| 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 | { |
| 248 | test_run(argc, argv, tests, SRCDIR "/tests/pgen"); |
| 249 | return (0); |
| 250 | } |
| 251 | |
| 252 | #endif |
| 253 | |
| 254 | /*----- That's all, folks -------------------------------------------------*/ |