1 /*
2 Copyright (C) 2013 Fredrik Johansson
3
4 This file is part of Arb.
5
6 Arb 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 <http://www.gnu.org/licenses/>.
10 */
11
12 #include "acb_poly.h"
13
14 void
_acb_poly_evaluate2_rectangular(acb_t y,acb_t z,acb_srcptr poly,slong len,const acb_t x,slong prec)15 _acb_poly_evaluate2_rectangular(acb_t y, acb_t z, acb_srcptr poly,
16 slong len, const acb_t x, slong prec)
17 {
18 slong i, j, m, r;
19 acb_ptr xs;
20 acb_t s, t, c;
21
22 if (len < 3)
23 {
24 if (len == 0)
25 {
26 acb_zero(y);
27 acb_zero(z);
28 }
29 else if (len == 1)
30 {
31 acb_set_round(y, poly + 0, prec);
32 acb_zero(z);
33 }
34 else if (len == 2)
35 {
36 acb_mul(y, x, poly + 1, prec);
37 acb_add(y, y, poly + 0, prec);
38 acb_set_round(z, poly + 1, prec);
39 }
40 return;
41 }
42
43 m = n_sqrt(len) + 1;
44 m *= 1;
45
46 r = (len + m - 1) / m;
47
48 xs = _acb_vec_init(m + 1);
49 acb_init(s);
50 acb_init(t);
51 acb_init(c);
52
53 _acb_vec_set_powers(xs, x, m + 1, prec);
54 acb_dot(y, poly + (r - 1) * m, 0, xs + 1, 1,
55 poly + (r - 1) * m + 1, 1, len - (r - 1) * m - 1, prec);
56
57 for (i = r - 2; i >= 0; i--)
58 {
59 acb_dot(s, poly + i * m, 0, xs + 1, 1,
60 poly + i * m + 1, 1, m - 1, prec);
61 acb_mul(y, y, xs + m, prec);
62 acb_add(y, y, s, prec);
63 }
64
65 /* todo: rewrite using acb_dot */
66 len -= 1;
67 r = (len + m - 1) / m;
68 acb_mul_ui(z, poly + (r - 1) * m + 1, (r - 1) * m + 1, ARF_PREC_EXACT);
69 for (j = 1; (r - 1) * m + j < len; j++)
70 {
71 acb_mul_ui(c, poly + (r - 1) * m + j + 1, (r - 1) * m + j + 1, ARF_PREC_EXACT);
72 acb_addmul(z, xs + j, c, prec);
73 }
74
75 for (i = r - 2; i >= 0; i--)
76 {
77 acb_mul_ui(s, poly + i * m + 1, i * m + 1, ARF_PREC_EXACT);
78
79 for (j = 1; j < m; j++)
80 {
81 acb_mul_ui(c, poly + i * m + j + 1, i * m + j + 1, ARF_PREC_EXACT);
82 acb_addmul(s, xs + j, c, prec);
83 }
84
85 acb_mul(z, z, xs + m, prec);
86 acb_add(z, z, s, prec);
87 }
88
89 _acb_vec_clear(xs, m + 1);
90 acb_clear(s);
91 acb_clear(t);
92 acb_clear(c);
93 }
94
95 void
acb_poly_evaluate2_rectangular(acb_t r,acb_t s,const acb_poly_t f,const acb_t a,slong prec)96 acb_poly_evaluate2_rectangular(acb_t r, acb_t s, const acb_poly_t f, const acb_t a, slong prec)
97 {
98 _acb_poly_evaluate2_rectangular(r, s, f->coeffs, f->length, a, prec);
99 }
100
101