MathExtrasTest.cpp

//===- unittests/Support/MathExtrasTest.cpp - math utils tests ------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include "llvm/Support/MathExtras.h"
#include "gtest/gtest.h"

using namespace llvm;

namespace {

TEST(MathExtras, countTrailingZeros) {
  uint8_t Z8 = 0;
  uint16_t Z16 = 0;
  uint32_t Z32 = 0;
  uint64_t Z64 = 0;
  EXPECT_EQ(8u, countTrailingZeros(Z8));
  EXPECT_EQ(16u, countTrailingZeros(Z16));
  EXPECT_EQ(32u, countTrailingZeros(Z32));
  EXPECT_EQ(64u, countTrailingZeros(Z64));

  uint8_t NZ8 = 42;
  uint16_t NZ16 = 42;
  uint32_t NZ32 = 42;
  uint64_t NZ64 = 42;
  EXPECT_EQ(1u, countTrailingZeros(NZ8));
  EXPECT_EQ(1u, countTrailingZeros(NZ16));
  EXPECT_EQ(1u, countTrailingZeros(NZ32));
  EXPECT_EQ(1u, countTrailingZeros(NZ64));
}

TEST(MathExtras, countLeadingZeros) {
  uint8_t Z8 = 0;
  uint16_t Z16 = 0;
  uint32_t Z32 = 0;
  uint64_t Z64 = 0;
  EXPECT_EQ(8u, countLeadingZeros(Z8));
  EXPECT_EQ(16u, countLeadingZeros(Z16));
  EXPECT_EQ(32u, countLeadingZeros(Z32));
  EXPECT_EQ(64u, countLeadingZeros(Z64));

  uint8_t NZ8 = 42;
  uint16_t NZ16 = 42;
  uint32_t NZ32 = 42;
  uint64_t NZ64 = 42;
  EXPECT_EQ(2u, countLeadingZeros(NZ8));
  EXPECT_EQ(10u, countLeadingZeros(NZ16));
  EXPECT_EQ(26u, countLeadingZeros(NZ32));
  EXPECT_EQ(58u, countLeadingZeros(NZ64));

  EXPECT_EQ(8u, countLeadingZeros(0x00F000FFu));
  EXPECT_EQ(8u, countLeadingZeros(0x00F12345u));
  for (unsigned i = 0; i <= 30; ++i) {
    EXPECT_EQ(31 - i, countLeadingZeros(1u << i));
  }

  EXPECT_EQ(8u, countLeadingZeros(0x00F1234500F12345ULL));
  EXPECT_EQ(1u, countLeadingZeros(1ULL << 62));
  for (unsigned i = 0; i <= 62; ++i) {
    EXPECT_EQ(63 - i, countLeadingZeros(1ULL << i));
  }
}

TEST(MathExtras, onesMask) {
  EXPECT_EQ(0U, maskLeadingOnes<uint8_t>(0));
  EXPECT_EQ(0U, maskTrailingOnes<uint8_t>(0));
  EXPECT_EQ(0U, maskLeadingOnes<uint16_t>(0));
  EXPECT_EQ(0U, maskTrailingOnes<uint16_t>(0));
  EXPECT_EQ(0U, maskLeadingOnes<uint32_t>(0));
  EXPECT_EQ(0U, maskTrailingOnes<uint32_t>(0));
  EXPECT_EQ(0U, maskLeadingOnes<uint64_t>(0));
  EXPECT_EQ(0U, maskTrailingOnes<uint64_t>(0));

  EXPECT_EQ(0x00000003U, maskTrailingOnes<uint32_t>(2U));
  EXPECT_EQ(0xC0000000U, maskLeadingOnes<uint32_t>(2U));

  EXPECT_EQ(0x000007FFU, maskTrailingOnes<uint32_t>(11U));
  EXPECT_EQ(0xFFE00000U, maskLeadingOnes<uint32_t>(11U));

  EXPECT_EQ(0xFFFFFFFFU, maskTrailingOnes<uint32_t>(32U));
  EXPECT_EQ(0xFFFFFFFFU, maskLeadingOnes<uint32_t>(32U));
  EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, maskTrailingOnes<uint64_t>(64U));
  EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, maskLeadingOnes<uint64_t>(64U));

  EXPECT_EQ(0x0000FFFFFFFFFFFFULL, maskTrailingOnes<uint64_t>(48U));
  EXPECT_EQ(0xFFFFFFFFFFFF0000ULL, maskLeadingOnes<uint64_t>(48U));
}

TEST(MathExtras, isIntN) {
  EXPECT_TRUE(isIntN(16, 32767));
  EXPECT_FALSE(isIntN(16, 32768));
}

TEST(MathExtras, isUIntN) {
  EXPECT_TRUE(isUIntN(16, 65535));
  EXPECT_FALSE(isUIntN(16, 65536));
  EXPECT_TRUE(isUIntN(1, 0));
  EXPECT_TRUE(isUIntN(6, 63));
}

TEST(MathExtras, maxIntN) {
  EXPECT_EQ(32767, maxIntN(16));
  EXPECT_EQ(2147483647, maxIntN(32));
  EXPECT_EQ(std::numeric_limits<int32_t>::max(), maxIntN(32));
  EXPECT_EQ(std::numeric_limits<int64_t>::max(), maxIntN(64));
}

TEST(MathExtras, minIntN) {
  EXPECT_EQ(-32768LL, minIntN(16));
  EXPECT_EQ(-64LL, minIntN(7));
  EXPECT_EQ(std::numeric_limits<int32_t>::min(), minIntN(32));
  EXPECT_EQ(std::numeric_limits<int64_t>::min(), minIntN(64));
}

TEST(MathExtras, maxUIntN) {
  EXPECT_EQ(0xffffULL, maxUIntN(16));
  EXPECT_EQ(0xffffffffULL, maxUIntN(32));
  EXPECT_EQ(0xffffffffffffffffULL, maxUIntN(64));
  EXPECT_EQ(1ULL, maxUIntN(1));
  EXPECT_EQ(0x0fULL, maxUIntN(4));
}

TEST(MathExtras, reverseBits) {
  uint8_t NZ8 = 42;
  uint16_t NZ16 = 42;
  uint32_t NZ32 = 42;
  uint64_t NZ64 = 42;
  EXPECT_EQ(0x54ULL, reverseBits(NZ8));
  EXPECT_EQ(0x5400ULL, reverseBits(NZ16));
  EXPECT_EQ(0x54000000ULL, reverseBits(NZ32));
  EXPECT_EQ(0x5400000000000000ULL, reverseBits(NZ64));
}

TEST(MathExtras, isShiftedMask_32) {
  EXPECT_FALSE(isShiftedMask_32(0x01010101));
  EXPECT_TRUE(isShiftedMask_32(0xf0000000));
  EXPECT_TRUE(isShiftedMask_32(0xffff0000));
  EXPECT_TRUE(isShiftedMask_32(0xff << 1));

  unsigned MaskIdx, MaskLen;
  EXPECT_FALSE(isShiftedMask_32(0x01010101, MaskIdx, MaskLen));
  EXPECT_TRUE(isShiftedMask_32(0xf0000000, MaskIdx, MaskLen));
  EXPECT_EQ(28, (int)MaskIdx);
  EXPECT_EQ(4, (int)MaskLen);
  EXPECT_TRUE(isShiftedMask_32(0xffff0000, MaskIdx, MaskLen));
  EXPECT_EQ(16, (int)MaskIdx);
  EXPECT_EQ(16, (int)MaskLen);
  EXPECT_TRUE(isShiftedMask_32(0xff << 1, MaskIdx, MaskLen));
  EXPECT_EQ(1, (int)MaskIdx);
  EXPECT_EQ(8, (int)MaskLen);
}

TEST(MathExtras, isShiftedMask_64) {
  EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull));
  EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull));
  EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull));
  EXPECT_TRUE(isShiftedMask_64(0xffull << 55));

  unsigned MaskIdx, MaskLen;
  EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull, MaskIdx, MaskLen));
  EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull, MaskIdx, MaskLen));
  EXPECT_EQ(60, (int)MaskIdx);
  EXPECT_EQ(4, (int)MaskLen);
  EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull, MaskIdx, MaskLen));
  EXPECT_EQ(48, (int)MaskIdx);
  EXPECT_EQ(16, (int)MaskLen);
  EXPECT_TRUE(isShiftedMask_64(0xffull << 55, MaskIdx, MaskLen));
  EXPECT_EQ(55, (int)MaskIdx);
  EXPECT_EQ(8, (int)MaskLen);
}

TEST(MathExtras, isPowerOf2_32) {
  EXPECT_FALSE(isPowerOf2_32(0));
  EXPECT_TRUE(isPowerOf2_32(1 << 6));
  EXPECT_TRUE(isPowerOf2_32(1 << 12));
  EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3));
  EXPECT_FALSE(isPowerOf2_32(0xABCDEF0));
}

TEST(MathExtras, isPowerOf2_64) {
  EXPECT_FALSE(isPowerOf2_64(0));
  EXPECT_TRUE(isPowerOf2_64(1LL << 46));
  EXPECT_TRUE(isPowerOf2_64(1LL << 12));
  EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3));
  EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL));
}

TEST(MathExtras, PowerOf2Ceil) {
  EXPECT_EQ(0U, PowerOf2Ceil(0U));
  EXPECT_EQ(8U, PowerOf2Ceil(8U));
  EXPECT_EQ(8U, PowerOf2Ceil(7U));
}

TEST(MathExtras, PowerOf2Floor) {
  EXPECT_EQ(0U, PowerOf2Floor(0U));
  EXPECT_EQ(8U, PowerOf2Floor(8U));
  EXPECT_EQ(4U, PowerOf2Floor(7U));
}

TEST(MathExtras, CTLog2) {
  EXPECT_EQ(CTLog2<1ULL << 0>(), 0U);
  EXPECT_EQ(CTLog2<1ULL << 1>(), 1U);
  EXPECT_EQ(CTLog2<1ULL << 2>(), 2U);
  EXPECT_EQ(CTLog2<1ULL << 3>(), 3U);
  EXPECT_EQ(CTLog2<1ULL << 4>(), 4U);
  EXPECT_EQ(CTLog2<1ULL << 5>(), 5U);
  EXPECT_EQ(CTLog2<1ULL << 6>(), 6U);
  EXPECT_EQ(CTLog2<1ULL << 7>(), 7U);
  EXPECT_EQ(CTLog2<1ULL << 8>(), 8U);
  EXPECT_EQ(CTLog2<1ULL << 9>(), 9U);
  EXPECT_EQ(CTLog2<1ULL << 10>(), 10U);
  EXPECT_EQ(CTLog2<1ULL << 11>(), 11U);
  EXPECT_EQ(CTLog2<1ULL << 12>(), 12U);
  EXPECT_EQ(CTLog2<1ULL << 13>(), 13U);
  EXPECT_EQ(CTLog2<1ULL << 14>(), 14U);
  EXPECT_EQ(CTLog2<1ULL << 15>(), 15U);
}

TEST(MathExtras, countLeadingOnes) {
  for (int i = 30; i >= 0; --i) {
    // Start with all ones and unset some bit.
    EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
  }
  for (int i = 62; i >= 0; --i) {
    // Start with all ones and unset some bit.
    EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i)));
  }
  for (int i = 30; i >= 0; --i) {
    // Start with all ones and unset some bit.
    EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
  }
}

TEST(MathExtras, FloatBits) {
  static const float kValue = 5632.34f;
  EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue)));
}

TEST(MathExtras, DoubleBits) {
  static const double kValue = 87987234.983498;
  EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue)));
}

TEST(MathExtras, MinAlign) {
  EXPECT_EQ(1u, MinAlign(2, 3));
  EXPECT_EQ(2u, MinAlign(2, 4));
  EXPECT_EQ(1u, MinAlign(17, 64));
  EXPECT_EQ(256u, MinAlign(256, 512));
}

TEST(MathExtras, NextPowerOf2) {
  EXPECT_EQ(4u, NextPowerOf2(3));
  EXPECT_EQ(16u, NextPowerOf2(15));
  EXPECT_EQ(256u, NextPowerOf2(128));
}

TEST(MathExtras, alignTo) {
  EXPECT_EQ(8u, alignTo(5, 8));
  EXPECT_EQ(24u, alignTo(17, 8));
  EXPECT_EQ(0u, alignTo(~0LL, 8));

  EXPECT_EQ(7u, alignTo(5, 8, 7));
  EXPECT_EQ(17u, alignTo(17, 8, 1));
  EXPECT_EQ(3u, alignTo(~0LL, 8, 3));
  EXPECT_EQ(552u, alignTo(321, 255, 42));
}

template <typename T> void SaturatingAddTestHelper() {
  const T Max = std::numeric_limits<T>::max();
  bool ResultOverflowed;

  EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2)));
  EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(Max, T(1)));
  EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1)));
  EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(T(1), Max));
  EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(Max, Max));
  EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3)));
  EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4)));
  EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0)));
  EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max));
  EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max, &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1)));
  EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1), &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max));
  EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1)));
  EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2)));
  EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max));
  EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);
}

TEST(MathExtras, SaturatingAdd) {
  SaturatingAddTestHelper<uint8_t>();
  SaturatingAddTestHelper<uint16_t>();
  SaturatingAddTestHelper<uint32_t>();
  SaturatingAddTestHelper<uint64_t>();
}

template<typename T>
void SaturatingMultiplyTestHelper()
{
  const T Max = std::numeric_limits<T>::max();
  bool ResultOverflowed;

  // Test basic multiplication.
  EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3)));
  EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2)));
  EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  // Test multiplication by zero.
  EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0)));
  EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0)));
  EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1)));
  EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0)));
  EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max));
  EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  // Test multiplication by maximum value.
  EXPECT_EQ(Max, SaturatingMultiply(Max, T(2)));
  EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingMultiply(T(2), Max));
  EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingMultiply(Max, Max));
  EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  // Test interesting boundary conditions for algorithm -
  // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1]
  // and A + B == std::numeric_limits<T>::digits.
  // We expect overflow iff A > B and K = 1.
  const int Digits = std::numeric_limits<T>::digits;
  for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) {
    for (int K = -1; K <= 1; ++K) {
      T X = (T(1) << A) - T(1);
      T Y = (T(1) << B) + K;
      bool OverflowExpected = A > B && K == 1;

      if(OverflowExpected) {
        EXPECT_EQ(Max, SaturatingMultiply(X, Y));
        EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed));
        EXPECT_TRUE(ResultOverflowed);
      } else {
        EXPECT_EQ(X * Y, SaturatingMultiply(X, Y));
        EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed));
        EXPECT_FALSE(ResultOverflowed);
      }
    }
  }
}

TEST(MathExtras, SaturatingMultiply) {
  SaturatingMultiplyTestHelper<uint8_t>();
  SaturatingMultiplyTestHelper<uint16_t>();
  SaturatingMultiplyTestHelper<uint32_t>();
  SaturatingMultiplyTestHelper<uint64_t>();
}

template<typename T>
void SaturatingMultiplyAddTestHelper()
{
  const T Max = std::numeric_limits<T>::max();
  bool ResultOverflowed;

  // Test basic multiply-add.
  EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10)));
  EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  // Test multiply overflows, add doesn't overflow
  EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  // Test multiply doesn't overflow, add overflows
  EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  // Test multiply-add with Max as operand
  EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed));
  EXPECT_TRUE(ResultOverflowed);

  // Test multiply-add with 0 as operand
  EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

  EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed));
  EXPECT_FALSE(ResultOverflowed);

}

TEST(MathExtras, SaturatingMultiplyAdd) {
  SaturatingMultiplyAddTestHelper<uint8_t>();
  SaturatingMultiplyAddTestHelper<uint16_t>();
  SaturatingMultiplyAddTestHelper<uint32_t>();
  SaturatingMultiplyAddTestHelper<uint64_t>();
}

TEST(MathExtras, IsShiftedUInt) {
  EXPECT_TRUE((isShiftedUInt<1, 0>(0)));
  EXPECT_TRUE((isShiftedUInt<1, 0>(1)));
  EXPECT_FALSE((isShiftedUInt<1, 0>(2)));
  EXPECT_FALSE((isShiftedUInt<1, 0>(3)));
  EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000)));
  EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000)));
  EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000)));
  EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000)));

  // 0x201 is ten bits long and has a 1 in the MSB and LSB.
  EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5)));
  EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4)));
  EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6)));
}

TEST(MathExtras, IsShiftedInt) {
  EXPECT_TRUE((isShiftedInt<1, 0>(0)));
  EXPECT_TRUE((isShiftedInt<1, 0>(-1)));
  EXPECT_FALSE((isShiftedInt<1, 0>(2)));
  EXPECT_FALSE((isShiftedInt<1, 0>(3)));
  EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000)));
  EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000)));
  EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000)));
  EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000)));

  // 0x201 is ten bits long and has a 1 in the MSB and LSB.
  EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5)));
  EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3)));
  EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6)));
  EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5))));
  EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3))));
  EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6))));

  EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15))));
  EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15)));
}

template <typename T>
class OverflowTest : public ::testing::Test { };

using OverflowTestTypes = ::testing::Types<signed char, short, int, long,
                                           long long>;

TYPED_TEST_SUITE(OverflowTest, OverflowTestTypes, );

TYPED_TEST(OverflowTest, AddNoOverflow) {
  TypeParam Result;
  EXPECT_FALSE(AddOverflow<TypeParam>(1, 2, Result));
  EXPECT_EQ(Result, TypeParam(3));
}

TYPED_TEST(OverflowTest, AddOverflowToNegative) {
  TypeParam Result;
  auto MaxValue = std::numeric_limits<TypeParam>::max();
  EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, MaxValue, Result));
  EXPECT_EQ(Result, TypeParam(-2));
}

TYPED_TEST(OverflowTest, AddOverflowToMin) {
  TypeParam Result;
  auto MaxValue = std::numeric_limits<TypeParam>::max();
  EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, TypeParam(1), Result));
  EXPECT_EQ(Result, std::numeric_limits<TypeParam>::min());
}

TYPED_TEST(OverflowTest, AddOverflowToZero) {
  TypeParam Result;
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, MinValue, Result));
  EXPECT_EQ(Result, TypeParam(0));
}

TYPED_TEST(OverflowTest, AddOverflowToMax) {
  TypeParam Result;
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, TypeParam(-1), Result));
  EXPECT_EQ(Result, std::numeric_limits<TypeParam>::max());
}

TYPED_TEST(OverflowTest, SubNoOverflow) {
  TypeParam Result;
  EXPECT_FALSE(SubOverflow<TypeParam>(1, 2, Result));
  EXPECT_EQ(Result, TypeParam(-1));
}

TYPED_TEST(OverflowTest, SubOverflowToMax) {
  TypeParam Result;
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
  EXPECT_EQ(Result, MinValue);
}

TYPED_TEST(OverflowTest, SubOverflowToMin) {
  TypeParam Result;
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
  EXPECT_EQ(Result, MinValue);
}

TYPED_TEST(OverflowTest, SubOverflowToNegative) {
  TypeParam Result;
  auto MaxValue = std::numeric_limits<TypeParam>::max();
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(SubOverflow<TypeParam>(MaxValue, MinValue, Result));
  EXPECT_EQ(Result, TypeParam(-1));
}

TYPED_TEST(OverflowTest, SubOverflowToPositive) {
  TypeParam Result;
  auto MaxValue = std::numeric_limits<TypeParam>::max();
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(SubOverflow<TypeParam>(MinValue, MaxValue, Result));
  EXPECT_EQ(Result, TypeParam(1));
}

TYPED_TEST(OverflowTest, MulNoOverflow) {
  TypeParam Result;
  EXPECT_FALSE(MulOverflow<TypeParam>(1, 2, Result));
  EXPECT_EQ(Result, 2);
  EXPECT_FALSE(MulOverflow<TypeParam>(-1, 3, Result));
  EXPECT_EQ(Result, -3);
  EXPECT_FALSE(MulOverflow<TypeParam>(4, -2, Result));
  EXPECT_EQ(Result, -8);
  EXPECT_FALSE(MulOverflow<TypeParam>(-6, -5, Result));
  EXPECT_EQ(Result, 30);
}

TYPED_TEST(OverflowTest, MulNoOverflowToMax) {
  TypeParam Result;
  auto MaxValue = std::numeric_limits<TypeParam>::max();
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_FALSE(MulOverflow<TypeParam>(MinValue + 1, -1, Result));
  EXPECT_EQ(Result, MaxValue);
}

TYPED_TEST(OverflowTest, MulOverflowToMin) {
  TypeParam Result;
  auto MinValue = std::numeric_limits<TypeParam>::min();
  EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, -1, Result));
  EXPECT_EQ(Result, MinValue);
}

TYPED_TEST(OverflowTest, MulOverflowMax) {
  TypeParam Result;
  auto MinValue = std::numeric_limits<TypeParam>::min();
  auto MaxValue = std::numeric_limits<TypeParam>::max();
  EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, MinValue, Result));
  EXPECT_EQ(Result, 0);
  EXPECT_TRUE(MulOverflow<TypeParam>(MaxValue, MaxValue, Result));
  EXPECT_EQ(Result, 1);
}

TYPED_TEST(OverflowTest, MulResultZero) {
  TypeParam Result;
  EXPECT_FALSE(MulOverflow<TypeParam>(4, 0, Result));
  EXPECT_EQ(Result, TypeParam(0));
  EXPECT_FALSE(MulOverflow<TypeParam>(-5, 0, Result));
  EXPECT_EQ(Result, TypeParam(0));
  EXPECT_FALSE(MulOverflow<TypeParam>(0, 5, Result));
  EXPECT_EQ(Result, TypeParam(0));
  EXPECT_FALSE(MulOverflow<TypeParam>(0, -5, Result));
  EXPECT_EQ(Result, TypeParam(0));
}

} // namespace