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/fastmath.h"
16
17 #include "gtest/gtest.h"
18
19 #if defined(__native_client__) || defined(__EMSCRIPTEN__)
20 // NACL has a less accurate implementation of std::log2 than most of
21 // the other platforms. For some values which should have integral results,
22 // sometimes NACL returns slightly larger values.
23 //
24 // The MUSL libc used by emscripten also has a similar bug.
25 #define ABSL_RANDOM_INACCURATE_LOG2
26 #endif
27
28 namespace {
29
TEST(FastMathTest,IntLog2FloorTest)30 TEST(FastMathTest, IntLog2FloorTest) {
31 using absl::random_internal::IntLog2Floor;
32 constexpr uint64_t kZero = 0;
33 EXPECT_EQ(0, IntLog2Floor(0)); // boundary. return 0.
34 EXPECT_EQ(0, IntLog2Floor(1));
35 EXPECT_EQ(1, IntLog2Floor(2));
36 EXPECT_EQ(63, IntLog2Floor(~kZero));
37
38 // A boundary case: Converting 0xffffffffffffffff requires > 53
39 // bits of precision, so the conversion to double rounds up,
40 // and the result of std::log2(x) > IntLog2Floor(x).
41 EXPECT_LT(IntLog2Floor(~kZero), static_cast<int>(std::log2(~kZero)));
42
43 for (int i = 0; i < 64; i++) {
44 const uint64_t i_pow_2 = static_cast<uint64_t>(1) << i;
45 EXPECT_EQ(i, IntLog2Floor(i_pow_2));
46 EXPECT_EQ(i, static_cast<int>(std::log2(i_pow_2)));
47
48 uint64_t y = i_pow_2;
49 for (int j = i - 1; j > 0; --j) {
50 y = y | (i_pow_2 >> j);
51 EXPECT_EQ(i, IntLog2Floor(y));
52 }
53 }
54 }
55
TEST(FastMathTest,IntLog2CeilTest)56 TEST(FastMathTest, IntLog2CeilTest) {
57 using absl::random_internal::IntLog2Ceil;
58 constexpr uint64_t kZero = 0;
59 EXPECT_EQ(0, IntLog2Ceil(0)); // boundary. return 0.
60 EXPECT_EQ(0, IntLog2Ceil(1));
61 EXPECT_EQ(1, IntLog2Ceil(2));
62 EXPECT_EQ(64, IntLog2Ceil(~kZero));
63
64 // A boundary case: Converting 0xffffffffffffffff requires > 53
65 // bits of precision, so the conversion to double rounds up,
66 // and the result of std::log2(x) > IntLog2Floor(x).
67 EXPECT_LE(IntLog2Ceil(~kZero), static_cast<int>(std::log2(~kZero)));
68
69 for (int i = 0; i < 64; i++) {
70 const uint64_t i_pow_2 = static_cast<uint64_t>(1) << i;
71 EXPECT_EQ(i, IntLog2Ceil(i_pow_2));
72 #ifndef ABSL_RANDOM_INACCURATE_LOG2
73 EXPECT_EQ(i, static_cast<int>(std::ceil(std::log2(i_pow_2))));
74 #endif
75
76 uint64_t y = i_pow_2;
77 for (int j = i - 1; j > 0; --j) {
78 y = y | (i_pow_2 >> j);
79 EXPECT_EQ(i + 1, IntLog2Ceil(y));
80 }
81 }
82 }
83
TEST(FastMathTest,StirlingLogFactorial)84 TEST(FastMathTest, StirlingLogFactorial) {
85 using absl::random_internal::StirlingLogFactorial;
86
87 EXPECT_NEAR(StirlingLogFactorial(1.0), 0, 1e-3);
88 EXPECT_NEAR(StirlingLogFactorial(1.50), 0.284683, 1e-3);
89 EXPECT_NEAR(StirlingLogFactorial(2.0), 0.69314718056, 1e-4);
90
91 for (int i = 2; i < 50; i++) {
92 double d = static_cast<double>(i);
93 EXPECT_NEAR(StirlingLogFactorial(d), std::lgamma(d + 1), 3e-5);
94 }
95 }
96
97 } // namespace
98