0f5ec153 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: pgen.c,v 1.1 1999/11/19 13:17:57 mdw Exp $ |
4 | * |
5 | * Finding and testing prime numbers |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: pgen.c,v $ |
33 | * Revision 1.1 1999/11/19 13:17:57 mdw |
34 | * Prime number generator and tester. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "mp.h" |
41 | #include "mpmont.h" |
42 | #include "pgen.h" |
43 | #include "ptab.h" |
44 | #include "rabin.h" |
45 | |
46 | /*----- Main code ---------------------------------------------------------*/ |
47 | |
48 | /* --- @pgen_create@ --- * |
49 | * |
50 | * Arguments: @pgen *p@ = pointer to prime generation context |
51 | * @mp *m@ = pointer to initial number to test |
52 | * |
53 | * Returns: One of the @PGEN@ constants above. |
54 | * |
55 | * Use: Tests an initial number for primality by computing its |
56 | * residue modulo various small prime numbers. This is fairly |
57 | * quick, but not particularly certain. If a @PGEN_MAYBE@ |
58 | * result is returned, perform Rabin-Miller tests to confirm. |
59 | */ |
60 | |
61 | int pgen_create(pgen *p, mp *m) |
62 | { |
63 | int rc = PGEN_MAYBE; |
64 | int i; |
65 | mp *r = MP_NEW; |
66 | mpw qw; |
67 | mp q; |
68 | |
69 | /* --- Take a copy of the number --- */ |
70 | |
71 | mp_shrink(m); |
72 | p->m = MP_COPY(m); |
73 | |
74 | /* --- Fill in the residues --- */ |
75 | |
76 | mp_build(&q, &qw, &qw + 1); |
77 | for (i = 0; i < NPRIME; i++) { |
78 | qw = ptab[i]; |
79 | mp_div(0, &r, m, &q); |
80 | p->r[i] = r->v[0]; |
81 | if (!p->r[i] && rc == PGEN_MAYBE) { |
82 | if (MP_LEN(m) == 1 && m->v[0] == ptab[i]) |
83 | rc = PGEN_PRIME; |
84 | else |
85 | rc = PGEN_COMPOSITE; |
86 | } |
87 | } |
88 | |
89 | /* --- Done --- */ |
90 | |
91 | mp_drop(r); |
92 | return (rc); |
93 | } |
94 | |
95 | /* --- @pgen_destroy@ --- * |
96 | * |
97 | * Arguments: @pgen *p@ = pointer to prime generation context |
98 | * |
99 | * Returns: --- |
100 | * |
101 | * Use: Discards a context and all the resources it holds. |
102 | */ |
103 | |
104 | void pgen_destroy(pgen *p) |
105 | { |
106 | mp_drop(p->m); |
107 | } |
108 | |
109 | /* --- @pgen_step@ --- * |
110 | * |
111 | * Arguments: @pgen *p@ = pointer to prime generation context |
112 | * @mpw step@ = how much to step the number |
113 | * |
114 | * Returns: One of the @PGEN@ constants above. |
115 | * |
116 | * Use: Steps a number by a small amount. Stepping is much faster |
117 | * than initializing with a new number. The test performed is |
118 | * the same simple one used by @ptab_create@, so @PGEN_MAYBE@ |
119 | * results should be followed up by a Rabin-Miller test. |
120 | */ |
121 | |
122 | int pgen_step(pgen *p, mpw step) |
123 | { |
124 | mp s; |
125 | int rc = PGEN_MAYBE; |
126 | int i; |
127 | |
128 | /* --- Add the step on to the number --- */ |
129 | |
130 | mp_build(&s, &step, &step + 1); |
131 | p->m = mp_add(p->m, p->m, &s); |
132 | |
133 | /* --- Update the residue table --- */ |
134 | |
135 | for (i = 0; i < NPRIME; i++) { |
136 | p->r[i] = (p->r[i] + step) % ptab[i]; |
137 | if (!p->r[i] && rc == PGEN_MAYBE) { |
138 | if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i]) |
139 | rc = PGEN_PRIME; |
140 | else |
141 | rc = PGEN_COMPOSITE; |
142 | } |
143 | } |
144 | |
145 | /* --- Done --- */ |
146 | |
147 | return (rc); |
148 | } |
149 | |
150 | /* --- @pgen_jump@ --- * |
151 | * |
152 | * Arguments: @pgen *p@ = pointer to prime generation context |
153 | * @pgen *j@ = pointer to another generation context |
154 | * |
155 | * Returns: One of the @PGEN@ constants above. |
156 | * |
157 | * Use: Steps a number by a large amount. Even so, jumping is much |
158 | * faster than initializing a new number. The test peformed is |
159 | * the same simple one used by @ptab_create@, so @PGEN_MAYBE@ |
160 | * results should be followed up by a Rabin-Miller test. |
161 | * |
162 | * Note that the number stored in the @j@ context is probably |
163 | * better off being even than prime. The important thing is |
164 | * that all of the residues for the number have already been |
165 | * computed. |
166 | */ |
167 | |
168 | int pgen_jump(pgen *p, pgen *j) |
169 | { |
170 | int rc = PGEN_MAYBE; |
171 | int i; |
172 | |
173 | /* --- Add the step on --- */ |
174 | |
175 | p->m = mp_add(p->m, p->m, j->m); |
176 | |
177 | /* --- Update the residue table --- */ |
178 | |
179 | for (i = 0; i < NPRIME; i++) { |
180 | p->r[i] = p->r[i] + j->r[i]; |
181 | if (p->r[i] > ptab[i]) |
182 | p->r[i] -= ptab[i]; |
183 | if (!p->r[i] && rc == PGEN_MAYBE) { |
184 | if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i]) |
185 | rc = PGEN_PRIME; |
186 | else |
187 | rc = PGEN_COMPOSITE; |
188 | } |
189 | } |
190 | |
191 | /* --- Done --- */ |
192 | |
193 | return (rc); |
194 | } |
195 | |
196 | /*----- Test code ---------------------------------------------------------*/ |
197 | |
198 | #ifdef TEST_RIG |
199 | |
200 | #include <mLib/testrig.h> |
201 | |
202 | static int verify(dstr *v) |
203 | { |
204 | mp *m = *(mp **)v[0].buf; |
205 | mp *r = *(mp **)v[1].buf; |
206 | pgen p; |
207 | mpw gw; |
208 | mp g; |
209 | int rc; |
210 | static char baton[] = "/-\\|"; |
211 | char *b = baton; |
212 | int ok = 1; |
213 | |
214 | mp_build(&g, &gw, &gw + 1); |
215 | rc = pgen_create(&p, m); |
216 | for (;;) { |
217 | if (rc == PGEN_PRIME) |
218 | break; |
219 | if (rc == PGEN_MAYBE) { |
220 | int i; |
221 | rabin r; |
222 | rabin_create(&r, p.m); |
223 | for (i = 0; i < 5; i++) { |
224 | gw = rand(); |
225 | if (rabin_test(&r, &g) == PGEN_COMPOSITE) |
226 | break; |
227 | } |
228 | rabin_destroy(&r); |
229 | if (i == 5) |
230 | break; |
231 | putc(*b++, stderr); |
232 | putc('\b', stderr); |
233 | if (!*b) |
234 | b = baton; |
235 | } |
236 | rc = pgen_step(&p, 2); |
237 | } |
238 | |
239 | if (MP_CMP(p.m, !=, r)) { |
240 | fputs("\n*** failed.", stderr); |
241 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
242 | fputs("\np = ", stderr); mp_writefile(p.m, stderr, 10); |
243 | fputs("\nr = ", stderr); mp_writefile(r, stderr, 10); |
244 | fputc('\n', stderr); |
245 | ok = 0; |
246 | } |
247 | |
248 | mp_drop(m); |
249 | mp_drop(r); |
250 | pgen_destroy(&p); |
251 | return (ok); |
252 | } |
253 | |
254 | static test_chunk tests[] = { |
255 | { "pgen", verify, { &type_mp, &type_mp, 0 } }, |
256 | { 0, 0, { 0 } } |
257 | }; |
258 | |
259 | int main(int argc, char *argv[]) |
260 | { |
261 | sub_init(); |
262 | test_run(argc, argv, tests, SRCDIR "/tests/pgen"); |
263 | return (0); |
264 | } |
265 | |
266 | #endif |
267 | |
268 | /*----- That's all, folks -------------------------------------------------*/ |