1 /*
2 Copyright (C) 2012 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_compose_series(acb_ptr res,acb_srcptr poly1,slong len1,acb_srcptr poly2,slong len2,slong n,slong prec)15 _acb_poly_compose_series(acb_ptr res, acb_srcptr poly1, slong len1,
16 acb_srcptr poly2, slong len2, slong n, slong prec)
17 {
18 if (len2 == 1)
19 {
20 acb_set_round(res, poly1, prec);
21 _acb_vec_zero(res + 1, n - 1);
22 }
23 else if (_acb_vec_is_zero(poly2 + 1, len2 - 2)) /* poly2 is a monomial */
24 {
25 slong i, j;
26 acb_t t;
27
28 acb_init(t);
29 acb_set(t, poly2 + len2 - 1);
30 acb_set_round(res, poly1, prec);
31
32 for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1)
33 {
34 acb_mul(res + j, poly1 + i, t, prec);
35
36 if (i + 1 < len1 && j + len2 - 1 < n)
37 acb_mul(t, t, poly2 + len2 - 1, prec);
38 }
39
40 if (len2 != 2)
41 for (i = 1; i < n; i++)
42 if (i % (len2 - 1) != 0)
43 acb_zero(res + i);
44
45 acb_clear(t);
46 }
47 else if (len1 < 6 || n < 6)
48 {
49 _acb_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, prec);
50 }
51 else
52 {
53 _acb_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, prec);
54 }
55 }
56
57 void
acb_poly_compose_series(acb_poly_t res,const acb_poly_t poly1,const acb_poly_t poly2,slong n,slong prec)58 acb_poly_compose_series(acb_poly_t res,
59 const acb_poly_t poly1,
60 const acb_poly_t poly2, slong n, slong prec)
61 {
62 slong len1 = poly1->length;
63 slong len2 = poly2->length;
64 slong lenr;
65
66 if (len2 != 0 && !acb_is_zero(poly2->coeffs))
67 {
68 flint_printf("exception: compose_series: inner "
69 "polynomial must have zero constant term\n");
70 flint_abort();
71 }
72
73 if (len1 == 0 || n == 0)
74 {
75 acb_poly_zero(res);
76 return;
77 }
78
79 if (len2 == 0 || len1 == 1)
80 {
81 acb_poly_set_acb(res, poly1->coeffs);
82 return;
83 }
84
85 lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
86 len1 = FLINT_MIN(len1, lenr);
87 len2 = FLINT_MIN(len2, lenr);
88
89 if ((res != poly1) && (res != poly2))
90 {
91 acb_poly_fit_length(res, lenr);
92 _acb_poly_compose_series(res->coeffs, poly1->coeffs, len1,
93 poly2->coeffs, len2, lenr, prec);
94 _acb_poly_set_length(res, lenr);
95 _acb_poly_normalise(res);
96 }
97 else
98 {
99 acb_poly_t t;
100 acb_poly_init2(t, lenr);
101 _acb_poly_compose_series(t->coeffs, poly1->coeffs, len1,
102 poly2->coeffs, len2, lenr, prec);
103 _acb_poly_set_length(t, lenr);
104 _acb_poly_normalise(t);
105 acb_poly_swap(res, t);
106 acb_poly_clear(t);
107 }
108 }
109