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