1 /* gmp_nextprime -- generate small primes reasonably efficiently for internal
2 GMP needs.
3
4 Contributed to the GNU project by Torbjorn Granlund. Miscellaneous
5 improvements by Martin Boij.
6
7 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
8 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
9 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
10
11 Copyright 2009 Free Software Foundation, Inc.
12
13 This file is part of the GNU MP Library.
14
15 The GNU MP Library is free software; you can redistribute it and/or modify
16 it under the terms of either:
17
18 * the GNU Lesser General Public License as published by the Free
19 Software Foundation; either version 3 of the License, or (at your
20 option) any later version.
21
22 or
23
24 * the GNU General Public License as published by the Free Software
25 Foundation; either version 2 of the License, or (at your option) any
26 later version.
27
28 or both in parallel, as here.
29
30 The GNU MP Library is distributed in the hope that it will be useful, but
31 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
32 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
33 for more details.
34
35 You should have received copies of the GNU General Public License and the
36 GNU Lesser General Public License along with the GNU MP Library. If not,
37 see https://www.gnu.org/licenses/. */
38
39 /*
40 Optimisation ideas:
41
42 1. Unroll the sieving loops. Should reach 1 write/cycle. That would be a 2x
43 improvement.
44
45 2. Separate sieving with primes p < SIEVESIZE and p >= SIEVESIZE. The latter
46 will need at most one write, and thus not need any inner loop.
47
48 3. For primes p >= SIEVESIZE, i.e., typically the majority of primes, we
49 perform more than one division per sieving write. That might dominate the
50 entire run time for the nextprime function. A incrementally initialised
51 remainder table of Pi(65536) = 6542 16-bit entries could replace that
52 division.
53 */
54
55 #include "gmp-impl.h"
56 #include <string.h> /* for memset */
57
58
59 unsigned long int
60 gmp_nextprime (gmp_primesieve_t *ps)
61 {
62 unsigned long p, d, pi;
63 unsigned char *sp;
64 static unsigned char addtab[] =
65 { 2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,
66 2,4,6,2,6,4,2,4,2,10,2,10 };
67 unsigned char *addp = addtab;
68 unsigned long ai;
69
70 /* Look for already sieved primes. A sentinel at the end of the sieving
71 area allows us to use a very simple loop here. */
72 d = ps->d;
73 sp = ps->s + d;
74 while (*sp != 0)
75 sp++;
76 if (sp != ps->s + SIEVESIZE)
77 {
78 d = sp - ps->s;
79 ps->d = d + 1;
80 return ps->s0 + 2 * d;
81 }
82
83 /* Handle the number 2 separately. */
84 if (ps->s0 < 3)
85 {
86 ps->s0 = 3 - 2 * SIEVESIZE; /* Tricky */
87 return 2;
88 }
89
90 /* Exhausted computed primes. Resieve, then call ourselves recursively. */
91
92 #if 0
93 for (sp = ps->s; sp < ps->s + SIEVESIZE; sp++)
94 *sp = 0;
95 #else
96 memset (ps->s, 0, SIEVESIZE);
97 #endif
98
99 ps->s0 += 2 * SIEVESIZE;
100
101 /* Update sqrt_s0 as needed. */
102 while ((ps->sqrt_s0 + 1) * (ps->sqrt_s0 + 1) <= ps->s0 + 2 * SIEVESIZE - 1)
103 ps->sqrt_s0++;
104
105 pi = ((ps->s0 + 3) / 2) % 3;
106 if (pi > 0)
107 pi = 3 - pi;
108 if (ps->s0 + 2 * pi <= 3)
109 pi += 3;
110 sp = ps->s + pi;
111 while (sp < ps->s + SIEVESIZE)
112 {
113 *sp = 1, sp += 3;
114 }
115
116 pi = ((ps->s0 + 5) / 2) % 5;
117 if (pi > 0)
118 pi = 5 - pi;
119 if (ps->s0 + 2 * pi <= 5)
120 pi += 5;
121 sp = ps->s + pi;
122 while (sp < ps->s + SIEVESIZE)
123 {
124 *sp = 1, sp += 5;
125 }
126
127 pi = ((ps->s0 + 7) / 2) % 7;
128 if (pi > 0)
129 pi = 7 - pi;
130 if (ps->s0 + 2 * pi <= 7)
131 pi += 7;
132 sp = ps->s + pi;
133 while (sp < ps->s + SIEVESIZE)
134 {
135 *sp = 1, sp += 7;
136 }
137
138 p = 11;
139 ai = 0;
140 while (p <= ps->sqrt_s0)
141 {
142 pi = ((ps->s0 + p) / 2) % p;
143 if (pi > 0)
144 pi = p - pi;
145 if (ps->s0 + 2 * pi <= p)
146 pi += p;
147 sp = ps->s + pi;
148 while (sp < ps->s + SIEVESIZE)
149 {
150 *sp = 1, sp += p;
151 }
152 p += addp[ai];
153 ai = (ai + 1) % 48;
154 }
155 ps->d = 0;
156 return gmp_nextprime (ps);
157 }
158
159 void
160 gmp_init_primesieve (gmp_primesieve_t *ps)
161 {
162 ps->s0 = 0;
163 ps->sqrt_s0 = 0;
164 ps->d = SIEVESIZE;
165 ps->s[SIEVESIZE] = 0; /* sentinel */
166 }