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_pow_series(acb_ptr h,acb_srcptr f,slong flen,acb_srcptr g,slong glen,slong len,slong prec)15 _acb_poly_pow_series(acb_ptr h,
16 acb_srcptr f, slong flen,
17 acb_srcptr g, slong glen, slong len, slong prec)
18 {
19 if (glen == 1)
20 {
21 _acb_poly_pow_acb_series(h, f, flen, g, len, prec);
22 return;
23 }
24
25 /* f^g = exp(g * log(f)) */
26 if (flen == 1)
27 {
28 acb_t t;
29 acb_init(t);
30 acb_log(t, f, prec);
31 _acb_vec_scalar_mul(h, g, glen, t, prec);
32 _acb_poly_exp_series(h, h, glen, len, prec);
33 acb_clear(t);
34 }
35 else
36 {
37 acb_ptr t;
38 t = _acb_vec_init(len);
39 _acb_poly_log_series(t, f, flen, len, prec);
40 _acb_poly_mullow(h, t, len, g, glen, len, prec);
41 _acb_poly_exp_series(h, h, len, len, prec);
42 _acb_vec_clear(t, len);
43
44 }
45 }
46
47 void
acb_poly_pow_series(acb_poly_t h,const acb_poly_t f,const acb_poly_t g,slong len,slong prec)48 acb_poly_pow_series(acb_poly_t h,
49 const acb_poly_t f, const acb_poly_t g, slong len, slong prec)
50 {
51 slong flen, glen;
52
53 flen = f->length;
54 glen = g->length;
55
56 flen = FLINT_MIN(flen, len);
57 glen = FLINT_MIN(glen, len);
58
59 if (len == 0)
60 {
61 acb_poly_zero(h);
62 return;
63 }
64
65 if (glen == 0)
66 {
67 acb_poly_one(h);
68 return;
69 }
70
71 if (flen == 0)
72 {
73 acb_poly_zero(h);
74 return;
75 }
76
77 if (flen == 1 && glen == 1)
78 {
79 acb_poly_fit_length(h, 1);
80 acb_pow(h->coeffs, f->coeffs, g->coeffs, prec);
81 _acb_poly_set_length(h, 1);
82 _acb_poly_normalise(h);
83 return;
84 }
85
86 if (f == h || g == h)
87 {
88 acb_poly_t t;
89 acb_poly_init2(t, len);
90 _acb_poly_pow_series(t->coeffs,
91 f->coeffs, flen, g->coeffs, glen, len, prec);
92 _acb_poly_set_length(t, len);
93 _acb_poly_normalise(t);
94 acb_poly_swap(t, h);
95 acb_poly_clear(t);
96 }
97 else
98 {
99 acb_poly_fit_length(h, len);
100 _acb_poly_pow_series(h->coeffs,
101 f->coeffs, flen, g->coeffs, glen, len, prec);
102 _acb_poly_set_length(h, len);
103 _acb_poly_normalise(h);
104 }
105 }
106
107