montgomery_test.cc

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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*/
 
# include <gtest/gtest.h>
 
# include <random>
 
# include <modular_arithmetic.H>
 
using namespace Aleph;
 
#if defined(__SIZEOF_INT128__)
 
namespace
{
  inline constexpr MontgomeryCtx kCtx3 = montgomery_ctx_for_mod<3>();
  inline constexpr MontgomeryCtx kCtx9 = montgomery_ctx_for_mod<9>();
 
  static_assert(kCtx3.mod() == 3);
  static_assert(kCtx9.mod() == 9);
 
  void
  expect_round_trip(const MontgomeryCtx & ctx,
                    const Array<uint64_t> & values)
  {
    const uint64_t mod = ctx.mod();
    for (size_t i = 0; i < values.size(); ++i)
      EXPECT_EQ(from_mont(to_mont(values[i], ctx), ctx), values[i] % mod)
        << "mod=" << mod << " value=" << values[i];
  }
 
  void
  expect_round_trip(const uint64_t mod,
                    const Array<uint64_t> & values)
  {
    expect_round_trip(montgomery_ctx(mod), values);
  }
 
  void
  expect_products(const MontgomeryCtx & ctx,
                  const Array<uint64_t> & lhs_values,
                  const Array<uint64_t> & rhs_values)
  {
    const uint64_t mod = ctx.mod();
    for (size_t i = 0; i < lhs_values.size(); ++i)
      for (size_t j = 0; j < rhs_values.size(); ++j)
        {
          const uint64_t lhs = lhs_values[i];
          const uint64_t rhs = rhs_values[j];
          const uint64_t got =
              from_mont(mont_mul(to_mont(lhs, ctx), to_mont(rhs, ctx), ctx),
                        ctx);
          EXPECT_EQ(got, mod_mul(lhs % mod, rhs % mod, mod))
            << "mod=" << mod << " lhs=" << lhs << " rhs=" << rhs;
        }
  }
 
  void
  expect_products(const uint64_t mod,
                  const Array<uint64_t> & lhs_values,
                  const Array<uint64_t> & rhs_values)
  {
    expect_products(montgomery_ctx(mod), lhs_values, rhs_values);
  }
 
  void
  expect_powers(const MontgomeryCtx & ctx,
                const Array<uint64_t> & bases,
                const Array<uint64_t> & exponents)
  {
    const uint64_t mod = ctx.mod();
    for (size_t j = 0; j < bases.size(); ++j)
      for (size_t k = 0; k < exponents.size(); ++k)
        {
          const uint64_t base = bases[j];
          const uint64_t exp = exponents[k];
          const uint64_t got =
              from_mont(mont_exp(to_mont(base, ctx), exp, ctx), ctx);
          EXPECT_EQ(got, mod_exp(base % mod, exp, mod))
            << "mod=" << mod << " base=" << base << " exp=" << exp;
        }
  }
}
 
TEST(MontgomeryTest, RejectsInvalidModuli)
{
  EXPECT_THROW(static_cast<void>(montgomery_ctx(0)), std::invalid_argument);
  EXPECT_THROW(static_cast<void>(montgomery_ctx(1)), std::invalid_argument);
  EXPECT_THROW(static_cast<void>(montgomery_ctx(2)), std::invalid_argument);
  EXPECT_THROW(static_cast<void>(montgomery_ctx(100)), std::invalid_argument);
}
 
TEST(MontgomeryTest, RoundTripOnFriendlyPrimes)
{
  const Array<uint64_t> mods =
      {9ULL, 998244353ULL, 469762049ULL, 1004535809ULL};
 
  for (size_t i = 0; i < mods.size(); ++i)
    {
      const uint64_t mod = mods[i];
      expect_round_trip(mod, {0ULL, 1ULL, 2ULL, mod - 2, mod - 1,
                              mod, mod + 1, mod * 2 + 7});
    }
}
 
TEST(MontgomeryTest, MultiplicationMatchesModMul)
{
  const Array<uint64_t> mods =
      {9ULL, 998244353ULL, 469762049ULL, 1004535809ULL};
 
  for (size_t i = 0; i < mods.size(); ++i)
    {
      const uint64_t mod = mods[i];
      expect_products(mod, {0ULL, 1ULL, 2ULL, mod - 2, mod - 1, mod + 5},
                       {0ULL, 1ULL, 3ULL, mod - 3, mod - 1, mod + 9});
 
      std::mt19937_64 rng(mod);
      const MontgomeryCtx ctx = montgomery_ctx(mod);
      for (size_t sample = 0; sample < 128; ++sample)
        {
          const uint64_t lhs = rng();
          const uint64_t rhs = rng();
          const uint64_t got =
              from_mont(mont_mul(to_mont(lhs, ctx), to_mont(rhs, ctx), ctx),
                        ctx);
          EXPECT_EQ(got, mod_mul(lhs % mod, rhs % mod, mod))
            << "mod=" << mod << " lhs=" << lhs << " rhs=" << rhs;
        }
    }
}
 
TEST(MontgomeryTest, ExponentiationMatchesModExp)
{
  const Array<uint64_t> mods =
      {9ULL, 998244353ULL, 469762049ULL, 1004535809ULL};
  const Array<uint64_t> exponents =
      {0ULL, 1ULL, 2ULL, 7ULL, 31ULL, 123456ULL};
 
  for (size_t i = 0; i < mods.size(); ++i)
    {
      const uint64_t mod = mods[i];
      const MontgomeryCtx ctx = montgomery_ctx(mod);
      const Array<uint64_t> bases =
          {0ULL, 1ULL, 2ULL, 5ULL, mod - 2, mod - 1, mod + 11};
      expect_powers(ctx, bases, exponents);
    }
}
 
TEST(MontgomeryTest, CompositeOddModulusRuntimePaths)
{
  const Array<uint64_t> bases = {0ULL, 1ULL, 2ULL, 5ULL, 7ULL, 8ULL, 9ULL, 17ULL};
  const Array<uint64_t> exponents = {0ULL, 1ULL, 2ULL, 7ULL, 31ULL};
 
  expect_round_trip(kCtx9, bases);
  expect_products(kCtx9, bases, {0ULL, 1ULL, 3ULL, 4ULL, 8ULL, 9ULL, 14ULL});
  expect_powers(kCtx9, bases, exponents);
}
 
TEST(MontgomeryTest, HandlesLargeOddModulusNearUint64Limit)
{
  constexpr uint64_t mod = 18446744073709551557ULL;
  const MontgomeryCtx ctx = montgomery_ctx(mod);
 
  expect_round_trip(ctx, {0ULL, 1ULL, 2ULL, mod - 2, mod - 1});
  expect_products(ctx, {mod - 1, mod - 2, mod - 3},
                   {mod - 4, mod - 5, mod - 6});
 
  EXPECT_EQ(from_mont(mont_exp(to_mont(mod - 1, ctx), 5, ctx), ctx),
            mod_exp(mod - 1, 5, mod));
}
 
#endif