generate_real_test.cc (19695B)
1 // Copyright 2017 The Abseil Authors. 2 // 3 // Licensed under the Apache License, Version 2.0 (the "License"); 4 // you may not use this file except in compliance with the License. 5 // You may obtain a copy of the License at 6 // 7 // https://www.apache.org/licenses/LICENSE-2.0 8 // 9 // Unless required by applicable law or agreed to in writing, software 10 // distributed under the License is distributed on an "AS IS" BASIS, 11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 // See the License for the specific language governing permissions and 13 // limitations under the License. 14 15 #include "absl/random/internal/generate_real.h" 16 17 #include <cfloat> 18 #include <cstddef> 19 #include <cstdint> 20 #include <string> 21 22 #include "gtest/gtest.h" 23 #include "absl/flags/flag.h" 24 #include "absl/numeric/bits.h" 25 26 ABSL_FLAG(int64_t, absl_random_test_trials, 50000, 27 "Number of trials for the probability tests."); 28 29 using absl::random_internal::GenerateNegativeTag; 30 using absl::random_internal::GeneratePositiveTag; 31 using absl::random_internal::GenerateRealFromBits; 32 using absl::random_internal::GenerateSignedTag; 33 34 namespace { 35 36 TEST(GenerateRealTest, U64ToFloat_Positive_NoZero_Test) { 37 auto ToFloat = [](uint64_t a) { 38 return GenerateRealFromBits<float, GeneratePositiveTag, false>(a); 39 }; 40 EXPECT_EQ(ToFloat(0x0000000000000000), 2.710505431e-20f); 41 EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f); 42 EXPECT_EQ(ToFloat(0x8000000000000000), 0.5); 43 EXPECT_EQ(ToFloat(0x8000000000000001), 0.5); 44 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); 45 } 46 47 TEST(GenerateRealTest, U64ToFloat_Positive_Zero_Test) { 48 auto ToFloat = [](uint64_t a) { 49 return GenerateRealFromBits<float, GeneratePositiveTag, true>(a); 50 }; 51 EXPECT_EQ(ToFloat(0x0000000000000000), 0.0); 52 EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f); 53 EXPECT_EQ(ToFloat(0x8000000000000000), 0.5); 54 EXPECT_EQ(ToFloat(0x8000000000000001), 0.5); 55 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); 56 } 57 58 TEST(GenerateRealTest, U64ToFloat_Negative_NoZero_Test) { 59 auto ToFloat = [](uint64_t a) { 60 return GenerateRealFromBits<float, GenerateNegativeTag, false>(a); 61 }; 62 EXPECT_EQ(ToFloat(0x0000000000000000), -2.710505431e-20f); 63 EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f); 64 EXPECT_EQ(ToFloat(0x8000000000000000), -0.5); 65 EXPECT_EQ(ToFloat(0x8000000000000001), -0.5); 66 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); 67 } 68 69 TEST(GenerateRealTest, U64ToFloat_Negative_Zero_Test) { 70 auto ToFloat = [](uint64_t a) { 71 return GenerateRealFromBits<float, GenerateNegativeTag, true>(a); 72 }; 73 EXPECT_EQ(ToFloat(0x0000000000000000), 0.0); 74 EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f); 75 EXPECT_EQ(ToFloat(0x8000000000000000), -0.5); 76 EXPECT_EQ(ToFloat(0x8000000000000001), -0.5); 77 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); 78 } 79 80 TEST(GenerateRealTest, U64ToFloat_Signed_NoZero_Test) { 81 auto ToFloat = [](uint64_t a) { 82 return GenerateRealFromBits<float, GenerateSignedTag, false>(a); 83 }; 84 EXPECT_EQ(ToFloat(0x0000000000000000), 5.421010862e-20f); 85 EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f); 86 EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f); 87 EXPECT_EQ(ToFloat(0x8000000000000000), -5.421010862e-20f); 88 EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f); 89 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); 90 } 91 92 TEST(GenerateRealTest, U64ToFloat_Signed_Zero_Test) { 93 auto ToFloat = [](uint64_t a) { 94 return GenerateRealFromBits<float, GenerateSignedTag, true>(a); 95 }; 96 EXPECT_EQ(ToFloat(0x0000000000000000), 0); 97 EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f); 98 EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f); 99 EXPECT_EQ(ToFloat(0x8000000000000000), 0); 100 EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f); 101 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); 102 } 103 104 TEST(GenerateRealTest, U64ToFloat_Signed_Bias_Test) { 105 auto ToFloat = [](uint64_t a) { 106 return GenerateRealFromBits<float, GenerateSignedTag, true>(a, 1); 107 }; 108 EXPECT_EQ(ToFloat(0x0000000000000000), 0); 109 EXPECT_EQ(ToFloat(0x0000000000000001), 2 * 1.084202172e-19f); 110 EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 2 * 0.9999999404f); 111 EXPECT_EQ(ToFloat(0x8000000000000000), 0); 112 EXPECT_EQ(ToFloat(0x8000000000000001), 2 * -1.084202172e-19f); 113 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 2 * -0.9999999404f); 114 } 115 116 TEST(GenerateRealTest, U64ToFloatTest) { 117 auto ToFloat = [](uint64_t a) -> float { 118 return GenerateRealFromBits<float, GeneratePositiveTag, true>(a); 119 }; 120 121 EXPECT_EQ(ToFloat(0x0000000000000000), 0.0f); 122 123 EXPECT_EQ(ToFloat(0x8000000000000000), 0.5f); 124 EXPECT_EQ(ToFloat(0x8000000000000001), 0.5f); 125 EXPECT_EQ(ToFloat(0x800000FFFFFFFFFF), 0.5f); 126 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); 127 128 EXPECT_GT(ToFloat(0x0000000000000001), 0.0f); 129 130 EXPECT_NE(ToFloat(0x7FFFFF0000000000), ToFloat(0x7FFFFEFFFFFFFFFF)); 131 132 EXPECT_LT(ToFloat(0xFFFFFFFFFFFFFFFF), 1.0f); 133 int32_t two_to_24 = 1 << 24; 134 EXPECT_EQ(static_cast<int32_t>(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24), 135 two_to_24 - 1); 136 EXPECT_NE(static_cast<int32_t>(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24 * 2), 137 two_to_24 * 2 - 1); 138 EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFF0000000000)); 139 EXPECT_NE(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFEFFFFFFFFFF)); 140 EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF8000000000)); 141 EXPECT_NE(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF7FFFFFFFFF)); 142 EXPECT_EQ(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFC000000000)); 143 EXPECT_NE(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFBFFFFFFFFF)); 144 145 // For values where every bit counts, the values scale as multiples of the 146 // input. 147 for (int i = 0; i < 100; ++i) { 148 EXPECT_EQ(i * ToFloat(0x0000000000000001), ToFloat(i)); 149 } 150 151 // For each i: value generated from (1 << i). 152 float exp_values[64]; 153 exp_values[63] = 0.5f; 154 for (int i = 62; i >= 0; --i) exp_values[i] = 0.5f * exp_values[i + 1]; 155 constexpr uint64_t one = 1; 156 for (int i = 0; i < 64; ++i) { 157 EXPECT_EQ(ToFloat(one << i), exp_values[i]); 158 for (int j = 1; j < FLT_MANT_DIG && i - j >= 0; ++j) { 159 EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]); 160 EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), 161 exp_values[i] + exp_values[i - j]); 162 } 163 for (int j = FLT_MANT_DIG; i - j >= 0; ++j) { 164 EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]); 165 EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), exp_values[i]); 166 } 167 } 168 } 169 170 TEST(GenerateRealTest, U64ToDouble_Positive_NoZero_Test) { 171 auto ToDouble = [](uint64_t a) { 172 return GenerateRealFromBits<double, GeneratePositiveTag, false>(a); 173 }; 174 175 EXPECT_EQ(ToDouble(0x0000000000000000), 2.710505431213761085e-20); 176 EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); 177 EXPECT_EQ(ToDouble(0x0000000000000002), 1.084202172485504434e-19); 178 EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); 179 EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); 180 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); 181 } 182 183 TEST(GenerateRealTest, U64ToDouble_Positive_Zero_Test) { 184 auto ToDouble = [](uint64_t a) { 185 return GenerateRealFromBits<double, GeneratePositiveTag, true>(a); 186 }; 187 188 EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); 189 EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); 190 EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); 191 EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); 192 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); 193 } 194 195 TEST(GenerateRealTest, U64ToDouble_Negative_NoZero_Test) { 196 auto ToDouble = [](uint64_t a) { 197 return GenerateRealFromBits<double, GenerateNegativeTag, false>(a); 198 }; 199 200 EXPECT_EQ(ToDouble(0x0000000000000000), -2.710505431213761085e-20); 201 EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20); 202 EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19); 203 EXPECT_EQ(ToDouble(0x8000000000000000), -0.5); 204 EXPECT_EQ(ToDouble(0x8000000000000001), -0.5); 205 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); 206 } 207 208 TEST(GenerateRealTest, U64ToDouble_Negative_Zero_Test) { 209 auto ToDouble = [](uint64_t a) { 210 return GenerateRealFromBits<double, GenerateNegativeTag, true>(a); 211 }; 212 213 EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); 214 EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20); 215 EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19); 216 EXPECT_EQ(ToDouble(0x8000000000000000), -0.5); 217 EXPECT_EQ(ToDouble(0x8000000000000001), -0.5); 218 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); 219 } 220 221 TEST(GenerateRealTest, U64ToDouble_Signed_NoZero_Test) { 222 auto ToDouble = [](uint64_t a) { 223 return GenerateRealFromBits<double, GenerateSignedTag, false>(a); 224 }; 225 226 EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20); 227 EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); 228 EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978); 229 EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20); 230 EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); 231 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); 232 } 233 234 TEST(GenerateRealTest, U64ToDouble_Signed_Zero_Test) { 235 auto ToDouble = [](uint64_t a) { 236 return GenerateRealFromBits<double, GenerateSignedTag, true>(a); 237 }; 238 EXPECT_EQ(ToDouble(0x0000000000000000), 0); 239 EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); 240 EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978); 241 EXPECT_EQ(ToDouble(0x8000000000000000), 0); 242 EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); 243 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); 244 } 245 246 TEST(GenerateRealTest, U64ToDouble_GenerateSignedTag_Bias_Test) { 247 auto ToDouble = [](uint64_t a) { 248 return GenerateRealFromBits<double, GenerateSignedTag, true>(a, -1); 249 }; 250 EXPECT_EQ(ToDouble(0x0000000000000000), 0); 251 EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19 / 2); 252 EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978 / 2); 253 EXPECT_EQ(ToDouble(0x8000000000000000), 0); 254 EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19 / 2); 255 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978 / 2); 256 } 257 258 TEST(GenerateRealTest, U64ToDoubleTest) { 259 auto ToDouble = [](uint64_t a) { 260 return GenerateRealFromBits<double, GeneratePositiveTag, true>(a); 261 }; 262 263 EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); 264 EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); 265 266 EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); 267 EXPECT_EQ(ToDouble(0x7fffffffffffffef), 0.499999999999999944489); 268 EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); 269 270 // For values > 0.5, RandU64ToDouble discards up to 11 bits. (64-53). 271 EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); 272 EXPECT_EQ(ToDouble(0x80000000000007FF), 0.5); 273 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); 274 EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF)); 275 276 EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFF), 1.0); 277 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF800)); 278 EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF7FF)); 279 EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00)); 280 EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFBFF)); 281 EXPECT_EQ(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFE00)); 282 EXPECT_NE(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFDFF)); 283 284 EXPECT_EQ(ToDouble(0x1000000000000001), 0.0625); 285 EXPECT_EQ(ToDouble(0x2000000000000001), 0.125); 286 EXPECT_EQ(ToDouble(0x3000000000000001), 0.1875); 287 EXPECT_EQ(ToDouble(0x4000000000000001), 0.25); 288 EXPECT_EQ(ToDouble(0x5000000000000001), 0.3125); 289 EXPECT_EQ(ToDouble(0x6000000000000001), 0.375); 290 EXPECT_EQ(ToDouble(0x7000000000000001), 0.4375); 291 EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); 292 EXPECT_EQ(ToDouble(0x9000000000000001), 0.5625); 293 EXPECT_EQ(ToDouble(0xa000000000000001), 0.625); 294 EXPECT_EQ(ToDouble(0xb000000000000001), 0.6875); 295 EXPECT_EQ(ToDouble(0xc000000000000001), 0.75); 296 EXPECT_EQ(ToDouble(0xd000000000000001), 0.8125); 297 EXPECT_EQ(ToDouble(0xe000000000000001), 0.875); 298 EXPECT_EQ(ToDouble(0xf000000000000001), 0.9375); 299 300 // Large powers of 2. 301 int64_t two_to_53 = int64_t{1} << 53; 302 EXPECT_EQ(static_cast<int64_t>(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53), 303 two_to_53 - 1); 304 EXPECT_NE(static_cast<int64_t>(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53 * 2), 305 two_to_53 * 2 - 1); 306 307 // For values where every bit counts, the values scale as multiples of the 308 // input. 309 for (int i = 0; i < 100; ++i) { 310 EXPECT_EQ(i * ToDouble(0x0000000000000001), ToDouble(i)); 311 } 312 313 // For each i: value generated from (1 << i). 314 double exp_values[64]; 315 exp_values[63] = 0.5; 316 for (int i = 62; i >= 0; --i) exp_values[i] = 0.5 * exp_values[i + 1]; 317 constexpr uint64_t one = 1; 318 for (int i = 0; i < 64; ++i) { 319 EXPECT_EQ(ToDouble(one << i), exp_values[i]); 320 for (int j = 1; j < DBL_MANT_DIG && i - j >= 0; ++j) { 321 EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]); 322 EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), 323 exp_values[i] + exp_values[i - j]); 324 } 325 for (int j = DBL_MANT_DIG; i - j >= 0; ++j) { 326 EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]); 327 EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), exp_values[i]); 328 } 329 } 330 } 331 332 TEST(GenerateRealTest, U64ToDoubleSignedTest) { 333 auto ToDouble = [](uint64_t a) { 334 return GenerateRealFromBits<double, GenerateSignedTag, false>(a); 335 }; 336 337 EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20); 338 EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); 339 340 EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20); 341 EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); 342 343 const double e_plus = ToDouble(0x0000000000000001); 344 const double e_minus = ToDouble(0x8000000000000001); 345 EXPECT_EQ(e_plus, 1.084202172485504434e-19); 346 EXPECT_EQ(e_minus, -1.084202172485504434e-19); 347 348 EXPECT_EQ(ToDouble(0x3fffffffffffffef), 0.499999999999999944489); 349 EXPECT_EQ(ToDouble(0xbfffffffffffffef), -0.499999999999999944489); 350 351 // For values > 0.5, RandU64ToDouble discards up to 10 bits. (63-53). 352 EXPECT_EQ(ToDouble(0x4000000000000000), 0.5); 353 EXPECT_EQ(ToDouble(0x4000000000000001), 0.5); 354 EXPECT_EQ(ToDouble(0x40000000000003FF), 0.5); 355 356 EXPECT_EQ(ToDouble(0xC000000000000000), -0.5); 357 EXPECT_EQ(ToDouble(0xC000000000000001), -0.5); 358 EXPECT_EQ(ToDouble(0xC0000000000003FF), -0.5); 359 360 EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFe), 0.999999999999999888978); 361 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999999999888978); 362 363 EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF)); 364 365 EXPECT_LT(ToDouble(0x7FFFFFFFFFFFFFFF), 1.0); 366 EXPECT_GT(ToDouble(0x7FFFFFFFFFFFFFFF), 0.9999999999); 367 368 EXPECT_GT(ToDouble(0xFFFFFFFFFFFFFFFe), -1.0); 369 EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999); 370 371 EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFFC00)); 372 EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00)); 373 EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFF3FF)); 374 EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFF3FF)); 375 376 EXPECT_EQ(ToDouble(0x1000000000000001), 0.125); 377 EXPECT_EQ(ToDouble(0x2000000000000001), 0.25); 378 EXPECT_EQ(ToDouble(0x3000000000000001), 0.375); 379 EXPECT_EQ(ToDouble(0x4000000000000001), 0.5); 380 EXPECT_EQ(ToDouble(0x5000000000000001), 0.625); 381 EXPECT_EQ(ToDouble(0x6000000000000001), 0.75); 382 EXPECT_EQ(ToDouble(0x7000000000000001), 0.875); 383 EXPECT_EQ(ToDouble(0x7800000000000001), 0.9375); 384 EXPECT_EQ(ToDouble(0x7c00000000000001), 0.96875); 385 EXPECT_EQ(ToDouble(0x7e00000000000001), 0.984375); 386 EXPECT_EQ(ToDouble(0x7f00000000000001), 0.9921875); 387 388 // 0x8000000000000000 ~= 0 389 EXPECT_EQ(ToDouble(0x9000000000000001), -0.125); 390 EXPECT_EQ(ToDouble(0xa000000000000001), -0.25); 391 EXPECT_EQ(ToDouble(0xb000000000000001), -0.375); 392 EXPECT_EQ(ToDouble(0xc000000000000001), -0.5); 393 EXPECT_EQ(ToDouble(0xd000000000000001), -0.625); 394 EXPECT_EQ(ToDouble(0xe000000000000001), -0.75); 395 EXPECT_EQ(ToDouble(0xf000000000000001), -0.875); 396 397 // Large powers of 2. 398 int64_t two_to_53 = int64_t{1} << 53; 399 EXPECT_EQ(static_cast<int64_t>(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53), 400 two_to_53 - 1); 401 EXPECT_EQ(static_cast<int64_t>(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53), 402 -(two_to_53 - 1)); 403 404 EXPECT_NE(static_cast<int64_t>(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53 * 2), 405 two_to_53 * 2 - 1); 406 407 // For values where every bit counts, the values scale as multiples of the 408 // input. 409 for (int i = 1; i < 100; ++i) { 410 EXPECT_EQ(i * e_plus, ToDouble(i)) << i; 411 EXPECT_EQ(i * e_minus, ToDouble(0x8000000000000000 | i)) << i; 412 } 413 } 414 415 TEST(GenerateRealTest, ExhaustiveFloat) { 416 auto ToFloat = [](uint64_t a) { 417 return GenerateRealFromBits<float, GeneratePositiveTag, true>(a); 418 }; 419 420 // Rely on RandU64ToFloat generating values from greatest to least when 421 // supplied with uint64_t values from greatest (0xfff...) to least (0x0). 422 // Thus, this algorithm stores the previous value, and if the new value is at 423 // greater than or equal to the previous value, then there is a collision in 424 // the generation algorithm. 425 // 426 // Use the computation below to convert the random value into a result: 427 // double res = a() * (1.0f - sample) + b() * sample; 428 float last_f = 1.0, last_g = 2.0; 429 uint64_t f_collisions = 0, g_collisions = 0; 430 uint64_t f_unique = 0, g_unique = 0; 431 uint64_t total = 0; 432 auto count = [&](const float r) { 433 total++; 434 // `f` is mapped to the range [0, 1) (default) 435 const float f = 0.0f * (1.0f - r) + 1.0f * r; 436 if (f >= last_f) { 437 f_collisions++; 438 } else { 439 f_unique++; 440 last_f = f; 441 } 442 // `g` is mapped to the range [1, 2) 443 const float g = 1.0f * (1.0f - r) + 2.0f * r; 444 if (g >= last_g) { 445 g_collisions++; 446 } else { 447 g_unique++; 448 last_g = g; 449 } 450 }; 451 452 size_t limit = absl::GetFlag(FLAGS_absl_random_test_trials); 453 454 // Generate all uint64_t which have unique floating point values. 455 // Counting down from 0xFFFFFFFFFFFFFFFFu ... 0x0u 456 uint64_t x = ~uint64_t(0); 457 for (; x != 0 && limit > 0;) { 458 constexpr int kDig = (64 - FLT_MANT_DIG); 459 // Set a decrement value & the next point at which to change 460 // the decrement value. By default these are 1, 0. 461 uint64_t dec = 1; 462 uint64_t chk = 0; 463 464 // Adjust decrement and check value based on how many leading 0 465 // bits are set in the current value. 466 const int clz = absl::countl_zero(x); 467 if (clz < kDig) { 468 dec <<= (kDig - clz); 469 chk = (~uint64_t(0)) >> (clz + 1); 470 } 471 for (; x > chk && limit > 0; x -= dec) { 472 count(ToFloat(x)); 473 --limit; 474 } 475 } 476 477 static_assert(FLT_MANT_DIG == 24, 478 "The float type is expected to have a 24 bit mantissa."); 479 480 if (limit != 0) { 481 // There are between 2^28 and 2^29 unique values in the range [0, 1). For 482 // the low values of x, there are 2^24 -1 unique values. Once x > 2^24, 483 // there are 40 * 2^24 unique values. Thus: 484 // (2 + 4 + 8 ... + 2^23) + 40 * 2^23 485 EXPECT_LT(1 << 28, f_unique); 486 EXPECT_EQ((1 << 24) + 40 * (1 << 23) - 1, f_unique); 487 EXPECT_EQ(total, f_unique); 488 EXPECT_EQ(0, f_collisions); 489 490 // Expect at least 2^23 unique values for the range [1, 2) 491 EXPECT_LE(1 << 23, g_unique); 492 EXPECT_EQ(total - g_unique, g_collisions); 493 } 494 } 495 496 } // namespace