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
165
166
167
168
169
170
171
172
173
174

/*
    Copyright (C) 2026 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 <stdint.h>
#include "radix.h"

/* TODO: consider storing a dynamic table in the radix context object. */

static const uint8_t inv2_tab[] = { 0, 1 };
static const uint8_t inv3_tab[] = { 0, 1, 2 };
static const uint8_t inv4_tab[] = { 0, 1, 0, 3 };
static const uint8_t inv5_tab[] = { 0, 1, 3, 2, 4 };
static const uint8_t inv6_tab[] = { 0, 1, 0, 0, 0, 5 };
static const uint8_t inv7_tab[] = { 0, 1, 4, 5, 2, 3, 6 };
static const uint8_t inv8_tab[] = { 0, 1, 0, 3, 0, 5, 0, 7 };
static const uint8_t inv9_tab[] = { 0, 1, 5, 0, 7, 2, 0, 4, 8 };
static const uint8_t inv10_tab[] = { 0, 1, 0, 7, 0, 0, 0, 3, 0, 9 };
static const uint8_t inv11_tab[] = { 0, 1, 6, 4, 3, 9, 2, 8, 7, 5, 10 };
static const uint8_t inv12_tab[] = { 0, 1, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11 };
static const uint8_t inv13_tab[] = { 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12 };
static const uint8_t inv14_tab[] = { 0, 1, 0, 5, 0, 3, 0, 0, 0, 11, 0, 9, 0, 13 };
static const uint8_t inv15_tab[] = { 0, 1, 8, 0, 4, 0, 0, 13, 2, 0, 0, 11, 0, 7, 14 };
static const uint8_t inv16_tab[] = { 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15 };
static const uint8_t inv17_tab[] = { 0, 1, 9, 6, 13, 7, 3, 5, 15, 2, 12, 14, 10, 4, 11, 8, 16 };
static const uint8_t inv18_tab[] = { 0, 1, 0, 0, 0, 11, 0, 13, 0, 0, 0, 5, 0, 7, 0, 0, 0, 17 };
static const uint8_t inv19_tab[] = { 0, 1, 10, 13, 5, 4, 16, 11, 12, 17, 2, 7, 8, 3, 15, 14, 6, 9, 18 };
static const uint8_t inv20_tab[] = { 0, 1, 0, 7, 0, 0, 0, 3, 0, 9, 0, 11, 0, 17, 0, 0, 0, 13, 0, 19 };
static const uint8_t inv21_tab[] = { 0, 1, 11, 0, 16, 17, 0, 0, 8, 0, 19, 2, 0, 13, 0, 0, 4, 5, 0, 10, 20 };
static const uint8_t inv22_tab[] = { 0, 1, 0, 15, 0, 9, 0, 19, 0, 5, 0, 0, 0, 17, 0, 3, 0, 13, 0, 7, 0, 21 };
static const uint8_t inv23_tab[] = { 0, 1, 12, 8, 6, 14, 4, 10, 3, 18, 7, 21, 2, 16, 5, 20, 13, 19, 9, 17, 15, 11, 22 };
static const uint8_t inv24_tab[] = { 0, 1, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23 };
static const uint8_t inv25_tab[] = { 0, 1, 13, 17, 19, 0, 21, 18, 22, 14, 0, 16, 23, 2, 9, 0, 11, 3, 7, 4, 0, 6, 8, 12, 24 };
static const uint8_t inv26_tab[] = { 0, 1, 0, 9, 0, 21, 0, 15, 0, 3, 0, 19, 0, 0, 0, 7, 0, 23, 0, 11, 0, 5, 0, 17, 0, 25 };
static const uint8_t inv27_tab[] = { 0, 1, 14, 0, 7, 11, 0, 4, 17, 0, 19, 5, 0, 25, 2, 0, 22, 8, 0, 10, 23, 0, 16, 20, 0, 13, 26 };
static const uint8_t inv28_tab[] = { 0, 1, 0, 19, 0, 17, 0, 0, 0, 25, 0, 23, 0, 13, 0, 15, 0, 5, 0, 3, 0, 0, 0, 11, 0, 9, 0, 27 };
static const uint8_t inv29_tab[] = { 0, 1, 15, 10, 22, 6, 5, 25, 11, 13, 3, 8, 17, 9, 27, 2, 20, 12, 21, 26, 16, 18, 4, 24, 23, 7, 19, 14, 28 };

static ulong
n_invmod_bn(ulong x, unsigned int exp, nmod_t bmod, nmod_t mod)
{
    ulong r, y;
    unsigned int e;

    FLINT_ASSERT(bmod.n >= 2);

    switch (bmod.n)
    {
        case 2: r = inv2_tab[x % 2]; break;
        case 3: r = inv3_tab[x % 3]; break;
        case 4: r = inv4_tab[x % 4]; break;
        case 5: r = inv5_tab[x % 5]; break;
        case 6: r = inv6_tab[x % 6]; break;
        case 7: r = inv7_tab[x % 7]; break;
        case 8: r = inv8_tab[x % 8]; break;
        case 9: r = inv9_tab[x % 9]; break;
        case 10: r = inv10_tab[x % 10]; break;
        case 11: r = inv11_tab[x % 11]; break;
        case 12: r = inv12_tab[x % 12]; break;
        case 13: r = inv13_tab[x % 13]; break;
        case 14: r = inv14_tab[x % 14]; break;
        case 15: r = inv15_tab[x % 15]; break;
        case 16: r = inv16_tab[x % 16]; break;
        case 17: r = inv17_tab[x % 17]; break;
        case 18: r = inv18_tab[x % 18]; break;
        case 19: r = inv19_tab[x % 19]; break;
        case 20: r = inv20_tab[x % 20]; break;
        case 21: r = inv21_tab[x % 21]; break;
        case 22: r = inv22_tab[x % 22]; break;
        case 23: r = inv23_tab[x % 23]; break;
        case 24: r = inv24_tab[x % 24]; break;
        case 25: r = inv25_tab[x % 25]; break;
        case 26: r = inv26_tab[x % 26]; break;
        case 27: r = inv27_tab[x % 27]; break;
        case 28: r = inv28_tab[x % 28]; break;
        case 29: r = inv29_tab[x % 29]; break;
        default:
            y = n_gcdinv(&r, nmod_set_ui(x, bmod), mod.n);
            if (y != 1)
                r = 0;
    }

    if (exp >= 2 && r != 0)
    {
        y = nmod_mul(x, r, mod) - 1;
        r = nmod_mul(r, nmod_sub(1, y, mod), mod);

        for (e = 2; e < exp; e *= 2)
        {
            y = nmod_mul(y, y, mod);
            r = nmod_mul(r, y + 1, mod);
        }
    }

    return r;
}

int
radix_invmod_bn(nn_ptr res, nn_srcptr x, slong xn, slong n, const radix_t radix)
{
    res[0] = n_invmod_bn(x[0], radix->exp, radix->b, radix->B);
    if (res[0] == 0)
        return 0;

    if (n == 1)
        return 1;

    ulong t2[2];
    ulong u2[2];
    ulong v2[2];

    /* 1 -> 2 */
    /* mul_1x1 */
    umul_ppmm(t2[1], t2[0], res[0], res[0]);
    u2[0] = flint_mpn_divrem_1_preinv(t2, t2, 2, radix->B.n, radix->B.ninv, radix->B.norm);
    u2[1] = t2[0];
    radix_mulmid(v2, u2, 2, x, FLINT_MIN(xn, 2), 0, 2, radix);
    res[1] = n_negmod(v2[1], radix->B.n);

    if (n == 2)
        return 1;

    nn_ptr u;
    TMP_INIT;
    TMP_START;
    /* Todo: can tighten allocation when we always do a mulhigh */
    u = TMP_ALLOC(n * sizeof(ulong));

    slong a[FLINT_BITS];
    slong i, m;
    a[i = 0] = n;
    while (n > 2)
        a[++i] = (n = (n + 1) / 2);

    for (i--; i >= 0; i--)
    {
        m = n;
        n = a[i];

        slong rxn = FLINT_MIN(n, m + xn);

        /* Can use middle product */
        if (m > 3 && LIMB_RADIX(radix) >= m && rxn > (m - 3))
        {
            ulong one = 1;
            radix_mulmid(u + m - 3, res, m, x, FLINT_MIN(n, xn), m - 3, rxn, radix);
            /* We know that the m least significant limbs of the full product
               res * x are 00...001. The approximate high product is either
               exact or 1 ulp too small. The latter is indicated by a
               nonzero m-1 limb (i.e. a borrow to be returned). */
            if (u[m - 1] != 0)
                radix_add(u + m, u + m, n - m, &one, 1, radix);
            radix_mulmid(res + m, u + m, rxn - m, res, m, 0, n - m, radix);
        }
        else
        {
            radix_mulmid(u, res, m, x, FLINT_MIN(n, xn), 0, rxn, radix);
            radix_mulmid(res + m, u + m, rxn - m, res, m, 0, n - m, radix);
        }
        radix_neg(res + m, res + m, n - m, radix);
    }

    TMP_END;

    return 1;
}