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

/*
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2011, 2023 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 "gr_vec.h"
#include "gr_poly.h"

int
_gr_poly_compose_series(gr_ptr res, gr_srcptr poly1, slong len1,
                            gr_srcptr poly2, slong len2, slong n, gr_ctx_t ctx)
{
    slong sz = ctx->sizeof_elem;
    int status = GR_SUCCESS;

    len1 = FLINT_MIN(len1, n);
    len2 = FLINT_MIN(len2, n);

    if (n == 1)
    {
        status |= gr_set(res, poly1, ctx);
    }
    else if (n == 2)
    {
        status |= gr_set(res, poly1, ctx);
        status |= gr_mul(GR_ENTRY(res, 1, sz), GR_ENTRY(poly1, 1, sz), GR_ENTRY(poly2, 1, sz), ctx);
    }
    else if (len1 == 1 || len2 == 1)
    {
        status |= gr_set(res, poly1, ctx);
        status |= _gr_vec_zero(GR_ENTRY(res, 1, sz), n - 1, ctx);
    }
    else if (n == 3)
    {
        status |= gr_set(res, poly1, ctx);
        status |= gr_mul(GR_ENTRY(res, 1, sz), GR_ENTRY(poly1, 1, sz), GR_ENTRY(poly2, 1, sz), ctx);

        if (len1 == 2 && len2 == 3)
        {
            status |= gr_mul(GR_ENTRY(res, 2, sz), GR_ENTRY(poly1, 1, sz), GR_ENTRY(poly2, 2, sz), ctx);
        }
        else
        {
            status |= gr_sqr(GR_ENTRY(res, 2, sz), GR_ENTRY(poly2, 1, sz), ctx);
            status |= gr_mul(GR_ENTRY(res, 2, sz), GR_ENTRY(res, 2, sz), GR_ENTRY(poly1, 2, sz), ctx);
            if (len2 == 3)
                status |= gr_addmul(GR_ENTRY(res, 2, sz), GR_ENTRY(poly1, 1, sz), GR_ENTRY(poly2, 2, sz), ctx);
        }
    }
    else if (_gr_vec_is_zero(GR_ENTRY(poly2, 1, sz), len2 - 2, ctx) == T_TRUE)  /* poly2 is a monomial */
    {
        slong i, j;
        gr_ptr t;

        GR_TMP_INIT(t, ctx);
        status |= gr_set(t, GR_ENTRY(poly2, len2 - 1, sz), ctx);
        status |= gr_set(res, poly1, ctx);

        for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1)
        {
            status |= gr_mul(GR_ENTRY(res, j, sz), GR_ENTRY(poly1, i, sz), t, ctx);

            if (i + 1 < len1 && j + len2 - 1 < n)
                status |= gr_mul(t, t, GR_ENTRY(poly2, len2 - 1, sz), ctx);
        }

        if (len2 != 2)
            for (i = 1; i < n; i++)
                if (i % (len2 - 1) != 0)
                    status |= gr_zero(GR_ENTRY(res, i, sz), ctx);

        GR_TMP_CLEAR(t, ctx);
    }
    else if (len1 <= 7 || n <= 7)
    {
        status |= _gr_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, ctx);
    }
    else if (len1 * len1 < n || (len1 - 1) * (len2 - 1) + 1 < 4 * n)  /* todo: tune these cutoffs */
    {
        status |= _gr_poly_compose_series_divconquer(res, poly1, len1, poly2, len2, n, ctx);
    }
    else
    {
        status |= _gr_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, ctx);
    }

    return status;
}

int
gr_poly_compose_series(gr_poly_t res,
                    const gr_poly_t poly1,
                    const gr_poly_t poly2, slong n, gr_ctx_t ctx)
{
    slong len1 = poly1->length;
    slong len2 = poly2->length;
    slong lenr;
    int status;

    if (len2 != 0)
    {
        truth_t is_zero = gr_is_zero(poly2->coeffs, ctx);

        if (is_zero == T_FALSE)
            return GR_DOMAIN;
        if (is_zero == T_UNKNOWN)
            return GR_UNABLE;
    }

    if (len1 == 0 || n == 0)
        return gr_poly_zero(res, ctx);

    if (len2 == 0 || len1 == 1)
        return gr_poly_set_scalar(res, poly1->coeffs, ctx);

    lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
    len1 = FLINT_MIN(len1, lenr);
    len2 = FLINT_MIN(len2, lenr);

    if ((res != poly1) && (res != poly2))
    {
        gr_poly_fit_length(res, lenr, ctx);
        status = _gr_poly_compose_series(res->coeffs, poly1->coeffs, len1,
                                        poly2->coeffs, len2, lenr, ctx);
        _gr_poly_set_length(res, lenr, ctx);
        _gr_poly_normalise(res, ctx);
    }
    else
    {
        gr_poly_t t;
        gr_poly_init2(t, lenr, ctx);
        status = _gr_poly_compose_series(t->coeffs, poly1->coeffs, len1,
                                        poly2->coeffs, len2, lenr, ctx);
        _gr_poly_set_length(t, lenr, ctx);
        _gr_poly_normalise(t, ctx);
        gr_poly_swap(res, t, ctx);
        gr_poly_clear(t, ctx);
    }

    return status;
}