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/*
Name: iprime.c
Purpose: Pseudoprimality testing routines
Author: M. J. Fromberger <http://www.dartmouth.edu/~sting/>
Info: $Id: iprime.c 19737 2007-01-05 21:01:48Z lha $
Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved.
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation files
(the "Software"), to deal in the Software without restriction,
including without limitation the rights to use, copy, modify, merge,
publish, distribute, sublicense, and/or sell copies of the Software,
and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#include "iprime.h"
#include <stdlib.h>
static const int s_ptab[] = {
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
4957, 4967, 4969, 4973, 4987, 4993, 4999
};
static const int s_ptab_size = sizeof(s_ptab)/sizeof(s_ptab[0]);
/* {{{ mp_int_is_prime(z) */
/* Test whether z is likely to be prime:
MP_TRUE means it is probably prime
MP_FALSE means it is definitely composite
*/
mp_result mp_int_is_prime(mp_int z)
{
int i, rem;
mp_result res;
/* First check for divisibility by small primes; this eliminates a
large number of composite candidates quickly
*/
for(i = 0; i < s_ptab_size; ++i) {
if((res = mp_int_div_value(z, s_ptab[i], NULL, &rem)) != MP_OK)
return res;
if(rem == 0)
return MP_FALSE;
}
/* Now try Fermat's test for several prime witnesses (since we now
know from the above that z is not a multiple of any of them)
*/
{
mpz_t tmp;
if((res = mp_int_init(&tmp)) != MP_OK) return res;
for(i = 0; i < 10 && i < s_ptab_size; ++i) {
if((res = mp_int_exptmod_bvalue(s_ptab[i], z, z, &tmp)) != MP_OK)
return res;
if(mp_int_compare_value(&tmp, s_ptab[i]) != 0) {
mp_int_clear(&tmp);
return MP_FALSE;
}
}
mp_int_clear(&tmp);
}
return MP_TRUE;
}
/* }}} */
/* {{{ mp_int_find_prime(z) */
/* Find the first apparent prime in ascending order from z */
mp_result mp_int_find_prime(mp_int z)
{
mp_result res;
if(mp_int_is_even(z) && ((res = mp_int_add_value(z, 1, z)) != MP_OK))
return res;
while((res = mp_int_is_prime(z)) == MP_FALSE) {
if((res = mp_int_add_value(z, 2, z)) != MP_OK)
break;
}
return res;
}
/* }}} */
/* Here there be dragons */
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