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 27 sqr(T x) 28 { 29 return x * x; 30 } 31 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
