using PerfectNumbers.Core.Gpu.Accelerators;

namespace PerfectNumbers.Core;

public class MersenneNumberLucasLehmerCpuTester
{
	public bool IsPrime(PrimeOrderCalculatorAccelerator gpu, ulong exponent)
	{
		// Early rejections aligned with incremental/order sieves, but safe for small p:
		// - If 3 | p and p != 3, then 7 | M_p -> composite.
		// - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast.
		// - If p is divisible by divisors specific to numbers ending with 1 or 7, reject fast.
		// TODO: Replace these `%` checks with Mod3/Mod5/Mod7/Mod11 helpers once Lucas–Lehmer CPU filtering
		// shares the benchmarked bitmask implementations and avoids slow modulo instructions in the hot path.
		if (
			((exponent % 3UL) == 0UL && exponent != 3UL) ||
			((exponent % 5UL) == 0UL && exponent != 5UL) ||
			((exponent % 7UL) == 0UL && exponent != 7UL) ||
			((exponent % 11UL) == 0UL && exponent != 11UL)
		)
		{
			return false;
		}

		if ((exponent & 3UL) == 1UL && exponent.SharesFactorWithExponentMinusOneCpu())
		{
			return false;
		}

		UInt128 s = UInt128Numbers.Four, two = UInt128Numbers.Two,
			m = (UInt128.One << (int)exponent) - UInt128.One;

		UInt128 limit = exponent - UInt128Numbers.Two;
		for (UInt128 i = UInt128.Zero; i < limit; i++)
		{
			// Lucas–Lehmer squares the evolving residue, so we stay on the Montgomery powmod path rather than the pow2-specific helper.
			s = s.PowModWithCycle(two, MersenneDivisorCycles.GetCycleCpu(m)) - two;
			if (s < UInt128.Zero)
			{
				s += m;
			}
		}

		return s == UInt128.Zero;
	}
}