primality.H

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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
  in the Software without restriction, including without limitation the rights
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*/
 
# ifndef PRIMALITY_H
# define PRIMALITY_H
 
# include <cstdint>
# include <initializer_list>
# include <modular_arithmetic.H>
 
namespace Aleph
{
 
namespace detail
{
[[nodiscard]] inline bool check_composite(uint64_t n, uint64_t a,
                                           uint64_t d, int s) noexcept
{
  uint64_t x = mod_exp(a, d, n);
  if (x == 1 or x == n - 1)
    return false;
  for (int r = 1; r < s; r++)
    {
      x = mod_mul(x, x, n);
      if (x == n - 1)
        return false;
    }
  return true;
}
} // namespace detail
 
[[nodiscard]] inline bool miller_rabin(uint64_t n) noexcept
{
  if (n < 2) return false;
  if (n == 2 or n == 3) return true;
  if (n % 2 == 0) return false;
 
  uint64_t d = n - 1;
  int s = 0;
  while ((d & 1) == 0)
    {
      d >>= 1;
      s++;
    }
 
  // These bases are sufficient for deterministic testing up to 2^64.
  // Using Jim Sinclair's minimal 7-witness set for 64-bit range.
  for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022})
    {
      if (n <= a)
        break;
      if (detail::check_composite(n, a, d, s))
        return false;
    }
  return true;
}
 
} // namespace Aleph
 
# endif // PRIMALITY_H