using System;
using System.Buffers.Binary;
using BenchmarkDotNet.Attributes;
using BenchmarkDotNet.Jobs;
using System.Numerics;
using PerfectNumbers.Core;

namespace EvenPerfectBitScanner.Benchmarks;

/// <remarks>
/// Benchmark results collected on AMD Ryzen 5 5625U (.NET 8.0, launchCount: 1, warmupCount: 1, iterationCount: 5):
/// Small sample (~1e6 random odd moduli)
/// - MontgomeryWithoutCycle: 35.41 µs (baseline)
/// - MontgomeryWithPrecomputedCycle: 25.81 µs (0.73× baseline)
/// - MontgomeryWithGpuCycleComputation: 54.09 ms (1,527× baseline, includes GPU cycle calculation)
/// Large sample (Mersenne-like moduli from 2^48-1 to 2^63-1)
/// - MontgomeryWithoutCycle: 117.33 µs (baseline)
/// - MontgomeryWithPrecomputedCycle: 9.12 µs (0.08× baseline)
/// - MontgomeryWithGpuCycleComputation: 12.91 µs (0.11× baseline)
/// </remarks>
[MemoryDiagnoser]
[SimpleJob(RuntimeMoniker.Net80, launchCount: 1, warmupCount: 1, iterationCount: 5)]
public class Pow2MontgomeryModBenchmarks
{
    private const int SampleCount = 256;
    private const ulong OneShiftedLeft63 = 1UL << 63;
    private const long OneShiftedLeft60 = 1L << 60;

    private readonly MontgomeryDivisorData[] _smallDivisors = new MontgomeryDivisorData[SampleCount];
    private readonly MontgomeryDivisorData[] _largeDivisors = new MontgomeryDivisorData[SampleCount];
    private readonly MontgomeryDivisorData[] _veryLargeDivisors = new MontgomeryDivisorData[SampleCount];
    private readonly UInt128[] _wideModuli = new UInt128[SampleCount];
    private readonly ulong[] _smallExponents = new ulong[SampleCount];
    private readonly ulong[] _largeExponents = new ulong[SampleCount];
    private readonly ulong[] _veryLargeExponents = new ulong[SampleCount];
    private readonly ulong[] _smallCycles = new ulong[SampleCount];
    private readonly ulong[] _largeCycles = new ulong[SampleCount];
    private readonly ulong[] _veryLargeCycles = new ulong[SampleCount];
    private readonly UInt128[] _wideCycles = new UInt128[SampleCount];

    private readonly Random _random = new(13);
    private readonly Random _heuristicRandom = new(113);
    private ulong? _previousPrimeOrder;
    private UInt128? _previousWidePrimeOrder;

    public enum InputScale
    {
        Small,
        Large,
        VeryLarge
    }

    [ParamsAllValues]
    public InputScale Scale { get; set; }

    [GlobalSetup]
    public void Setup()
    {
        for (int i = 0; i < SampleCount; i++)
        {
#if DEBUG
            Console.WriteLine($"Generating sample {i}");
#endif
            ulong smallModulus = NextSmallOddModulus();
            _smallDivisors[i] = CreateMontgomeryDivisorData(smallModulus);
            _smallExponents[i] = NextSmallExponent();
            _smallCycles[i] = MersenneDivisorCycles.CalculateCycleLength(smallModulus, MontgomeryDivisorData.FromModulus(smallModulus));

            (ulong largeModulus, ulong largeCycle) = NextLargeModulusAndCycle();
            _largeDivisors[i] = CreateMontgomeryDivisorData(largeModulus);
            _largeExponents[i] = NextLargeExponent();
            _largeCycles[i] = largeCycle;

            ulong veryLargeModulus = NextVeryLargeOddModulus();
            _veryLargeDivisors[i] = CreateMontgomeryDivisorData(veryLargeModulus);
            _veryLargeExponents[i] = NextVeryLargeExponent();
#if DEBUG
            Console.WriteLine($"Calculating cycle length {veryLargeModulus}");
#endif
            _veryLargeCycles[i] = CalculateCycleLengthWithHeuristics(veryLargeModulus);

            Console.WriteLine($"Generating wide sample {i}");
            UInt128 wideModulus = NextWideOddModulus();
            _wideModuli[i] = wideModulus;
            _wideCycles[i] = CalculateCycleLengthWithHeuristics(wideModulus);
        }
    }

    /// <summary>
    /// Baseline right-to-left Montgomery ladder; measured 36.36 μs on the small sample set and 117.32 μs on the large one.
    /// </summary>
    [Benchmark(Baseline = true)]
    public ulong BaselineCpu()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= exponents[i].Pow2MontgomeryModWindowedCpu(divisors[i], keepMontgomery: false);
        }

        return checksum;
    }

    /// <summary>
    /// Baseline right-to-left Montgomery ladder; measured ??.?? μs on the small sample set and ??.?? μs on the large one.
    /// </summary>
    [Benchmark]
    public ulong BaselineGpu()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= exponents[i].Pow2MontgomeryModWindowedGpu(divisors[i], keepMontgomery: false);
        }

        return checksum;
    }

    /// <summary>
    /// Uses a known divisor cycle to fold the exponent first, dropping runtimes to 26.04 μs on small inputs (0.72× baseline) and 9.53 μs on large inputs (0.08× baseline).
    /// </summary>
    [Benchmark]
    public ulong BaselineWithKnownCycleCpu()
    {
        GetData(out var exponents, out var divisors, out var cycles);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycles[i], divisors[i]);
        }

        return checksum;
    }

    /// <summary>
    /// Uses a known divisor cycle to fold the exponent first, dropping runtimes to 26.04 μs on small inputs (0.72× baseline) and 9.53 μs on large inputs (0.08× baseline).
    /// </summary>
    [Benchmark]
    public ulong BaselineWithKnownCycleGpu()
    {
        GetData(out var exponents, out var divisors, out var cycles);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycles[i], divisors[i]);
        }

        return checksum;
    }

    /// <summary>
    /// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
    /// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
    /// </summary>
    // [Benchmark]
    public ulong MontgomeryWithGpuCycleComputationCpu()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
            checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycle, divisors[i]);
        }

        return checksum;
    }

    /// <summary>
    /// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
    /// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
    /// </summary>
    // [Benchmark]
    public ulong MontgomeryWithGpuCycleComputationGpu()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
            checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycle, divisors[i]);
        }

        return checksum;
    }

    [Benchmark]
    public ulong MontgomeryWithHeuristicCycleComputationCpu()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
            checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycle, divisors[i]);
        }

        return checksum;
    }

    // [Benchmark]
    public ulong MontgomeryWithHeuristicCycleComputationGpu()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
            checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycle, divisors[i]);
        }

        return checksum;
    }

    // [Benchmark]
    public UInt128 HeuristicWideCycleComputation()
    {
        UInt128 checksum = UInt128.Zero;

        for (int i = 0; i < SampleCount; i++)
        {
            UInt128 cycle = CalculateCycleLengthWithHeuristics(_wideModuli[i]);
            _wideCycles[i] = cycle;
            checksum ^= cycle;
        }

        return checksum;
    }

    /// <summary>
    /// Left-to-right Montgomery scan that trails the baseline: 39.11 μs on small inputs (1.08×) and 126.38 μs on large ones (1.08×).
    /// </summary>
    [Benchmark]
    public ulong LeftToRight()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= Pow2MontgomeryModLeftToRight(exponents[i], divisors[i]);
        }

        return checksum;
    }

    /// <summary>
    /// Processes four exponent bits per loop, finishing at 38.74 μs on small cases (1.07× baseline) and 120.11 μs on large ones (1.02×).
    /// </summary>
    [Benchmark]
    public ulong Batched4()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= Pow2MontgomeryModBatched4(exponents[i], divisors[i]);
        }

        return checksum;
    }

    /// <summary>
    /// Windowed Montgomery ladder (width 5) that lags behind the baseline at 52.82 μs on small samples (1.45×) and 124.13 μs on large samples (1.06×).
    /// </summary>
    [Benchmark]
    public ulong SlidingWindow()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= Pow2MontgomeryModSlidingWindow(exponents[i], divisors[i]);
        }

        return checksum;
    }

    /// <summary>
    /// Classic binary ladder without Montgomery reduction; runs 24.75 μs on small inputs (0.68× baseline) but collapses to 295.29 μs on large ones (2.52×).
    /// </summary>
    [Benchmark]
    public ulong BinaryMod()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= Pow2ModBinary(exponents[i], divisors[i].Modulus);
        }

        return checksum;
    }

    /// <summary>
    /// Precomputes all squarings once; 30.18 μs on small inputs (0.83× baseline) but 289.80 μs on large ones (2.47×).
    /// </summary>
    [Benchmark]
    public ulong PrecomputedTableMod()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= Pow2ModPrecomputedTable(exponents[i], divisors[i].Modulus);
        }

        return checksum;
    }

    /// <summary>
    /// Relies on <see cref="BigInteger.ModPow"/>; fastest on small inputs at 17.21 μs (0.47× baseline) but slowest on large ones at 562.78 μs (4.80×).
    /// </summary>
    [Benchmark]
    public ulong BigIntegerMod()
    {
        GetData(out var exponents, out var divisors, out _);
        ulong checksum = 0UL;

        for (int i = 0; i < SampleCount; i++)
        {
            checksum ^= Pow2ModBigInteger(exponents[i], divisors[i].Modulus);
        }

        return checksum;
    }

    private void GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles)
    {
        switch (Scale)
        {
            case InputScale.Small:
                exponents = _smallExponents;
                divisors = _smallDivisors;
                cycles = _smallCycles;
                break;
            case InputScale.Large:
                exponents = _largeExponents;
                divisors = _largeDivisors;
                cycles = _largeCycles;
                break;
            case InputScale.VeryLarge:
                exponents = _veryLargeExponents;
                divisors = _veryLargeDivisors;
                cycles = _veryLargeCycles;
                break;
            default:
                throw new ArgumentOutOfRangeException(nameof(Scale), Scale, null);
        }
    }

    private ulong NextSmallExponent() => (ulong)_random.NextInt64(1L, 1_000_000L);

    private ulong NextLargeExponent() => (ulong)_random.NextInt64(OneShiftedLeft60, long.MaxValue);

    private ulong NextVeryLargeExponent()
    {
        Span<byte> buffer = stackalloc byte[8];
        _heuristicRandom.NextBytes(buffer);
        ulong value = checked(BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63);
        return value;
    }

    private ulong NextSmallOddModulus()
    {
        ulong value = (ulong)_random.NextInt64(3L, 1_000_000L);
        return value | 1UL;
    }

    private (ulong modulus, ulong cycleLength) NextLargeModulusAndCycle()
    {
        int bitLength = _random.Next(48, 64);
        ulong modulus = (1UL << bitLength) - 1UL;
        return (modulus, (ulong)bitLength);
    }

    private ulong NextVeryLargeOddModulus()
    {
        Span<byte> buffer = stackalloc byte[8];
        _heuristicRandom.NextBytes(buffer);
        ulong value = BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63 | 1UL;
        return value;
    }

    private UInt128 NextWideOddModulus()
    {
        Span<byte> buffer = stackalloc byte[16];
        _heuristicRandom.NextBytes(buffer);

        ulong low = BinaryPrimitives.ReadUInt64LittleEndian(buffer);
        Span<byte> highSlice = buffer.Slice(8, 8);
        ulong high = BinaryPrimitives.ReadUInt64LittleEndian(highSlice) | (1UL << 63);

        UInt128 value = ((UInt128)high << 64) | low;
        return value | UInt128.One;
    }

    private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
    {
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL, 0UL);
        }

        ulong nPrime = ComputeMontgomeryNPrime(modulus);
        ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
        ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);

        return new MontgomeryDivisorData(
            modulus,
            nPrime,
            montgomeryOne,
            montgomeryTwo,
            montgomeryTwoSquared);
    }

    private ulong CalculateCycleLengthWithHeuristics(ulong modulus, ulong fallbackOrder = 0UL)
    {
        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(modulus);
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
        }

#if DEBUG
        Console.WriteLine("Trying heuristic. Prime order calculation");
#endif
        ulong order = PrimeOrderCalculator.Calculate(
            modulus,
            _previousPrimeOrder,
            divisorData,
            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
            PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);

        if (order != 0UL)
        {
            _previousPrimeOrder = order;
            return order;
        }

        _previousPrimeOrder = null;

        Console.WriteLine($"Heuristic failed for {modulus}, falling back to full cycle calculation");
        return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
    }

    private UInt128 CalculateCycleLengthWithHeuristics(UInt128 modulus)
    {
        if (modulus <= UInt128.One || (modulus & UInt128.One) == UInt128.Zero)
        {
            return MersenneDivisorCycles.GetCycle(modulus);
        }

#if DEBUG
        Console.WriteLine("Trying heuristic. Wide prime order calculation");
#endif
        UInt128 order = PrimeOrderCalculator.Calculate(
            modulus,
            _previousWidePrimeOrder,
            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
            PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);

        if (order != UInt128.Zero)
        {
            _previousWidePrimeOrder = order;
            return order;
        }

        _previousWidePrimeOrder = null;

        Console.WriteLine($"Wide heuristic failed for {modulus}, falling back to full cycle calculation");
        return MersenneDivisorCycles.GetCycle(modulus);
    }

    private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);

    private static ulong ComputeMontgomeryNPrime(ulong modulus)
    {
        ulong inv = modulus;
        inv *= unchecked(2UL - modulus * inv);
        inv *= unchecked(2UL - modulus * inv);
        inv *= unchecked(2UL - modulus * inv);
        inv *= unchecked(2UL - modulus * inv);
        inv *= unchecked(2UL - modulus * inv);
        inv *= unchecked(2UL - modulus * inv);
        return unchecked(0UL - inv);
    }

    private static ulong Pow2MontgomeryModLeftToRight(ulong exponent, in MontgomeryDivisorData divisor)
    {
        ulong modulus = divisor.Modulus;
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return 0UL;
        }

        ulong result = divisor.MontgomeryOne;
        ulong baseVal = divisor.MontgomeryTwo;
        ulong nPrime = divisor.NPrime;

        if (exponent == 0UL)
        {
            return result.MontgomeryMultiply(1UL, modulus, nPrime);
        }

        int msbIndex = 63 - BitOperations.LeadingZeroCount(exponent);

        for (int bitIndex = msbIndex; bitIndex >= 0; bitIndex--)
        {
            result = result.MontgomeryMultiply(result, modulus, nPrime);

            if (((exponent >> bitIndex) & 1UL) != 0UL)
            {
                result = result.MontgomeryMultiply(baseVal, modulus, nPrime);
            }
        }

        return result.MontgomeryMultiply(1UL, modulus, nPrime);
    }

    private static ulong Pow2MontgomeryModBatched4(ulong exponent, in MontgomeryDivisorData divisor)
    {
        ulong modulus = divisor.Modulus;
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return 0UL;
        }

        ulong result = divisor.MontgomeryOne;
        ulong baseVal = divisor.MontgomeryTwo;
        ulong nPrime = divisor.NPrime;
        ulong remainingExponent = exponent;

        while (remainingExponent != 0UL)
        {
            ulong nibble = remainingExponent & 0xFUL;

            ulong base0 = baseVal;
            ulong base1 = base0.MontgomeryMultiply(base0, modulus, nPrime);
            ulong base2 = base1.MontgomeryMultiply(base1, modulus, nPrime);
            ulong base3 = base2.MontgomeryMultiply(base2, modulus, nPrime);

            if ((nibble & 1UL) != 0UL)
            {
                result = result.MontgomeryMultiply(base0, modulus, nPrime);
            }

            if ((nibble & 2UL) != 0UL)
            {
                result = result.MontgomeryMultiply(base1, modulus, nPrime);
            }

            if ((nibble & 4UL) != 0UL)
            {
                result = result.MontgomeryMultiply(base2, modulus, nPrime);
            }

            if ((nibble & 8UL) != 0UL)
            {
                result = result.MontgomeryMultiply(base3, modulus, nPrime);
            }

            baseVal = base3.MontgomeryMultiply(base3, modulus, nPrime);
            remainingExponent >>= 4;
        }

        return result.MontgomeryMultiply(1UL, modulus, nPrime);
    }

    private static ulong Pow2MontgomeryModSlidingWindow(ulong exponent, in MontgomeryDivisorData divisor)
    {
        ulong modulus = divisor.Modulus;
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return 0UL;
        }

        ulong nPrime = divisor.NPrime;
        ulong result = divisor.MontgomeryOne;
        ulong baseVal = divisor.MontgomeryTwo;

        if (exponent == 0UL)
        {
            return result.MontgomeryMultiply(1UL, modulus, nPrime);
        }

        const int WindowSize = 5;
        Span<ulong> oddPowers = stackalloc ulong[1 << (WindowSize - 1)];
        oddPowers[0] = baseVal;
        ulong baseSquared = baseVal.MontgomeryMultiply(baseVal, modulus, nPrime);
        for (int i = 1; i < oddPowers.Length; i++)
        {
            oddPowers[i] = oddPowers[i - 1].MontgomeryMultiply(baseSquared, modulus, nPrime);
        }

        int bitIndex = 63 - BitOperations.LeadingZeroCount(exponent);

        while (bitIndex >= 0)
        {
            if (((exponent >> bitIndex) & 1UL) == 0UL)
            {
                result = result.MontgomeryMultiply(result, modulus, nPrime);
                bitIndex--;
                continue;
            }

            int windowStart = Math.Max(bitIndex - WindowSize + 1, 0);
            ulong windowValue = (exponent >> windowStart) & ((1UL << (bitIndex - windowStart + 1)) - 1UL);

            while ((windowValue & 1UL) == 0UL)
            {
                windowValue >>= 1;
                windowStart++;
            }

            int squares = bitIndex - windowStart + 1;
            for (int i = 0; i < squares; i++)
            {
                result = result.MontgomeryMultiply(result, modulus, nPrime);
            }

            result = result.MontgomeryMultiply(oddPowers[(int)(windowValue >> 1)], modulus, nPrime);
            bitIndex = windowStart - 1;
        }

        return result.MontgomeryMultiply(1UL, modulus, nPrime);
    }

    private static ulong Pow2ModBinary(ulong exponent, ulong modulus)
    {
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return 0UL;
        }

        ulong result = 1UL % modulus;
        ulong baseVal = 2UL % modulus;
        ulong remainingExponent = exponent;

        while (remainingExponent > 0UL)
        {
            if ((remainingExponent & 1UL) != 0UL)
            {
                result = MultiplyMod(result, baseVal, modulus);
            }

            remainingExponent >>= 1;
            if (remainingExponent == 0UL)
            {
                break;
            }

            baseVal = MultiplyMod(baseVal, baseVal, modulus);
        }

        return result;
    }

    private static ulong Pow2ModPrecomputedTable(ulong exponent, ulong modulus)
    {
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return 0UL;
        }

        if (exponent == 0UL)
        {
            return 1UL % modulus;
        }

        Span<ulong> powers = stackalloc ulong[64];
        powers[0] = 2UL % modulus;
        int highestBit = 63 - BitOperations.LeadingZeroCount(exponent);

        for (int index = 1; index <= highestBit; index++)
        {
            powers[index] = MultiplyMod(powers[index - 1], powers[index - 1], modulus);
        }

        ulong result = 1UL % modulus;
        ulong remainingExponent = exponent;
        int bitIndex = 0;

        while (remainingExponent > 0UL)
        {
            if ((remainingExponent & 1UL) != 0UL)
            {
                result = MultiplyMod(result, powers[bitIndex], modulus);
            }

            remainingExponent >>= 1;
            bitIndex++;
        }

        return result;
    }

    private static ulong Pow2ModBigInteger(ulong exponent, ulong modulus)
    {
        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
        {
            return 0UL;
        }

        BigInteger mod = modulus;
        BigInteger result = BigInteger.ModPow(2, exponent, mod);
        return (ulong)result;
    }

    private static ulong MultiplyMod(ulong x, ulong y, ulong modulus)
    {
        UInt128 product = (UInt128)x * y;
        return (ulong)(product % modulus);
    }
}