math_nt_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
 
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 of this software and associated documentation files (the "Software"), to deal
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 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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 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
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*/
 
# include <gtest/gtest.h>
# include <chrono>
# include <cstdlib>
# include <random>
# include <algorithm>
# include <numeric>
# include <modular_arithmetic.H>
 
# include <primality.H>
# include <pollard_rho.H>
# include <modular_combinatorics.H>
# include <modular_linalg.H>
# include <tpl_dynMat.H>
 
using namespace Aleph;
 
TEST(MathNT, ModMulAndExp)
{
  uint64_t m = 1000000007;
  EXPECT_EQ(mod_mul(2, 3, m), 6);
  EXPECT_EQ(mod_exp(2, 10, m), 1024);
  
  // Test mod_exp with m = 1
  EXPECT_EQ(mod_exp(2, 10, 1), 0ULL);
  EXPECT_EQ(mod_exp(2, 0, 1), 0ULL);
  
  uint64_t big_m = 4000000000000000000ULL; // > 32 bits
  uint64_t a = 3000000000000000000ULL;
  uint64_t b = 2000000000000000000ULL;
  // 3e18 * 2e18 = 6e36
  // 6e36 % 4e18 = 0
  EXPECT_EQ(mod_mul(a, b, big_m), 0ULL);
  
  EXPECT_EQ(mod_mul(a + 1, b, big_m), 2000000000000000000ULL);
}
 
TEST(MathNT, ExtGCDAndInv)
{
  int64_t x, y;
  int64_t g = ext_gcd<int64_t>(30, 20, x, y);
  EXPECT_EQ(g, 10);
  EXPECT_EQ(30 * x + 20 * y, 10);
 
  EXPECT_EQ(mod_inv(3, 11), 4); // 3 * 4 = 12 = 1 mod 11
  EXPECT_THROW(mod_inv(2, 4), std::invalid_argument);
}
 
TEST(MathNT, CRT)
{
  Array<uint64_t> rem = {2, 3, 2};
  Array<uint64_t> mod = {3, 5, 7};
  // x = 2 mod 3
  // x = 3 mod 5
  // x = 2 mod 7
  // Answer is 23
  EXPECT_EQ(crt(rem, mod), 23);
}
 
TEST(MathNT, MillerRabin)
{
  EXPECT_FALSE(miller_rabin(1));
  EXPECT_TRUE(miller_rabin(2));
  EXPECT_TRUE(miller_rabin(3));
  EXPECT_FALSE(miller_rabin(4));
  EXPECT_TRUE(miller_rabin(97));
  EXPECT_FALSE(miller_rabin(100));
  EXPECT_TRUE(miller_rabin(1000000007));
  EXPECT_TRUE(miller_rabin(2147483647)); 
 
  // Property-based checks with fixed seed
  std::mt19937_64 rng(42);
  for (int i = 0; i < 100; ++i)
  {
    uint64_t n = rng() % 1000000;
    if (n < 2) continue;
    bool is_p = miller_rabin(n);
    
    // Simple primality oracle for validation
    bool oracle = true;
    for (uint64_t d = 2; d * d <= n; ++d)
      if (n % d == 0) { oracle = false; break; }
    EXPECT_EQ(is_p, oracle) << "n=" << n;
  }
}
 
TEST(MathNT, PollardRho)
{
  auto factors = pollard_rho(12);
  Array<uint64_t> exp12 = {2, 2, 3};
  EXPECT_EQ(factors, exp12);
 
  auto factors_prime = pollard_rho(97);
  Array<uint64_t> exp97 = {97};
  EXPECT_EQ(factors_prime, exp97);
 
  auto big_factors = pollard_rho(1000000007ULL * 97ULL);
  Array<uint64_t> exp_big = {97, 1000000007};
  EXPECT_EQ(big_factors, exp_big);
 
  // Randomized property check
  std::mt19937_64 rng(1337);
  for (int i = 0; i < 20; ++i)
  {
    uint64_t n = rng() % 1000000000000ULL + 2;
    auto res = pollard_rho(n);
    
    uint64_t prod = 1;
    for (const auto f : res)
    {
      EXPECT_TRUE(miller_rabin(f)) << "Factor " << f << " of " << n << " is not prime";
      prod *= f;
    }
    EXPECT_EQ(prod, n) << "Product of factors doesn't match original n";
  }
}
 
TEST(MathNT, PerformanceRegression)
{
  if (not std::getenv("ENABLE_PERF_TESTS"))
    GTEST_SKIP() << "Skipping performance regression (set ENABLE_PERF_TESTS to enable)";
 
  // 1. Pollard Rho on a large composite (product of two 31-bit primes)
  uint64_t p1 = 2147483647; // prime
  uint64_t p2 = 1000000007; // prime
  uint64_t n = p1 * p2;
 
  auto start = std::chrono::steady_clock::now();
  auto factors = pollard_rho(n);
  auto end = std::chrono::steady_clock::now();
  
  auto duration = std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count();
  
  EXPECT_EQ(factors.size(), 2);
  EXPECT_TRUE(std::find(factors.begin(), factors.end(), p1) != factors.end());
  EXPECT_TRUE(std::find(factors.begin(), factors.end(), p2) != factors.end());
  
  EXPECT_LE(duration, 500) << "Pollard-Rho performance regression detected";
 
}
 
TEST(MathNT, ModularCombinatorics)
{
  ModularCombinatorics mc(10, 1000000007);
  EXPECT_EQ(mc.nCk(5, 2), 10);
  EXPECT_EQ(mc.nCk(5, 0), 1);
  EXPECT_EQ(mc.nCk(5, 6), 0);
  EXPECT_EQ(mc.nCk(0, 0), 1);
  EXPECT_EQ(mc.nCk(10, 5), 252);
  
  // Bounds check
  EXPECT_THROW(mc.nCk(11, 2), std::out_of_range);
 
  // Lucas Theorem test
  ModularCombinatorics mc_small(10, 3); // Modulo 3
  // C(5, 2) = 10 = 1 mod 3
  EXPECT_EQ(mc_small.lucas_nCk(5, 2), 1);
  EXPECT_EQ(mc_small.lucas_nCk(5, 0), 1);
  EXPECT_EQ(mc_small.lucas_nCk(0, 0), 1);
}
 
TEST(MathNT, ModularLinalg)
{
  Array<Array<uint64_t>> m_data;
  m_data.append(Array<uint64_t>({1, 2}));
  m_data.append(Array<uint64_t>({3, 4}));
 
  ModularMatrix mat(m_data, 5); // modulo 5
  // det = 1*4 - 2*3 = 4 - 6 = -2 = 3 mod 5
  EXPECT_EQ(mat.determinant(), 3);
 
  auto inv_opt = mat.inverse();
  ASSERT_TRUE(inv_opt.has_value());
  auto inv_mat = inv_opt->get();
  
  // Check A^-1 * A = I
  EXPECT_EQ((inv_mat[0][0] * 1 + inv_mat[0][1] * 3) % 5, 1);
  EXPECT_EQ((inv_mat[0][0] * 2 + inv_mat[0][1] * 4) % 5, 0);
  EXPECT_EQ((inv_mat[1][0] * 1 + inv_mat[1][1] * 3) % 5, 0);
  EXPECT_EQ((inv_mat[1][0] * 2 + inv_mat[1][1] * 4) % 5, 1);
}
 
TEST(MathNT, ModularSparseMatrix)
{
  // Sparse matrix with DynMatrix
  DynMatrix<uint64_t> m_data(3, 3, 0);
  m_data.write(0, 0, 2);
  m_data.write(1, 1, 3);
  m_data.write(2, 2, 4);
 
  ModularSparseMatrix mat(m_data, 7); // modulo 7
  // det = 2*3*4 = 24 = 3 mod 7
  EXPECT_EQ(mat.determinant(), 3);
 
  auto inv_opt = mat.inverse();
  ASSERT_TRUE(inv_opt.has_value());
  auto inv_mat = inv_opt->get();
 
  // Inverses of 2, 3, 4 mod 7 are 4, 5, 2
  EXPECT_EQ(inv_mat.read(0, 0), 4);
  EXPECT_EQ(inv_mat.read(1, 1), 5);
  EXPECT_EQ(inv_mat.read(2, 2), 2);
  EXPECT_EQ(inv_mat.read(0, 1), 0);
}
 
TEST(MathNT, ModularSparseMatrixRowSwap)
{
  // Matrix that requires a row swap for pivoting
  // [ 0 1 ]
  // [ 1 1 ] mod 5
  DynMatrix<uint64_t> m_data(2, 2, 0);
  m_data.write(0, 1, 1);
  m_data.write(1, 0, 1);
  m_data.write(1, 1, 1);
 
  ModularSparseMatrix mat(m_data, 5);
  // det = 0*1 - 1*1 = -1 = 4 mod 5
  EXPECT_EQ(mat.determinant(), 4);
 
  auto inv_opt = mat.inverse();
  ASSERT_TRUE(inv_opt.has_value());
  auto inv_mat = inv_opt->get();
 
  // Check inverse: [ 4 1 ] [ 0 1 ] = [ 1 0 ]
  //                [ 1 0 ] [ 1 1 ] = [ 0 1 ]
  EXPECT_EQ(inv_mat.read(0, 0), 4);
  EXPECT_EQ(inv_mat.read(0, 1), 1);
  EXPECT_EQ(inv_mat.read(1, 0), 1);
  EXPECT_EQ(inv_mat.read(1, 1), 0);
}
 
TEST(MathNT, ModularSparseMatrixSingular)
{
  // Singular matrix
  // [ 1 2 ]
  // [ 2 4 ] mod 7
  DynMatrix<uint64_t> m_data(2, 2, 0);
  m_data.write(0, 0, 1);
  m_data.write(0, 1, 2);
  m_data.write(1, 0, 2);
  m_data.write(1, 1, 4);
 
  ModularSparseMatrix mat(m_data, 7);
  EXPECT_EQ(mat.determinant(), 0);
  EXPECT_FALSE(mat.inverse().has_value());
}