diff options
Diffstat (limited to 'boost/random/exponential_distribution.hpp')
| -rw-r--r-- | boost/random/exponential_distribution.hpp | 210 |
1 files changed, 207 insertions, 3 deletions
diff --git a/boost/random/exponential_distribution.hpp b/boost/random/exponential_distribution.hpp index 53eaa93865..b4b95c5472 100644 --- a/boost/random/exponential_distribution.hpp +++ b/boost/random/exponential_distribution.hpp @@ -2,6 +2,7 @@ * * Copyright Jens Maurer 2000-2001 * Copyright Steven Watanabe 2011 + * Copyright Jason Rhinelander 2016 * Distributed under the Boost Software License, Version 1.0. (See * accompanying file LICENSE_1_0.txt or copy at * http://www.boost.org/LICENSE_1_0.txt) @@ -23,16 +24,220 @@ #include <boost/limits.hpp> #include <boost/random/detail/config.hpp> #include <boost/random/detail/operators.hpp> +#include <boost/random/detail/int_float_pair.hpp> #include <boost/random/uniform_01.hpp> namespace boost { namespace random { +namespace detail { + +// tables for the ziggurat algorithm +template<class RealType> +struct exponential_table { + static const RealType table_x[257]; + static const RealType table_y[257]; +}; + +template<class RealType> +const RealType exponential_table<RealType>::table_x[257] = { + 8.6971174701310497140, 7.6971174701310497140, 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, 3.7345288940397975350, 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, 3.1640533580259734580, 3.1349388580844407393, 3.1063890623398246660, + 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, 2.7548991965623453650, 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, 2.0215853383189260770, 2.0069417578945183144, + 1.9924049782135764992, 1.9779727009573602295, 1.9636426877895480401, 1.9494127580071845659, + 1.9352807862970511135, 1.9212447005915276767, 1.9073024800183871196, 1.8934521529393077332, + 1.8796917950722108462, 1.8660195276928275962, 1.8524335159111751661, 1.8389319670188793980, + 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, + 1.5721092393862294810, 1.5600804835278879161, 1.5481036037145133070, 1.5361774550410318943, + 1.5243009082192260050, 1.5124728488721167573, 1.5006921768428164936, 1.4889578055167456003, + 1.4772686611561334579, 1.4656236822457450411, 1.4540218188487932264, 1.4424620319720121876, + 1.4309432929388794104, 1.4194645827699828254, 1.4080248915695353509, 1.3966232179170417110, + 1.3852585682631217189, 1.3739299563284902176, 1.3626364025050864742, 1.3513769332583349176, + 1.3401505805295045843, 1.3289563811371163220, 1.3177933761763245480, 1.3066606104151739482, + 1.2955571316866007210, 1.2844819902750125450, 1.2734342382962410994, 1.2624129290696153434, + 1.2514171164808525098, 1.2404458543344064544, 1.2294981956938491599, 1.2185731922087903071, + 1.2076698934267612830, 1.1967873460884031665, 1.1859245934042023557, 1.1750806743109117687, + 1.1642546227056790397, 1.1534454666557748056, 1.1426522275816728928, 1.1318739194110786733, + 1.1211095477013306083, 1.1103581087274114281, 1.0996185885325976575, 1.0888899619385472598, + 1.0781711915113727024, 1.0674612264799681530, 1.0567590016025518414, 1.0460634359770445503, + 1.0353734317905289496, 1.0246878730026178052, 1.0140056239570971074, 1.0033255279156973717, + 0.99264640550727647009, 0.98196705308506317914, 0.97128624098390397896, 0.96060271166866709917, + 0.94991517776407659940, 0.93922231995526297952, 0.92852278474721113999, 0.91781518207004493915, + 0.90709808271569100600, 0.89637001558989069006, 0.88562946476175228052, 0.87487486629102585352, + 0.86410460481100519511, 0.85331700984237406386, 0.84251035181036928333, 0.83168283773427388393, + 0.82083260655441252290, 0.80995772405741906620, 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, + 0.54682012516331112550, 0.53441788123716615385, 0.52188505159213564105, 0.50921198244365495319, + 0.49638804551867159754, 0.48340149165346224782, 0.47023927508216945338, 0.45688684093142071279, + 0.44332786607355296305, 0.42954394022541129589, 0.41551416960035700100, 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, 0.13730498094001380420, 0.10483850756582017915, 0.063852163815003480173, + 0 +}; + +template<class RealType> +const RealType exponential_table<RealType>::table_y[257] = { + 0, 0.00045413435384149675545, 0.00096726928232717452884, 0.0015362997803015723824, + 0.0021459677437189061793, 0.0027887987935740759640, 0.0034602647778369039855, 0.0041572951208337952532, + 0.0048776559835423925804, 0.0056196422072054831710, 0.0063819059373191794422, 0.0071633531836349841425, + 0.0079630774380170392396, 0.0087803149858089752347, 0.0096144136425022094101, 0.010464810181029979488, + 0.011331013597834597488, 0.012212592426255380661, 0.013109164931254991070, 0.014020391403181937334, + 0.014945968011691148079, 0.015885621839973162490, 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, 0.039792391023374122670, + 0.041017441380414820816, 0.042254122413316231413, 0.043502413568888183301, 0.044762297732943280694, + 0.046033761076175166762, 0.047316792913181548703, 0.048611385573379494401, 0.049917534282706374944, + 0.051235237055126279830, 0.052564494593071689595, 0.053905310196046085104, 0.055257689676697038322, + 0.056621641283742874438, 0.057997175631200659098, 0.059384305633420264487, 0.060783046445479636051, + 0.062193415408540996150, 0.063615431999807331076, 0.065049117786753755036, 0.066494496385339779043, + 0.067951593421936607770, 0.069420436498728751675, 0.070901055162371828426, 0.072393480875708743023, + 0.073897746992364746308, 0.075413888734058408453, 0.076941943170480510100, 0.078481949201606426042, + 0.080033947542319910023, 0.081597980709237420930, 0.083174093009632380354, 0.084762330532368125386, + 0.086362741140756912277, 0.087975374467270219300, 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, + 0.12858020454522817870, 0.13050573846833078225, 0.13244532790138752023, 0.13439907170221363078, + 0.13636707092642885841, 0.13834942886358021406, 0.14034625107486244210, 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, 0.17211353531532005700, 0.17435816917135348788, 0.17661945459049489581, + 0.17889754657247831241, 0.18119260347549629488, 0.18350478709776746150, 0.18583426276219711495, + 0.18818119940425430485, 0.19054576966319540013, 0.19292814997677133873, 0.19532852067956322315, + 0.19774706610509886464, 0.20018397469191127727, 0.20263943909370901930, 0.20511365629383770880, + 0.20760682772422204205, 0.21011915938898825914, 0.21265086199297827522, 0.21520215107537867786, + 0.21777324714870053264, 0.22036437584335949720, 0.22297576805812018050, 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, 0.27986883323697289920, 0.28297041453878076010, + 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, + 0.34021714906678004560, 0.34388044470450243010, 0.34758049462163698567, 0.35131801643748334681, + 0.35509375286678745925, 0.35890847294874976196, 0.36276297335481777335, 0.36665807978151414890, + 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, 0.49134386959403255500, 0.49690198724154955294, + 0.50254950184134769289, 0.50828977641064283495, 0.51412639381474855788, 0.52006317736823356823, + 0.52610421398361972602, 0.53225388026304326945, 0.53851687200286186590, 0.54489823767243963663, + 0.55140341654064131685, 0.55803828226258748140, 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, 0.68956649611707798890, 0.70019265508278816709, 0.71127476080507597882, + 0.72286765959357200702, 0.73503809243142351530, 0.74786862198519510742, 0.76146338884989624862, + 0.77595685204011559675, 0.79152763697249565519, 0.80842165152300838005, 0.82699329664305033399, + 0.84778550062398962096, 0.87170433238120363669, 0.90046992992574643800, 0.93814368086217467916, + 1 +}; + +template<class RealType = double> +struct unit_exponential_distribution +{ + template<class Engine> + RealType operator()(Engine& eng) { + const double * const table_x = exponential_table<double>::table_x; + const double * const table_y = exponential_table<double>::table_y; + RealType shift(0); + for(;;) { + std::pair<RealType, int> vals = generate_int_float_pair<RealType, 8>(eng); + int i = vals.second; + RealType x = vals.first * RealType(table_x[i]); + if(x < RealType(table_x[i + 1])) return shift + x; + // For i=0 we need to generate from the tail, but because this is an exponential + // distribution, the tail looks exactly like the body, so we can simply repeat with a + // shift: + if (i == 0) shift += RealType(table_x[1]); + else { + RealType y01 = uniform_01<RealType>()(eng); + RealType y = RealType(table_y[i]) + y01 * RealType(table_y[i+1] - table_y[i]); + + // All we care about is whether these are < or > 0; these values are equal to + // (lbound) or proportional to (ubound) `y` minus the lower/upper bound. + RealType y_above_ubound = RealType(table_x[i] - table_x[i+1]) * y01 - (RealType(table_x[i]) - x), + y_above_lbound = y - (RealType(table_y[i+1]) + (RealType(table_x[i+1]) - x) * RealType(table_y[i+1])); + + if (y_above_ubound < 0 // if above the upper bound reject immediately + && + ( + y_above_lbound < 0 // If below the lower bound accept immediately + || + y < f(x) // Otherwise it's between the bounds and we need a full check + ) + ) { + return x + shift; + } + } + } + } + static RealType f(RealType x) { + using std::exp; + return exp(-x); + } +}; + +} // namespace detail + + /** * The exponential distribution is a model of \random_distribution with * a single parameter lambda. * * It has \f$\displaystyle p(x) = \lambda e^{-\lambda x}\f$ + * + * The implementation uses the "ziggurat" algorithm, as described in + * + * @blockquote + * "The Ziggurat Method for Generating Random Variables", + * George Marsaglia and Wai Wan Tsang, Journal of Statistical Software + * Volume 5, Number 8 (2000), 1-7. + * @endblockquote */ template<class RealType = double> class exponential_distribution @@ -127,9 +332,8 @@ public: template<class Engine> result_type operator()(Engine& eng) const { - using std::log; - return -result_type(1) / - _lambda * log(result_type(1)-uniform_01<RealType>()(eng)); + detail::unit_exponential_distribution<RealType> impl; + return impl(eng) / _lambda; } /** |