 * z0) */
65     flint_mpn_mulmod_preinvn(z, ecm_inf->w, ecm_inf->u, ecm_inf->n_size, n,
66                              ecm_inf->ninv, ecm_inf->normbits);
67 }
68