libstdc++-v3/include/bits/random.tcc

   1 // random number generation (out of line) -*- C++ -*-
   2
   3 // Copyright (C) 2009-2017 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15
  16 // Under Section 7 of GPL version 3, you are granted additional
  17 // permissions described in the GCC Runtime Library Exception, version
  18 // 3.1, as published by the Free Software Foundation.
  19
  20 // You should have received a copy of the GNU General Public License and
  21 // a copy of the GCC Runtime Library Exception along with this program;
  22 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  23 // <http://www.gnu.org/licenses/>.
  24
  25 /** @file bits/random.tcc
  26  *  This is an internal header file, included by other library headers.
  27  *  Do not attempt to use it directly. @headername{random}
  28  */
  29
  30 #ifndef _RANDOM_TCC
  31 #define _RANDOM_TCC 1
  32
  33 #include <numeric> // std::accumulate and std::partial_sum
  34
  35 namespace std _GLIBCXX_VISIBILITY(default)
  36 {
  37   /*
  38    * (Further) implementation-space details.
  39    */
  40   namespace __detail
  41   {
  42   _GLIBCXX_BEGIN_NAMESPACE_VERSION
  43
  44     // General case for x = (ax + c) mod m -- use Schrage's algorithm
  45     // to avoid integer overflow.
  46     //
  47     // Preconditions:  a > 0, m > 0.
  48     //
  49     // Note: only works correctly for __m % __a < __m / __a.
  50     template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
  51       _Tp
  52       _Mod<_Tp, __m, __a, __c, false, true>::
  53       __calc(_Tp __x)
  54       {
  55         if (__a == 1)
  56           __x %= __m;
  57         else
  58           {
  59             static const _Tp __q = __m / __a;
  60             static const _Tp __r = __m % __a;
  61
  62             _Tp __t1 = __a * (__x % __q);
  63             _Tp __t2 = __r * (__x / __q);
  64             if (__t1 >= __t2)
  65               __x = __t1 - __t2;
  66             else
  67               __x = __m - __t2 + __t1;
  68           }
  69
  70         if (__c != 0)
  71           {
  72             const _Tp __d = __m - __x;
  73             if (__d > __c)
  74               __x += __c;
  75             else
  76               __x = __c - __d;
  77           }
  78         return __x;
  79       }
  80
  81     template<typename _InputIterator, typename _OutputIterator,
  82              typename _Tp>
  83       _OutputIterator
  84       __normalize(_InputIterator __first, _InputIterator __last,
  85                   _OutputIterator __result, const _Tp& __factor)
  86       {
  87         for (; __first != __last; ++__first, ++__result)
  88           *__result = *__first / __factor;
  89         return __result;
  90       }
  91
  92   _GLIBCXX_END_NAMESPACE_VERSION
  93   } // namespace __detail
  94
  95 _GLIBCXX_BEGIN_NAMESPACE_VERSION
  96
  97   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
  98     constexpr _UIntType
  99     linear_congruential_engine<_UIntType, __a, __c, __m>::multiplier;
 100
 101   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 102     constexpr _UIntType
 103     linear_congruential_engine<_UIntType, __a, __c, __m>::increment;
 104
 105   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 106     constexpr _UIntType
 107     linear_congruential_engine<_UIntType, __a, __c, __m>::modulus;
 108
 109   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 110     constexpr _UIntType
 111     linear_congruential_engine<_UIntType, __a, __c, __m>::default_seed;
 112
 113   /**
 114    * Seeds the LCR with integral value @p __s, adjusted so that the
 115    * ring identity is never a member of the convergence set.
 116    */
 117   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 118     void
 119     linear_congruential_engine<_UIntType, __a, __c, __m>::
 120     seed(result_type __s)
 121     {
 122       if ((__detail::__mod<_UIntType, __m>(__c) == 0)
 123           && (__detail::__mod<_UIntType, __m>(__s) == 0))
 124         _M_x = 1;
 125       else
 126         _M_x = __detail::__mod<_UIntType, __m>(__s);
 127     }
 128
 129   /**
 130    * Seeds the LCR engine with a value generated by @p __q.
 131    */
 132   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 133     template<typename _Sseq>
 134       typename std::enable_if<std::is_class<_Sseq>::value>::type
 135       linear_congruential_engine<_UIntType, __a, __c, __m>::
 136       seed(_Sseq& __q)
 137       {
 138         const _UIntType __k0 = __m == 0 ? std::numeric_limits<_UIntType>::digits
 139                                         : std::__lg(__m);
 140         const _UIntType __k = (__k0 + 31) / 32;
 141         uint_least32_t __arr[__k + 3];
 142         __q.generate(__arr + 0, __arr + __k + 3);
 143         _UIntType __factor = 1u;
 144         _UIntType __sum = 0u;
 145         for (size_t __j = 0; __j < __k; ++__j)
 146           {
 147             __sum += __arr[__j + 3] * __factor;
 148             __factor *= __detail::_Shift<_UIntType, 32>::__value;
 149           }
 150         seed(__sum);
 151       }
 152
 153   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
 154            typename _CharT, typename _Traits>
 155     std::basic_ostream<_CharT, _Traits>&
 156     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 157                const linear_congruential_engine<_UIntType,
 158                                                 __a, __c, __m>& __lcr)
 159     {
 160       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 161       typedef typename __ostream_type::ios_base    __ios_base;
 162
 163       const typename __ios_base::fmtflags __flags = __os.flags();
 164       const _CharT __fill = __os.fill();
 165       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
 166       __os.fill(__os.widen(' '));
 167
 168       __os << __lcr._M_x;
 169
 170       __os.flags(__flags);
 171       __os.fill(__fill);
 172       return __os;
 173     }
 174
 175   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
 176            typename _CharT, typename _Traits>
 177     std::basic_istream<_CharT, _Traits>&
 178     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 179                linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
 180     {
 181       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
 182       typedef typename __istream_type::ios_base    __ios_base;
 183
 184       const typename __ios_base::fmtflags __flags = __is.flags();
 185       __is.flags(__ios_base::dec);
 186
 187       __is >> __lcr._M_x;
 188
 189       __is.flags(__flags);
 190       return __is;
 191     }
 192
 193
 194   template<typename _UIntType,
 195            size_t __w, size_t __n, size_t __m, size_t __r,
 196            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 197            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 198            _UIntType __f>
 199     constexpr size_t
 200     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 201                             __s, __b, __t, __c, __l, __f>::word_size;
 202
 203   template<typename _UIntType,
 204            size_t __w, size_t __n, size_t __m, size_t __r,
 205            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 206            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 207            _UIntType __f>
 208     constexpr size_t
 209     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 210                             __s, __b, __t, __c, __l, __f>::state_size;
 211
 212   template<typename _UIntType,
 213            size_t __w, size_t __n, size_t __m, size_t __r,
 214            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 215            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 216            _UIntType __f>
 217     constexpr size_t
 218     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 219                             __s, __b, __t, __c, __l, __f>::shift_size;
 220
 221   template<typename _UIntType,
 222            size_t __w, size_t __n, size_t __m, size_t __r,
 223            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 224            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 225            _UIntType __f>
 226     constexpr size_t
 227     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 228                             __s, __b, __t, __c, __l, __f>::mask_bits;
 229
 230   template<typename _UIntType,
 231            size_t __w, size_t __n, size_t __m, size_t __r,
 232            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 233            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 234            _UIntType __f>
 235     constexpr _UIntType
 236     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 237                             __s, __b, __t, __c, __l, __f>::xor_mask;
 238
 239   template<typename _UIntType,
 240            size_t __w, size_t __n, size_t __m, size_t __r,
 241            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 242            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 243            _UIntType __f>
 244     constexpr size_t
 245     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 246                             __s, __b, __t, __c, __l, __f>::tempering_u;
 247
 248   template<typename _UIntType,
 249            size_t __w, size_t __n, size_t __m, size_t __r,
 250            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 251            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 252            _UIntType __f>
 253     constexpr _UIntType
 254     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 255                             __s, __b, __t, __c, __l, __f>::tempering_d;
 256
 257   template<typename _UIntType,
 258            size_t __w, size_t __n, size_t __m, size_t __r,
 259            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 260            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 261            _UIntType __f>
 262     constexpr size_t
 263     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 264                             __s, __b, __t, __c, __l, __f>::tempering_s;
 265
 266   template<typename _UIntType,
 267            size_t __w, size_t __n, size_t __m, size_t __r,
 268            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 269            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 270            _UIntType __f>
 271     constexpr _UIntType
 272     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 273                             __s, __b, __t, __c, __l, __f>::tempering_b;
 274
 275   template<typename _UIntType,
 276            size_t __w, size_t __n, size_t __m, size_t __r,
 277            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 278            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 279            _UIntType __f>
 280     constexpr size_t
 281     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 282                             __s, __b, __t, __c, __l, __f>::tempering_t;
 283
 284   template<typename _UIntType,
 285            size_t __w, size_t __n, size_t __m, size_t __r,
 286            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 287            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 288            _UIntType __f>
 289     constexpr _UIntType
 290     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 291                             __s, __b, __t, __c, __l, __f>::tempering_c;
 292
 293   template<typename _UIntType,
 294            size_t __w, size_t __n, size_t __m, size_t __r,
 295            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 296            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 297            _UIntType __f>
 298     constexpr size_t
 299     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 300                             __s, __b, __t, __c, __l, __f>::tempering_l;
 301
 302   template<typename _UIntType,
 303            size_t __w, size_t __n, size_t __m, size_t __r,
 304            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 305            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 306            _UIntType __f>
 307     constexpr _UIntType
 308     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 309                             __s, __b, __t, __c, __l, __f>::
 310                                               initialization_multiplier;
 311
 312   template<typename _UIntType,
 313            size_t __w, size_t __n, size_t __m, size_t __r,
 314            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 315            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 316            _UIntType __f>
 317     constexpr _UIntType
 318     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 319                             __s, __b, __t, __c, __l, __f>::default_seed;
 320
 321   template<typename _UIntType,
 322            size_t __w, size_t __n, size_t __m, size_t __r,
 323            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 324            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 325            _UIntType __f>
 326     void
 327     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 328                             __s, __b, __t, __c, __l, __f>::
 329     seed(result_type __sd)
 330     {
 331       _M_x[0] = __detail::__mod<_UIntType,
 332         __detail::_Shift<_UIntType, __w>::__value>(__sd);
 333
 334       for (size_t __i = 1; __i < state_size; ++__i)
 335         {
 336           _UIntType __x = _M_x[__i - 1];
 337           __x ^= __x >> (__w - 2);
 338           __x *= __f;
 339           __x += __detail::__mod<_UIntType, __n>(__i);
 340           _M_x[__i] = __detail::__mod<_UIntType,
 341             __detail::_Shift<_UIntType, __w>::__value>(__x);
 342         }
 343       _M_p = state_size;
 344     }
 345
 346   template<typename _UIntType,
 347            size_t __w, size_t __n, size_t __m, size_t __r,
 348            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 349            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 350            _UIntType __f>
 351     template<typename _Sseq>
 352       typename std::enable_if<std::is_class<_Sseq>::value>::type
 353       mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 354                               __s, __b, __t, __c, __l, __f>::
 355       seed(_Sseq& __q)
 356       {
 357         const _UIntType __upper_mask = (~_UIntType()) << __r;
 358         const size_t __k = (__w + 31) / 32;
 359         uint_least32_t __arr[__n * __k];
 360         __q.generate(__arr + 0, __arr + __n * __k);
 361
 362         bool __zero = true;
 363         for (size_t __i = 0; __i < state_size; ++__i)
 364           {
 365             _UIntType __factor = 1u;
 366             _UIntType __sum = 0u;
 367             for (size_t __j = 0; __j < __k; ++__j)
 368               {
 369                 __sum += __arr[__k * __i + __j] * __factor;
 370                 __factor *= __detail::_Shift<_UIntType, 32>::__value;
 371               }
 372             _M_x[__i] = __detail::__mod<_UIntType,
 373               __detail::_Shift<_UIntType, __w>::__value>(__sum);
 374
 375             if (__zero)
 376               {
 377                 if (__i == 0)
 378                   {
 379                     if ((_M_x[0] & __upper_mask) != 0u)
 380                       __zero = false;
 381                   }
 382                 else if (_M_x[__i] != 0u)
 383                   __zero = false;
 384               }
 385           }
 386         if (__zero)
 387           _M_x[0] = __detail::_Shift<_UIntType, __w - 1>::__value;
 388         _M_p = state_size;
 389       }
 390
 391   template<typename _UIntType, size_t __w,
 392            size_t __n, size_t __m, size_t __r,
 393            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 394            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 395            _UIntType __f>
 396     void
 397     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 398                             __s, __b, __t, __c, __l, __f>::
 399     _M_gen_rand(void)
 400     {
 401       const _UIntType __upper_mask = (~_UIntType()) << __r;
 402       const _UIntType __lower_mask = ~__upper_mask;
 403
 404       for (size_t __k = 0; __k < (__n - __m); ++__k)
 405         {
 406           _UIntType __y = ((_M_x[__k] & __upper_mask)
 407                            | (_M_x[__k + 1] & __lower_mask));
 408           _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
 409                        ^ ((__y & 0x01) ? __a : 0));
 410         }
 411
 412       for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
 413         {
 414           _UIntType __y = ((_M_x[__k] & __upper_mask)
 415                            | (_M_x[__k + 1] & __lower_mask));
 416           _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
 417                        ^ ((__y & 0x01) ? __a : 0));
 418         }
 419
 420       _UIntType __y = ((_M_x[__n - 1] & __upper_mask)
 421                        | (_M_x[0] & __lower_mask));
 422       _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
 423                        ^ ((__y & 0x01) ? __a : 0));
 424       _M_p = 0;
 425     }
 426
 427   template<typename _UIntType, size_t __w,
 428            size_t __n, size_t __m, size_t __r,
 429            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 430            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 431            _UIntType __f>
 432     void
 433     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 434                             __s, __b, __t, __c, __l, __f>::
 435     discard(unsigned long long __z)
 436     {
 437       while (__z > state_size - _M_p)
 438         {
 439           __z -= state_size - _M_p;
 440           _M_gen_rand();
 441         }
 442       _M_p += __z;
 443     }
 444
 445   template<typename _UIntType, size_t __w,
 446            size_t __n, size_t __m, size_t __r,
 447            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 448            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 449            _UIntType __f>
 450     typename
 451     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 452                             __s, __b, __t, __c, __l, __f>::result_type
 453     mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
 454                             __s, __b, __t, __c, __l, __f>::
 455     operator()()
 456     {
 457       // Reload the vector - cost is O(n) amortized over n calls.
 458       if (_M_p >= state_size)
 459         _M_gen_rand();
 460
 461       // Calculate o(x(i)).
 462       result_type __z = _M_x[_M_p++];
 463       __z ^= (__z >> __u) & __d;
 464       __z ^= (__z << __s) & __b;
 465       __z ^= (__z << __t) & __c;
 466       __z ^= (__z >> __l);
 467
 468       return __z;
 469     }
 470
 471   template<typename _UIntType, size_t __w,
 472            size_t __n, size_t __m, size_t __r,
 473            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 474            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 475            _UIntType __f, typename _CharT, typename _Traits>
 476     std::basic_ostream<_CharT, _Traits>&
 477     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 478                const mersenne_twister_engine<_UIntType, __w, __n, __m,
 479                __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
 480     {
 481       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 482       typedef typename __ostream_type::ios_base    __ios_base;
 483
 484       const typename __ios_base::fmtflags __flags = __os.flags();
 485       const _CharT __fill = __os.fill();
 486       const _CharT __space = __os.widen(' ');
 487       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
 488       __os.fill(__space);
 489
 490       for (size_t __i = 0; __i < __n; ++__i)
 491         __os << __x._M_x[__i] << __space;
 492       __os << __x._M_p;
 493
 494       __os.flags(__flags);
 495       __os.fill(__fill);
 496       return __os;
 497     }
 498
 499   template<typename _UIntType, size_t __w,
 500            size_t __n, size_t __m, size_t __r,
 501            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 502            _UIntType __b, size_t __t, _UIntType __c, size_t __l,
 503            _UIntType __f, typename _CharT, typename _Traits>
 504     std::basic_istream<_CharT, _Traits>&
 505     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 506                mersenne_twister_engine<_UIntType, __w, __n, __m,
 507                __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
 508     {
 509       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
 510       typedef typename __istream_type::ios_base    __ios_base;
 511
 512       const typename __ios_base::fmtflags __flags = __is.flags();
 513       __is.flags(__ios_base::dec | __ios_base::skipws);
 514
 515       for (size_t __i = 0; __i < __n; ++__i)
 516         __is >> __x._M_x[__i];
 517       __is >> __x._M_p;
 518
 519       __is.flags(__flags);
 520       return __is;
 521     }
 522
 523
 524   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 525     constexpr size_t
 526     subtract_with_carry_engine<_UIntType, __w, __s, __r>::word_size;
 527
 528   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 529     constexpr size_t
 530     subtract_with_carry_engine<_UIntType, __w, __s, __r>::short_lag;
 531
 532   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 533     constexpr size_t
 534     subtract_with_carry_engine<_UIntType, __w, __s, __r>::long_lag;
 535
 536   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 537     constexpr _UIntType
 538     subtract_with_carry_engine<_UIntType, __w, __s, __r>::default_seed;
 539
 540   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 541     void
 542     subtract_with_carry_engine<_UIntType, __w, __s, __r>::
 543     seed(result_type __value)
 544     {
 545       std::linear_congruential_engine<result_type, 40014u, 0u, 2147483563u>
 546         __lcg(__value == 0u ? default_seed : __value);
 547
 548       const size_t __n = (__w + 31) / 32;
 549
 550       for (size_t __i = 0; __i < long_lag; ++__i)
 551         {
 552           _UIntType __sum = 0u;
 553           _UIntType __factor = 1u;
 554           for (size_t __j = 0; __j < __n; ++__j)
 555             {
 556               __sum += __detail::__mod<uint_least32_t,
 557                        __detail::_Shift<uint_least32_t, 32>::__value>
 558                          (__lcg()) * __factor;
 559               __factor *= __detail::_Shift<_UIntType, 32>::__value;
 560             }
 561           _M_x[__i] = __detail::__mod<_UIntType,
 562             __detail::_Shift<_UIntType, __w>::__value>(__sum);
 563         }
 564       _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
 565       _M_p = 0;
 566     }
 567
 568   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 569     template<typename _Sseq>
 570       typename std::enable_if<std::is_class<_Sseq>::value>::type
 571       subtract_with_carry_engine<_UIntType, __w, __s, __r>::
 572       seed(_Sseq& __q)
 573       {
 574         const size_t __k = (__w + 31) / 32;
 575         uint_least32_t __arr[__r * __k];
 576         __q.generate(__arr + 0, __arr + __r * __k);
 577
 578         for (size_t __i = 0; __i < long_lag; ++__i)
 579           {
 580             _UIntType __sum = 0u;
 581             _UIntType __factor = 1u;
 582             for (size_t __j = 0; __j < __k; ++__j)
 583               {
 584                 __sum += __arr[__k * __i + __j] * __factor;
 585                 __factor *= __detail::_Shift<_UIntType, 32>::__value;
 586               }
 587             _M_x[__i] = __detail::__mod<_UIntType,
 588               __detail::_Shift<_UIntType, __w>::__value>(__sum);
 589           }
 590         _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
 591         _M_p = 0;
 592       }
 593
 594   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 595     typename subtract_with_carry_engine<_UIntType, __w, __s, __r>::
 596              result_type
 597     subtract_with_carry_engine<_UIntType, __w, __s, __r>::
 598     operator()()
 599     {
 600       // Derive short lag index from current index.
 601       long __ps = _M_p - short_lag;
 602       if (__ps < 0)
 603         __ps += long_lag;
 604
 605       // Calculate new x(i) without overflow or division.
 606       // NB: Thanks to the requirements for _UIntType, _M_x[_M_p] + _M_carry
 607       // cannot overflow.
 608       _UIntType __xi;
 609       if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
 610         {
 611           __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
 612           _M_carry = 0;
 613         }
 614       else
 615         {
 616           __xi = (__detail::_Shift<_UIntType, __w>::__value
 617                   - _M_x[_M_p] - _M_carry + _M_x[__ps]);
 618           _M_carry = 1;
 619         }
 620       _M_x[_M_p] = __xi;
 621
 622       // Adjust current index to loop around in ring buffer.
 623       if (++_M_p >= long_lag)
 624         _M_p = 0;
 625
 626       return __xi;
 627     }
 628
 629   template<typename _UIntType, size_t __w, size_t __s, size_t __r,
 630            typename _CharT, typename _Traits>
 631     std::basic_ostream<_CharT, _Traits>&
 632     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 633                const subtract_with_carry_engine<_UIntType,
 634                                                 __w, __s, __r>& __x)
 635     {
 636       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 637       typedef typename __ostream_type::ios_base    __ios_base;
 638
 639       const typename __ios_base::fmtflags __flags = __os.flags();
 640       const _CharT __fill = __os.fill();
 641       const _CharT __space = __os.widen(' ');
 642       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
 643       __os.fill(__space);
 644
 645       for (size_t __i = 0; __i < __r; ++__i)
 646         __os << __x._M_x[__i] << __space;
 647       __os << __x._M_carry << __space << __x._M_p;
 648
 649       __os.flags(__flags);
 650       __os.fill(__fill);
 651       return __os;
 652     }
 653
 654   template<typename _UIntType, size_t __w, size_t __s, size_t __r,
 655            typename _CharT, typename _Traits>
 656     std::basic_istream<_CharT, _Traits>&
 657     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 658                subtract_with_carry_engine<_UIntType, __w, __s, __r>& __x)
 659     {
 660       typedef std::basic_ostream<_CharT, _Traits>  __istream_type;
 661       typedef typename __istream_type::ios_base    __ios_base;
 662
 663       const typename __ios_base::fmtflags __flags = __is.flags();
 664       __is.flags(__ios_base::dec | __ios_base::skipws);
 665
 666       for (size_t __i = 0; __i < __r; ++__i)
 667         __is >> __x._M_x[__i];
 668       __is >> __x._M_carry;
 669       __is >> __x._M_p;
 670
 671       __is.flags(__flags);
 672       return __is;
 673     }
 674
 675
 676   template<typename _RandomNumberEngine, size_t __p, size_t __r>
 677     constexpr size_t
 678     discard_block_engine<_RandomNumberEngine, __p, __r>::block_size;
 679
 680   template<typename _RandomNumberEngine, size_t __p, size_t __r>
 681     constexpr size_t
 682     discard_block_engine<_RandomNumberEngine, __p, __r>::used_block;
 683
 684   template<typename _RandomNumberEngine, size_t __p, size_t __r>
 685     typename discard_block_engine<_RandomNumberEngine,
 686                            __p, __r>::result_type
 687     discard_block_engine<_RandomNumberEngine, __p, __r>::
 688     operator()()
 689     {
 690       if (_M_n >= used_block)
 691         {
 692           _M_b.discard(block_size - _M_n);
 693           _M_n = 0;
 694         }
 695       ++_M_n;
 696       return _M_b();
 697     }
 698
 699   template<typename _RandomNumberEngine, size_t __p, size_t __r,
 700            typename _CharT, typename _Traits>
 701     std::basic_ostream<_CharT, _Traits>&
 702     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 703                const discard_block_engine<_RandomNumberEngine,
 704                __p, __r>& __x)
 705     {
 706       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 707       typedef typename __ostream_type::ios_base    __ios_base;
 708
 709       const typename __ios_base::fmtflags __flags = __os.flags();
 710       const _CharT __fill = __os.fill();
 711       const _CharT __space = __os.widen(' ');
 712       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
 713       __os.fill(__space);
 714
 715       __os << __x.base() << __space << __x._M_n;
 716
 717       __os.flags(__flags);
 718       __os.fill(__fill);
 719       return __os;
 720     }
 721
 722   template<typename _RandomNumberEngine, size_t __p, size_t __r,
 723            typename _CharT, typename _Traits>
 724     std::basic_istream<_CharT, _Traits>&
 725     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 726                discard_block_engine<_RandomNumberEngine, __p, __r>& __x)
 727     {
 728       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
 729       typedef typename __istream_type::ios_base    __ios_base;
 730
 731       const typename __ios_base::fmtflags __flags = __is.flags();
 732       __is.flags(__ios_base::dec | __ios_base::skipws);
 733
 734       __is >> __x._M_b >> __x._M_n;
 735
 736       __is.flags(__flags);
 737       return __is;
 738     }
 739
 740
 741   template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
 742     typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
 743       result_type
 744     independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
 745     operator()()
 746     {
 747       typedef typename _RandomNumberEngine::result_type _Eresult_type;
 748       const _Eresult_type __r
 749         = (_M_b.max() - _M_b.min() < std::numeric_limits<_Eresult_type>::max()
 750            ? _M_b.max() - _M_b.min() + 1 : 0);
 751       const unsigned __edig = std::numeric_limits<_Eresult_type>::digits;
 752       const unsigned __m = __r ? std::__lg(__r) : __edig;
 753
 754       typedef typename std::common_type<_Eresult_type, result_type>::type
 755         __ctype;
 756       const unsigned __cdig = std::numeric_limits<__ctype>::digits;
 757
 758       unsigned __n, __n0;
 759       __ctype __s0, __s1, __y0, __y1;
 760
 761       for (size_t __i = 0; __i < 2; ++__i)
 762         {
 763           __n = (__w + __m - 1) / __m + __i;
 764           __n0 = __n - __w % __n;
 765           const unsigned __w0 = __w / __n;  // __w0 <= __m
 766
 767           __s0 = 0;
 768           __s1 = 0;
 769           if (__w0 < __cdig)
 770             {
 771               __s0 = __ctype(1) << __w0;
 772               __s1 = __s0 << 1;
 773             }
 774
 775           __y0 = 0;
 776           __y1 = 0;
 777           if (__r)
 778             {
 779               __y0 = __s0 * (__r / __s0);
 780               if (__s1)
 781                 __y1 = __s1 * (__r / __s1);
 782
 783               if (__r - __y0 <= __y0 / __n)
 784                 break;
 785             }
 786           else
 787             break;
 788         }
 789
 790       result_type __sum = 0;
 791       for (size_t __k = 0; __k < __n0; ++__k)
 792         {
 793           __ctype __u;
 794           do
 795             __u = _M_b() - _M_b.min();
 796           while (__y0 && __u >= __y0);
 797           __sum = __s0 * __sum + (__s0 ? __u % __s0 : __u);
 798         }
 799       for (size_t __k = __n0; __k < __n; ++__k)
 800         {
 801           __ctype __u;
 802           do
 803             __u = _M_b() - _M_b.min();
 804           while (__y1 && __u >= __y1);
 805           __sum = __s1 * __sum + (__s1 ? __u % __s1 : __u);
 806         }
 807       return __sum;
 808     }
 809
 810
 811   template<typename _RandomNumberEngine, size_t __k>
 812     constexpr size_t
 813     shuffle_order_engine<_RandomNumberEngine, __k>::table_size;
 814
 815   template<typename _RandomNumberEngine, size_t __k>
 816     typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
 817     shuffle_order_engine<_RandomNumberEngine, __k>::
 818     operator()()
 819     {
 820       size_t __j = __k * ((_M_y - _M_b.min())
 821                           / (_M_b.max() - _M_b.min() + 1.0L));
 822       _M_y = _M_v[__j];
 823       _M_v[__j] = _M_b();
 824
 825       return _M_y;
 826     }
 827
 828   template<typename _RandomNumberEngine, size_t __k,
 829            typename _CharT, typename _Traits>
 830     std::basic_ostream<_CharT, _Traits>&
 831     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 832                const shuffle_order_engine<_RandomNumberEngine, __k>& __x)
 833     {
 834       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 835       typedef typename __ostream_type::ios_base    __ios_base;
 836
 837       const typename __ios_base::fmtflags __flags = __os.flags();
 838       const _CharT __fill = __os.fill();
 839       const _CharT __space = __os.widen(' ');
 840       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
 841       __os.fill(__space);
 842
 843       __os << __x.base();
 844       for (size_t __i = 0; __i < __k; ++__i)
 845         __os << __space << __x._M_v[__i];
 846       __os << __space << __x._M_y;
 847
 848       __os.flags(__flags);
 849       __os.fill(__fill);
 850       return __os;
 851     }
 852
 853   template<typename _RandomNumberEngine, size_t __k,
 854            typename _CharT, typename _Traits>
 855     std::basic_istream<_CharT, _Traits>&
 856     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 857                shuffle_order_engine<_RandomNumberEngine, __k>& __x)
 858     {
 859       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
 860       typedef typename __istream_type::ios_base    __ios_base;
 861
 862       const typename __ios_base::fmtflags __flags = __is.flags();
 863       __is.flags(__ios_base::dec | __ios_base::skipws);
 864
 865       __is >> __x._M_b;
 866       for (size_t __i = 0; __i < __k; ++__i)
 867         __is >> __x._M_v[__i];
 868       __is >> __x._M_y;
 869
 870       __is.flags(__flags);
 871       return __is;
 872     }
 873
 874
 875   template<typename _IntType, typename _CharT, typename _Traits>
 876     std::basic_ostream<_CharT, _Traits>&
 877     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 878                const uniform_int_distribution<_IntType>& __x)
 879     {
 880       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 881       typedef typename __ostream_type::ios_base    __ios_base;
 882
 883       const typename __ios_base::fmtflags __flags = __os.flags();
 884       const _CharT __fill = __os.fill();
 885       const _CharT __space = __os.widen(' ');
 886       __os.flags(__ios_base::scientific | __ios_base::left);
 887       __os.fill(__space);
 888
 889       __os << __x.a() << __space << __x.b();
 890
 891       __os.flags(__flags);
 892       __os.fill(__fill);
 893       return __os;
 894     }
 895
 896   template<typename _IntType, typename _CharT, typename _Traits>
 897     std::basic_istream<_CharT, _Traits>&
 898     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 899                uniform_int_distribution<_IntType>& __x)
 900     {
 901       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
 902       typedef typename __istream_type::ios_base    __ios_base;
 903
 904       const typename __ios_base::fmtflags __flags = __is.flags();
 905       __is.flags(__ios_base::dec | __ios_base::skipws);
 906
 907       _IntType __a, __b;
 908       __is >> __a >> __b;
 909       __x.param(typename uniform_int_distribution<_IntType>::
 910                 param_type(__a, __b));
 911
 912       __is.flags(__flags);
 913       return __is;
 914     }
 915
 916
 917   template<typename _RealType>
 918     template<typename _ForwardIterator,
 919              typename _UniformRandomNumberGenerator>
 920       void
 921       uniform_real_distribution<_RealType>::
 922       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
 923                       _UniformRandomNumberGenerator& __urng,
 924                       const param_type& __p)
 925       {
 926         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
 927         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
 928           __aurng(__urng);
 929         auto __range = __p.b() - __p.a();
 930         while (__f != __t)
 931           *__f++ = __aurng() * __range + __p.a();
 932       }
 933
 934   template<typename _RealType, typename _CharT, typename _Traits>
 935     std::basic_ostream<_CharT, _Traits>&
 936     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 937                const uniform_real_distribution<_RealType>& __x)
 938     {
 939       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
 940       typedef typename __ostream_type::ios_base    __ios_base;
 941
 942       const typename __ios_base::fmtflags __flags = __os.flags();
 943       const _CharT __fill = __os.fill();
 944       const std::streamsize __precision = __os.precision();
 945       const _CharT __space = __os.widen(' ');
 946       __os.flags(__ios_base::scientific | __ios_base::left);
 947       __os.fill(__space);
 948       __os.precision(std::numeric_limits<_RealType>::max_digits10);
 949
 950       __os << __x.a() << __space << __x.b();
 951
 952       __os.flags(__flags);
 953       __os.fill(__fill);
 954       __os.precision(__precision);
 955       return __os;
 956     }
 957
 958   template<typename _RealType, typename _CharT, typename _Traits>
 959     std::basic_istream<_CharT, _Traits>&
 960     operator>>(std::basic_istream<_CharT, _Traits>& __is,
 961                uniform_real_distribution<_RealType>& __x)
 962     {
 963       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
 964       typedef typename __istream_type::ios_base    __ios_base;
 965
 966       const typename __ios_base::fmtflags __flags = __is.flags();
 967       __is.flags(__ios_base::skipws);
 968
 969       _RealType __a, __b;
 970       __is >> __a >> __b;
 971       __x.param(typename uniform_real_distribution<_RealType>::
 972                 param_type(__a, __b));
 973
 974       __is.flags(__flags);
 975       return __is;
 976     }
 977
 978
 979   template<typename _ForwardIterator,
 980            typename _UniformRandomNumberGenerator>
 981     void
 982     std::bernoulli_distribution::
 983     __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
 984                     _UniformRandomNumberGenerator& __urng,
 985                     const param_type& __p)
 986     {
 987       __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
 988       __detail::_Adaptor<_UniformRandomNumberGenerator, double>
 989         __aurng(__urng);
 990       auto __limit = __p.p() * (__aurng.max() - __aurng.min());
 991
 992       while (__f != __t)
 993         *__f++ = (__aurng() - __aurng.min()) < __limit;
 994     }
 995
 996   template<typename _CharT, typename _Traits>
 997     std::basic_ostream<_CharT, _Traits>&
 998     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
 999                const bernoulli_distribution& __x)
1000     {
1001       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1002       typedef typename __ostream_type::ios_base    __ios_base;
1003
1004       const typename __ios_base::fmtflags __flags = __os.flags();
1005       const _CharT __fill = __os.fill();
1006       const std::streamsize __precision = __os.precision();
1007       __os.flags(__ios_base::scientific | __ios_base::left);
1008       __os.fill(__os.widen(' '));
1009       __os.precision(std::numeric_limits<double>::max_digits10);
1010
1011       __os << __x.p();
1012
1013       __os.flags(__flags);
1014       __os.fill(__fill);
1015       __os.precision(__precision);
1016       return __os;
1017     }
1018
1019
1020   template<typename _IntType>
1021     template<typename _UniformRandomNumberGenerator>
1022       typename geometric_distribution<_IntType>::result_type
1023       geometric_distribution<_IntType>::
1024       operator()(_UniformRandomNumberGenerator& __urng,
1025                  const param_type& __param)
1026       {
1027         // About the epsilon thing see this thread:
1028         // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1029         const double __naf =
1030           (1 - std::numeric_limits<double>::epsilon()) / 2;
1031         // The largest _RealType convertible to _IntType.
1032         const double __thr =
1033           std::numeric_limits<_IntType>::max() + __naf;
1034         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1035           __aurng(__urng);
1036
1037         double __cand;
1038         do
1039           __cand = std::floor(std::log(1.0 - __aurng()) / __param._M_log_1_p);
1040         while (__cand >= __thr);
1041
1042         return result_type(__cand + __naf);
1043       }
1044
1045   template<typename _IntType>
1046     template<typename _ForwardIterator,
1047              typename _UniformRandomNumberGenerator>
1048       void
1049       geometric_distribution<_IntType>::
1050       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1051                       _UniformRandomNumberGenerator& __urng,
1052                       const param_type& __param)
1053       {
1054         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1055         // About the epsilon thing see this thread:
1056         // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1057         const double __naf =
1058           (1 - std::numeric_limits<double>::epsilon()) / 2;
1059         // The largest _RealType convertible to _IntType.
1060         const double __thr =
1061           std::numeric_limits<_IntType>::max() + __naf;
1062         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1063           __aurng(__urng);
1064
1065         while (__f != __t)
1066           {
1067             double __cand;
1068             do
1069               __cand = std::floor(std::log(1.0 - __aurng())
1070                                   / __param._M_log_1_p);
1071             while (__cand >= __thr);
1072
1073             *__f++ = __cand + __naf;
1074           }
1075       }
1076
1077   template<typename _IntType,
1078            typename _CharT, typename _Traits>
1079     std::basic_ostream<_CharT, _Traits>&
1080     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1081                const geometric_distribution<_IntType>& __x)
1082     {
1083       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1084       typedef typename __ostream_type::ios_base    __ios_base;
1085
1086       const typename __ios_base::fmtflags __flags = __os.flags();
1087       const _CharT __fill = __os.fill();
1088       const std::streamsize __precision = __os.precision();
1089       __os.flags(__ios_base::scientific | __ios_base::left);
1090       __os.fill(__os.widen(' '));
1091       __os.precision(std::numeric_limits<double>::max_digits10);
1092
1093       __os << __x.p();
1094
1095       __os.flags(__flags);
1096       __os.fill(__fill);
1097       __os.precision(__precision);
1098       return __os;
1099     }
1100
1101   template<typename _IntType,
1102            typename _CharT, typename _Traits>
1103     std::basic_istream<_CharT, _Traits>&
1104     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1105                geometric_distribution<_IntType>& __x)
1106     {
1107       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1108       typedef typename __istream_type::ios_base    __ios_base;
1109
1110       const typename __ios_base::fmtflags __flags = __is.flags();
1111       __is.flags(__ios_base::skipws);
1112
1113       double __p;
1114       __is >> __p;
1115       __x.param(typename geometric_distribution<_IntType>::param_type(__p));
1116
1117       __is.flags(__flags);
1118       return __is;
1119     }
1120
1121   // This is Leger's algorithm, also in Devroye, Ch. X, Example 1.5.
1122   template<typename _IntType>
1123     template<typename _UniformRandomNumberGenerator>
1124       typename negative_binomial_distribution<_IntType>::result_type
1125       negative_binomial_distribution<_IntType>::
1126       operator()(_UniformRandomNumberGenerator& __urng)
1127       {
1128         const double __y = _M_gd(__urng);
1129
1130         // XXX Is the constructor too slow?
1131         std::poisson_distribution<result_type> __poisson(__y);
1132         return __poisson(__urng);
1133       }
1134
1135   template<typename _IntType>
1136     template<typename _UniformRandomNumberGenerator>
1137       typename negative_binomial_distribution<_IntType>::result_type
1138       negative_binomial_distribution<_IntType>::
1139       operator()(_UniformRandomNumberGenerator& __urng,
1140                  const param_type& __p)
1141       {
1142         typedef typename std::gamma_distribution<double>::param_type
1143           param_type;
1144
1145         const double __y =
1146           _M_gd(__urng, param_type(__p.k(), (1.0 - __p.p()) / __p.p()));
1147
1148         std::poisson_distribution<result_type> __poisson(__y);
1149         return __poisson(__urng);
1150       }
1151
1152   template<typename _IntType>
1153     template<typename _ForwardIterator,
1154              typename _UniformRandomNumberGenerator>
1155       void
1156       negative_binomial_distribution<_IntType>::
1157       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1158                       _UniformRandomNumberGenerator& __urng)
1159       {
1160         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1161         while (__f != __t)
1162           {
1163             const double __y = _M_gd(__urng);
1164
1165             // XXX Is the constructor too slow?
1166             std::poisson_distribution<result_type> __poisson(__y);
1167             *__f++ = __poisson(__urng);
1168           }
1169       }
1170
1171   template<typename _IntType>
1172     template<typename _ForwardIterator,
1173              typename _UniformRandomNumberGenerator>
1174       void
1175       negative_binomial_distribution<_IntType>::
1176       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1177                       _UniformRandomNumberGenerator& __urng,
1178                       const param_type& __p)
1179       {
1180         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1181         typename std::gamma_distribution<result_type>::param_type
1182           __p2(__p.k(), (1.0 - __p.p()) / __p.p());
1183
1184         while (__f != __t)
1185           {
1186             const double __y = _M_gd(__urng, __p2);
1187
1188             std::poisson_distribution<result_type> __poisson(__y);
1189             *__f++ = __poisson(__urng);
1190           }
1191       }
1192
1193   template<typename _IntType, typename _CharT, typename _Traits>
1194     std::basic_ostream<_CharT, _Traits>&
1195     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1196                const negative_binomial_distribution<_IntType>& __x)
1197     {
1198       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1199       typedef typename __ostream_type::ios_base    __ios_base;
1200
1201       const typename __ios_base::fmtflags __flags = __os.flags();
1202       const _CharT __fill = __os.fill();
1203       const std::streamsize __precision = __os.precision();
1204       const _CharT __space = __os.widen(' ');
1205       __os.flags(__ios_base::scientific | __ios_base::left);
1206       __os.fill(__os.widen(' '));
1207       __os.precision(std::numeric_limits<double>::max_digits10);
1208
1209       __os << __x.k() << __space << __x.p()
1210            << __space << __x._M_gd;
1211
1212       __os.flags(__flags);
1213       __os.fill(__fill);
1214       __os.precision(__precision);
1215       return __os;
1216     }
1217
1218   template<typename _IntType, typename _CharT, typename _Traits>
1219     std::basic_istream<_CharT, _Traits>&
1220     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1221                negative_binomial_distribution<_IntType>& __x)
1222     {
1223       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1224       typedef typename __istream_type::ios_base    __ios_base;
1225
1226       const typename __ios_base::fmtflags __flags = __is.flags();
1227       __is.flags(__ios_base::skipws);
1228
1229       _IntType __k;
1230       double __p;
1231       __is >> __k >> __p >> __x._M_gd;
1232       __x.param(typename negative_binomial_distribution<_IntType>::
1233                 param_type(__k, __p));
1234
1235       __is.flags(__flags);
1236       return __is;
1237     }
1238
1239
1240   template<typename _IntType>
1241     void
1242     poisson_distribution<_IntType>::param_type::
1243     _M_initialize()
1244     {
1245 #if _GLIBCXX_USE_C99_MATH_TR1
1246       if (_M_mean >= 12)
1247         {
1248           const double __m = std::floor(_M_mean);
1249           _M_lm_thr = std::log(_M_mean);
1250           _M_lfm = std::lgamma(__m + 1);
1251           _M_sm = std::sqrt(__m);
1252
1253           const double __pi_4 = 0.7853981633974483096156608458198757L;
1254           const double __dx = std::sqrt(2 * __m * std::log(32 * __m
1255                                                               / __pi_4));
1256           _M_d = std::round(std::max<double>(6.0, std::min(__m, __dx)));
1257           const double __cx = 2 * __m + _M_d;
1258           _M_scx = std::sqrt(__cx / 2);
1259           _M_1cx = 1 / __cx;
1260
1261           _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
1262           _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2))
1263                 / _M_d;
1264         }
1265       else
1266 #endif
1267         _M_lm_thr = std::exp(-_M_mean);
1268       }
1269
1270   /**
1271    * A rejection algorithm when mean >= 12 and a simple method based
1272    * upon the multiplication of uniform random variates otherwise.
1273    * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1274    * is defined.
1275    *
1276    * Reference:
1277    * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1278    * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
1279    */
1280   template<typename _IntType>
1281     template<typename _UniformRandomNumberGenerator>
1282       typename poisson_distribution<_IntType>::result_type
1283       poisson_distribution<_IntType>::
1284       operator()(_UniformRandomNumberGenerator& __urng,
1285                  const param_type& __param)
1286       {
1287         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1288           __aurng(__urng);
1289 #if _GLIBCXX_USE_C99_MATH_TR1
1290         if (__param.mean() >= 12)
1291           {
1292             double __x;
1293
1294             // See comments above...
1295             const double __naf =
1296               (1 - std::numeric_limits<double>::epsilon()) / 2;
1297             const double __thr =
1298               std::numeric_limits<_IntType>::max() + __naf;
1299
1300             const double __m = std::floor(__param.mean());
1301             // sqrt(pi / 2)
1302             const double __spi_2 = 1.2533141373155002512078826424055226L;
1303             const double __c1 = __param._M_sm * __spi_2;
1304             const double __c2 = __param._M_c2b + __c1;
1305             const double __c3 = __c2 + 1;
1306             const double __c4 = __c3 + 1;
1307             // e^(1 / 78)
1308             const double __e178 = 1.0129030479320018583185514777512983L;
1309             const double __c5 = __c4 + __e178;
1310             const double __c = __param._M_cb + __c5;
1311             const double __2cx = 2 * (2 * __m + __param._M_d);
1312
1313             bool __reject = true;
1314             do
1315               {
1316                 const double __u = __c * __aurng();
1317                 const double __e = -std::log(1.0 - __aurng());
1318
1319                 double __w = 0.0;
1320
1321                 if (__u <= __c1)
1322                   {
1323                     const double __n = _M_nd(__urng);
1324                     const double __y = -std::abs(__n) * __param._M_sm - 1;
1325                     __x = std::floor(__y);
1326                     __w = -__n * __n / 2;
1327                     if (__x < -__m)
1328                       continue;
1329                   }
1330                 else if (__u <= __c2)
1331                   {
1332                     const double __n = _M_nd(__urng);
1333                     const double __y = 1 + std::abs(__n) * __param._M_scx;
1334                     __x = std::ceil(__y);
1335                     __w = __y * (2 - __y) * __param._M_1cx;
1336                     if (__x > __param._M_d)
1337                       continue;
1338                   }
1339                 else if (__u <= __c3)
1340                   // NB: This case not in the book, nor in the Errata,
1341                   // but should be ok...
1342                   __x = -1;
1343                 else if (__u <= __c4)
1344                   __x = 0;
1345                 else if (__u <= __c5)
1346                   __x = 1;
1347                 else
1348                   {
1349                     const double __v = -std::log(1.0 - __aurng());
1350                     const double __y = __param._M_d
1351                                      + __v * __2cx / __param._M_d;
1352                     __x = std::ceil(__y);
1353                     __w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
1354                   }
1355
1356                 __reject = (__w - __e - __x * __param._M_lm_thr
1357                             > __param._M_lfm - std::lgamma(__x + __m + 1));
1358
1359                 __reject |= __x + __m >= __thr;
1360
1361               } while (__reject);
1362
1363             return result_type(__x + __m + __naf);
1364           }
1365         else
1366 #endif
1367           {
1368             _IntType     __x = 0;
1369             double __prod = 1.0;
1370
1371             do
1372               {
1373                 __prod *= __aurng();
1374                 __x += 1;
1375               }
1376             while (__prod > __param._M_lm_thr);
1377
1378             return __x - 1;
1379           }
1380       }
1381
1382   template<typename _IntType>
1383     template<typename _ForwardIterator,
1384              typename _UniformRandomNumberGenerator>
1385       void
1386       poisson_distribution<_IntType>::
1387       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1388                       _UniformRandomNumberGenerator& __urng,
1389                       const param_type& __param)
1390       {
1391         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1392         // We could duplicate everything from operator()...
1393         while (__f != __t)
1394           *__f++ = this->operator()(__urng, __param);
1395       }
1396
1397   template<typename _IntType,
1398            typename _CharT, typename _Traits>
1399     std::basic_ostream<_CharT, _Traits>&
1400     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1401                const poisson_distribution<_IntType>& __x)
1402     {
1403       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1404       typedef typename __ostream_type::ios_base    __ios_base;
1405
1406       const typename __ios_base::fmtflags __flags = __os.flags();
1407       const _CharT __fill = __os.fill();
1408       const std::streamsize __precision = __os.precision();
1409       const _CharT __space = __os.widen(' ');
1410       __os.flags(__ios_base::scientific | __ios_base::left);
1411       __os.fill(__space);
1412       __os.precision(std::numeric_limits<double>::max_digits10);
1413
1414       __os << __x.mean() << __space << __x._M_nd;
1415
1416       __os.flags(__flags);
1417       __os.fill(__fill);
1418       __os.precision(__precision);
1419       return __os;
1420     }
1421
1422   template<typename _IntType,
1423            typename _CharT, typename _Traits>
1424     std::basic_istream<_CharT, _Traits>&
1425     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1426                poisson_distribution<_IntType>& __x)
1427     {
1428       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1429       typedef typename __istream_type::ios_base    __ios_base;
1430
1431       const typename __ios_base::fmtflags __flags = __is.flags();
1432       __is.flags(__ios_base::skipws);
1433
1434       double __mean;
1435       __is >> __mean >> __x._M_nd;
1436       __x.param(typename poisson_distribution<_IntType>::param_type(__mean));
1437
1438       __is.flags(__flags);
1439       return __is;
1440     }
1441
1442
1443   template<typename _IntType>
1444     void
1445     binomial_distribution<_IntType>::param_type::
1446     _M_initialize()
1447     {
1448       const double __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
1449
1450       _M_easy = true;
1451
1452 #if _GLIBCXX_USE_C99_MATH_TR1
1453       if (_M_t * __p12 >= 8)
1454         {
1455           _M_easy = false;
1456           const double __np = std::floor(_M_t * __p12);
1457           const double __pa = __np / _M_t;
1458           const double __1p = 1 - __pa;
1459
1460           const double __pi_4 = 0.7853981633974483096156608458198757L;
1461           const double __d1x =
1462             std::sqrt(__np * __1p * std::log(32 * __np
1463                                              / (81 * __pi_4 * __1p)));
1464           _M_d1 = std::round(std::max<double>(1.0, __d1x));
1465           const double __d2x =
1466             std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
1467                                              / (__pi_4 * __pa)));
1468           _M_d2 = std::round(std::max<double>(1.0, __d2x));
1469
1470           // sqrt(pi / 2)
1471           const double __spi_2 = 1.2533141373155002512078826424055226L;
1472           _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
1473           _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p));
1474           _M_c = 2 * _M_d1 / __np;
1475           _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
1476           const double __a12 = _M_a1 + _M_s2 * __spi_2;
1477           const double __s1s = _M_s1 * _M_s1;
1478           _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
1479                              * 2 * __s1s / _M_d1
1480                              * std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
1481           const double __s2s = _M_s2 * _M_s2;
1482           _M_s = (_M_a123 + 2 * __s2s / _M_d2
1483                   * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
1484           _M_lf = (std::lgamma(__np + 1)
1485                    + std::lgamma(_M_t - __np + 1));
1486           _M_lp1p = std::log(__pa / __1p);
1487
1488           _M_q = -std::log(1 - (__p12 - __pa) / __1p);
1489         }
1490       else
1491 #endif
1492         _M_q = -std::log(1 - __p12);
1493     }
1494
1495   template<typename _IntType>
1496     template<typename _UniformRandomNumberGenerator>
1497       typename binomial_distribution<_IntType>::result_type
1498       binomial_distribution<_IntType>::
1499       _M_waiting(_UniformRandomNumberGenerator& __urng,
1500                  _IntType __t, double __q)
1501       {
1502         _IntType __x = 0;
1503         double __sum = 0.0;
1504         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1505           __aurng(__urng);
1506
1507         do
1508           {
1509             if (__t == __x)
1510               return __x;
1511             const double __e = -std::log(1.0 - __aurng());
1512             __sum += __e / (__t - __x);
1513             __x += 1;
1514           }
1515         while (__sum <= __q);
1516
1517         return __x - 1;
1518       }
1519
1520   /**
1521    * A rejection algorithm when t * p >= 8 and a simple waiting time
1522    * method - the second in the referenced book - otherwise.
1523    * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1524    * is defined.
1525    *
1526    * Reference:
1527    * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1528    * New York, 1986, Ch. X, Sect. 4 (+ Errata!).
1529    */
1530   template<typename _IntType>
1531     template<typename _UniformRandomNumberGenerator>
1532       typename binomial_distribution<_IntType>::result_type
1533       binomial_distribution<_IntType>::
1534       operator()(_UniformRandomNumberGenerator& __urng,
1535                  const param_type& __param)
1536       {
1537         result_type __ret;
1538         const _IntType __t = __param.t();
1539         const double __p = __param.p();
1540         const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
1541         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1542           __aurng(__urng);
1543
1544 #if _GLIBCXX_USE_C99_MATH_TR1
1545         if (!__param._M_easy)
1546           {
1547             double __x;
1548
1549             // See comments above...
1550             const double __naf =
1551               (1 - std::numeric_limits<double>::epsilon()) / 2;
1552             const double __thr =
1553               std::numeric_limits<_IntType>::max() + __naf;
1554
1555             const double __np = std::floor(__t * __p12);
1556
1557             // sqrt(pi / 2)
1558             const double __spi_2 = 1.2533141373155002512078826424055226L;
1559             const double __a1 = __param._M_a1;
1560             const double __a12 = __a1 + __param._M_s2 * __spi_2;
1561             const double __a123 = __param._M_a123;
1562             const double __s1s = __param._M_s1 * __param._M_s1;
1563             const double __s2s = __param._M_s2 * __param._M_s2;
1564
1565             bool __reject;
1566             do
1567               {
1568                 const double __u = __param._M_s * __aurng();
1569
1570                 double __v;
1571
1572                 if (__u <= __a1)
1573                   {
1574                     const double __n = _M_nd(__urng);
1575                     const double __y = __param._M_s1 * std::abs(__n);
1576                     __reject = __y >= __param._M_d1;
1577                     if (!__reject)
1578                       {
1579                         const double __e = -std::log(1.0 - __aurng());
1580                         __x = std::floor(__y);
1581                         __v = -__e - __n * __n / 2 + __param._M_c;
1582                       }
1583                   }
1584                 else if (__u <= __a12)
1585                   {
1586                     const double __n = _M_nd(__urng);
1587                     const double __y = __param._M_s2 * std::abs(__n);
1588                     __reject = __y >= __param._M_d2;
1589                     if (!__reject)
1590                       {
1591                         const double __e = -std::log(1.0 - __aurng());
1592                         __x = std::floor(-__y);
1593                         __v = -__e - __n * __n / 2;
1594                       }
1595                   }
1596                 else if (__u <= __a123)
1597                   {
1598                     const double __e1 = -std::log(1.0 - __aurng());
1599                     const double __e2 = -std::log(1.0 - __aurng());
1600
1601                     const double __y = __param._M_d1
1602                                      + 2 * __s1s * __e1 / __param._M_d1;
1603                     __x = std::floor(__y);
1604                     __v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
1605                                                     -__y / (2 * __s1s)));
1606                     __reject = false;
1607                   }
1608                 else
1609                   {
1610                     const double __e1 = -std::log(1.0 - __aurng());
1611                     const double __e2 = -std::log(1.0 - __aurng());
1612
1613                     const double __y = __param._M_d2
1614                                      + 2 * __s2s * __e1 / __param._M_d2;
1615                     __x = std::floor(-__y);
1616                     __v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
1617                     __reject = false;
1618                   }
1619
1620                 __reject = __reject || __x < -__np || __x > __t - __np;
1621                 if (!__reject)
1622                   {
1623                     const double __lfx =
1624                       std::lgamma(__np + __x + 1)
1625                       + std::lgamma(__t - (__np + __x) + 1);
1626                     __reject = __v > __param._M_lf - __lfx
1627                              + __x * __param._M_lp1p;
1628                   }
1629
1630                 __reject |= __x + __np >= __thr;
1631               }
1632             while (__reject);
1633
1634             __x += __np + __naf;
1635
1636             const _IntType __z = _M_waiting(__urng, __t - _IntType(__x),
1637                                             __param._M_q);
1638             __ret = _IntType(__x) + __z;
1639           }
1640         else
1641 #endif
1642           __ret = _M_waiting(__urng, __t, __param._M_q);
1643
1644         if (__p12 != __p)
1645           __ret = __t - __ret;
1646         return __ret;
1647       }
1648
1649   template<typename _IntType>
1650     template<typename _ForwardIterator,
1651              typename _UniformRandomNumberGenerator>
1652       void
1653       binomial_distribution<_IntType>::
1654       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1655                       _UniformRandomNumberGenerator& __urng,
1656                       const param_type& __param)
1657       {
1658         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1659         // We could duplicate everything from operator()...
1660         while (__f != __t)
1661           *__f++ = this->operator()(__urng, __param);
1662       }
1663
1664   template<typename _IntType,
1665            typename _CharT, typename _Traits>
1666     std::basic_ostream<_CharT, _Traits>&
1667     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1668                const binomial_distribution<_IntType>& __x)
1669     {
1670       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1671       typedef typename __ostream_type::ios_base    __ios_base;
1672
1673       const typename __ios_base::fmtflags __flags = __os.flags();
1674       const _CharT __fill = __os.fill();
1675       const std::streamsize __precision = __os.precision();
1676       const _CharT __space = __os.widen(' ');
1677       __os.flags(__ios_base::scientific | __ios_base::left);
1678       __os.fill(__space);
1679       __os.precision(std::numeric_limits<double>::max_digits10);
1680
1681       __os << __x.t() << __space << __x.p()
1682            << __space << __x._M_nd;
1683
1684       __os.flags(__flags);
1685       __os.fill(__fill);
1686       __os.precision(__precision);
1687       return __os;
1688     }
1689
1690   template<typename _IntType,
1691            typename _CharT, typename _Traits>
1692     std::basic_istream<_CharT, _Traits>&
1693     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1694                binomial_distribution<_IntType>& __x)
1695     {
1696       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1697       typedef typename __istream_type::ios_base    __ios_base;
1698
1699       const typename __ios_base::fmtflags __flags = __is.flags();
1700       __is.flags(__ios_base::dec | __ios_base::skipws);
1701
1702       _IntType __t;
1703       double __p;
1704       __is >> __t >> __p >> __x._M_nd;
1705       __x.param(typename binomial_distribution<_IntType>::
1706                 param_type(__t, __p));
1707
1708       __is.flags(__flags);
1709       return __is;
1710     }
1711
1712
1713   template<typename _RealType>
1714     template<typename _ForwardIterator,
1715              typename _UniformRandomNumberGenerator>
1716       void
1717       std::exponential_distribution<_RealType>::
1718       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1719                       _UniformRandomNumberGenerator& __urng,
1720                       const param_type& __p)
1721       {
1722         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1723         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1724           __aurng(__urng);
1725         while (__f != __t)
1726           *__f++ = -std::log(result_type(1) - __aurng()) / __p.lambda();
1727       }
1728
1729   template<typename _RealType, typename _CharT, typename _Traits>
1730     std::basic_ostream<_CharT, _Traits>&
1731     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1732                const exponential_distribution<_RealType>& __x)
1733     {
1734       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1735       typedef typename __ostream_type::ios_base    __ios_base;
1736
1737       const typename __ios_base::fmtflags __flags = __os.flags();
1738       const _CharT __fill = __os.fill();
1739       const std::streamsize __precision = __os.precision();
1740       __os.flags(__ios_base::scientific | __ios_base::left);
1741       __os.fill(__os.widen(' '));
1742       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1743
1744       __os << __x.lambda();
1745
1746       __os.flags(__flags);
1747       __os.fill(__fill);
1748       __os.precision(__precision);
1749       return __os;
1750     }
1751
1752   template<typename _RealType, typename _CharT, typename _Traits>
1753     std::basic_istream<_CharT, _Traits>&
1754     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1755                exponential_distribution<_RealType>& __x)
1756     {
1757       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1758       typedef typename __istream_type::ios_base    __ios_base;
1759
1760       const typename __ios_base::fmtflags __flags = __is.flags();
1761       __is.flags(__ios_base::dec | __ios_base::skipws);
1762
1763       _RealType __lambda;
1764       __is >> __lambda;
1765       __x.param(typename exponential_distribution<_RealType>::
1766                 param_type(__lambda));
1767
1768       __is.flags(__flags);
1769       return __is;
1770     }
1771
1772
1773   /**
1774    * Polar method due to Marsaglia.
1775    *
1776    * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1777    * New York, 1986, Ch. V, Sect. 4.4.
1778    */
1779   template<typename _RealType>
1780     template<typename _UniformRandomNumberGenerator>
1781       typename normal_distribution<_RealType>::result_type
1782       normal_distribution<_RealType>::
1783       operator()(_UniformRandomNumberGenerator& __urng,
1784                  const param_type& __param)
1785       {
1786         result_type __ret;
1787         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1788           __aurng(__urng);
1789
1790         if (_M_saved_available)
1791           {
1792             _M_saved_available = false;
1793             __ret = _M_saved;
1794           }
1795         else
1796           {
1797             result_type __x, __y, __r2;
1798             do
1799               {
1800                 __x = result_type(2.0) * __aurng() - 1.0;
1801                 __y = result_type(2.0) * __aurng() - 1.0;
1802                 __r2 = __x * __x + __y * __y;
1803               }
1804             while (__r2 > 1.0 || __r2 == 0.0);
1805
1806             const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1807             _M_saved = __x * __mult;
1808             _M_saved_available = true;
1809             __ret = __y * __mult;
1810           }
1811
1812         __ret = __ret * __param.stddev() + __param.mean();
1813         return __ret;
1814       }
1815
1816   template<typename _RealType>
1817     template<typename _ForwardIterator,
1818              typename _UniformRandomNumberGenerator>
1819       void
1820       normal_distribution<_RealType>::
1821       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1822                       _UniformRandomNumberGenerator& __urng,
1823                       const param_type& __param)
1824       {
1825         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1826
1827         if (__f == __t)
1828           return;
1829
1830         if (_M_saved_available)
1831           {
1832             _M_saved_available = false;
1833             *__f++ = _M_saved * __param.stddev() + __param.mean();
1834
1835             if (__f == __t)
1836               return;
1837           }
1838
1839         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1840           __aurng(__urng);
1841
1842         while (__f + 1 < __t)
1843           {
1844             result_type __x, __y, __r2;
1845             do
1846               {
1847                 __x = result_type(2.0) * __aurng() - 1.0;
1848                 __y = result_type(2.0) * __aurng() - 1.0;
1849                 __r2 = __x * __x + __y * __y;
1850               }
1851             while (__r2 > 1.0 || __r2 == 0.0);
1852
1853             const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1854             *__f++ = __y * __mult * __param.stddev() + __param.mean();
1855             *__f++ = __x * __mult * __param.stddev() + __param.mean();
1856           }
1857
1858         if (__f != __t)
1859           {
1860             result_type __x, __y, __r2;
1861             do
1862               {
1863                 __x = result_type(2.0) * __aurng() - 1.0;
1864                 __y = result_type(2.0) * __aurng() - 1.0;
1865                 __r2 = __x * __x + __y * __y;
1866               }
1867             while (__r2 > 1.0 || __r2 == 0.0);
1868
1869             const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1870             _M_saved = __x * __mult;
1871             _M_saved_available = true;
1872             *__f = __y * __mult * __param.stddev() + __param.mean();
1873           }
1874       }
1875
1876   template<typename _RealType>
1877     bool
1878     operator==(const std::normal_distribution<_RealType>& __d1,
1879                const std::normal_distribution<_RealType>& __d2)
1880     {
1881       if (__d1._M_param == __d2._M_param
1882           && __d1._M_saved_available == __d2._M_saved_available)
1883         {
1884           if (__d1._M_saved_available
1885               && __d1._M_saved == __d2._M_saved)
1886             return true;
1887           else if(!__d1._M_saved_available)
1888             return true;
1889           else
1890             return false;
1891         }
1892       else
1893         return false;
1894     }
1895
1896   template<typename _RealType, typename _CharT, typename _Traits>
1897     std::basic_ostream<_CharT, _Traits>&
1898     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1899                const normal_distribution<_RealType>& __x)
1900     {
1901       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1902       typedef typename __ostream_type::ios_base    __ios_base;
1903
1904       const typename __ios_base::fmtflags __flags = __os.flags();
1905       const _CharT __fill = __os.fill();
1906       const std::streamsize __precision = __os.precision();
1907       const _CharT __space = __os.widen(' ');
1908       __os.flags(__ios_base::scientific | __ios_base::left);
1909       __os.fill(__space);
1910       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1911
1912       __os << __x.mean() << __space << __x.stddev()
1913            << __space << __x._M_saved_available;
1914       if (__x._M_saved_available)
1915         __os << __space << __x._M_saved;
1916
1917       __os.flags(__flags);
1918       __os.fill(__fill);
1919       __os.precision(__precision);
1920       return __os;
1921     }
1922
1923   template<typename _RealType, typename _CharT, typename _Traits>
1924     std::basic_istream<_CharT, _Traits>&
1925     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1926                normal_distribution<_RealType>& __x)
1927     {
1928       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1929       typedef typename __istream_type::ios_base    __ios_base;
1930
1931       const typename __ios_base::fmtflags __flags = __is.flags();
1932       __is.flags(__ios_base::dec | __ios_base::skipws);
1933
1934       double __mean, __stddev;
1935       __is >> __mean >> __stddev
1936            >> __x._M_saved_available;
1937       if (__x._M_saved_available)
1938         __is >> __x._M_saved;
1939       __x.param(typename normal_distribution<_RealType>::
1940                 param_type(__mean, __stddev));
1941
1942       __is.flags(__flags);
1943       return __is;
1944     }
1945
1946
1947   template<typename _RealType>
1948     template<typename _ForwardIterator,
1949              typename _UniformRandomNumberGenerator>
1950       void
1951       lognormal_distribution<_RealType>::
1952       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1953                       _UniformRandomNumberGenerator& __urng,
1954                       const param_type& __p)
1955       {
1956         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1957           while (__f != __t)
1958             *__f++ = std::exp(__p.s() * _M_nd(__urng) + __p.m());
1959       }
1960
1961   template<typename _RealType, typename _CharT, typename _Traits>
1962     std::basic_ostream<_CharT, _Traits>&
1963     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1964                const lognormal_distribution<_RealType>& __x)
1965     {
1966       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1967       typedef typename __ostream_type::ios_base    __ios_base;
1968
1969       const typename __ios_base::fmtflags __flags = __os.flags();
1970       const _CharT __fill = __os.fill();
1971       const std::streamsize __precision = __os.precision();
1972       const _CharT __space = __os.widen(' ');
1973       __os.flags(__ios_base::scientific | __ios_base::left);
1974       __os.fill(__space);
1975       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1976
1977       __os << __x.m() << __space << __x.s()
1978            << __space << __x._M_nd;
1979
1980       __os.flags(__flags);
1981       __os.fill(__fill);
1982       __os.precision(__precision);
1983       return __os;
1984     }
1985
1986   template<typename _RealType, typename _CharT, typename _Traits>
1987     std::basic_istream<_CharT, _Traits>&
1988     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1989                lognormal_distribution<_RealType>& __x)
1990     {
1991       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1992       typedef typename __istream_type::ios_base    __ios_base;
1993
1994       const typename __ios_base::fmtflags __flags = __is.flags();
1995       __is.flags(__ios_base::dec | __ios_base::skipws);
1996
1997       _RealType __m, __s;
1998       __is >> __m >> __s >> __x._M_nd;
1999       __x.param(typename lognormal_distribution<_RealType>::
2000                 param_type(__m, __s));
2001
2002       __is.flags(__flags);
2003       return __is;
2004     }
2005
2006   template<typename _RealType>
2007     template<typename _ForwardIterator,
2008              typename _UniformRandomNumberGenerator>
2009       void
2010       std::chi_squared_distribution<_RealType>::
2011       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2012                       _UniformRandomNumberGenerator& __urng)
2013       {
2014         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2015         while (__f != __t)
2016           *__f++ = 2 * _M_gd(__urng);
2017       }
2018
2019   template<typename _RealType>
2020     template<typename _ForwardIterator,
2021              typename _UniformRandomNumberGenerator>
2022       void
2023       std::chi_squared_distribution<_RealType>::
2024       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2025                       _UniformRandomNumberGenerator& __urng,
2026                       const typename
2027                       std::gamma_distribution<result_type>::param_type& __p)
2028       {
2029         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2030         while (__f != __t)
2031           *__f++ = 2 * _M_gd(__urng, __p);
2032       }
2033
2034   template<typename _RealType, typename _CharT, typename _Traits>
2035     std::basic_ostream<_CharT, _Traits>&
2036     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2037                const chi_squared_distribution<_RealType>& __x)
2038     {
2039       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2040       typedef typename __ostream_type::ios_base    __ios_base;
2041
2042       const typename __ios_base::fmtflags __flags = __os.flags();
2043       const _CharT __fill = __os.fill();
2044       const std::streamsize __precision = __os.precision();
2045       const _CharT __space = __os.widen(' ');
2046       __os.flags(__ios_base::scientific | __ios_base::left);
2047       __os.fill(__space);
2048       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2049
2050       __os << __x.n() << __space << __x._M_gd;
2051
2052       __os.flags(__flags);
2053       __os.fill(__fill);
2054       __os.precision(__precision);
2055       return __os;
2056     }
2057
2058   template<typename _RealType, typename _CharT, typename _Traits>
2059     std::basic_istream<_CharT, _Traits>&
2060     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2061                chi_squared_distribution<_RealType>& __x)
2062     {
2063       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2064       typedef typename __istream_type::ios_base    __ios_base;
2065
2066       const typename __ios_base::fmtflags __flags = __is.flags();
2067       __is.flags(__ios_base::dec | __ios_base::skipws);
2068
2069       _RealType __n;
2070       __is >> __n >> __x._M_gd;
2071       __x.param(typename chi_squared_distribution<_RealType>::
2072                 param_type(__n));
2073
2074       __is.flags(__flags);
2075       return __is;
2076     }
2077
2078
2079   template<typename _RealType>
2080     template<typename _UniformRandomNumberGenerator>
2081       typename cauchy_distribution<_RealType>::result_type
2082       cauchy_distribution<_RealType>::
2083       operator()(_UniformRandomNumberGenerator& __urng,
2084                  const param_type& __p)
2085       {
2086         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2087           __aurng(__urng);
2088         _RealType __u;
2089         do
2090           __u = __aurng();
2091         while (__u == 0.5);
2092
2093         const _RealType __pi = 3.1415926535897932384626433832795029L;
2094         return __p.a() + __p.b() * std::tan(__pi * __u);
2095       }
2096
2097   template<typename _RealType>
2098     template<typename _ForwardIterator,
2099              typename _UniformRandomNumberGenerator>
2100       void
2101       cauchy_distribution<_RealType>::
2102       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2103                       _UniformRandomNumberGenerator& __urng,
2104                       const param_type& __p)
2105       {
2106         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2107         const _RealType __pi = 3.1415926535897932384626433832795029L;
2108         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2109           __aurng(__urng);
2110         while (__f != __t)
2111           {
2112             _RealType __u;
2113             do
2114               __u = __aurng();
2115             while (__u == 0.5);
2116
2117             *__f++ = __p.a() + __p.b() * std::tan(__pi * __u);
2118           }
2119       }
2120
2121   template<typename _RealType, typename _CharT, typename _Traits>
2122     std::basic_ostream<_CharT, _Traits>&
2123     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2124                const cauchy_distribution<_RealType>& __x)
2125     {
2126       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2127       typedef typename __ostream_type::ios_base    __ios_base;
2128
2129       const typename __ios_base::fmtflags __flags = __os.flags();
2130       const _CharT __fill = __os.fill();
2131       const std::streamsize __precision = __os.precision();
2132       const _CharT __space = __os.widen(' ');
2133       __os.flags(__ios_base::scientific | __ios_base::left);
2134       __os.fill(__space);
2135       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2136
2137       __os << __x.a() << __space << __x.b();
2138
2139       __os.flags(__flags);
2140       __os.fill(__fill);
2141       __os.precision(__precision);
2142       return __os;
2143     }
2144
2145   template<typename _RealType, typename _CharT, typename _Traits>
2146     std::basic_istream<_CharT, _Traits>&
2147     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2148                cauchy_distribution<_RealType>& __x)
2149     {
2150       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2151       typedef typename __istream_type::ios_base    __ios_base;
2152
2153       const typename __ios_base::fmtflags __flags = __is.flags();
2154       __is.flags(__ios_base::dec | __ios_base::skipws);
2155
2156       _RealType __a, __b;
2157       __is >> __a >> __b;
2158       __x.param(typename cauchy_distribution<_RealType>::
2159                 param_type(__a, __b));
2160
2161       __is.flags(__flags);
2162       return __is;
2163     }
2164
2165
2166   template<typename _RealType>
2167     template<typename _ForwardIterator,
2168              typename _UniformRandomNumberGenerator>
2169       void
2170       std::fisher_f_distribution<_RealType>::
2171       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2172                       _UniformRandomNumberGenerator& __urng)
2173       {
2174         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2175         while (__f != __t)
2176           *__f++ = ((_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()));
2177       }
2178
2179   template<typename _RealType>
2180     template<typename _ForwardIterator,
2181              typename _UniformRandomNumberGenerator>
2182       void
2183       std::fisher_f_distribution<_RealType>::
2184       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2185                       _UniformRandomNumberGenerator& __urng,
2186                       const param_type& __p)
2187       {
2188         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2189         typedef typename std::gamma_distribution<result_type>::param_type
2190           param_type;
2191         param_type __p1(__p.m() / 2);
2192         param_type __p2(__p.n() / 2);
2193         while (__f != __t)
2194           *__f++ = ((_M_gd_x(__urng, __p1) * n())
2195                     / (_M_gd_y(__urng, __p2) * m()));
2196       }
2197
2198   template<typename _RealType, typename _CharT, typename _Traits>
2199     std::basic_ostream<_CharT, _Traits>&
2200     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2201                const fisher_f_distribution<_RealType>& __x)
2202     {
2203       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2204       typedef typename __ostream_type::ios_base    __ios_base;
2205
2206       const typename __ios_base::fmtflags __flags = __os.flags();
2207       const _CharT __fill = __os.fill();
2208       const std::streamsize __precision = __os.precision();
2209       const _CharT __space = __os.widen(' ');
2210       __os.flags(__ios_base::scientific | __ios_base::left);
2211       __os.fill(__space);
2212       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2213
2214       __os << __x.m() << __space << __x.n()
2215            << __space << __x._M_gd_x << __space << __x._M_gd_y;
2216
2217       __os.flags(__flags);
2218       __os.fill(__fill);
2219       __os.precision(__precision);
2220       return __os;
2221     }
2222
2223   template<typename _RealType, typename _CharT, typename _Traits>
2224     std::basic_istream<_CharT, _Traits>&
2225     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2226                fisher_f_distribution<_RealType>& __x)
2227     {
2228       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2229       typedef typename __istream_type::ios_base    __ios_base;
2230
2231       const typename __ios_base::fmtflags __flags = __is.flags();
2232       __is.flags(__ios_base::dec | __ios_base::skipws);
2233
2234       _RealType __m, __n;
2235       __is >> __m >> __n >> __x._M_gd_x >> __x._M_gd_y;
2236       __x.param(typename fisher_f_distribution<_RealType>::
2237                 param_type(__m, __n));
2238
2239       __is.flags(__flags);
2240       return __is;
2241     }
2242
2243
2244   template<typename _RealType>
2245     template<typename _ForwardIterator,
2246              typename _UniformRandomNumberGenerator>
2247       void
2248       std::student_t_distribution<_RealType>::
2249       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2250                       _UniformRandomNumberGenerator& __urng)
2251       {
2252         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2253         while (__f != __t)
2254           *__f++ = _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng));
2255       }
2256
2257   template<typename _RealType>
2258     template<typename _ForwardIterator,
2259              typename _UniformRandomNumberGenerator>
2260       void
2261       std::student_t_distribution<_RealType>::
2262       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2263                       _UniformRandomNumberGenerator& __urng,
2264                       const param_type& __p)
2265       {
2266         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2267         typename std::gamma_distribution<result_type>::param_type
2268           __p2(__p.n() / 2, 2);
2269         while (__f != __t)
2270           *__f++ =  _M_nd(__urng) * std::sqrt(__p.n() / _M_gd(__urng, __p2));
2271       }
2272
2273   template<typename _RealType, typename _CharT, typename _Traits>
2274     std::basic_ostream<_CharT, _Traits>&
2275     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2276                const student_t_distribution<_RealType>& __x)
2277     {
2278       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2279       typedef typename __ostream_type::ios_base    __ios_base;
2280
2281       const typename __ios_base::fmtflags __flags = __os.flags();
2282       const _CharT __fill = __os.fill();
2283       const std::streamsize __precision = __os.precision();
2284       const _CharT __space = __os.widen(' ');
2285       __os.flags(__ios_base::scientific | __ios_base::left);
2286       __os.fill(__space);
2287       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2288
2289       __os << __x.n() << __space << __x._M_nd << __space << __x._M_gd;
2290
2291       __os.flags(__flags);
2292       __os.fill(__fill);
2293       __os.precision(__precision);
2294       return __os;
2295     }
2296
2297   template<typename _RealType, typename _CharT, typename _Traits>
2298     std::basic_istream<_CharT, _Traits>&
2299     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2300                student_t_distribution<_RealType>& __x)
2301     {
2302       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2303       typedef typename __istream_type::ios_base    __ios_base;
2304
2305       const typename __ios_base::fmtflags __flags = __is.flags();
2306       __is.flags(__ios_base::dec | __ios_base::skipws);
2307
2308       _RealType __n;
2309       __is >> __n >> __x._M_nd >> __x._M_gd;
2310       __x.param(typename student_t_distribution<_RealType>::param_type(__n));
2311
2312       __is.flags(__flags);
2313       return __is;
2314     }
2315
2316
2317   template<typename _RealType>
2318     void
2319     gamma_distribution<_RealType>::param_type::
2320     _M_initialize()
2321     {
2322       _M_malpha = _M_alpha < 1.0 ? _M_alpha + _RealType(1.0) : _M_alpha;
2323
2324       const _RealType __a1 = _M_malpha - _RealType(1.0) / _RealType(3.0);
2325       _M_a2 = _RealType(1.0) / std::sqrt(_RealType(9.0) * __a1);
2326     }
2327
2328   /**
2329    * Marsaglia, G. and Tsang, W. W.
2330    * "A Simple Method for Generating Gamma Variables"
2331    * ACM Transactions on Mathematical Software, 26, 3, 363-372, 2000.
2332    */
2333   template<typename _RealType>
2334     template<typename _UniformRandomNumberGenerator>
2335       typename gamma_distribution<_RealType>::result_type
2336       gamma_distribution<_RealType>::
2337       operator()(_UniformRandomNumberGenerator& __urng,
2338                  const param_type& __param)
2339       {
2340         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2341           __aurng(__urng);
2342
2343         result_type __u, __v, __n;
2344         const result_type __a1 = (__param._M_malpha
2345                                   - _RealType(1.0) / _RealType(3.0));
2346
2347         do
2348           {
2349             do
2350               {
2351                 __n = _M_nd(__urng);
2352                 __v = result_type(1.0) + __param._M_a2 * __n;
2353               }
2354             while (__v <= 0.0);
2355
2356             __v = __v * __v * __v;
2357             __u = __aurng();
2358           }
2359         while (__u > result_type(1.0) - 0.331 * __n * __n * __n * __n
2360                && (std::log(__u) > (0.5 * __n * __n + __a1
2361                                     * (1.0 - __v + std::log(__v)))));
2362
2363         if (__param.alpha() == __param._M_malpha)
2364           return __a1 * __v * __param.beta();
2365         else
2366           {
2367             do
2368               __u = __aurng();
2369             while (__u == 0.0);
2370
2371             return (std::pow(__u, result_type(1.0) / __param.alpha())
2372                     * __a1 * __v * __param.beta());
2373           }
2374       }
2375
2376   template<typename _RealType>
2377     template<typename _ForwardIterator,
2378              typename _UniformRandomNumberGenerator>
2379       void
2380       gamma_distribution<_RealType>::
2381       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2382                       _UniformRandomNumberGenerator& __urng,
2383                       const param_type& __param)
2384       {
2385         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2386         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2387           __aurng(__urng);
2388
2389         result_type __u, __v, __n;
2390         const result_type __a1 = (__param._M_malpha
2391                                   - _RealType(1.0) / _RealType(3.0));
2392
2393         if (__param.alpha() == __param._M_malpha)
2394           while (__f != __t)
2395             {
2396               do
2397                 {
2398                   do
2399                     {
2400                       __n = _M_nd(__urng);
2401                       __v = result_type(1.0) + __param._M_a2 * __n;
2402                     }
2403                   while (__v <= 0.0);
2404
2405                   __v = __v * __v * __v;
2406                   __u = __aurng();
2407                 }
2408               while (__u > result_type(1.0) - 0.331 * __n * __n * __n * __n
2409                      && (std::log(__u) > (0.5 * __n * __n + __a1
2410                                           * (1.0 - __v + std::log(__v)))));
2411
2412               *__f++ = __a1 * __v * __param.beta();
2413             }
2414         else
2415           while (__f != __t)
2416             {
2417               do
2418                 {
2419                   do
2420                     {
2421                       __n = _M_nd(__urng);
2422                       __v = result_type(1.0) + __param._M_a2 * __n;
2423                     }
2424                   while (__v <= 0.0);
2425
2426                   __v = __v * __v * __v;
2427                   __u = __aurng();
2428                 }
2429               while (__u > result_type(1.0) - 0.331 * __n * __n * __n * __n
2430                      && (std::log(__u) > (0.5 * __n * __n + __a1
2431                                           * (1.0 - __v + std::log(__v)))));
2432
2433               do
2434                 __u = __aurng();
2435               while (__u == 0.0);
2436
2437               *__f++ = (std::pow(__u, result_type(1.0) / __param.alpha())
2438                         * __a1 * __v * __param.beta());
2439             }
2440       }
2441
2442   template<typename _RealType, typename _CharT, typename _Traits>
2443     std::basic_ostream<_CharT, _Traits>&
2444     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2445                const gamma_distribution<_RealType>& __x)
2446     {
2447       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2448       typedef typename __ostream_type::ios_base    __ios_base;
2449
2450       const typename __ios_base::fmtflags __flags = __os.flags();
2451       const _CharT __fill = __os.fill();
2452       const std::streamsize __precision = __os.precision();
2453       const _CharT __space = __os.widen(' ');
2454       __os.flags(__ios_base::scientific | __ios_base::left);
2455       __os.fill(__space);
2456       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2457
2458       __os << __x.alpha() << __space << __x.beta()
2459            << __space << __x._M_nd;
2460
2461       __os.flags(__flags);
2462       __os.fill(__fill);
2463       __os.precision(__precision);
2464       return __os;
2465     }
2466
2467   template<typename _RealType, typename _CharT, typename _Traits>
2468     std::basic_istream<_CharT, _Traits>&
2469     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2470                gamma_distribution<_RealType>& __x)
2471     {
2472       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2473       typedef typename __istream_type::ios_base    __ios_base;
2474
2475       const typename __ios_base::fmtflags __flags = __is.flags();
2476       __is.flags(__ios_base::dec | __ios_base::skipws);
2477
2478       _RealType __alpha_val, __beta_val;
2479       __is >> __alpha_val >> __beta_val >> __x._M_nd;
2480       __x.param(typename gamma_distribution<_RealType>::
2481                 param_type(__alpha_val, __beta_val));
2482
2483       __is.flags(__flags);
2484       return __is;
2485     }
2486
2487
2488   template<typename _RealType>
2489     template<typename _UniformRandomNumberGenerator>
2490       typename weibull_distribution<_RealType>::result_type
2491       weibull_distribution<_RealType>::
2492       operator()(_UniformRandomNumberGenerator& __urng,
2493                  const param_type& __p)
2494       {
2495         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2496           __aurng(__urng);
2497         return __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2498                                   result_type(1) / __p.a());
2499       }
2500
2501   template<typename _RealType>
2502     template<typename _ForwardIterator,
2503              typename _UniformRandomNumberGenerator>
2504       void
2505       weibull_distribution<_RealType>::
2506       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2507                       _UniformRandomNumberGenerator& __urng,
2508                       const param_type& __p)
2509       {
2510         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2511         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2512           __aurng(__urng);
2513         auto __inv_a = result_type(1) / __p.a();
2514
2515         while (__f != __t)
2516           *__f++ = __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2517                                       __inv_a);
2518       }
2519
2520   template<typename _RealType, typename _CharT, typename _Traits>
2521     std::basic_ostream<_CharT, _Traits>&
2522     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2523                const weibull_distribution<_RealType>& __x)
2524     {
2525       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2526       typedef typename __ostream_type::ios_base    __ios_base;
2527
2528       const typename __ios_base::fmtflags __flags = __os.flags();
2529       const _CharT __fill = __os.fill();
2530       const std::streamsize __precision = __os.precision();
2531       const _CharT __space = __os.widen(' ');
2532       __os.flags(__ios_base::scientific | __ios_base::left);
2533       __os.fill(__space);
2534       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2535
2536       __os << __x.a() << __space << __x.b();
2537
2538       __os.flags(__flags);
2539       __os.fill(__fill);
2540       __os.precision(__precision);
2541       return __os;
2542     }
2543
2544   template<typename _RealType, typename _CharT, typename _Traits>
2545     std::basic_istream<_CharT, _Traits>&
2546     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2547                weibull_distribution<_RealType>& __x)
2548     {
2549       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2550       typedef typename __istream_type::ios_base    __ios_base;
2551
2552       const typename __ios_base::fmtflags __flags = __is.flags();
2553       __is.flags(__ios_base::dec | __ios_base::skipws);
2554
2555       _RealType __a, __b;
2556       __is >> __a >> __b;
2557       __x.param(typename weibull_distribution<_RealType>::
2558                 param_type(__a, __b));
2559
2560       __is.flags(__flags);
2561       return __is;
2562     }
2563
2564
2565   template<typename _RealType>
2566     template<typename _UniformRandomNumberGenerator>
2567       typename extreme_value_distribution<_RealType>::result_type
2568       extreme_value_distribution<_RealType>::
2569       operator()(_UniformRandomNumberGenerator& __urng,
2570                  const param_type& __p)
2571       {
2572         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2573           __aurng(__urng);
2574         return __p.a() - __p.b() * std::log(-std::log(result_type(1)
2575                                                       - __aurng()));
2576       }
2577
2578   template<typename _RealType>
2579     template<typename _ForwardIterator,
2580              typename _UniformRandomNumberGenerator>
2581       void
2582       extreme_value_distribution<_RealType>::
2583       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2584                       _UniformRandomNumberGenerator& __urng,
2585                       const param_type& __p)
2586       {
2587         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2588         __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2589           __aurng(__urng);
2590
2591         while (__f != __t)
2592           *__f++ = __p.a() - __p.b() * std::log(-std::log(result_type(1)
2593                                                           - __aurng()));
2594       }
2595
2596   template<typename _RealType, typename _CharT, typename _Traits>
2597     std::basic_ostream<_CharT, _Traits>&
2598     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2599                const extreme_value_distribution<_RealType>& __x)
2600     {
2601       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2602       typedef typename __ostream_type::ios_base    __ios_base;
2603
2604       const typename __ios_base::fmtflags __flags = __os.flags();
2605       const _CharT __fill = __os.fill();
2606       const std::streamsize __precision = __os.precision();
2607       const _CharT __space = __os.widen(' ');
2608       __os.flags(__ios_base::scientific | __ios_base::left);
2609       __os.fill(__space);
2610       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2611
2612       __os << __x.a() << __space << __x.b();
2613
2614       __os.flags(__flags);
2615       __os.fill(__fill);
2616       __os.precision(__precision);
2617       return __os;
2618     }
2619
2620   template<typename _RealType, typename _CharT, typename _Traits>
2621     std::basic_istream<_CharT, _Traits>&
2622     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2623                extreme_value_distribution<_RealType>& __x)
2624     {
2625       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2626       typedef typename __istream_type::ios_base    __ios_base;
2627
2628       const typename __ios_base::fmtflags __flags = __is.flags();
2629       __is.flags(__ios_base::dec | __ios_base::skipws);
2630
2631       _RealType __a, __b;
2632       __is >> __a >> __b;
2633       __x.param(typename extreme_value_distribution<_RealType>::
2634                 param_type(__a, __b));
2635
2636       __is.flags(__flags);
2637       return __is;
2638     }
2639
2640
2641   template<typename _IntType>
2642     void
2643     discrete_distribution<_IntType>::param_type::
2644     _M_initialize()
2645     {
2646       if (_M_prob.size() < 2)
2647         {
2648           _M_prob.clear();
2649           return;
2650         }
2651
2652       const double __sum = std::accumulate(_M_prob.begin(),
2653                                            _M_prob.end(), 0.0);
2654       // Now normalize the probabilites.
2655       __detail::__normalize(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
2656                             __sum);
2657       // Accumulate partial sums.
2658       _M_cp.reserve(_M_prob.size());
2659       std::partial_sum(_M_prob.begin(), _M_prob.end(),
2660                        std::back_inserter(_M_cp));
2661       // Make sure the last cumulative probability is one.
2662       _M_cp[_M_cp.size() - 1] = 1.0;
2663     }
2664
2665   template<typename _IntType>
2666     template<typename _Func>
2667       discrete_distribution<_IntType>::param_type::
2668       param_type(size_t __nw, double __xmin, double __xmax, _Func __fw)
2669       : _M_prob(), _M_cp()
2670       {
2671         const size_t __n = __nw == 0 ? 1 : __nw;
2672         const double __delta = (__xmax - __xmin) / __n;
2673
2674         _M_prob.reserve(__n);
2675         for (size_t __k = 0; __k < __nw; ++__k)
2676           _M_prob.push_back(__fw(__xmin + __k * __delta + 0.5 * __delta));
2677
2678         _M_initialize();
2679       }
2680
2681   template<typename _IntType>
2682     template<typename _UniformRandomNumberGenerator>
2683       typename discrete_distribution<_IntType>::result_type
2684       discrete_distribution<_IntType>::
2685       operator()(_UniformRandomNumberGenerator& __urng,
2686                  const param_type& __param)
2687       {
2688         if (__param._M_cp.empty())
2689           return result_type(0);
2690
2691         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2692           __aurng(__urng);
2693
2694         const double __p = __aurng();
2695         auto __pos = std::lower_bound(__param._M_cp.begin(),
2696                                       __param._M_cp.end(), __p);
2697
2698         return __pos - __param._M_cp.begin();
2699       }
2700
2701   template<typename _IntType>
2702     template<typename _ForwardIterator,
2703              typename _UniformRandomNumberGenerator>
2704       void
2705       discrete_distribution<_IntType>::
2706       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2707                       _UniformRandomNumberGenerator& __urng,
2708                       const param_type& __param)
2709       {
2710         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2711
2712         if (__param._M_cp.empty())
2713           {
2714             while (__f != __t)
2715               *__f++ = result_type(0);
2716             return;
2717           }
2718
2719         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2720           __aurng(__urng);
2721
2722         while (__f != __t)
2723           {
2724             const double __p = __aurng();
2725             auto __pos = std::lower_bound(__param._M_cp.begin(),
2726                                           __param._M_cp.end(), __p);
2727
2728             *__f++ = __pos - __param._M_cp.begin();
2729           }
2730       }
2731
2732   template<typename _IntType, typename _CharT, typename _Traits>
2733     std::basic_ostream<_CharT, _Traits>&
2734     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2735                const discrete_distribution<_IntType>& __x)
2736     {
2737       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2738       typedef typename __ostream_type::ios_base    __ios_base;
2739
2740       const typename __ios_base::fmtflags __flags = __os.flags();
2741       const _CharT __fill = __os.fill();
2742       const std::streamsize __precision = __os.precision();
2743       const _CharT __space = __os.widen(' ');
2744       __os.flags(__ios_base::scientific | __ios_base::left);
2745       __os.fill(__space);
2746       __os.precision(std::numeric_limits<double>::max_digits10);
2747
2748       std::vector<double> __prob = __x.probabilities();
2749       __os << __prob.size();
2750       for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
2751         __os << __space << *__dit;
2752
2753       __os.flags(__flags);
2754       __os.fill(__fill);
2755       __os.precision(__precision);
2756       return __os;
2757     }
2758
2759   template<typename _IntType, typename _CharT, typename _Traits>
2760     std::basic_istream<_CharT, _Traits>&
2761     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2762                discrete_distribution<_IntType>& __x)
2763     {
2764       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2765       typedef typename __istream_type::ios_base    __ios_base;
2766
2767       const typename __ios_base::fmtflags __flags = __is.flags();
2768       __is.flags(__ios_base::dec | __ios_base::skipws);
2769
2770       size_t __n;
2771       __is >> __n;
2772
2773       std::vector<double> __prob_vec;
2774       __prob_vec.reserve(__n);
2775       for (; __n != 0; --__n)
2776         {
2777           double __prob;
2778           __is >> __prob;
2779           __prob_vec.push_back(__prob);
2780         }
2781
2782       __x.param(typename discrete_distribution<_IntType>::
2783                 param_type(__prob_vec.begin(), __prob_vec.end()));
2784
2785       __is.flags(__flags);
2786       return __is;
2787     }
2788
2789
2790   template<typename _RealType>
2791     void
2792     piecewise_constant_distribution<_RealType>::param_type::
2793     _M_initialize()
2794     {
2795       if (_M_int.size() < 2
2796           || (_M_int.size() == 2
2797               && _M_int[0] == _RealType(0)
2798               && _M_int[1] == _RealType(1)))
2799         {
2800           _M_int.clear();
2801           _M_den.clear();
2802           return;
2803         }
2804
2805       const double __sum = std::accumulate(_M_den.begin(),
2806                                            _M_den.end(), 0.0);
2807
2808       __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
2809                             __sum);
2810
2811       _M_cp.reserve(_M_den.size());
2812       std::partial_sum(_M_den.begin(), _M_den.end(),
2813                        std::back_inserter(_M_cp));
2814
2815       // Make sure the last cumulative probability is one.
2816       _M_cp[_M_cp.size() - 1] = 1.0;
2817
2818       for (size_t __k = 0; __k < _M_den.size(); ++__k)
2819         _M_den[__k] /= _M_int[__k + 1] - _M_int[__k];
2820     }
2821
2822   template<typename _RealType>
2823     template<typename _InputIteratorB, typename _InputIteratorW>
2824       piecewise_constant_distribution<_RealType>::param_type::
2825       param_type(_InputIteratorB __bbegin,
2826                  _InputIteratorB __bend,
2827                  _InputIteratorW __wbegin)
2828       : _M_int(), _M_den(), _M_cp()
2829       {
2830         if (__bbegin != __bend)
2831           {
2832             for (;;)
2833               {
2834                 _M_int.push_back(*__bbegin);
2835                 ++__bbegin;
2836                 if (__bbegin == __bend)
2837                   break;
2838
2839                 _M_den.push_back(*__wbegin);
2840                 ++__wbegin;
2841               }
2842           }
2843
2844         _M_initialize();
2845       }
2846
2847   template<typename _RealType>
2848     template<typename _Func>
2849       piecewise_constant_distribution<_RealType>::param_type::
2850       param_type(initializer_list<_RealType> __bl, _Func __fw)
2851       : _M_int(), _M_den(), _M_cp()
2852       {
2853         _M_int.reserve(__bl.size());
2854         for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
2855           _M_int.push_back(*__biter);
2856
2857         _M_den.reserve(_M_int.size() - 1);
2858         for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
2859           _M_den.push_back(__fw(0.5 * (_M_int[__k + 1] + _M_int[__k])));
2860
2861         _M_initialize();
2862       }
2863
2864   template<typename _RealType>
2865     template<typename _Func>
2866       piecewise_constant_distribution<_RealType>::param_type::
2867       param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
2868       : _M_int(), _M_den(), _M_cp()
2869       {
2870         const size_t __n = __nw == 0 ? 1 : __nw;
2871         const _RealType __delta = (__xmax - __xmin) / __n;
2872
2873         _M_int.reserve(__n + 1);
2874         for (size_t __k = 0; __k <= __nw; ++__k)
2875           _M_int.push_back(__xmin + __k * __delta);
2876
2877         _M_den.reserve(__n);
2878         for (size_t __k = 0; __k < __nw; ++__k)
2879           _M_den.push_back(__fw(_M_int[__k] + 0.5 * __delta));
2880
2881         _M_initialize();
2882       }
2883
2884   template<typename _RealType>
2885     template<typename _UniformRandomNumberGenerator>
2886       typename piecewise_constant_distribution<_RealType>::result_type
2887       piecewise_constant_distribution<_RealType>::
2888       operator()(_UniformRandomNumberGenerator& __urng,
2889                  const param_type& __param)
2890       {
2891         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2892           __aurng(__urng);
2893
2894         const double __p = __aurng();
2895         if (__param._M_cp.empty())
2896           return __p;
2897
2898         auto __pos = std::lower_bound(__param._M_cp.begin(),
2899                                       __param._M_cp.end(), __p);
2900         const size_t __i = __pos - __param._M_cp.begin();
2901
2902         const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2903
2904         return __param._M_int[__i] + (__p - __pref) / __param._M_den[__i];
2905       }
2906
2907   template<typename _RealType>
2908     template<typename _ForwardIterator,
2909              typename _UniformRandomNumberGenerator>
2910       void
2911       piecewise_constant_distribution<_RealType>::
2912       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2913                       _UniformRandomNumberGenerator& __urng,
2914                       const param_type& __param)
2915       {
2916         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2917         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2918           __aurng(__urng);
2919
2920         if (__param._M_cp.empty())
2921           {
2922             while (__f != __t)
2923               *__f++ = __aurng();
2924             return;
2925           }
2926
2927         while (__f != __t)
2928           {
2929             const double __p = __aurng();
2930
2931             auto __pos = std::lower_bound(__param._M_cp.begin(),
2932                                           __param._M_cp.end(), __p);
2933             const size_t __i = __pos - __param._M_cp.begin();
2934
2935             const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2936
2937             *__f++ = (__param._M_int[__i]
2938                       + (__p - __pref) / __param._M_den[__i]);
2939           }
2940       }
2941
2942   template<typename _RealType, typename _CharT, typename _Traits>
2943     std::basic_ostream<_CharT, _Traits>&
2944     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2945                const piecewise_constant_distribution<_RealType>& __x)
2946     {
2947       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
2948       typedef typename __ostream_type::ios_base    __ios_base;
2949
2950       const typename __ios_base::fmtflags __flags = __os.flags();
2951       const _CharT __fill = __os.fill();
2952       const std::streamsize __precision = __os.precision();
2953       const _CharT __space = __os.widen(' ');
2954       __os.flags(__ios_base::scientific | __ios_base::left);
2955       __os.fill(__space);
2956       __os.precision(std::numeric_limits<_RealType>::max_digits10);
2957
2958       std::vector<_RealType> __int = __x.intervals();
2959       __os << __int.size() - 1;
2960
2961       for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
2962         __os << __space << *__xit;
2963
2964       std::vector<double> __den = __x.densities();
2965       for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
2966         __os << __space << *__dit;
2967
2968       __os.flags(__flags);
2969       __os.fill(__fill);
2970       __os.precision(__precision);
2971       return __os;
2972     }
2973
2974   template<typename _RealType, typename _CharT, typename _Traits>
2975     std::basic_istream<_CharT, _Traits>&
2976     operator>>(std::basic_istream<_CharT, _Traits>& __is,
2977                piecewise_constant_distribution<_RealType>& __x)
2978     {
2979       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
2980       typedef typename __istream_type::ios_base    __ios_base;
2981
2982       const typename __ios_base::fmtflags __flags = __is.flags();
2983       __is.flags(__ios_base::dec | __ios_base::skipws);
2984
2985       size_t __n;
2986       __is >> __n;
2987
2988       std::vector<_RealType> __int_vec;
2989       __int_vec.reserve(__n + 1);
2990       for (size_t __i = 0; __i <= __n; ++__i)
2991         {
2992           _RealType __int;
2993           __is >> __int;
2994           __int_vec.push_back(__int);
2995         }
2996
2997       std::vector<double> __den_vec;
2998       __den_vec.reserve(__n);
2999       for (size_t __i = 0; __i < __n; ++__i)
3000         {
3001           double __den;
3002           __is >> __den;
3003           __den_vec.push_back(__den);
3004         }
3005
3006       __x.param(typename piecewise_constant_distribution<_RealType>::
3007           param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));
3008
3009       __is.flags(__flags);
3010       return __is;
3011     }
3012
3013
3014   template<typename _RealType>
3015     void
3016     piecewise_linear_distribution<_RealType>::param_type::
3017     _M_initialize()
3018     {
3019       if (_M_int.size() < 2
3020           || (_M_int.size() == 2
3021               && _M_int[0] == _RealType(0)
3022               && _M_int[1] == _RealType(1)
3023               && _M_den[0] == _M_den[1]))
3024         {
3025           _M_int.clear();
3026           _M_den.clear();
3027           return;
3028         }
3029
3030       double __sum = 0.0;
3031       _M_cp.reserve(_M_int.size() - 1);
3032       _M_m.reserve(_M_int.size() - 1);
3033       for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
3034         {
3035           const _RealType __delta = _M_int[__k + 1] - _M_int[__k];
3036           __sum += 0.5 * (_M_den[__k + 1] + _M_den[__k]) * __delta;
3037           _M_cp.push_back(__sum);
3038           _M_m.push_back((_M_den[__k + 1] - _M_den[__k]) / __delta);
3039         }
3040
3041       //  Now normalize the densities...
3042       __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
3043                             __sum);
3044       //  ... and partial sums...
3045       __detail::__normalize(_M_cp.begin(), _M_cp.end(), _M_cp.begin(), __sum);
3046       //  ... and slopes.
3047       __detail::__normalize(_M_m.begin(), _M_m.end(), _M_m.begin(), __sum);
3048
3049       //  Make sure the last cumulative probablility is one.
3050       _M_cp[_M_cp.size() - 1] = 1.0;
3051      }
3052
3053   template<typename _RealType>
3054     template<typename _InputIteratorB, typename _InputIteratorW>
3055       piecewise_linear_distribution<_RealType>::param_type::
3056       param_type(_InputIteratorB __bbegin,
3057                  _InputIteratorB __bend,
3058                  _InputIteratorW __wbegin)
3059       : _M_int(), _M_den(), _M_cp(), _M_m()
3060       {
3061         for (; __bbegin != __bend; ++__bbegin, ++__wbegin)
3062           {
3063             _M_int.push_back(*__bbegin);
3064             _M_den.push_back(*__wbegin);
3065           }
3066
3067         _M_initialize();
3068       }
3069
3070   template<typename _RealType>
3071     template<typename _Func>
3072       piecewise_linear_distribution<_RealType>::param_type::
3073       param_type(initializer_list<_RealType> __bl, _Func __fw)
3074       : _M_int(), _M_den(), _M_cp(), _M_m()
3075       {
3076         _M_int.reserve(__bl.size());
3077         _M_den.reserve(__bl.size());
3078         for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
3079           {
3080             _M_int.push_back(*__biter);
3081             _M_den.push_back(__fw(*__biter));
3082           }
3083
3084         _M_initialize();
3085       }
3086
3087   template<typename _RealType>
3088     template<typename _Func>
3089       piecewise_linear_distribution<_RealType>::param_type::
3090       param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
3091       : _M_int(), _M_den(), _M_cp(), _M_m()
3092       {
3093         const size_t __n = __nw == 0 ? 1 : __nw;
3094         const _RealType __delta = (__xmax - __xmin) / __n;
3095
3096         _M_int.reserve(__n + 1);
3097         _M_den.reserve(__n + 1);
3098         for (size_t __k = 0; __k <= __nw; ++__k)
3099           {
3100             _M_int.push_back(__xmin + __k * __delta);
3101             _M_den.push_back(__fw(_M_int[__k] + __delta));
3102           }
3103
3104         _M_initialize();
3105       }
3106
3107   template<typename _RealType>
3108     template<typename _UniformRandomNumberGenerator>
3109       typename piecewise_linear_distribution<_RealType>::result_type
3110       piecewise_linear_distribution<_RealType>::
3111       operator()(_UniformRandomNumberGenerator& __urng,
3112                  const param_type& __param)
3113       {
3114         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
3115           __aurng(__urng);
3116
3117         const double __p = __aurng();
3118         if (__param._M_cp.empty())
3119           return __p;
3120
3121         auto __pos = std::lower_bound(__param._M_cp.begin(),
3122                                       __param._M_cp.end(), __p);
3123         const size_t __i = __pos - __param._M_cp.begin();
3124
3125         const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
3126
3127         const double __a = 0.5 * __param._M_m[__i];
3128         const double __b = __param._M_den[__i];
3129         const double __cm = __p - __pref;
3130
3131         _RealType __x = __param._M_int[__i];
3132         if (__a == 0)
3133           __x += __cm / __b;
3134         else
3135           {
3136             const double __d = __b * __b + 4.0 * __a * __cm;
3137             __x += 0.5 * (std::sqrt(__d) - __b) / __a;
3138           }
3139
3140         return __x;
3141       }
3142
3143   template<typename _RealType>
3144     template<typename _ForwardIterator,
3145              typename _UniformRandomNumberGenerator>
3146       void
3147       piecewise_linear_distribution<_RealType>::
3148       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3149                       _UniformRandomNumberGenerator& __urng,
3150                       const param_type& __param)
3151       {
3152         __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
3153         // We could duplicate everything from operator()...
3154         while (__f != __t)
3155           *__f++ = this->operator()(__urng, __param);
3156       }
3157
3158   template<typename _RealType, typename _CharT, typename _Traits>
3159     std::basic_ostream<_CharT, _Traits>&
3160     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3161                const piecewise_linear_distribution<_RealType>& __x)
3162     {
3163       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
3164       typedef typename __ostream_type::ios_base    __ios_base;
3165
3166       const typename __ios_base::fmtflags __flags = __os.flags();
3167       const _CharT __fill = __os.fill();
3168       const std::streamsize __precision = __os.precision();
3169       const _CharT __space = __os.widen(' ');
3170       __os.flags(__ios_base::scientific | __ios_base::left);
3171       __os.fill(__space);
3172       __os.precision(std::numeric_limits<_RealType>::max_digits10);
3173
3174       std::vector<_RealType> __int = __x.intervals();
3175       __os << __int.size() - 1;
3176
3177       for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
3178         __os << __space << *__xit;
3179
3180       std::vector<double> __den = __x.densities();
3181       for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
3182         __os << __space << *__dit;
3183
3184       __os.flags(__flags);
3185       __os.fill(__fill);
3186       __os.precision(__precision);
3187       return __os;
3188     }
3189
3190   template<typename _RealType, typename _CharT, typename _Traits>
3191     std::basic_istream<_CharT, _Traits>&
3192     operator>>(std::basic_istream<_CharT, _Traits>& __is,
3193                piecewise_linear_distribution<_RealType>& __x)
3194     {
3195       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
3196       typedef typename __istream_type::ios_base    __ios_base;
3197
3198       const typename __ios_base::fmtflags __flags = __is.flags();
3199       __is.flags(__ios_base::dec | __ios_base::skipws);
3200
3201       size_t __n;
3202       __is >> __n;
3203
3204       std::vector<_RealType> __int_vec;
3205       __int_vec.reserve(__n + 1);
3206       for (size_t __i = 0; __i <= __n; ++__i)
3207         {
3208           _RealType __int;
3209           __is >> __int;
3210           __int_vec.push_back(__int);
3211         }
3212
3213       std::vector<double> __den_vec;
3214       __den_vec.reserve(__n + 1);
3215       for (size_t __i = 0; __i <= __n; ++__i)
3216         {
3217           double __den;
3218           __is >> __den;
3219           __den_vec.push_back(__den);
3220         }
3221
3222       __x.param(typename piecewise_linear_distribution<_RealType>::
3223           param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));
3224
3225       __is.flags(__flags);
3226       return __is;
3227     }
3228
3229
3230   template<typename _IntType>
3231     seed_seq::seed_seq(std::initializer_list<_IntType> __il)
3232     {
3233       for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
3234         _M_v.push_back(__detail::__mod<result_type,
3235                        __detail::_Shift<result_type, 32>::__value>(*__iter));
3236     }
3237
3238   template<typename _InputIterator>
3239     seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
3240     {
3241       for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
3242         _M_v.push_back(__detail::__mod<result_type,
3243                        __detail::_Shift<result_type, 32>::__value>(*__iter));
3244     }
3245
3246   template<typename _RandomAccessIterator>
3247     void
3248     seed_seq::generate(_RandomAccessIterator __begin,
3249                        _RandomAccessIterator __end)
3250     {
3251       typedef typename iterator_traits<_RandomAccessIterator>::value_type
3252         _Type;
3253
3254       if (__begin == __end)
3255         return;
3256
3257       std::fill(__begin, __end, _Type(0x8b8b8b8bu));
3258
3259       const size_t __n = __end - __begin;
3260       const size_t __s = _M_v.size();
3261       const size_t __t = (__n >= 623) ? 11
3262                        : (__n >=  68) ? 7
3263                        : (__n >=  39) ? 5
3264                        : (__n >=   7) ? 3
3265                        : (__n - 1) / 2;
3266       const size_t __p = (__n - __t) / 2;
3267       const size_t __q = __p + __t;
3268       const size_t __m = std::max(size_t(__s + 1), __n);
3269
3270       for (size_t __k = 0; __k < __m; ++__k)
3271         {
3272           _Type __arg = (__begin[__k % __n]
3273                          ^ __begin[(__k + __p) % __n]
3274                          ^ __begin[(__k - 1) % __n]);
3275           _Type __r1 = __arg ^ (__arg >> 27);
3276           __r1 = __detail::__mod<_Type,
3277                     __detail::_Shift<_Type, 32>::__value>(1664525u * __r1);
3278           _Type __r2 = __r1;
3279           if (__k == 0)
3280             __r2 += __s;
3281           else if (__k <= __s)
3282             __r2 += __k % __n + _M_v[__k - 1];
3283           else
3284             __r2 += __k % __n;
3285           __r2 = __detail::__mod<_Type,
3286                    __detail::_Shift<_Type, 32>::__value>(__r2);
3287           __begin[(__k + __p) % __n] += __r1;
3288           __begin[(__k + __q) % __n] += __r2;
3289           __begin[__k % __n] = __r2;
3290         }
3291
3292       for (size_t __k = __m; __k < __m + __n; ++__k)
3293         {
3294           _Type __arg = (__begin[__k % __n]
3295                          + __begin[(__k + __p) % __n]
3296                          + __begin[(__k - 1) % __n]);
3297           _Type __r3 = __arg ^ (__arg >> 27);
3298           __r3 = __detail::__mod<_Type,
3299                    __detail::_Shift<_Type, 32>::__value>(1566083941u * __r3);
3300           _Type __r4 = __r3 - __k % __n;
3301           __r4 = __detail::__mod<_Type,
3302                    __detail::_Shift<_Type, 32>::__value>(__r4);
3303           __begin[(__k + __p) % __n] ^= __r3;
3304           __begin[(__k + __q) % __n] ^= __r4;
3305           __begin[__k % __n] = __r4;
3306         }
3307     }
3308
3309   template<typename _RealType, size_t __bits,
3310            typename _UniformRandomNumberGenerator>
3311     _RealType
3312     generate_canonical(_UniformRandomNumberGenerator& __urng)
3313     {
3314       static_assert(std::is_floating_point<_RealType>::value,
3315                     "template argument must be a floating point type");
3316
3317       const size_t __b
3318         = std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
3319                    __bits);
3320       const long double __r = static_cast<long double>(__urng.max())
3321                             - static_cast<long double>(__urng.min()) + 1.0L;
3322       const size_t __log2r = std::log(__r) / std::log(2.0L);
3323       const size_t __m = std::max<size_t>(1UL,
3324                                           (__b + __log2r - 1UL) / __log2r);
3325       _RealType __ret;
3326       _RealType __sum = _RealType(0);
3327       _RealType __tmp = _RealType(1);
3328       for (size_t __k = __m; __k != 0; --__k)
3329         {
3330           __sum += _RealType(__urng() - __urng.min()) * __tmp;
3331           __tmp *= __r;
3332         }
3333       __ret = __sum / __tmp;
3334       if (__builtin_expect(__ret >= _RealType(1), 0))
3335         {
3336 #if _GLIBCXX_USE_C99_MATH_TR1
3337           __ret = std::nextafter(_RealType(1), _RealType(0));
3338 #else
3339           __ret = _RealType(1)
3340             - std::numeric_limits<_RealType>::epsilon() / _RealType(2);
3341 #endif
3342         }
3343       return __ret;
3344     }
3345
3346 _GLIBCXX_END_NAMESPACE_VERSION
3347 } // namespace
3348
3349 #endif