1 //===----------------------------------------------------------------------===//
2 //
3 // The LLVM Compiler Infrastructure
4 //
5 // This file is dual licensed under the MIT and the University of Illinois Open
6 // Source Licenses. See LICENSE.TXT for details.
7 //
8 //===----------------------------------------------------------------------===//
9 //
10 // REQUIRES: long_tests
11
12 // <random>
13
14 // template<class IntType = int>
15 // class binomial_distribution
16
17 // template<class _URNG> result_type operator()(_URNG& g);
18
19 #include <random>
20 #include <numeric>
21 #include <vector>
22 #include <cassert>
23
24 template <class T>
25 inline
26 T
sqr(T x)27 sqr(T x)
28 {
29 return x * x;
30 }
31
main()32 int main()
33 {
34 {
35 typedef std::binomial_distribution<> D;
36 typedef std::mt19937_64 G;
37 G g;
38 D d(5, .75);
39 const int N = 1000000;
40 std::vector<D::result_type> u;
41 for (int i = 0; i < N; ++i)
42 {
43 D::result_type v = d(g);
44 assert(d.min() <= v && v <= d.max());
45 u.push_back(v);
46 }
47 double mean = std::accumulate(u.begin(), u.end(),
48 double(0)) / u.size();
49 double var = 0;
50 double skew = 0;
51 double kurtosis = 0;
52 for (int i = 0; i < u.size(); ++i)
53 {
54 double d = (u[i] - mean);
55 double d2 = sqr(d);
56 var += d2;
57 skew += d * d2;
58 kurtosis += d2 * d2;
59 }
60 var /= u.size();
61 double dev = std::sqrt(var);
62 skew /= u.size() * dev * var;
63 kurtosis /= u.size() * var * var;
64 kurtosis -= 3;
65 double x_mean = d.t() * d.p();
66 double x_var = x_mean*(1-d.p());
67 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
68 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
69 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
70 assert(std::abs((var - x_var) / x_var) < 0.01);
71 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
72 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
73 }
74 {
75 typedef std::binomial_distribution<> D;
76 typedef std::mt19937 G;
77 G g;
78 D d(30, .03125);
79 const int N = 100000;
80 std::vector<D::result_type> u;
81 for (int i = 0; i < N; ++i)
82 {
83 D::result_type v = d(g);
84 assert(d.min() <= v && v <= d.max());
85 u.push_back(v);
86 }
87 double mean = std::accumulate(u.begin(), u.end(),
88 double(0)) / u.size();
89 double var = 0;
90 double skew = 0;
91 double kurtosis = 0;
92 for (int i = 0; i < u.size(); ++i)
93 {
94 double d = (u[i] - mean);
95 double d2 = sqr(d);
96 var += d2;
97 skew += d * d2;
98 kurtosis += d2 * d2;
99 }
100 var /= u.size();
101 double dev = std::sqrt(var);
102 skew /= u.size() * dev * var;
103 kurtosis /= u.size() * var * var;
104 kurtosis -= 3;
105 double x_mean = d.t() * d.p();
106 double x_var = x_mean*(1-d.p());
107 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
108 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
109 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
110 assert(std::abs((var - x_var) / x_var) < 0.01);
111 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
112 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
113 }
114 {
115 typedef std::binomial_distribution<> D;
116 typedef std::mt19937 G;
117 G g;
118 D d(40, .25);
119 const int N = 100000;
120 std::vector<D::result_type> u;
121 for (int i = 0; i < N; ++i)
122 {
123 D::result_type v = d(g);
124 assert(d.min() <= v && v <= d.max());
125 u.push_back(v);
126 }
127 double mean = std::accumulate(u.begin(), u.end(),
128 double(0)) / u.size();
129 double var = 0;
130 double skew = 0;
131 double kurtosis = 0;
132 for (int i = 0; i < u.size(); ++i)
133 {
134 double d = (u[i] - mean);
135 double d2 = sqr(d);
136 var += d2;
137 skew += d * d2;
138 kurtosis += d2 * d2;
139 }
140 var /= u.size();
141 double dev = std::sqrt(var);
142 skew /= u.size() * dev * var;
143 kurtosis /= u.size() * var * var;
144 kurtosis -= 3;
145 double x_mean = d.t() * d.p();
146 double x_var = x_mean*(1-d.p());
147 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
148 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
149 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
150 assert(std::abs((var - x_var) / x_var) < 0.01);
151 assert(std::abs((skew - x_skew) / x_skew) < 0.03);
152 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
153 }
154 {
155 typedef std::binomial_distribution<> D;
156 typedef std::mt19937 G;
157 G g;
158 D d(40, 0);
159 const int N = 100000;
160 std::vector<D::result_type> u;
161 for (int i = 0; i < N; ++i)
162 {
163 D::result_type v = d(g);
164 assert(d.min() <= v && v <= d.max());
165 u.push_back(v);
166 }
167 double mean = std::accumulate(u.begin(), u.end(),
168 double(0)) / u.size();
169 double var = 0;
170 double skew = 0;
171 double kurtosis = 0;
172 for (int i = 0; i < u.size(); ++i)
173 {
174 double d = (u[i] - mean);
175 double d2 = sqr(d);
176 var += d2;
177 skew += d * d2;
178 kurtosis += d2 * d2;
179 }
180 var /= u.size();
181 double dev = std::sqrt(var);
182 // In this case:
183 // skew computes to 0./0. == nan
184 // kurtosis computes to 0./0. == nan
185 // x_skew == inf
186 // x_kurtosis == inf
187 // These tests are commented out because UBSan warns about division by 0
188 // skew /= u.size() * dev * var;
189 // kurtosis /= u.size() * var * var;
190 // kurtosis -= 3;
191 double x_mean = d.t() * d.p();
192 double x_var = x_mean*(1-d.p());
193 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
194 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
195 assert(mean == x_mean);
196 assert(var == x_var);
197 // assert(skew == x_skew);
198 // assert(kurtosis == x_kurtosis);
199 }
200 {
201 typedef std::binomial_distribution<> D;
202 typedef std::mt19937 G;
203 G g;
204 D d(40, 1);
205 const int N = 100000;
206 std::vector<D::result_type> u;
207 for (int i = 0; i < N; ++i)
208 {
209 D::result_type v = d(g);
210 assert(d.min() <= v && v <= d.max());
211 u.push_back(v);
212 }
213 double mean = std::accumulate(u.begin(), u.end(),
214 double(0)) / u.size();
215 double var = 0;
216 double skew = 0;
217 double kurtosis = 0;
218 for (int i = 0; i < u.size(); ++i)
219 {
220 double d = (u[i] - mean);
221 double d2 = sqr(d);
222 var += d2;
223 skew += d * d2;
224 kurtosis += d2 * d2;
225 }
226 var /= u.size();
227 double dev = std::sqrt(var);
228 // In this case:
229 // skew computes to 0./0. == nan
230 // kurtosis computes to 0./0. == nan
231 // x_skew == -inf
232 // x_kurtosis == inf
233 // These tests are commented out because UBSan warns about division by 0
234 // skew /= u.size() * dev * var;
235 // kurtosis /= u.size() * var * var;
236 // kurtosis -= 3;
237 double x_mean = d.t() * d.p();
238 double x_var = x_mean*(1-d.p());
239 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
240 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
241 assert(mean == x_mean);
242 assert(var == x_var);
243 // assert(skew == x_skew);
244 // assert(kurtosis == x_kurtosis);
245 }
246 {
247 typedef std::binomial_distribution<> D;
248 typedef std::mt19937 G;
249 G g;
250 D d(400, 0.5);
251 const int N = 100000;
252 std::vector<D::result_type> u;
253 for (int i = 0; i < N; ++i)
254 {
255 D::result_type v = d(g);
256 assert(d.min() <= v && v <= d.max());
257 u.push_back(v);
258 }
259 double mean = std::accumulate(u.begin(), u.end(),
260 double(0)) / u.size();
261 double var = 0;
262 double skew = 0;
263 double kurtosis = 0;
264 for (int i = 0; i < u.size(); ++i)
265 {
266 double d = (u[i] - mean);
267 double d2 = sqr(d);
268 var += d2;
269 skew += d * d2;
270 kurtosis += d2 * d2;
271 }
272 var /= u.size();
273 double dev = std::sqrt(var);
274 skew /= u.size() * dev * var;
275 kurtosis /= u.size() * var * var;
276 kurtosis -= 3;
277 double x_mean = d.t() * d.p();
278 double x_var = x_mean*(1-d.p());
279 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
280 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
281 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
282 assert(std::abs((var - x_var) / x_var) < 0.01);
283 assert(std::abs(skew - x_skew) < 0.01);
284 assert(std::abs(kurtosis - x_kurtosis) < 0.01);
285 }
286 {
287 typedef std::binomial_distribution<> D;
288 typedef std::mt19937 G;
289 G g;
290 D d(1, 0.5);
291 const int N = 100000;
292 std::vector<D::result_type> u;
293 for (int i = 0; i < N; ++i)
294 {
295 D::result_type v = d(g);
296 assert(d.min() <= v && v <= d.max());
297 u.push_back(v);
298 }
299 double mean = std::accumulate(u.begin(), u.end(),
300 double(0)) / u.size();
301 double var = 0;
302 double skew = 0;
303 double kurtosis = 0;
304 for (int i = 0; i < u.size(); ++i)
305 {
306 double d = (u[i] - mean);
307 double d2 = sqr(d);
308 var += d2;
309 skew += d * d2;
310 kurtosis += d2 * d2;
311 }
312 var /= u.size();
313 double dev = std::sqrt(var);
314 skew /= u.size() * dev * var;
315 kurtosis /= u.size() * var * var;
316 kurtosis -= 3;
317 double x_mean = d.t() * d.p();
318 double x_var = x_mean*(1-d.p());
319 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
320 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
321 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
322 assert(std::abs((var - x_var) / x_var) < 0.01);
323 assert(std::abs(skew - x_skew) < 0.01);
324 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
325 }
326 {
327 const int N = 100000;
328 std::mt19937 gen1;
329 std::mt19937 gen2;
330
331 std::binomial_distribution<> dist1(5, 0.1);
332 std::binomial_distribution<unsigned> dist2(5, 0.1);
333
334 for(int i = 0; i < N; ++i)
335 assert(dist1(gen1) == dist2(gen2));
336 }
337 {
338 typedef std::binomial_distribution<> D;
339 typedef std::mt19937 G;
340 G g;
341 D d(0, 0.005);
342 const int N = 100000;
343 std::vector<D::result_type> u;
344 for (int i = 0; i < N; ++i)
345 {
346 D::result_type v = d(g);
347 assert(d.min() <= v && v <= d.max());
348 u.push_back(v);
349 }
350 double mean = std::accumulate(u.begin(), u.end(),
351 double(0)) / u.size();
352 double var = 0;
353 double skew = 0;
354 double kurtosis = 0;
355 for (int i = 0; i < u.size(); ++i)
356 {
357 double d = (u[i] - mean);
358 double d2 = sqr(d);
359 var += d2;
360 skew += d * d2;
361 kurtosis += d2 * d2;
362 }
363 var /= u.size();
364 double dev = std::sqrt(var);
365 // In this case:
366 // skew computes to 0./0. == nan
367 // kurtosis computes to 0./0. == nan
368 // x_skew == inf
369 // x_kurtosis == inf
370 // These tests are commented out because UBSan warns about division by 0
371 // skew /= u.size() * dev * var;
372 // kurtosis /= u.size() * var * var;
373 // kurtosis -= 3;
374 double x_mean = d.t() * d.p();
375 double x_var = x_mean*(1-d.p());
376 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
377 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
378 assert(mean == x_mean);
379 assert(var == x_var);
380 // assert(skew == x_skew);
381 // assert(kurtosis == x_kurtosis);
382 }
383 {
384 typedef std::binomial_distribution<> D;
385 typedef std::mt19937 G;
386 G g;
387 D d(0, 0);
388 const int N = 100000;
389 std::vector<D::result_type> u;
390 for (int i = 0; i < N; ++i)
391 {
392 D::result_type v = d(g);
393 assert(d.min() <= v && v <= d.max());
394 u.push_back(v);
395 }
396 double mean = std::accumulate(u.begin(), u.end(),
397 double(0)) / u.size();
398 double var = 0;
399 double skew = 0;
400 double kurtosis = 0;
401 for (int i = 0; i < u.size(); ++i)
402 {
403 double d = (u[i] - mean);
404 double d2 = sqr(d);
405 var += d2;
406 skew += d * d2;
407 kurtosis += d2 * d2;
408 }
409 var /= u.size();
410 double dev = std::sqrt(var);
411 // In this case:
412 // skew computes to 0./0. == nan
413 // kurtosis computes to 0./0. == nan
414 // x_skew == inf
415 // x_kurtosis == inf
416 // These tests are commented out because UBSan warns about division by 0
417 // skew /= u.size() * dev * var;
418 // kurtosis /= u.size() * var * var;
419 // kurtosis -= 3;
420 double x_mean = d.t() * d.p();
421 double x_var = x_mean*(1-d.p());
422 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
423 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
424 assert(mean == x_mean);
425 assert(var == x_var);
426 // assert(skew == x_skew);
427 // assert(kurtosis == x_kurtosis);
428 }
429 {
430 typedef std::binomial_distribution<> D;
431 typedef std::mt19937 G;
432 G g;
433 D d(0, 1);
434 const int N = 100000;
435 std::vector<D::result_type> u;
436 for (int i = 0; i < N; ++i)
437 {
438 D::result_type v = d(g);
439 assert(d.min() <= v && v <= d.max());
440 u.push_back(v);
441 }
442 double mean = std::accumulate(u.begin(), u.end(),
443 double(0)) / u.size();
444 double var = 0;
445 double skew = 0;
446 double kurtosis = 0;
447 for (int i = 0; i < u.size(); ++i)
448 {
449 double d = (u[i] - mean);
450 double d2 = sqr(d);
451 var += d2;
452 skew += d * d2;
453 kurtosis += d2 * d2;
454 }
455 var /= u.size();
456 double dev = std::sqrt(var);
457 // In this case:
458 // skew computes to 0./0. == nan
459 // kurtosis computes to 0./0. == nan
460 // x_skew == -inf
461 // x_kurtosis == inf
462 // These tests are commented out because UBSan warns about division by 0
463 // skew /= u.size() * dev * var;
464 // kurtosis /= u.size() * var * var;
465 // kurtosis -= 3;
466 double x_mean = d.t() * d.p();
467 double x_var = x_mean*(1-d.p());
468 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
469 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
470 assert(mean == x_mean);
471 assert(var == x_var);
472 // assert(skew == x_skew);
473 // assert(kurtosis == x_kurtosis);
474 }
475 }
476