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1d6d3b01 MW |
1 | /* -*-c-*- |
2 | * | |
3 | * Iterate over small primes efficiently | |
4 | * | |
5 | * (c) 2007 Straylight/Edgeware | |
6 | */ | |
7 | ||
8 | /*----- Licensing notice --------------------------------------------------* | |
9 | * | |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
16 | * | |
17 | * Catacomb is distributed in the hope that it will be useful, | |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
21 | * | |
22 | * You should have received a copy of the GNU Library General Public | |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
28 | /*----- Header files ------------------------------------------------------*/ | |
29 | ||
30 | #include "fibrand.h" | |
31 | #include "mp.h" | |
32 | #include "pgen.h" | |
33 | #include "primeiter.h" | |
34 | #include "primetab.h" | |
35 | #include "wheel.h" | |
36 | ||
37 | /*----- Theory ------------------------------------------------------------* | |
38 | * | |
39 | * For small primes, we can just pluck them out of the small primes table. | |
40 | * For larger primes, we can test them individually, or build a sieve or | |
41 | * something, but since we don't know when to stop, that could be tricky. | |
42 | * | |
43 | * We've built a `wheel', as follows. Let %$m$% be the product of the first | |
44 | * %$n$% primes. There are %$\phi(m)$% integers %$n_i$%, with %$0 < n_i < | |
45 | * m$% coprime to %$m$%, and any integer %$j > n$% must be congruent to some | |
46 | * %$n_i$% modulo %$m$%. The wheel itself doesn't list the %$n_i$%, but | |
47 | * rather the differences %$\delta_i = n_i - n_{i-1}$% (wrapping around | |
48 | * appropriately at the ends), so you can just add simple offsets to step | |
49 | * onwards. The wheel assumes you start at 1 and move on round. | |
50 | */ | |
51 | ||
52 | /*----- Main code ---------------------------------------------------------*/ | |
53 | ||
54 | /* --- @wheelsync@ --- * | |
55 | * | |
56 | * Arguments: @primeiter *pi@ = iterator to synchronize | |
57 | * @mp *where@ = value to synchronize | |
58 | * | |
59 | * Returns: --- | |
60 | * | |
61 | * Use: Sets up the wheel index to match the given integer. After | |
62 | * this, we can step along the wheel to find candidate primes. | |
63 | */ | |
64 | ||
65 | static void wheelsync(primeiter *pi, mp *where) | |
66 | { | |
67 | mpw w; | |
68 | mp t; | |
69 | mpw rr; | |
70 | mp *r = MP_NEW; | |
71 | unsigned i, n; | |
72 | ||
73 | w = WHEELMOD; | |
74 | mp_build(&t, &w, &w + 1); | |
75 | mp_div(0, &r, where, &t); | |
76 | rr = MP_ZEROP(r) ? 0 : r->v[0]; | |
77 | ||
78 | for (i = 0, n = 1; rr > n; n += wheel[i], i++); | |
79 | w = n - rr; | |
80 | pi->p = mp_add(MP_NEW, where, &t); | |
81 | pi->i = i; | |
82 | pi->r = fibrand_create(0); | |
83 | MP_DROP(r); | |
84 | } | |
85 | ||
86 | /* --- @primeiter_create@ --- * | |
87 | * | |
88 | * Arguments: @primeiter *pi@ = pointer to an iterator structure | |
89 | * @mp *start@ = where to start | |
90 | * | |
91 | * Returns: --- | |
92 | * | |
93 | * Use: Initializes a prime iterator. The first output will be the | |
94 | * smallest prime not less than @start@. | |
95 | */ | |
96 | ||
97 | void primeiter_create(primeiter *pi, mp *start) | |
98 | { | |
99 | mpw n; | |
100 | unsigned l, h, m; | |
101 | ||
102 | if (!start || MP_CMP(start, <=, MP_TWO)) | |
103 | start = MP_TWO; | |
104 | ||
105 | if (MP_LEN(start) <= 1) { | |
106 | n = start->v[0]; | |
107 | if (n <= MAXPRIME) { | |
108 | l = 0; | |
109 | h = NPRIME; | |
110 | for (;;) { | |
111 | m = l + (h - l)/2; | |
112 | if (primetab[m] == n) break; | |
113 | else if (m == l) { m++; break; } | |
114 | else if (primetab[m] < n) l = m; | |
115 | else h = m; | |
116 | } | |
117 | pi->i = m; | |
118 | pi->mode = PIMODE_PTAB; | |
119 | mp_build(&pi->pp, &pi->w, &pi->w + 1); | |
120 | pi->p = &pi->pp; | |
121 | return; | |
122 | } | |
123 | } | |
124 | ||
125 | wheelsync(pi, start); | |
126 | pi->mode = PIMODE_STALL; | |
127 | } | |
128 | ||
129 | /* --- @primeiter_destroy@ --- * | |
130 | * | |
131 | * Arguments: @primeiter *pi@ = pointer to iterator structure | |
132 | * | |
133 | * Returns: --- | |
134 | * | |
135 | * Use: Frees up an iterator structure when it's no longer wanted. | |
136 | */ | |
137 | ||
138 | void primeiter_destroy(primeiter *pi) | |
139 | { | |
140 | switch (pi->mode) { | |
141 | case PIMODE_PTAB: | |
142 | break; | |
143 | case PIMODE_STALL: | |
144 | case PIMODE_WHEEL: | |
145 | MP_DROP(pi->p); | |
146 | GR_DESTROY(pi->r); | |
147 | break; | |
148 | default: | |
149 | abort(); | |
150 | } | |
151 | } | |
152 | ||
153 | /* --- @primeiter_next@ --- * | |
154 | * | |
155 | * Arguments: @primeiter *pi@ = pointer to an iterator structure | |
156 | * @mp *d@ = fake destination | |
157 | * | |
158 | * Returns: The next prime number from the iterator. | |
159 | * | |
160 | * Use: Returns a new prime number. | |
161 | */ | |
162 | ||
163 | mp *primeiter_next(primeiter *pi, mp *d) | |
164 | { | |
165 | mp *p; | |
166 | ||
167 | switch (pi->mode) { | |
168 | case PIMODE_PTAB: | |
169 | pi->w = primetab[pi->i++]; | |
170 | if (pi->i >= NPRIME) { | |
171 | wheelsync(pi, pi->p); | |
172 | pi->mode = PIMODE_WHEEL; | |
173 | } | |
174 | p = MP_COPY(pi->p); | |
175 | MP_SPLIT(p); | |
176 | break; | |
177 | case PIMODE_STALL: | |
178 | pi->mode = PIMODE_WHEEL; | |
179 | goto loop; | |
180 | case PIMODE_WHEEL: | |
181 | do { | |
182 | MP_DEST(pi->p, MP_LEN(pi->p) + 1, pi->p->f); | |
183 | MPX_UADDN(pi->p->v, pi->p->vl, wheel[pi->i++]); | |
184 | MP_SHRINK(pi->p); | |
185 | if (pi->i >= WHEELN) pi->i = 0; | |
186 | loop:; | |
187 | } while (!pgen_primep(pi->p, pi->r)); | |
188 | p = MP_COPY(pi->p); | |
189 | break; | |
190 | default: | |
191 | abort(); | |
192 | } | |
193 | if (d) MP_DROP(d); | |
194 | return (p); | |
195 | } | |
196 | ||
197 | /*----- Test rig ----------------------------------------------------------*/ | |
198 | ||
199 | #ifdef TEST_RIG | |
200 | ||
201 | #include <mLib/macros.h> | |
202 | #include <mLib/testrig.h> | |
203 | ||
204 | static int test(dstr *v) | |
205 | { | |
206 | mp *start = *(mp **)v[0].buf; | |
207 | mp *pp[5], *ret[5]; | |
208 | int i; | |
209 | primeiter pi; | |
210 | int ok = 1; | |
211 | ||
212 | for (i = 0; i < N(pp); i++) | |
213 | pp[i] = *(mp **)v[i + 1].buf; | |
214 | primeiter_create(&pi, start); | |
215 | for (i = 0; i < N(pp); i++) { | |
216 | ret[i] = primeiter_next(&pi, MP_NEW); | |
217 | if (!MP_EQ(ret[i], pp[i])) ok = 0; | |
218 | } | |
219 | if (!ok) { | |
220 | fprintf(stderr, "\n*** primeiter test failure:\n*** start = "); | |
221 | mp_writefile(start, stderr, 10); | |
222 | for (i = 0; i < N(pp); i++) { | |
223 | fprintf(stderr, "\n*** p[%d] = ", i); | |
224 | mp_writefile(ret[i], stderr, 10); | |
225 | fprintf(stderr, " %s ", MP_EQ(ret[i], pp[i]) ? "==" : "!="); | |
226 | mp_writefile(pp[i], stderr, 10); | |
227 | } | |
228 | fputc('\n', stderr); | |
229 | } | |
230 | for (i = 0; i < N(pp); i++) { | |
231 | MP_DROP(pp[i]); | |
232 | MP_DROP(ret[i]); | |
233 | } | |
234 | primeiter_destroy(&pi); | |
235 | MP_DROP(start); | |
236 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
237 | return (ok); | |
238 | } | |
239 | ||
240 | static test_chunk tests[] = { | |
241 | { "primeiter", test, | |
242 | { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, } }, | |
243 | { 0 } | |
244 | }; | |
245 | ||
246 | int main(int argc, char *argv[]) | |
247 | { | |
0f00dc4c | 248 | test_run(argc, argv, tests, SRCDIR "/t/pgen"); |
1d6d3b01 MW |
249 | return (0); |
250 | } | |
251 | ||
252 | #endif | |
253 | ||
254 | /*----- That's all, folks -------------------------------------------------*/ |