absl/random/internal/fastmath_test.cc

// 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 <cmath>
#include <cstdint>

#include "gtest/gtest.h"

#if defined(__EMSCRIPTEN__)
// Emscripten has a less accurate implementation of std::log2 than most of
// the other platforms. For some values which should have integral results,
// sometimes Emscripten returns slightly larger values.
#define ABSL_RANDOM_INACCURATE_LOG2
#endif

namespace {

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