Ticket #12099: scratch.cpp

#include <boost/random/mersenne_twister.hpp>
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/gamma_distribution_new.hpp>
#include <boost/math/special_functions/erf.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/timer.hpp>
#include <iostream>
#include <random>

volatile double val;

template<class RealType>
struct exponential_table {
    static const RealType table_x[];
    static const RealType table_y[];
};

template<class RealType>
const RealType exponential_table<RealType>::table_x[] = {
    8.697117470131049714, 7.697117470131049714, 6.9410336293772123602, 6.4783784938325698538,
    6.1441646657724730491, 5.8821443157953997963, 5.6664101674540337371, 5.4828906275260628694,
    5.3230905057543986131, 5.1814872813015010392, 5.0542884899813047117, 4.9387770859012514838,
    4.8329397410251125881, 4.7352429966017412526, 4.6444918854200854873, 4.5597370617073515513,
    4.4802117465284221949, 4.4052876934735729805, 4.3344436803172730116, 4.2672424802773661873,
    4.2033137137351843802, 4.1423408656640511251, 4.0840513104082974638, 4.0282085446479365106,
    3.9746060666737884793, 3.9230625001354895926, 3.8734176703995089983, 3.8255294185223367372,
    3.7792709924116678992, 3.734528894039797535, 3.6912010902374189454, 3.6491955157608538478,
    3.6084288131289096339, 3.5688252656483374051, 3.5303158891293438633, 3.4928376547740601814,
    3.4563328211327607625, 3.4207483572511205323, 3.3860354424603017887, 3.3521490309001100106,
    3.3190474709707487166, 3.2866921715990692095, 3.2550473085704501813, 3.2240795652862645207,
    3.1937579032122407483, 3.164053358025973458, 3.1349388580844407393, 3.106389062339824666,
    3.0783802152540905188, 3.0508900166154554479, 3.0238975044556767713, 2.9973829495161306949,
    2.9713277599210896472, 2.9457143948950456386, 2.9205262865127406647, 2.8957477686001416838,
    2.8713640120155362592, 2.8473609656351888266, 2.8237253024500354905, 2.8004443702507381944,
    2.7775061464397572041, 2.754899196562345365, 2.7326126361947007411, 2.7106360958679293686,
    2.6889596887418041593, 2.6675739807732670816, 2.6464699631518093905, 2.6256390267977886123,
    2.6050729387408355373, 2.5847638202141406911, 2.5647041263169053687, 2.5448866271118700928,
    2.5253043900378279427, 2.5059507635285939648, 2.4868193617402096807, 2.4679040502973649846,
    2.4491989329782498908, 2.4306983392644199088, 2.4123968126888708336, 2.3942890999214583288,
    2.3763701405361408194, 2.3586350574093374601, 2.3410791477030346875, 2.3236978743901964559,
    2.3064868582835798692, 2.2894418705322694265, 2.2725588255531546952, 2.2558337743672190441,
    2.2392628983129087111, 2.2228425031110364013, 2.2065690132576635755, 2.1904389667232199235,
    2.1744490099377744673, 2.1585958930438856781, 2.1428764653998416425, 2.1272876713173679737,
    2.1118265460190418108, 2.0964902118017147637, 2.0812758743932248696, 2.0661808194905755036,
    2.0512024094685848641, 2.0363380802487695916, 2.021585338318926077, 2.0069417578945183144,
    1.9924049782135764992, 1.9779727009573602295, 1.9636426877895480401, 1.9494127580071845659,
    1.9352807862970511135, 1.9212447005915276767, 1.9073024800183871196, 1.8934521529393077332,
    1.8796917950722108462, 1.8660195276928275962, 1.8524335159111751661, 1.838931967018879398,
    1.8255131289035192212, 1.8121752885263901413, 1.7989167704602903934, 1.7857359354841254047,
    1.7726311792313049959, 1.7596009308890742369, 1.7466436519460739352, 1.7337578349855711926,
    1.7209420025219350428, 1.7081947058780575683, 1.6955145241015377061, 1.6829000629175537544,
    1.6703499537164519163, 1.6578628525741725325, 1.6454374393037234057, 1.6330724165359912048,
    1.6207665088282577216, 1.6085184617988580769, 1.5963270412864831349, 1.5841910325326886695,
    1.572109239386229481, 1.5600804835278879161, 1.548103603714513307, 1.5361774550410318943,
    1.524300908219226005, 1.5124728488721167573, 1.5006921768428164936, 1.4889578055167456003,
    1.4772686611561334579, 1.4656236822457450411, 1.4540218188487932264, 1.4424620319720121876,
    1.4309432929388794104, 1.4194645827699828254, 1.4080248915695353509, 1.396623217917041711,
    1.3852585682631217189, 1.3739299563284902176, 1.3626364025050864742, 1.3513769332583349176,
    1.3401505805295045843, 1.328956381137116322, 1.317793376176324548, 1.3066606104151739482,
    1.295557131686600721, 1.284481990275012545, 1.2734342382962410994, 1.2624129290696153434,
    1.2514171164808525098, 1.2404458543344064544, 1.2294981956938491599, 1.2185731922087903071,
    1.207669893426761283, 1.1967873460884031665, 1.1859245934042023557, 1.1750806743109117687,
    1.1642546227056790397, 1.1534454666557748056, 1.1426522275816728928, 1.1318739194110786733,
    1.1211095477013306083, 1.1103581087274114281, 1.0996185885325976575, 1.0888899619385472598,
    1.0781711915113727024, 1.067461226479968153, 1.0567590016025518414, 1.0460634359770445503,
    1.0353734317905289496, 1.0246878730026178052, 1.0140056239570971074, 1.0033255279156973717,
    0.99264640550727647009, 0.98196705308506317914, 0.97128624098390397896, 0.96060271166866709917,
    0.9499151777640765994, 0.93922231995526297952, 0.92852278474721113999, 0.91781518207004493915,
    0.907098082715691006, 0.89637001558989069006, 0.88562946476175228052, 0.87487486629102585352,
    0.86410460481100519511, 0.85331700984237406386, 0.84251035181036928333, 0.83168283773427388393,
    0.8208326065544125229, 0.8099577240574190662, 0.79905617735548788109, 0.78812586886949324977,
    0.77716460975913043936, 0.76617011273543541328, 0.75513998418198289808, 0.74407171550050873971,
    0.73296267358436604916, 0.72181009030875689912, 0.71061105090965570413, 0.69936248110323266174,
    0.68806113277374858613, 0.67670356802952337911, 0.66528614139267855405, 0.65380497984766565353,
    0.64225596042453703448, 0.63063468493349100113, 0.61893645139487678178, 0.60715622162030085137,
    0.59528858429150359384, 0.58332771274877027785, 0.57126731653258903915, 0.55910058551154127652,
    0.5468201251633111255, 0.53441788123716615385, 0.52188505159213564105, 0.50921198244365495319,
    0.49638804551867159754, 0.48340149165346224782, 0.47023927508216945338, 0.45688684093142071279,
    0.44332786607355296305, 0.42954394022541129589, 0.415514169600357001, 0.40121467889627836229,
    0.38661797794112021568, 0.37169214532991786118, 0.35639976025839443721, 0.34069648106484979674,
    0.32452911701691008547, 0.30783295467493287307, 0.29052795549123115167, 0.27251318547846547924,
    0.25365836338591284433, 0.23379048305967553619, 0.21267151063096745264, 0.18995868962243277774,
    0.16512762256418831796, 0.1373049809400138042, 0.10483850756582017915, 0.063852163815003480173,
    0,
};

template<class RealType>
const RealType exponential_table<RealType>::table_y[] = {
    0, 0.00045413435384149675545, 0.00096726928232717452884, 0.0015362997803015723824,
    0.0021459677437189061793, 0.002788798793574075964, 0.0034602647778369039855, 0.0041572951208337952532,
    0.0048776559835423925804, 0.005619642207205483171, 0.0063819059373191794422, 0.0071633531836349841425,
    0.0079630774380170392396, 0.0087803149858089752347, 0.0096144136425022094101, 0.010464810181029979488,
    0.011331013597834597488, 0.012212592426255380661, 0.01310916493125499107, 0.014020391403181937334,
    0.014945968011691148079, 0.01588562183997316249, 0.016839106826039946359, 0.017806200410911360563,
    0.018786700744696029497, 0.019780424338009741737, 0.020787204072578117603, 0.021806887504283582125,
    0.022839335406385238829, 0.023884420511558170348, 0.024942026419731782971, 0.026012046645134218076,
    0.027094383780955798424, 0.028188948763978634421, 0.029295660224637394015, 0.030414443910466605492,
    0.031545232172893605499, 0.032687963508959533317, 0.033842582150874329031, 0.035009037697397411067,
    0.036187284781931419754, 0.037377282772959360128, 0.038578995503074859626, 0.03979239102337412267,
    0.041017441380414820816, 0.042254122413316231413, 0.043502413568888183301, 0.044762297732943280694,
    0.046033761076175166762, 0.047316792913181548703, 0.048611385573379494401, 0.049917534282706374944,
    0.05123523705512627983, 0.052564494593071689595, 0.053905310196046085104, 0.055257689676697038322,
    0.056621641283742874438, 0.057997175631200659098, 0.059384305633420264487, 0.060783046445479636051,
    0.06219341540854099615, 0.063615431999807331076, 0.065049117786753755036, 0.066494496385339779043,
    0.06795159342193660777, 0.069420436498728751675, 0.070901055162371828426, 0.072393480875708743023,
    0.073897746992364746308, 0.075413888734058408453, 0.0769419431704805101, 0.078481949201606426042,
    0.080033947542319910023, 0.08159798070923742093, 0.083174093009632380354, 0.084762330532368125386,
    0.086362741140756912277, 0.0879753744672702193, 0.089600281910032864534, 0.091237516631040162057,
    0.092887133556043546523, 0.094549189376055853718, 0.096223742550432800103, 0.097910853311492199618,
    0.099610583670637128826, 0.10132299742595363588, 0.10304816017125771553, 0.10478613930657016928,
    0.10653700405000166218, 0.10830082545103379867, 0.11007767640518539026, 0.11186763167005629731,
    0.11367076788274431301, 0.11548716357863353664, 0.11731689921155557057, 0.11916005717532768467,
    0.12101672182667483729, 0.12288697950954513498, 0.12477091858083096578, 0.12666862943751066518,
    0.1285802045452281787, 0.13050573846833078225, 0.13244532790138752023, 0.13439907170221363078,
    0.13636707092642885841, 0.13834942886358021406, 0.1403462510748624421, 0.14235764543247220043,
    0.14438372216063476473, 0.14642459387834493787, 0.14848037564386679222, 0.15055118500103990354,
    0.15263714202744286154, 0.15473836938446807312, 0.15685499236936522013, 0.15898713896931420572,
    0.16113493991759203183, 0.16329852875190180795, 0.16547804187493600915, 0.16767361861725019322,
    0.16988540130252766513, 0.172113535315320057, 0.17435816917135348788, 0.17661945459049489581,
    0.17889754657247831241, 0.18119260347549629488, 0.1835047870977674615, 0.18583426276219711495,
    0.18818119940425430485, 0.19054576966319540013, 0.19292814997677133873, 0.19532852067956322315,
    0.19774706610509886464, 0.20018397469191127727, 0.2026394390937090193, 0.2051136562938377088,
    0.20760682772422204205, 0.21011915938898825914, 0.21265086199297827522, 0.21520215107537867786,
    0.21777324714870053264, 0.2203643758433594972, 0.2229757680581201805, 0.22560766011668406495,
    0.22826029393071670664, 0.23093391716962742173, 0.23362878343743333945, 0.23634515245705964715,
    0.23908329026244917002, 0.24184346939887722761, 0.24462596913189210901, 0.24743107566532763894,
    0.25025908236886230967, 0.25311029001562948171, 0.25598500703041538015, 0.25888354974901621678,
    0.26180624268936295243, 0.26475341883506220209, 0.26772541993204481808, 0.27072259679906003167,
    0.27374530965280298302, 0.27679392844851734458, 0.2798688332369728992, 0.2829704145387807601,
    0.28609907373707684673, 0.28925522348967773308, 0.29243928816189258772, 0.29565170428126120948,
    0.29889292101558177099, 0.30216340067569352897, 0.30546361924459023541, 0.30879406693456016794,
    0.31215524877417956945, 0.31554768522712893632, 0.31897191284495723773, 0.32242848495608914289,
    0.32591797239355619822, 0.32944096426413633091, 0.33299806876180896713, 0.33658991402867758144,
    0.3402171490667800456, 0.3438804447045024301, 0.34758049462163698567, 0.35131801643748334681,
    0.35509375286678745925, 0.35890847294874976196, 0.36276297335481777335, 0.3666580797815141489,
    0.37059464843514599421, 0.37457356761590215193, 0.37859575940958081092, 0.38266218149600982112,
    0.38677382908413768115, 0.39093173698479710717, 0.39513698183329015336, 0.39939068447523107877,
    0.40369401253053026739, 0.40804818315203238238, 0.41245446599716116772, 0.41691418643300289465,
    0.42142872899761659635, 0.42599954114303435739, 0.43062813728845883923, 0.43531610321563659758,
    0.44006510084235387501, 0.44487687341454851593, 0.44975325116275498919, 0.45469615747461548049,
    0.45970761564213768669, 0.46478975625042618067, 0.46994482528395999841, 0.47517519303737738299,
    0.48048336393045423016, 0.48587198734188493564, 0.491343869594032555, 0.49690198724154955294,
    0.50254950184134769289, 0.50828977641064283495, 0.51412639381474855788, 0.52006317736823356823,
    0.52610421398361972602, 0.53225388026304326945, 0.5385168720028618659, 0.54489823767243963663,
    0.55140341654064131685, 0.5580382822625874814, 0.56480919291240022434, 0.57172304866482579008,
    0.57878735860284503057, 0.58601031847726802755, 0.59340090169173341521, 0.60096896636523224742,
    0.60872538207962206507, 0.61668218091520762326, 0.62485273870366592605, 0.63325199421436607968,
    0.64189671642726607018, 0.65080583341457104881, 0.66000084107899974178, 0.66950631673192477684,
    0.67935057226476538741, 0.6895664961170779889, 0.70019265508278816709, 0.71127476080507597882,
    0.72286765959357200702, 0.7350380924314235153, 0.74786862198519510742, 0.76146338884989624862,
    0.77595685204011559675, 0.79152763697249565519, 0.80842165152300838005, 0.82699329664305033399,
    0.84778550062398962096, 0.87170433238120363669, 0.900469929925746438, 0.93814368086217467916,
    1,
};

template<class RealType = double>
struct unit_exponential_distribution {
    template<class Engine>
    RealType operator()(Engine& eng) {
        const RealType * const table_x = exponential_table<RealType>::table_x;
        const RealType * const table_y = exponential_table<RealType>::table_y;
        for(;;) {
            std::pair<RealType, int> values = boost::random::detail::generate_int_float_pair<RealType, 8>(eng);
            int i = values.second;
            RealType x = values.first * table_x[i];
            if(x < table_x[i + 1]) return x;
            if(i == 0) return table_x[1] + operator()(eng);
            RealType y = table_y[i] + boost::random::uniform_01<RealType>()(eng) * (table_y[i + 1] - table_y[i]);
            if (log(y) < -x) {
                return x;
            }
        }
    }
};

#if 1

// f(x) must be a decreasing function whose value is in [low, high]
template<class F, class RealType>
RealType invert(const F& f, RealType x, RealType low, RealType high) {
    RealType lowv = f(low);
    RealType highv = f(high);
    RealType mid = low + (high - low) / 2;
    RealType midv = f(mid);

    while(low != mid && high != mid) {
        // std::cout << "f(" << low << ")=" << lowv << ", f(" << mid << ")=" << midv << ", f(" << high << ")=" << highv << std::endl;
        if(highv > x) {
            return high;
        }
        if(lowv < x) {
            return low;
        }
        if (midv < x) {
            high = mid;
            highv = midv;
        } else {
            low = mid;
            lowv = midv;
        }
        mid = low + (high - low) / 2;
        midv = f(mid);
    }
    return mid;
}

template<class RealType, int N>
struct ziggurat_table {
    RealType x[N + 1];
    RealType y[N + 1];

    template<class F>
    void fill(F f, RealType guess_x1, RealType tail) {
        y[0] = 0;
        x[1] = guess_x1;
        y[1] = f(x[1]);
        RealType a = x[1] * y[1] + tail;
        x[0] = a / y[1];
        for(int i = 1; i < N; ++i) {
            //std::cout << "i=" << i << std::endl;
            y[i + 1] = a / x[i] + y[i];
            x[i + 1] = invert(f, y[i + 1], RealType(0), guess_x1);
        }
    }
};

int count = 0;

template<class RealType, int N, class F, class FTail>
struct finder {
    RealType operator()(RealType x0) const {
        //if (++count % 2 == 0) {
        //    std::cout << "on " << count << std::endl;
        //}
        std::cout << x0 << std::endl;
        ziggurat_table<RealType, N> table;
        table.fill(f, x0, ftail(x0));
        return table.y[N];
    }
    F f;
    FTail ftail;
};

struct unnormalized_normal {
    template<class RealType>
    RealType operator()(RealType x) const {
        return exp(-x*x/2);
    }
};

struct unnormalized_normal_tail {
    template<class RealType>
    RealType operator()(RealType x) const {
        return boost::math::constants::root_half_pi<RealType>()*
            boost::math::erfc(x*boost::math::constants::one_div_root_two<RealType>());
    }
};

struct unnormalized_exponential {
    template<class RealType>
    RealType operator()(RealType x) const {
        return exp(-x);
    }
};

struct unnormalized_exponential_tail {
    template<class RealType>
    RealType operator()(RealType x) const {
        return exp(-x);
    }
};

template<class RealType>
RealType invert(const unnormalized_exponential& f, RealType x, RealType low, RealType high) {
    if (x < RealType(0))
        return high;
    if (x > f(low)) return low;
    return std::max(std::min(RealType(-log(x)), high), low);
}

static const int table_size = 256;

template<class RealType>
void print_table(RealType low, RealType high) {
    // finder<RealType, 64, unnormalized_normal, unnormalized_normal_tail> f;
    finder<RealType, table_size, unnormalized_exponential, unnormalized_exponential_tail> f;
    std::cout << std::setprecision(50);
    RealType x0 = invert(f, f.f(RealType(0.0)), low, high);
    std::cout << std::setprecision(20) << x0 << std::endl;
    std::cout << std::setprecision(20) << f(x0) << std::endl;
    ziggurat_table<RealType, table_size> table;
    table.fill(f.f, x0, f.ftail(x0));
    std::cout << "x: ";
    for(int i = 0; i <= table_size; ++i) {
        if(i % 4 == 0) std::cout << "\n    ";
        else std::cout << " ";
        std::cout << table.x[i];
        std::cout << ",";
    }
    std::cout << "\ny: ";
    for(int i = 0; i <= table_size; ++i) {
        if(i % 4 == 0) std::cout << "\n    ";
        else std::cout << " ";
        std::cout << table.y[i];
        std::cout << ",";
    }
    std::cout << std::endl;
}

#endif

int main() {
#if 0
    {
        boost::mt19937 gen;
        boost::random::gamma_distribution<> dist(2.5);
        boost::timer timer;
            for(int i = 0; i < 100000000; ++i)
                val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        boost::random::gamma_distribution_new<> dist(2.5);
        boost::timer timer;
            for(int i = 0; i < 100000000; ++i)
                val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        std::gamma_distribution<> dist(2.5);
        boost::timer timer;
            for(int i = 0; i < 100000000; ++i)
                val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
#endif
#if 0
    {
        boost::mt19937 gen;
        boost::random::normal_distribution<float> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        unit_normal_distribution<float> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        std::normal_distribution<float> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
#endif
#if 1
    {
        boost::mt19937 gen;
        boost::random::exponential_distribution<> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        boost::random::detail::unit_exponential_distribution<> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        unit_exponential_distribution<> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
    {
        boost::mt19937 gen;
        std::exponential_distribution<> dist;
        boost::timer timer;
        for(int i = 0; i < 100000000; ++i)
            val = dist(gen);
        std::cout << timer.elapsed() << std::endl;
    }
#endif
#if 0
    boost::multiprecision::cpp_dec_float_50 low(6);
    boost::multiprecision::cpp_dec_float_50 high(8);
    print_table(low, high);
    //print_table(3.0, 10.0);
#endif
}