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
156
157
158
159
160
161
162
163
164

/*
    Copyright (C) 2011 William Hart
    Copyright (C) 2012 Sebastian Pancratz
    Copyright (C) 2013 Mike Hansen
    Copyright (C) 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_xgcd_generic(slong * lenG, gr_ptr G, gr_ptr S, gr_ptr T, gr_srcptr A, slong lenA, gr_srcptr B, slong lenB, gr_ctx_t ctx)
{
    FLINT_ASSERT(lenA >= lenB);
    FLINT_ASSERT(lenB >= 1);

    return _gr_poly_xgcd_euclidean(lenG, G, S, T, A, lenA, B, lenB, ctx);
}

int
gr_poly_xgcd_wrapper(gr_method_poly_xgcd_op _xgcd_op, gr_poly_t G, gr_poly_t S, gr_poly_t T, const gr_poly_t A, const gr_poly_t B, gr_ctx_t ctx)
{
    if (A->length < B->length)
    {
        return gr_poly_xgcd_wrapper(_xgcd_op, G, T, S, B, A, ctx);
    }
    else                        /* lenA >= lenB >= 0 */
    {
        const slong lenA = A->length, lenB = B->length;
        int status = GR_SUCCESS;
        slong sz = ctx->sizeof_elem;
        gr_ptr t;


        if (lenA == 0)          /* lenA = lenB = 0 */
        {
            status |= gr_poly_zero(G, ctx);
            status |= gr_poly_zero(S, ctx);
            status |= gr_poly_zero(T, ctx);
        }
        else if (lenB == 0)     /* lenA > lenB = 0 */
        {
            GR_TMP_INIT(t, ctx);
            status |= gr_inv(t, GR_ENTRY(A->coeffs, lenA - 1, sz), ctx);
            status |= gr_poly_mul_scalar(G, A, t, ctx);
            status |= gr_poly_zero(T, ctx);
            status |= gr_poly_set_scalar(S, t, ctx);
            GR_TMP_CLEAR(t, ctx);
        }
        else if (gr_is_zero(GR_ENTRY(A->coeffs, A->length - 1, sz), ctx) != T_FALSE ||
                gr_is_zero(GR_ENTRY(B->coeffs, B->length - 1, sz), ctx) != T_FALSE)
        {
            status |= GR_UNABLE;
        }
        else if (lenB == 1)  /* lenA >= lenB = 1 */
        {
            GR_TMP_INIT(t, ctx);
            status |= gr_inv(t, B->coeffs, ctx);
            status |= gr_poly_set_scalar(T, t, ctx);
            status |= gr_poly_one(G, ctx);
            status |= gr_poly_zero(S, ctx);
            GR_TMP_CLEAR(t, ctx);
        }
        else                    /* lenA >= lenB >= 2 */
        {
            gr_ptr g, *s, *t;
            slong lenG;

            if (G == A || G == B)
            {
                g = flint_malloc(sz * FLINT_MIN(lenA, lenB));
                _gr_vec_init(g, FLINT_MIN(lenA, lenB), ctx);
            }
            else
            {
                gr_poly_fit_length(G, FLINT_MIN(lenA, lenB), ctx);
                g = G->coeffs;
            }

            if (S == A || S == B)
            {
                s = flint_malloc(sz * lenB);
                _gr_vec_init(s, lenB, ctx);
            }
            else
            {
                gr_poly_fit_length(S, lenB, ctx);
                s = S->coeffs;
            }

            if (T == A || T == B)
            {
                t = flint_malloc(sz * lenA);
                _gr_vec_init(t, lenA, ctx);
            }
            else
            {
                gr_poly_fit_length(T, lenA, ctx);
                t = T->coeffs;
            }

            status |= _xgcd_op(&lenG, g, s, t, A->coeffs, lenA, B->coeffs, lenB, ctx);

            if (G == A || G == B)
            {
                _gr_vec_clear(G->coeffs, G->alloc, ctx);
                flint_free(G->coeffs);
                G->coeffs = g;
                G->alloc = FLINT_MIN(lenA, lenB);
                G->length = G->alloc;
            }

            if (S == A || S == B)
            {
                _gr_vec_clear(S->coeffs, S->alloc, ctx);
                flint_free(S->coeffs);
                S->coeffs = s;
                S->alloc = lenB;
                S->length = S->alloc;
            }

            if (T == A || T == B)
            {
                _gr_vec_clear(T->coeffs, T->alloc, ctx);
                flint_free(T->coeffs);
                T->coeffs = t;
                T->alloc = lenA;
                T->length = T->alloc;
            }

            _gr_poly_set_length(G, lenG, ctx);
            _gr_poly_set_length(S, FLINT_MAX(lenB - lenG, 1), ctx);
            _gr_poly_set_length(T, FLINT_MAX(lenA - lenG, 1), ctx);
            _gr_poly_normalise(S, ctx);
            _gr_poly_normalise(T, ctx);

            if (status == GR_SUCCESS && gr_is_one(GR_ENTRY(G->coeffs, G->length - 1, sz), ctx) != T_TRUE)
            {
                GR_TMP_INIT(t, ctx);
                status |= gr_inv(t, GR_ENTRY(G->coeffs, G->length - 1, sz), ctx);
                status |= gr_poly_mul_scalar(G, G, t, ctx);
                status |= gr_poly_mul_scalar(S, S, t, ctx);
                status |= gr_poly_mul_scalar(T, T, t, ctx);
                GR_TMP_CLEAR(t, ctx);
            }
        }

        return status;
    }
}

int
gr_poly_xgcd(gr_poly_t G, gr_poly_t S, gr_poly_t T, const gr_poly_t A, const gr_poly_t B, gr_ctx_t ctx)
{
    return gr_poly_xgcd_wrapper((gr_method_poly_xgcd_op) _gr_poly_xgcd, G, S, T, A, B, ctx);
}