1 /* gen-trialdivtab.c
2
3 Contributed to the GNU project by Torbjorn Granlund.
4
5 Copyright 2009, 2012, 2013, 2016, 2018 Free Software Foundation, Inc.
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 /*
34 Generate tables for fast, division-free trial division for GMP.
35
36 There is one main table, ptab. It contains primes, multiplied together, and
37 several types of pre-computed inverses. It refers to tables of the type
38 dtab, via the last two indices. That table contains the individual primes in
39 the range, except that the primes are not actually included in the table (see
40 the P macro; it sneakingly excludes the primes themselves). Instead, the
41 dtab tables contains tuples for each prime (modular-inverse, limit) used for
42 divisibility checks.
43
44 This interface is not intended for division of very many primes, since then
45 other algorithms apply.
46 */
47
48 #include <stdlib.h>
49 #include <stdio.h>
50 #include "bootstrap.c"
51
52 int sumspills (mpz_t, mpz_t *, int);
53 void mpn_mod_1s_4p_cps (mpz_t [7], mpz_t);
54
55 int limb_bits;
56
57 mpz_t B;
58
59 int
main(int argc,char * argv[])60 main (int argc, char *argv[])
61 {
62 int t, p;
63 mpz_t ppp, acc, inv, gmp_numb_max, tmp, Bhalf;
64 mpz_t pre[7];
65 int i;
66 int start_p, end_p, interval_start, interval_end, omitted_p;
67 const char *endtok;
68 int stop;
69 int np, start_idx;
70
71 if (argc < 2)
72 {
73 fprintf (stderr, "usage: %s bits endprime\n", argv[0]);
74 exit (1);
75 }
76
77 limb_bits = atoi (argv[1]);
78
79 end_p = 1290; /* default end prime */
80 if (argc == 3)
81 end_p = atoi (argv[2]);
82
83 printf ("#if GMP_LIMB_BITS != %d\n", limb_bits);
84 printf ("#error This table is for GMP_LIMB_BITS = %d\n", limb_bits);
85 printf ("#endif\n\n");
86
87 printf ("#if GMP_NAIL_BITS != 0\n");
88 printf ("#error This table does not support nails\n");
89 printf ("#endif\n\n");
90
91 for (i = 0; i < 7; i++)
92 mpz_init (pre[i]);
93
94 mpz_init (B);
95 mpz_setbit (B, limb_bits);
96 mpz_init_set (gmp_numb_max, B);
97 mpz_sub_ui (gmp_numb_max, gmp_numb_max, 1);
98
99 mpz_init (tmp);
100 mpz_init (inv);
101
102 mpz_init (Bhalf);
103 mpz_setbit (Bhalf, limb_bits - 1);
104
105 start_p = 3;
106
107 mpz_init_set_ui (ppp, 1);
108 mpz_init (acc);
109 interval_start = start_p;
110 omitted_p = 3;
111 interval_end = 0;
112
113 /* printf ("static struct gmp_primes_dtab gmp_primes_dtab[] = {\n"); */
114
115 printf ("#ifdef WANT_dtab\n");
116
117 for (t = start_p; t <= end_p; t += 2)
118 {
119 if (! isprime (t))
120 continue;
121
122 mpz_mul_ui (acc, ppp, t);
123 stop = mpz_cmp (acc, Bhalf) >= 0;
124 if (!stop)
125 {
126 mpn_mod_1s_4p_cps (pre, acc);
127 stop = sumspills (acc, pre + 2, 5);
128 }
129
130 if (stop)
131 {
132 for (p = interval_start; p <= interval_end; p += 2)
133 {
134 if (! isprime (p))
135 continue;
136
137 printf (" P(%d,", (int) p);
138 mpz_invert_ui_2exp (inv, p, limb_bits);
139 printf ("CNST_LIMB(0x"); mpz_out_str (stdout, 16, inv); printf ("),");
140
141 mpz_tdiv_q_ui (tmp, gmp_numb_max, p);
142 printf ("CNST_LIMB(0x"); mpz_out_str (stdout, 16, tmp);
143 printf (")),\n");
144 }
145 mpz_set_ui (ppp, t);
146 interval_start = t;
147 omitted_p = t;
148 }
149 else
150 {
151 mpz_set (ppp, acc);
152 }
153 interval_end = t;
154 }
155 printf ("#define SMALLEST_OMITTED_PRIME %d\n", (int) omitted_p);
156 printf ("#endif\n");
157
158 printf ("#ifdef WANT_ptab\n");
159
160 /* printf ("static struct gmp_primes_ptab gmp_primes_ptab[] = {\n"); */
161
162 endtok = "";
163
164 mpz_set_ui (ppp, 1);
165 interval_start = start_p;
166 interval_end = 0;
167 np = 0;
168 start_idx = 0;
169 for (t = start_p; t <= end_p; t += 2)
170 {
171 if (! isprime (t))
172 continue;
173
174 mpz_mul_ui (acc, ppp, t);
175
176 stop = mpz_cmp (acc, Bhalf) >= 0;
177 if (!stop)
178 {
179 mpn_mod_1s_4p_cps (pre, acc);
180 stop = sumspills (acc, pre + 2, 5);
181 }
182
183 if (stop)
184 {
185 mpn_mod_1s_4p_cps (pre, ppp);
186 printf ("%s", endtok);
187 printf (" {CNST_LIMB(0x"); mpz_out_str (stdout, 16, ppp);
188 printf ("),{CNST_LIMB(0x"); mpz_out_str (stdout, 16, pre[0]);
189 printf ("),%d", (int) PTR(pre[1])[0]);
190 for (i = 0; i < 5; i++)
191 {
192 printf (",");
193 printf ("CNST_LIMB(0x"); mpz_out_str (stdout, 16, pre[2 + i]);
194 printf (")");
195 }
196 printf ("},");
197 printf ("%d,", start_idx);
198 printf ("%d}", np - start_idx);
199
200 endtok = ",\n";
201 mpz_set_ui (ppp, t);
202 interval_start = t;
203 start_idx = np;
204 }
205 else
206 {
207 mpz_set (ppp, acc);
208 }
209 interval_end = t;
210 np++;
211 }
212
213 printf ("\n");
214 printf ("#endif\n");
215
216 return 0;
217 }
218
219 unsigned long
mpz_log2(mpz_t x)220 mpz_log2 (mpz_t x)
221 {
222 return mpz_sgn (x) ? mpz_sizeinbase (x, 2) : 0;
223 }
224
225 void
mpn_mod_1s_4p_cps(mpz_t cps[7],mpz_t bparm)226 mpn_mod_1s_4p_cps (mpz_t cps[7], mpz_t bparm)
227 {
228 mpz_t b, bi;
229 mpz_t B1modb, B2modb, B3modb, B4modb, B5modb;
230 mpz_t t;
231 int cnt;
232
233 mpz_init_set (b, bparm);
234
235 cnt = limb_bits - mpz_log2 (b);
236
237 mpz_init (bi);
238 mpz_init (t);
239 mpz_init (B1modb);
240 mpz_init (B2modb);
241 mpz_init (B3modb);
242 mpz_init (B4modb);
243 mpz_init (B5modb);
244
245 mpz_set_ui (t, 1);
246 mpz_mul_2exp (t, t, limb_bits - cnt);
247 mpz_sub (t, t, b);
248 mpz_mul_2exp (t, t, limb_bits);
249 mpz_tdiv_q (bi, t, b); /* bi = B^2/b, except msb */
250
251 mpz_set_ui (t, 1);
252 mpz_mul_2exp (t, t, limb_bits); /* t = B */
253 mpz_tdiv_r (B1modb, t, b);
254
255 mpz_mul_2exp (t, B1modb, limb_bits);
256 mpz_tdiv_r (B2modb, t, b);
257
258 mpz_mul_2exp (t, B2modb, limb_bits);
259 mpz_tdiv_r (B3modb, t, b);
260
261 mpz_mul_2exp (t, B3modb, limb_bits);
262 mpz_tdiv_r (B4modb, t, b);
263
264 mpz_mul_2exp (t, B4modb, limb_bits);
265 mpz_tdiv_r (B5modb, t, b);
266
267 mpz_set (cps[0], bi);
268 mpz_set_ui (cps[1], cnt);
269 mpz_tdiv_q_2exp (cps[2], B1modb, 0);
270 mpz_tdiv_q_2exp (cps[3], B2modb, 0);
271 mpz_tdiv_q_2exp (cps[4], B3modb, 0);
272 mpz_tdiv_q_2exp (cps[5], B4modb, 0);
273 mpz_tdiv_q_2exp (cps[6], B5modb, 0);
274
275 mpz_clear (b);
276 mpz_clear (bi);
277 mpz_clear (t);
278 mpz_clear (B1modb);
279 mpz_clear (B2modb);
280 mpz_clear (B3modb);
281 mpz_clear (B4modb);
282 mpz_clear (B5modb);
283 }
284
285 int
sumspills(mpz_t ppp,mpz_t * a,int n)286 sumspills (mpz_t ppp, mpz_t *a, int n)
287 {
288 mpz_t s;
289 int i, ret;
290
291 mpz_init_set (s, a[0]);
292
293 for (i = 1; i < n; i++)
294 {
295 mpz_add (s, s, a[i]);
296 }
297 ret = mpz_cmp (s, B) >= 0;
298 mpz_clear (s);
299
300 return ret;
301 }
302