1 | /////////////////////////////////////////////////////////////// |
2 | // Copyright 2012 John Maddock. Distributed under the Boost |
3 | // Software License, Version 1.0. (See accompanying file |
4 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ |
5 | |
6 | #ifndef BOOST_MP_MR_HPP |
7 | #define BOOST_MP_MR_HPP |
8 | |
9 | #include <boost/multiprecision/random.hpp> |
10 | #include <boost/multiprecision/integer.hpp> |
11 | |
12 | namespace boost{ |
13 | namespace multiprecision{ |
14 | namespace detail{ |
15 | |
16 | template <class I> |
17 | bool check_small_factors(const I& n) |
18 | { |
19 | static const boost::uint32_t small_factors1[] = { |
20 | 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u }; |
21 | static const boost::uint32_t pp1 = 223092870u; |
22 | |
23 | boost::uint32_t m1 = integer_modulus(n, pp1); |
24 | |
25 | for(unsigned i = 0; i < sizeof(small_factors1) / sizeof(small_factors1[0]); ++i) |
26 | { |
27 | BOOST_ASSERT(pp1 % small_factors1[i] == 0); |
28 | if(m1 % small_factors1[i] == 0) |
29 | return false; |
30 | } |
31 | |
32 | static const boost::uint32_t small_factors2[] = { |
33 | 29u, 31u, 37u, 41u, 43u, 47u }; |
34 | static const boost::uint32_t pp2 = 2756205443u; |
35 | |
36 | m1 = integer_modulus(n, pp2); |
37 | |
38 | for(unsigned i = 0; i < sizeof(small_factors2) / sizeof(small_factors2[0]); ++i) |
39 | { |
40 | BOOST_ASSERT(pp2 % small_factors2[i] == 0); |
41 | if(m1 % small_factors2[i] == 0) |
42 | return false; |
43 | } |
44 | |
45 | static const boost::uint32_t small_factors3[] = { |
46 | 53u, 59u, 61u, 67u, 71u }; |
47 | static const boost::uint32_t pp3 = 907383479u; |
48 | |
49 | m1 = integer_modulus(n, pp3); |
50 | |
51 | for(unsigned i = 0; i < sizeof(small_factors3) / sizeof(small_factors3[0]); ++i) |
52 | { |
53 | BOOST_ASSERT(pp3 % small_factors3[i] == 0); |
54 | if(m1 % small_factors3[i] == 0) |
55 | return false; |
56 | } |
57 | |
58 | static const boost::uint32_t small_factors4[] = { |
59 | 73u, 79u, 83u, 89u, 97u }; |
60 | static const boost::uint32_t pp4 = 4132280413u; |
61 | |
62 | m1 = integer_modulus(n, pp4); |
63 | |
64 | for(unsigned i = 0; i < sizeof(small_factors4) / sizeof(small_factors4[0]); ++i) |
65 | { |
66 | BOOST_ASSERT(pp4 % small_factors4[i] == 0); |
67 | if(m1 % small_factors4[i] == 0) |
68 | return false; |
69 | } |
70 | |
71 | static const boost::uint32_t small_factors5[6][4] = { |
72 | { 101u, 103u, 107u, 109u }, |
73 | { 113u, 127u, 131u, 137u }, |
74 | { 139u, 149u, 151u, 157u }, |
75 | { 163u, 167u, 173u, 179u }, |
76 | { 181u, 191u, 193u, 197u }, |
77 | { 199u, 211u, 223u, 227u } |
78 | }; |
79 | static const boost::uint32_t pp5[6] = |
80 | { |
81 | 121330189u, |
82 | 113u * 127u * 131u * 137u, |
83 | 139u * 149u * 151u * 157u, |
84 | 163u * 167u * 173u * 179u, |
85 | 181u * 191u * 193u * 197u, |
86 | 199u * 211u * 223u * 227u |
87 | }; |
88 | |
89 | for(unsigned k = 0; k < sizeof(pp5) / sizeof(*pp5); ++k) |
90 | { |
91 | m1 = integer_modulus(n, pp5[k]); |
92 | |
93 | for(unsigned i = 0; i < 4; ++i) |
94 | { |
95 | BOOST_ASSERT(pp5[k] % small_factors5[k][i] == 0); |
96 | if(m1 % small_factors5[k][i] == 0) |
97 | return false; |
98 | } |
99 | } |
100 | return true; |
101 | } |
102 | |
103 | inline bool is_small_prime(unsigned n) |
104 | { |
105 | static const unsigned char p[] = |
106 | { |
107 | 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u, |
108 | 37u, 41u, 43u, 47u, 53u, 59u, 61u, 67u, 71u, 73u, |
109 | 79u, 83u, 89u, 97u, 101u, 103u, 107u, 109u, 113u, |
110 | 127u, 131u, 137u, 139u, 149u, 151u, 157u, 163u, |
111 | 167u, 173u, 179u, 181u, 191u, 193u, 197u, 199u, |
112 | 211u, 223u, 227u |
113 | }; |
114 | for(unsigned i = 0; i < sizeof(p) / sizeof(*p); ++i) |
115 | { |
116 | if(n == p[i]) |
117 | return true; |
118 | } |
119 | return false; |
120 | } |
121 | |
122 | template <class I> |
123 | typename enable_if_c<is_convertible<I, unsigned>::value, unsigned>::type |
124 | cast_to_unsigned(const I& val) |
125 | { |
126 | return static_cast<unsigned>(val); |
127 | } |
128 | template <class I> |
129 | typename disable_if_c<is_convertible<I, unsigned>::value, unsigned>::type |
130 | cast_to_unsigned(const I& val) |
131 | { |
132 | return val.template convert_to<unsigned>(); |
133 | } |
134 | |
135 | } // namespace detail |
136 | |
137 | template <class I, class Engine> |
138 | typename enable_if_c<number_category<I>::value == number_kind_integer, bool>::type |
139 | miller_rabin_test(const I& n, unsigned trials, Engine& gen) |
140 | { |
141 | #ifdef BOOST_MSVC |
142 | #pragma warning(push) |
143 | #pragma warning(disable:4127) |
144 | #endif |
145 | typedef I number_type; |
146 | |
147 | if (n == 2) |
148 | return true; // Trivial special case. |
149 | if(bit_test(n, 0) == 0) |
150 | return false; // n is even |
151 | if(n <= 227) |
152 | return detail::is_small_prime(n: detail::cast_to_unsigned(n)); |
153 | |
154 | if(!detail::check_small_factors(n)) |
155 | return false; |
156 | |
157 | number_type nm1 = n - 1; |
158 | // |
159 | // Begin with a single Fermat test - it excludes a lot of candidates: |
160 | // |
161 | number_type q(228), x, y; // We know n is greater than this, as we've excluded small factors |
162 | x = powm(q, nm1, n); |
163 | if(x != 1u) |
164 | return false; |
165 | |
166 | q = n - 1; |
167 | unsigned k = lsb(q); |
168 | q >>= k; |
169 | |
170 | // Declare our random number generator: |
171 | boost::random::uniform_int_distribution<number_type> dist(2, n - 2); |
172 | // |
173 | // Execute the trials: |
174 | // |
175 | for(unsigned i = 0; i < trials; ++i) |
176 | { |
177 | x = dist(gen); |
178 | y = powm(x, q, n); |
179 | unsigned j = 0; |
180 | while(true) |
181 | { |
182 | if(y == nm1) |
183 | break; |
184 | if(y == 1) |
185 | { |
186 | if(j == 0) |
187 | break; |
188 | return false; // test failed |
189 | } |
190 | if(++j == k) |
191 | return false; // failed |
192 | y = powm(y, 2, n); |
193 | } |
194 | } |
195 | return true; // Yeheh! probably prime. |
196 | #ifdef BOOST_MSVC |
197 | #pragma warning(pop) |
198 | #endif |
199 | } |
200 | |
201 | template <class I> |
202 | typename enable_if_c<number_category<I>::value == number_kind_integer, bool>::type |
203 | miller_rabin_test(const I& x, unsigned trials) |
204 | { |
205 | static mt19937 gen; |
206 | return miller_rabin_test(x, trials, gen); |
207 | } |
208 | |
209 | template <class tag, class Arg1, class Arg2, class Arg3, class Arg4, class Engine> |
210 | bool miller_rabin_test(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4> & n, unsigned trials, Engine& gen) |
211 | { |
212 | typedef typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type number_type; |
213 | return miller_rabin_test(number_type(n), trials, gen); |
214 | } |
215 | |
216 | template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> |
217 | bool miller_rabin_test(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4> & n, unsigned trials) |
218 | { |
219 | typedef typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type number_type; |
220 | return miller_rabin_test(number_type(n), trials); |
221 | } |
222 | |
223 | }} // namespaces |
224 | |
225 | #endif |
226 | |
227 | |