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tvl-depot/absl/random/internal/generate_real_test.cc
Abseil Team 078b89b3c0 Export of internal Abseil changes 
--
e54b9c7bbb0c58475676c268e2e19c69f4bce48a by Jorg Brown <jorg@google.com>:

Tweak ABSL_PREDICT_TRUE slightly, for better code on some platforms and/or
optimization levels.  "false || (x)" is more verbose than "!!(x)", but
ultimately more efficient.

For example, given this code:

void InitIfNecessary() {
  if (ABSL_PREDICT_TRUE(NeedsInit())) {
    SlowInitIfNecessary();
  }
}

Clang with default optimization level will produce:

Before this CL              After this CL
InitIfNecessary:            InitIfNecessary:
  push rbp                    push rbp
  mov  rbp, rsp               mov  rbp, rsp
  call NeedsInit              call NeedsInit
  xor  al, -1
  xor  al, -1
  test al, 1                  test al, 1
  jne  .LBB2_1                jne  .LBB3_1
  jmp  .LBB2_2                jmp  .LBB3_2
.LBB2_1:                    .LBB3_1:
  call SlowInitIfNecessary    call SlowInitIfNecessary
.LBB2_2:                    .LBB3_2:
  pop  rbp                    pop  rbp
  ret                         ret
PiperOrigin-RevId: 276401386

--
0a3c4dfd8342bf2b1b11a87f1c662c883f73cab7 by Abseil Team <absl-team@google.com>:

Fix comment nit: sem_open => sem_init.

The code calls sem_init, not sem_open, to initialize an unnamed semaphore.
(sem_open creates or opens a named semaphore.)

PiperOrigin-RevId: 276344072

--
b36a664e9459057509a90e83d3482e1d3a4c44c7 by Abseil Team <absl-team@google.com>:

Fix typo in flat_hash_map.h: exchaged -> exchanged

PiperOrigin-RevId: 276295792

--
7bbd8d18276eb110c8335743e35fceb662ddf3d6 by Samuel Benzaquen <sbenza@google.com>:

Add assertions to verify use of iterators.

PiperOrigin-RevId: 276283300

--
677398a8ffcb1f59182cffe57a4fe7ff147a0404 by Laramie Leavitt <lar@google.com>:

Migrate distribution_impl.h/cc to generate_real.h/cc.

Combine the methods RandU64To<Float,Double> into a single method:
GenerateRealFromBits().

Remove rejection sampling from absl::uniform_real_distribution.

PiperOrigin-RevId: 276158675

--
c60c9d11d24b0c546329d998e78e15a84b3153f5 by Abseil Team <absl-team@google.com>:

Internal change

PiperOrigin-RevId: 276126962

--
4c840cab6a8d86efa29b397cafaf7520eece68cc by Andy Soffer <asoffer@google.com>:

Update CMakeLists.txt to address https://github.com/abseil/abseil-cpp/issues/365.
This does not cover every platform, but it does at least address the
first-order issue of assuming gcc implies x86.

PiperOrigin-RevId: 276116253

--
98da366e6b5d51afe5d7ac6722126aca23d85ee6 by Abseil Team <absl-team@google.com>:

Internal change

PiperOrigin-RevId: 276097452
GitOrigin-RevId: e54b9c7bbb0c58475676c268e2e19c69f4bce48a
Change-Id: I02d84454bb71ab21ad3d39650acf6cc6e36f58d7
2019-10-24 10:29:13 -04:00

497 lines
19 KiB
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Raw Blame History

// Copyright 2017 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "absl/random/internal/generate_real.h"
#include <cfloat>
#include <cstddef>
#include <cstdint>
#include <string>
#include "gtest/gtest.h"
#include "absl/base/internal/bits.h"
#include "absl/flags/flag.h"
ABSL_FLAG(int64_t, absl_random_test_trials, 50000,
"Number of trials for the probability tests.");
using absl::random_internal::GenerateNegativeTag;
using absl::random_internal::GeneratePositiveTag;
using absl::random_internal::GenerateRealFromBits;
using absl::random_internal::GenerateSignedTag;
namespace {
TEST(GenerateRealTest, U64ToFloat_Positive_NoZero_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GeneratePositiveTag, false>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 2.710505431e-20f);
EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f);
EXPECT_EQ(ToFloat(0x8000000000000000), 0.5);
EXPECT_EQ(ToFloat(0x8000000000000001), 0.5);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloat_Positive_Zero_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GeneratePositiveTag, true>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 0.0);
EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f);
EXPECT_EQ(ToFloat(0x8000000000000000), 0.5);
EXPECT_EQ(ToFloat(0x8000000000000001), 0.5);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloat_Negative_NoZero_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GenerateNegativeTag, false>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), -2.710505431e-20f);
EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f);
EXPECT_EQ(ToFloat(0x8000000000000000), -0.5);
EXPECT_EQ(ToFloat(0x8000000000000001), -0.5);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloat_Negative_Zero_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GenerateNegativeTag, true>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 0.0);
EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f);
EXPECT_EQ(ToFloat(0x8000000000000000), -0.5);
EXPECT_EQ(ToFloat(0x8000000000000001), -0.5);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloat_Signed_NoZero_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GenerateSignedTag, false>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 5.421010862e-20f);
EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f);
EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f);
EXPECT_EQ(ToFloat(0x8000000000000000), -5.421010862e-20f);
EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloat_Signed_Zero_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GenerateSignedTag, true>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 0);
EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f);
EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f);
EXPECT_EQ(ToFloat(0x8000000000000000), 0);
EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloat_Signed_Bias_Test) {
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GenerateSignedTag, true>(a, 1);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 0);
EXPECT_EQ(ToFloat(0x0000000000000001), 2 * 1.084202172e-19f);
EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 2 * 0.9999999404f);
EXPECT_EQ(ToFloat(0x8000000000000000), 0);
EXPECT_EQ(ToFloat(0x8000000000000001), 2 * -1.084202172e-19f);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 2 * -0.9999999404f);
}
TEST(GenerateRealTest, U64ToFloatTest) {
auto ToFloat = [](uint64_t a) -> float {
return GenerateRealFromBits<float, GeneratePositiveTag, true>(a);
};
EXPECT_EQ(ToFloat(0x0000000000000000), 0.0f);
EXPECT_EQ(ToFloat(0x8000000000000000), 0.5f);
EXPECT_EQ(ToFloat(0x8000000000000001), 0.5f);
EXPECT_EQ(ToFloat(0x800000FFFFFFFFFF), 0.5f);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f);
EXPECT_GT(ToFloat(0x0000000000000001), 0.0f);
EXPECT_NE(ToFloat(0x7FFFFF0000000000), ToFloat(0x7FFFFEFFFFFFFFFF));
EXPECT_LT(ToFloat(0xFFFFFFFFFFFFFFFF), 1.0f);
int32_t two_to_24 = 1 << 24;
EXPECT_EQ(static_cast<int32_t>(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24),
two_to_24 - 1);
EXPECT_NE(static_cast<int32_t>(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24 * 2),
two_to_24 * 2 - 1);
EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFF0000000000));
EXPECT_NE(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFEFFFFFFFFFF));
EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF8000000000));
EXPECT_NE(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF7FFFFFFFFF));
EXPECT_EQ(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFC000000000));
EXPECT_NE(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFBFFFFFFFFF));
// For values where every bit counts, the values scale as multiples of the
// input.
for (int i = 0; i < 100; ++i) {
EXPECT_EQ(i * ToFloat(0x0000000000000001), ToFloat(i));
}
// For each i: value generated from (1 << i).
float exp_values[64];
exp_values[63] = 0.5f;
for (int i = 62; i >= 0; --i) exp_values[i] = 0.5f * exp_values[i + 1];
constexpr uint64_t one = 1;
for (int i = 0; i < 64; ++i) {
EXPECT_EQ(ToFloat(one << i), exp_values[i]);
for (int j = 1; j < FLT_MANT_DIG && i - j >= 0; ++j) {
EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]);
EXPECT_EQ(ToFloat((one << i) + (one << (i - j))),
exp_values[i] + exp_values[i - j]);
}
for (int j = FLT_MANT_DIG; i - j >= 0; ++j) {
EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]);
EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), exp_values[i]);
}
}
}
TEST(GenerateRealTest, U64ToDouble_Positive_NoZero_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GeneratePositiveTag, false>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 2.710505431213761085e-20);
EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x0000000000000002), 1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x8000000000000000), 0.5);
EXPECT_EQ(ToDouble(0x8000000000000001), 0.5);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978);
}
TEST(GenerateRealTest, U64ToDouble_Positive_Zero_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GeneratePositiveTag, true>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 0.0);
EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x8000000000000000), 0.5);
EXPECT_EQ(ToDouble(0x8000000000000001), 0.5);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978);
}
TEST(GenerateRealTest, U64ToDouble_Negative_NoZero_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GenerateNegativeTag, false>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), -2.710505431213761085e-20);
EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x8000000000000000), -0.5);
EXPECT_EQ(ToDouble(0x8000000000000001), -0.5);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978);
}
TEST(GenerateRealTest, U64ToDouble_Negative_Zero_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GenerateNegativeTag, true>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 0.0);
EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x8000000000000000), -0.5);
EXPECT_EQ(ToDouble(0x8000000000000001), -0.5);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978);
}
TEST(GenerateRealTest, U64ToDouble_Signed_NoZero_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GenerateSignedTag, false>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978);
EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978);
}
TEST(GenerateRealTest, U64ToDouble_Signed_Zero_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GenerateSignedTag, true>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 0);
EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978);
EXPECT_EQ(ToDouble(0x8000000000000000), 0);
EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978);
}
TEST(GenerateRealTest, U64ToDouble_GenerateSignedTag_Bias_Test) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GenerateSignedTag, true>(a, -1);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 0);
EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19 / 2);
EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978 / 2);
EXPECT_EQ(ToDouble(0x8000000000000000), 0);
EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19 / 2);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978 / 2);
}
TEST(GenerateRealTest, U64ToDoubleTest) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GeneratePositiveTag, true>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 0.0);
EXPECT_EQ(ToDouble(0x0000000000000000), 0.0);
EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x7fffffffffffffef), 0.499999999999999944489);
EXPECT_EQ(ToDouble(0x8000000000000000), 0.5);
// For values > 0.5, RandU64ToDouble discards up to 11 bits. (64-53).
EXPECT_EQ(ToDouble(0x8000000000000001), 0.5);
EXPECT_EQ(ToDouble(0x80000000000007FF), 0.5);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978);
EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF));
EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFF), 1.0);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF800));
EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF7FF));
EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00));
EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFBFF));
EXPECT_EQ(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFE00));
EXPECT_NE(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFDFF));
EXPECT_EQ(ToDouble(0x1000000000000001), 0.0625);
EXPECT_EQ(ToDouble(0x2000000000000001), 0.125);
EXPECT_EQ(ToDouble(0x3000000000000001), 0.1875);
EXPECT_EQ(ToDouble(0x4000000000000001), 0.25);
EXPECT_EQ(ToDouble(0x5000000000000001), 0.3125);
EXPECT_EQ(ToDouble(0x6000000000000001), 0.375);
EXPECT_EQ(ToDouble(0x7000000000000001), 0.4375);
EXPECT_EQ(ToDouble(0x8000000000000001), 0.5);
EXPECT_EQ(ToDouble(0x9000000000000001), 0.5625);
EXPECT_EQ(ToDouble(0xa000000000000001), 0.625);
EXPECT_EQ(ToDouble(0xb000000000000001), 0.6875);
EXPECT_EQ(ToDouble(0xc000000000000001), 0.75);
EXPECT_EQ(ToDouble(0xd000000000000001), 0.8125);
EXPECT_EQ(ToDouble(0xe000000000000001), 0.875);
EXPECT_EQ(ToDouble(0xf000000000000001), 0.9375);
// Large powers of 2.
int64_t two_to_53 = int64_t{1} << 53;
EXPECT_EQ(static_cast<int64_t>(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53),
two_to_53 - 1);
EXPECT_NE(static_cast<int64_t>(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53 * 2),
two_to_53 * 2 - 1);
// For values where every bit counts, the values scale as multiples of the
// input.
for (int i = 0; i < 100; ++i) {
EXPECT_EQ(i * ToDouble(0x0000000000000001), ToDouble(i));
}
// For each i: value generated from (1 << i).
double exp_values[64];
exp_values[63] = 0.5;
for (int i = 62; i >= 0; --i) exp_values[i] = 0.5 * exp_values[i + 1];
constexpr uint64_t one = 1;
for (int i = 0; i < 64; ++i) {
EXPECT_EQ(ToDouble(one << i), exp_values[i]);
for (int j = 1; j < DBL_MANT_DIG && i - j >= 0; ++j) {
EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]);
EXPECT_EQ(ToDouble((one << i) + (one << (i - j))),
exp_values[i] + exp_values[i - j]);
}
for (int j = DBL_MANT_DIG; i - j >= 0; ++j) {
EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]);
EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), exp_values[i]);
}
}
}
TEST(GenerateRealTest, U64ToDoubleSignedTest) {
auto ToDouble = [](uint64_t a) {
return GenerateRealFromBits<double, GenerateSignedTag, false>(a);
};
EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20);
EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19);
const double e_plus = ToDouble(0x0000000000000001);
const double e_minus = ToDouble(0x8000000000000001);
EXPECT_EQ(e_plus, 1.084202172485504434e-19);
EXPECT_EQ(e_minus, -1.084202172485504434e-19);
EXPECT_EQ(ToDouble(0x3fffffffffffffef), 0.499999999999999944489);
EXPECT_EQ(ToDouble(0xbfffffffffffffef), -0.499999999999999944489);
// For values > 0.5, RandU64ToDouble discards up to 10 bits. (63-53).
EXPECT_EQ(ToDouble(0x4000000000000000), 0.5);
EXPECT_EQ(ToDouble(0x4000000000000001), 0.5);
EXPECT_EQ(ToDouble(0x40000000000003FF), 0.5);
EXPECT_EQ(ToDouble(0xC000000000000000), -0.5);
EXPECT_EQ(ToDouble(0xC000000000000001), -0.5);
EXPECT_EQ(ToDouble(0xC0000000000003FF), -0.5);
EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFe), 0.999999999999999888978);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999999999888978);
EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF));
EXPECT_LT(ToDouble(0x7FFFFFFFFFFFFFFF), 1.0);
EXPECT_GT(ToDouble(0x7FFFFFFFFFFFFFFF), 0.9999999999);
EXPECT_GT(ToDouble(0xFFFFFFFFFFFFFFFe), -1.0);
EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999);
EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFFC00));
EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00));
EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFF3FF));
EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFF3FF));
EXPECT_EQ(ToDouble(0x1000000000000001), 0.125);
EXPECT_EQ(ToDouble(0x2000000000000001), 0.25);
EXPECT_EQ(ToDouble(0x3000000000000001), 0.375);
EXPECT_EQ(ToDouble(0x4000000000000001), 0.5);
EXPECT_EQ(ToDouble(0x5000000000000001), 0.625);
EXPECT_EQ(ToDouble(0x6000000000000001), 0.75);
EXPECT_EQ(ToDouble(0x7000000000000001), 0.875);
EXPECT_EQ(ToDouble(0x7800000000000001), 0.9375);
EXPECT_EQ(ToDouble(0x7c00000000000001), 0.96875);
EXPECT_EQ(ToDouble(0x7e00000000000001), 0.984375);
EXPECT_EQ(ToDouble(0x7f00000000000001), 0.9921875);
// 0x8000000000000000 ~= 0
EXPECT_EQ(ToDouble(0x9000000000000001), -0.125);
EXPECT_EQ(ToDouble(0xa000000000000001), -0.25);
EXPECT_EQ(ToDouble(0xb000000000000001), -0.375);
EXPECT_EQ(ToDouble(0xc000000000000001), -0.5);
EXPECT_EQ(ToDouble(0xd000000000000001), -0.625);
EXPECT_EQ(ToDouble(0xe000000000000001), -0.75);
EXPECT_EQ(ToDouble(0xf000000000000001), -0.875);
// Large powers of 2.
int64_t two_to_53 = int64_t{1} << 53;
EXPECT_EQ(static_cast<int64_t>(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53),
two_to_53 - 1);
EXPECT_EQ(static_cast<int64_t>(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53),
-(two_to_53 - 1));
EXPECT_NE(static_cast<int64_t>(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53 * 2),
two_to_53 * 2 - 1);
// For values where every bit counts, the values scale as multiples of the
// input.
for (int i = 1; i < 100; ++i) {
EXPECT_EQ(i * e_plus, ToDouble(i)) << i;
EXPECT_EQ(i * e_minus, ToDouble(0x8000000000000000 | i)) << i;
}
}
TEST(GenerateRealTest, ExhaustiveFloat) {
using absl::base_internal::CountLeadingZeros64;
auto ToFloat = [](uint64_t a) {
return GenerateRealFromBits<float, GeneratePositiveTag, true>(a);
};
// Rely on RandU64ToFloat generating values from greatest to least when
// supplied with uint64_t values from greatest (0xfff...) to least (0x0). Thus,
// this algorithm stores the previous value, and if the new value is at
// greater than or equal to the previous value, then there is a collision in
// the generation algorithm.
//
// Use the computation below to convert the random value into a result:
// double res = a() * (1.0f - sample) + b() * sample;
float last_f = 1.0, last_g = 2.0;
uint64_t f_collisions = 0, g_collisions = 0;
uint64_t f_unique = 0, g_unique = 0;
uint64_t total = 0;
auto count = [&](const float r) {
total++;
// `f` is mapped to the range [0, 1) (default)
const float f = 0.0f * (1.0f - r) + 1.0f * r;
if (f >= last_f) {
f_collisions++;
} else {
f_unique++;
last_f = f;
}
// `g` is mapped to the range [1, 2)
const float g = 1.0f * (1.0f - r) + 2.0f * r;
if (g >= last_g) {
g_collisions++;
} else {
g_unique++;
last_g = g;
}
};
size_t limit = absl::GetFlag(FLAGS_absl_random_test_trials);
// Generate all uint64_t which have unique floating point values.
// Counting down from 0xFFFFFFFFFFFFFFFFu ... 0x0u
uint64_t x = ~uint64_t(0);
for (; x != 0 && limit > 0;) {
constexpr int kDig = (64 - FLT_MANT_DIG);
// Set a decrement value & the next point at which to change
// the decrement value. By default these are 1, 0.
uint64_t dec = 1;
uint64_t chk = 0;
// Adjust decrement and check value based on how many leading 0
// bits are set in the current value.
const int clz = CountLeadingZeros64(x);
if (clz < kDig) {
dec <<= (kDig - clz);
chk = (~uint64_t(0)) >> (clz + 1);
}
for (; x > chk && limit > 0; x -= dec) {
count(ToFloat(x));
--limit;
}
}
static_assert(FLT_MANT_DIG == 24,
"The float type is expected to have a 24 bit mantissa.");
if (limit != 0) {
// There are between 2^28 and 2^29 unique values in the range [0, 1). For
// the low values of x, there are 2^24 -1 unique values. Once x > 2^24,
// there are 40 * 2^24 unique values. Thus:
// (2 + 4 + 8 ... + 2^23) + 40 * 2^23
EXPECT_LT(1 << 28, f_unique);
EXPECT_EQ((1 << 24) + 40 * (1 << 23) - 1, f_unique);
EXPECT_EQ(total, f_unique);
EXPECT_EQ(0, f_collisions);
// Expect at least 2^23 unique values for the range [1, 2)
EXPECT_LE(1 << 23, g_unique);
EXPECT_EQ(total - g_unique, g_collisions);
}
}
} // namespace
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