flint3-sys 3.2.3

Rust bindings to the FLINT C library
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
165
166

/*
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2010 William Hart
    Copyright (C) 2011 Fredrik Johansson
    Copyright (C) 2012 Lina Kulakova

    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_mod.h"
#include "fmpz_mod_poly.h"

void
_fmpz_mod_poly_powmod_fmpz_binexp(fmpz * res, const fmpz * poly,
                                  const fmpz_t e, const fmpz * f,
                                  slong lenf, const fmpz_mod_ctx_t ctx)
{
    fmpz * T, * Q;
    fmpz_t invf;
    slong lenT, lenQ;
    slong i;

    if (lenf == 2)
    {
        fmpz_mod_pow_fmpz(res, poly, e, ctx);
        return;
    }

    lenT = 2 * lenf - 3;
    lenQ = lenT - lenf + 1;

    T = _fmpz_vec_init(lenT + lenQ);
    Q = T + lenT;

    fmpz_init(invf);
    fmpz_mod_inv(invf, f + lenf - 1, ctx);

    _fmpz_vec_set(res, poly, lenf - 1);

    for (i = fmpz_sizeinbase(e, 2) - 2; i >= 0; i--)
    {
        _fmpz_mod_poly_sqr(T, res, lenf - 1, ctx);
        _fmpz_mod_poly_divrem(Q, res, T, 2 * lenf - 3, f, lenf, invf, ctx);

        if (fmpz_tstbit(e, i))
        {
            _fmpz_mod_poly_mul(T, res, lenf - 1, poly, lenf - 1, ctx);
            _fmpz_mod_poly_divrem(Q, res, T, 2 * lenf - 3, f, lenf, invf, ctx);
        }
    }

    fmpz_clear(invf);
    _fmpz_vec_clear(T, lenT + lenQ);
}


void
fmpz_mod_poly_powmod_fmpz_binexp(fmpz_mod_poly_t res,
                           const fmpz_mod_poly_t poly, const fmpz_t e,
                             const fmpz_mod_poly_t f, const fmpz_mod_ctx_t ctx)
{
    fmpz * q;
    slong len = poly->length;
    slong lenf = f->length;
    slong trunc = lenf - 1;
    int qcopy = 0;

    if (lenf == 0)
    {
        flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_powmod_fmpz_binexp). Divide by zero\n");
    }

    if (lenf == 1)
    {
        fmpz_mod_poly_zero(res, ctx);
        return;
    }

    if (fmpz_sgn(e) < 0)
    {
        flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_powmod_fmpz_binexp). negative exp not implemented\n");
    }

    if (len >= lenf)
    {
        fmpz_mod_poly_t t, r;
        fmpz_mod_poly_init(t, ctx);
        fmpz_mod_poly_init(r, ctx);
        fmpz_mod_poly_divrem(t, r, poly, f, ctx);
        fmpz_mod_poly_powmod_fmpz_binexp(res, r, e, f, ctx);
        fmpz_mod_poly_clear(t, ctx);
        fmpz_mod_poly_clear(r, ctx);
        return;
    }

    if (fmpz_abs_fits_ui(e))
    {
        ulong exp = fmpz_get_ui(e);

        if (exp <= 2)
        {
            if (exp == UWORD(0))
            {
                fmpz_mod_poly_fit_length(res, 1, ctx);
                fmpz_one(res->coeffs);
                _fmpz_mod_poly_set_length(res, 1);
            }
            else if (exp == UWORD(1))
            {
                fmpz_mod_poly_set(res, poly, ctx);
            }
            else
            {
                fmpz_mod_poly_mulmod(res, poly, poly, f, ctx);
            }
            return;
        }
    }

    if (len == 0)
    {
        fmpz_mod_poly_zero(res, ctx);
        return;
    }

    if (poly->length < trunc)
    {
        q = _fmpz_vec_init(trunc);
        _fmpz_vec_set(q, poly->coeffs, len);
        _fmpz_vec_zero(q + len, trunc - len);
        qcopy = 1;
    }
    else
    {
        q = poly->coeffs;
    }

    if ((res == poly && !qcopy) || (res == f))
    {
        fmpz_mod_poly_t t;
        fmpz_mod_poly_init2(t, 2*lenf - 3, ctx);
        _fmpz_mod_poly_powmod_fmpz_binexp(t->coeffs,
                             q, e, f->coeffs, lenf, ctx);
        fmpz_mod_poly_swap(res, t, ctx);
        fmpz_mod_poly_clear(t, ctx);
    }
    else
    {
        fmpz_mod_poly_fit_length(res, 2*lenf - 3, ctx);
        _fmpz_mod_poly_powmod_fmpz_binexp(res->coeffs,
                             q, e, f->coeffs, lenf, ctx);
    }

    if (qcopy)
        _fmpz_vec_clear(q, trunc);

    _fmpz_mod_poly_set_length(res, trunc);
    _fmpz_mod_poly_normalise(res);
}