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