1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
|
/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "arb_poly.h"
arb_ptr * _arb_poly_tree_alloc(slong len)
{
arb_ptr * tree = NULL;
if (len)
{
slong i, height = FLINT_CLOG2(len);
tree = flint_malloc(sizeof(arb_ptr) * (height + 1));
for (i = 0; i <= height; i++)
tree[i] = _arb_vec_init(len + (len >> i) + 1);
}
return tree;
}
void _arb_poly_tree_free(arb_ptr * tree, slong len)
{
if (len)
{
slong i, height = FLINT_CLOG2(len);
for (i = 0; i <= height; i++)
_arb_vec_clear(tree[i], len + (len >> i) + 1);
flint_free(tree);
}
}
void
_arb_poly_tree_build(arb_ptr * tree, arb_srcptr roots, slong len, slong prec)
{
slong height, pow, left, i;
arb_ptr pa, pb;
arb_srcptr a, b;
if (len == 0)
return;
height = FLINT_CLOG2(len);
/* zeroth level, (x-a) */
for (i = 0; i < len; i++)
{
arb_one(tree[0] + (2 * i + 1));
arb_neg(tree[0] + (2 * i), roots + i);
}
/* first level, (x-a)(x-b) = x^2 + (-a-b)*x + a*b */
if (height > 1)
{
pa = tree[1];
for (i = 0; i < len / 2; i++)
{
a = (arb_srcptr) (roots + (2 * i));
b = (arb_srcptr) (roots + (2 * i + 1));
arb_mul(pa + (3 * i), a, b, prec);
arb_add(pa + (3 * i + 1), a, b, prec);
arb_neg(pa + (3 * i + 1), pa + (3 * i + 1));
arb_one(pa + (3 * i + 2));
}
if (len & 1)
{
arb_neg(pa + (3 * (len / 2)), roots + len - 1);
arb_one(pa + (3 * (len / 2) + 1));
}
}
for (i = 1; i < height - 1; i++)
{
left = len;
pow = WORD(1) << i;
pa = tree[i];
pb = tree[i + 1];
while (left >= 2 * pow)
{
_arb_poly_mul_monic(pb, pa, pow + 1, pa + pow + 1, pow + 1, prec);
left -= 2 * pow;
pa += 2 * pow + 2;
pb += 2 * pow + 1;
}
if (left > pow)
{
_arb_poly_mul_monic(pb, pa, pow + 1, pa + pow + 1, left - pow + 1, prec);
}
else if (left > 0)
_arb_vec_set(pb, pa, left + 1);
}
}
|
