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llvm-project/llvm/unittests/Support/MathExtrasTest.cpp

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//===- 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, findFirstSet) {
uint8_t Z8 = 0;
uint16_t Z16 = 0;
uint32_t Z32 = 0;
uint64_t Z64 = 0;
EXPECT_EQ(0xFFULL, findFirstSet(Z8));
EXPECT_EQ(0xFFFFULL, findFirstSet(Z16));
EXPECT_EQ(0xFFFFFFFFULL, findFirstSet(Z32));
EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, findFirstSet(Z64));
uint8_t NZ8 = 42;
uint16_t NZ16 = 42;
uint32_t NZ32 = 42;
uint64_t NZ64 = 42;
EXPECT_EQ(1u, findFirstSet(NZ8));
EXPECT_EQ(1u, findFirstSet(NZ16));
EXPECT_EQ(1u, findFirstSet(NZ32));
EXPECT_EQ(1u, findFirstSet(NZ64));
}
TEST(MathExtras, findLastSet) {
uint8_t Z8 = 0;
uint16_t Z16 = 0;
uint32_t Z32 = 0;
uint64_t Z64 = 0;
EXPECT_EQ(0xFFULL, findLastSet(Z8));
EXPECT_EQ(0xFFFFULL, findLastSet(Z16));
EXPECT_EQ(0xFFFFFFFFULL, findLastSet(Z32));
EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, findLastSet(Z64));
uint8_t NZ8 = 42;
uint16_t NZ16 = 42;
uint32_t NZ32 = 42;
uint64_t NZ64 = 42;
EXPECT_EQ(5u, findLastSet(NZ8));
EXPECT_EQ(5u, findLastSet(NZ16));
EXPECT_EQ(5u, findLastSet(NZ32));
EXPECT_EQ(5u, findLastSet(NZ64));
}
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, 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, ByteSwap_32) {
EXPECT_EQ(0x44332211u, ByteSwap_32(0x11223344));
EXPECT_EQ(0xDDCCBBAAu, ByteSwap_32(0xAABBCCDD));
}
TEST(MathExtras, ByteSwap_64) {
EXPECT_EQ(0x8877665544332211ULL, ByteSwap_64(0x1122334455667788LL));
EXPECT_EQ(0x1100FFEEDDCCBBAAULL, ByteSwap_64(0xAABBCCDDEEFF0011LL));
}
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);
}
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)));
}
} // namespace
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