Chris@16: /* boost random/normal_distribution.hpp header file
Chris@16:  *
Chris@16:  * Copyright Jens Maurer 2000-2001
Chris@16:  * Copyright Steven Watanabe 2010-2011
Chris@16:  * Distributed under the Boost Software License, Version 1.0. (See
Chris@16:  * accompanying file LICENSE_1_0.txt or copy at
Chris@16:  * http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  *
Chris@16:  * See http://www.boost.org for most recent version including documentation.
Chris@16:  *
Chris@101:  * $Id$
Chris@16:  *
Chris@16:  * Revision history
Chris@16:  *  2001-02-18  moved to individual header files
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP
Chris@16: #define BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP
Chris@16: 
Chris@16: #include <boost/config/no_tr1/cmath.hpp>
Chris@16: #include <istream>
Chris@16: #include <iosfwd>
Chris@16: #include <boost/assert.hpp>
Chris@16: #include <boost/limits.hpp>
Chris@16: #include <boost/static_assert.hpp>
Chris@101: #include <boost/integer.hpp>
Chris@101: #include <boost/integer/integer_mask.hpp>
Chris@101: #include <boost/type_traits/is_integral.hpp>
Chris@101: #include <boost/type_traits/make_unsigned.hpp>
Chris@16: #include <boost/random/detail/config.hpp>
Chris@16: #include <boost/random/detail/operators.hpp>
Chris@101: #include <boost/random/detail/integer_log2.hpp>
Chris@16: #include <boost/random/uniform_01.hpp>
Chris@101: #include <boost/random/uniform_int_distribution.hpp>
Chris@101: #include <boost/random/exponential_distribution.hpp>
Chris@101: #include <boost/mpl/bool.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace random {
Chris@16: 
Chris@101: namespace detail {
Chris@101: 
Chris@101: // tables for the ziggurat algorithm
Chris@101: template<class RealType>
Chris@101: struct normal_table {
Chris@101:     static const RealType table_x[129];
Chris@101:     static const RealType table_y[129];
Chris@101: };
Chris@101: 
Chris@101: template<class RealType>
Chris@101: const RealType normal_table<RealType>::table_x[129] = {
Chris@101:     3.7130862467403632609, 3.4426198558966521214, 3.2230849845786185446, 3.0832288582142137009,
Chris@101:     2.9786962526450169606, 2.8943440070186706210, 2.8231253505459664379, 2.7611693723841538514,
Chris@101:     2.7061135731187223371, 2.6564064112581924999, 2.6109722484286132035, 2.5690336259216391328,
Chris@101:     2.5300096723854666170, 2.4934545220919507609, 2.4590181774083500943, 2.4264206455302115930,
Chris@101:     2.3954342780074673425, 2.3658713701139875435, 2.3375752413355307354, 2.3104136836950021558,
Chris@101:     2.2842740596736568056, 2.2590595738653295251, 2.2346863955870569803, 2.2110814088747278106,
Chris@101:     2.1881804320720206093, 2.1659267937448407377, 2.1442701823562613518, 2.1231657086697899595,
Chris@101:     2.1025731351849988838, 2.0824562379877246441, 2.0627822745039633575, 2.0435215366506694976,
Chris@101:     2.0246469733729338782, 2.0061338699589668403, 1.9879595741230607243, 1.9701032608497132242,
Chris@101:     1.9525457295488889058, 1.9352692282919002011, 1.9182573008597320303, 1.9014946531003176140,
Chris@101:     1.8849670357028692380, 1.8686611409895420085, 1.8525645117230870617, 1.8366654602533840447,
Chris@101:     1.8209529965910050740, 1.8054167642140487420, 1.7900469825946189862, 1.7748343955807692457,
Chris@101:     1.7597702248942318749, 1.7448461281083765085, 1.7300541605582435350, 1.7153867407081165482,
Chris@101:     1.7008366185643009437, 1.6863968467734863258, 1.6720607540918522072, 1.6578219209482075462,
Chris@101:     1.6436741568569826489, 1.6296114794646783962, 1.6156280950371329644, 1.6017183802152770587,
Chris@101:     1.5878768648844007019, 1.5740982160167497219, 1.5603772223598406870, 1.5467087798535034608,
Chris@101:     1.5330878776675560787, 1.5195095847593707806, 1.5059690368565502602, 1.4924614237746154081,
Chris@101:     1.4789819769830978546, 1.4655259573357946276, 1.4520886428822164926, 1.4386653166774613138,
Chris@101:     1.4252512545068615734, 1.4118417124397602509, 1.3984319141236063517, 1.3850170377251486449,
Chris@101:     1.3715922024197322698, 1.3581524543224228739, 1.3446927517457130432, 1.3312079496576765017,
Chris@101:     1.3176927832013429910, 1.3041418501204215390, 1.2905495919178731508, 1.2769102735516997175,
Chris@101:     1.2632179614460282310, 1.2494664995643337480, 1.2356494832544811749, 1.2217602305309625678,
Chris@101:     1.2077917504067576028, 1.1937367078237721994, 1.1795873846544607035, 1.1653356361550469083,
Chris@101:     1.1509728421389760651, 1.1364898520030755352, 1.1218769225722540661, 1.1071236475235353980,
Chris@101:     1.0922188768965537614, 1.0771506248819376573, 1.0619059636836193998, 1.0464709007525802629,
Chris@101:     1.0308302360564555907, 1.0149673952392994716, 0.99886423348064351303, 0.98250080350276038481,
Chris@101:     0.96585507938813059489, 0.94890262549791195381, 0.93161619660135381056, 0.91396525100880177644,
Chris@101:     0.89591535256623852894, 0.87742742909771569142, 0.85845684317805086354, 0.83895221428120745572,
Chris@101:     0.81885390668331772331, 0.79809206062627480454, 0.77658398787614838598, 0.75423066443451007146,
Chris@101:     0.73091191062188128150, 0.70647961131360803456, 0.68074791864590421664, 0.65347863871504238702,
Chris@101:     0.62435859730908822111, 0.59296294244197797913, 0.55869217837551797140, 0.52065603872514491759,
Chris@101:     0.47743783725378787681, 0.42654798630330512490, 0.36287143102841830424, 0.27232086470466385065,
Chris@101:     0
Chris@101: };
Chris@101: 
Chris@101: template<class RealType>
Chris@101: const RealType normal_table<RealType>::table_y[129] = {
Chris@101:     0, 0.0026696290839025035092, 0.0055489952208164705392, 0.0086244844129304709682,
Chris@101:     0.011839478657982313715, 0.015167298010672042468, 0.018592102737165812650, 0.022103304616111592615,
Chris@101:     0.025693291936149616572, 0.029356317440253829618, 0.033087886146505155566, 0.036884388786968774128,
Chris@101:     0.040742868074790604632, 0.044660862200872429800, 0.048636295860284051878, 0.052667401903503169793,
Chris@101:     0.056752663481538584188, 0.060890770348566375972, 0.065080585213631873753, 0.069321117394180252601,
Chris@101:     0.073611501884754893389, 0.077950982514654714188, 0.082338898242957408243, 0.086774671895542968998,
Chris@101:     0.091257800827634710201, 0.09578784912257815216, 0.10036444102954554013, 0.10498725541035453978,
Chris@101:     0.10965602101581776100, 0.11437051244988827452, 0.11913054670871858767, 0.12393598020398174246,
Chris@101:     0.12878670619710396109, 0.13368265258464764118, 0.13862377998585103702, 0.14361008009193299469,
Chris@101:     0.14864157424369696566, 0.15371831220958657066, 0.15884037114093507813, 0.16400785468492774791,
Chris@101:     0.16922089223892475176, 0.17447963833240232295, 0.17978427212496211424, 0.18513499701071343216,
Chris@101:     0.19053204032091372112, 0.19597565311811041399, 0.20146611007620324118, 0.20700370944187380064,
Chris@101:     0.21258877307373610060, 0.21822164655637059599, 0.22390269938713388747, 0.22963232523430270355,
Chris@101:     0.23541094226572765600, 0.24123899354775131610, 0.24711694751469673582, 0.25304529850976585934,
Chris@101:     0.25902456739871074263, 0.26505530225816194029, 0.27113807914102527343, 0.27727350292189771153,
Chris@101:     0.28346220822601251779, 0.28970486044581049771, 0.29600215684985583659, 0.30235482778947976274,
Chris@101:     0.30876363800925192282, 0.31522938806815752222, 0.32175291587920862031, 0.32833509837615239609,
Chris@101:     0.33497685331697116147, 0.34167914123501368412, 0.34844296754987246935, 0.35526938485154714435,
Chris@101:     0.36215949537303321162, 0.36911445366827513952, 0.37613546951445442947, 0.38322381105988364587,
Chris@101:     0.39038080824138948916, 0.39760785649804255208, 0.40490642081148835099, 0.41227804010702462062,
Chris@101:     0.41972433205403823467, 0.42724699830956239880, 0.43484783025466189638, 0.44252871528024661483,
Chris@101:     0.45029164368692696086, 0.45813871627287196483, 0.46607215269457097924, 0.47409430069824960453,
Chris@101:     0.48220764633483869062, 0.49041482528932163741, 0.49871863547658432422, 0.50712205108130458951,
Chris@101:     0.51562823824987205196, 0.52424057267899279809, 0.53296265938998758838, 0.54179835503172412311,
Chris@101:     0.55075179312105527738, 0.55982741271069481791, 0.56902999107472161225, 0.57836468112670231279,
Chris@101:     0.58783705444182052571, 0.59745315095181228217, 0.60721953663260488551, 0.61714337082656248870,
Chris@101:     0.62723248525781456578, 0.63749547734314487428, 0.64794182111855080873, 0.65858200005865368016,
Chris@101:     0.66942766735770616891, 0.68049184100641433355, 0.69178914344603585279, 0.70333609902581741633,
Chris@101:     0.71515150742047704368, 0.72725691835450587793, 0.73967724368333814856, 0.75244155918570380145,
Chris@101:     0.76558417390923599480, 0.77914608594170316563, 0.79317701178385921053, 0.80773829469612111340,
Chris@101:     0.82290721139526200050, 0.83878360531064722379, 0.85550060788506428418, 0.87324304892685358879,
Chris@101:     0.89228165080230272301, 0.91304364799203805999, 0.93628268170837107547, 0.96359969315576759960,
Chris@101:     1
Chris@101: };
Chris@101: 
Chris@101: template<class Engine>
Chris@101: inline typename boost::make_unsigned<typename Engine::result_type>::type
Chris@101: generate_one_digit(Engine& eng, std::size_t bits)
Chris@101: {
Chris@101:     typedef typename Engine::result_type base_result;
Chris@101:     typedef typename boost::make_unsigned<base_result>::type base_unsigned;
Chris@101:     
Chris@101:     base_unsigned range =
Chris@101:         detail::subtract<base_result>()((eng.max)(), (eng.min)());
Chris@101:     base_unsigned y0_mask = (base_unsigned(2) << (bits - 1)) - 1;
Chris@101:     base_unsigned y0 = (range + 1) & ~y0_mask;
Chris@101:     base_unsigned u;
Chris@101:     do {
Chris@101:         u = detail::subtract<base_result>()(eng(), (eng.min)());
Chris@101:     } while(y0 != 0 && u > base_unsigned(y0 - 1));
Chris@101:     return u & y0_mask;
Chris@101: }
Chris@101: 
Chris@101: template<class RealType, std::size_t w, class Engine>
Chris@101: std::pair<RealType, int> generate_int_float_pair(Engine& eng, boost::mpl::true_)
Chris@101: {
Chris@101:     typedef typename Engine::result_type base_result;
Chris@101:     typedef typename boost::make_unsigned<base_result>::type base_unsigned;
Chris@101:     
Chris@101:     base_unsigned range =
Chris@101:         detail::subtract<base_result>()((eng.max)(), (eng.min)());
Chris@101:     
Chris@101:     std::size_t m =
Chris@101:         (range == (std::numeric_limits<base_unsigned>::max)()) ?
Chris@101:             std::numeric_limits<base_unsigned>::digits :
Chris@101:             detail::integer_log2(range + 1);
Chris@101:             
Chris@101:     int bucket = 0;
Chris@101:     // process as many full digits as possible into the int part
Chris@101:     for(std::size_t i = 0; i < w/m; ++i) {
Chris@101:         base_unsigned u = generate_one_digit(eng, m);
Chris@101:         bucket = (bucket << m) | u;
Chris@101:     }
Chris@101:     RealType r;
Chris@101: 
Chris@101:     const std::size_t digits = std::numeric_limits<RealType>::digits;
Chris@101:     {
Chris@101:         base_unsigned u = generate_one_digit(eng, m);
Chris@101:         base_unsigned mask = (base_unsigned(1) << (w%m)) - 1;
Chris@101:         bucket = (bucket << (w%m)) | (mask & u);
Chris@101:         const RealType mult = RealType(1)/RealType(base_unsigned(1) << (m - w%m));
Chris@101:         // zero out unused bits
Chris@101:         if (m - w%m > digits) {
Chris@101:             u &= ~(base_unsigned(1) << (m - digits));
Chris@101:         }
Chris@101:         r = RealType(u >> (w%m)) * mult;
Chris@101:     }
Chris@101:     for(std::size_t i = m - w%m; i + m < digits; ++i) {
Chris@101:         base_unsigned u = generate_one_digit(eng, m);
Chris@101:         r += u;
Chris@101:         r *= RealType(0.5)/RealType(base_unsigned(1) << (m - 1));
Chris@101:     }
Chris@101:     if (m - w%m < digits)
Chris@101:     {
Chris@101:         const std::size_t remaining = (digits - m + w%m) % m;
Chris@101:         base_unsigned u = generate_one_digit(eng, m);
Chris@101:         r += u & ((base_unsigned(2) << (remaining - 1)) - 1);
Chris@101:         const RealType mult = RealType(0.5)/RealType(base_unsigned(1) << (remaining - 1));
Chris@101:         r *= mult;
Chris@101:     }
Chris@101:     return std::make_pair(r, bucket);
Chris@101: }
Chris@101: 
Chris@101: template<class RealType, std::size_t w, class Engine>
Chris@101: inline std::pair<RealType, int> generate_int_float_pair(Engine& eng, boost::mpl::false_)
Chris@101: {
Chris@101:     int bucket = uniform_int_distribution<>(0, (1 << w) - 1)(eng);
Chris@101:     RealType r = uniform_01<RealType>()(eng);
Chris@101:     return std::make_pair(r, bucket);
Chris@101: }
Chris@101: 
Chris@101: template<class RealType, std::size_t w, class Engine>
Chris@101: inline std::pair<RealType, int> generate_int_float_pair(Engine& eng)
Chris@101: {
Chris@101:     typedef typename Engine::result_type base_result;
Chris@101:     return generate_int_float_pair<RealType, w>(eng,
Chris@101:         boost::is_integral<base_result>());
Chris@101: }
Chris@101: 
Chris@101: template<class RealType = double>
Chris@101: struct unit_normal_distribution
Chris@101: {
Chris@101:     template<class Engine>
Chris@101:     RealType operator()(Engine& eng) {
Chris@101:         const double * const table_x = normal_table<double>::table_x;
Chris@101:         const double * const table_y = normal_table<double>::table_y;
Chris@101:         for(;;) {
Chris@101:             std::pair<RealType, int> vals = generate_int_float_pair<RealType, 8>(eng);
Chris@101:             int i = vals.second;
Chris@101:             int sign = (i & 1) * 2 - 1;
Chris@101:             i = i >> 1;
Chris@101:             RealType x = vals.first * RealType(table_x[i]);
Chris@101:             if(x < table_x[i + 1]) return x * sign;
Chris@101:             if(i == 0) return generate_tail(eng) * sign;
Chris@101:             RealType y = RealType(table_y[i]) + uniform_01<RealType>()(eng) * RealType(table_y[i + 1] - table_y[i]);
Chris@101:             if (y < f(x)) return x * sign;
Chris@101:         }
Chris@101:     }
Chris@101:     static RealType f(RealType x) {
Chris@101:         using std::exp;
Chris@101:         return exp(-x*x/2);
Chris@101:     }
Chris@101:     template<class Engine>
Chris@101:     RealType generate_tail(Engine& eng) {
Chris@101:         boost::random::exponential_distribution<RealType> exponential;
Chris@101:         const RealType tail_start = RealType(normal_table<double>::table_x[1]);
Chris@101:         for(;;) {
Chris@101:             RealType x = exponential(eng)/tail_start;
Chris@101:             RealType y = exponential(eng);
Chris@101:             if(2*y > x*x) return x + tail_start;
Chris@101:         }
Chris@101:     }
Chris@101: };
Chris@101: 
Chris@101: }
Chris@101: 
Chris@16: // deterministic Box-Muller method, uses trigonometric functions
Chris@16: 
Chris@16: /**
Chris@16:  * Instantiations of class template normal_distribution model a
Chris@16:  * \random_distribution. Such a distribution produces random numbers
Chris@16:  * @c x distributed with probability density function
Chris@16:  * \f$\displaystyle p(x) =
Chris@101:  *   \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
Chris@16:  * \f$,
Chris@16:  * where mean and sigma are the parameters of the distribution.
Chris@16:  */
Chris@16: template<class RealType = double>
Chris@16: class normal_distribution
Chris@16: {
Chris@16: public:
Chris@16:     typedef RealType input_type;
Chris@16:     typedef RealType result_type;
Chris@16: 
Chris@16:     class param_type {
Chris@16:     public:
Chris@16:         typedef normal_distribution distribution_type;
Chris@16: 
Chris@16:         /**
Chris@16:          * Constructs a @c param_type with a given mean and
Chris@16:          * standard deviation.
Chris@16:          *
Chris@16:          * Requires: sigma >= 0
Chris@16:          */
Chris@16:         explicit param_type(RealType mean_arg = RealType(0.0),
Chris@16:                             RealType sigma_arg = RealType(1.0))
Chris@16:           : _mean(mean_arg),
Chris@16:             _sigma(sigma_arg)
Chris@16:         {}
Chris@16: 
Chris@16:         /** Returns the mean of the distribution. */
Chris@16:         RealType mean() const { return _mean; }
Chris@16: 
Chris@16:         /** Returns the standand deviation of the distribution. */
Chris@16:         RealType sigma() const { return _sigma; }
Chris@16: 
Chris@16:         /** Writes a @c param_type to a @c std::ostream. */
Chris@16:         BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
Chris@16:         { os << parm._mean << " " << parm._sigma ; return os; }
Chris@16: 
Chris@16:         /** Reads a @c param_type from a @c std::istream. */
Chris@16:         BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
Chris@16:         { is >> parm._mean >> std::ws >> parm._sigma; return is; }
Chris@16: 
Chris@16:         /** Returns true if the two sets of parameters are the same. */
Chris@16:         BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
Chris@16:         { return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma; }
Chris@16:         
Chris@16:         /** Returns true if the two sets of parameters are the different. */
Chris@16:         BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
Chris@16: 
Chris@16:     private:
Chris@16:         RealType _mean;
Chris@16:         RealType _sigma;
Chris@16:     };
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c normal_distribution object. @c mean and @c sigma are
Chris@16:      * the parameters for the distribution.
Chris@16:      *
Chris@16:      * Requires: sigma >= 0
Chris@16:      */
Chris@16:     explicit normal_distribution(const RealType& mean_arg = RealType(0.0),
Chris@16:                                  const RealType& sigma_arg = RealType(1.0))
Chris@101:       : _mean(mean_arg), _sigma(sigma_arg)
Chris@16:     {
Chris@16:         BOOST_ASSERT(_sigma >= RealType(0));
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c normal_distribution object from its parameters.
Chris@16:      */
Chris@16:     explicit normal_distribution(const param_type& parm)
Chris@101:       : _mean(parm.mean()), _sigma(parm.sigma())
Chris@16:     {}
Chris@16: 
Chris@16:     /**  Returns the mean of the distribution. */
Chris@16:     RealType mean() const { return _mean; }
Chris@16:     /** Returns the standard deviation of the distribution. */
Chris@16:     RealType sigma() const { return _sigma; }
Chris@16: 
Chris@16:     /** Returns the smallest value that the distribution can produce. */
Chris@16:     RealType min BOOST_PREVENT_MACRO_SUBSTITUTION () const
Chris@16:     { return -std::numeric_limits<RealType>::infinity(); }
Chris@16:     /** Returns the largest value that the distribution can produce. */
Chris@16:     RealType max BOOST_PREVENT_MACRO_SUBSTITUTION () const
Chris@16:     { return std::numeric_limits<RealType>::infinity(); }
Chris@16: 
Chris@16:     /** Returns the parameters of the distribution. */
Chris@16:     param_type param() const { return param_type(_mean, _sigma); }
Chris@16:     /** Sets the parameters of the distribution. */
Chris@16:     void param(const param_type& parm)
Chris@16:     {
Chris@16:         _mean = parm.mean();
Chris@16:         _sigma = parm.sigma();
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Effects: Subsequent uses of the distribution do not depend
Chris@16:      * on values produced by any engine prior to invoking reset.
Chris@16:      */
Chris@101:     void reset() { }
Chris@16: 
Chris@16:     /**  Returns a normal variate. */
Chris@16:     template<class Engine>
Chris@16:     result_type operator()(Engine& eng)
Chris@16:     {
Chris@101:         detail::unit_normal_distribution<RealType> impl;
Chris@101:         return impl(eng) * _sigma + _mean;
Chris@16:     }
Chris@16: 
Chris@16:     /** Returns a normal variate with parameters specified by @c param. */
Chris@16:     template<class URNG>
Chris@16:     result_type operator()(URNG& urng, const param_type& parm)
Chris@16:     {
Chris@16:         return normal_distribution(parm)(urng);
Chris@16:     }
Chris@16: 
Chris@16:     /** Writes a @c normal_distribution to a @c std::ostream. */
Chris@16:     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, normal_distribution, nd)
Chris@16:     {
Chris@101:         os << nd._mean << " " << nd._sigma;
Chris@16:         return os;
Chris@16:     }
Chris@16: 
Chris@16:     /** Reads a @c normal_distribution from a @c std::istream. */
Chris@16:     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, normal_distribution, nd)
Chris@16:     {
Chris@101:         is >> std::ws >> nd._mean >> std::ws >> nd._sigma;
Chris@16:         return is;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns true if the two instances of @c normal_distribution will
Chris@16:      * return identical sequences of values given equal generators.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(normal_distribution, lhs, rhs)
Chris@16:     {
Chris@101:         return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns true if the two instances of @c normal_distribution will
Chris@16:      * return different sequences of values given equal generators.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(normal_distribution)
Chris@16: 
Chris@16: private:
Chris@16:     RealType _mean, _sigma;
Chris@16: 
Chris@16: };
Chris@16: 
Chris@16: } // namespace random
Chris@16: 
Chris@16: using random::normal_distribution;
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP