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
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232

/*
    Copyright (C) 2008 Peter Shrimpton
    Copyright (C) 2009 William Hart
    Copyright (C) 2014, 2015 Dana Jacobsen
    Copyright (C) 2015 Kushagra Singh

    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 <math.h>
#include "ulong_extras.h"

int n_is_prime(ulong n)
{
    /* flint's "BPSW" checked against Feitsma and Galway's database [1, 2]
       up to 2^64 by Dana Jacobsen.
       [1]  http://www.janfeitsma.nl/math/psp2/database
       [2]  http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html
    */

    if (n < 11) {
        if (n == 2 || n == 3 || n == 5 || n == 7)   return 1;
        else                                        return 0;
    }
    if (!(n%2) || !(n%3) || !(n%5) || !(n%7))       return 0;
    if (n <  121) /* 11*11 */                       return 1;
    if (!(n%11) || !(n%13) || !(n%17) || !(n%19) ||
        !(n%23) || !(n%29) || !(n%31) || !(n%37) ||
        !(n%41) || !(n%43) || !(n%47) || !(n%53))   return 0;
    if (n < 3481) /* 59*59 */                       return 1;
    if (n > 1000000 &&
        (!(n% 59) || !(n% 61) || !(n% 67) || !(n% 71) || !(n% 73) ||
         !(n% 79) || !(n% 83) || !(n% 89) || !(n% 97) || !(n%101) ||
         !(n%103) || !(n%107) || !(n%109) || !(n%113) || !(n%127) ||
         !(n%131) || !(n%137) || !(n%139) || !(n%149)))  return 0;

    return n_is_probabprime(n);
}

int
n_is_prime_pocklington(ulong n, ulong iterations)
{
    int pass;
    slong i;
    ulong j;
    ulong n1, cofactor, b, c, ninv, limit, F, Fsq, det, rootn, val, c1, c2, upper_limit;
    n_factor_t factors;
    c = 0;

#if FLINT64
    upper_limit = 2642246;                  /* 2642246^3 is approximately 2^64 */
#else
    upper_limit = 1626;                     /* 1626^3 is approximately 2^32 */
#endif

    if (n == 1)
        return 0;
    else if (n % 2 == 0)
        return (n == UWORD(2));

    rootn = n_sqrt(n);                      /* floor(sqrt(n)) */

    if (n == rootn*rootn)
        return 0;

    n1 = n - 1;
    n_factor_init(&factors);
    limit = (ulong) pow((double)n1, 1.0/3);

    val = n_pow(limit, 3);

    while (val < n1 && limit < upper_limit)    /* ensuring that limit >= n1^(1/3) */
    {
        limit++;
        val = n_pow(limit, 3);
    }


    cofactor = n_factor_partial(&factors, n1, limit, 1);

    if (cofactor != 1)                      /* check that cofactor is coprime to factors found */
    {
        for (i = 0; i < factors.num; i++)
        {
            if (factors.p[i] > FLINT_FACTOR_TRIAL_PRIMES_PRIME)
            {
                while (cofactor >= factors.p[i] && (cofactor % factors.p[i]) == 0)
                {
                    factors.exp[i]++;
                    cofactor /= factors.p[i];
                }
            }
        }
    }
    F = n1/cofactor;                        /* n1 = F*cofactor */
    Fsq = F*F;

    if (F <= rootn)                         /* cube root method applicable only if n^1/3 <= F < n^1/2 */
    {
        c2 = n1/(Fsq);                      /* expressing n as c2*F^2 + c1*F + 1  */
        c1 = (n1 - c2*Fsq )/F;
        det = c1*c1 - 4*c2;
        if (n_is_square(det))               /* BSL's test for (n^1/3 <= F < n^1/2) */
            return 0;
    }
    ninv = n_preinvert_limb(n);
    c = 1;
    for (i = factors.num - 1; i >= 0; i--)
    {
        ulong exp = n1 / factors.p[i];
        pass = 0;

        for (j = 2; j < iterations && pass == 0; j++)
        {
            b = n_powmod2_preinv(j, exp, n, ninv);
            if (n_powmod2_ui_preinv(b, factors.p[i], n, ninv) != UWORD(1))
                return 0;

            b = n_submod(b, UWORD(1), n);
            if (b != UWORD(0))
            {
                c = n_mulmod2_preinv(c, b, n, ninv);
                pass = 1;
            }
            else if (c == 0)
                return 0;
        }
        if (j == iterations)
            return -1;
    }
    return (n_gcd(n, c) == UWORD(1));
}

ulong flint_pseudosquares[] = {17, 73, 241, 1009, 2641, 8089, 18001,
          53881, 87481, 117049, 515761, 1083289, 3206641, 3818929, 9257329,
          22000801, 48473881, 48473881, 175244281, 427733329, 427733329,
          898716289u, 2805544681u, 2805544681u, 2805544681u
#ifndef FLINT64
          };
#else
          , 10310263441u, 23616331489u, 85157610409u, 85157610409u,
          196265095009u, 196265095009u, 2871842842801u, 2871842842801u,
          2871842842801u, 26250887023729u, 26250887023729u, 112434732901969u,
          112434732901969u, 112434732901969u, 178936222537081u,
          178936222537081u, 696161110209049u, 696161110209049u,
          2854909648103881u, 6450045516630769u, 6450045516630769u,
          11641399247947921u, 11641399247947921u, 190621428905186449u,
          196640248121928601u, 712624335095093521u, 1773855791877850321u };
#endif

#if FLINT64
#define FLINT_NUM_PSEUDOSQUARES 52
#else
#define FLINT_NUM_PSEUDOSQUARES 25
#endif

int n_is_prime_pseudosquare(ulong n)
{
    unsigned int i, j, m1;
    ulong p, B, NB, exp, mod8;
    const ulong * primes;
    const double * inverses;

    if (n < UWORD(2))
        return 0;
    else if ((n & UWORD(1)) == UWORD(0))
        return (n == UWORD(2));

    primes = n_primes_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF+1);
    inverses = n_prime_inverses_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF+1);

    for (i = 0; i < FLINT_PSEUDOSQUARES_CUTOFF; i++)
    {
        double ppre;
        p = primes[i];
        if (p*p > n)
            return 1;
        ppre = inverses[i];
        if (!n_mod2_precomp(n, p, ppre))
            return 0;
    }

    B  = primes[FLINT_PSEUDOSQUARES_CUTOFF];
    NB = (n - 1)/B + 1;
    m1 = 0;

    for (i = 0; i < FLINT_NUM_PSEUDOSQUARES; i++)
        if (flint_pseudosquares[i] > NB)
            break;

    exp = (n - 1)/2;

    for (j = 0; j <= i; j++)
    {
        ulong mod = n_powmod2(primes[j], exp, n);
        if ((mod != UWORD(1)) && (mod != n - 1))
            return 0;
        else if (mod == n - 1)
            m1 = 1;
    }

    mod8 = n % 8;

    if ((mod8 == 3) || (mod8 == 7))
        return 1;
    else if (mod8 == 5)
    {
        ulong mod = n_powmod2(UWORD(2), exp, n);
        if (mod == n - 1)
            return 1;
        else
            flint_throw(FLINT_ERROR, "Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
    }
    else
    {
        if (m1) return 1;
        for (j = i + 1; j < FLINT_NUM_PSEUDOSQUARES + 1; j++)
        {
            ulong mod = n_powmod2(primes[j], exp, n);
            if (mod == n - 1)
                return 1;
            else if (mod != 1)
                flint_throw(FLINT_ERROR, "Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
        }
        flint_throw(FLINT_ERROR, "Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
    }
}