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_INTEGER_HPP |
7 | #define BOOST_MP_INTEGER_HPP |
8 | |
9 | #include <boost/multiprecision/cpp_int.hpp> |
10 | #include <boost/multiprecision/detail/bitscan.hpp> |
11 | |
12 | namespace boost{ |
13 | namespace multiprecision{ |
14 | |
15 | template <class Integer, class I2> |
16 | typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type |
17 | multiply(Integer& result, const I2& a, const I2& b) |
18 | { |
19 | return result = static_cast<Integer>(a) * static_cast<Integer>(b); |
20 | } |
21 | template <class Integer, class I2> |
22 | typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type |
23 | add(Integer& result, const I2& a, const I2& b) |
24 | { |
25 | return result = static_cast<Integer>(a) + static_cast<Integer>(b); |
26 | } |
27 | template <class Integer, class I2> |
28 | typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type |
29 | subtract(Integer& result, const I2& a, const I2& b) |
30 | { |
31 | return result = static_cast<Integer>(a) - static_cast<Integer>(b); |
32 | } |
33 | |
34 | template <class Integer> |
35 | typename enable_if_c<is_integral<Integer>::value>::type divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r) |
36 | { |
37 | q = x / y; |
38 | r = x % y; |
39 | } |
40 | |
41 | template <class I1, class I2> |
42 | typename enable_if_c<is_integral<I1>::value && is_integral<I2>::value, I2>::type integer_modulus(const I1& x, I2 val) |
43 | { |
44 | return static_cast<I2>(x % val); |
45 | } |
46 | |
47 | namespace detail{ |
48 | // |
49 | // Figure out the kind of integer that has twice as many bits as some builtin |
50 | // integer type I. Use a native type if we can (including types which may not |
51 | // be recognised by boost::int_t because they're larger than boost::long_long_type), |
52 | // otherwise synthesize a cpp_int to do the job. |
53 | // |
54 | template <class I> |
55 | struct double_integer |
56 | { |
57 | static const unsigned int_t_digits = |
58 | 2 * sizeof(I) <= sizeof(boost::long_long_type) ? std::numeric_limits<I>::digits * 2 : 1; |
59 | |
60 | typedef typename mpl::if_c< |
61 | 2 * sizeof(I) <= sizeof(boost::long_long_type), |
62 | typename mpl::if_c< |
63 | is_signed<I>::value, |
64 | typename boost::int_t<int_t_digits>::least, |
65 | typename boost::uint_t<int_t_digits>::least |
66 | >::type, |
67 | typename mpl::if_c< |
68 | 2 * sizeof(I) <= sizeof(double_limb_type), |
69 | typename mpl::if_c< |
70 | is_signed<I>::value, |
71 | signed_double_limb_type, |
72 | double_limb_type |
73 | >::type, |
74 | number<cpp_int_backend<sizeof(I)*CHAR_BIT*2, sizeof(I)*CHAR_BIT*2, (is_signed<I>::value ? signed_magnitude : unsigned_magnitude), unchecked, void> > |
75 | >::type |
76 | >::type type; |
77 | }; |
78 | |
79 | } |
80 | |
81 | template <class I1, class I2, class I3> |
82 | typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_integral<I3>::value, I1>::type |
83 | powm(const I1& a, I2 b, I3 c) |
84 | { |
85 | typedef typename detail::double_integer<I1>::type double_type; |
86 | |
87 | I1 x(1), y(a); |
88 | double_type result; |
89 | |
90 | while(b > 0) |
91 | { |
92 | if(b & 1) |
93 | { |
94 | multiply(result, x, y); |
95 | x = integer_modulus(result, c); |
96 | } |
97 | multiply(result, y, y); |
98 | y = integer_modulus(result, c); |
99 | b >>= 1; |
100 | } |
101 | return x % c; |
102 | } |
103 | |
104 | template <class I1, class I2, class I3> |
105 | inline typename enable_if_c<is_integral<I1>::value && is_signed<I2>::value && is_integral<I3>::value, I1>::type |
106 | powm(const I1& a, I2 b, I3 c) |
107 | { |
108 | if(b < 0) |
109 | { |
110 | BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent." )); |
111 | } |
112 | return powm(a, static_cast<typename make_unsigned<I2>::type>(b), c); |
113 | } |
114 | |
115 | template <class Integer> |
116 | typename enable_if_c<is_integral<Integer>::value, unsigned>::type lsb(const Integer& val) |
117 | { |
118 | if(val <= 0) |
119 | { |
120 | if(val == 0) |
121 | { |
122 | BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand." )); |
123 | } |
124 | else |
125 | { |
126 | BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined." )); |
127 | } |
128 | } |
129 | return detail::find_lsb(val); |
130 | } |
131 | |
132 | template <class Integer> |
133 | typename enable_if_c<is_integral<Integer>::value, unsigned>::type msb(Integer val) |
134 | { |
135 | if(val <= 0) |
136 | { |
137 | if(val == 0) |
138 | { |
139 | BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand." )); |
140 | } |
141 | else |
142 | { |
143 | BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined." )); |
144 | } |
145 | } |
146 | return detail::find_msb(val); |
147 | } |
148 | |
149 | template <class Integer> |
150 | typename enable_if_c<is_integral<Integer>::value, bool>::type bit_test(const Integer& val, unsigned index) |
151 | { |
152 | Integer mask = 1; |
153 | if(index >= sizeof(Integer) * CHAR_BIT) |
154 | return 0; |
155 | if(index) |
156 | mask <<= index; |
157 | return val & mask ? true : false; |
158 | } |
159 | |
160 | template <class Integer> |
161 | typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_set(Integer& val, unsigned index) |
162 | { |
163 | Integer mask = 1; |
164 | if(index >= sizeof(Integer) * CHAR_BIT) |
165 | return val; |
166 | if(index) |
167 | mask <<= index; |
168 | val |= mask; |
169 | return val; |
170 | } |
171 | |
172 | template <class Integer> |
173 | typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_unset(Integer& val, unsigned index) |
174 | { |
175 | Integer mask = 1; |
176 | if(index >= sizeof(Integer) * CHAR_BIT) |
177 | return val; |
178 | if(index) |
179 | mask <<= index; |
180 | val &= ~mask; |
181 | return val; |
182 | } |
183 | |
184 | template <class Integer> |
185 | typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_flip(Integer& val, unsigned index) |
186 | { |
187 | Integer mask = 1; |
188 | if(index >= sizeof(Integer) * CHAR_BIT) |
189 | return val; |
190 | if(index) |
191 | mask <<= index; |
192 | val ^= mask; |
193 | return val; |
194 | } |
195 | |
196 | template <class Integer> |
197 | typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x, Integer& r) |
198 | { |
199 | // |
200 | // This is slow bit-by-bit integer square root, see for example |
201 | // http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29 |
202 | // There are better methods such as http://hal.inria.fr/docs/00/07/28/54/PDF/RR-3805.pdf |
203 | // and http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf which should be implemented |
204 | // at some point. |
205 | // |
206 | Integer s = 0; |
207 | if(x == 0) |
208 | { |
209 | r = 0; |
210 | return s; |
211 | } |
212 | int g = msb(x); |
213 | if(g == 0) |
214 | { |
215 | r = 1; |
216 | return s; |
217 | } |
218 | |
219 | Integer t = 0; |
220 | r = x; |
221 | g /= 2; |
222 | bit_set(s, g); |
223 | bit_set(t, 2 * g); |
224 | r = x - t; |
225 | --g; |
226 | do |
227 | { |
228 | t = s; |
229 | t <<= g + 1; |
230 | bit_set(t, 2 * g); |
231 | if(t <= r) |
232 | { |
233 | bit_set(s, g); |
234 | r -= t; |
235 | } |
236 | --g; |
237 | } |
238 | while(g >= 0); |
239 | return s; |
240 | } |
241 | |
242 | template <class Integer> |
243 | typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x) |
244 | { |
245 | Integer r; |
246 | return sqrt(x, r); |
247 | } |
248 | |
249 | }} // namespaces |
250 | |
251 | #endif |
252 | |