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int128_test.cc
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int128_test.cc
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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/numeric/int128.h"
#include <algorithm>
#include <limits>
#include <random>
#include <type_traits>
#include <utility>
#include <vector>
#include "gtest/gtest.h"
#include "absl/base/internal/cycleclock.h"
#include "absl/hash/hash_testing.h"
#include "absl/meta/type_traits.h"
#if defined(_MSC_VER) && _MSC_VER == 1900
// Disable "unary minus operator applied to unsigned type" warnings in Microsoft
// Visual C++ 14 (2015).
#pragma warning(disable:4146)
#endif
namespace {
template <typename T>
class Uint128IntegerTraitsTest : public ::testing::Test {};
typedef ::testing::Types<bool, char, signed char, unsigned char, char16_t,
char32_t, wchar_t,
short, // NOLINT(runtime/int)
unsigned short, // NOLINT(runtime/int)
int, unsigned int,
long, // NOLINT(runtime/int)
unsigned long, // NOLINT(runtime/int)
long long, // NOLINT(runtime/int)
unsigned long long> // NOLINT(runtime/int)
IntegerTypes;
template <typename T>
class Uint128FloatTraitsTest : public ::testing::Test {};
typedef ::testing::Types<float, double, long double> FloatingPointTypes;
TYPED_TEST_SUITE(Uint128IntegerTraitsTest, IntegerTypes);
TYPED_TEST(Uint128IntegerTraitsTest, ConstructAssignTest) {
static_assert(std::is_constructible<absl::uint128, TypeParam>::value,
"absl::uint128 must be constructible from TypeParam");
static_assert(std::is_assignable<absl::uint128&, TypeParam>::value,
"absl::uint128 must be assignable from TypeParam");
static_assert(!std::is_assignable<TypeParam&, absl::uint128>::value,
"TypeParam must not be assignable from absl::uint128");
}
TYPED_TEST_SUITE(Uint128FloatTraitsTest, FloatingPointTypes);
TYPED_TEST(Uint128FloatTraitsTest, ConstructAssignTest) {
static_assert(std::is_constructible<absl::uint128, TypeParam>::value,
"absl::uint128 must be constructible from TypeParam");
static_assert(!std::is_assignable<absl::uint128&, TypeParam>::value,
"absl::uint128 must not be assignable from TypeParam");
static_assert(!std::is_assignable<TypeParam&, absl::uint128>::value,
"TypeParam must not be assignable from absl::uint128");
}
#ifdef ABSL_HAVE_INTRINSIC_INT128
// These type traits done separately as TYPED_TEST requires typeinfo, and not
// all platforms have this for __int128 even though they define the type.
TEST(Uint128, IntrinsicTypeTraitsTest) {
static_assert(std::is_constructible<absl::uint128, __int128>::value,
"absl::uint128 must be constructible from __int128");
static_assert(std::is_assignable<absl::uint128&, __int128>::value,
"absl::uint128 must be assignable from __int128");
static_assert(!std::is_assignable<__int128&, absl::uint128>::value,
"__int128 must not be assignable from absl::uint128");
static_assert(std::is_constructible<absl::uint128, unsigned __int128>::value,
"absl::uint128 must be constructible from unsigned __int128");
static_assert(std::is_assignable<absl::uint128&, unsigned __int128>::value,
"absl::uint128 must be assignable from unsigned __int128");
static_assert(!std::is_assignable<unsigned __int128&, absl::uint128>::value,
"unsigned __int128 must not be assignable from absl::uint128");
}
#endif // ABSL_HAVE_INTRINSIC_INT128
TEST(Uint128, TrivialTraitsTest) {
static_assert(absl::is_trivially_default_constructible<absl::uint128>::value,
"");
static_assert(absl::is_trivially_copy_constructible<absl::uint128>::value,
"");
static_assert(absl::is_trivially_copy_assignable<absl::uint128>::value, "");
static_assert(std::is_trivially_destructible<absl::uint128>::value, "");
}
TEST(Uint128, AllTests) {
absl::uint128 zero = 0;
absl::uint128 one = 1;
absl::uint128 one_2arg = absl::MakeUint128(0, 1);
absl::uint128 two = 2;
absl::uint128 three = 3;
absl::uint128 big = absl::MakeUint128(2000, 2);
absl::uint128 big_minus_one = absl::MakeUint128(2000, 1);
absl::uint128 bigger = absl::MakeUint128(2001, 1);
absl::uint128 biggest = absl::Uint128Max();
absl::uint128 high_low = absl::MakeUint128(1, 0);
absl::uint128 low_high =
absl::MakeUint128(0, std::numeric_limits<uint64_t>::max());
EXPECT_LT(one, two);
EXPECT_GT(two, one);
EXPECT_LT(one, big);
EXPECT_LT(one, big);
EXPECT_EQ(one, one_2arg);
EXPECT_NE(one, two);
EXPECT_GT(big, one);
EXPECT_GE(big, two);
EXPECT_GE(big, big_minus_one);
EXPECT_GT(big, big_minus_one);
EXPECT_LT(big_minus_one, big);
EXPECT_LE(big_minus_one, big);
EXPECT_NE(big_minus_one, big);
EXPECT_LT(big, biggest);
EXPECT_LE(big, biggest);
EXPECT_GT(biggest, big);
EXPECT_GE(biggest, big);
EXPECT_EQ(big, ~~big);
EXPECT_EQ(one, one | one);
EXPECT_EQ(big, big | big);
EXPECT_EQ(one, one | zero);
EXPECT_EQ(one, one & one);
EXPECT_EQ(big, big & big);
EXPECT_EQ(zero, one & zero);
EXPECT_EQ(zero, big & ~big);
EXPECT_EQ(zero, one ^ one);
EXPECT_EQ(zero, big ^ big);
EXPECT_EQ(one, one ^ zero);
// Shift operators.
EXPECT_EQ(big, big << 0);
EXPECT_EQ(big, big >> 0);
EXPECT_GT(big << 1, big);
EXPECT_LT(big >> 1, big);
EXPECT_EQ(big, (big << 10) >> 10);
EXPECT_EQ(big, (big >> 1) << 1);
EXPECT_EQ(one, (one << 80) >> 80);
EXPECT_EQ(zero, (one >> 80) << 80);
// Shift assignments.
absl::uint128 big_copy = big;
EXPECT_EQ(big << 0, big_copy <<= 0);
big_copy = big;
EXPECT_EQ(big >> 0, big_copy >>= 0);
big_copy = big;
EXPECT_EQ(big << 1, big_copy <<= 1);
big_copy = big;
EXPECT_EQ(big >> 1, big_copy >>= 1);
big_copy = big;
EXPECT_EQ(big << 10, big_copy <<= 10);
big_copy = big;
EXPECT_EQ(big >> 10, big_copy >>= 10);
big_copy = big;
EXPECT_EQ(big << 64, big_copy <<= 64);
big_copy = big;
EXPECT_EQ(big >> 64, big_copy >>= 64);
big_copy = big;
EXPECT_EQ(big << 73, big_copy <<= 73);
big_copy = big;
EXPECT_EQ(big >> 73, big_copy >>= 73);
EXPECT_EQ(absl::Uint128High64(biggest), std::numeric_limits<uint64_t>::max());
EXPECT_EQ(absl::Uint128Low64(biggest), std::numeric_limits<uint64_t>::max());
EXPECT_EQ(zero + one, one);
EXPECT_EQ(one + one, two);
EXPECT_EQ(big_minus_one + one, big);
EXPECT_EQ(one - one, zero);
EXPECT_EQ(one - zero, one);
EXPECT_EQ(zero - one, biggest);
EXPECT_EQ(big - big, zero);
EXPECT_EQ(big - one, big_minus_one);
EXPECT_EQ(big + std::numeric_limits<uint64_t>::max(), bigger);
EXPECT_EQ(biggest + 1, zero);
EXPECT_EQ(zero - 1, biggest);
EXPECT_EQ(high_low - one, low_high);
EXPECT_EQ(low_high + one, high_low);
EXPECT_EQ(absl::Uint128High64((absl::uint128(1) << 64) - 1), 0);
EXPECT_EQ(absl::Uint128Low64((absl::uint128(1) << 64) - 1),
std::numeric_limits<uint64_t>::max());
EXPECT_TRUE(!!one);
EXPECT_TRUE(!!high_low);
EXPECT_FALSE(!!zero);
EXPECT_FALSE(!one);
EXPECT_FALSE(!high_low);
EXPECT_TRUE(!zero);
EXPECT_TRUE(zero == 0); // NOLINT(readability/check)
EXPECT_FALSE(zero != 0); // NOLINT(readability/check)
EXPECT_FALSE(one == 0); // NOLINT(readability/check)
EXPECT_TRUE(one != 0); // NOLINT(readability/check)
EXPECT_FALSE(high_low == 0); // NOLINT(readability/check)
EXPECT_TRUE(high_low != 0); // NOLINT(readability/check)
absl::uint128 test = zero;
EXPECT_EQ(++test, one);
EXPECT_EQ(test, one);
EXPECT_EQ(test++, one);
EXPECT_EQ(test, two);
EXPECT_EQ(test -= 2, zero);
EXPECT_EQ(test, zero);
EXPECT_EQ(test += 2, two);
EXPECT_EQ(test, two);
EXPECT_EQ(--test, one);
EXPECT_EQ(test, one);
EXPECT_EQ(test--, one);
EXPECT_EQ(test, zero);
EXPECT_EQ(test |= three, three);
EXPECT_EQ(test &= one, one);
EXPECT_EQ(test ^= three, two);
EXPECT_EQ(test >>= 1, one);
EXPECT_EQ(test <<= 1, two);
EXPECT_EQ(big, +big);
EXPECT_EQ(two, +two);
EXPECT_EQ(absl::Uint128Max(), +absl::Uint128Max());
EXPECT_EQ(zero, +zero);
EXPECT_EQ(big, -(-big));
EXPECT_EQ(two, -((-one) - 1));
EXPECT_EQ(absl::Uint128Max(), -one);
EXPECT_EQ(zero, -zero);
EXPECT_EQ(absl::Uint128Max(), absl::kuint128max);
}
TEST(Int128, RightShiftOfNegativeNumbers) {
absl::int128 minus_six = -6;
absl::int128 minus_three = -3;
absl::int128 minus_two = -2;
absl::int128 minus_one = -1;
if ((-6 >> 1) == -3) {
// Right shift is arithmetic (sign propagates)
EXPECT_EQ(minus_six >> 1, minus_three);
EXPECT_EQ(minus_six >> 2, minus_two);
EXPECT_EQ(minus_six >> 65, minus_one);
} else {
// Right shift is logical (zeros shifted in at MSB)
EXPECT_EQ(minus_six >> 1, absl::int128(absl::uint128(minus_six) >> 1));
EXPECT_EQ(minus_six >> 2, absl::int128(absl::uint128(minus_six) >> 2));
EXPECT_EQ(minus_six >> 65, absl::int128(absl::uint128(minus_six) >> 65));
}
}
TEST(Uint128, ConversionTests) {
EXPECT_TRUE(absl::MakeUint128(1, 0));
#ifdef ABSL_HAVE_INTRINSIC_INT128
unsigned __int128 intrinsic =
(static_cast<unsigned __int128>(0x3a5b76c209de76f6) << 64) +
0x1f25e1d63a2b46c5;
absl::uint128 custom =
absl::MakeUint128(0x3a5b76c209de76f6, 0x1f25e1d63a2b46c5);
EXPECT_EQ(custom, absl::uint128(intrinsic));
EXPECT_EQ(custom, absl::uint128(static_cast<__int128>(intrinsic)));
EXPECT_EQ(intrinsic, static_cast<unsigned __int128>(custom));
EXPECT_EQ(intrinsic, static_cast<__int128>(custom));
#endif // ABSL_HAVE_INTRINSIC_INT128
// verify that an integer greater than 2**64 that can be stored precisely
// inside a double is converted to a absl::uint128 without loss of
// information.
double precise_double = 0x530e * std::pow(2.0, 64.0) + 0xda74000000000000;
absl::uint128 from_precise_double(precise_double);
absl::uint128 from_precise_ints =
absl::MakeUint128(0x530e, 0xda74000000000000);
EXPECT_EQ(from_precise_double, from_precise_ints);
EXPECT_DOUBLE_EQ(static_cast<double>(from_precise_ints), precise_double);
double approx_double = 0xffffeeeeddddcccc * std::pow(2.0, 64.0) +
0xbbbbaaaa99998888;
absl::uint128 from_approx_double(approx_double);
EXPECT_DOUBLE_EQ(static_cast<double>(from_approx_double), approx_double);
double round_to_zero = 0.7;
double round_to_five = 5.8;
double round_to_nine = 9.3;
EXPECT_EQ(static_cast<absl::uint128>(round_to_zero), 0);
EXPECT_EQ(static_cast<absl::uint128>(round_to_five), 5);
EXPECT_EQ(static_cast<absl::uint128>(round_to_nine), 9);
absl::uint128 highest_precision_in_long_double =
~absl::uint128{} >> (128 - std::numeric_limits<long double>::digits);
EXPECT_EQ(highest_precision_in_long_double,
static_cast<absl::uint128>(
static_cast<long double>(highest_precision_in_long_double)));
// Apply a mask just to make sure all the bits are the right place.
const absl::uint128 arbitrary_mask =
absl::MakeUint128(0xa29f622677ded751, 0xf8ca66add076f468);
EXPECT_EQ(highest_precision_in_long_double & arbitrary_mask,
static_cast<absl::uint128>(static_cast<long double>(
highest_precision_in_long_double & arbitrary_mask)));
EXPECT_EQ(static_cast<absl::uint128>(-0.1L), 0);
}
TEST(Uint128, OperatorAssignReturnRef) {
absl::uint128 v(1);
(v += 4) -= 3;
EXPECT_EQ(2, v);
}
TEST(Uint128, Multiply) {
absl::uint128 a, b, c;
// Zero test.
a = 0;
b = 0;
c = a * b;
EXPECT_EQ(0, c);
// Max carries.
a = absl::uint128(0) - 1;
b = absl::uint128(0) - 1;
c = a * b;
EXPECT_EQ(1, c);
// Self-operation with max carries.
c = absl::uint128(0) - 1;
c *= c;
EXPECT_EQ(1, c);
// 1-bit x 1-bit.
for (int i = 0; i < 64; ++i) {
for (int j = 0; j < 64; ++j) {
a = absl::uint128(1) << i;
b = absl::uint128(1) << j;
c = a * b;
EXPECT_EQ(absl::uint128(1) << (i + j), c);
}
}
// Verified with dc.
a = absl::MakeUint128(0xffffeeeeddddcccc, 0xbbbbaaaa99998888);
b = absl::MakeUint128(0x7777666655554444, 0x3333222211110000);
c = a * b;
EXPECT_EQ(absl::MakeUint128(0x530EDA741C71D4C3, 0xBF25975319080000), c);
EXPECT_EQ(0, c - b * a);
EXPECT_EQ(a*a - b*b, (a+b) * (a-b));
// Verified with dc.
a = absl::MakeUint128(0x0123456789abcdef, 0xfedcba9876543210);
b = absl::MakeUint128(0x02468ace13579bdf, 0xfdb97531eca86420);
c = a * b;
EXPECT_EQ(absl::MakeUint128(0x97a87f4f261ba3f2, 0x342d0bbf48948200), c);
EXPECT_EQ(0, c - b * a);
EXPECT_EQ(a*a - b*b, (a+b) * (a-b));
}
TEST(Uint128, AliasTests) {
absl::uint128 x1 = absl::MakeUint128(1, 2);
absl::uint128 x2 = absl::MakeUint128(2, 4);
x1 += x1;
EXPECT_EQ(x2, x1);
absl::uint128 x3 = absl::MakeUint128(1, static_cast<uint64_t>(1) << 63);
absl::uint128 x4 = absl::MakeUint128(3, 0);
x3 += x3;
EXPECT_EQ(x4, x3);
}
TEST(Uint128, DivideAndMod) {
using std::swap;
// a := q * b + r
absl::uint128 a, b, q, r;
// Zero test.
a = 0;
b = 123;
q = a / b;
r = a % b;
EXPECT_EQ(0, q);
EXPECT_EQ(0, r);
a = absl::MakeUint128(0x530eda741c71d4c3, 0xbf25975319080000);
q = absl::MakeUint128(0x4de2cab081, 0x14c34ab4676e4bab);
b = absl::uint128(0x1110001);
r = absl::uint128(0x3eb455);
ASSERT_EQ(a, q * b + r); // Sanity-check.
absl::uint128 result_q, result_r;
result_q = a / b;
result_r = a % b;
EXPECT_EQ(q, result_q);
EXPECT_EQ(r, result_r);
// Try the other way around.
swap(q, b);
result_q = a / b;
result_r = a % b;
EXPECT_EQ(q, result_q);
EXPECT_EQ(r, result_r);
// Restore.
swap(b, q);
// Dividend < divisor; result should be q:0 r:<dividend>.
swap(a, b);
result_q = a / b;
result_r = a % b;
EXPECT_EQ(0, result_q);
EXPECT_EQ(a, result_r);
// Try the other way around.
swap(a, q);
result_q = a / b;
result_r = a % b;
EXPECT_EQ(0, result_q);
EXPECT_EQ(a, result_r);
// Restore.
swap(q, a);
swap(b, a);
// Try a large remainder.
b = a / 2 + 1;
absl::uint128 expected_r =
absl::MakeUint128(0x29876d3a0e38ea61, 0xdf92cba98c83ffff);
// Sanity checks.
ASSERT_EQ(a / 2 - 1, expected_r);
ASSERT_EQ(a, b + expected_r);
result_q = a / b;
result_r = a % b;
EXPECT_EQ(1, result_q);
EXPECT_EQ(expected_r, result_r);
}
TEST(Uint128, DivideAndModRandomInputs) {
const int kNumIters = 1 << 18;
std::minstd_rand random(testing::UnitTest::GetInstance()->random_seed());
std::uniform_int_distribution<uint64_t> uniform_uint64;
for (int i = 0; i < kNumIters; ++i) {
const absl::uint128 a =
absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
const absl::uint128 b =
absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
if (b == 0) {
continue; // Avoid a div-by-zero.
}
const absl::uint128 q = a / b;
const absl::uint128 r = a % b;
ASSERT_EQ(a, b * q + r);
}
}
TEST(Uint128, ConstexprTest) {
constexpr absl::uint128 zero = absl::uint128();
constexpr absl::uint128 one = 1;
constexpr absl::uint128 minus_two = -2;
EXPECT_EQ(zero, absl::uint128(0));
EXPECT_EQ(one, absl::uint128(1));
EXPECT_EQ(minus_two, absl::MakeUint128(-1, -2));
}
TEST(Uint128, NumericLimitsTest) {
static_assert(std::numeric_limits<absl::uint128>::is_specialized, "");
static_assert(!std::numeric_limits<absl::uint128>::is_signed, "");
static_assert(std::numeric_limits<absl::uint128>::is_integer, "");
EXPECT_EQ(static_cast<int>(128 * std::log10(2)),
std::numeric_limits<absl::uint128>::digits10);
EXPECT_EQ(0, std::numeric_limits<absl::uint128>::min());
EXPECT_EQ(0, std::numeric_limits<absl::uint128>::lowest());
EXPECT_EQ(absl::Uint128Max(), std::numeric_limits<absl::uint128>::max());
}
TEST(Uint128, Hash) {
EXPECT_TRUE(absl::VerifyTypeImplementsAbslHashCorrectly({
// Some simple values
absl::uint128{0},
absl::uint128{1},
~absl::uint128{},
// 64 bit limits
absl::uint128{std::numeric_limits<int64_t>::max()},
absl::uint128{std::numeric_limits<uint64_t>::max()} + 0,
absl::uint128{std::numeric_limits<uint64_t>::max()} + 1,
absl::uint128{std::numeric_limits<uint64_t>::max()} + 2,
// Keeping high same
absl::uint128{1} << 62,
absl::uint128{1} << 63,
// Keeping low same
absl::uint128{1} << 64,
absl::uint128{1} << 65,
// 128 bit limits
std::numeric_limits<absl::uint128>::max(),
std::numeric_limits<absl::uint128>::max() - 1,
std::numeric_limits<absl::uint128>::min() + 1,
std::numeric_limits<absl::uint128>::min(),
}));
}
TEST(Int128Uint128, ConversionTest) {
absl::int128 nonnegative_signed_values[] = {
0,
1,
0xffeeddccbbaa9988,
absl::MakeInt128(0x7766554433221100, 0),
absl::MakeInt128(0x1234567890abcdef, 0xfedcba0987654321),
absl::Int128Max()};
for (absl::int128 value : nonnegative_signed_values) {
EXPECT_EQ(value, absl::int128(absl::uint128(value)));
absl::uint128 assigned_value;
assigned_value = value;
EXPECT_EQ(value, absl::int128(assigned_value));
}
absl::int128 negative_values[] = {
-1, -0x1234567890abcdef,
absl::MakeInt128(-0x5544332211ffeedd, 0),
-absl::MakeInt128(0x76543210fedcba98, 0xabcdef0123456789)};
for (absl::int128 value : negative_values) {
EXPECT_EQ(absl::uint128(-value), -absl::uint128(value));
absl::uint128 assigned_value;
assigned_value = value;
EXPECT_EQ(absl::uint128(-value), -assigned_value);
}
}
template <typename T>
class Int128IntegerTraitsTest : public ::testing::Test {};
TYPED_TEST_SUITE(Int128IntegerTraitsTest, IntegerTypes);
TYPED_TEST(Int128IntegerTraitsTest, ConstructAssignTest) {
static_assert(std::is_constructible<absl::int128, TypeParam>::value,
"absl::int128 must be constructible from TypeParam");
static_assert(std::is_assignable<absl::int128&, TypeParam>::value,
"absl::int128 must be assignable from TypeParam");
static_assert(!std::is_assignable<TypeParam&, absl::int128>::value,
"TypeParam must not be assignable from absl::int128");
}
template <typename T>
class Int128FloatTraitsTest : public ::testing::Test {};
TYPED_TEST_SUITE(Int128FloatTraitsTest, FloatingPointTypes);
TYPED_TEST(Int128FloatTraitsTest, ConstructAssignTest) {
static_assert(std::is_constructible<absl::int128, TypeParam>::value,
"absl::int128 must be constructible from TypeParam");
static_assert(!std::is_assignable<absl::int128&, TypeParam>::value,
"absl::int128 must not be assignable from TypeParam");
static_assert(!std::is_assignable<TypeParam&, absl::int128>::value,
"TypeParam must not be assignable from absl::int128");
}
#ifdef ABSL_HAVE_INTRINSIC_INT128
// These type traits done separately as TYPED_TEST requires typeinfo, and not
// all platforms have this for __int128 even though they define the type.
TEST(Int128, IntrinsicTypeTraitsTest) {
static_assert(std::is_constructible<absl::int128, __int128>::value,
"absl::int128 must be constructible from __int128");
static_assert(std::is_assignable<absl::int128&, __int128>::value,
"absl::int128 must be assignable from __int128");
static_assert(!std::is_assignable<__int128&, absl::int128>::value,
"__int128 must not be assignable from absl::int128");
static_assert(std::is_constructible<absl::int128, unsigned __int128>::value,
"absl::int128 must be constructible from unsigned __int128");
static_assert(!std::is_assignable<absl::int128&, unsigned __int128>::value,
"absl::int128 must be assignable from unsigned __int128");
static_assert(!std::is_assignable<unsigned __int128&, absl::int128>::value,
"unsigned __int128 must not be assignable from absl::int128");
}
#endif // ABSL_HAVE_INTRINSIC_INT128
TEST(Int128, TrivialTraitsTest) {
static_assert(absl::is_trivially_default_constructible<absl::int128>::value,
"");
static_assert(absl::is_trivially_copy_constructible<absl::int128>::value, "");
static_assert(absl::is_trivially_copy_assignable<absl::int128>::value, "");
static_assert(std::is_trivially_destructible<absl::int128>::value, "");
}
TEST(Int128, BoolConversionTest) {
EXPECT_FALSE(absl::int128(0));
for (int i = 0; i < 64; ++i) {
EXPECT_TRUE(absl::MakeInt128(0, uint64_t{1} << i));
}
for (int i = 0; i < 63; ++i) {
EXPECT_TRUE(absl::MakeInt128(int64_t{1} << i, 0));
}
EXPECT_TRUE(absl::Int128Min());
EXPECT_EQ(absl::int128(1), absl::int128(true));
EXPECT_EQ(absl::int128(0), absl::int128(false));
}
template <typename T>
class Int128IntegerConversionTest : public ::testing::Test {};
TYPED_TEST_SUITE(Int128IntegerConversionTest, IntegerTypes);
TYPED_TEST(Int128IntegerConversionTest, RoundTripTest) {
EXPECT_EQ(TypeParam{0}, static_cast<TypeParam>(absl::int128(0)));
EXPECT_EQ(std::numeric_limits<TypeParam>::min(),
static_cast<TypeParam>(
absl::int128(std::numeric_limits<TypeParam>::min())));
EXPECT_EQ(std::numeric_limits<TypeParam>::max(),
static_cast<TypeParam>(
absl::int128(std::numeric_limits<TypeParam>::max())));
}
template <typename T>
class Int128FloatConversionTest : public ::testing::Test {};
TYPED_TEST_SUITE(Int128FloatConversionTest, FloatingPointTypes);
TYPED_TEST(Int128FloatConversionTest, ConstructAndCastTest) {
// Conversions where the floating point values should be exactly the same.
// 0x9f5b is a randomly chosen small value.
for (int i = 0; i < 110; ++i) { // 110 = 126 - #bits in 0x9f5b
SCOPED_TRACE(::testing::Message() << "i = " << i);
TypeParam float_value = std::ldexp(static_cast<TypeParam>(0x9f5b), i);
absl::int128 int_value = absl::int128(0x9f5b) << i;
EXPECT_EQ(float_value, static_cast<TypeParam>(int_value));
EXPECT_EQ(-float_value, static_cast<TypeParam>(-int_value));
EXPECT_EQ(int_value, absl::int128(float_value));
EXPECT_EQ(-int_value, absl::int128(-float_value));
}
// Round trip conversions with a small sample of randomly generated uint64_t
// values (less than int64_t max so that value * 2^64 fits into int128).
uint64_t values[] = {0x6d4492c24fb86199, 0x26ead65e4cb359b5,
0x2c43407433ba3fd1, 0x3b574ec668df6b55,
0x1c750e55a29f4f0f};
for (uint64_t value : values) {
for (int i = 0; i <= 64; ++i) {
SCOPED_TRACE(::testing::Message()
<< "value = " << value << "; i = " << i);
TypeParam fvalue = std::ldexp(static_cast<TypeParam>(value), i);
EXPECT_DOUBLE_EQ(fvalue, static_cast<TypeParam>(absl::int128(fvalue)));
EXPECT_DOUBLE_EQ(-fvalue, static_cast<TypeParam>(-absl::int128(fvalue)));
EXPECT_DOUBLE_EQ(-fvalue, static_cast<TypeParam>(absl::int128(-fvalue)));
EXPECT_DOUBLE_EQ(fvalue, static_cast<TypeParam>(-absl::int128(-fvalue)));
}
}
// Round trip conversions with a small sample of random large positive values.
absl::int128 large_values[] = {
absl::MakeInt128(0x5b0640d96c7b3d9f, 0xb7a7189e51d18622),
absl::MakeInt128(0x34bed042c6f65270, 0x73b236570669a089),
absl::MakeInt128(0x43deba9e6da12724, 0xf7f0f83da686797d),
absl::MakeInt128(0x71e8d383be4e5589, 0x75c3f96fb00752b6)};
for (absl::int128 value : large_values) {
// Make value have as many significant bits as can be represented by
// the mantissa, also making sure the highest and lowest bit in the range
// are set.
value >>= (127 - std::numeric_limits<TypeParam>::digits);
value |= absl::int128(1) << (std::numeric_limits<TypeParam>::digits - 1);
value |= 1;
for (int i = 0; i < 127 - std::numeric_limits<TypeParam>::digits; ++i) {
absl::int128 int_value = value << i;
EXPECT_EQ(int_value,
static_cast<absl::int128>(static_cast<TypeParam>(int_value)));
EXPECT_EQ(-int_value,
static_cast<absl::int128>(static_cast<TypeParam>(-int_value)));
}
}
// Small sample of checks that rounding is toward zero
EXPECT_EQ(0, absl::int128(TypeParam(0.1)));
EXPECT_EQ(17, absl::int128(TypeParam(17.8)));
EXPECT_EQ(0, absl::int128(TypeParam(-0.8)));
EXPECT_EQ(-53, absl::int128(TypeParam(-53.1)));
EXPECT_EQ(0, absl::int128(TypeParam(0.5)));
EXPECT_EQ(0, absl::int128(TypeParam(-0.5)));
TypeParam just_lt_one = std::nexttoward(TypeParam(1), TypeParam(0));
EXPECT_EQ(0, absl::int128(just_lt_one));
TypeParam just_gt_minus_one = std::nexttoward(TypeParam(-1), TypeParam(0));
EXPECT_EQ(0, absl::int128(just_gt_minus_one));
// Check limits
EXPECT_DOUBLE_EQ(std::ldexp(static_cast<TypeParam>(1), 127),
static_cast<TypeParam>(absl::Int128Max()));
EXPECT_DOUBLE_EQ(-std::ldexp(static_cast<TypeParam>(1), 127),
static_cast<TypeParam>(absl::Int128Min()));
}
TEST(Int128, FactoryTest) {
EXPECT_EQ(absl::int128(-1), absl::MakeInt128(-1, -1));
EXPECT_EQ(absl::int128(-31), absl::MakeInt128(-1, -31));
EXPECT_EQ(absl::int128(std::numeric_limits<int64_t>::min()),
absl::MakeInt128(-1, std::numeric_limits<int64_t>::min()));
EXPECT_EQ(absl::int128(0), absl::MakeInt128(0, 0));
EXPECT_EQ(absl::int128(1), absl::MakeInt128(0, 1));
EXPECT_EQ(absl::int128(std::numeric_limits<int64_t>::max()),
absl::MakeInt128(0, std::numeric_limits<int64_t>::max()));
}
TEST(Int128, HighLowTest) {
struct HighLowPair {
int64_t high;
uint64_t low;
};
HighLowPair values[]{{0, 0}, {0, 1}, {1, 0}, {123, 456}, {-654, 321}};
for (const HighLowPair& pair : values) {
absl::int128 value = absl::MakeInt128(pair.high, pair.low);
EXPECT_EQ(pair.low, absl::Int128Low64(value));
EXPECT_EQ(pair.high, absl::Int128High64(value));
}
}
TEST(Int128, LimitsTest) {
EXPECT_EQ(absl::MakeInt128(0x7fffffffffffffff, 0xffffffffffffffff),
absl::Int128Max());
EXPECT_EQ(absl::Int128Max(), ~absl::Int128Min());
}
#if defined(ABSL_HAVE_INTRINSIC_INT128)
TEST(Int128, IntrinsicConversionTest) {
__int128 intrinsic =
(static_cast<__int128>(0x3a5b76c209de76f6) << 64) + 0x1f25e1d63a2b46c5;
absl::int128 custom =
absl::MakeInt128(0x3a5b76c209de76f6, 0x1f25e1d63a2b46c5);
EXPECT_EQ(custom, absl::int128(intrinsic));
EXPECT_EQ(intrinsic, static_cast<__int128>(custom));
}
#endif // ABSL_HAVE_INTRINSIC_INT128
TEST(Int128, ConstexprTest) {
constexpr absl::int128 zero = absl::int128();
constexpr absl::int128 one = 1;
constexpr absl::int128 minus_two = -2;
constexpr absl::int128 min = absl::Int128Min();
constexpr absl::int128 max = absl::Int128Max();
EXPECT_EQ(zero, absl::int128(0));
EXPECT_EQ(one, absl::int128(1));
EXPECT_EQ(minus_two, absl::MakeInt128(-1, -2));
EXPECT_GT(max, one);
EXPECT_LT(min, minus_two);
}
TEST(Int128, ComparisonTest) {
struct TestCase {
absl::int128 smaller;
absl::int128 larger;
};
TestCase cases[] = {
{absl::int128(0), absl::int128(123)},
{absl::MakeInt128(-12, 34), absl::MakeInt128(12, 34)},
{absl::MakeInt128(1, 1000), absl::MakeInt128(1000, 1)},
{absl::MakeInt128(-1000, 1000), absl::MakeInt128(-1, 1)},
};
for (const TestCase& pair : cases) {
SCOPED_TRACE(::testing::Message() << "pair.smaller = " << pair.smaller
<< "; pair.larger = " << pair.larger);
EXPECT_TRUE(pair.smaller == pair.smaller); // NOLINT(readability/check)
EXPECT_TRUE(pair.larger == pair.larger); // NOLINT(readability/check)
EXPECT_FALSE(pair.smaller == pair.larger); // NOLINT(readability/check)
EXPECT_TRUE(pair.smaller != pair.larger); // NOLINT(readability/check)
EXPECT_FALSE(pair.smaller != pair.smaller); // NOLINT(readability/check)
EXPECT_FALSE(pair.larger != pair.larger); // NOLINT(readability/check)
EXPECT_TRUE(pair.smaller < pair.larger); // NOLINT(readability/check)
EXPECT_FALSE(pair.larger < pair.smaller); // NOLINT(readability/check)
EXPECT_TRUE(pair.larger > pair.smaller); // NOLINT(readability/check)
EXPECT_FALSE(pair.smaller > pair.larger); // NOLINT(readability/check)
EXPECT_TRUE(pair.smaller <= pair.larger); // NOLINT(readability/check)
EXPECT_FALSE(pair.larger <= pair.smaller); // NOLINT(readability/check)
EXPECT_TRUE(pair.smaller <= pair.smaller); // NOLINT(readability/check)
EXPECT_TRUE(pair.larger <= pair.larger); // NOLINT(readability/check)
EXPECT_TRUE(pair.larger >= pair.smaller); // NOLINT(readability/check)
EXPECT_FALSE(pair.smaller >= pair.larger); // NOLINT(readability/check)
EXPECT_TRUE(pair.smaller >= pair.smaller); // NOLINT(readability/check)
EXPECT_TRUE(pair.larger >= pair.larger); // NOLINT(readability/check)
}
}
TEST(Int128, UnaryPlusTest) {
int64_t values64[] = {0, 1, 12345, 0x4000000000000000,
std::numeric_limits<int64_t>::max()};
for (int64_t value : values64) {
SCOPED_TRACE(::testing::Message() << "value = " << value);
EXPECT_EQ(absl::int128(value), +absl::int128(value));
EXPECT_EQ(absl::int128(-value), +absl::int128(-value));
EXPECT_EQ(absl::MakeInt128(value, 0), +absl::MakeInt128(value, 0));
EXPECT_EQ(absl::MakeInt128(-value, 0), +absl::MakeInt128(-value, 0));
}
}
TEST(Int128, UnaryNegationTest) {
int64_t values64[] = {0, 1, 12345, 0x4000000000000000,
std::numeric_limits<int64_t>::max()};
for (int64_t value : values64) {
SCOPED_TRACE(::testing::Message() << "value = " << value);
EXPECT_EQ(absl::int128(-value), -absl::int128(value));
EXPECT_EQ(absl::int128(value), -absl::int128(-value));
EXPECT_EQ(absl::MakeInt128(-value, 0), -absl::MakeInt128(value, 0));
EXPECT_EQ(absl::MakeInt128(value, 0), -absl::MakeInt128(-value, 0));
}
}
TEST(Int128, LogicalNotTest) {
EXPECT_TRUE(!absl::int128(0));
for (int i = 0; i < 64; ++i) {
EXPECT_FALSE(!absl::MakeInt128(0, uint64_t{1} << i));
}
for (int i = 0; i < 63; ++i) {
EXPECT_FALSE(!absl::MakeInt128(int64_t{1} << i, 0));
}
}
TEST(Int128, AdditionSubtractionTest) {
// 64 bit pairs that will not cause overflow / underflow. These test negative
// carry; positive carry must be checked separately.
std::pair<int64_t, int64_t> cases[]{
{0, 0}, // 0, 0
{0, 2945781290834}, // 0, +
{1908357619234, 0}, // +, 0
{0, -1204895918245}, // 0, -
{-2957928523560, 0}, // -, 0
{89023982312461, 98346012567134}, // +, +
{-63454234568239, -23456235230773}, // -, -
{98263457263502, -21428561935925}, // +, -
{-88235237438467, 15923659234573}, // -, +
};
for (const auto& pair : cases) {
SCOPED_TRACE(::testing::Message()
<< "pair = {" << pair.first << ", " << pair.second << '}');
EXPECT_EQ(absl::int128(pair.first + pair.second),
absl::int128(pair.first) + absl::int128(pair.second));
EXPECT_EQ(absl::int128(pair.second + pair.first),
absl::int128(pair.second) += absl::int128(pair.first));
EXPECT_EQ(absl::int128(pair.first - pair.second),
absl::int128(pair.first) - absl::int128(pair.second));
EXPECT_EQ(absl::int128(pair.second - pair.first),
absl::int128(pair.second) -= absl::int128(pair.first));
EXPECT_EQ(
absl::MakeInt128(pair.second + pair.first, 0),
absl::MakeInt128(pair.second, 0) + absl::MakeInt128(pair.first, 0));
EXPECT_EQ(
absl::MakeInt128(pair.first + pair.second, 0),
absl::MakeInt128(pair.first, 0) += absl::MakeInt128(pair.second, 0));
EXPECT_EQ(
absl::MakeInt128(pair.second - pair.first, 0),
absl::MakeInt128(pair.second, 0) - absl::MakeInt128(pair.first, 0));
EXPECT_EQ(
absl::MakeInt128(pair.first - pair.second, 0),
absl::MakeInt128(pair.first, 0) -= absl::MakeInt128(pair.second, 0));
}
// check positive carry
EXPECT_EQ(absl::MakeInt128(31, 0),
absl::MakeInt128(20, 1) +
absl::MakeInt128(10, std::numeric_limits<uint64_t>::max()));
}
TEST(Int128, IncrementDecrementTest) {
absl::int128 value = 0;
EXPECT_EQ(0, value++);
EXPECT_EQ(1, value);
EXPECT_EQ(1, value--);
EXPECT_EQ(0, value);
EXPECT_EQ(-1, --value);
EXPECT_EQ(-1, value);
EXPECT_EQ(0, ++value);
EXPECT_EQ(0, value);
}
TEST(Int128, MultiplicationTest) {
// 1 bit x 1 bit, and negative combinations
for (int i = 0; i < 64; ++i) {
for (int j = 0; j < 127 - i; ++j) {
SCOPED_TRACE(::testing::Message() << "i = " << i << "; j = " << j);
absl::int128 a = absl::int128(1) << i;
absl::int128 b = absl::int128(1) << j;
absl::int128 c = absl::int128(1) << (i + j);
EXPECT_EQ(c, a * b);
EXPECT_EQ(-c, -a * b);
EXPECT_EQ(-c, a * -b);
EXPECT_EQ(c, -a * -b);
EXPECT_EQ(c, absl::int128(a) *= b);
EXPECT_EQ(-c, absl::int128(-a) *= b);
EXPECT_EQ(-c, absl::int128(a) *= -b);
EXPECT_EQ(c, absl::int128(-a) *= -b);
}
}
// Pairs of random values that will not overflow signed 64-bit multiplication
std::pair<int64_t, int64_t> small_values[] = {
{0x5e61, 0xf29f79ca14b4}, // +, +
{0x3e033b, -0x612c0ee549}, // +, -
{-0x052ce7e8, 0x7c728f0f}, // -, +
{-0x3af7054626, -0xfb1e1d}, // -, -
};
for (const std::pair<int64_t, int64_t>& pair : small_values) {
SCOPED_TRACE(::testing::Message()
<< "pair = {" << pair.first << ", " << pair.second << '}');
EXPECT_EQ(absl::int128(pair.first * pair.second),
absl::int128(pair.first) * absl::int128(pair.second));
EXPECT_EQ(absl::int128(pair.first * pair.second),
absl::int128(pair.first) *= absl::int128(pair.second));
EXPECT_EQ(absl::MakeInt128(pair.first * pair.second, 0),
absl::MakeInt128(pair.first, 0) * absl::int128(pair.second));
EXPECT_EQ(absl::MakeInt128(pair.first * pair.second, 0),
absl::MakeInt128(pair.first, 0) *= absl::int128(pair.second));
}
// Pairs of positive random values that will not overflow 64-bit
// multiplication and can be left shifted by 32 without overflow
std::pair<int64_t, int64_t> small_values2[] = {
{0x1bb0a110, 0x31487671},
{0x4792784e, 0x28add7d7},
{0x7b66553a, 0x11dff8ef},
};
for (const std::pair<int64_t, int64_t>& pair : small_values2) {
SCOPED_TRACE(::testing::Message()
<< "pair = {" << pair.first << ", " << pair.second << '}');
absl::int128 a = absl::int128(pair.first << 32);
absl::int128 b = absl::int128(pair.second << 32);
absl::int128 c = absl::MakeInt128(pair.first * pair.second, 0);
EXPECT_EQ(c, a * b);
EXPECT_EQ(-c, -a * b);
EXPECT_EQ(-c, a * -b);
EXPECT_EQ(c, -a * -b);
EXPECT_EQ(c, absl::int128(a) *= b);
EXPECT_EQ(-c, absl::int128(-a) *= b);
EXPECT_EQ(-c, absl::int128(a) *= -b);
EXPECT_EQ(c, absl::int128(-a) *= -b);
}
// check 0, 1, and -1 behavior with large values
absl::int128 large_values[] = {
{absl::MakeInt128(0xd66f061af02d0408, 0x727d2846cb475b53)},
{absl::MakeInt128(0x27b8d5ed6104452d, 0x03f8a33b0ee1df4f)},
{-absl::MakeInt128(0x621b6626b9e8d042, 0x27311ac99df00938)},
{-absl::MakeInt128(0x34e0656f1e95fb60, 0x4281cfd731257a47)},
};
for (absl::int128 value : large_values) {
EXPECT_EQ(0, 0 * value);
EXPECT_EQ(0, value * 0);
EXPECT_EQ(0, absl::int128(0) *= value);
EXPECT_EQ(0, value *= 0);
EXPECT_EQ(value, 1 * value);
EXPECT_EQ(value, value * 1);
EXPECT_EQ(value, absl::int128(1) *= value);
EXPECT_EQ(value, value *= 1);
EXPECT_EQ(-value, -1 * value);
EXPECT_EQ(-value, value * -1);
EXPECT_EQ(-value, absl::int128(-1) *= value);
EXPECT_EQ(-value, value *= -1);
}
// Manually calculated random large value cases
EXPECT_EQ(absl::MakeInt128(0xcd0efd3442219bb, 0xde47c05bcd9df6e1),
absl::MakeInt128(0x7c6448, 0x3bc4285c47a9d253) * 0x1a6037537b);
EXPECT_EQ(-absl::MakeInt128(0x1f8f149850b1e5e6, 0x1e50d6b52d272c3e),
-absl::MakeInt128(0x23, 0x2e68a513ca1b8859) * 0xe5a434cd14866e);
EXPECT_EQ(-absl::MakeInt128(0x55cae732029d1fce, 0xca6474b6423263e4),
0xa9b98a8ddf66bc * -absl::MakeInt128(0x81, 0x672e58231e2469d7));
EXPECT_EQ(absl::MakeInt128(0x19c8b7620b507dc4, 0xfec042b71a5f29a4),
-0x3e39341147 * -absl::MakeInt128(0x6a14b2, 0x5ed34cca42327b3c));
EXPECT_EQ(absl::MakeInt128(0xcd0efd3442219bb, 0xde47c05bcd9df6e1),
absl::MakeInt128(0x7c6448, 0x3bc4285c47a9d253) *= 0x1a6037537b);
EXPECT_EQ(-absl::MakeInt128(0x1f8f149850b1e5e6, 0x1e50d6b52d272c3e),
-absl::MakeInt128(0x23, 0x2e68a513ca1b8859) *= 0xe5a434cd14866e);
EXPECT_EQ(-absl::MakeInt128(0x55cae732029d1fce, 0xca6474b6423263e4),
absl::int128(0xa9b98a8ddf66bc) *=