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
/*
Copyright (C) 2010 Sebastian Pancratz
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
#define FLINT_DIV_DIVCONQUER_CUTOFF 16
int
_fmpz_poly_div_divconquer_recursive(fmpz * Q, fmpz * temp,
const fmpz * A, const fmpz * B, slong lenB, int exact)
{
if (lenB <= FLINT_DIV_DIVCONQUER_CUTOFF)
{
return _fmpz_poly_div_basecase(Q, temp,
A, 2 * lenB - 1, B, lenB, exact);
}
else
{
const slong n2 = lenB / 2;
const slong n1 = lenB - n2;
fmpz * q0 = Q;
fmpz * q1 = Q + n2;
/*
t is a vector of length lenB - 1, h points to the top n2 coeffs
of t; r1 is vector of length lenB >= 2 n1 - 1
*/
fmpz * t = temp;
fmpz * h = temp + (n1 - 1);
fmpz * r1 = temp + (lenB - 1);
/*
Set {q1, n1}, {r1, 2 n1 - 1} to the quotient and remainder of
{A + 2 n2, 2 n1 - 1} divided by {B + n2, n1}
*/
if (!_fmpz_poly_divremlow_divconquer_recursive(q1, r1,
A + 2 * n2, B + n2, n1, exact))
return 0;
_fmpz_vec_sub(r1, A + 2 * n2, r1, n1 - 1);
/*
Set the top n2 coeffs of t to the top n2 coeffs of the product of
{q1, n1} and {B, n2}; the bottom n1 - 1 coeffs may be arbitrary
For sufficiently large polynomials, computing the full product
using Kronecker segmentation is faster than computing the opposite
short product via Karatsuba
*/
_fmpz_poly_mul(t, q1, n1, B, n2);
/*
If lenB is odd, set {h, n2} to {r1, n2} - {h, n2}, otherwise, to
{A + lenB - 1, 1} + {x * r1, n2} - {h, n2}
*/
if (lenB & WORD(1))
{
_fmpz_vec_sub(h, r1, h, n2);
}
else
{
_fmpz_vec_sub(h + 1, r1, h + 1, n2 - 1);
fmpz_neg(h, h);
fmpz_add(h, h, A + lenB - 1);
}
/*
Set t to h shifted to the right by n2 - 1, and set q0 to the
quotient of {t, 2 n2 - 1} and {B + n1, n2}
Note the bottom n2 - 1 coefficients of t are irrelevant
*/
t += (lenB & WORD(1));
return _fmpz_poly_div_divconquer_recursive(q0, temp + lenB,
t, B + n1, n2, exact);
}
}