abseil-cpp/absl/random/internal/generate_real_test.cc
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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
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