1 /* mpz_nextprime(p,t) - compute the next prime > t and store that in p.
2
3 Copyright 1999-2001, 2008, 2009, 2012 Free Software Foundation, Inc.
4
5 Contributed to the GNU project by Niels Möller and Torbjorn Granlund.
6
7 This file is part of the GNU MP Library.
8
9 The GNU MP Library is free software; you can redistribute it and/or modify
10 it under the terms of either:
11
12 * the GNU Lesser General Public License as published by the Free
13 Software Foundation; either version 3 of the License, or (at your
14 option) any later version.
15
16 or
17
18 * the GNU General Public License as published by the Free Software
19 Foundation; either version 2 of the License, or (at your option) any
20 later version.
21
22 or both in parallel, as here.
23
24 The GNU MP Library is distributed in the hope that it will be useful, but
25 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
26 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
27 for more details.
28
29 You should have received copies of the GNU General Public License and the
30 GNU Lesser General Public License along with the GNU MP Library. If not,
31 see https://www.gnu.org/licenses/. */
32
33 #include "gmp-impl.h"
34 #include "longlong.h"
35
36 static const unsigned char primegap[] =
37 {
38 2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,
39 2,10,2,6,6,4,6,6,2,10,2,4,2,12,12,4,2,4,6,2,10,6,6,6,2,6,4,2,10,14,4,2,
40 4,14,6,10,2,4,6,8,6,6,4,6,8,4,8,10,2,10,2,6,4,6,8,4,2,4,12,8,4,8,4,6,
41 12,2,18,6,10,6,6,2,6,10,6,6,2,6,6,4,2,12,10,2,4,6,6,2,12,4,6,8,10,8,10,8,
42 6,6,4,8,6,4,8,4,14,10,12,2,10,2,4,2,10,14,4,2,4,14,4,2,4,20,4,8,10,8,4,6,
43 6,14,4,6,6,8,6,12
44 };
45
46 #define NUMBER_OF_PRIMES 167
47
48 void
mpz_nextprime(mpz_ptr p,mpz_srcptr n)49 mpz_nextprime (mpz_ptr p, mpz_srcptr n)
50 {
51 unsigned short *moduli;
52 unsigned long difference;
53 int i;
54 unsigned prime_limit;
55 unsigned long prime;
56 mp_size_t pn;
57 mp_bitcnt_t nbits;
58 unsigned incr;
59 TMP_SDECL;
60
61 /* First handle tiny numbers */
62 if (mpz_cmp_ui (n, 2) < 0)
63 {
64 mpz_set_ui (p, 2);
65 return;
66 }
67 mpz_add_ui (p, n, 1);
68 mpz_setbit (p, 0);
69
70 if (mpz_cmp_ui (p, 7) <= 0)
71 return;
72
73 pn = SIZ(p);
74 MPN_SIZEINBASE_2EXP(nbits, PTR(p), pn, 1);
75 if (nbits / 2 >= NUMBER_OF_PRIMES)
76 prime_limit = NUMBER_OF_PRIMES - 1;
77 else
78 prime_limit = nbits / 2;
79
80 TMP_SMARK;
81
82 /* Compute residues modulo small odd primes */
83 moduli = TMP_SALLOC_TYPE (prime_limit, unsigned short);
84
85 for (;;)
86 {
87 /* FIXME: Compute lazily? */
88 prime = 3;
89 for (i = 0; i < prime_limit; i++)
90 {
91 moduli[i] = mpz_tdiv_ui (p, prime);
92 prime += primegap[i];
93 }
94
95 #define INCR_LIMIT 0x10000 /* deep science */
96
97 for (difference = incr = 0; incr < INCR_LIMIT; difference += 2)
98 {
99 /* First check residues */
100 prime = 3;
101 for (i = 0; i < prime_limit; i++)
102 {
103 unsigned r;
104 /* FIXME: Reduce moduli + incr and store back, to allow for
105 division-free reductions. Alternatively, table primes[]'s
106 inverses (mod 2^16). */
107 r = (moduli[i] + incr) % prime;
108 prime += primegap[i];
109
110 if (r == 0)
111 goto next;
112 }
113
114 mpz_add_ui (p, p, difference);
115 difference = 0;
116
117 /* Miller-Rabin test */
118 if (mpz_millerrabin (p, 25))
119 goto done;
120 next:;
121 incr += 2;
122 }
123 mpz_add_ui (p, p, difference);
124 difference = 0;
125 }
126 done:
127 TMP_SFREE;
128 }
129