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DEFINITIONS
This source file includes following definitions.
- mp_int_is_prime
- mp_int_find_prime
1 /*
2 Name: iprime.c
3 Purpose: Pseudoprimality testing routines
4 Author: M. J. Fromberger <http://spinning-yarns.org/michael/>
5 Info: $Id: iprime.c 635 2008-01-08 18:19:40Z sting $
6
7 Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved.
8
9 Permission is hereby granted, free of charge, to any person
10 obtaining a copy of this software and associated documentation files
11 (the "Software"), to deal in the Software without restriction,
12 including without limitation the rights to use, copy, modify, merge,
13 publish, distribute, sublicense, and/or sell copies of the Software,
14 and to permit persons to whom the Software is furnished to do so,
15 subject to the following conditions:
16
17 The above copyright notice and this permission notice shall be
18 included in all copies or substantial portions of the Software.
19
20 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
21 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
22 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
23 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
24 BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
25 ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
26 CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
27 SOFTWARE.
28 */
29
30 #include "iprime.h"
31 #include <stdlib.h>
32
33 static const int s_ptab[] = {
34 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
35 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
36 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
37 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
38 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
39 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
40 331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
41 389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
42 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
43 509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
44 587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
45 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
46 709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
47 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
48 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
49 919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
50 991, 997
51 #ifdef IMATH_LARGE_PRIME_TABLE
52 , 1009, 1013, 1019, 1021, 1031, 1033,
53 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
54 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
55 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
56 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
57 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
58 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
59 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
60 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
61 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
62 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
63 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
64 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
65 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
66 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
67 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
68 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
69 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
70 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
71 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
72 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
73 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
74 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
75 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
76 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
77 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
78 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
79 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
80 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
81 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
82 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
83 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
84 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
85 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
86 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
87 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
88 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
89 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
90 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
91 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
92 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
93 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
94 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
95 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
96 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
97 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
98 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
99 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
100 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
101 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
102 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
103 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
104 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
105 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
106 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
107 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
108 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
109 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
110 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
111 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
112 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
113 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
114 4957, 4967, 4969, 4973, 4987, 4993, 4999
115 #endif
116 };
117 static const int s_ptab_size = sizeof(s_ptab)/sizeof(s_ptab[0]);
118
119 /* {{{ mp_int_is_prime(z) */
120
121 /* Test whether z is likely to be prime:
122 MP_TRUE means it is probably prime
123 MP_FALSE means it is definitely composite
124 */
125 mp_result mp_int_is_prime(mp_int z)
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126 {
127 int i;
128 mp_small rem;
129 mp_result res;
130
131 /* First check for divisibility by small primes; this eliminates a
132 large number of composite candidates quickly
133 */
134 for(i = 0; i < s_ptab_size; ++i) {
135 if((res = mp_int_div_value(z, s_ptab[i], NULL, &rem)) != MP_OK)
136 return res;
137
138 if(rem == 0)
139 return MP_FALSE;
140 }
141
142 /* Now try Fermat's test for several prime witnesses (since we now
143 know from the above that z is not a multiple of any of them)
144 */
145 {
146 mpz_t tmp;
147
148 if((res = mp_int_init(&tmp)) != MP_OK) return res;
149
150 for(i = 0; i < 10 && i < s_ptab_size; ++i) {
151 if((res = mp_int_exptmod_bvalue(s_ptab[i], z, z, &tmp)) != MP_OK)
152 return res;
153
154 if(mp_int_compare_value(&tmp, s_ptab[i]) != 0) {
155 mp_int_clear(&tmp);
156 return MP_FALSE;
157 }
158 }
159
160 mp_int_clear(&tmp);
161 }
162
163 return MP_TRUE;
164 }
165
166 /* }}} */
167
168 /* {{{ mp_int_find_prime(z) */
169
170 /* Find the first apparent prime in ascending order from z */
171 mp_result mp_int_find_prime(mp_int z)
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172 {
173 mp_result res;
174
175 if(mp_int_is_even(z) && ((res = mp_int_add_value(z, 1, z)) != MP_OK))
176 return res;
177
178 while((res = mp_int_is_prime(z)) == MP_FALSE) {
179 if((res = mp_int_add_value(z, 2, z)) != MP_OK)
180 break;
181
182 }
183
184 return res;
185 }
186
187 /* }}} */
188
189 /* Here there be dragons */