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// 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/fastmath.h"
#include "gtest/gtest.h"
#if defined(__native_client__) || defined(__EMSCRIPTEN__)
// NACL has a less accurate implementation of std::log2 than most of
// the other platforms. For some values which should have integral results,
// sometimes NACL returns slightly larger values.
//
// The MUSL libc used by emscripten also has a similar bug.
#define ABSL_RANDOM_INACCURATE_LOG2
#endif
namespace {
TEST(DistributionImplTest, LeadingSetBit) {
using absl::random_internal::LeadingSetBit;
constexpr uint64_t kZero = 0;
EXPECT_EQ(0, LeadingSetBit(kZero));
EXPECT_EQ(64, LeadingSetBit(~kZero));
for (int index = 0; index < 64; index++) {
uint64_t x = static_cast<uint64_t>(1) << index;
EXPECT_EQ(index + 1, LeadingSetBit(x)) << index;
EXPECT_EQ(index + 1, LeadingSetBit(x + x - 1)) << index;
}
}
TEST(FastMathTest, IntLog2FloorTest) {
using absl::random_internal::IntLog2Floor;
constexpr uint64_t kZero = 0;
EXPECT_EQ(0, IntLog2Floor(0)); // boundary. return 0.
EXPECT_EQ(0, IntLog2Floor(1));
EXPECT_EQ(1, IntLog2Floor(2));
EXPECT_EQ(63, IntLog2Floor(~kZero));
// A boundary case: Converting 0xffffffffffffffff requires > 53
// bits of precision, so the conversion to double rounds up,
// and the result of std::log2(x) > IntLog2Floor(x).
EXPECT_LT(IntLog2Floor(~kZero), static_cast<int>(std::log2(~kZero)));
for (int i = 0; i < 64; i++) {
const uint64_t i_pow_2 = static_cast<uint64_t>(1) << i;
EXPECT_EQ(i, IntLog2Floor(i_pow_2));
EXPECT_EQ(i, static_cast<int>(std::log2(i_pow_2)));
uint64_t y = i_pow_2;
for (int j = i - 1; j > 0; --j) {
y = y | (i_pow_2 >> j);
EXPECT_EQ(i, IntLog2Floor(y));
}
}
}
TEST(FastMathTest, IntLog2CeilTest) {
using absl::random_internal::IntLog2Ceil;
constexpr uint64_t kZero = 0;
EXPECT_EQ(0, IntLog2Ceil(0)); // boundary. return 0.
EXPECT_EQ(0, IntLog2Ceil(1));
EXPECT_EQ(1, IntLog2Ceil(2));
EXPECT_EQ(64, IntLog2Ceil(~kZero));
// A boundary case: Converting 0xffffffffffffffff requires > 53
// bits of precision, so the conversion to double rounds up,
// and the result of std::log2(x) > IntLog2Floor(x).
EXPECT_LE(IntLog2Ceil(~kZero), static_cast<int>(std::log2(~kZero)));
for (int i = 0; i < 64; i++) {
const uint64_t i_pow_2 = static_cast<uint64_t>(1) << i;
EXPECT_EQ(i, IntLog2Ceil(i_pow_2));
#ifndef ABSL_RANDOM_INACCURATE_LOG2
EXPECT_EQ(i, static_cast<int>(std::ceil(std::log2(i_pow_2))));
#endif
uint64_t y = i_pow_2;
for (int j = i - 1; j > 0; --j) {
y = y | (i_pow_2 >> j);
EXPECT_EQ(i + 1, IntLog2Ceil(y));
}
}
}
TEST(FastMathTest, StirlingLogFactorial) {
using absl::random_internal::StirlingLogFactorial;
EXPECT_NEAR(StirlingLogFactorial(1.0), 0, 1e-3);
EXPECT_NEAR(StirlingLogFactorial(1.50), 0.284683, 1e-3);
EXPECT_NEAR(StirlingLogFactorial(2.0), 0.69314718056, 1e-4);
for (int i = 2; i < 50; i++) {
double d = static_cast<double>(i);
EXPECT_NEAR(StirlingLogFactorial(d), std::lgamma(d + 1), 3e-5);
}
}
} // namespace
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