File: integer.hpp

package info (click to toggle)
boost1.62 1.62.0+dfsg-10
  • links: PTS, VCS
  • area: main
  • in suites: sid
  • size: 687,152 kB
  • sloc: cpp: 2,613,639; xml: 972,558; ansic: 53,674; python: 32,448; sh: 9,305; asm: 3,071; cs: 2,121; makefile: 967; perl: 859; yacc: 472; php: 132; ruby: 94; f90: 55; sql: 13; csh: 6
file content (251 lines) | stat: -rw-r--r-- 6,852 bytes parent folder | download | duplicates (11)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
///////////////////////////////////////////////////////////////
//  Copyright 2012 John Maddock. Distributed under the Boost
//  Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_

#ifndef BOOST_MP_INTEGER_HPP
#define BOOST_MP_INTEGER_HPP

#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/detail/bitscan.hpp>

namespace boost{
namespace multiprecision{

template <class Integer, class I2>
typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
   multiply(Integer& result, const I2& a, const I2& b)
{
   return result = static_cast<Integer>(a) * static_cast<Integer>(b);
}
template <class Integer, class I2>
typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
   add(Integer& result, const I2& a, const I2& b)
{
   return result = static_cast<Integer>(a) + static_cast<Integer>(b);
}
template <class Integer, class I2>
typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
   subtract(Integer& result, const I2& a, const I2& b)
{
   return result = static_cast<Integer>(a) - static_cast<Integer>(b);
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value>::type divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r)
{
   q = x / y;
   r = x % y;
}

template <class I1, class I2>
typename enable_if_c<is_integral<I1>::value && is_integral<I2>::value, I2>::type integer_modulus(const I1& x, I2 val)
{
   return static_cast<I2>(x % val);
}

namespace detail{
//
// Figure out the kind of integer that has twice as many bits as some builtin
// integer type I.  Use a native type if we can (including types which may not
// be recognised by boost::int_t because they're larger than boost::long_long_type),
// otherwise synthesize a cpp_int to do the job.
//
template <class I>
struct double_integer
{
   static const unsigned int_t_digits =
      2 * sizeof(I) <= sizeof(boost::long_long_type) ? std::numeric_limits<I>::digits * 2 : 1;

   typedef typename mpl::if_c<
      2 * sizeof(I) <= sizeof(boost::long_long_type),
      typename mpl::if_c<
         is_signed<I>::value,
         typename boost::int_t<int_t_digits>::least,
         typename boost::uint_t<int_t_digits>::least
      >::type,
      typename mpl::if_c<
         2 * sizeof(I) <= sizeof(double_limb_type),
         typename mpl::if_c<
            is_signed<I>::value,
            signed_double_limb_type,
            double_limb_type
         >::type,
         number<cpp_int_backend<sizeof(I)*CHAR_BIT*2, sizeof(I)*CHAR_BIT*2, (is_signed<I>::value ? signed_magnitude : unsigned_magnitude), unchecked, void> >
      >::type
   >::type type;
};

}

template <class I1, class I2, class I3>
typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_integral<I3>::value, I1>::type
   powm(const I1& a, I2 b, I3 c)
{
   typedef typename detail::double_integer<I1>::type double_type;

   I1 x(1), y(a);
   double_type result;

   while(b > 0)
   {
      if(b & 1)
      {
         multiply(result, x, y);
         x = integer_modulus(result, c);
      }
      multiply(result, y, y);
      y = integer_modulus(result, c);
      b >>= 1;
   }
   return x % c;
}

template <class I1, class I2, class I3>
inline typename enable_if_c<is_integral<I1>::value && is_signed<I2>::value && is_integral<I3>::value, I1>::type
   powm(const I1& a, I2 b, I3 c)
{
   if(b < 0)
   {
      BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
   }
   return powm(a, static_cast<typename make_unsigned<I2>::type>(b), c);
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, unsigned>::type lsb(const Integer& val)
{
   if(val <= 0)
   {
      if(val == 0)
      {
         BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
      }
      else
      {
         BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
      }
   }
   return detail::find_lsb(val);
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, unsigned>::type msb(Integer val)
{
   if(val <= 0)
   {
      if(val == 0)
      {
         BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
      }
      else
      {
         BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
      }
   }
   return detail::find_msb(val);
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, bool>::type bit_test(const Integer& val, unsigned index)
{
   Integer mask = 1;
   if(index >= sizeof(Integer) * CHAR_BIT)
      return 0;
   if(index)
      mask <<= index;
   return val & mask ? true : false;
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_set(Integer& val, unsigned index)
{
   Integer mask = 1;
   if(index >= sizeof(Integer) * CHAR_BIT)
      return val;
   if(index)
      mask <<= index;
   val |= mask;
   return val;
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_unset(Integer& val, unsigned index)
{
   Integer mask = 1;
   if(index >= sizeof(Integer) * CHAR_BIT)
      return val;
   if(index)
      mask <<= index;
   val &= ~mask;
   return val;
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_flip(Integer& val, unsigned index)
{
   Integer mask = 1;
   if(index >= sizeof(Integer) * CHAR_BIT)
      return val;
   if(index)
      mask <<= index;
   val ^= mask;
   return val;
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x, Integer& r)
{
   //
   // This is slow bit-by-bit integer square root, see for example
   // http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29
   // There are better methods such as http://hal.inria.fr/docs/00/07/28/54/PDF/RR-3805.pdf
   // and http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf which should be implemented
   // at some point.
   //
   Integer s = 0;
   if(x == 0)
   {
      r = 0;
      return s;
   }
   int g = msb(x);
   if(g == 0)
   {
      r = 1;
      return s;
   }
   
   Integer t = 0;
   r = x;
   g /= 2;
   bit_set(s, g);
   bit_set(t, 2 * g);
   r = x - t;
   --g;
   do
   {
      t = s;
      t <<= g + 1;
      bit_set(t, 2 * g);
      if(t <= r)
      {
         bit_set(s, g);
         r -= t;
      }
      --g;
   }
   while(g >= 0);
   return s;
}

template <class Integer>
typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x)
{
   Integer r;
   return sqrt(x, r);
}

}} // namespaces

#endif