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/base/internal/bits.h"
24 #include "absl/flags/flag.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
TEST(GenerateRealTest,U64ToFloat_Positive_NoZero_Test)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
TEST(GenerateRealTest,U64ToFloat_Positive_Zero_Test)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
TEST(GenerateRealTest,U64ToFloat_Negative_NoZero_Test)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
TEST(GenerateRealTest,U64ToFloat_Negative_Zero_Test)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
TEST(GenerateRealTest,U64ToFloat_Signed_NoZero_Test)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
TEST(GenerateRealTest,U64ToFloat_Signed_Zero_Test)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
TEST(GenerateRealTest,U64ToFloat_Signed_Bias_Test)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
TEST(GenerateRealTest,U64ToFloatTest)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
TEST(GenerateRealTest,U64ToDouble_Positive_NoZero_Test)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
TEST(GenerateRealTest,U64ToDouble_Positive_Zero_Test)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
TEST(GenerateRealTest,U64ToDouble_Negative_NoZero_Test)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
TEST(GenerateRealTest,U64ToDouble_Negative_Zero_Test)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
TEST(GenerateRealTest,U64ToDouble_Signed_NoZero_Test)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
TEST(GenerateRealTest,U64ToDouble_Signed_Zero_Test)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
TEST(GenerateRealTest,U64ToDouble_GenerateSignedTag_Bias_Test)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
TEST(GenerateRealTest,U64ToDoubleTest)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
TEST(GenerateRealTest,U64ToDoubleSignedTest)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
TEST(GenerateRealTest,ExhaustiveFloat)415 TEST(GenerateRealTest, ExhaustiveFloat) {
416 using absl::base_internal::CountLeadingZeros64;
417 auto ToFloat = [](uint64_t a) {
418 return GenerateRealFromBits<float, GeneratePositiveTag, true>(a);
419 };
420
421 // Rely on RandU64ToFloat generating values from greatest to least when
422 // supplied with uint64_t values from greatest (0xfff...) to least (0x0).
423 // Thus, this algorithm stores the previous value, and if the new value is at
424 // greater than or equal to the previous value, then there is a collision in
425 // the generation algorithm.
426 //
427 // Use the computation below to convert the random value into a result:
428 // double res = a() * (1.0f - sample) + b() * sample;
429 float last_f = 1.0, last_g = 2.0;
430 uint64_t f_collisions = 0, g_collisions = 0;
431 uint64_t f_unique = 0, g_unique = 0;
432 uint64_t total = 0;
433 auto count = [&](const float r) {
434 total++;
435 // `f` is mapped to the range [0, 1) (default)
436 const float f = 0.0f * (1.0f - r) + 1.0f * r;
437 if (f >= last_f) {
438 f_collisions++;
439 } else {
440 f_unique++;
441 last_f = f;
442 }
443 // `g` is mapped to the range [1, 2)
444 const float g = 1.0f * (1.0f - r) + 2.0f * r;
445 if (g >= last_g) {
446 g_collisions++;
447 } else {
448 g_unique++;
449 last_g = g;
450 }
451 };
452
453 size_t limit = absl::GetFlag(FLAGS_absl_random_test_trials);
454
455 // Generate all uint64_t which have unique floating point values.
456 // Counting down from 0xFFFFFFFFFFFFFFFFu ... 0x0u
457 uint64_t x = ~uint64_t(0);
458 for (; x != 0 && limit > 0;) {
459 constexpr int kDig = (64 - FLT_MANT_DIG);
460 // Set a decrement value & the next point at which to change
461 // the decrement value. By default these are 1, 0.
462 uint64_t dec = 1;
463 uint64_t chk = 0;
464
465 // Adjust decrement and check value based on how many leading 0
466 // bits are set in the current value.
467 const int clz = CountLeadingZeros64(x);
468 if (clz < kDig) {
469 dec <<= (kDig - clz);
470 chk = (~uint64_t(0)) >> (clz + 1);
471 }
472 for (; x > chk && limit > 0; x -= dec) {
473 count(ToFloat(x));
474 --limit;
475 }
476 }
477
478 static_assert(FLT_MANT_DIG == 24,
479 "The float type is expected to have a 24 bit mantissa.");
480
481 if (limit != 0) {
482 // There are between 2^28 and 2^29 unique values in the range [0, 1). For
483 // the low values of x, there are 2^24 -1 unique values. Once x > 2^24,
484 // there are 40 * 2^24 unique values. Thus:
485 // (2 + 4 + 8 ... + 2^23) + 40 * 2^23
486 EXPECT_LT(1 << 28, f_unique);
487 EXPECT_EQ((1 << 24) + 40 * (1 << 23) - 1, f_unique);
488 EXPECT_EQ(total, f_unique);
489 EXPECT_EQ(0, f_collisions);
490
491 // Expect at least 2^23 unique values for the range [1, 2)
492 EXPECT_LE(1 << 23, g_unique);
493 EXPECT_EQ(total - g_unique, g_collisions);
494 }
495 }
496
497 } // namespace
498