1 | /* boost random/normal_distribution.hpp header file |
2 | * |
3 | * Copyright Jens Maurer 2000-2001 |
4 | * Copyright Steven Watanabe 2010-2011 |
5 | * Distributed under the Boost Software License, Version 1.0. (See |
6 | * accompanying file LICENSE_1_0.txt or copy at |
7 | * http://www.boost.org/LICENSE_1_0.txt) |
8 | * |
9 | * See http://www.boost.org for most recent version including documentation. |
10 | * |
11 | * $Id$ |
12 | * |
13 | * Revision history |
14 | * 2001-02-18 moved to individual header files |
15 | */ |
16 | |
17 | #ifndef BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP |
18 | #define BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP |
19 | |
20 | #include <boost/config/no_tr1/cmath.hpp> |
21 | #include <istream> |
22 | #include <iosfwd> |
23 | #include <boost/assert.hpp> |
24 | #include <boost/limits.hpp> |
25 | #include <boost/static_assert.hpp> |
26 | #include <boost/integer.hpp> |
27 | #include <boost/integer/integer_mask.hpp> |
28 | #include <boost/type_traits/is_integral.hpp> |
29 | #include <boost/type_traits/make_unsigned.hpp> |
30 | #include <boost/random/detail/config.hpp> |
31 | #include <boost/random/detail/operators.hpp> |
32 | #include <boost/random/detail/integer_log2.hpp> |
33 | #include <boost/random/uniform_01.hpp> |
34 | #include <boost/random/uniform_int_distribution.hpp> |
35 | #include <boost/random/exponential_distribution.hpp> |
36 | #include <boost/mpl/bool.hpp> |
37 | |
38 | namespace boost { |
39 | namespace random { |
40 | |
41 | namespace detail { |
42 | |
43 | // tables for the ziggurat algorithm |
44 | template<class RealType> |
45 | struct normal_table { |
46 | static const RealType table_x[129]; |
47 | static const RealType table_y[129]; |
48 | }; |
49 | |
50 | template<class RealType> |
51 | const RealType normal_table<RealType>::table_x[129] = { |
52 | 3.7130862467403632609, 3.4426198558966521214, 3.2230849845786185446, 3.0832288582142137009, |
53 | 2.9786962526450169606, 2.8943440070186706210, 2.8231253505459664379, 2.7611693723841538514, |
54 | 2.7061135731187223371, 2.6564064112581924999, 2.6109722484286132035, 2.5690336259216391328, |
55 | 2.5300096723854666170, 2.4934545220919507609, 2.4590181774083500943, 2.4264206455302115930, |
56 | 2.3954342780074673425, 2.3658713701139875435, 2.3375752413355307354, 2.3104136836950021558, |
57 | 2.2842740596736568056, 2.2590595738653295251, 2.2346863955870569803, 2.2110814088747278106, |
58 | 2.1881804320720206093, 2.1659267937448407377, 2.1442701823562613518, 2.1231657086697899595, |
59 | 2.1025731351849988838, 2.0824562379877246441, 2.0627822745039633575, 2.0435215366506694976, |
60 | 2.0246469733729338782, 2.0061338699589668403, 1.9879595741230607243, 1.9701032608497132242, |
61 | 1.9525457295488889058, 1.9352692282919002011, 1.9182573008597320303, 1.9014946531003176140, |
62 | 1.8849670357028692380, 1.8686611409895420085, 1.8525645117230870617, 1.8366654602533840447, |
63 | 1.8209529965910050740, 1.8054167642140487420, 1.7900469825946189862, 1.7748343955807692457, |
64 | 1.7597702248942318749, 1.7448461281083765085, 1.7300541605582435350, 1.7153867407081165482, |
65 | 1.7008366185643009437, 1.6863968467734863258, 1.6720607540918522072, 1.6578219209482075462, |
66 | 1.6436741568569826489, 1.6296114794646783962, 1.6156280950371329644, 1.6017183802152770587, |
67 | 1.5878768648844007019, 1.5740982160167497219, 1.5603772223598406870, 1.5467087798535034608, |
68 | 1.5330878776675560787, 1.5195095847593707806, 1.5059690368565502602, 1.4924614237746154081, |
69 | 1.4789819769830978546, 1.4655259573357946276, 1.4520886428822164926, 1.4386653166774613138, |
70 | 1.4252512545068615734, 1.4118417124397602509, 1.3984319141236063517, 1.3850170377251486449, |
71 | 1.3715922024197322698, 1.3581524543224228739, 1.3446927517457130432, 1.3312079496576765017, |
72 | 1.3176927832013429910, 1.3041418501204215390, 1.2905495919178731508, 1.2769102735516997175, |
73 | 1.2632179614460282310, 1.2494664995643337480, 1.2356494832544811749, 1.2217602305309625678, |
74 | 1.2077917504067576028, 1.1937367078237721994, 1.1795873846544607035, 1.1653356361550469083, |
75 | 1.1509728421389760651, 1.1364898520030755352, 1.1218769225722540661, 1.1071236475235353980, |
76 | 1.0922188768965537614, 1.0771506248819376573, 1.0619059636836193998, 1.0464709007525802629, |
77 | 1.0308302360564555907, 1.0149673952392994716, 0.99886423348064351303, 0.98250080350276038481, |
78 | 0.96585507938813059489, 0.94890262549791195381, 0.93161619660135381056, 0.91396525100880177644, |
79 | 0.89591535256623852894, 0.87742742909771569142, 0.85845684317805086354, 0.83895221428120745572, |
80 | 0.81885390668331772331, 0.79809206062627480454, 0.77658398787614838598, 0.75423066443451007146, |
81 | 0.73091191062188128150, 0.70647961131360803456, 0.68074791864590421664, 0.65347863871504238702, |
82 | 0.62435859730908822111, 0.59296294244197797913, 0.55869217837551797140, 0.52065603872514491759, |
83 | 0.47743783725378787681, 0.42654798630330512490, 0.36287143102841830424, 0.27232086470466385065, |
84 | 0 |
85 | }; |
86 | |
87 | template<class RealType> |
88 | const RealType normal_table<RealType>::table_y[129] = { |
89 | 0, 0.0026696290839025035092, 0.0055489952208164705392, 0.0086244844129304709682, |
90 | 0.011839478657982313715, 0.015167298010672042468, 0.018592102737165812650, 0.022103304616111592615, |
91 | 0.025693291936149616572, 0.029356317440253829618, 0.033087886146505155566, 0.036884388786968774128, |
92 | 0.040742868074790604632, 0.044660862200872429800, 0.048636295860284051878, 0.052667401903503169793, |
93 | 0.056752663481538584188, 0.060890770348566375972, 0.065080585213631873753, 0.069321117394180252601, |
94 | 0.073611501884754893389, 0.077950982514654714188, 0.082338898242957408243, 0.086774671895542968998, |
95 | 0.091257800827634710201, 0.09578784912257815216, 0.10036444102954554013, 0.10498725541035453978, |
96 | 0.10965602101581776100, 0.11437051244988827452, 0.11913054670871858767, 0.12393598020398174246, |
97 | 0.12878670619710396109, 0.13368265258464764118, 0.13862377998585103702, 0.14361008009193299469, |
98 | 0.14864157424369696566, 0.15371831220958657066, 0.15884037114093507813, 0.16400785468492774791, |
99 | 0.16922089223892475176, 0.17447963833240232295, 0.17978427212496211424, 0.18513499701071343216, |
100 | 0.19053204032091372112, 0.19597565311811041399, 0.20146611007620324118, 0.20700370944187380064, |
101 | 0.21258877307373610060, 0.21822164655637059599, 0.22390269938713388747, 0.22963232523430270355, |
102 | 0.23541094226572765600, 0.24123899354775131610, 0.24711694751469673582, 0.25304529850976585934, |
103 | 0.25902456739871074263, 0.26505530225816194029, 0.27113807914102527343, 0.27727350292189771153, |
104 | 0.28346220822601251779, 0.28970486044581049771, 0.29600215684985583659, 0.30235482778947976274, |
105 | 0.30876363800925192282, 0.31522938806815752222, 0.32175291587920862031, 0.32833509837615239609, |
106 | 0.33497685331697116147, 0.34167914123501368412, 0.34844296754987246935, 0.35526938485154714435, |
107 | 0.36215949537303321162, 0.36911445366827513952, 0.37613546951445442947, 0.38322381105988364587, |
108 | 0.39038080824138948916, 0.39760785649804255208, 0.40490642081148835099, 0.41227804010702462062, |
109 | 0.41972433205403823467, 0.42724699830956239880, 0.43484783025466189638, 0.44252871528024661483, |
110 | 0.45029164368692696086, 0.45813871627287196483, 0.46607215269457097924, 0.47409430069824960453, |
111 | 0.48220764633483869062, 0.49041482528932163741, 0.49871863547658432422, 0.50712205108130458951, |
112 | 0.51562823824987205196, 0.52424057267899279809, 0.53296265938998758838, 0.54179835503172412311, |
113 | 0.55075179312105527738, 0.55982741271069481791, 0.56902999107472161225, 0.57836468112670231279, |
114 | 0.58783705444182052571, 0.59745315095181228217, 0.60721953663260488551, 0.61714337082656248870, |
115 | 0.62723248525781456578, 0.63749547734314487428, 0.64794182111855080873, 0.65858200005865368016, |
116 | 0.66942766735770616891, 0.68049184100641433355, 0.69178914344603585279, 0.70333609902581741633, |
117 | 0.71515150742047704368, 0.72725691835450587793, 0.73967724368333814856, 0.75244155918570380145, |
118 | 0.76558417390923599480, 0.77914608594170316563, 0.79317701178385921053, 0.80773829469612111340, |
119 | 0.82290721139526200050, 0.83878360531064722379, 0.85550060788506428418, 0.87324304892685358879, |
120 | 0.89228165080230272301, 0.91304364799203805999, 0.93628268170837107547, 0.96359969315576759960, |
121 | 1 |
122 | }; |
123 | |
124 | template<class Engine> |
125 | inline typename boost::make_unsigned<typename Engine::result_type>::type |
126 | generate_one_digit(Engine& eng, std::size_t bits) |
127 | { |
128 | typedef typename Engine::result_type base_result; |
129 | typedef typename boost::make_unsigned<base_result>::type base_unsigned; |
130 | |
131 | base_unsigned range = |
132 | detail::subtract<base_result>()((eng.max)(), (eng.min)()); |
133 | base_unsigned y0_mask = (base_unsigned(2) << (bits - 1)) - 1; |
134 | base_unsigned y0 = (range + 1) & ~y0_mask; |
135 | base_unsigned u; |
136 | do { |
137 | u = detail::subtract<base_result>()(eng(), (eng.min)()); |
138 | } while(y0 != 0 && u > base_unsigned(y0 - 1)); |
139 | return u & y0_mask; |
140 | } |
141 | |
142 | template<class RealType, std::size_t w, class Engine> |
143 | std::pair<RealType, int> generate_int_float_pair(Engine& eng, boost::mpl::true_) |
144 | { |
145 | typedef typename Engine::result_type base_result; |
146 | typedef typename boost::make_unsigned<base_result>::type base_unsigned; |
147 | |
148 | base_unsigned range = |
149 | detail::subtract<base_result>()((eng.max)(), (eng.min)()); |
150 | |
151 | std::size_t m = |
152 | (range == (std::numeric_limits<base_unsigned>::max)()) ? |
153 | std::numeric_limits<base_unsigned>::digits : |
154 | detail::integer_log2(range + 1); |
155 | |
156 | int bucket = 0; |
157 | // process as many full digits as possible into the int part |
158 | for(std::size_t i = 0; i < w/m; ++i) { |
159 | base_unsigned u = generate_one_digit(eng, m); |
160 | bucket = (bucket << m) | u; |
161 | } |
162 | RealType r; |
163 | |
164 | const std::size_t digits = std::numeric_limits<RealType>::digits; |
165 | { |
166 | base_unsigned u = generate_one_digit(eng, m); |
167 | base_unsigned mask = (base_unsigned(1) << (w%m)) - 1; |
168 | bucket = (bucket << (w%m)) | (mask & u); |
169 | const RealType mult = RealType(1)/RealType(base_unsigned(1) << (m - w%m)); |
170 | // zero out unused bits |
171 | if (m - w%m > digits) { |
172 | u &= ~(base_unsigned(1) << (m - digits)); |
173 | } |
174 | r = RealType(u >> (w%m)) * mult; |
175 | } |
176 | for(std::size_t i = m - w%m; i + m < digits; ++i) { |
177 | base_unsigned u = generate_one_digit(eng, m); |
178 | r += u; |
179 | r *= RealType(0.5)/RealType(base_unsigned(1) << (m - 1)); |
180 | } |
181 | if (m - w%m < digits) |
182 | { |
183 | const std::size_t remaining = (digits - m + w%m) % m; |
184 | base_unsigned u = generate_one_digit(eng, m); |
185 | r += u & ((base_unsigned(2) << (remaining - 1)) - 1); |
186 | const RealType mult = RealType(0.5)/RealType(base_unsigned(1) << (remaining - 1)); |
187 | r *= mult; |
188 | } |
189 | return std::make_pair(r, bucket); |
190 | } |
191 | |
192 | template<class RealType, std::size_t w, class Engine> |
193 | inline std::pair<RealType, int> generate_int_float_pair(Engine& eng, boost::mpl::false_) |
194 | { |
195 | int bucket = uniform_int_distribution<>(0, (1 << w) - 1)(eng); |
196 | RealType r = uniform_01<RealType>()(eng); |
197 | return std::make_pair(r, bucket); |
198 | } |
199 | |
200 | template<class RealType, std::size_t w, class Engine> |
201 | inline std::pair<RealType, int> generate_int_float_pair(Engine& eng) |
202 | { |
203 | typedef typename Engine::result_type base_result; |
204 | return generate_int_float_pair<RealType, w>(eng, |
205 | boost::is_integral<base_result>()); |
206 | } |
207 | |
208 | template<class RealType = double> |
209 | struct unit_normal_distribution |
210 | { |
211 | template<class Engine> |
212 | RealType operator()(Engine& eng) { |
213 | const double * const table_x = normal_table<double>::table_x; |
214 | const double * const table_y = normal_table<double>::table_y; |
215 | for(;;) { |
216 | std::pair<RealType, int> vals = generate_int_float_pair<RealType, 8>(eng); |
217 | int i = vals.second; |
218 | int sign = (i & 1) * 2 - 1; |
219 | i = i >> 1; |
220 | RealType x = vals.first * RealType(table_x[i]); |
221 | if(x < table_x[i + 1]) return x * sign; |
222 | if(i == 0) return generate_tail(eng) * sign; |
223 | RealType y = RealType(table_y[i]) + uniform_01<RealType>()(eng) * RealType(table_y[i + 1] - table_y[i]); |
224 | if (y < f(x)) return x * sign; |
225 | } |
226 | } |
227 | static RealType f(RealType x) { |
228 | using std::exp; |
229 | return exp(-x*x/2); |
230 | } |
231 | template<class Engine> |
232 | RealType generate_tail(Engine& eng) { |
233 | boost::random::exponential_distribution<RealType> exponential; |
234 | const RealType tail_start = RealType(normal_table<double>::table_x[1]); |
235 | for(;;) { |
236 | RealType x = exponential(eng)/tail_start; |
237 | RealType y = exponential(eng); |
238 | if(2*y > x*x) return x + tail_start; |
239 | } |
240 | } |
241 | }; |
242 | |
243 | } |
244 | |
245 | // deterministic Box-Muller method, uses trigonometric functions |
246 | |
247 | /** |
248 | * Instantiations of class template normal_distribution model a |
249 | * \random_distribution. Such a distribution produces random numbers |
250 | * @c x distributed with probability density function |
251 | * \f$\displaystyle p(x) = |
252 | * \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} |
253 | * \f$, |
254 | * where mean and sigma are the parameters of the distribution. |
255 | */ |
256 | template<class RealType = double> |
257 | class normal_distribution |
258 | { |
259 | public: |
260 | typedef RealType input_type; |
261 | typedef RealType result_type; |
262 | |
263 | class param_type { |
264 | public: |
265 | typedef normal_distribution distribution_type; |
266 | |
267 | /** |
268 | * Constructs a @c param_type with a given mean and |
269 | * standard deviation. |
270 | * |
271 | * Requires: sigma >= 0 |
272 | */ |
273 | explicit param_type(RealType mean_arg = RealType(0.0), |
274 | RealType sigma_arg = RealType(1.0)) |
275 | : _mean(mean_arg), |
276 | _sigma(sigma_arg) |
277 | {} |
278 | |
279 | /** Returns the mean of the distribution. */ |
280 | RealType mean() const { return _mean; } |
281 | |
282 | /** Returns the standand deviation of the distribution. */ |
283 | RealType sigma() const { return _sigma; } |
284 | |
285 | /** Writes a @c param_type to a @c std::ostream. */ |
286 | BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm) |
287 | { os << parm._mean << " " << parm._sigma ; return os; } |
288 | |
289 | /** Reads a @c param_type from a @c std::istream. */ |
290 | BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm) |
291 | { is >> parm._mean >> std::ws >> parm._sigma; return is; } |
292 | |
293 | /** Returns true if the two sets of parameters are the same. */ |
294 | BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs) |
295 | { return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma; } |
296 | |
297 | /** Returns true if the two sets of parameters are the different. */ |
298 | BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type) |
299 | |
300 | private: |
301 | RealType _mean; |
302 | RealType _sigma; |
303 | }; |
304 | |
305 | /** |
306 | * Constructs a @c normal_distribution object. @c mean and @c sigma are |
307 | * the parameters for the distribution. |
308 | * |
309 | * Requires: sigma >= 0 |
310 | */ |
311 | explicit normal_distribution(const RealType& mean_arg = RealType(0.0), |
312 | const RealType& sigma_arg = RealType(1.0)) |
313 | : _mean(mean_arg), _sigma(sigma_arg) |
314 | { |
315 | BOOST_ASSERT(_sigma >= RealType(0)); |
316 | } |
317 | |
318 | /** |
319 | * Constructs a @c normal_distribution object from its parameters. |
320 | */ |
321 | explicit normal_distribution(const param_type& parm) |
322 | : _mean(parm.mean()), _sigma(parm.sigma()) |
323 | {} |
324 | |
325 | /** Returns the mean of the distribution. */ |
326 | RealType mean() const { return _mean; } |
327 | /** Returns the standard deviation of the distribution. */ |
328 | RealType sigma() const { return _sigma; } |
329 | |
330 | /** Returns the smallest value that the distribution can produce. */ |
331 | RealType min BOOST_PREVENT_MACRO_SUBSTITUTION () const |
332 | { return -std::numeric_limits<RealType>::infinity(); } |
333 | /** Returns the largest value that the distribution can produce. */ |
334 | RealType max BOOST_PREVENT_MACRO_SUBSTITUTION () const |
335 | { return std::numeric_limits<RealType>::infinity(); } |
336 | |
337 | /** Returns the parameters of the distribution. */ |
338 | param_type param() const { return param_type(_mean, _sigma); } |
339 | /** Sets the parameters of the distribution. */ |
340 | void param(const param_type& parm) |
341 | { |
342 | _mean = parm.mean(); |
343 | _sigma = parm.sigma(); |
344 | } |
345 | |
346 | /** |
347 | * Effects: Subsequent uses of the distribution do not depend |
348 | * on values produced by any engine prior to invoking reset. |
349 | */ |
350 | void reset() { } |
351 | |
352 | /** Returns a normal variate. */ |
353 | template<class Engine> |
354 | result_type operator()(Engine& eng) |
355 | { |
356 | detail::unit_normal_distribution<RealType> impl; |
357 | return impl(eng) * _sigma + _mean; |
358 | } |
359 | |
360 | /** Returns a normal variate with parameters specified by @c param. */ |
361 | template<class URNG> |
362 | result_type operator()(URNG& urng, const param_type& parm) |
363 | { |
364 | return normal_distribution(parm)(urng); |
365 | } |
366 | |
367 | /** Writes a @c normal_distribution to a @c std::ostream. */ |
368 | BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, normal_distribution, nd) |
369 | { |
370 | os << nd._mean << " " << nd._sigma; |
371 | return os; |
372 | } |
373 | |
374 | /** Reads a @c normal_distribution from a @c std::istream. */ |
375 | BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, normal_distribution, nd) |
376 | { |
377 | is >> std::ws >> nd._mean >> std::ws >> nd._sigma; |
378 | return is; |
379 | } |
380 | |
381 | /** |
382 | * Returns true if the two instances of @c normal_distribution will |
383 | * return identical sequences of values given equal generators. |
384 | */ |
385 | BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(normal_distribution, lhs, rhs) |
386 | { |
387 | return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma; |
388 | } |
389 | |
390 | /** |
391 | * Returns true if the two instances of @c normal_distribution will |
392 | * return different sequences of values given equal generators. |
393 | */ |
394 | BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(normal_distribution) |
395 | |
396 | private: |
397 | RealType _mean, _sigma; |
398 | |
399 | }; |
400 | |
401 | } // namespace random |
402 | |
403 | using random::normal_distribution; |
404 | |
405 | } // namespace boost |
406 | |
407 | #endif // BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP |
408 | |