/*
* Copyright 2018 Google LLC.
* 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 "int256.h"
#include <algorithm>
#include <random>
#include <sstream>
#include <type_traits>
#include <utility>
#include <glog/logging.h>
#include <gtest/gtest.h>
#include "absl/container/fixed_array.h"
#include "absl/numeric/int128.h"
namespace rlwe {
TEST(Int256, AllTests) {
uint256 zero(0);
uint256 one(1);
uint256 minus_one(-1);
uint256 minus_one_2arg(-1, -1);
uint256 one_2arg(0, 1);
uint256 two(0, 2);
uint256 three(0, 3);
uint256 big(2000, 2);
uint256 big_minus_one(2000, 1);
uint256 bigger(2001, 1);
uint256 biggest(kuint256max);
uint256 high_low(1, 0);
uint256 low_high(0, absl::Uint128Max());
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);
EXPECT_LE(minus_one_2arg, biggest);
EXPECT_LE(minus_one, biggest);
EXPECT_EQ(minus_one, minus_one_2arg);
// 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);
EXPECT_EQ(zero, big >> 256);
EXPECT_EQ(zero, big << 256);
// Shift assignments.
uint256 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);
big_copy = big;
EXPECT_EQ(big << 128, big_copy <<= 128);
big_copy = big;
EXPECT_EQ(big >> 128, big_copy >>= 128);
big_copy = big;
EXPECT_EQ(big << 192, big_copy <<= 192);
big_copy = big;
EXPECT_EQ(big >> 192, big_copy >>= 192);
big_copy = big;
EXPECT_EQ(big << 256, big_copy <<= 256);
big_copy = big;
EXPECT_EQ(big >> 256, big_copy >>= 256);
EXPECT_EQ(Uint256High128(biggest), absl::Uint128Max());
EXPECT_EQ(Uint256Low128(biggest), absl::Uint128Max());
EXPECT_EQ(zero + one, one);
EXPECT_EQ(zero + minus_one, minus_one);
EXPECT_EQ(one + minus_one, zero);
EXPECT_EQ(one - minus_one, two);
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 + low_high, bigger);
EXPECT_EQ(biggest + 1, zero);
EXPECT_EQ(minus_one + 1, zero);
EXPECT_EQ(zero - 1, biggest);
EXPECT_EQ(zero - 1, minus_one);
EXPECT_EQ(high_low - one, low_high);
EXPECT_EQ(low_high + one, high_low);
EXPECT_EQ(Uint256High128((uint256(1) << 128) - 1), 0);
EXPECT_EQ(Uint256Low128((uint256(1) << 128) - 1), absl::Uint128Max());
EXPECT_TRUE(!!one);
EXPECT_TRUE(!!high_low);
EXPECT_FALSE(!!zero);
EXPECT_FALSE(!one);
EXPECT_FALSE(!high_low);
EXPECT_TRUE(!zero);
// These 4 checks are explicitly for the comparison operators.
EXPECT_TRUE(zero == 0);
EXPECT_FALSE(zero != 0);
EXPECT_FALSE(one == 0);
EXPECT_TRUE(one != 0);
uint256 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, -((-one) - 1));
EXPECT_EQ(kuint256max, -one);
EXPECT_EQ(zero, -zero);
EXPECT_EQ(one, -minus_one);
EXPECT_EQ(-one, minus_one);
// Test ++ and -- when hi and lo are both modified.
test = low_high;
EXPECT_EQ(++test, high_low);
EXPECT_EQ(test, high_low);
EXPECT_EQ(--test, low_high);
EXPECT_EQ(test, low_high);
EXPECT_EQ(test++, low_high);
EXPECT_EQ(test, high_low);
EXPECT_EQ(test--, high_low);
EXPECT_EQ(test, low_high);
test = minus_one;
EXPECT_EQ(++test, zero);
EXPECT_EQ(test, zero);
EXPECT_EQ(--test, minus_one);
EXPECT_EQ(test, minus_one);
EXPECT_EQ(test++, minus_one);
EXPECT_EQ(test, zero);
EXPECT_EQ(test--, zero);
EXPECT_EQ(test, minus_one);
LOG(INFO) << one;
LOG(INFO) << big_minus_one;
}
TEST(Int256, PodTests) {
uint256_pod pod = {12345, 67890};
uint256 from_pod(pod);
EXPECT_EQ(12345, Uint256High128(from_pod));
EXPECT_EQ(67890, Uint256Low128(from_pod));
uint256 zero(0);
uint256_pod zero_pod = {0, 0};
uint256 one(1);
uint256_pod one_pod = {0, 1};
uint256 two(2);
uint256_pod two_pod = {0, 2};
uint256 three(3);
uint256_pod three_pod = {0, 3};
uint256 big(1, 0);
uint256_pod big_pod = {1, 0};
EXPECT_EQ(zero, zero_pod);
EXPECT_EQ(zero_pod, zero);
EXPECT_EQ(zero_pod, zero_pod);
EXPECT_EQ(one, one_pod);
EXPECT_EQ(one_pod, one);
EXPECT_EQ(one_pod, one_pod);
EXPECT_EQ(two, two_pod);
EXPECT_EQ(two_pod, two);
EXPECT_EQ(two_pod, two_pod);
EXPECT_NE(one, two_pod);
EXPECT_NE(one_pod, two);
EXPECT_NE(one_pod, two_pod);
EXPECT_LT(one, two_pod);
EXPECT_LT(one_pod, two);
EXPECT_LT(one_pod, two_pod);
EXPECT_LE(one, one_pod);
EXPECT_LE(one_pod, one);
EXPECT_LE(one_pod, one_pod);
EXPECT_LE(one, two_pod);
EXPECT_LE(one_pod, two);
EXPECT_LE(one_pod, two_pod);
EXPECT_GT(two, one_pod);
EXPECT_GT(two_pod, one);
EXPECT_GT(two_pod, one_pod);
EXPECT_GE(two, two_pod);
EXPECT_GE(two_pod, two);
EXPECT_GE(two_pod, two_pod);
EXPECT_GE(two, one_pod);
EXPECT_GE(two_pod, one);
EXPECT_GE(two_pod, one_pod);
EXPECT_EQ(three, one | two_pod);
EXPECT_EQ(three, one_pod | two);
EXPECT_EQ(three, one_pod | two_pod);
EXPECT_EQ(one, three & one_pod);
EXPECT_EQ(one, three_pod & one);
EXPECT_EQ(one, three_pod & one_pod);
EXPECT_EQ(two, three ^ one_pod);
EXPECT_EQ(two, three_pod ^ one);
EXPECT_EQ(two, three_pod ^ one_pod);
EXPECT_EQ(two, three & (~one));
EXPECT_EQ(three, ~~three);
EXPECT_EQ(two, two_pod << 0);
EXPECT_EQ(two, one_pod << 1);
EXPECT_EQ(big, one_pod << 128);
EXPECT_EQ(zero, one_pod << 256);
EXPECT_EQ(two, two_pod >> 0);
EXPECT_EQ(one, two_pod >> 1);
EXPECT_EQ(one, big_pod >> 128);
EXPECT_EQ(one, zero + one_pod);
EXPECT_EQ(one, zero_pod + one);
EXPECT_EQ(one, zero_pod + one_pod);
EXPECT_EQ(one, two - one_pod);
EXPECT_EQ(one, two_pod - one);
EXPECT_EQ(one, two_pod - one_pod);
}
TEST(Int256, OperatorAssignReturnRef) {
uint256 v(1);
(v += 4) -= 3;
EXPECT_EQ(2, v);
}
TEST(Int256, Multiply) {
uint256 a, b, c;
// Zero test.
a = 0;
b = 0;
c = a * b;
EXPECT_EQ(0, c);
// Max carries.
a = uint256(0) - 1;
b = uint256(0) - 1;
c = a * b;
EXPECT_EQ(1, c);
// Self-operation with max carries.
c = uint256(0) - 1;
c *= c;
EXPECT_EQ(1, c);
// 1-bit x 1-bit.
for (int i = 0; i < 128; ++i) {
for (int j = 0; j < 128; ++j) {
a = uint256(1) << i;
b = uint256(1) << j;
c = a * b;
EXPECT_EQ(uint256(1) << (i + j), c);
}
}
// Verified with dc.
a = uint256(absl::MakeUint128(static_cast<Uint64>(0xffffeeeeddddcccc),
static_cast<Uint64>(0xffffeeeeddddcccc)),
absl::MakeUint128(static_cast<Uint64>(0xbbbbaaaa99998888),
static_cast<Uint64>(0xbbbbaaaa99998888)));
b = uint256(absl::MakeUint128(static_cast<Uint64>(0x7777666655554444),
static_cast<Uint64>(0x7777666655554444)),
absl::MakeUint128(static_cast<Uint64>(0x3333222211110000),
static_cast<Uint64>(0x3333222211110000)));
c = a * b;
EXPECT_EQ(uint256(absl::MakeUint128(static_cast<Uint64>(0x0B60BCDF06D3A4FA),
static_cast<Uint64>(0x37C054321A2B4567)),
absl::MakeUint128(static_cast<Uint64>(0xA3D7111116C170A3),
static_cast<Uint64>(0xBF25975319080000))),
c);
EXPECT_EQ(0, c - b * a);
EXPECT_EQ(a * a - b * b, (a + b) * (a - b));
// Verified with dc.
a = uint256(absl::MakeUint128(static_cast<Uint64>(0x0123456789abcdef),
static_cast<Uint64>(0x0123456789abcdef)),
absl::MakeUint128(static_cast<Uint64>(0xfedcba9876543210),
static_cast<Uint64>(0xfedcba9876543210)));
b = uint256(absl::MakeUint128(static_cast<Uint64>(0x02468ace13579bdf),
static_cast<Uint64>(0x02468ace13579bdf)),
absl::MakeUint128(static_cast<Uint64>(0xfdb97531eca86420),
static_cast<Uint64>(0xfdb97531eca86420)));
c = a * b;
EXPECT_EQ(uint256(absl::MakeUint128(static_cast<Uint64>(0x361CDAA0607023AD),
static_cast<Uint64>(0xC86E51A688F16415)),
absl::MakeUint128(static_cast<Uint64>(0x64F2DE16AB6A4222),
static_cast<Uint64>(0x342D0BBF48948200))),
c);
EXPECT_EQ(0, c - b * a);
EXPECT_EQ(a * a - b * b, (a + b) * (a - b));
}
TEST(Int256, AliasTests) {
uint256 x1(1, 2);
uint256 x2(2, 4);
x1 += x1;
EXPECT_EQ(x2, x1);
uint256 x3(1, absl::uint128(1) << 127);
uint256 x4(3, 0);
x3 += x3;
EXPECT_EQ(x4, x3);
}
TEST(Int256, DivideAndMod) {
// a := q * b + r
uint256 a, b, q, r;
// a == b
a = 123;
b = a;
q = a / b;
r = a % b;
EXPECT_EQ(1, q);
EXPECT_EQ(0, r);
// Zero test.
a = 0;
b = 123;
q = a / b;
r = a % b;
EXPECT_EQ(0, q);
EXPECT_EQ(0, r);
a = uint256(0, absl::MakeUint128(static_cast<Uint64>(0x530eda741c71d4c3),
static_cast<Uint64>(0xbf25975319080000)));
q = uint256(0, absl::MakeUint128(static_cast<Uint64>(0x4de2cab081),
static_cast<Uint64>(0x14c34ab4676e4bab)));
b = uint256(0x1110001);
r = uint256(0x3eb455);
ASSERT_EQ(a, q * b + r); // Sanity-check.
uint256 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.
using std::swap;
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;
uint256 expected_r(
0, absl::MakeUint128(static_cast<Uint64>(0x29876d3a0e38ea61),
static_cast<Uint64>(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(Int256, DivideAndModRandomInputs) {
const int kNumIters = 1 << 18;
std::minstd_rand random(testing::UnitTest::GetInstance()->random_seed());
std::uniform_int_distribution<Uint64> uniform_uint64;
for (int i = 0; i < kNumIters; ++i) {
const uint256 a(uniform_uint64(random), uniform_uint64(random));
const uint256 b(uniform_uint64(random), uniform_uint64(random));
if (b == 0) {
continue; // Avoid a div-by-zero.
}
const uint256 q = a / b;
const uint256 r = a % b;
ASSERT_EQ(a, b * q + r);
}
}
TEST(Int256, ConstexprTest) {
constexpr uint256 one = 1;
constexpr uint256_pod pod = {2, 3};
constexpr uint256 from_pod = pod;
constexpr uint256 minus_two = -2;
EXPECT_EQ(one, uint256(1));
EXPECT_EQ(from_pod, uint256(2, 3));
EXPECT_EQ(minus_two, uint256(absl::uint128(-1), absl::uint128(-2)));
}
TEST(Int256, Traits) {
EXPECT_TRUE(std::is_trivially_copy_constructible<uint256>::value);
EXPECT_TRUE(std::is_trivially_copy_assignable<uint256>::value);
EXPECT_TRUE(std::is_trivially_destructible<uint256>::value);
}
TEST(Int256, OStream) {
struct {
uint256 val;
std::ios_base::fmtflags flags;
std::streamsize width;
char fill;
const char* rep;
} cases[] = {
// zero with different bases
{uint256(0), std::ios::dec, 0, '_', "0"},
{uint256(0), std::ios::oct, 0, '_', "0"},
{uint256(0), std::ios::hex, 0, '_', "0"},
// crossover between lo_ and hi_
{uint256(0, -1), std::ios::dec, 0, '_',
"340282366920938463463374607431768211455"},
{uint256(0, -1), std::ios::oct, 0, '_',
"3777777777777777777777777777777777777777777"},
{uint256(0, -1), std::ios::hex, 0, '_',
"ffffffffffffffffffffffffffffffff"},
{uint256(1, 0), std::ios::dec, 0, '_',
"340282366920938463463374607431768211456"},
{uint256(1, 0), std::ios::oct, 0, '_',
"4000000000000000000000000000000000000000000"},
{uint256(1, 0), std::ios::hex, 0, '_',
"100000000000000000000000000000000"},
// just the top bit
{uint256(static_cast<Uint64>(0x8000000000000000), 0), std::ios::dec, 0,
'_', "3138550867693340381917894711603833208051177722232017256448"},
{uint256(static_cast<Uint64>(0x8000000000000000), 0), std::ios::oct, 0,
'_', "4000000000000000000000000000000000000000000000000000000000000000"},
{uint256(static_cast<Uint64>(0x8000000000000000), 0), std::ios::hex, 0,
'_', "800000000000000000000000000000000000000000000000"},
// maximum uint256 value
{uint256(-1, -1), std::ios::dec, 0, '_',
"115792089237316195423570985008687907853"
"269984665640564039457584007913129639935"},
{uint256(-1, -1), std::ios::oct, 0, '_',
"1777777777777777777777777777777777777777777"
"7777777777777777777777777777777777777777777"},
{uint256(-1, -1), std::ios::hex, 0, '_',
"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"},
// uppercase
{uint256(-1, -1), std::ios::hex | std::ios::uppercase, 0, '_',
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"},
// showbase
{uint256(1), std::ios::dec | std::ios::showbase, 0, '_', "1"},
{uint256(1), std::ios::oct | std::ios::showbase, 0, '_', "01"},
{uint256(1), std::ios::hex | std::ios::showbase, 0, '_', "0x1"},
// showbase does nothing on zero
{uint256(0), std::ios::dec | std::ios::showbase, 0, '_', "0"},
{uint256(0), std::ios::oct | std::ios::showbase, 0, '_', "0"},
{uint256(0), std::ios::hex | std::ios::showbase, 0, '_', "0"},
// showpos does nothing on unsigned types
{uint256(1), std::ios::dec | std::ios::showpos, 0, '_', "1"},
// padding
{uint256(9), std::ios::dec, 6, '_', "_____9"},
{uint256(12345), std::ios::dec, 6, '_', "_12345"},
// left adjustment
{uint256(9), std::ios::dec | std::ios::left, 6, '_', "9_____"},
{uint256(12345), std::ios::dec | std::ios::left, 6, '_', "12345_"},
};
for (size_t i = 0; i < ABSL_ARRAYSIZE(cases); ++i) {
std::ostringstream os;
os.flags(cases[i].flags);
os.width(cases[i].width);
os.fill(cases[i].fill);
os << cases[i].val;
EXPECT_EQ(cases[i].rep, os.str());
}
}
TEST(Int256, SizeOfTest) { EXPECT_EQ(sizeof(uint256), 32); }
} // namespace rlwe
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