[Boost-commit] svn:boost r81018 - trunk/boost/random

Subject: [Boost-commit] svn:boost r81018 - trunk/boost/random
From: steven_at_[hidden]
Date: 2012-10-19 14:32:54

Author: steven_watanabe
Date: 2012-10-19 14:32:53 EDT (Fri, 19 Oct 2012)
New Revision: 81018
URL: http://svn.boost.org/trac/boost/changeset/81018

Log:
Implement the ziggurat algorithm for the normal distribution.
Text files modified: 
   trunk/boost/random/normal_distribution.hpp |   255 ++++++++++++++++++++++++++++++++++----- 
   1 files changed, 219 insertions(+), 36 deletions(-)

Modified: trunk/boost/random/normal_distribution.hpp
==============================================================================
--- trunk/boost/random/normal_distribution.hpp	(original)
+++ trunk/boost/random/normal_distribution.hpp	2012-10-19 14:32:53 EDT (Fri, 19 Oct 2012)
@@ -23,13 +23,224 @@
 #include <boost/assert.hpp>
 #include <boost/limits.hpp>
 #include <boost/static_assert.hpp>
+#include <boost/integer.hpp>
+#include <boost/integer/integer_mask.hpp>
+#include <boost/type_traits/is_integral.hpp>
+#include <boost/type_traits/make_unsigned.hpp>
 #include <boost/random/detail/config.hpp>
 #include <boost/random/detail/operators.hpp>
+#include <boost/random/detail/integer_log2.hpp>
 #include <boost/random/uniform_01.hpp>
+#include <boost/random/uniform_int_distribution.hpp>
+#include <boost/random/exponential_distribution.hpp>
 
 namespace boost {
 namespace random {
 
+namespace detail {
+
+// tables for the ziggurat algorithm
+template<class RealType>
+struct normal_table {
+    static const RealType table_x[129];
+    static const RealType table_y[129];
+};
+
+template<class RealType>
+const RealType normal_table<RealType>::table_x[129] = {
+    3.7130862467403632609, 3.4426198558966521214, 3.2230849845786185446, 3.0832288582142137009,
+    2.9786962526450169606, 2.8943440070186706210, 2.8231253505459664379, 2.7611693723841538514,
+    2.7061135731187223371, 2.6564064112581924999, 2.6109722484286132035, 2.5690336259216391328,
+    2.5300096723854666170, 2.4934545220919507609, 2.4590181774083500943, 2.4264206455302115930,
+    2.3954342780074673425, 2.3658713701139875435, 2.3375752413355307354, 2.3104136836950021558,
+    2.2842740596736568056, 2.2590595738653295251, 2.2346863955870569803, 2.2110814088747278106,
+    2.1881804320720206093, 2.1659267937448407377, 2.1442701823562613518, 2.1231657086697899595,
+    2.1025731351849988838, 2.0824562379877246441, 2.0627822745039633575, 2.0435215366506694976,
+    2.0246469733729338782, 2.0061338699589668403, 1.9879595741230607243, 1.9701032608497132242,
+    1.9525457295488889058, 1.9352692282919002011, 1.9182573008597320303, 1.9014946531003176140,
+    1.8849670357028692380, 1.8686611409895420085, 1.8525645117230870617, 1.8366654602533840447,
+    1.8209529965910050740, 1.8054167642140487420, 1.7900469825946189862, 1.7748343955807692457,
+    1.7597702248942318749, 1.7448461281083765085, 1.7300541605582435350, 1.7153867407081165482,
+    1.7008366185643009437, 1.6863968467734863258, 1.6720607540918522072, 1.6578219209482075462,
+    1.6436741568569826489, 1.6296114794646783962, 1.6156280950371329644, 1.6017183802152770587,
+    1.5878768648844007019, 1.5740982160167497219, 1.5603772223598406870, 1.5467087798535034608,
+    1.5330878776675560787, 1.5195095847593707806, 1.5059690368565502602, 1.4924614237746154081,
+    1.4789819769830978546, 1.4655259573357946276, 1.4520886428822164926, 1.4386653166774613138,
+    1.4252512545068615734, 1.4118417124397602509, 1.3984319141236063517, 1.3850170377251486449,
+    1.3715922024197322698, 1.3581524543224228739, 1.3446927517457130432, 1.3312079496576765017,
+    1.3176927832013429910, 1.3041418501204215390, 1.2905495919178731508, 1.2769102735516997175,
+    1.2632179614460282310, 1.2494664995643337480, 1.2356494832544811749, 1.2217602305309625678,
+    1.2077917504067576028, 1.1937367078237721994, 1.1795873846544607035, 1.1653356361550469083,
+    1.1509728421389760651, 1.1364898520030755352, 1.1218769225722540661, 1.1071236475235353980,
+    1.0922188768965537614, 1.0771506248819376573, 1.0619059636836193998, 1.0464709007525802629,
+    1.0308302360564555907, 1.0149673952392994716, 0.99886423348064351303, 0.98250080350276038481,
+    0.96585507938813059489, 0.94890262549791195381, 0.93161619660135381056, 0.91396525100880177644,
+    0.89591535256623852894, 0.87742742909771569142, 0.85845684317805086354, 0.83895221428120745572,
+    0.81885390668331772331, 0.79809206062627480454, 0.77658398787614838598, 0.75423066443451007146,
+    0.73091191062188128150, 0.70647961131360803456, 0.68074791864590421664, 0.65347863871504238702,
+    0.62435859730908822111, 0.59296294244197797913, 0.55869217837551797140, 0.52065603872514491759,
+    0.47743783725378787681, 0.42654798630330512490, 0.36287143102841830424, 0.27232086470466385065,
+    0
+};
+
+template<class RealType>
+const RealType normal_table<RealType>::table_y[129] = {
+    0, 0.0026696290839025035092, 0.0055489952208164705392, 0.0086244844129304709682,
+    0.011839478657982313715, 0.015167298010672042468, 0.018592102737165812650, 0.022103304616111592615,
+    0.025693291936149616572, 0.029356317440253829618, 0.033087886146505155566, 0.036884388786968774128,
+    0.040742868074790604632, 0.044660862200872429800, 0.048636295860284051878, 0.052667401903503169793,
+    0.056752663481538584188, 0.060890770348566375972, 0.065080585213631873753, 0.069321117394180252601,
+    0.073611501884754893389, 0.077950982514654714188, 0.082338898242957408243, 0.086774671895542968998,
+    0.091257800827634710201, 0.09578784912257815216, 0.10036444102954554013, 0.10498725541035453978,
+    0.10965602101581776100, 0.11437051244988827452, 0.11913054670871858767, 0.12393598020398174246,
+    0.12878670619710396109, 0.13368265258464764118, 0.13862377998585103702, 0.14361008009193299469,
+    0.14864157424369696566, 0.15371831220958657066, 0.15884037114093507813, 0.16400785468492774791,
+    0.16922089223892475176, 0.17447963833240232295, 0.17978427212496211424, 0.18513499701071343216,
+    0.19053204032091372112, 0.19597565311811041399, 0.20146611007620324118, 0.20700370944187380064,
+    0.21258877307373610060, 0.21822164655637059599, 0.22390269938713388747, 0.22963232523430270355,
+    0.23541094226572765600, 0.24123899354775131610, 0.24711694751469673582, 0.25304529850976585934,
+    0.25902456739871074263, 0.26505530225816194029, 0.27113807914102527343, 0.27727350292189771153,
+    0.28346220822601251779, 0.28970486044581049771, 0.29600215684985583659, 0.30235482778947976274,
+    0.30876363800925192282, 0.31522938806815752222, 0.32175291587920862031, 0.32833509837615239609,
+    0.33497685331697116147, 0.34167914123501368412, 0.34844296754987246935, 0.35526938485154714435,
+    0.36215949537303321162, 0.36911445366827513952, 0.37613546951445442947, 0.38322381105988364587,
+    0.39038080824138948916, 0.39760785649804255208, 0.40490642081148835099, 0.41227804010702462062,
+    0.41972433205403823467, 0.42724699830956239880, 0.43484783025466189638, 0.44252871528024661483,
+    0.45029164368692696086, 0.45813871627287196483, 0.46607215269457097924, 0.47409430069824960453,
+    0.48220764633483869062, 0.49041482528932163741, 0.49871863547658432422, 0.50712205108130458951,
+    0.51562823824987205196, 0.52424057267899279809, 0.53296265938998758838, 0.54179835503172412311,
+    0.55075179312105527738, 0.55982741271069481791, 0.56902999107472161225, 0.57836468112670231279,
+    0.58783705444182052571, 0.59745315095181228217, 0.60721953663260488551, 0.61714337082656248870,
+    0.62723248525781456578, 0.63749547734314487428, 0.64794182111855080873, 0.65858200005865368016,
+    0.66942766735770616891, 0.68049184100641433355, 0.69178914344603585279, 0.70333609902581741633,
+    0.71515150742047704368, 0.72725691835450587793, 0.73967724368333814856, 0.75244155918570380145,
+    0.76558417390923599480, 0.77914608594170316563, 0.79317701178385921053, 0.80773829469612111340,
+    0.82290721139526200050, 0.83878360531064722379, 0.85550060788506428418, 0.87324304892685358879,
+    0.89228165080230272301, 0.91304364799203805999, 0.93628268170837107547, 0.96359969315576759960,
+    1
+};
+
+template<class Engine>
+inline typename boost::make_unsigned<typename Engine::result_type>::type
+generate_one_digit(Engine& eng, std::size_t bits)
+{
+    typedef typename Engine::result_type base_result;
+    typedef typename boost::make_unsigned<base_result>::type base_unsigned;
+    
+    base_unsigned range =
+        detail::subtract<base_result>()((eng.max)(), (eng.min)());
+    base_unsigned y0_mask = (base_unsigned(2) << (bits - 1)) - 1;
+    base_unsigned y0 = (range + 1) & ~y0_mask;
+    base_unsigned u;
+    do {
+        u = detail::subtract<base_result>()(eng(), (eng.min)());
+    } while(y0 != 0 && u > base_unsigned(y0 - 1));
+    return u & y0_mask;
+}
+
+template<class RealType, std::size_t w, class Engine>
+std::pair<RealType, int> generate_int_float_pair(Engine& eng, boost::mpl::true_)
+{
+    typedef typename Engine::result_type base_result;
+    typedef typename boost::make_unsigned<base_result>::type base_unsigned;
+    
+    base_unsigned range =
+        detail::subtract<base_result>()((eng.max)(), (eng.min)());
+    
+    std::size_t m =
+        (range == (std::numeric_limits<base_unsigned>::max)()) ?
+            std::numeric_limits<base_unsigned>::digits :
+            detail::integer_log2(range + 1);
+            
+    int bucket = 0;
+    // process as many full digits as possible into the int part
+    for(std::size_t i = 0; i < w/m; ++i) {
+        base_unsigned u = generate_one_digit(eng, m);
+        bucket = (bucket << m) | u;
+    }
+    RealType r;
+
+    const std::size_t digits = std::numeric_limits<RealType>::digits;
+    {
+        base_unsigned u = generate_one_digit(eng, m);
+        base_unsigned mask = (base_unsigned(1) << (w%m)) - 1;
+        bucket = (bucket << (w%m)) | (mask & u);
+        const RealType mult = RealType(1)/RealType(base_unsigned(1) << (m - w%m));
+        // zero out unused bits
+        if (m - w%m > digits) {
+            u &= ~(base_unsigned(1) << (m - digits));
+        }
+        r = RealType(u >> (w%m)) * mult;
+    }
+    for(std::size_t i = m - w%m; i + m < digits; ++i) {
+        base_unsigned u = generate_one_digit(eng, m);
+        r += u;
+        r *= RealType(0.5)/RealType(base_unsigned(1) << (m - 1));
+    }
+    if (m - w%m < digits)
+    {
+        const std::size_t remaining = (digits - m + w%m) % m;
+        base_unsigned u = generate_one_digit(eng, m);
+        r += u & ((base_unsigned(2) << (remaining - 1)) - 1);
+        const RealType mult = RealType(0.5)/RealType(base_unsigned(1) << (remaining - 1));
+        r *= mult;
+    }
+    return std::make_pair(r, bucket);
+}
+
+template<class RealType, std::size_t w, class Engine>
+inline std::pair<RealType, int> generate_int_float_pair(Engine& eng, boost::mpl::false_)
+{
+    int bucket = uniform_int_distribution<>(0, (1 << w) - 1)(eng);
+    RealType r = uniform_01<RealType>()(eng);
+    return std::make_pair(r, bucket);
+}
+
+template<class RealType, std::size_t w, class Engine>
+inline std::pair<RealType, int> generate_int_float_pair(Engine& eng)
+{
+    typedef typename Engine::result_type base_result;
+    return generate_int_float_pair<RealType, w>(eng,
+        boost::is_integral<base_result>());
+}
+
+template<class RealType = double>
+struct unit_normal_distribution
+{
+    template<class Engine>
+    RealType operator()(Engine& eng) {
+        const double * const table_x = normal_table<double>::table_x;
+        const double * const table_y = normal_table<double>::table_y;
+        for(;;) {
+            std::pair<RealType, int> vals = generate_int_float_pair<RealType, 8>(eng);
+            int i = vals.second;
+            int sign = (i & 1) * 2 - 1;
+            i = i >> 1;
+            RealType x = vals.first * RealType(table_x[i]);
+            if(x < table_x[i + 1]) return x * sign;
+            if(i == 0) return generate_tail(eng) * sign;
+            RealType y = RealType(table_y[i]) + uniform_01<RealType>()(eng) * RealType(table_y[i + 1] - table_y[i]);
+            if (y < f(x)) return x * sign;
+        }
+    }
+    static RealType f(RealType x) {
+        using std::exp;
+        return exp(-x*x/2);
+    }
+    template<class Engine>
+    RealType generate_tail(Engine& eng) {
+        boost::random::exponential_distribution<RealType> exponential;
+        const RealType tail_start(normal_table<double>::table_x[1]);
+        for(;;) {
+            RealType x = exponential(eng)/tail_start;
+            RealType y = exponential(eng);
+            if(2*y > x*x) return x + tail_start;
+        }
+    }
+};
+
+}
+
 // deterministic Box-Muller method, uses trigonometric functions
 
 /**
@@ -98,8 +309,7 @@
      */
     explicit normal_distribution(const RealType& mean_arg = RealType(0.0),
                                  const RealType& sigma_arg = RealType(1.0))
-      : _mean(mean_arg), _sigma(sigma_arg),
-        _r1(0), _r2(0), _cached_rho(0), _valid(false)
+      : _mean(mean_arg), _sigma(sigma_arg)
     {
         BOOST_ASSERT(_sigma >= RealType(0));
     }
@@ -108,8 +318,7 @@
      * Constructs a @c normal_distribution object from its parameters.
      */
     explicit normal_distribution(const param_type& parm)
-      : _mean(parm.mean()), _sigma(parm.sigma()),
-        _r1(0), _r2(0), _cached_rho(0), _valid(false)
+      : _mean(parm.mean()), _sigma(parm.sigma())
     {}
 
     /**  Returns the mean of the distribution. */
@@ -131,39 +340,20 @@
     {
         _mean = parm.mean();
         _sigma = parm.sigma();
-        _valid = false;
     }
 
     /**
      * Effects: Subsequent uses of the distribution do not depend
      * on values produced by any engine prior to invoking reset.
      */
-    void reset() { _valid = false; }
+    void reset() { }
 
     /**  Returns a normal variate. */
     template<class Engine>
     result_type operator()(Engine& eng)
     {
-        using std::sqrt;
-        using std::log;
-        using std::sin;
-        using std::cos;
-
-        if(!_valid) {
-            _r1 = boost::uniform_01<RealType>()(eng);
-            _r2 = boost::uniform_01<RealType>()(eng);
-            _cached_rho = sqrt(-result_type(2) * log(result_type(1)-_r2));
-            _valid = true;
-        } else {
-            _valid = false;
-        }
-        // Can we have a boost::mathconst please?
-        const result_type pi = result_type(3.14159265358979323846);
-
-        return _cached_rho * (_valid ?
-                              cos(result_type(2)*pi*_r1) :
-                              sin(result_type(2)*pi*_r1))
-            * _sigma + _mean;
+        detail::unit_normal_distribution<RealType> impl;
+        return impl(eng) * _sigma + _mean;
     }
 
     /** Returns a normal variate with parameters specified by @c param. */
@@ -176,17 +366,14 @@
     /** Writes a @c normal_distribution to a @c std::ostream. */
     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, normal_distribution, nd)
     {
-        os << nd._mean << " " << nd._sigma << " "
-           << nd._valid << " " << nd._cached_rho << " " << nd._r1;
+        os << nd._mean << " " << nd._sigma;
         return os;
     }
 
     /** Reads a @c normal_distribution from a @c std::istream. */
     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, normal_distribution, nd)
     {
-        is >> std::ws >> nd._mean >> std::ws >> nd._sigma
-           >> std::ws >> nd._valid >> std::ws >> nd._cached_rho
-           >> std::ws >> nd._r1;
+        is >> std::ws >> nd._mean >> std::ws >> nd._sigma;
         return is;
     }
 
@@ -196,9 +383,7 @@
      */
     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(normal_distribution, lhs, rhs)
     {
-        return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma
-            && lhs._valid == rhs._valid
-            && (!lhs._valid || (lhs._r1 == rhs._r1 && lhs._r2 == rhs._r2));
+        return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma;
     }
 
     /**
@@ -209,8 +394,6 @@
 
 private:
     RealType _mean, _sigma;
-    RealType _r1, _r2, _cached_rho;
-    bool _valid;
 
 };