third_party/shell-encryption/src/int256_test.cc - chromium/src.git - Git at Google

 /*
  * 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::kuint128max);
   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::kuint128max);
   EXPECT_EQ(Uint256Low128(biggest), absl::kuint128max);
   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::kuint128max);
   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
	/*
	* 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::kuint128max);
	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::kuint128max);
	EXPECT_EQ(Uint256Low128(biggest), absl::kuint128max);
	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::kuint128max);
	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