flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155

/*
    Copyright (C) 2010 William Hart
    Copyright (C) 2021 Fredrik Johansson

    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 "mpn_extras.h"
#include "nmod.h"
#include "nmod_vec.h"
#include "nmod_poly.h"

/* Assumes poly1 and poly2 are not length 0. */
void
_nmod_poly_mul_classical(nn_ptr res, nn_srcptr poly1,
                         slong len1, nn_srcptr poly2, slong len2, nmod_t mod)
{
    slong i, j, n1, n2;
    int squaring;
    ulong c;

    if (len1 == 1)
    {
        res[0] = nmod_mul(poly1[0], poly2[0], mod);
        return;
    }

    if (len2 == 1)
    {
        _nmod_vec_scalar_mul_nmod(res, poly1, len1, poly2[0], mod);
        return;
    }

    squaring = (poly1 == poly2 && len1 == len2);

    const dot_params_t params = _nmod_vec_dot_params(FLINT_MIN(len1, len2), mod);

    if (params.method <= _DOT1)
    {
        flint_mpn_zero(res, len1 + len2 - 1);

        if (squaring)
        {
            for (i = 0; i < len1; i++)
            {
                c = poly1[i];

                res[2 * i] += c * c;
                c *= 2;

                for (j = i + 1; j < len1; j++)
                    res[i + j] += poly1[j] * c;
            }
        }
        else
        {
            for (i = 0; i < len1; i++)
            {
                ulong c = poly1[i];

                for (j = 0; j < len2; j++)
                    res[i + j] += c * poly2[j];
            }
        }

        _nmod_vec_reduce(res, res, len1 + len2 - 1, mod);
        return;
    }

    if (len2 == 2)
    {
        _nmod_vec_scalar_mul_nmod(res, poly1, len1, poly2[0], mod);
        _nmod_vec_scalar_addmul_nmod(res + 1, poly1, len1 - 1, poly2[1], mod);
        res[len1 + len2 - 2] = nmod_mul(poly1[len1 - 1], poly2[len2 - 1], mod);
        return;
    }

    if (squaring)
    {
        for (i = 0; i < 2 * len1 - 1; i++)
        {
            n1 = FLINT_MAX(0, i - len1 + 1);
            n2 = FLINT_MIN(len1 - 1, (i + 1) / 2 - 1);

            c = _nmod_vec_dot_rev(poly1 + n1, poly1 + i - n2, n2 - n1 + 1, mod, params);
            c = nmod_add(c, c, mod);

            if (i % 2 == 0 && i / 2 < len1)
                NMOD_ADDMUL(c, poly1[i / 2], poly1[i / 2], mod);

            res[i] = c;
        }
    }
    else
    {
        for (i = 0; i < len1 + len2 - 1; i++)
        {
            n1 = FLINT_MIN(len1 - 1, i);
            n2 = FLINT_MIN(len2 - 1, i);

            res[i] = _nmod_vec_dot_rev(poly1 + i - n2,
                                       poly2 + i - n1,
                                       n1 + n2 - i + 1, mod, params);
        }
    }
}

void
nmod_poly_mul_classical(nmod_poly_t res,
                        const nmod_poly_t poly1, const nmod_poly_t poly2)
{
    slong len_out;

    if ((poly1->length == 0) || (poly2->length == 0))
    {
        nmod_poly_zero(res);
        return;
    }

    len_out = poly1->length + poly2->length - 1;

    if (res == poly1 || res == poly2)
    {
        nmod_poly_t temp;
        nmod_poly_init2_preinv(temp, poly1->mod.n, poly1->mod.ninv, len_out);
        if (poly1->length >= poly2->length)
            _nmod_poly_mul_classical(temp->coeffs, poly1->coeffs,
                                     poly1->length, poly2->coeffs,
                                     poly2->length, poly1->mod);
        else
            _nmod_poly_mul_classical(temp->coeffs, poly2->coeffs,
                                     poly2->length, poly1->coeffs,
                                     poly1->length, poly1->mod);
        nmod_poly_swap(res, temp);
        nmod_poly_clear(temp);
    }
    else
    {
        nmod_poly_fit_length(res, len_out);
        if (poly1->length >= poly2->length)
            _nmod_poly_mul_classical(res->coeffs, poly1->coeffs, poly1->length,
                                     poly2->coeffs, poly2->length, poly1->mod);
        else
            _nmod_poly_mul_classical(res->coeffs, poly2->coeffs, poly2->length,
                                     poly1->coeffs, poly1->length, poly1->mod);
    }

    res->length = len_out;
    _nmod_poly_normalise(res);
}