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

   1 // random number generation -*- C++ -*-
   2
   3 // Copyright (C) 2009, 2010 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 /**
  26  * @file bits/random.h
  27  *  This is an internal header file, included by other library headers.
  28  *  You should not attempt to use it directly.
  29  */
  30
  31 #ifndef _RANDOM_H
  32 #define _RANDOM_H 1
  33
  34 #include <vector>
  35
  36 namespace std
  37 {
  38   // [26.4] Random number generation
  39
  40   /**
  41    * @defgroup random Random Number Generation
  42    * @ingroup numerics
  43    *
  44    * A facility for generating random numbers on selected distributions.
  45    * @{
  46    */
  47
  48   /**
  49    * @brief A function template for converting the output of a (integral)
  50    * uniform random number generator to a floatng point result in the range
  51    * [0-1).
  52    */
  53   template<typename _RealType, size_t __bits,
  54            typename _UniformRandomNumberGenerator>
  55     _RealType
  56     generate_canonical(_UniformRandomNumberGenerator& __g);
  57
  58   /*
  59    * Implementation-space details.
  60    */
  61   namespace __detail
  62   {
  63     template<typename _UIntType, size_t __w,
  64              bool = __w < static_cast<size_t>
  65                           (std::numeric_limits<_UIntType>::digits)>
  66       struct _Shift
  67       { static const _UIntType __value = 0; };
  68
  69     template<typename _UIntType, size_t __w>
  70       struct _Shift<_UIntType, __w, true>
  71       { static const _UIntType __value = _UIntType(1) << __w; };
  72
  73     template<typename _Tp, _Tp __m, _Tp __a, _Tp __c, bool>
  74       struct _Mod;
  75
  76     // Dispatch based on modulus value to prevent divide-by-zero compile-time
  77     // errors when m == 0.
  78     template<typename _Tp, _Tp __m, _Tp __a = 1, _Tp __c = 0>
  79       inline _Tp
  80       __mod(_Tp __x)
  81       { return _Mod<_Tp, __m, __a, __c, __m == 0>::__calc(__x); }
  82
  83     /*
  84      * An adaptor class for converting the output of any Generator into
  85      * the input for a specific Distribution.
  86      */
  87     template<typename _Engine, typename _DInputType>
  88       struct _Adaptor
  89       {
  90
  91       public:
  92         _Adaptor(_Engine& __g)
  93         : _M_g(__g) { }
  94
  95         _DInputType
  96         min() const
  97         { return _DInputType(0); }
  98
  99         _DInputType
 100         max() const
 101         { return _DInputType(1); }
 102
 103         /*
 104          * Converts a value generated by the adapted random number generator
 105          * into a value in the input domain for the dependent random number
 106          * distribution.
 107          */
 108         _DInputType
 109         operator()()
 110         {
 111           return std::generate_canonical<_DInputType,
 112                                     std::numeric_limits<_DInputType>::digits,
 113                                     _Engine>(_M_g);
 114         }
 115
 116       private:
 117         _Engine& _M_g;
 118       };
 119   } // namespace __detail
 120
 121   /**
 122    * @addtogroup random_generators Random Number Generators
 123    * @ingroup random
 124    *
 125    * These classes define objects which provide random or pseudorandom
 126    * numbers, either from a discrete or a continuous interval.  The
 127    * random number generator supplied as a part of this library are
 128    * all uniform random number generators which provide a sequence of
 129    * random number uniformly distributed over their range.
 130    *
 131    * A number generator is a function object with an operator() that
 132    * takes zero arguments and returns a number.
 133    *
 134    * A compliant random number generator must satisfy the following
 135    * requirements.  <table border=1 cellpadding=10 cellspacing=0>
 136    * <caption align=top>Random Number Generator Requirements</caption>
 137    * <tr><td>To be documented.</td></tr> </table>
 138    *
 139    * @{
 140    */
 141
 142   /**
 143    * @brief A model of a linear congruential random number generator.
 144    *
 145    * A random number generator that produces pseudorandom numbers via
 146    * linear function:
 147    * @f[
 148    *     x_{i+1}\leftarrow(ax_{i} + c) \bmod m
 149    * @f]
 150    *
 151    * The template parameter @p _UIntType must be an unsigned integral type
 152    * large enough to store values up to (__m-1). If the template parameter
 153    * @p __m is 0, the modulus @p __m used is
 154    * std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template
 155    * parameters @p __a and @p __c must be less than @p __m.
 156    *
 157    * The size of the state is @f$1@f$.
 158    */
 159   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 160     class linear_congruential_engine
 161     {
 162       static_assert(std::is_unsigned<_UIntType>::value, "template argument "
 163                     "substituting _UIntType not an unsigned integral type");
 164       static_assert(__m == 0u || (__a < __m && __c < __m),
 165                     "template argument substituting __m out of bounds");
 166
 167     public:
 168       /** The type of the generated random value. */
 169       typedef _UIntType result_type;
 170
 171       /** The multiplier. */
 172       static constexpr result_type multiplier   = __a;
 173       /** An increment. */
 174       static constexpr result_type increment    = __c;
 175       /** The modulus. */
 176       static constexpr result_type modulus      = __m;
 177       static constexpr result_type default_seed = 1u;
 178
 179       /**
 180        * @brief Constructs a %linear_congruential_engine random number
 181        *        generator engine with seed @p __s.  The default seed value
 182        *        is 1.
 183        *
 184        * @param __s The initial seed value.
 185        */
 186       explicit
 187       linear_congruential_engine(result_type __s = default_seed)
 188       { seed(__s); }
 189
 190       /**
 191        * @brief Constructs a %linear_congruential_engine random number
 192        *        generator engine seeded from the seed sequence @p __q.
 193        *
 194        * @param __q the seed sequence.
 195        */
 196       template<typename _Sseq, typename = typename
 197         std::enable_if<!std::is_same<_Sseq, linear_congruential_engine>::value>
 198                ::type>
 199         explicit
 200         linear_congruential_engine(_Sseq& __q)
 201         { seed(__q); }
 202
 203       /**
 204        * @brief Reseeds the %linear_congruential_engine random number generator
 205        *        engine sequence to the seed @p __s.
 206        *
 207        * @param __s The new seed.
 208        */
 209       void
 210       seed(result_type __s = default_seed);
 211
 212       /**
 213        * @brief Reseeds the %linear_congruential_engine random number generator
 214        *        engine
 215        * sequence using values from the seed sequence @p __q.
 216        *
 217        * @param __q the seed sequence.
 218        */
 219       template<typename _Sseq>
 220         typename std::enable_if<std::is_class<_Sseq>::value>::type
 221         seed(_Sseq& __q);
 222
 223       /**
 224        * @brief Gets the smallest possible value in the output range.
 225        *
 226        * The minimum depends on the @p __c parameter: if it is zero, the
 227        * minimum generated must be > 0, otherwise 0 is allowed.
 228        */
 229       static constexpr result_type
 230       min()
 231       { return __c == 0u ? 1u : 0u; }
 232
 233       /**
 234        * @brief Gets the largest possible value in the output range.
 235        */
 236       static constexpr result_type
 237       max()
 238       { return __m - 1u; }
 239
 240       /**
 241        * @brief Discard a sequence of random numbers.
 242        */
 243       void
 244       discard(unsigned long long __z)
 245       {
 246         for (; __z != 0ULL; --__z)
 247           (*this)();
 248       }
 249
 250       /**
 251        * @brief Gets the next random number in the sequence.
 252        */
 253       result_type
 254       operator()()
 255       {
 256         _M_x = __detail::__mod<_UIntType, __m, __a, __c>(_M_x);
 257         return _M_x;
 258       }
 259
 260       /**
 261        * @brief Compares two linear congruential random number generator
 262        * objects of the same type for equality.
 263        *
 264        * @param __lhs A linear congruential random number generator object.
 265        * @param __rhs Another linear congruential random number generator
 266        *              object.
 267        *
 268        * @returns true if the infinite sequences of generated values
 269        *          would be equal, false otherwise.
 270        */
 271       friend bool
 272       operator==(const linear_congruential_engine& __lhs,
 273                  const linear_congruential_engine& __rhs)
 274       { return __lhs._M_x == __rhs._M_x; }
 275
 276       /**
 277        * @brief Writes the textual representation of the state x(i) of x to
 278        *        @p __os.
 279        *
 280        * @param __os  The output stream.
 281        * @param __lcr A % linear_congruential_engine random number generator.
 282        * @returns __os.
 283        */
 284       template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
 285                _UIntType1 __m1, typename _CharT, typename _Traits>
 286         friend std::basic_ostream<_CharT, _Traits>&
 287         operator<<(std::basic_ostream<_CharT, _Traits>&,
 288                    const std::linear_congruential_engine<_UIntType1,
 289                    __a1, __c1, __m1>&);
 290
 291       /**
 292        * @brief Sets the state of the engine by reading its textual
 293        *        representation from @p __is.
 294        *
 295        * The textual representation must have been previously written using
 296        * an output stream whose imbued locale and whose type's template
 297        * specialization arguments _CharT and _Traits were the same as those
 298        * of @p __is.
 299        *
 300        * @param __is  The input stream.
 301        * @param __lcr A % linear_congruential_engine random number generator.
 302        * @returns __is.
 303        */
 304       template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
 305                _UIntType1 __m1, typename _CharT, typename _Traits>
 306         friend std::basic_istream<_CharT, _Traits>&
 307         operator>>(std::basic_istream<_CharT, _Traits>&,
 308                    std::linear_congruential_engine<_UIntType1, __a1,
 309                    __c1, __m1>&);
 310
 311     private:
 312       _UIntType _M_x;
 313     };
 314
 315   /**
 316    * @brief Compares two linear congruential random number generator
 317    * objects of the same type for inequality.
 318    *
 319    * @param __lhs A linear congruential random number generator object.
 320    * @param __rhs Another linear congruential random number generator
 321    *              object.
 322    *
 323    * @returns true if the infinite sequences of generated values
 324    *          would be different, false otherwise.
 325    */
 326   template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
 327     inline bool
 328     operator!=(const std::linear_congruential_engine<_UIntType, __a,
 329                __c, __m>& __lhs,
 330                const std::linear_congruential_engine<_UIntType, __a,
 331                __c, __m>& __rhs)
 332     { return !(__lhs == __rhs); }
 333
 334
 335   /**
 336    * A generalized feedback shift register discrete random number generator.
 337    *
 338    * This algorithm avoids multiplication and division and is designed to be
 339    * friendly to a pipelined architecture.  If the parameters are chosen
 340    * correctly, this generator will produce numbers with a very long period and
 341    * fairly good apparent entropy, although still not cryptographically strong.
 342    *
 343    * The best way to use this generator is with the predefined mt19937 class.
 344    *
 345    * This algorithm was originally invented by Makoto Matsumoto and
 346    * Takuji Nishimura.
 347    *
 348    * @var word_size   The number of bits in each element of the state vector.
 349    * @var state_size  The degree of recursion.
 350    * @var shift_size  The period parameter.
 351    * @var mask_bits   The separation point bit index.
 352    * @var parameter_a The last row of the twist matrix.
 353    * @var output_u    The first right-shift tempering matrix parameter.
 354    * @var output_s    The first left-shift tempering matrix parameter.
 355    * @var output_b    The first left-shift tempering matrix mask.
 356    * @var output_t    The second left-shift tempering matrix parameter.
 357    * @var output_c    The second left-shift tempering matrix mask.
 358    * @var output_l    The second right-shift tempering matrix parameter.
 359    */
 360   template<typename _UIntType, size_t __w,
 361            size_t __n, size_t __m, size_t __r,
 362            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 363            _UIntType __b, size_t __t,
 364            _UIntType __c, size_t __l, _UIntType __f>
 365     class mersenne_twister_engine
 366     {
 367       static_assert(std::is_unsigned<_UIntType>::value, "template argument "
 368                     "substituting _UIntType not an unsigned integral type");
 369       static_assert(1u <= __m && __m <= __n,
 370                     "template argument substituting __m out of bounds");
 371       static_assert(__r <= __w, "template argument substituting "
 372                     "__r out of bound");
 373       static_assert(__u <= __w, "template argument substituting "
 374                     "__u out of bound");
 375       static_assert(__s <= __w, "template argument substituting "
 376                     "__s out of bound");
 377       static_assert(__t <= __w, "template argument substituting "
 378                     "__t out of bound");
 379       static_assert(__l <= __w, "template argument substituting "
 380                     "__l out of bound");
 381       static_assert(__w <= std::numeric_limits<_UIntType>::digits,
 382                     "template argument substituting __w out of bound");
 383       static_assert(__a <= (__detail::_Shift<_UIntType, __w>::__value - 1),
 384                     "template argument substituting __a out of bound");
 385       static_assert(__b <= (__detail::_Shift<_UIntType, __w>::__value - 1),
 386                     "template argument substituting __b out of bound");
 387       static_assert(__c <= (__detail::_Shift<_UIntType, __w>::__value - 1),
 388                     "template argument substituting __c out of bound");
 389       static_assert(__d <= (__detail::_Shift<_UIntType, __w>::__value - 1),
 390                     "template argument substituting __d out of bound");
 391       static_assert(__f <= (__detail::_Shift<_UIntType, __w>::__value - 1),
 392                     "template argument substituting __f out of bound");
 393
 394     public:
 395       /** The type of the generated random value. */
 396       typedef _UIntType result_type;
 397
 398       // parameter values
 399       static constexpr size_t      word_size                 = __w;
 400       static constexpr size_t      state_size                = __n;
 401       static constexpr size_t      shift_size                = __m;
 402       static constexpr size_t      mask_bits                 = __r;
 403       static constexpr result_type xor_mask                  = __a;
 404       static constexpr size_t      tempering_u               = __u;
 405       static constexpr result_type tempering_d               = __d;
 406       static constexpr size_t      tempering_s               = __s;
 407       static constexpr result_type tempering_b               = __b;
 408       static constexpr size_t      tempering_t               = __t;
 409       static constexpr result_type tempering_c               = __c;
 410       static constexpr size_t      tempering_l               = __l;
 411       static constexpr result_type initialization_multiplier = __f;
 412       static constexpr result_type default_seed = 5489u;
 413
 414       // constructors and member function
 415       explicit
 416       mersenne_twister_engine(result_type __sd = default_seed)
 417       { seed(__sd); }
 418
 419       /**
 420        * @brief Constructs a %mersenne_twister_engine random number generator
 421        *        engine seeded from the seed sequence @p __q.
 422        *
 423        * @param __q the seed sequence.
 424        */
 425       template<typename _Sseq, typename = typename
 426         std::enable_if<!std::is_same<_Sseq, mersenne_twister_engine>::value>
 427                ::type>
 428         explicit
 429         mersenne_twister_engine(_Sseq& __q)
 430         { seed(__q); }
 431
 432       void
 433       seed(result_type __sd = default_seed);
 434
 435       template<typename _Sseq>
 436         typename std::enable_if<std::is_class<_Sseq>::value>::type
 437         seed(_Sseq& __q);
 438
 439       /**
 440        * @brief Gets the smallest possible value in the output range.
 441        */
 442       static constexpr result_type
 443       min()
 444       { return 0; };
 445
 446       /**
 447        * @brief Gets the largest possible value in the output range.
 448        */
 449       static constexpr result_type
 450       max()
 451       { return __detail::_Shift<_UIntType, __w>::__value - 1; }
 452
 453       /**
 454        * @brief Discard a sequence of random numbers.
 455        */
 456       void
 457       discard(unsigned long long __z)
 458       {
 459         for (; __z != 0ULL; --__z)
 460           (*this)();
 461       }
 462
 463       result_type
 464       operator()();
 465
 466       /**
 467        * @brief Compares two % mersenne_twister_engine random number generator
 468        *        objects of the same type for equality.
 469        *
 470        * @param __lhs A % mersenne_twister_engine random number generator
 471        *              object.
 472        * @param __rhs Another % mersenne_twister_engine random number
 473        *              generator object.
 474        *
 475        * @returns true if the infinite sequences of generated values
 476        *          would be equal, false otherwise.
 477        */
 478       friend bool
 479       operator==(const mersenne_twister_engine& __lhs,
 480                  const mersenne_twister_engine& __rhs)
 481       { return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); }
 482
 483       /**
 484        * @brief Inserts the current state of a % mersenne_twister_engine
 485        *        random number generator engine @p __x into the output stream
 486        *        @p __os.
 487        *
 488        * @param __os An output stream.
 489        * @param __x  A % mersenne_twister_engine random number generator
 490        *             engine.
 491        *
 492        * @returns The output stream with the state of @p __x inserted or in
 493        * an error state.
 494        */
 495       template<typename _UIntType1,
 496                size_t __w1, size_t __n1,
 497                size_t __m1, size_t __r1,
 498                _UIntType1 __a1, size_t __u1,
 499                _UIntType1 __d1, size_t __s1,
 500                _UIntType1 __b1, size_t __t1,
 501                _UIntType1 __c1, size_t __l1, _UIntType1 __f1,
 502                typename _CharT, typename _Traits>
 503         friend std::basic_ostream<_CharT, _Traits>&
 504         operator<<(std::basic_ostream<_CharT, _Traits>&,
 505                    const std::mersenne_twister_engine<_UIntType1, __w1, __n1,
 506                    __m1, __r1, __a1, __u1, __d1, __s1, __b1, __t1, __c1,
 507                    __l1, __f1>&);
 508
 509       /**
 510        * @brief Extracts the current state of a % mersenne_twister_engine
 511        *        random number generator engine @p __x from the input stream
 512        *        @p __is.
 513        *
 514        * @param __is An input stream.
 515        * @param __x  A % mersenne_twister_engine random number generator
 516        *             engine.
 517        *
 518        * @returns The input stream with the state of @p __x extracted or in
 519        * an error state.
 520        */
 521       template<typename _UIntType1,
 522                size_t __w1, size_t __n1,
 523                size_t __m1, size_t __r1,
 524                _UIntType1 __a1, size_t __u1,
 525                _UIntType1 __d1, size_t __s1,
 526                _UIntType1 __b1, size_t __t1,
 527                _UIntType1 __c1, size_t __l1, _UIntType1 __f1,
 528                typename _CharT, typename _Traits>
 529         friend std::basic_istream<_CharT, _Traits>&
 530         operator>>(std::basic_istream<_CharT, _Traits>&,
 531                    std::mersenne_twister_engine<_UIntType1, __w1, __n1, __m1,
 532                    __r1, __a1, __u1, __d1, __s1, __b1, __t1, __c1,
 533                    __l1, __f1>&);
 534
 535     private:
 536       _UIntType _M_x[state_size];
 537       size_t    _M_p;
 538     };
 539
 540   /**
 541    * @brief Compares two % mersenne_twister_engine random number generator
 542    *        objects of the same type for inequality.
 543    *
 544    * @param __lhs A % mersenne_twister_engine random number generator
 545    *              object.
 546    * @param __rhs Another % mersenne_twister_engine random number
 547    *              generator object.
 548    *
 549    * @returns true if the infinite sequences of generated values
 550    *          would be different, false otherwise.
 551    */
 552   template<typename _UIntType, size_t __w,
 553            size_t __n, size_t __m, size_t __r,
 554            _UIntType __a, size_t __u, _UIntType __d, size_t __s,
 555            _UIntType __b, size_t __t,
 556            _UIntType __c, size_t __l, _UIntType __f>
 557     inline bool
 558     operator!=(const std::mersenne_twister_engine<_UIntType, __w, __n, __m,
 559                __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __lhs,
 560                const std::mersenne_twister_engine<_UIntType, __w, __n, __m,
 561                __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __rhs)
 562     { return !(__lhs == __rhs); }
 563
 564
 565   /**
 566    * @brief The Marsaglia-Zaman generator.
 567    *
 568    * This is a model of a Generalized Fibonacci discrete random number
 569    * generator, sometimes referred to as the SWC generator.
 570    *
 571    * A discrete random number generator that produces pseudorandom
 572    * numbers using:
 573    * @f[
 574    *     x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m
 575    * @f]
 576    *
 577    * The size of the state is @f$r@f$
 578    * and the maximum period of the generator is @f$(m^r - m^s - 1)@f$.
 579    *
 580    * @var _M_x     The state of the generator.  This is a ring buffer.
 581    * @var _M_carry The carry.
 582    * @var _M_p     Current index of x(i - r).
 583    */
 584   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 585     class subtract_with_carry_engine
 586     {
 587       static_assert(std::is_unsigned<_UIntType>::value, "template argument "
 588                     "substituting _UIntType not an unsigned integral type");
 589       static_assert(0u < __s && __s < __r,
 590                     "template argument substituting __s out of bounds");
 591       static_assert(0u < __w && __w <= std::numeric_limits<_UIntType>::digits,
 592                     "template argument substituting __w out of bounds");
 593
 594     public:
 595       /** The type of the generated random value. */
 596       typedef _UIntType result_type;
 597
 598       // parameter values
 599       static constexpr size_t      word_size    = __w;
 600       static constexpr size_t      short_lag    = __s;
 601       static constexpr size_t      long_lag     = __r;
 602       static constexpr result_type default_seed = 19780503u;
 603
 604       /**
 605        * @brief Constructs an explicitly seeded % subtract_with_carry_engine
 606        *        random number generator.
 607        */
 608       explicit
 609       subtract_with_carry_engine(result_type __sd = default_seed)
 610       { seed(__sd); }
 611
 612       /**
 613        * @brief Constructs a %subtract_with_carry_engine random number engine
 614        *        seeded from the seed sequence @p __q.
 615        *
 616        * @param __q the seed sequence.
 617        */
 618       template<typename _Sseq, typename = typename
 619         std::enable_if<!std::is_same<_Sseq, subtract_with_carry_engine>::value>
 620                ::type>
 621         explicit
 622         subtract_with_carry_engine(_Sseq& __q)
 623         { seed(__q); }
 624
 625       /**
 626        * @brief Seeds the initial state @f$x_0@f$ of the random number
 627        *        generator.
 628        *
 629        * N1688[4.19] modifies this as follows.  If @p __value == 0,
 630        * sets value to 19780503.  In any case, with a linear
 631        * congruential generator lcg(i) having parameters @f$ m_{lcg} =
 632        * 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value
 633        * @f$, sets @f$ x_{-r} \dots x_{-1} @f$ to @f$ lcg(1) \bmod m
 634        * \dots lcg(r) \bmod m @f$ respectively.  If @f$ x_{-1} = 0 @f$
 635        * set carry to 1, otherwise sets carry to 0.
 636        */
 637       void
 638       seed(result_type __sd = default_seed);
 639
 640       /**
 641        * @brief Seeds the initial state @f$x_0@f$ of the
 642        * % subtract_with_carry_engine random number generator.
 643        */
 644       template<typename _Sseq>
 645         typename std::enable_if<std::is_class<_Sseq>::value>::type
 646         seed(_Sseq& __q);
 647
 648       /**
 649        * @brief Gets the inclusive minimum value of the range of random
 650        * integers returned by this generator.
 651        */
 652       static constexpr result_type
 653       min()
 654       { return 0; }
 655
 656       /**
 657        * @brief Gets the inclusive maximum value of the range of random
 658        * integers returned by this generator.
 659        */
 660       static constexpr result_type
 661       max()
 662       { return __detail::_Shift<_UIntType, __w>::__value - 1; }
 663
 664       /**
 665        * @brief Discard a sequence of random numbers.
 666        */
 667       void
 668       discard(unsigned long long __z)
 669       {
 670         for (; __z != 0ULL; --__z)
 671           (*this)();
 672       }
 673
 674       /**
 675        * @brief Gets the next random number in the sequence.
 676        */
 677       result_type
 678       operator()();
 679
 680       /**
 681        * @brief Compares two % subtract_with_carry_engine random number
 682        *        generator objects of the same type for equality.
 683        *
 684        * @param __lhs A % subtract_with_carry_engine random number generator
 685        *              object.
 686        * @param __rhs Another % subtract_with_carry_engine random number
 687        *              generator object.
 688        *
 689        * @returns true if the infinite sequences of generated values
 690        *          would be equal, false otherwise.
 691       */
 692       friend bool
 693       operator==(const subtract_with_carry_engine& __lhs,
 694                  const subtract_with_carry_engine& __rhs)
 695       { return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); }
 696
 697       /**
 698        * @brief Inserts the current state of a % subtract_with_carry_engine
 699        *        random number generator engine @p __x into the output stream
 700        *        @p __os.
 701        *
 702        * @param __os An output stream.
 703        * @param __x  A % subtract_with_carry_engine random number generator
 704        *             engine.
 705        *
 706        * @returns The output stream with the state of @p __x inserted or in
 707        * an error state.
 708        */
 709       template<typename _UIntType1, size_t __w1, size_t __s1, size_t __r1,
 710                typename _CharT, typename _Traits>
 711         friend std::basic_ostream<_CharT, _Traits>&
 712         operator<<(std::basic_ostream<_CharT, _Traits>&,
 713                    const std::subtract_with_carry_engine<_UIntType1, __w1,
 714                    __s1, __r1>&);
 715
 716       /**
 717        * @brief Extracts the current state of a % subtract_with_carry_engine
 718        *        random number generator engine @p __x from the input stream
 719        *        @p __is.
 720        *
 721        * @param __is An input stream.
 722        * @param __x  A % subtract_with_carry_engine random number generator
 723        *             engine.
 724        *
 725        * @returns The input stream with the state of @p __x extracted or in
 726        * an error state.
 727        */
 728       template<typename _UIntType1, size_t __w1, size_t __s1, size_t __r1,
 729                typename _CharT, typename _Traits>
 730         friend std::basic_istream<_CharT, _Traits>&
 731         operator>>(std::basic_istream<_CharT, _Traits>&,
 732                    std::subtract_with_carry_engine<_UIntType1, __w1,
 733                    __s1, __r1>&);
 734
 735     private:
 736       _UIntType  _M_x[long_lag];
 737       _UIntType  _M_carry;
 738       size_t     _M_p;
 739     };
 740
 741   /**
 742    * @brief Compares two % subtract_with_carry_engine random number
 743    *        generator objects of the same type for inequality.
 744    *
 745    * @param __lhs A % subtract_with_carry_engine random number generator
 746    *              object.
 747    * @param __rhs Another % subtract_with_carry_engine random number
 748    *              generator object.
 749    *
 750    * @returns true if the infinite sequences of generated values
 751    *          would be different, false otherwise.
 752    */
 753   template<typename _UIntType, size_t __w, size_t __s, size_t __r>
 754     inline bool
 755     operator!=(const std::subtract_with_carry_engine<_UIntType, __w,
 756                __s, __r>& __lhs,
 757                const std::subtract_with_carry_engine<_UIntType, __w,
 758                __s, __r>& __rhs)
 759     { return !(__lhs == __rhs); }
 760
 761
 762   /**
 763    * Produces random numbers from some base engine by discarding blocks of
 764    * data.
 765    *
 766    * 0 <= @p __r <= @p __p
 767    */
 768   template<typename _RandomNumberEngine, size_t __p, size_t __r>
 769     class discard_block_engine
 770     {
 771       static_assert(1 <= __r && __r <= __p,
 772                     "template argument substituting __r out of bounds");
 773
 774     public:
 775       /** The type of the generated random value. */
 776       typedef typename _RandomNumberEngine::result_type result_type;
 777
 778       // parameter values
 779       static constexpr size_t block_size = __p;
 780       static constexpr size_t used_block = __r;
 781
 782       /**
 783        * @brief Constructs a default %discard_block_engine engine.
 784        *
 785        * The underlying engine is default constructed as well.
 786        */
 787       discard_block_engine()
 788       : _M_b(), _M_n(0) { }
 789
 790       /**
 791        * @brief Copy constructs a %discard_block_engine engine.
 792        *
 793        * Copies an existing base class random number generator.
 794        * @param rng An existing (base class) engine object.
 795        */
 796       explicit
 797       discard_block_engine(const _RandomNumberEngine& __rne)
 798       : _M_b(__rne), _M_n(0) { }
 799
 800       /**
 801        * @brief Move constructs a %discard_block_engine engine.
 802        *
 803        * Copies an existing base class random number generator.
 804        * @param rng An existing (base class) engine object.
 805        */
 806       explicit
 807       discard_block_engine(_RandomNumberEngine&& __rne)
 808       : _M_b(std::move(__rne)), _M_n(0) { }
 809
 810       /**
 811        * @brief Seed constructs a %discard_block_engine engine.
 812        *
 813        * Constructs the underlying generator engine seeded with @p __s.
 814        * @param __s A seed value for the base class engine.
 815        */
 816       explicit
 817       discard_block_engine(result_type __s)
 818       : _M_b(__s), _M_n(0) { }
 819
 820       /**
 821        * @brief Generator construct a %discard_block_engine engine.
 822        *
 823        * @param __q A seed sequence.
 824        */
 825       template<typename _Sseq, typename = typename
 826         std::enable_if<!std::is_same<_Sseq, discard_block_engine>::value
 827                        && !std::is_same<_Sseq, _RandomNumberEngine>::value>
 828                ::type>
 829         explicit
 830         discard_block_engine(_Sseq& __q)
 831         : _M_b(__q), _M_n(0)
 832         { }
 833
 834       /**
 835        * @brief Reseeds the %discard_block_engine object with the default
 836        *        seed for the underlying base class generator engine.
 837        */
 838       void
 839       seed()
 840       {
 841         _M_b.seed();
 842         _M_n = 0;
 843       }
 844
 845       /**
 846        * @brief Reseeds the %discard_block_engine object with the default
 847        *        seed for the underlying base class generator engine.
 848        */
 849       void
 850       seed(result_type __s)
 851       {
 852         _M_b.seed(__s);
 853         _M_n = 0;
 854       }
 855
 856       /**
 857        * @brief Reseeds the %discard_block_engine object with the given seed
 858        *        sequence.
 859        * @param __q A seed generator function.
 860        */
 861       template<typename _Sseq>
 862         void
 863         seed(_Sseq& __q)
 864         {
 865           _M_b.seed(__q);
 866           _M_n = 0;
 867         }
 868
 869       /**
 870        * @brief Gets a const reference to the underlying generator engine
 871        *        object.
 872        */
 873       const _RandomNumberEngine&
 874       base() const
 875       { return _M_b; }
 876
 877       /**
 878        * @brief Gets the minimum value in the generated random number range.
 879        */
 880       static constexpr result_type
 881       min()
 882       { return _RandomNumberEngine::min(); }
 883
 884       /**
 885        * @brief Gets the maximum value in the generated random number range.
 886        */
 887       static constexpr result_type
 888       max()
 889       { return _RandomNumberEngine::max(); }
 890
 891       /**
 892        * @brief Discard a sequence of random numbers.
 893        */
 894       void
 895       discard(unsigned long long __z)
 896       {
 897         for (; __z != 0ULL; --__z)
 898           (*this)();
 899       }
 900
 901       /**
 902        * @brief Gets the next value in the generated random number sequence.
 903        */
 904       result_type
 905       operator()();
 906
 907       /**
 908        * @brief Compares two %discard_block_engine random number generator
 909        *        objects of the same type for equality.
 910        *
 911        * @param __lhs A %discard_block_engine random number generator object.
 912        * @param __rhs Another %discard_block_engine random number generator
 913        *              object.
 914        *
 915        * @returns true if the infinite sequences of generated values
 916        *          would be equal, false otherwise.
 917        */
 918       friend bool
 919       operator==(const discard_block_engine& __lhs,
 920                  const discard_block_engine& __rhs)
 921       { return __lhs._M_b == __rhs._M_b && __lhs._M_n == __rhs._M_n; }
 922
 923       /**
 924        * @brief Inserts the current state of a %discard_block_engine random
 925        *        number generator engine @p __x into the output stream
 926        *        @p __os.
 927        *
 928        * @param __os An output stream.
 929        * @param __x  A %discard_block_engine random number generator engine.
 930        *
 931        * @returns The output stream with the state of @p __x inserted or in
 932        * an error state.
 933        */
 934       template<typename _RandomNumberEngine1, size_t __p1, size_t __r1,
 935                typename _CharT, typename _Traits>
 936         friend std::basic_ostream<_CharT, _Traits>&
 937         operator<<(std::basic_ostream<_CharT, _Traits>&,
 938                    const std::discard_block_engine<_RandomNumberEngine1,
 939                    __p1, __r1>&);
 940
 941       /**
 942        * @brief Extracts the current state of a % subtract_with_carry_engine
 943        *        random number generator engine @p __x from the input stream
 944        *        @p __is.
 945        *
 946        * @param __is An input stream.
 947        * @param __x  A %discard_block_engine random number generator engine.
 948        *
 949        * @returns The input stream with the state of @p __x extracted or in
 950        * an error state.
 951        */
 952       template<typename _RandomNumberEngine1, size_t __p1, size_t __r1,
 953                typename _CharT, typename _Traits>
 954         friend std::basic_istream<_CharT, _Traits>&
 955         operator>>(std::basic_istream<_CharT, _Traits>&,
 956                    std::discard_block_engine<_RandomNumberEngine1,
 957                    __p1, __r1>&);
 958
 959     private:
 960       _RandomNumberEngine _M_b;
 961       size_t _M_n;
 962     };
 963
 964   /**
 965    * @brief Compares two %discard_block_engine random number generator
 966    *        objects of the same type for inequality.
 967    *
 968    * @param __lhs A %discard_block_engine random number generator object.
 969    * @param __rhs Another %discard_block_engine random number generator
 970    *              object.
 971    *
 972    * @returns true if the infinite sequences of generated values
 973    *          would be different, false otherwise.
 974    */
 975   template<typename _RandomNumberEngine, size_t __p, size_t __r>
 976     inline bool
 977     operator!=(const std::discard_block_engine<_RandomNumberEngine, __p,
 978                __r>& __lhs,
 979                const std::discard_block_engine<_RandomNumberEngine, __p,
 980                __r>& __rhs)
 981     { return !(__lhs == __rhs); }
 982
 983
 984   /**
 985    * Produces random numbers by combining random numbers from some base
 986    * engine to produce random numbers with a specifies number of bits @p __w.
 987    */
 988   template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
 989     class independent_bits_engine
 990     {
 991       static_assert(std::is_unsigned<_UIntType>::value, "template argument "
 992                     "substituting _UIntType not an unsigned integral type");
 993       static_assert(0u < __w && __w <= std::numeric_limits<_UIntType>::digits,
 994                     "template argument substituting __w out of bounds");
 995
 996     public:
 997       /** The type of the generated random value. */
 998       typedef _UIntType result_type;
 999
1000       /**
1001        * @brief Constructs a default %independent_bits_engine engine.
1002        *
1003        * The underlying engine is default constructed as well.
1004        */
1005       independent_bits_engine()
1006       : _M_b() { }
1007
1008       /**
1009        * @brief Copy constructs a %independent_bits_engine engine.
1010        *
1011        * Copies an existing base class random number generator.
1012        * @param rng An existing (base class) engine object.
1013        */
1014       explicit
1015       independent_bits_engine(const _RandomNumberEngine& __rne)
1016       : _M_b(__rne) { }
1017
1018       /**
1019        * @brief Move constructs a %independent_bits_engine engine.
1020        *
1021        * Copies an existing base class random number generator.
1022        * @param rng An existing (base class) engine object.
1023        */
1024       explicit
1025       independent_bits_engine(_RandomNumberEngine&& __rne)
1026       : _M_b(std::move(__rne)) { }
1027
1028       /**
1029        * @brief Seed constructs a %independent_bits_engine engine.
1030        *
1031        * Constructs the underlying generator engine seeded with @p __s.
1032        * @param __s A seed value for the base class engine.
1033        */
1034       explicit
1035       independent_bits_engine(result_type __s)
1036       : _M_b(__s) { }
1037
1038       /**
1039        * @brief Generator construct a %independent_bits_engine engine.
1040        *
1041        * @param __q A seed sequence.
1042        */
1043       template<typename _Sseq, typename = typename
1044         std::enable_if<!std::is_same<_Sseq, independent_bits_engine>::value
1045                        && !std::is_same<_Sseq, _RandomNumberEngine>::value>
1046                ::type>
1047         explicit
1048         independent_bits_engine(_Sseq& __q)
1049         : _M_b(__q)
1050         { }
1051
1052       /**
1053        * @brief Reseeds the %independent_bits_engine object with the default
1054        *        seed for the underlying base class generator engine.
1055        */
1056       void
1057       seed()
1058       { _M_b.seed(); }
1059
1060       /**
1061        * @brief Reseeds the %independent_bits_engine object with the default
1062        *        seed for the underlying base class generator engine.
1063        */
1064       void
1065       seed(result_type __s)
1066       { _M_b.seed(__s); }
1067
1068       /**
1069        * @brief Reseeds the %independent_bits_engine object with the given
1070        *        seed sequence.
1071        * @param __q A seed generator function.
1072        */
1073       template<typename _Sseq>
1074         void
1075         seed(_Sseq& __q)
1076         { _M_b.seed(__q); }
1077
1078       /**
1079        * @brief Gets a const reference to the underlying generator engine
1080        *        object.
1081        */
1082       const _RandomNumberEngine&
1083       base() const
1084       { return _M_b; }
1085
1086       /**
1087        * @brief Gets the minimum value in the generated random number range.
1088        */
1089       static constexpr result_type
1090       min()
1091       { return 0U; }
1092
1093       /**
1094        * @brief Gets the maximum value in the generated random number range.
1095        */
1096       static constexpr result_type
1097       max()
1098       { return __detail::_Shift<_UIntType, __w>::__value - 1; }
1099
1100       /**
1101        * @brief Discard a sequence of random numbers.
1102        */
1103       void
1104       discard(unsigned long long __z)
1105       {
1106         for (; __z != 0ULL; --__z)
1107           (*this)();
1108       }
1109
1110       /**
1111        * @brief Gets the next value in the generated random number sequence.
1112        */
1113       result_type
1114       operator()();
1115
1116       /**
1117        * @brief Compares two %independent_bits_engine random number generator
1118        * objects of the same type for equality.
1119        *
1120        * @param __lhs A %independent_bits_engine random number generator
1121        *              object.
1122        * @param __rhs Another %independent_bits_engine random number generator
1123        *              object.
1124        *
1125        * @returns true if the infinite sequences of generated values
1126        *          would be equal, false otherwise.
1127        */
1128       friend bool
1129       operator==(const independent_bits_engine& __lhs,
1130                  const independent_bits_engine& __rhs)
1131       { return __lhs._M_b == __rhs._M_b; }
1132
1133       /**
1134        * @brief Extracts the current state of a % subtract_with_carry_engine
1135        *        random number generator engine @p __x from the input stream
1136        *        @p __is.
1137        *
1138        * @param __is An input stream.
1139        * @param __x  A %independent_bits_engine random number generator
1140        *             engine.
1141        *
1142        * @returns The input stream with the state of @p __x extracted or in
1143        *          an error state.
1144        */
1145       template<typename _CharT, typename _Traits>
1146         friend std::basic_istream<_CharT, _Traits>&
1147         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1148                    std::independent_bits_engine<_RandomNumberEngine,
1149                    __w, _UIntType>& __x)
1150         {
1151           __is >> __x._M_b;
1152           return __is;
1153         }
1154
1155     private:
1156       _RandomNumberEngine _M_b;
1157     };
1158
1159   /**
1160    * @brief Compares two %independent_bits_engine random number generator
1161    * objects of the same type for inequality.
1162    *
1163    * @param __lhs A %independent_bits_engine random number generator
1164    *              object.
1165    * @param __rhs Another %independent_bits_engine random number generator
1166    *              object.
1167    *
1168    * @returns true if the infinite sequences of generated values
1169    *          would be different, false otherwise.
1170    */
1171   template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
1172     inline bool
1173     operator!=(const std::independent_bits_engine<_RandomNumberEngine, __w,
1174                _UIntType>& __lhs,
1175                const std::independent_bits_engine<_RandomNumberEngine, __w,
1176                _UIntType>& __rhs)
1177     { return !(__lhs == __rhs); }
1178
1179   /**
1180    * @brief Inserts the current state of a %independent_bits_engine random
1181    *        number generator engine @p __x into the output stream @p __os.
1182    *
1183    * @param __os An output stream.
1184    * @param __x  A %independent_bits_engine random number generator engine.
1185    *
1186    * @returns The output stream with the state of @p __x inserted or in
1187    *          an error state.
1188    */
1189   template<typename _RandomNumberEngine, size_t __w, typename _UIntType,
1190            typename _CharT, typename _Traits>
1191     std::basic_ostream<_CharT, _Traits>&
1192     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1193                const std::independent_bits_engine<_RandomNumberEngine,
1194                __w, _UIntType>& __x)
1195     {
1196       __os << __x.base();
1197       return __os;
1198     }
1199
1200
1201   /**
1202    * @brief Produces random numbers by combining random numbers from some
1203    * base engine to produce random numbers with a specifies number of bits
1204    * @p __w.
1205    */
1206   template<typename _RandomNumberEngine, size_t __k>
1207     class shuffle_order_engine
1208     {
1209       static_assert(1u <= __k, "template argument substituting "
1210                     "__k out of bound");
1211
1212     public:
1213       /** The type of the generated random value. */
1214       typedef typename _RandomNumberEngine::result_type result_type;
1215
1216       static constexpr size_t table_size = __k;
1217
1218       /**
1219        * @brief Constructs a default %shuffle_order_engine engine.
1220        *
1221        * The underlying engine is default constructed as well.
1222        */
1223       shuffle_order_engine()
1224       : _M_b()
1225       { _M_initialize(); }
1226
1227       /**
1228        * @brief Copy constructs a %shuffle_order_engine engine.
1229        *
1230        * Copies an existing base class random number generator.
1231        * @param rng An existing (base class) engine object.
1232        */
1233       explicit
1234       shuffle_order_engine(const _RandomNumberEngine& __rne)
1235       : _M_b(__rne)
1236       { _M_initialize(); }
1237
1238       /**
1239        * @brief Move constructs a %shuffle_order_engine engine.
1240        *
1241        * Copies an existing base class random number generator.
1242        * @param rng An existing (base class) engine object.
1243        */
1244       explicit
1245       shuffle_order_engine(_RandomNumberEngine&& __rne)
1246       : _M_b(std::move(__rne))
1247       { _M_initialize(); }
1248
1249       /**
1250        * @brief Seed constructs a %shuffle_order_engine engine.
1251        *
1252        * Constructs the underlying generator engine seeded with @p __s.
1253        * @param __s A seed value for the base class engine.
1254        */
1255       explicit
1256       shuffle_order_engine(result_type __s)
1257       : _M_b(__s)
1258       { _M_initialize(); }
1259
1260       /**
1261        * @brief Generator construct a %shuffle_order_engine engine.
1262        *
1263        * @param __q A seed sequence.
1264        */
1265       template<typename _Sseq, typename = typename
1266         std::enable_if<!std::is_same<_Sseq, shuffle_order_engine>::value
1267                        && !std::is_same<_Sseq, _RandomNumberEngine>::value>
1268                ::type>
1269         explicit
1270         shuffle_order_engine(_Sseq& __q)
1271         : _M_b(__q)
1272         { _M_initialize(); }
1273
1274       /**
1275        * @brief Reseeds the %shuffle_order_engine object with the default seed
1276                 for the underlying base class generator engine.
1277        */
1278       void
1279       seed()
1280       {
1281         _M_b.seed();
1282         _M_initialize();
1283       }
1284
1285       /**
1286        * @brief Reseeds the %shuffle_order_engine object with the default seed
1287        *        for the underlying base class generator engine.
1288        */
1289       void
1290       seed(result_type __s)
1291       {
1292         _M_b.seed(__s);
1293         _M_initialize();
1294       }
1295
1296       /**
1297        * @brief Reseeds the %shuffle_order_engine object with the given seed
1298        *        sequence.
1299        * @param __q A seed generator function.
1300        */
1301       template<typename _Sseq>
1302         void
1303         seed(_Sseq& __q)
1304         {
1305           _M_b.seed(__q);
1306           _M_initialize();
1307         }
1308
1309       /**
1310        * Gets a const reference to the underlying generator engine object.
1311        */
1312       const _RandomNumberEngine&
1313       base() const
1314       { return _M_b; }
1315
1316       /**
1317        * Gets the minimum value in the generated random number range.
1318        */
1319       static constexpr result_type
1320       min()
1321       { return _RandomNumberEngine::min(); }
1322
1323       /**
1324        * Gets the maximum value in the generated random number range.
1325        */
1326       static constexpr result_type
1327       max()
1328       { return _RandomNumberEngine::max(); }
1329
1330       /**
1331        * Discard a sequence of random numbers.
1332        */
1333       void
1334       discard(unsigned long long __z)
1335       {
1336         for (; __z != 0ULL; --__z)
1337           (*this)();
1338       }
1339
1340       /**
1341        * Gets the next value in the generated random number sequence.
1342        */
1343       result_type
1344       operator()();
1345
1346       /**
1347        * Compares two %shuffle_order_engine random number generator objects
1348        * of the same type for equality.
1349        *
1350        * @param __lhs A %shuffle_order_engine random number generator object.
1351        * @param __rhs Another %shuffle_order_engine random number generator
1352        *              object.
1353        *
1354        * @returns true if the infinite sequences of generated values
1355        *          would be equal, false otherwise.
1356       */
1357       friend bool
1358       operator==(const shuffle_order_engine& __lhs,
1359                  const shuffle_order_engine& __rhs)
1360       { return __lhs._M_b == __rhs._M_b; }
1361
1362       /**
1363        * @brief Inserts the current state of a %shuffle_order_engine random
1364        *        number generator engine @p __x into the output stream
1365         @p __os.
1366        *
1367        * @param __os An output stream.
1368        * @param __x  A %shuffle_order_engine random number generator engine.
1369        *
1370        * @returns The output stream with the state of @p __x inserted or in
1371        * an error state.
1372        */
1373       template<typename _RandomNumberEngine1, size_t __k1,
1374                typename _CharT, typename _Traits>
1375         friend std::basic_ostream<_CharT, _Traits>&
1376         operator<<(std::basic_ostream<_CharT, _Traits>&,
1377                    const std::shuffle_order_engine<_RandomNumberEngine1,
1378                    __k1>&);
1379
1380       /**
1381        * @brief Extracts the current state of a % subtract_with_carry_engine
1382        *        random number generator engine @p __x from the input stream
1383        *        @p __is.
1384        *
1385        * @param __is An input stream.
1386        * @param __x  A %shuffle_order_engine random number generator engine.
1387        *
1388        * @returns The input stream with the state of @p __x extracted or in
1389        * an error state.
1390        */
1391       template<typename _RandomNumberEngine1, size_t __k1,
1392                typename _CharT, typename _Traits>
1393         friend std::basic_istream<_CharT, _Traits>&
1394         operator>>(std::basic_istream<_CharT, _Traits>&,
1395                    std::shuffle_order_engine<_RandomNumberEngine1, __k1>&);
1396
1397     private:
1398       void _M_initialize()
1399       {
1400         for (size_t __i = 0; __i < __k; ++__i)
1401           _M_v[__i] = _M_b();
1402         _M_y = _M_b();
1403       }
1404
1405       _RandomNumberEngine _M_b;
1406       result_type _M_v[__k];
1407       result_type _M_y;
1408     };
1409
1410   /**
1411    * Compares two %shuffle_order_engine random number generator objects
1412    * of the same type for inequality.
1413    *
1414    * @param __lhs A %shuffle_order_engine random number generator object.
1415    * @param __rhs Another %shuffle_order_engine random number generator
1416    *              object.
1417    *
1418    * @returns true if the infinite sequences of generated values
1419    *          would be different, false otherwise.
1420    */
1421   template<typename _RandomNumberEngine, size_t __k>
1422     inline bool
1423     operator!=(const std::shuffle_order_engine<_RandomNumberEngine,
1424                __k>& __lhs,
1425                const std::shuffle_order_engine<_RandomNumberEngine,
1426                __k>& __rhs)
1427     { return !(__lhs == __rhs); }
1428
1429
1430   /**
1431    * The classic Minimum Standard rand0 of Lewis, Goodman, and Miller.
1432    */
1433   typedef linear_congruential_engine<uint_fast32_t, 16807UL, 0UL, 2147483647UL>
1434   minstd_rand0;
1435
1436   /**
1437    * An alternative LCR (Lehmer Generator function).
1438    */
1439   typedef linear_congruential_engine<uint_fast32_t, 48271UL, 0UL, 2147483647UL>
1440   minstd_rand;
1441
1442   /**
1443    * The classic Mersenne Twister.
1444    *
1445    * Reference:
1446    * M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-Dimensionally
1447    * Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions
1448    * on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
1449    */
1450   typedef mersenne_twister_engine<
1451     uint_fast32_t,
1452     32, 624, 397, 31,
1453     0x9908b0dfUL, 11,
1454     0xffffffffUL, 7,
1455     0x9d2c5680UL, 15,
1456     0xefc60000UL, 18, 1812433253UL> mt19937;
1457
1458   /**
1459    * An alternative Mersenne Twister.
1460    */
1461   typedef mersenne_twister_engine<
1462     uint_fast64_t,
1463     64, 312, 156, 31,
1464     0xb5026f5aa96619e9ULL, 29,
1465     0x5555555555555555ULL, 17,
1466     0x71d67fffeda60000ULL, 37,
1467     0xfff7eee000000000ULL, 43,
1468     6364136223846793005ULL> mt19937_64;
1469
1470   typedef subtract_with_carry_engine<uint_fast32_t, 24, 10, 24>
1471     ranlux24_base;
1472
1473   typedef subtract_with_carry_engine<uint_fast64_t, 48, 5, 12>
1474     ranlux48_base;
1475
1476   typedef discard_block_engine<ranlux24_base, 223, 23> ranlux24;
1477
1478   typedef discard_block_engine<ranlux48_base, 389, 11> ranlux48;
1479
1480   typedef shuffle_order_engine<minstd_rand0, 256> knuth_b;
1481
1482   typedef minstd_rand0 default_random_engine;
1483
1484   /**
1485    * A standard interface to a platform-specific non-deterministic
1486    * random number generator (if any are available).
1487    */
1488   class random_device
1489   {
1490   public:
1491     /** The type of the generated random value. */
1492     typedef unsigned int result_type;
1493
1494     // constructors, destructors and member functions
1495
1496 #ifdef _GLIBCXX_USE_RANDOM_TR1
1497
1498     explicit
1499     random_device(const std::string& __token = "/dev/urandom")
1500     {
1501       if ((__token != "/dev/urandom" && __token != "/dev/random")
1502           || !(_M_file = std::fopen(__token.c_str(), "rb")))
1503         std::__throw_runtime_error(__N("random_device::"
1504                                        "random_device(const std::string&)"));
1505     }
1506
1507     ~random_device()
1508     { std::fclose(_M_file); }
1509
1510 #else
1511
1512     explicit
1513     random_device(const std::string& __token = "mt19937")
1514     : _M_mt(_M_strtoul(__token)) { }
1515
1516   private:
1517     static unsigned long
1518     _M_strtoul(const std::string& __str)
1519     {
1520       unsigned long __ret = 5489UL;
1521       if (__str != "mt19937")
1522         {
1523           const char* __nptr = __str.c_str();
1524           char* __endptr;
1525           __ret = std::strtoul(__nptr, &__endptr, 0);
1526           if (*__nptr == '\0' || *__endptr != '\0')
1527             std::__throw_runtime_error(__N("random_device::_M_strtoul"
1528                                            "(const std::string&)"));
1529         }
1530       return __ret;
1531     }
1532
1533   public:
1534
1535 #endif
1536
1537     result_type
1538     min() const
1539     { return std::numeric_limits<result_type>::min(); }
1540
1541     result_type
1542     max() const
1543     { return std::numeric_limits<result_type>::max(); }
1544
1545     double
1546     entropy() const
1547     { return 0.0; }
1548
1549     result_type
1550     operator()()
1551     {
1552 #ifdef _GLIBCXX_USE_RANDOM_TR1
1553       result_type __ret;
1554       std::fread(reinterpret_cast<void*>(&__ret), sizeof(result_type),
1555                  1, _M_file);
1556       return __ret;
1557 #else
1558       return _M_mt();
1559 #endif
1560     }
1561
1562     // No copy functions.
1563     random_device(const random_device&) = delete;
1564     void operator=(const random_device&) = delete;
1565
1566   private:
1567
1568 #ifdef _GLIBCXX_USE_RANDOM_TR1
1569     FILE*        _M_file;
1570 #else
1571     mt19937      _M_mt;
1572 #endif
1573   };
1574
1575   /* @} */ // group random_generators
1576
1577   /**
1578    * @addtogroup random_distributions Random Number Distributions
1579    * @ingroup random
1580    * @{
1581    */
1582
1583   /**
1584    * @addtogroup random_distributions_uniform Uniform Distributions
1585    * @ingroup random_distributions
1586    * @{
1587    */
1588
1589   /**
1590    * @brief Uniform discrete distribution for random numbers.
1591    * A discrete random distribution on the range @f$[min, max]@f$ with equal
1592    * probability throughout the range.
1593    */
1594   template<typename _IntType = int>
1595     class uniform_int_distribution
1596     {
1597       static_assert(std::is_integral<_IntType>::value,
1598                     "template argument not an integral type");
1599
1600     public:
1601       /** The type of the range of the distribution. */
1602       typedef _IntType result_type;
1603       /** Parameter type. */
1604       struct param_type
1605       {
1606         typedef uniform_int_distribution<_IntType> distribution_type;
1607
1608         explicit
1609         param_type(_IntType __a = 0,
1610                    _IntType __b = std::numeric_limits<_IntType>::max())
1611         : _M_a(__a), _M_b(__b)
1612         {
1613           _GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b);
1614         }
1615
1616         result_type
1617         a() const
1618         { return _M_a; }
1619
1620         result_type
1621         b() const
1622         { return _M_b; }
1623
1624         friend bool
1625         operator==(const param_type& __p1, const param_type& __p2)
1626         { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
1627
1628       private:
1629         _IntType _M_a;
1630         _IntType _M_b;
1631       };
1632
1633     public:
1634       /**
1635        * @brief Constructs a uniform distribution object.
1636        */
1637       explicit
1638       uniform_int_distribution(_IntType __a = 0,
1639                            _IntType __b = std::numeric_limits<_IntType>::max())
1640       : _M_param(__a, __b)
1641       { }
1642
1643       explicit
1644       uniform_int_distribution(const param_type& __p)
1645       : _M_param(__p)
1646       { }
1647
1648       /**
1649        * @brief Resets the distribution state.
1650        *
1651        * Does nothing for the uniform integer distribution.
1652        */
1653       void
1654       reset() { }
1655
1656       result_type
1657       a() const
1658       { return _M_param.a(); }
1659
1660       result_type
1661       b() const
1662       { return _M_param.b(); }
1663
1664       /**
1665        * @brief Returns the parameter set of the distribution.
1666        */
1667       param_type
1668       param() const
1669       { return _M_param; }
1670
1671       /**
1672        * @brief Sets the parameter set of the distribution.
1673        * @param __param The new parameter set of the distribution.
1674        */
1675       void
1676       param(const param_type& __param)
1677       { _M_param = __param; }
1678
1679       /**
1680        * @brief Returns the inclusive lower bound of the distribution range.
1681        */
1682       result_type
1683       min() const
1684       { return this->a(); }
1685
1686       /**
1687        * @brief Returns the inclusive upper bound of the distribution range.
1688        */
1689       result_type
1690       max() const
1691       { return this->b(); }
1692
1693       /**
1694        * @brief Generating functions.
1695        */
1696       template<typename _UniformRandomNumberGenerator>
1697         result_type
1698         operator()(_UniformRandomNumberGenerator& __urng)
1699         { return this->operator()(__urng, this->param()); }
1700
1701       template<typename _UniformRandomNumberGenerator>
1702         result_type
1703         operator()(_UniformRandomNumberGenerator& __urng,
1704                    const param_type& __p);
1705
1706       param_type _M_param;
1707     };
1708
1709   /**
1710    * @brief Return true if two uniform integer distributions have
1711    *        the same parameters.
1712    */
1713   template<typename _IntType>
1714     inline bool
1715     operator==(const std::uniform_int_distribution<_IntType>& __d1,
1716                const std::uniform_int_distribution<_IntType>& __d2)
1717     { return __d1.param() == __d2.param(); }
1718
1719   /**
1720    * @brief Return true if two uniform integer distributions have
1721    *        different parameters.
1722    */
1723   template<typename _IntType>
1724     inline bool
1725     operator!=(const std::uniform_int_distribution<_IntType>& __d1,
1726                const std::uniform_int_distribution<_IntType>& __d2)
1727     { return !(__d1 == __d2); }
1728
1729   /**
1730    * @brief Inserts a %uniform_int_distribution random number
1731    *        distribution @p __x into the output stream @p os.
1732    *
1733    * @param __os An output stream.
1734    * @param __x  A %uniform_int_distribution random number distribution.
1735    *
1736    * @returns The output stream with the state of @p __x inserted or in
1737    * an error state.
1738    */
1739   template<typename _IntType, typename _CharT, typename _Traits>
1740     std::basic_ostream<_CharT, _Traits>&
1741     operator<<(std::basic_ostream<_CharT, _Traits>&,
1742                const std::uniform_int_distribution<_IntType>&);
1743
1744   /**
1745    * @brief Extracts a %uniform_int_distribution random number distribution
1746    * @p __x from the input stream @p __is.
1747    *
1748    * @param __is An input stream.
1749    * @param __x  A %uniform_int_distribution random number generator engine.
1750    *
1751    * @returns The input stream with @p __x extracted or in an error state.
1752    */
1753   template<typename _IntType, typename _CharT, typename _Traits>
1754     std::basic_istream<_CharT, _Traits>&
1755     operator>>(std::basic_istream<_CharT, _Traits>&,
1756                std::uniform_int_distribution<_IntType>&);
1757
1758
1759   /**
1760    * @brief Uniform continuous distribution for random numbers.
1761    *
1762    * A continuous random distribution on the range [min, max) with equal
1763    * probability throughout the range.  The URNG should be real-valued and
1764    * deliver number in the range [0, 1).
1765    */
1766   template<typename _RealType = double>
1767     class uniform_real_distribution
1768     {
1769       static_assert(std::is_floating_point<_RealType>::value,
1770                     "template argument not a floating point type");
1771
1772     public:
1773       /** The type of the range of the distribution. */
1774       typedef _RealType result_type;
1775       /** Parameter type. */
1776       struct param_type
1777       {
1778         typedef uniform_real_distribution<_RealType> distribution_type;
1779
1780         explicit
1781         param_type(_RealType __a = _RealType(0),
1782                    _RealType __b = _RealType(1))
1783         : _M_a(__a), _M_b(__b)
1784         {
1785           _GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b);
1786         }
1787
1788         result_type
1789         a() const
1790         { return _M_a; }
1791
1792         result_type
1793         b() const
1794         { return _M_b; }
1795
1796         friend bool
1797         operator==(const param_type& __p1, const param_type& __p2)
1798         { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
1799
1800       private:
1801         _RealType _M_a;
1802         _RealType _M_b;
1803       };
1804
1805     public:
1806       /**
1807        * @brief Constructs a uniform_real_distribution object.
1808        *
1809        * @param __min [IN]  The lower bound of the distribution.
1810        * @param __max [IN]  The upper bound of the distribution.
1811        */
1812       explicit
1813       uniform_real_distribution(_RealType __a = _RealType(0),
1814                                 _RealType __b = _RealType(1))
1815       : _M_param(__a, __b)
1816       { }
1817
1818       explicit
1819       uniform_real_distribution(const param_type& __p)
1820       : _M_param(__p)
1821       { }
1822
1823       /**
1824        * @brief Resets the distribution state.
1825        *
1826        * Does nothing for the uniform real distribution.
1827        */
1828       void
1829       reset() { }
1830
1831       result_type
1832       a() const
1833       { return _M_param.a(); }
1834
1835       result_type
1836       b() const
1837       { return _M_param.b(); }
1838
1839       /**
1840        * @brief Returns the parameter set of the distribution.
1841        */
1842       param_type
1843       param() const
1844       { return _M_param; }
1845
1846       /**
1847        * @brief Sets the parameter set of the distribution.
1848        * @param __param The new parameter set of the distribution.
1849        */
1850       void
1851       param(const param_type& __param)
1852       { _M_param = __param; }
1853
1854       /**
1855        * @brief Returns the inclusive lower bound of the distribution range.
1856        */
1857       result_type
1858       min() const
1859       { return this->a(); }
1860
1861       /**
1862        * @brief Returns the inclusive upper bound of the distribution range.
1863        */
1864       result_type
1865       max() const
1866       { return this->b(); }
1867
1868       /**
1869        * @brief Generating functions.
1870        */
1871       template<typename _UniformRandomNumberGenerator>
1872         result_type
1873         operator()(_UniformRandomNumberGenerator& __urng)
1874         { return this->operator()(__urng, this->param()); }
1875
1876       template<typename _UniformRandomNumberGenerator>
1877         result_type
1878         operator()(_UniformRandomNumberGenerator& __urng,
1879                    const param_type& __p)
1880         {
1881           __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1882             __aurng(__urng);
1883           return (__aurng() * (__p.b() - __p.a())) + __p.a();
1884         }
1885
1886     private:
1887       param_type _M_param;
1888     };
1889
1890   /**
1891    * @brief Return true if two uniform real distributions have
1892    *        the same parameters.
1893    */
1894   template<typename _IntType>
1895     inline bool
1896     operator==(const std::uniform_real_distribution<_IntType>& __d1,
1897                const std::uniform_real_distribution<_IntType>& __d2)
1898     { return __d1.param() == __d2.param(); }
1899
1900   /**
1901    * @brief Return true if two uniform real distributions have
1902    *        different parameters.
1903    */
1904   template<typename _IntType>
1905     inline bool
1906     operator!=(const std::uniform_real_distribution<_IntType>& __d1,
1907                const std::uniform_real_distribution<_IntType>& __d2)
1908     { return !(__d1 == __d2); }
1909
1910   /**
1911    * @brief Inserts a %uniform_real_distribution random number
1912    *        distribution @p __x into the output stream @p __os.
1913    *
1914    * @param __os An output stream.
1915    * @param __x  A %uniform_real_distribution random number distribution.
1916    *
1917    * @returns The output stream with the state of @p __x inserted or in
1918    *          an error state.
1919    */
1920   template<typename _RealType, typename _CharT, typename _Traits>
1921     std::basic_ostream<_CharT, _Traits>&
1922     operator<<(std::basic_ostream<_CharT, _Traits>&,
1923                const std::uniform_real_distribution<_RealType>&);
1924
1925   /**
1926    * @brief Extracts a %uniform_real_distribution random number distribution
1927    * @p __x from the input stream @p __is.
1928    *
1929    * @param __is An input stream.
1930    * @param __x  A %uniform_real_distribution random number generator engine.
1931    *
1932    * @returns The input stream with @p __x extracted or in an error state.
1933    */
1934   template<typename _RealType, typename _CharT, typename _Traits>
1935     std::basic_istream<_CharT, _Traits>&
1936     operator>>(std::basic_istream<_CharT, _Traits>&,
1937                std::uniform_real_distribution<_RealType>&);
1938
1939   /* @} */ // group random_distributions_uniform
1940
1941   /**
1942    * @addtogroup random_distributions_normal Normal Distributions
1943    * @ingroup random_distributions
1944    * @{
1945    */
1946
1947   /**
1948    * @brief A normal continuous distribution for random numbers.
1949    *
1950    * The formula for the normal probability density function is
1951    * @f[
1952    *     p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}}
1953    *            e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} }
1954    * @f]
1955    */
1956   template<typename _RealType = double>
1957     class normal_distribution
1958     {
1959       static_assert(std::is_floating_point<_RealType>::value,
1960                     "template argument not a floating point type");
1961
1962     public:
1963       /** The type of the range of the distribution. */
1964       typedef _RealType result_type;
1965       /** Parameter type. */
1966       struct param_type
1967       {
1968         typedef normal_distribution<_RealType> distribution_type;
1969
1970         explicit
1971         param_type(_RealType __mean = _RealType(0),
1972                    _RealType __stddev = _RealType(1))
1973         : _M_mean(__mean), _M_stddev(__stddev)
1974         {
1975           _GLIBCXX_DEBUG_ASSERT(_M_stddev > _RealType(0));
1976         }
1977
1978         _RealType
1979         mean() const
1980         { return _M_mean; }
1981
1982         _RealType
1983         stddev() const
1984         { return _M_stddev; }
1985
1986         friend bool
1987         operator==(const param_type& __p1, const param_type& __p2)
1988         { return (__p1._M_mean == __p2._M_mean
1989                   && __p1._M_stddev == __p2._M_stddev); }
1990
1991       private:
1992         _RealType _M_mean;
1993         _RealType _M_stddev;
1994       };
1995
1996     public:
1997       /**
1998        * Constructs a normal distribution with parameters @f$mean@f$ and
1999        * standard deviation.
2000        */
2001       explicit
2002       normal_distribution(result_type __mean = result_type(0),
2003                           result_type __stddev = result_type(1))
2004       : _M_param(__mean, __stddev), _M_saved_available(false)
2005       { }
2006
2007       explicit
2008       normal_distribution(const param_type& __p)
2009       : _M_param(__p), _M_saved_available(false)
2010       { }
2011
2012       /**
2013        * @brief Resets the distribution state.
2014        */
2015       void
2016       reset()
2017       { _M_saved_available = false; }
2018
2019       /**
2020        * @brief Returns the mean of the distribution.
2021        */
2022       _RealType
2023       mean() const
2024       { return _M_param.mean(); }
2025
2026       /**
2027        * @brief Returns the standard deviation of the distribution.
2028        */
2029       _RealType
2030       stddev() const
2031       { return _M_param.stddev(); }
2032
2033       /**
2034        * @brief Returns the parameter set of the distribution.
2035        */
2036       param_type
2037       param() const
2038       { return _M_param; }
2039
2040       /**
2041        * @brief Sets the parameter set of the distribution.
2042        * @param __param The new parameter set of the distribution.
2043        */
2044       void
2045       param(const param_type& __param)
2046       { _M_param = __param; }
2047
2048       /**
2049        * @brief Returns the greatest lower bound value of the distribution.
2050        */
2051       result_type
2052       min() const
2053       { return std::numeric_limits<result_type>::min(); }
2054
2055       /**
2056        * @brief Returns the least upper bound value of the distribution.
2057        */
2058       result_type
2059       max() const
2060       { return std::numeric_limits<result_type>::max(); }
2061
2062       /**
2063        * @brief Generating functions.
2064        */
2065       template<typename _UniformRandomNumberGenerator>
2066         result_type
2067         operator()(_UniformRandomNumberGenerator& __urng)
2068         { return this->operator()(__urng, this->param()); }
2069
2070       template<typename _UniformRandomNumberGenerator>
2071         result_type
2072         operator()(_UniformRandomNumberGenerator& __urng,
2073                    const param_type& __p);
2074
2075       /**
2076        * @brief Return true if two normal distributions have
2077        *        the same parameters and the sequences that would
2078        *        be generated are equal.
2079        */
2080       template<typename _RealType1>
2081         friend bool
2082         operator==(const std::normal_distribution<_RealType1>& __d1,
2083                    const std::normal_distribution<_RealType1>& __d2);
2084
2085       /**
2086        * @brief Inserts a %normal_distribution random number distribution
2087        * @p __x into the output stream @p __os.
2088        *
2089        * @param __os An output stream.
2090        * @param __x  A %normal_distribution random number distribution.
2091        *
2092        * @returns The output stream with the state of @p __x inserted or in
2093        * an error state.
2094        */
2095       template<typename _RealType1, typename _CharT, typename _Traits>
2096         friend std::basic_ostream<_CharT, _Traits>&
2097         operator<<(std::basic_ostream<_CharT, _Traits>&,
2098                    const std::normal_distribution<_RealType1>&);
2099
2100       /**
2101        * @brief Extracts a %normal_distribution random number distribution
2102        * @p __x from the input stream @p __is.
2103        *
2104        * @param __is An input stream.
2105        * @param __x  A %normal_distribution random number generator engine.
2106        *
2107        * @returns The input stream with @p __x extracted or in an error
2108        *          state.
2109        */
2110       template<typename _RealType1, typename _CharT, typename _Traits>
2111         friend std::basic_istream<_CharT, _Traits>&
2112         operator>>(std::basic_istream<_CharT, _Traits>&,
2113                    std::normal_distribution<_RealType1>&);
2114
2115     private:
2116       param_type  _M_param;
2117       result_type _M_saved;
2118       bool        _M_saved_available;
2119     };
2120
2121   /**
2122    * @brief Return true if two normal distributions are different.
2123    */
2124   template<typename _RealType>
2125     inline bool
2126     operator!=(const std::normal_distribution<_RealType>& __d1,
2127                const std::normal_distribution<_RealType>& __d2)
2128     { return !(__d1 == __d2); }
2129
2130
2131   /**
2132    * @brief A lognormal_distribution random number distribution.
2133    *
2134    * The formula for the normal probability mass function is
2135    * @f[
2136    *     p(x|m,s) = \frac{1}{sx\sqrt{2\pi}}
2137    *                \exp{-\frac{(\ln{x} - m)^2}{2s^2}}
2138    * @f]
2139    */
2140   template<typename _RealType = double>
2141     class lognormal_distribution
2142     {
2143       static_assert(std::is_floating_point<_RealType>::value,
2144                     "template argument not a floating point type");
2145
2146     public:
2147       /** The type of the range of the distribution. */
2148       typedef _RealType result_type;
2149       /** Parameter type. */
2150       struct param_type
2151       {
2152         typedef lognormal_distribution<_RealType> distribution_type;
2153
2154         explicit
2155         param_type(_RealType __m = _RealType(0),
2156                    _RealType __s = _RealType(1))
2157         : _M_m(__m), _M_s(__s)
2158         { }
2159
2160         _RealType
2161         m() const
2162         { return _M_m; }
2163
2164         _RealType
2165         s() const
2166         { return _M_s; }
2167
2168         friend bool
2169         operator==(const param_type& __p1, const param_type& __p2)
2170         { return __p1._M_m == __p2._M_m && __p1._M_s == __p2._M_s; }
2171
2172       private:
2173         _RealType _M_m;
2174         _RealType _M_s;
2175       };
2176
2177       explicit
2178       lognormal_distribution(_RealType __m = _RealType(0),
2179                              _RealType __s = _RealType(1))
2180       : _M_param(__m, __s), _M_nd()
2181       { }
2182
2183       explicit
2184       lognormal_distribution(const param_type& __p)
2185       : _M_param(__p), _M_nd()
2186       { }
2187
2188       /**
2189        * Resets the distribution state.
2190        */
2191       void
2192       reset()
2193       { _M_nd.reset(); }
2194
2195       /**
2196        *
2197        */
2198       _RealType
2199       m() const
2200       { return _M_param.m(); }
2201
2202       _RealType
2203       s() const
2204       { return _M_param.s(); }
2205
2206       /**
2207        * @brief Returns the parameter set of the distribution.
2208        */
2209       param_type
2210       param() const
2211       { return _M_param; }
2212
2213       /**
2214        * @brief Sets the parameter set of the distribution.
2215        * @param __param The new parameter set of the distribution.
2216        */
2217       void
2218       param(const param_type& __param)
2219       { _M_param = __param; }
2220
2221       /**
2222        * @brief Returns the greatest lower bound value of the distribution.
2223        */
2224       result_type
2225       min() const
2226       { return result_type(0); }
2227
2228       /**
2229        * @brief Returns the least upper bound value of the distribution.
2230        */
2231       result_type
2232       max() const
2233       { return std::numeric_limits<result_type>::max(); }
2234
2235       /**
2236        * @brief Generating functions.
2237        */
2238       template<typename _UniformRandomNumberGenerator>
2239         result_type
2240         operator()(_UniformRandomNumberGenerator& __urng)
2241         { return this->operator()(__urng, this->param()); }
2242
2243       template<typename _UniformRandomNumberGenerator>
2244         result_type
2245         operator()(_UniformRandomNumberGenerator& __urng,
2246                    const param_type& __p)
2247         { return std::exp(__p.s() * _M_nd(__urng) + __p.m()); }
2248
2249       /**
2250        * @brief Return true if two lognormal distributions have
2251        *        the same parameters and the sequences that would
2252        *        be generated are equal.
2253        */
2254       template<typename _RealType1>
2255         friend bool
2256         operator==(const std::lognormal_distribution<_RealType1>& __d1,
2257                    const std::lognormal_distribution<_RealType1>& __d2)
2258         { return (__d1.param() == __d2.param()
2259                   && __d1._M_nd == __d2._M_nd); }
2260
2261       /**
2262        * @brief Inserts a %lognormal_distribution random number distribution
2263        * @p __x into the output stream @p __os.
2264        *
2265        * @param __os An output stream.
2266        * @param __x  A %lognormal_distribution random number distribution.
2267        *
2268        * @returns The output stream with the state of @p __x inserted or in
2269        * an error state.
2270        */
2271       template<typename _RealType1, typename _CharT, typename _Traits>
2272         friend std::basic_ostream<_CharT, _Traits>&
2273         operator<<(std::basic_ostream<_CharT, _Traits>&,
2274                    const std::lognormal_distribution<_RealType1>&);
2275
2276       /**
2277        * @brief Extracts a %lognormal_distribution random number distribution
2278        * @p __x from the input stream @p __is.
2279        *
2280        * @param __is An input stream.
2281        * @param __x A %lognormal_distribution random number
2282        *            generator engine.
2283        *
2284        * @returns The input stream with @p __x extracted or in an error state.
2285        */
2286       template<typename _RealType1, typename _CharT, typename _Traits>
2287         friend std::basic_istream<_CharT, _Traits>&
2288         operator>>(std::basic_istream<_CharT, _Traits>&,
2289                    std::lognormal_distribution<_RealType1>&);
2290
2291     private:
2292       param_type _M_param;
2293
2294       std::normal_distribution<result_type> _M_nd;
2295     };
2296
2297   /**
2298    * @brief Return true if two lognormal distributions are different.
2299    */
2300   template<typename _RealType>
2301     inline bool
2302     operator!=(const std::lognormal_distribution<_RealType>& __d1,
2303                const std::lognormal_distribution<_RealType>& __d2)
2304     { return !(__d1 == __d2); }
2305
2306
2307   /**
2308    * @brief A gamma continuous distribution for random numbers.
2309    *
2310    * The formula for the gamma probability density function is:
2311    * @f[
2312    *     p(x|\alpha,\beta) = \frac{1}{\beta\Gamma(\alpha)}
2313    *                         (x/\beta)^{\alpha - 1} e^{-x/\beta}
2314    * @f]
2315    */
2316   template<typename _RealType = double>
2317     class gamma_distribution
2318     {
2319       static_assert(std::is_floating_point<_RealType>::value,
2320                     "template argument not a floating point type");
2321
2322     public:
2323       /** The type of the range of the distribution. */
2324       typedef _RealType result_type;
2325       /** Parameter type. */
2326       struct param_type
2327       {
2328         typedef gamma_distribution<_RealType> distribution_type;
2329         friend class gamma_distribution<_RealType>;
2330
2331         explicit
2332         param_type(_RealType __alpha_val = _RealType(1),
2333                    _RealType __beta_val = _RealType(1))
2334         : _M_alpha(__alpha_val), _M_beta(__beta_val)
2335         {
2336           _GLIBCXX_DEBUG_ASSERT(_M_alpha > _RealType(0));
2337           _M_initialize();
2338         }
2339
2340         _RealType
2341         alpha() const
2342         { return _M_alpha; }
2343
2344         _RealType
2345         beta() const
2346         { return _M_beta; }
2347
2348         friend bool
2349         operator==(const param_type& __p1, const param_type& __p2)
2350         { return (__p1._M_alpha == __p2._M_alpha
2351                   && __p1._M_beta == __p2._M_beta); }
2352
2353       private:
2354         void
2355         _M_initialize();
2356
2357         _RealType _M_alpha;
2358         _RealType _M_beta;
2359
2360         _RealType _M_malpha, _M_a2;
2361       };
2362
2363     public:
2364       /**
2365        * @brief Constructs a gamma distribution with parameters
2366        * @f$\alpha@f$ and @f$\beta@f$.
2367        */
2368       explicit
2369       gamma_distribution(_RealType __alpha_val = _RealType(1),
2370                          _RealType __beta_val = _RealType(1))
2371       : _M_param(__alpha_val, __beta_val), _M_nd()
2372       { }
2373
2374       explicit
2375       gamma_distribution(const param_type& __p)
2376       : _M_param(__p), _M_nd()
2377       { }
2378
2379       /**
2380        * @brief Resets the distribution state.
2381        */
2382       void
2383       reset()
2384       { _M_nd.reset(); }
2385
2386       /**
2387        * @brief Returns the @f$\alpha@f$ of the distribution.
2388        */
2389       _RealType
2390       alpha() const
2391       { return _M_param.alpha(); }
2392
2393       /**
2394        * @brief Returns the @f$\beta@f$ of the distribution.
2395        */
2396       _RealType
2397       beta() const
2398       { return _M_param.beta(); }
2399
2400       /**
2401        * @brief Returns the parameter set of the distribution.
2402        */
2403       param_type
2404       param() const
2405       { return _M_param; }
2406
2407       /**
2408        * @brief Sets the parameter set of the distribution.
2409        * @param __param The new parameter set of the distribution.
2410        */
2411       void
2412       param(const param_type& __param)
2413       { _M_param = __param; }
2414
2415       /**
2416        * @brief Returns the greatest lower bound value of the distribution.
2417        */
2418       result_type
2419       min() const
2420       { return result_type(0); }
2421
2422       /**
2423        * @brief Returns the least upper bound value of the distribution.
2424        */
2425       result_type
2426       max() const
2427       { return std::numeric_limits<result_type>::max(); }
2428
2429       /**
2430        * @brief Generating functions.
2431        */
2432       template<typename _UniformRandomNumberGenerator>
2433         result_type
2434         operator()(_UniformRandomNumberGenerator& __urng)
2435         { return this->operator()(__urng, this->param()); }
2436
2437       template<typename _UniformRandomNumberGenerator>
2438         result_type
2439         operator()(_UniformRandomNumberGenerator& __urng,
2440                    const param_type& __p);
2441
2442       /**
2443        * @brief Return true if two gamma distributions have the same
2444        *        parameters and the sequences that would be generated
2445        *        are equal.
2446        */
2447       template<typename _RealType1>
2448         friend bool
2449         operator==(const std::gamma_distribution<_RealType1>& __d1,
2450                    const std::gamma_distribution<_RealType1>& __d2)
2451         { return (__d1.param() == __d2.param()
2452                   && __d1._M_nd == __d2._M_nd); }
2453
2454       /**
2455        * @brief Inserts a %gamma_distribution random number distribution
2456        * @p __x into the output stream @p __os.
2457        *
2458        * @param __os An output stream.
2459        * @param __x  A %gamma_distribution random number distribution.
2460        *
2461        * @returns The output stream with the state of @p __x inserted or in
2462        * an error state.
2463        */
2464       template<typename _RealType1, typename _CharT, typename _Traits>
2465         friend std::basic_ostream<_CharT, _Traits>&
2466         operator<<(std::basic_ostream<_CharT, _Traits>&,
2467                    const std::gamma_distribution<_RealType1>&);
2468
2469       /**
2470        * @brief Extracts a %gamma_distribution random number distribution
2471        * @p __x from the input stream @p __is.
2472        *
2473        * @param __is An input stream.
2474        * @param __x  A %gamma_distribution random number generator engine.
2475        *
2476        * @returns The input stream with @p __x extracted or in an error state.
2477        */
2478       template<typename _RealType1, typename _CharT, typename _Traits>
2479         friend std::basic_istream<_CharT, _Traits>&
2480         operator>>(std::basic_istream<_CharT, _Traits>&,
2481                    std::gamma_distribution<_RealType1>&);
2482
2483     private:
2484       param_type _M_param;
2485
2486       std::normal_distribution<result_type> _M_nd;
2487     };
2488
2489   /**
2490    * @brief Return true if two gamma distributions are different.
2491    */
2492    template<typename _RealType>
2493     inline bool
2494      operator!=(const std::gamma_distribution<_RealType>& __d1,
2495                 const std::gamma_distribution<_RealType>& __d2)
2496     { return !(__d1 == __d2); }
2497
2498
2499   /**
2500    * @brief A chi_squared_distribution random number distribution.
2501    *
2502    * The formula for the normal probability mass function is
2503    * @f$p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}@f$
2504    */
2505   template<typename _RealType = double>
2506     class chi_squared_distribution
2507     {
2508       static_assert(std::is_floating_point<_RealType>::value,
2509                     "template argument not a floating point type");
2510
2511     public:
2512       /** The type of the range of the distribution. */
2513       typedef _RealType result_type;
2514       /** Parameter type. */
2515       struct param_type
2516       {
2517         typedef chi_squared_distribution<_RealType> distribution_type;
2518
2519         explicit
2520         param_type(_RealType __n = _RealType(1))
2521         : _M_n(__n)
2522         { }
2523
2524         _RealType
2525         n() const
2526         { return _M_n; }
2527
2528         friend bool
2529         operator==(const param_type& __p1, const param_type& __p2)
2530         { return __p1._M_n == __p2._M_n; }
2531
2532       private:
2533         _RealType _M_n;
2534       };
2535
2536       explicit
2537       chi_squared_distribution(_RealType __n = _RealType(1))
2538       : _M_param(__n), _M_gd(__n / 2)
2539       { }
2540
2541       explicit
2542       chi_squared_distribution(const param_type& __p)
2543       : _M_param(__p), _M_gd(__p.n() / 2)
2544       { }
2545
2546       /**
2547        * @brief Resets the distribution state.
2548        */
2549       void
2550       reset()
2551       { _M_gd.reset(); }
2552
2553       /**
2554        *
2555        */
2556       _RealType
2557       n() const
2558       { return _M_param.n(); }
2559
2560       /**
2561        * @brief Returns the parameter set of the distribution.
2562        */
2563       param_type
2564       param() const
2565       { return _M_param; }
2566
2567       /**
2568        * @brief Sets the parameter set of the distribution.
2569        * @param __param The new parameter set of the distribution.
2570        */
2571       void
2572       param(const param_type& __param)
2573       { _M_param = __param; }
2574
2575       /**
2576        * @brief Returns the greatest lower bound value of the distribution.
2577        */
2578       result_type
2579       min() const
2580       { return result_type(0); }
2581
2582       /**
2583        * @brief Returns the least upper bound value of the distribution.
2584        */
2585       result_type
2586       max() const
2587       { return std::numeric_limits<result_type>::max(); }
2588
2589       /**
2590        * @brief Generating functions.
2591        */
2592       template<typename _UniformRandomNumberGenerator>
2593         result_type
2594         operator()(_UniformRandomNumberGenerator& __urng)
2595         { return 2 * _M_gd(__urng); }
2596
2597       template<typename _UniformRandomNumberGenerator>
2598         result_type
2599         operator()(_UniformRandomNumberGenerator& __urng,
2600                    const param_type& __p)
2601         {
2602           typedef typename std::gamma_distribution<result_type>::param_type
2603             param_type;
2604           return 2 * _M_gd(__urng, param_type(__p.n() / 2));
2605         }
2606
2607       /**
2608        * @brief Return true if two Chi-squared distributions have
2609        *        the same parameters and the sequences that would be
2610        *        generated are equal.
2611        */
2612       template<typename _RealType1>
2613         friend bool
2614         operator==(const std::chi_squared_distribution<_RealType1>& __d1,
2615                    const std::chi_squared_distribution<_RealType1>& __d2)
2616         { return __d1.param() == __d2.param() && __d1._M_gd == __d2._M_gd; }
2617
2618       /**
2619        * @brief Inserts a %chi_squared_distribution random number distribution
2620        * @p __x into the output stream @p __os.
2621        *
2622        * @param __os An output stream.
2623        * @param __x  A %chi_squared_distribution random number distribution.
2624        *
2625        * @returns The output stream with the state of @p __x inserted or in
2626        * an error state.
2627        */
2628       template<typename _RealType1, typename _CharT, typename _Traits>
2629         friend std::basic_ostream<_CharT, _Traits>&
2630         operator<<(std::basic_ostream<_CharT, _Traits>&,
2631                    const std::chi_squared_distribution<_RealType1>&);
2632
2633       /**
2634        * @brief Extracts a %chi_squared_distribution random number distribution
2635        * @p __x from the input stream @p __is.
2636        *
2637        * @param __is An input stream.
2638        * @param __x A %chi_squared_distribution random number
2639        *            generator engine.
2640        *
2641        * @returns The input stream with @p __x extracted or in an error state.
2642        */
2643       template<typename _RealType1, typename _CharT, typename _Traits>
2644         friend std::basic_istream<_CharT, _Traits>&
2645         operator>>(std::basic_istream<_CharT, _Traits>&,
2646                    std::chi_squared_distribution<_RealType1>&);
2647
2648     private:
2649       param_type _M_param;
2650
2651       std::gamma_distribution<result_type> _M_gd;
2652     };
2653
2654   /**
2655    * @brief Return true if two Chi-squared distributions are different.
2656    */
2657   template<typename _RealType>
2658     inline bool
2659     operator!=(const std::chi_squared_distribution<_RealType>& __d1,
2660                const std::chi_squared_distribution<_RealType>& __d2)
2661     { return !(__d1 == __d2); }
2662
2663
2664   /**
2665    * @brief A cauchy_distribution random number distribution.
2666    *
2667    * The formula for the normal probability mass function is
2668    * @f$p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}@f$
2669    */
2670   template<typename _RealType = double>
2671     class cauchy_distribution
2672     {
2673       static_assert(std::is_floating_point<_RealType>::value,
2674                     "template argument not a floating point type");
2675
2676     public:
2677       /** The type of the range of the distribution. */
2678       typedef _RealType result_type;
2679       /** Parameter type. */
2680       struct param_type
2681       {
2682         typedef cauchy_distribution<_RealType> distribution_type;
2683
2684         explicit
2685         param_type(_RealType __a = _RealType(0),
2686                    _RealType __b = _RealType(1))
2687         : _M_a(__a), _M_b(__b)
2688         { }
2689
2690         _RealType
2691         a() const
2692         { return _M_a; }
2693
2694         _RealType
2695         b() const
2696         { return _M_b; }
2697
2698         friend bool
2699         operator==(const param_type& __p1, const param_type& __p2)
2700         { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
2701
2702       private:
2703         _RealType _M_a;
2704         _RealType _M_b;
2705       };
2706
2707       explicit
2708       cauchy_distribution(_RealType __a = _RealType(0),
2709                           _RealType __b = _RealType(1))
2710       : _M_param(__a, __b)
2711       { }
2712
2713       explicit
2714       cauchy_distribution(const param_type& __p)
2715       : _M_param(__p)
2716       { }
2717
2718       /**
2719        * @brief Resets the distribution state.
2720        */
2721       void
2722       reset()
2723       { }
2724
2725       /**
2726        *
2727        */
2728       _RealType
2729       a() const
2730       { return _M_param.a(); }
2731
2732       _RealType
2733       b() const
2734       { return _M_param.b(); }
2735
2736       /**
2737        * @brief Returns the parameter set of the distribution.
2738        */
2739       param_type
2740       param() const
2741       { return _M_param; }
2742
2743       /**
2744        * @brief Sets the parameter set of the distribution.
2745        * @param __param The new parameter set of the distribution.
2746        */
2747       void
2748       param(const param_type& __param)
2749       { _M_param = __param; }
2750
2751       /**
2752        * @brief Returns the greatest lower bound value of the distribution.
2753        */
2754       result_type
2755       min() const
2756       { return std::numeric_limits<result_type>::min(); }
2757
2758       /**
2759        * @brief Returns the least upper bound value of the distribution.
2760        */
2761       result_type
2762       max() const
2763       { return std::numeric_limits<result_type>::max(); }
2764
2765       /**
2766        * @brief Generating functions.
2767        */
2768       template<typename _UniformRandomNumberGenerator>
2769         result_type
2770         operator()(_UniformRandomNumberGenerator& __urng)
2771         { return this->operator()(__urng, this->param()); }
2772
2773       template<typename _UniformRandomNumberGenerator>
2774         result_type
2775         operator()(_UniformRandomNumberGenerator& __urng,
2776                    const param_type& __p);
2777
2778     private:
2779       param_type _M_param;
2780     };
2781
2782   /**
2783    * @brief Return true if two Cauchy distributions have
2784    *        the same parameters.
2785    */
2786   template<typename _RealType>
2787     inline bool
2788     operator==(const std::cauchy_distribution<_RealType>& __d1,
2789                const std::cauchy_distribution<_RealType>& __d2)
2790     { return __d1.param() == __d2.param(); }
2791
2792   /**
2793    * @brief Return true if two Cauchy distributions have
2794    *        different parameters.
2795    */
2796   template<typename _RealType>
2797     inline bool
2798     operator!=(const std::cauchy_distribution<_RealType>& __d1,
2799                const std::cauchy_distribution<_RealType>& __d2)
2800     { return !(__d1 == __d2); }
2801
2802   /**
2803    * @brief Inserts a %cauchy_distribution random number distribution
2804    * @p __x into the output stream @p __os.
2805    *
2806    * @param __os An output stream.
2807    * @param __x  A %cauchy_distribution random number distribution.
2808    *
2809    * @returns The output stream with the state of @p __x inserted or in
2810    * an error state.
2811    */
2812   template<typename _RealType, typename _CharT, typename _Traits>
2813     std::basic_ostream<_CharT, _Traits>&
2814     operator<<(std::basic_ostream<_CharT, _Traits>&,
2815                const std::cauchy_distribution<_RealType>&);
2816
2817   /**
2818    * @brief Extracts a %cauchy_distribution random number distribution
2819    * @p __x from the input stream @p __is.
2820    *
2821    * @param __is An input stream.
2822    * @param __x A %cauchy_distribution random number
2823    *            generator engine.
2824    *
2825    * @returns The input stream with @p __x extracted or in an error state.
2826    */
2827   template<typename _RealType, typename _CharT, typename _Traits>
2828     std::basic_istream<_CharT, _Traits>&
2829     operator>>(std::basic_istream<_CharT, _Traits>&,
2830                std::cauchy_distribution<_RealType>&);
2831
2832
2833   /**
2834    * @brief A fisher_f_distribution random number distribution.
2835    *
2836    * The formula for the normal probability mass function is
2837    * @f[
2838    *     p(x|m,n) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)}
2839    *                (\frac{m}{n})^{m/2} x^{(m/2)-1}
2840    *                (1 + \frac{mx}{n})^{-(m+n)/2}
2841    * @f]
2842    */
2843   template<typename _RealType = double>
2844     class fisher_f_distribution
2845     {
2846       static_assert(std::is_floating_point<_RealType>::value,
2847                     "template argument not a floating point type");
2848
2849     public:
2850       /** The type of the range of the distribution. */
2851       typedef _RealType result_type;
2852       /** Parameter type. */
2853       struct param_type
2854       {
2855         typedef fisher_f_distribution<_RealType> distribution_type;
2856
2857         explicit
2858         param_type(_RealType __m = _RealType(1),
2859                    _RealType __n = _RealType(1))
2860         : _M_m(__m), _M_n(__n)
2861         { }
2862
2863         _RealType
2864         m() const
2865         { return _M_m; }
2866
2867         _RealType
2868         n() const
2869         { return _M_n; }
2870
2871         friend bool
2872         operator==(const param_type& __p1, const param_type& __p2)
2873         { return __p1._M_m == __p2._M_m && __p1._M_n == __p2._M_n; }
2874
2875       private:
2876         _RealType _M_m;
2877         _RealType _M_n;
2878       };
2879
2880       explicit
2881       fisher_f_distribution(_RealType __m = _RealType(1),
2882                             _RealType __n = _RealType(1))
2883       : _M_param(__m, __n), _M_gd_x(__m / 2), _M_gd_y(__n / 2)
2884       { }
2885
2886       explicit
2887       fisher_f_distribution(const param_type& __p)
2888       : _M_param(__p), _M_gd_x(__p.m() / 2), _M_gd_y(__p.n() / 2)
2889       { }
2890
2891       /**
2892        * @brief Resets the distribution state.
2893        */
2894       void
2895       reset()
2896       {
2897         _M_gd_x.reset();
2898         _M_gd_y.reset();
2899       }
2900
2901       /**
2902        *
2903        */
2904       _RealType
2905       m() const
2906       { return _M_param.m(); }
2907
2908       _RealType
2909       n() const
2910       { return _M_param.n(); }
2911
2912       /**
2913        * @brief Returns the parameter set of the distribution.
2914        */
2915       param_type
2916       param() const
2917       { return _M_param; }
2918
2919       /**
2920        * @brief Sets the parameter set of the distribution.
2921        * @param __param The new parameter set of the distribution.
2922        */
2923       void
2924       param(const param_type& __param)
2925       { _M_param = __param; }
2926
2927       /**
2928        * @brief Returns the greatest lower bound value of the distribution.
2929        */
2930       result_type
2931       min() const
2932       { return result_type(0); }
2933
2934       /**
2935        * @brief Returns the least upper bound value of the distribution.
2936        */
2937       result_type
2938       max() const
2939       { return std::numeric_limits<result_type>::max(); }
2940
2941       /**
2942        * @brief Generating functions.
2943        */
2944       template<typename _UniformRandomNumberGenerator>
2945         result_type
2946         operator()(_UniformRandomNumberGenerator& __urng)
2947         { return (_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()); }
2948
2949       template<typename _UniformRandomNumberGenerator>
2950         result_type
2951         operator()(_UniformRandomNumberGenerator& __urng,
2952                    const param_type& __p)
2953         {
2954           typedef typename std::gamma_distribution<result_type>::param_type
2955             param_type;
2956           return ((_M_gd_x(__urng, param_type(__p.m() / 2)) * n())
2957                   / (_M_gd_y(__urng, param_type(__p.n() / 2)) * m()));
2958         }
2959
2960       /**
2961        * @brief Return true if two Fisher f distributions have
2962        *        the same parameters and the sequences that would
2963        *        be generated are equal.
2964        */
2965       template<typename _RealType1>
2966         friend bool
2967         operator==(const std::fisher_f_distribution<_RealType1>& __d1,
2968                    const std::fisher_f_distribution<_RealType1>& __d2)
2969         { return (__d1.param() == __d2.param()
2970                   && __d1._M_gd_x == __d2._M_gd_x
2971                   && __d1._M_gd_y == __d2._M_gd_y); }
2972
2973       /**
2974        * @brief Inserts a %fisher_f_distribution random number distribution
2975        * @p __x into the output stream @p __os.
2976        *
2977        * @param __os An output stream.
2978        * @param __x  A %fisher_f_distribution random number distribution.
2979        *
2980        * @returns The output stream with the state of @p __x inserted or in
2981        * an error state.
2982        */
2983       template<typename _RealType1, typename _CharT, typename _Traits>
2984         friend std::basic_ostream<_CharT, _Traits>&
2985         operator<<(std::basic_ostream<_CharT, _Traits>&,
2986                    const std::fisher_f_distribution<_RealType1>&);
2987
2988       /**
2989        * @brief Extracts a %fisher_f_distribution random number distribution
2990        * @p __x from the input stream @p __is.
2991        *
2992        * @param __is An input stream.
2993        * @param __x A %fisher_f_distribution random number
2994        *            generator engine.
2995        *
2996        * @returns The input stream with @p __x extracted or in an error state.
2997        */
2998       template<typename _RealType1, typename _CharT, typename _Traits>
2999         friend std::basic_istream<_CharT, _Traits>&
3000         operator>>(std::basic_istream<_CharT, _Traits>&,
3001                    std::fisher_f_distribution<_RealType1>&);
3002
3003     private:
3004       param_type _M_param;
3005
3006       std::gamma_distribution<result_type> _M_gd_x, _M_gd_y;
3007     };
3008
3009   /**
3010    * @brief Return true if two Fisher f distributions are diferent.
3011    */
3012   template<typename _RealType>
3013     inline bool
3014     operator!=(const std::fisher_f_distribution<_RealType>& __d1,
3015                const std::fisher_f_distribution<_RealType>& __d2)
3016     { return !(__d1 == __d2); }
3017
3018   /**
3019    * @brief A student_t_distribution random number distribution.
3020    *
3021    * The formula for the normal probability mass function is:
3022    * @f[
3023    *     p(x|n) = \frac{1}{\sqrt(n\pi)} \frac{\Gamma((n+1)/2)}{\Gamma(n/2)}
3024    *              (1 + \frac{x^2}{n}) ^{-(n+1)/2}
3025    * @f]
3026    */
3027   template<typename _RealType = double>
3028     class student_t_distribution
3029     {
3030       static_assert(std::is_floating_point<_RealType>::value,
3031                     "template argument not a floating point type");
3032
3033     public:
3034       /** The type of the range of the distribution. */
3035       typedef _RealType result_type;
3036       /** Parameter type. */
3037       struct param_type
3038       {
3039         typedef student_t_distribution<_RealType> distribution_type;
3040
3041         explicit
3042         param_type(_RealType __n = _RealType(1))
3043         : _M_n(__n)
3044         { }
3045
3046         _RealType
3047         n() const
3048         { return _M_n; }
3049
3050         friend bool
3051         operator==(const param_type& __p1, const param_type& __p2)
3052         { return __p1._M_n == __p2._M_n; }
3053
3054       private:
3055         _RealType _M_n;
3056       };
3057
3058       explicit
3059       student_t_distribution(_RealType __n = _RealType(1))
3060       : _M_param(__n), _M_nd(), _M_gd(__n / 2, 2)
3061       { }
3062
3063       explicit
3064       student_t_distribution(const param_type& __p)
3065       : _M_param(__p), _M_nd(), _M_gd(__p.n() / 2, 2)
3066       { }
3067
3068       /**
3069        * @brief Resets the distribution state.
3070        */
3071       void
3072       reset()
3073       {
3074         _M_nd.reset();
3075         _M_gd.reset();
3076       }
3077
3078       /**
3079        *
3080        */
3081       _RealType
3082       n() const
3083       { return _M_param.n(); }
3084
3085       /**
3086        * @brief Returns the parameter set of the distribution.
3087        */
3088       param_type
3089       param() const
3090       { return _M_param; }
3091
3092       /**
3093        * @brief Sets the parameter set of the distribution.
3094        * @param __param The new parameter set of the distribution.
3095        */
3096       void
3097       param(const param_type& __param)
3098       { _M_param = __param; }
3099
3100       /**
3101        * @brief Returns the greatest lower bound value of the distribution.
3102        */
3103       result_type
3104       min() const
3105       { return std::numeric_limits<result_type>::min(); }
3106
3107       /**
3108        * @brief Returns the least upper bound value of the distribution.
3109        */
3110       result_type
3111       max() const
3112       { return std::numeric_limits<result_type>::max(); }
3113
3114       /**
3115        * @brief Generating functions.
3116        */
3117       template<typename _UniformRandomNumberGenerator>
3118         result_type
3119         operator()(_UniformRandomNumberGenerator& __urng)
3120         { return _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng)); }
3121
3122       template<typename _UniformRandomNumberGenerator>
3123         result_type
3124         operator()(_UniformRandomNumberGenerator& __urng,
3125                    const param_type& __p)
3126         {
3127           typedef typename std::gamma_distribution<result_type>::param_type
3128             param_type;
3129
3130           const result_type __g = _M_gd(__urng, param_type(__p.n() / 2, 2));
3131           return _M_nd(__urng) * std::sqrt(__p.n() / __g);
3132         }
3133
3134       /**
3135        * @brief Return true if two Student t distributions have
3136        *        the same parameters and the sequences that would
3137        *        be generated are equal.
3138        */
3139       template<typename _RealType1>
3140         friend bool
3141         operator==(const std::student_t_distribution<_RealType1>& __d1,
3142                    const std::student_t_distribution<_RealType1>& __d2)
3143         { return (__d1.param() == __d2.param()
3144                   && __d1._M_nd == __d2._M_nd && __d1._M_gd == __d2._M_gd); }
3145
3146       /**
3147        * @brief Inserts a %student_t_distribution random number distribution
3148        * @p __x into the output stream @p __os.
3149        *
3150        * @param __os An output stream.
3151        * @param __x  A %student_t_distribution random number distribution.
3152        *
3153        * @returns The output stream with the state of @p __x inserted or in
3154        * an error state.
3155        */
3156       template<typename _RealType1, typename _CharT, typename _Traits>
3157         friend std::basic_ostream<_CharT, _Traits>&
3158         operator<<(std::basic_ostream<_CharT, _Traits>&,
3159                    const std::student_t_distribution<_RealType1>&);
3160
3161       /**
3162        * @brief Extracts a %student_t_distribution random number distribution
3163        * @p __x from the input stream @p __is.
3164        *
3165        * @param __is An input stream.
3166        * @param __x A %student_t_distribution random number
3167        *            generator engine.
3168        *
3169        * @returns The input stream with @p __x extracted or in an error state.
3170        */
3171       template<typename _RealType1, typename _CharT, typename _Traits>
3172         friend std::basic_istream<_CharT, _Traits>&
3173         operator>>(std::basic_istream<_CharT, _Traits>&,
3174                    std::student_t_distribution<_RealType1>&);
3175
3176     private:
3177       param_type _M_param;
3178
3179       std::normal_distribution<result_type> _M_nd;
3180       std::gamma_distribution<result_type> _M_gd;
3181     };
3182
3183   /**
3184    * @brief Return true if two Student t distributions are different.
3185    */
3186   template<typename _RealType>
3187     inline bool
3188     operator!=(const std::student_t_distribution<_RealType>& __d1,
3189                const std::student_t_distribution<_RealType>& __d2)
3190     { return !(__d1 == __d2); }
3191
3192
3193   /* @} */ // group random_distributions_normal
3194
3195   /**
3196    * @addtogroup random_distributions_bernoulli Bernoulli Distributions
3197    * @ingroup random_distributions
3198    * @{
3199    */
3200
3201   /**
3202    * @brief A Bernoulli random number distribution.
3203    *
3204    * Generates a sequence of true and false values with likelihood @f$p@f$
3205    * that true will come up and @f$(1 - p)@f$ that false will appear.
3206    */
3207   class bernoulli_distribution
3208   {
3209   public:
3210     /** The type of the range of the distribution. */
3211     typedef bool result_type;
3212     /** Parameter type. */
3213     struct param_type
3214     {
3215       typedef bernoulli_distribution distribution_type;
3216
3217       explicit
3218       param_type(double __p = 0.5)
3219       : _M_p(__p)
3220       {
3221         _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0));
3222       }
3223
3224       double
3225       p() const
3226       { return _M_p; }
3227
3228       friend bool
3229       operator==(const param_type& __p1, const param_type& __p2)
3230       { return __p1._M_p == __p2._M_p; }
3231
3232     private:
3233       double _M_p;
3234     };
3235
3236   public:
3237     /**
3238      * @brief Constructs a Bernoulli distribution with likelihood @p p.
3239      *
3240      * @param __p  [IN]  The likelihood of a true result being returned.
3241      *                   Must be in the interval @f$[0, 1]@f$.
3242      */
3243     explicit
3244     bernoulli_distribution(double __p = 0.5)
3245     : _M_param(__p)
3246     { }
3247
3248     explicit
3249     bernoulli_distribution(const param_type& __p)
3250     : _M_param(__p)
3251     { }
3252
3253     /**
3254      * @brief Resets the distribution state.
3255      *
3256      * Does nothing for a Bernoulli distribution.
3257      */
3258     void
3259     reset() { }
3260
3261     /**
3262      * @brief Returns the @p p parameter of the distribution.
3263      */
3264     double
3265     p() const
3266     { return _M_param.p(); }
3267
3268     /**
3269      * @brief Returns the parameter set of the distribution.
3270      */
3271     param_type
3272     param() const
3273     { return _M_param; }
3274
3275     /**
3276      * @brief Sets the parameter set of the distribution.
3277      * @param __param The new parameter set of the distribution.
3278      */
3279     void
3280     param(const param_type& __param)
3281     { _M_param = __param; }
3282
3283     /**
3284      * @brief Returns the greatest lower bound value of the distribution.
3285      */
3286     result_type
3287     min() const
3288     { return std::numeric_limits<result_type>::min(); }
3289
3290     /**
3291      * @brief Returns the least upper bound value of the distribution.
3292      */
3293     result_type
3294     max() const
3295     { return std::numeric_limits<result_type>::max(); }
3296
3297     /**
3298      * @brief Generating functions.
3299      */
3300     template<typename _UniformRandomNumberGenerator>
3301       result_type
3302       operator()(_UniformRandomNumberGenerator& __urng)
3303       { return this->operator()(__urng, this->param()); }
3304
3305     template<typename _UniformRandomNumberGenerator>
3306       result_type
3307       operator()(_UniformRandomNumberGenerator& __urng,
3308                  const param_type& __p)
3309       {
3310         __detail::_Adaptor<_UniformRandomNumberGenerator, double>
3311           __aurng(__urng);
3312         if ((__aurng() - __aurng.min())
3313              < __p.p() * (__aurng.max() - __aurng.min()))
3314           return true;
3315         return false;
3316       }
3317
3318   private:
3319     param_type _M_param;
3320   };
3321
3322   /**
3323    * @brief Return true if two Bernoulli distributions have
3324    *        the same parameters.
3325    */
3326   inline bool
3327   operator==(const std::bernoulli_distribution& __d1,
3328              const std::bernoulli_distribution& __d2)
3329   { return __d1.param() == __d2.param(); }
3330
3331   /**
3332    * @brief Return true if two Bernoulli distributions have
3333    *        different parameters.
3334    */
3335   inline bool
3336   operator!=(const std::bernoulli_distribution& __d1,
3337              const std::bernoulli_distribution& __d2)
3338   { return !(__d1 == __d2); }
3339
3340   /**
3341    * @brief Inserts a %bernoulli_distribution random number distribution
3342    * @p __x into the output stream @p __os.
3343    *
3344    * @param __os An output stream.
3345    * @param __x  A %bernoulli_distribution random number distribution.
3346    *
3347    * @returns The output stream with the state of @p __x inserted or in
3348    * an error state.
3349    */
3350   template<typename _CharT, typename _Traits>
3351     std::basic_ostream<_CharT, _Traits>&
3352     operator<<(std::basic_ostream<_CharT, _Traits>&,
3353                const std::bernoulli_distribution&);
3354
3355   /**
3356    * @brief Extracts a %bernoulli_distribution random number distribution
3357    * @p __x from the input stream @p __is.
3358    *
3359    * @param __is An input stream.
3360    * @param __x  A %bernoulli_distribution random number generator engine.
3361    *
3362    * @returns The input stream with @p __x extracted or in an error state.
3363    */
3364   template<typename _CharT, typename _Traits>
3365     std::basic_istream<_CharT, _Traits>&
3366     operator>>(std::basic_istream<_CharT, _Traits>& __is,
3367                std::bernoulli_distribution& __x)
3368     {
3369       double __p;
3370       __is >> __p;
3371       __x.param(bernoulli_distribution::param_type(__p));
3372       return __is;
3373     }
3374
3375
3376   /**
3377    * @brief A discrete binomial random number distribution.
3378    *
3379    * The formula for the binomial probability density function is
3380    * @f$p(i|t,p) = \binom{n}{i} p^i (1 - p)^{t - i}@f$ where @f$t@f$
3381    * and @f$p@f$ are the parameters of the distribution.
3382    */
3383   template<typename _IntType = int>
3384     class binomial_distribution
3385     {
3386       static_assert(std::is_integral<_IntType>::value,
3387                     "template argument not an integral type");
3388
3389     public:
3390       /** The type of the range of the distribution. */
3391       typedef _IntType result_type;
3392       /** Parameter type. */
3393       struct param_type
3394       {
3395         typedef binomial_distribution<_IntType> distribution_type;
3396         friend class binomial_distribution<_IntType>;
3397
3398         explicit
3399         param_type(_IntType __t = _IntType(1), double __p = 0.5)
3400         : _M_t(__t), _M_p(__p)
3401         {
3402           _GLIBCXX_DEBUG_ASSERT((_M_t >= _IntType(0))
3403                                 && (_M_p >= 0.0)
3404                                 && (_M_p <= 1.0));
3405           _M_initialize();
3406         }
3407
3408         _IntType
3409         t() const
3410         { return _M_t; }
3411
3412         double
3413         p() const
3414         { return _M_p; }
3415
3416         friend bool
3417         operator==(const param_type& __p1, const param_type& __p2)
3418         { return __p1._M_t == __p2._M_t && __p1._M_p == __p2._M_p; }
3419
3420       private:
3421         void
3422         _M_initialize();
3423
3424         _IntType _M_t;
3425         double _M_p;
3426
3427         double _M_q;
3428 #if _GLIBCXX_USE_C99_MATH_TR1
3429         double _M_d1, _M_d2, _M_s1, _M_s2, _M_c,
3430                _M_a1, _M_a123, _M_s, _M_lf, _M_lp1p;
3431 #endif
3432         bool   _M_easy;
3433       };
3434
3435       // constructors and member function
3436       explicit
3437       binomial_distribution(_IntType __t = _IntType(1),
3438                             double __p = 0.5)
3439       : _M_param(__t, __p), _M_nd()
3440       { }
3441
3442       explicit
3443       binomial_distribution(const param_type& __p)
3444       : _M_param(__p), _M_nd()
3445       { }
3446
3447       /**
3448        * @brief Resets the distribution state.
3449        */
3450       void
3451       reset()
3452       { _M_nd.reset(); }
3453
3454       /**
3455        * @brief Returns the distribution @p t parameter.
3456        */
3457       _IntType
3458       t() const
3459       { return _M_param.t(); }
3460
3461       /**
3462        * @brief Returns the distribution @p p parameter.
3463        */
3464       double
3465       p() const
3466       { return _M_param.p(); }
3467
3468       /**
3469        * @brief Returns the parameter set of the distribution.
3470        */
3471       param_type
3472       param() const
3473       { return _M_param; }
3474
3475       /**
3476        * @brief Sets the parameter set of the distribution.
3477        * @param __param The new parameter set of the distribution.
3478        */
3479       void
3480       param(const param_type& __param)
3481       { _M_param = __param; }
3482
3483       /**
3484        * @brief Returns the greatest lower bound value of the distribution.
3485        */
3486       result_type
3487       min() const
3488       { return 0; }
3489
3490       /**
3491        * @brief Returns the least upper bound value of the distribution.
3492        */
3493       result_type
3494       max() const
3495       { return _M_param.t(); }
3496
3497       /**
3498        * @brief Generating functions.
3499        */
3500       template<typename _UniformRandomNumberGenerator>
3501         result_type
3502         operator()(_UniformRandomNumberGenerator& __urng)
3503         { return this->operator()(__urng, this->param()); }
3504
3505       template<typename _UniformRandomNumberGenerator>
3506         result_type
3507         operator()(_UniformRandomNumberGenerator& __urng,
3508                    const param_type& __p);
3509
3510       /**
3511        * @brief Return true if two binomial distributions have
3512        *        the same parameters and the sequences that would
3513        *        be generated are equal.
3514        */
3515       template<typename _IntType1>
3516         friend bool
3517         operator==(const std::binomial_distribution<_IntType1>& __d1,
3518                    const std::binomial_distribution<_IntType1>& __d2)
3519 #ifdef _GLIBCXX_USE_C99_MATH_TR1
3520         { return __d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd; }
3521 #else
3522         { return __d1.param() == __d2.param(); }
3523 #endif
3524
3525       /**
3526        * @brief Inserts a %binomial_distribution random number distribution
3527        * @p __x into the output stream @p __os.
3528        *
3529        * @param __os An output stream.
3530        * @param __x  A %binomial_distribution random number distribution.
3531        *
3532        * @returns The output stream with the state of @p __x inserted or in
3533        * an error state.
3534        */
3535       template<typename _IntType1,
3536                typename _CharT, typename _Traits>
3537         friend std::basic_ostream<_CharT, _Traits>&
3538         operator<<(std::basic_ostream<_CharT, _Traits>&,
3539                    const std::binomial_distribution<_IntType1>&);
3540
3541       /**
3542        * @brief Extracts a %binomial_distribution random number distribution
3543        * @p __x from the input stream @p __is.
3544        *
3545        * @param __is An input stream.
3546        * @param __x  A %binomial_distribution random number generator engine.
3547        *
3548        * @returns The input stream with @p __x extracted or in an error
3549        *          state.
3550        */
3551       template<typename _IntType1,
3552                typename _CharT, typename _Traits>
3553         friend std::basic_istream<_CharT, _Traits>&
3554         operator>>(std::basic_istream<_CharT, _Traits>&,
3555                    std::binomial_distribution<_IntType1>&);
3556
3557     private:
3558       template<typename _UniformRandomNumberGenerator>
3559         result_type
3560         _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t);
3561
3562       param_type _M_param;
3563
3564       // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
3565       std::normal_distribution<double> _M_nd;
3566     };
3567
3568   /**
3569    * @brief Return true if two binomial distributions are different.
3570    */
3571   template<typename _IntType>
3572     inline bool
3573     operator!=(const std::binomial_distribution<_IntType>& __d1,
3574                const std::binomial_distribution<_IntType>& __d2)
3575     { return !(__d1 == __d2); }
3576
3577
3578   /**
3579    * @brief A discrete geometric random number distribution.
3580    *
3581    * The formula for the geometric probability density function is
3582    * @f$p(i|p) = (1 - p)p^{i-1}@f$ where @f$p@f$ is the parameter of the
3583    * distribution.
3584    */
3585   template<typename _IntType = int>
3586     class geometric_distribution
3587     {
3588       static_assert(std::is_integral<_IntType>::value,
3589                     "template argument not an integral type");
3590
3591     public:
3592       /** The type of the range of the distribution. */
3593       typedef _IntType  result_type;
3594       /** Parameter type. */
3595       struct param_type
3596       {
3597         typedef geometric_distribution<_IntType> distribution_type;
3598         friend class geometric_distribution<_IntType>;
3599
3600         explicit
3601         param_type(double __p = 0.5)
3602         : _M_p(__p)
3603         {
3604           _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0)
3605                              && (_M_p <= 1.0));
3606           _M_initialize();
3607         }
3608
3609         double
3610         p() const
3611         { return _M_p; }
3612
3613         friend bool
3614         operator==(const param_type& __p1, const param_type& __p2)
3615         { return __p1._M_p == __p2._M_p; }
3616
3617       private:
3618         void
3619         _M_initialize()
3620         { _M_log_p = std::log(_M_p); }
3621
3622         double _M_p;
3623
3624         double _M_log_p;
3625       };
3626
3627       // constructors and member function
3628       explicit
3629       geometric_distribution(double __p = 0.5)
3630       : _M_param(__p)
3631       { }
3632
3633       explicit
3634       geometric_distribution(const param_type& __p)
3635       : _M_param(__p)
3636       { }
3637
3638       /**
3639        * @brief Resets the distribution state.
3640        *
3641        * Does nothing for the geometric distribution.
3642        */
3643       void
3644       reset() { }
3645
3646       /**
3647        * @brief Returns the distribution parameter @p p.
3648        */
3649       double
3650       p() const
3651       { return _M_param.p(); }
3652
3653       /**
3654        * @brief Returns the parameter set of the distribution.
3655        */
3656       param_type
3657       param() const
3658       { return _M_param; }
3659
3660       /**
3661        * @brief Sets the parameter set of the distribution.
3662        * @param __param The new parameter set of the distribution.
3663        */
3664       void
3665       param(const param_type& __param)
3666       { _M_param = __param; }
3667
3668       /**
3669        * @brief Returns the greatest lower bound value of the distribution.
3670        */
3671       result_type
3672       min() const
3673       { return 0; }
3674
3675       /**
3676        * @brief Returns the least upper bound value of the distribution.
3677        */
3678       result_type
3679       max() const
3680       { return std::numeric_limits<result_type>::max(); }
3681
3682       /**
3683        * @brief Generating functions.
3684        */
3685       template<typename _UniformRandomNumberGenerator>
3686         result_type
3687         operator()(_UniformRandomNumberGenerator& __urng)
3688         { return this->operator()(__urng, this->param()); }
3689
3690       template<typename _UniformRandomNumberGenerator>
3691         result_type
3692         operator()(_UniformRandomNumberGenerator& __urng,
3693                    const param_type& __p);
3694
3695     private:
3696       param_type _M_param;
3697     };
3698
3699   /**
3700    * @brief Return true if two geometric distributions have
3701    *        the same parameters.
3702    */
3703   template<typename _IntType>
3704     inline bool
3705     operator==(const std::geometric_distribution<_IntType>& __d1,
3706                const std::geometric_distribution<_IntType>& __d2)
3707     { return __d1.param() == __d2.param(); }
3708
3709   /**
3710    * @brief Return true if two geometric distributions have
3711    *        different parameters.
3712    */
3713   template<typename _IntType>
3714     inline bool
3715     operator!=(const std::geometric_distribution<_IntType>& __d1,
3716                const std::geometric_distribution<_IntType>& __d2)
3717     { return !(__d1 == __d2); }
3718
3719   /**
3720    * @brief Inserts a %geometric_distribution random number distribution
3721    * @p __x into the output stream @p __os.
3722    *
3723    * @param __os An output stream.
3724    * @param __x  A %geometric_distribution random number distribution.
3725    *
3726    * @returns The output stream with the state of @p __x inserted or in
3727    * an error state.
3728    */
3729   template<typename _IntType,
3730            typename _CharT, typename _Traits>
3731     std::basic_ostream<_CharT, _Traits>&
3732     operator<<(std::basic_ostream<_CharT, _Traits>&,
3733                const std::geometric_distribution<_IntType>&);
3734
3735   /**
3736    * @brief Extracts a %geometric_distribution random number distribution
3737    * @p __x from the input stream @p __is.
3738    *
3739    * @param __is An input stream.
3740    * @param __x  A %geometric_distribution random number generator engine.
3741    *
3742    * @returns The input stream with @p __x extracted or in an error state.
3743    */
3744   template<typename _IntType,
3745            typename _CharT, typename _Traits>
3746     std::basic_istream<_CharT, _Traits>&
3747     operator>>(std::basic_istream<_CharT, _Traits>&,
3748                std::geometric_distribution<_IntType>&);
3749
3750
3751   /**
3752    * @brief A negative_binomial_distribution random number distribution.
3753    *
3754    * The formula for the negative binomial probability mass function is
3755    * @f$p(i) = \binom{n}{i} p^i (1 - p)^{t - i}@f$ where @f$t@f$
3756    * and @f$p@f$ are the parameters of the distribution.
3757    */
3758   template<typename _IntType = int>
3759     class negative_binomial_distribution
3760     {
3761       static_assert(std::is_integral<_IntType>::value,
3762                     "template argument not an integral type");
3763
3764     public:
3765       /** The type of the range of the distribution. */
3766       typedef _IntType result_type;
3767       /** Parameter type. */
3768       struct param_type
3769       {
3770         typedef negative_binomial_distribution<_IntType> distribution_type;
3771
3772         explicit
3773         param_type(_IntType __k = 1, double __p = 0.5)
3774         : _M_k(__k), _M_p(__p)
3775         { }
3776
3777         _IntType
3778         k() const
3779         { return _M_k; }
3780
3781         double
3782         p() const
3783         { return _M_p; }
3784
3785         friend bool
3786         operator==(const param_type& __p1, const param_type& __p2)
3787         { return __p1._M_k == __p2._M_k && __p1._M_p == __p2._M_p; }
3788
3789       private:
3790         _IntType _M_k;
3791         double _M_p;
3792       };
3793
3794       explicit
3795       negative_binomial_distribution(_IntType __k = 1, double __p = 0.5)
3796       : _M_param(__k, __p), _M_gd(__k, __p / (1.0 - __p))
3797       { }
3798
3799       explicit
3800       negative_binomial_distribution(const param_type& __p)
3801       : _M_param(__p), _M_gd(__p.k(), __p.p() / (1.0 - __p.p()))
3802       { }
3803
3804       /**
3805        * @brief Resets the distribution state.
3806        */
3807       void
3808       reset()
3809       { _M_gd.reset(); }
3810
3811       /**
3812        * @brief Return the @f$k@f$ parameter of the distribution.
3813        */
3814       _IntType
3815       k() const
3816       { return _M_param.k(); }
3817
3818       /**
3819        * @brief Return the @f$p@f$ parameter of the distribution.
3820        */
3821       double
3822       p() const
3823       { return _M_param.p(); }
3824
3825       /**
3826        * @brief Returns the parameter set of the distribution.
3827        */
3828       param_type
3829       param() const
3830       { return _M_param; }
3831
3832       /**
3833        * @brief Sets the parameter set of the distribution.
3834        * @param __param The new parameter set of the distribution.
3835        */
3836       void
3837       param(const param_type& __param)
3838       { _M_param = __param; }
3839
3840       /**
3841        * @brief Returns the greatest lower bound value of the distribution.
3842        */
3843       result_type
3844       min() const
3845       { return result_type(0); }
3846
3847       /**
3848        * @brief Returns the least upper bound value of the distribution.
3849        */
3850       result_type
3851       max() const
3852       { return std::numeric_limits<result_type>::max(); }
3853
3854       /**
3855        * @brief Generating functions.
3856        */
3857       template<typename _UniformRandomNumberGenerator>
3858         result_type
3859         operator()(_UniformRandomNumberGenerator& __urng);
3860
3861       template<typename _UniformRandomNumberGenerator>
3862         result_type
3863         operator()(_UniformRandomNumberGenerator& __urng,
3864                    const param_type& __p);
3865
3866       /**
3867        * @brief Return true if two negative binomial distributions have
3868        *        the same parameters and the sequences that would be
3869        *        generated are equal.
3870        */
3871       template<typename _IntType1>
3872         friend bool
3873         operator==(const std::negative_binomial_distribution<_IntType1>& __d1,
3874                    const std::negative_binomial_distribution<_IntType1>& __d2)
3875         { return __d1.param() == __d2.param() && __d1._M_gd == __d2._M_gd; }
3876
3877       /**
3878        * @brief Inserts a %negative_binomial_distribution random
3879        *        number distribution @p __x into the output stream @p __os.
3880        *
3881        * @param __os An output stream.
3882        * @param __x  A %negative_binomial_distribution random number
3883        *             distribution.
3884        *
3885        * @returns The output stream with the state of @p __x inserted or in
3886        *          an error state.
3887        */
3888       template<typename _IntType1, typename _CharT, typename _Traits>
3889         friend std::basic_ostream<_CharT, _Traits>&
3890         operator<<(std::basic_ostream<_CharT, _Traits>&,
3891                    const std::negative_binomial_distribution<_IntType1>&);
3892
3893       /**
3894        * @brief Extracts a %negative_binomial_distribution random number
3895        *        distribution @p __x from the input stream @p __is.
3896        *
3897        * @param __is An input stream.
3898        * @param __x A %negative_binomial_distribution random number
3899        *            generator engine.
3900        *
3901        * @returns The input stream with @p __x extracted or in an error state.
3902        */
3903       template<typename _IntType1, typename _CharT, typename _Traits>
3904         friend std::basic_istream<_CharT, _Traits>&
3905         operator>>(std::basic_istream<_CharT, _Traits>&,
3906                    std::negative_binomial_distribution<_IntType1>&);
3907
3908     private:
3909       param_type _M_param;
3910
3911       std::gamma_distribution<double> _M_gd;
3912     };
3913
3914   /**
3915    * @brief Return true if two negative binomial distributions are different.
3916    */
3917   template<typename _IntType>
3918     inline bool
3919     operator!=(const std::negative_binomial_distribution<_IntType>& __d1,
3920                const std::negative_binomial_distribution<_IntType>& __d2)
3921     { return !(__d1 == __d2); }
3922
3923
3924   /* @} */ // group random_distributions_bernoulli
3925
3926   /**
3927    * @addtogroup random_distributions_poisson Poisson Distributions
3928    * @ingroup random_distributions
3929    * @{
3930    */
3931
3932   /**
3933    * @brief A discrete Poisson random number distribution.
3934    *
3935    * The formula for the Poisson probability density function is
3936    * @f$p(i|\mu) = \frac{\mu^i}{i!} e^{-\mu}@f$ where @f$\mu@f$ is the
3937    * parameter of the distribution.
3938    */
3939   template<typename _IntType = int>
3940     class poisson_distribution
3941     {
3942       static_assert(std::is_integral<_IntType>::value,
3943                     "template argument not an integral type");
3944
3945     public:
3946       /** The type of the range of the distribution. */
3947       typedef _IntType  result_type;
3948       /** Parameter type. */
3949       struct param_type
3950       {
3951         typedef poisson_distribution<_IntType> distribution_type;
3952         friend class poisson_distribution<_IntType>;
3953
3954         explicit
3955         param_type(double __mean = 1.0)
3956         : _M_mean(__mean)
3957         {
3958           _GLIBCXX_DEBUG_ASSERT(_M_mean > 0.0);
3959           _M_initialize();
3960         }
3961
3962         double
3963         mean() const
3964         { return _M_mean; }
3965
3966         friend bool
3967         operator==(const param_type& __p1, const param_type& __p2)
3968         { return __p1._M_mean == __p2._M_mean; }
3969
3970       private:
3971         // Hosts either log(mean) or the threshold of the simple method.
3972         void
3973         _M_initialize();
3974
3975         double _M_mean;
3976
3977         double _M_lm_thr;
3978 #if _GLIBCXX_USE_C99_MATH_TR1
3979         double _M_lfm, _M_sm, _M_d, _M_scx, _M_1cx, _M_c2b, _M_cb;
3980 #endif
3981       };
3982
3983       // constructors and member function
3984       explicit
3985       poisson_distribution(double __mean = 1.0)
3986       : _M_param(__mean), _M_nd()
3987       { }
3988
3989       explicit
3990       poisson_distribution(const param_type& __p)
3991       : _M_param(__p), _M_nd()
3992       { }
3993
3994       /**
3995        * @brief Resets the distribution state.
3996        */
3997       void
3998       reset()
3999       { _M_nd.reset(); }
4000
4001       /**
4002        * @brief Returns the distribution parameter @p mean.
4003        */
4004       double
4005       mean() const
4006       { return _M_param.mean(); }
4007
4008       /**
4009        * @brief Returns the parameter set of the distribution.
4010        */
4011       param_type
4012       param() const
4013       { return _M_param; }
4014
4015       /**
4016        * @brief Sets the parameter set of the distribution.
4017        * @param __param The new parameter set of the distribution.
4018        */
4019       void
4020       param(const param_type& __param)
4021       { _M_param = __param; }
4022
4023       /**
4024        * @brief Returns the greatest lower bound value of the distribution.
4025        */
4026       result_type
4027       min() const
4028       { return 0; }
4029
4030       /**
4031        * @brief Returns the least upper bound value of the distribution.
4032        */
4033       result_type
4034       max() const
4035       { return std::numeric_limits<result_type>::max(); }
4036
4037       /**
4038        * @brief Generating functions.
4039        */
4040       template<typename _UniformRandomNumberGenerator>
4041         result_type
4042         operator()(_UniformRandomNumberGenerator& __urng)
4043         { return this->operator()(__urng, this->param()); }
4044
4045       template<typename _UniformRandomNumberGenerator>
4046         result_type
4047         operator()(_UniformRandomNumberGenerator& __urng,
4048                    const param_type& __p);
4049
4050        /**
4051         * @brief Return true if two Poisson distributions have the same
4052         *        parameters and the sequences that would be generated
4053         *        are equal.
4054         */
4055       template<typename _IntType1>
4056         friend bool
4057         operator==(const std::poisson_distribution<_IntType1>& __d1,
4058                    const std::poisson_distribution<_IntType1>& __d2)
4059 #ifdef _GLIBCXX_USE_C99_MATH_TR1
4060         { return __d1.param() == __d2.param() && __d1._M_nd == __d2._M_nd; }
4061 #else
4062         { return __d1.param() == __d2.param(); }
4063 #endif
4064
4065       /**
4066        * @brief Inserts a %poisson_distribution random number distribution
4067        * @p __x into the output stream @p __os.
4068        *
4069        * @param __os An output stream.
4070        * @param __x  A %poisson_distribution random number distribution.
4071        *
4072        * @returns The output stream with the state of @p __x inserted or in
4073        * an error state.
4074        */
4075       template<typename _IntType1, typename _CharT, typename _Traits>
4076         friend std::basic_ostream<_CharT, _Traits>&
4077         operator<<(std::basic_ostream<_CharT, _Traits>&,
4078                    const std::poisson_distribution<_IntType1>&);
4079
4080       /**
4081        * @brief Extracts a %poisson_distribution random number distribution
4082        * @p __x from the input stream @p __is.
4083        *
4084        * @param __is An input stream.
4085        * @param __x  A %poisson_distribution random number generator engine.
4086        *
4087        * @returns The input stream with @p __x extracted or in an error
4088        *          state.
4089        */
4090       template<typename _IntType1, typename _CharT, typename _Traits>
4091         friend std::basic_istream<_CharT, _Traits>&
4092         operator>>(std::basic_istream<_CharT, _Traits>&,
4093                    std::poisson_distribution<_IntType1>&);
4094
4095     private:
4096       param_type _M_param;
4097
4098       // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
4099       std::normal_distribution<double> _M_nd;
4100     };
4101
4102   /**
4103    * @brief Return true if two Poisson distributions are different.
4104    */
4105   template<typename _IntType>
4106     inline bool
4107     operator!=(const std::poisson_distribution<_IntType>& __d1,
4108                const std::poisson_distribution<_IntType>& __d2)
4109     { return !(__d1 == __d2); }
4110
4111
4112   /**
4113    * @brief An exponential continuous distribution for random numbers.
4114    *
4115    * The formula for the exponential probability density function is
4116    * @f$p(x|\lambda) = \lambda e^{-\lambda x}@f$.
4117    *
4118    * <table border=1 cellpadding=10 cellspacing=0>
4119    * <caption align=top>Distribution Statistics</caption>
4120    * <tr><td>Mean</td><td>@f$\frac{1}{\lambda}@f$</td></tr>
4121    * <tr><td>Median</td><td>@f$\frac{\ln 2}{\lambda}@f$</td></tr>
4122    * <tr><td>Mode</td><td>@f$zero@f$</td></tr>
4123    * <tr><td>Range</td><td>@f$[0, \infty]@f$</td></tr>
4124    * <tr><td>Standard Deviation</td><td>@f$\frac{1}{\lambda}@f$</td></tr>
4125    * </table>
4126    */
4127   template<typename _RealType = double>
4128     class exponential_distribution
4129     {
4130       static_assert(std::is_floating_point<_RealType>::value,
4131                     "template argument not a floating point type");
4132
4133     public:
4134       /** The type of the range of the distribution. */
4135       typedef _RealType result_type;
4136       /** Parameter type. */
4137       struct param_type
4138       {
4139         typedef exponential_distribution<_RealType> distribution_type;
4140
4141         explicit
4142         param_type(_RealType __lambda = _RealType(1))
4143         : _M_lambda(__lambda)
4144         {
4145           _GLIBCXX_DEBUG_ASSERT(_M_lambda > _RealType(0));
4146         }
4147
4148         _RealType
4149         lambda() const
4150         { return _M_lambda; }
4151
4152         friend bool
4153         operator==(const param_type& __p1, const param_type& __p2)
4154         { return __p1._M_lambda == __p2._M_lambda; }
4155
4156       private:
4157         _RealType _M_lambda;
4158       };
4159
4160     public:
4161       /**
4162        * @brief Constructs an exponential distribution with inverse scale
4163        *        parameter @f$\lambda@f$.
4164        */
4165       explicit
4166       exponential_distribution(const result_type& __lambda = result_type(1))
4167       : _M_param(__lambda)
4168       { }
4169
4170       explicit
4171       exponential_distribution(const param_type& __p)
4172       : _M_param(__p)
4173       { }
4174
4175       /**
4176        * @brief Resets the distribution state.
4177        *
4178        * Has no effect on exponential distributions.
4179        */
4180       void
4181       reset() { }
4182
4183       /**
4184        * @brief Returns the inverse scale parameter of the distribution.
4185        */
4186       _RealType
4187       lambda() const
4188       { return _M_param.lambda(); }
4189
4190       /**
4191        * @brief Returns the parameter set of the distribution.
4192        */
4193       param_type
4194       param() const
4195       { return _M_param; }
4196
4197       /**
4198        * @brief Sets the parameter set of the distribution.
4199        * @param __param The new parameter set of the distribution.
4200        */
4201       void
4202       param(const param_type& __param)
4203       { _M_param = __param; }
4204
4205       /**
4206        * @brief Returns the greatest lower bound value of the distribution.
4207        */
4208       result_type
4209       min() const
4210       { return result_type(0); }
4211
4212       /**
4213        * @brief Returns the least upper bound value of the distribution.
4214        */
4215       result_type
4216       max() const
4217       { return std::numeric_limits<result_type>::max(); }
4218
4219       /**
4220        * @brief Generating functions.
4221        */
4222       template<typename _UniformRandomNumberGenerator>
4223         result_type
4224         operator()(_UniformRandomNumberGenerator& __urng)
4225         { return this->operator()(__urng, this->param()); }
4226
4227       template<typename _UniformRandomNumberGenerator>
4228         result_type
4229         operator()(_UniformRandomNumberGenerator& __urng,
4230                    const param_type& __p)
4231         {
4232           __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
4233             __aurng(__urng);
4234           return -std::log(__aurng()) / __p.lambda();
4235         }
4236
4237     private:
4238       param_type _M_param;
4239     };
4240
4241   /**
4242    * @brief Return true if two exponential distributions have the same
4243    *        parameters.
4244    */
4245   template<typename _RealType>
4246     inline bool
4247     operator==(const std::exponential_distribution<_RealType>& __d1,
4248                const std::exponential_distribution<_RealType>& __d2)
4249     { return __d1.param() == __d2.param(); }
4250
4251   /**
4252    * @brief Return true if two exponential distributions have different
4253    *        parameters.
4254    */
4255   template<typename _RealType>
4256     inline bool
4257     operator!=(const std::exponential_distribution<_RealType>& __d1,
4258                const std::exponential_distribution<_RealType>& __d2)
4259     { return !(__d1 == __d2); }
4260
4261   /**
4262    * @brief Inserts a %exponential_distribution random number distribution
4263    * @p __x into the output stream @p __os.
4264    *
4265    * @param __os An output stream.
4266    * @param __x  A %exponential_distribution random number distribution.
4267    *
4268    * @returns The output stream with the state of @p __x inserted or in
4269    * an error state.
4270    */
4271   template<typename _RealType, typename _CharT, typename _Traits>
4272     std::basic_ostream<_CharT, _Traits>&
4273     operator<<(std::basic_ostream<_CharT, _Traits>&,
4274                const std::exponential_distribution<_RealType>&);
4275
4276   /**
4277    * @brief Extracts a %exponential_distribution random number distribution
4278    * @p __x from the input stream @p __is.
4279    *
4280    * @param __is An input stream.
4281    * @param __x A %exponential_distribution random number
4282    *            generator engine.
4283    *
4284    * @returns The input stream with @p __x extracted or in an error state.
4285    */
4286   template<typename _RealType, typename _CharT, typename _Traits>
4287     std::basic_istream<_CharT, _Traits>&
4288     operator>>(std::basic_istream<_CharT, _Traits>&,
4289                std::exponential_distribution<_RealType>&);
4290
4291
4292   /**
4293    * @brief A weibull_distribution random number distribution.
4294    *
4295    * The formula for the normal probability density function is:
4296    * @f[
4297    *     p(x|\alpha,\beta) = \frac{\alpha}{\beta} (\frac{x}{\beta})^{\alpha-1}
4298    *                         \exp{(-(\frac{x}{\beta})^\alpha)}
4299    * @f]
4300    */
4301   template<typename _RealType = double>
4302     class weibull_distribution
4303     {
4304       static_assert(std::is_floating_point<_RealType>::value,
4305                     "template argument not a floating point type");
4306
4307     public:
4308       /** The type of the range of the distribution. */
4309       typedef _RealType result_type;
4310       /** Parameter type. */
4311       struct param_type
4312       {
4313         typedef weibull_distribution<_RealType> distribution_type;
4314
4315         explicit
4316         param_type(_RealType __a = _RealType(1),
4317                    _RealType __b = _RealType(1))
4318         : _M_a(__a), _M_b(__b)
4319         { }
4320
4321         _RealType
4322         a() const
4323         { return _M_a; }
4324
4325         _RealType
4326         b() const
4327         { return _M_b; }
4328
4329         friend bool
4330         operator==(const param_type& __p1, const param_type& __p2)
4331         { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
4332
4333       private:
4334         _RealType _M_a;
4335         _RealType _M_b;
4336       };
4337
4338       explicit
4339       weibull_distribution(_RealType __a = _RealType(1),
4340                            _RealType __b = _RealType(1))
4341       : _M_param(__a, __b)
4342       { }
4343
4344       explicit
4345       weibull_distribution(const param_type& __p)
4346       : _M_param(__p)
4347       { }
4348
4349       /**
4350        * @brief Resets the distribution state.
4351        */
4352       void
4353       reset()
4354       { }
4355
4356       /**
4357        * @brief Return the @f$a@f$ parameter of the distribution.
4358        */
4359       _RealType
4360       a() const
4361       { return _M_param.a(); }
4362
4363       /**
4364        * @brief Return the @f$b@f$ parameter of the distribution.
4365        */
4366       _RealType
4367       b() const
4368       { return _M_param.b(); }
4369
4370       /**
4371        * @brief Returns the parameter set of the distribution.
4372        */
4373       param_type
4374       param() const
4375       { return _M_param; }
4376
4377       /**
4378        * @brief Sets the parameter set of the distribution.
4379        * @param __param The new parameter set of the distribution.
4380        */
4381       void
4382       param(const param_type& __param)
4383       { _M_param = __param; }
4384
4385       /**
4386        * @brief Returns the greatest lower bound value of the distribution.
4387        */
4388       result_type
4389       min() const
4390       { return result_type(0); }
4391
4392       /**
4393        * @brief Returns the least upper bound value of the distribution.
4394        */
4395       result_type
4396       max() const
4397       { return std::numeric_limits<result_type>::max(); }
4398
4399       /**
4400        * @brief Generating functions.
4401        */
4402       template<typename _UniformRandomNumberGenerator>
4403         result_type
4404         operator()(_UniformRandomNumberGenerator& __urng)
4405         { return this->operator()(__urng, this->param()); }
4406
4407       template<typename _UniformRandomNumberGenerator>
4408         result_type
4409         operator()(_UniformRandomNumberGenerator& __urng,
4410                    const param_type& __p);
4411
4412     private:
4413       param_type _M_param;
4414     };
4415
4416    /**
4417     * @brief Return true if two Weibull distributions have the same
4418     *        parameters.
4419     */
4420   template<typename _RealType>
4421     inline bool
4422     operator==(const std::weibull_distribution<_RealType>& __d1,
4423                const std::weibull_distribution<_RealType>& __d2)
4424     { return __d1.param() == __d2.param(); }
4425
4426    /**
4427     * @brief Return true if two Weibull distributions have different
4428     *        parameters.
4429     */
4430   template<typename _RealType>
4431     inline bool
4432     operator!=(const std::weibull_distribution<_RealType>& __d1,
4433                const std::weibull_distribution<_RealType>& __d2)
4434     { return !(__d1 == __d2); }
4435
4436   /**
4437    * @brief Inserts a %weibull_distribution random number distribution
4438    * @p __x into the output stream @p __os.
4439    *
4440    * @param __os An output stream.
4441    * @param __x  A %weibull_distribution random number distribution.
4442    *
4443    * @returns The output stream with the state of @p __x inserted or in
4444    * an error state.
4445    */
4446   template<typename _RealType, typename _CharT, typename _Traits>
4447     std::basic_ostream<_CharT, _Traits>&
4448     operator<<(std::basic_ostream<_CharT, _Traits>&,
4449                const std::weibull_distribution<_RealType>&);
4450
4451   /**
4452    * @brief Extracts a %weibull_distribution random number distribution
4453    * @p __x from the input stream @p __is.
4454    *
4455    * @param __is An input stream.
4456    * @param __x A %weibull_distribution random number
4457    *            generator engine.
4458    *
4459    * @returns The input stream with @p __x extracted or in an error state.
4460    */
4461   template<typename _RealType, typename _CharT, typename _Traits>
4462     std::basic_istream<_CharT, _Traits>&
4463     operator>>(std::basic_istream<_CharT, _Traits>&,
4464                std::weibull_distribution<_RealType>&);
4465
4466
4467   /**
4468    * @brief A extreme_value_distribution random number distribution.
4469    *
4470    * The formula for the normal probability mass function is
4471    * @f[
4472    *     p(x|a,b) = \frac{1}{b}
4473    *                \exp( \frac{a-x}{b} - \exp(\frac{a-x}{b}))
4474    * @f]
4475    */
4476   template<typename _RealType = double>
4477     class extreme_value_distribution
4478     {
4479       static_assert(std::is_floating_point<_RealType>::value,
4480                     "template argument not a floating point type");
4481
4482     public:
4483       /** The type of the range of the distribution. */
4484       typedef _RealType result_type;
4485       /** Parameter type. */
4486       struct param_type
4487       {
4488         typedef extreme_value_distribution<_RealType> distribution_type;
4489
4490         explicit
4491         param_type(_RealType __a = _RealType(0),
4492                    _RealType __b = _RealType(1))
4493         : _M_a(__a), _M_b(__b)
4494         { }
4495
4496         _RealType
4497         a() const
4498         { return _M_a; }
4499
4500         _RealType
4501         b() const
4502         { return _M_b; }
4503
4504         friend bool
4505         operator==(const param_type& __p1, const param_type& __p2)
4506         { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
4507
4508       private:
4509         _RealType _M_a;
4510         _RealType _M_b;
4511       };
4512
4513       explicit
4514       extreme_value_distribution(_RealType __a = _RealType(0),
4515                                  _RealType __b = _RealType(1))
4516       : _M_param(__a, __b)
4517       { }
4518
4519       explicit
4520       extreme_value_distribution(const param_type& __p)
4521       : _M_param(__p)
4522       { }
4523
4524       /**
4525        * @brief Resets the distribution state.
4526        */
4527       void
4528       reset()
4529       { }
4530
4531       /**
4532        * @brief Return the @f$a@f$ parameter of the distribution.
4533        */
4534       _RealType
4535       a() const
4536       { return _M_param.a(); }
4537
4538       /**
4539        * @brief Return the @f$b@f$ parameter of the distribution.
4540        */
4541       _RealType
4542       b() const
4543       { return _M_param.b(); }
4544
4545       /**
4546        * @brief Returns the parameter set of the distribution.
4547        */
4548       param_type
4549       param() const
4550       { return _M_param; }
4551
4552       /**
4553        * @brief Sets the parameter set of the distribution.
4554        * @param __param The new parameter set of the distribution.
4555        */
4556       void
4557       param(const param_type& __param)
4558       { _M_param = __param; }
4559
4560       /**
4561        * @brief Returns the greatest lower bound value of the distribution.
4562        */
4563       result_type
4564       min() const
4565       { return std::numeric_limits<result_type>::min(); }
4566
4567       /**
4568        * @brief Returns the least upper bound value of the distribution.
4569        */
4570       result_type
4571       max() const
4572       { return std::numeric_limits<result_type>::max(); }
4573
4574       /**
4575        * @brief Generating functions.
4576        */
4577       template<typename _UniformRandomNumberGenerator>
4578         result_type
4579         operator()(_UniformRandomNumberGenerator& __urng)
4580         { return this->operator()(__urng, this->param()); }
4581
4582       template<typename _UniformRandomNumberGenerator>
4583         result_type
4584         operator()(_UniformRandomNumberGenerator& __urng,
4585                    const param_type& __p);
4586
4587     private:
4588       param_type _M_param;
4589     };
4590
4591   /**
4592     * @brief Return true if two extreme value distributions have the same
4593     *        parameters.
4594    */
4595   template<typename _RealType>
4596     inline bool
4597     operator==(const std::extreme_value_distribution<_RealType>& __d1,
4598                const std::extreme_value_distribution<_RealType>& __d2)
4599     { return __d1.param() == __d2.param(); }
4600
4601   /**
4602     * @brief Return true if two extreme value distributions have different
4603     *        parameters.
4604    */
4605   template<typename _RealType>
4606     inline bool
4607     operator!=(const std::extreme_value_distribution<_RealType>& __d1,
4608                const std::extreme_value_distribution<_RealType>& __d2)
4609     { return !(__d1 == __d2); }
4610
4611   /**
4612    * @brief Inserts a %extreme_value_distribution random number distribution
4613    * @p __x into the output stream @p __os.
4614    *
4615    * @param __os An output stream.
4616    * @param __x  A %extreme_value_distribution random number distribution.
4617    *
4618    * @returns The output stream with the state of @p __x inserted or in
4619    * an error state.
4620    */
4621   template<typename _RealType, typename _CharT, typename _Traits>
4622     std::basic_ostream<_CharT, _Traits>&
4623     operator<<(std::basic_ostream<_CharT, _Traits>&,
4624                const std::extreme_value_distribution<_RealType>&);
4625
4626   /**
4627    * @brief Extracts a %extreme_value_distribution random number
4628    *        distribution @p __x from the input stream @p __is.
4629    *
4630    * @param __is An input stream.
4631    * @param __x A %extreme_value_distribution random number
4632    *            generator engine.
4633    *
4634    * @returns The input stream with @p __x extracted or in an error state.
4635    */
4636   template<typename _RealType, typename _CharT, typename _Traits>
4637     std::basic_istream<_CharT, _Traits>&
4638     operator>>(std::basic_istream<_CharT, _Traits>&,
4639                std::extreme_value_distribution<_RealType>&);
4640
4641
4642   /**
4643    * @brief A discrete_distribution random number distribution.
4644    *
4645    * The formula for the discrete probability mass function is
4646    *
4647    */
4648   template<typename _IntType = int>
4649     class discrete_distribution
4650     {
4651       static_assert(std::is_integral<_IntType>::value,
4652                     "template argument not an integral type");
4653
4654     public:
4655       /** The type of the range of the distribution. */
4656       typedef _IntType result_type;
4657       /** Parameter type. */
4658       struct param_type
4659       {
4660         typedef discrete_distribution<_IntType> distribution_type;
4661         friend class discrete_distribution<_IntType>;
4662
4663         param_type()
4664         : _M_prob(), _M_cp()
4665         { }
4666
4667         template<typename _InputIterator>
4668           param_type(_InputIterator __wbegin,
4669                      _InputIterator __wend)
4670           : _M_prob(__wbegin, __wend), _M_cp()
4671           { _M_initialize(); }
4672
4673         param_type(initializer_list<double> __wil)
4674         : _M_prob(__wil.begin(), __wil.end()), _M_cp()
4675         { _M_initialize(); }
4676
4677         template<typename _Func>
4678           param_type(size_t __nw, double __xmin, double __xmax,
4679                      _Func __fw);
4680
4681         // See: http://cpp-next.com/archive/2010/10/implicit-move-must-go/
4682         param_type(const param_type&) = default;
4683         param_type& operator=(const param_type&) = default;
4684
4685         std::vector<double>
4686         probabilities() const
4687         { return _M_prob.empty() ? std::vector<double>(1, 1.0) : _M_prob; }
4688
4689         friend bool
4690         operator==(const param_type& __p1, const param_type& __p2)
4691         { return __p1._M_prob == __p2._M_prob; }
4692
4693       private:
4694         void
4695         _M_initialize();
4696
4697         std::vector<double> _M_prob;
4698         std::vector<double> _M_cp;
4699       };
4700
4701       discrete_distribution()
4702       : _M_param()
4703       { }
4704
4705       template<typename _InputIterator>
4706         discrete_distribution(_InputIterator __wbegin,
4707                               _InputIterator __wend)
4708         : _M_param(__wbegin, __wend)
4709         { }
4710
4711       discrete_distribution(initializer_list<double> __wl)
4712       : _M_param(__wl)
4713       { }
4714
4715       template<typename _Func>
4716         discrete_distribution(size_t __nw, double __xmin, double __xmax,
4717                               _Func __fw)
4718         : _M_param(__nw, __xmin, __xmax, __fw)
4719         { }
4720
4721       explicit
4722       discrete_distribution(const param_type& __p)
4723       : _M_param(__p)
4724       { }
4725
4726       /**
4727        * @brief Resets the distribution state.
4728        */
4729       void
4730       reset()
4731       { }
4732
4733       /**
4734        * @brief Returns the probabilities of the distribution.
4735        */
4736       std::vector<double>
4737       probabilities() const
4738       {
4739         return _M_param._M_prob.empty()
4740           ? std::vector<double>(1, 1.0) : _M_param._M_prob;
4741       }
4742
4743       /**
4744        * @brief Returns the parameter set of the distribution.
4745        */
4746       param_type
4747       param() const
4748       { return _M_param; }
4749
4750       /**
4751        * @brief Sets the parameter set of the distribution.
4752        * @param __param The new parameter set of the distribution.
4753        */
4754       void
4755       param(const param_type& __param)
4756       { _M_param = __param; }
4757
4758       /**
4759        * @brief Returns the greatest lower bound value of the distribution.
4760        */
4761       result_type
4762       min() const
4763       { return result_type(0); }
4764
4765       /**
4766        * @brief Returns the least upper bound value of the distribution.
4767        */
4768       result_type
4769       max() const
4770       {
4771         return _M_param._M_prob.empty()
4772           ? result_type(0) : result_type(_M_param._M_prob.size() - 1);
4773       }
4774
4775       /**
4776        * @brief Generating functions.
4777        */
4778       template<typename _UniformRandomNumberGenerator>
4779         result_type
4780         operator()(_UniformRandomNumberGenerator& __urng)
4781         { return this->operator()(__urng, this->param()); }
4782
4783       template<typename _UniformRandomNumberGenerator>
4784         result_type
4785         operator()(_UniformRandomNumberGenerator& __urng,
4786                    const param_type& __p);
4787
4788       /**
4789        * @brief Inserts a %discrete_distribution random number distribution
4790        * @p __x into the output stream @p __os.
4791        *
4792        * @param __os An output stream.
4793        * @param __x  A %discrete_distribution random number distribution.
4794        *
4795        * @returns The output stream with the state of @p __x inserted or in
4796        * an error state.
4797        */
4798       template<typename _IntType1, typename _CharT, typename _Traits>
4799         friend std::basic_ostream<_CharT, _Traits>&
4800         operator<<(std::basic_ostream<_CharT, _Traits>&,
4801                    const std::discrete_distribution<_IntType1>&);
4802
4803       /**
4804        * @brief Extracts a %discrete_distribution random number distribution
4805        * @p __x from the input stream @p __is.
4806        *
4807        * @param __is An input stream.
4808        * @param __x A %discrete_distribution random number
4809        *            generator engine.
4810        *
4811        * @returns The input stream with @p __x extracted or in an error
4812        *          state.
4813        */
4814       template<typename _IntType1, typename _CharT, typename _Traits>
4815         friend std::basic_istream<_CharT, _Traits>&
4816         operator>>(std::basic_istream<_CharT, _Traits>&,
4817                    std::discrete_distribution<_IntType1>&);
4818
4819     private:
4820       param_type _M_param;
4821     };
4822
4823   /**
4824     * @brief Return true if two discrete distributions have the same
4825     *        parameters.
4826     */
4827   template<typename _IntType>
4828     inline bool
4829     operator==(const std::discrete_distribution<_IntType>& __d1,
4830                const std::discrete_distribution<_IntType>& __d2)
4831     { return __d1.param() == __d2.param(); }
4832
4833   /**
4834     * @brief Return true if two discrete distributions have different
4835     *        parameters.
4836     */
4837   template<typename _IntType>
4838     inline bool
4839     operator!=(const std::discrete_distribution<_IntType>& __d1,
4840                const std::discrete_distribution<_IntType>& __d2)
4841     { return !(__d1 == __d2); }
4842
4843
4844   /**
4845    * @brief A piecewise_constant_distribution random number distribution.
4846    *
4847    * The formula for the piecewise constant probability mass function is
4848    *
4849    */
4850   template<typename _RealType = double>
4851     class piecewise_constant_distribution
4852     {
4853       static_assert(std::is_floating_point<_RealType>::value,
4854                     "template argument not a floating point type");
4855
4856     public:
4857       /** The type of the range of the distribution. */
4858       typedef _RealType result_type;
4859       /** Parameter type. */
4860       struct param_type
4861       {
4862         typedef piecewise_constant_distribution<_RealType> distribution_type;
4863         friend class piecewise_constant_distribution<_RealType>;
4864
4865         param_type()
4866         : _M_int(), _M_den(), _M_cp()
4867         { }
4868
4869         template<typename _InputIteratorB, typename _InputIteratorW>
4870           param_type(_InputIteratorB __bfirst,
4871                      _InputIteratorB __bend,
4872                      _InputIteratorW __wbegin);
4873
4874         template<typename _Func>
4875           param_type(initializer_list<_RealType> __bi, _Func __fw);
4876
4877         template<typename _Func>
4878           param_type(size_t __nw, _RealType __xmin, _RealType __xmax,
4879                      _Func __fw);
4880
4881         // See: http://cpp-next.com/archive/2010/10/implicit-move-must-go/
4882         param_type(const param_type&) = default;
4883         param_type& operator=(const param_type&) = default;
4884
4885         std::vector<_RealType>
4886         intervals() const
4887         {
4888           if (_M_int.empty())
4889             {
4890               std::vector<_RealType> __tmp(2);
4891               __tmp[1] = _RealType(1);
4892               return __tmp;
4893             }
4894           else
4895             return _M_int;
4896         }
4897
4898         std::vector<double>
4899         densities() const
4900         { return _M_den.empty() ? std::vector<double>(1, 1.0) : _M_den; }
4901
4902         friend bool
4903         operator==(const param_type& __p1, const param_type& __p2)
4904         { return __p1._M_int == __p2._M_int && __p1._M_den == __p2._M_den; }
4905
4906       private:
4907         void
4908         _M_initialize();
4909
4910         std::vector<_RealType> _M_int;
4911         std::vector<double> _M_den;
4912         std::vector<double> _M_cp;
4913       };
4914
4915       explicit
4916       piecewise_constant_distribution()
4917       : _M_param()
4918       { }
4919
4920       template<typename _InputIteratorB, typename _InputIteratorW>
4921         piecewise_constant_distribution(_InputIteratorB __bfirst,
4922                                         _InputIteratorB __bend,
4923                                         _InputIteratorW __wbegin)
4924         : _M_param(__bfirst, __bend, __wbegin)
4925         { }
4926
4927       template<typename _Func>
4928         piecewise_constant_distribution(initializer_list<_RealType> __bl,
4929                                         _Func __fw)
4930         : _M_param(__bl, __fw)
4931         { }
4932
4933       template<typename _Func>
4934         piecewise_constant_distribution(size_t __nw,
4935                                         _RealType __xmin, _RealType __xmax,
4936                                         _Func __fw)
4937         : _M_param(__nw, __xmin, __xmax, __fw)
4938         { }
4939
4940       explicit
4941       piecewise_constant_distribution(const param_type& __p)
4942       : _M_param(__p)
4943       { }
4944
4945       /**
4946        * @brief Resets the distribution state.
4947        */
4948       void
4949       reset()
4950       { }
4951
4952       /**
4953        * @brief Returns a vector of the intervals.
4954        */
4955       std::vector<_RealType>
4956       intervals() const
4957       {
4958         if (_M_param._M_int.empty())
4959           {
4960             std::vector<_RealType> __tmp(2);
4961             __tmp[1] = _RealType(1);
4962             return __tmp;
4963           }
4964         else
4965           return _M_param._M_int;
4966       }
4967
4968       /**
4969        * @brief Returns a vector of the probability densities.
4970        */
4971       std::vector<double>
4972       densities() const
4973       {
4974         return _M_param._M_den.empty()
4975           ? std::vector<double>(1, 1.0) : _M_param._M_den;
4976       }
4977
4978       /**
4979        * @brief Returns the parameter set of the distribution.
4980        */
4981       param_type
4982       param() const
4983       { return _M_param; }
4984
4985       /**
4986        * @brief Sets the parameter set of the distribution.
4987        * @param __param The new parameter set of the distribution.
4988        */
4989       void
4990       param(const param_type& __param)
4991       { _M_param = __param; }
4992
4993       /**
4994        * @brief Returns the greatest lower bound value of the distribution.
4995        */
4996       result_type
4997       min() const
4998       {
4999         return _M_param._M_int.empty()
5000           ? result_type(0) : _M_param._M_int.front();
5001       }
5002
5003       /**
5004        * @brief Returns the least upper bound value of the distribution.
5005        */
5006       result_type
5007       max() const
5008       {
5009         return _M_param._M_int.empty()
5010           ? result_type(1) : _M_param._M_int.back();
5011       }
5012
5013       /**
5014        * @brief Generating functions.
5015        */
5016       template<typename _UniformRandomNumberGenerator>
5017         result_type
5018         operator()(_UniformRandomNumberGenerator& __urng)
5019         { return this->operator()(__urng, this->param()); }
5020
5021       template<typename _UniformRandomNumberGenerator>
5022         result_type
5023         operator()(_UniformRandomNumberGenerator& __urng,
5024                    const param_type& __p);
5025
5026       /**
5027        * @brief Inserts a %piecewise_constan_distribution random
5028        *        number distribution @p __x into the output stream @p __os.
5029        *
5030        * @param __os An output stream.
5031        * @param __x  A %piecewise_constan_distribution random number
5032        *             distribution.
5033        *
5034        * @returns The output stream with the state of @p __x inserted or in
5035        * an error state.
5036        */
5037       template<typename _RealType1, typename _CharT, typename _Traits>
5038         friend std::basic_ostream<_CharT, _Traits>&
5039         operator<<(std::basic_ostream<_CharT, _Traits>&,
5040                    const std::piecewise_constant_distribution<_RealType1>&);
5041
5042       /**
5043        * @brief Extracts a %piecewise_constan_distribution random
5044        *        number distribution @p __x from the input stream @p __is.
5045        *
5046        * @param __is An input stream.
5047        * @param __x A %piecewise_constan_distribution random number
5048        *            generator engine.
5049        *
5050        * @returns The input stream with @p __x extracted or in an error
5051        *          state.
5052        */
5053       template<typename _RealType1, typename _CharT, typename _Traits>
5054         friend std::basic_istream<_CharT, _Traits>&
5055         operator>>(std::basic_istream<_CharT, _Traits>&,
5056                    std::piecewise_constant_distribution<_RealType1>&);
5057
5058     private:
5059       param_type _M_param;
5060     };
5061
5062   /**
5063     * @brief Return true if two piecewise constant distributions have the
5064     *        same parameters.
5065    */
5066   template<typename _RealType>
5067     inline bool
5068     operator==(const std::piecewise_constant_distribution<_RealType>& __d1,
5069                const std::piecewise_constant_distribution<_RealType>& __d2)
5070     { return __d1.param() == __d2.param(); }
5071
5072   /**
5073     * @brief Return true if two piecewise constant distributions have
5074     *        different parameters.
5075    */
5076   template<typename _RealType>
5077     inline bool
5078     operator!=(const std::piecewise_constant_distribution<_RealType>& __d1,
5079                const std::piecewise_constant_distribution<_RealType>& __d2)
5080     { return !(__d1 == __d2); }
5081
5082
5083   /**
5084    * @brief A piecewise_linear_distribution random number distribution.
5085    *
5086    * The formula for the piecewise linear probability mass function is
5087    *
5088    */
5089   template<typename _RealType = double>
5090     class piecewise_linear_distribution
5091     {
5092       static_assert(std::is_floating_point<_RealType>::value,
5093                     "template argument not a floating point type");
5094
5095     public:
5096       /** The type of the range of the distribution. */
5097       typedef _RealType result_type;
5098       /** Parameter type. */
5099       struct param_type
5100       {
5101         typedef piecewise_linear_distribution<_RealType> distribution_type;
5102         friend class piecewise_linear_distribution<_RealType>;
5103
5104         param_type()
5105         : _M_int(), _M_den(), _M_cp(), _M_m()
5106         { }
5107
5108         template<typename _InputIteratorB, typename _InputIteratorW>
5109           param_type(_InputIteratorB __bfirst,
5110                      _InputIteratorB __bend,
5111                      _InputIteratorW __wbegin);
5112
5113         template<typename _Func>
5114           param_type(initializer_list<_RealType> __bl, _Func __fw);
5115
5116         template<typename _Func>
5117           param_type(size_t __nw, _RealType __xmin, _RealType __xmax,
5118                      _Func __fw);
5119
5120         // See: http://cpp-next.com/archive/2010/10/implicit-move-must-go/
5121         param_type(const param_type&) = default;
5122         param_type& operator=(const param_type&) = default;
5123
5124         std::vector<_RealType>
5125         intervals() const
5126         {
5127           if (_M_int.empty())
5128             {
5129               std::vector<_RealType> __tmp(2);
5130               __tmp[1] = _RealType(1);
5131               return __tmp;
5132             }
5133           else
5134             return _M_int;
5135         }
5136
5137         std::vector<double>
5138         densities() const
5139         { return _M_den.empty() ? std::vector<double>(2, 1.0) : _M_den; }
5140
5141         friend bool
5142         operator==(const param_type& __p1, const param_type& __p2)
5143         { return (__p1._M_int == __p2._M_int
5144                   && __p1._M_den == __p2._M_den); }
5145
5146       private:
5147         void
5148         _M_initialize();
5149
5150         std::vector<_RealType> _M_int;
5151         std::vector<double> _M_den;
5152         std::vector<double> _M_cp;
5153         std::vector<double> _M_m;
5154       };
5155
5156       explicit
5157       piecewise_linear_distribution()
5158       : _M_param()
5159       { }
5160
5161       template<typename _InputIteratorB, typename _InputIteratorW>
5162         piecewise_linear_distribution(_InputIteratorB __bfirst,
5163                                       _InputIteratorB __bend,
5164                                       _InputIteratorW __wbegin)
5165         : _M_param(__bfirst, __bend, __wbegin)
5166         { }
5167
5168       template<typename _Func>
5169         piecewise_linear_distribution(initializer_list<_RealType> __bl,
5170                                       _Func __fw)
5171         : _M_param(__bl, __fw)
5172         { }
5173
5174       template<typename _Func>
5175         piecewise_linear_distribution(size_t __nw,
5176                                       _RealType __xmin, _RealType __xmax,
5177                                       _Func __fw)
5178         : _M_param(__nw, __xmin, __xmax, __fw)
5179         { }
5180
5181       explicit
5182       piecewise_linear_distribution(const param_type& __p)
5183       : _M_param(__p)
5184       { }
5185
5186       /**
5187        * Resets the distribution state.
5188        */
5189       void
5190       reset()
5191       { }
5192
5193       /**
5194        * @brief Return the intervals of the distribution.
5195        */
5196       std::vector<_RealType>
5197       intervals() const
5198       {
5199         if (_M_param._M_int.empty())
5200           {
5201             std::vector<_RealType> __tmp(2);
5202             __tmp[1] = _RealType(1);
5203             return __tmp;
5204           }
5205         else
5206           return _M_param._M_int;
5207       }
5208
5209       /**
5210        * @brief Return a vector of the probability densities of the
5211        *        distribution.
5212        */
5213       std::vector<double>
5214       densities() const
5215       {
5216         return _M_param._M_den.empty()
5217           ? std::vector<double>(2, 1.0) : _M_param._M_den;
5218       }
5219
5220       /**
5221        * @brief Returns the parameter set of the distribution.
5222        */
5223       param_type
5224       param() const
5225       { return _M_param; }
5226
5227       /**
5228        * @brief Sets the parameter set of the distribution.
5229        * @param __param The new parameter set of the distribution.
5230        */
5231       void
5232       param(const param_type& __param)
5233       { _M_param = __param; }
5234
5235       /**
5236        * @brief Returns the greatest lower bound value of the distribution.
5237        */
5238       result_type
5239       min() const
5240       {
5241         return _M_param._M_int.empty()
5242           ? result_type(0) : _M_param._M_int.front();
5243       }
5244
5245       /**
5246        * @brief Returns the least upper bound value of the distribution.
5247        */
5248       result_type
5249       max() const
5250       {
5251         return _M_param._M_int.empty()
5252           ? result_type(1) : _M_param._M_int.back();
5253       }
5254
5255       /**
5256        * @brief Generating functions.
5257        */
5258       template<typename _UniformRandomNumberGenerator>
5259         result_type
5260         operator()(_UniformRandomNumberGenerator& __urng)
5261         { return this->operator()(__urng, this->param()); }
5262
5263       template<typename _UniformRandomNumberGenerator>
5264         result_type
5265         operator()(_UniformRandomNumberGenerator& __urng,
5266                    const param_type& __p);
5267
5268       /**
5269        * @brief Inserts a %piecewise_linear_distribution random number
5270        *        distribution @p __x into the output stream @p __os.
5271        *
5272        * @param __os An output stream.
5273        * @param __x  A %piecewise_linear_distribution random number
5274        *             distribution.
5275        *
5276        * @returns The output stream with the state of @p __x inserted or in
5277        *          an error state.
5278        */
5279       template<typename _RealType1, typename _CharT, typename _Traits>
5280         friend std::basic_ostream<_CharT, _Traits>&
5281         operator<<(std::basic_ostream<_CharT, _Traits>&,
5282                    const std::piecewise_linear_distribution<_RealType1>&);
5283
5284       /**
5285        * @brief Extracts a %piecewise_linear_distribution random number
5286        *        distribution @p __x from the input stream @p __is.
5287        *
5288        * @param __is An input stream.
5289        * @param __x  A %piecewise_linear_distribution random number
5290        *             generator engine.
5291        *
5292        * @returns The input stream with @p __x extracted or in an error
5293        *          state.
5294        */
5295       template<typename _RealType1, typename _CharT, typename _Traits>
5296         friend std::basic_istream<_CharT, _Traits>&
5297         operator>>(std::basic_istream<_CharT, _Traits>&,
5298                    std::piecewise_linear_distribution<_RealType1>&);
5299
5300     private:
5301       param_type _M_param;
5302     };
5303
5304   /**
5305     * @brief Return true if two piecewise linear distributions have the
5306     *        same parameters.
5307    */
5308   template<typename _RealType>
5309     inline bool
5310     operator==(const std::piecewise_linear_distribution<_RealType>& __d1,
5311                const std::piecewise_linear_distribution<_RealType>& __d2)
5312     { return __d1.param() == __d2.param(); }
5313
5314   /**
5315     * @brief Return true if two piecewise linear distributions have
5316     *        different parameters.
5317    */
5318   template<typename _RealType>
5319     inline bool
5320     operator!=(const std::piecewise_linear_distribution<_RealType>& __d1,
5321                const std::piecewise_linear_distribution<_RealType>& __d2)
5322     { return !(__d1 == __d2); }
5323
5324
5325   /* @} */ // group random_distributions_poisson
5326
5327   /* @} */ // group random_distributions
5328
5329   /**
5330    * @addtogroup random_utilities Random Number Utilities
5331    * @ingroup random
5332    * @{
5333    */
5334
5335   /**
5336    * @brief The seed_seq class generates sequences of seeds for random
5337    *        number generators.
5338    */
5339   class seed_seq
5340   {
5341
5342   public:
5343     /** The type of the seed vales. */
5344     typedef uint_least32_t result_type;
5345
5346     /** Default constructor. */
5347     seed_seq()
5348     : _M_v()
5349     { }
5350
5351     template<typename _IntType>
5352       seed_seq(std::initializer_list<_IntType> il);
5353
5354     template<typename _InputIterator>
5355       seed_seq(_InputIterator __begin, _InputIterator __end);
5356
5357     // generating functions
5358     template<typename _RandomAccessIterator>
5359       void
5360       generate(_RandomAccessIterator __begin, _RandomAccessIterator __end);
5361
5362     // property functions
5363     size_t size() const
5364     { return _M_v.size(); }
5365
5366     template<typename OutputIterator>
5367       void
5368       param(OutputIterator __dest) const
5369       { std::copy(_M_v.begin(), _M_v.end(), __dest); }
5370
5371   private:
5372     ///
5373     std::vector<result_type> _M_v;
5374   };
5375
5376   /* @} */ // group random_utilities
5377
5378   /* @} */ // group random
5379 }
5380
5381 #endif