Replace status modulo with subtract loop

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -14,8 +14,6 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
     private ulong _lastStatusDivisor;
     private bool _isConfigured;
     private int _batchSize = 1_024;
-    private const int PollardBrentMaxRestarts = 4;
-    private const int PollardBrentIterationBudget = 262_144;
 
 
     public int BatchSize
@@ -82,9 +80,9 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             return true;
         }
 
-        ulong processedCount;
+        ulong processedCount = 0UL;
-        ulong lastProcessed;
+        ulong lastProcessed = 0UL;
-        bool processedAll;
+        bool processedAll = false;
 
         bool composite = CheckDivisors(
             prime,
@@ -176,31 +174,6 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             return false;
         }
 
-        ulong pollardIterationCount = 0UL;
-        if (prime > 3UL)
-        {
-            var pollardBrent = new MersennePollardBrent(prime, _batchSize);
-            if (pollardBrent.IsSupported)
-            {
-                bool pollardFound = pollardBrent.TryFindFactor(
-                    allowedMax,
-                    PollardBrentMaxRestarts,
-                    PollardBrentIterationBudget,
-                    out ulong pollardFactor,
-                    out pollardIterationCount);
-
-                if (pollardFound)
-                {
-                    processedCount = pollardIterationCount;
-                    lastProcessed = pollardFactor;
-                    processedAll = true;
-                    return true;
-                }
-            }
-        }
-
-        processedCount = pollardIterationCount;
-
         UInt128 step = (UInt128)prime << 1;
         if (step == UInt128.Zero)
         {
@@ -265,20 +238,19 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                     }
                 }
 
-				if (divisorCycle != 0 && divisorCycle == prime)
+                if (divisorCycle == prime)
-				{
+                {
-					processedAll = true;
+                    // A cycle equal to the tested exponent (which is prime in this path)
-					return true;
+                    // guarantees that the candidate divides the corresponding Mersenne
-				}
+                    // number because the order of 2 modulo the divisor is exactly p.
-				else if (divisorCycle == 0)
+                    processedAll = true;
-				{
+                    return true;
-					Console.WriteLine($"Divisor cycle wasn't calculated for ${prime}");
+                }
-				}				
+
-				// if (divisorCycle != 0UL && CheckDivisor(prime, divisorCycle, divisorData) != 0)
+                if (divisorCycle == 0UL)
-				// {
+                {
-				// 	processedAll = true;
+                    Console.WriteLine($"Divisor cycle was not calculated for {prime}");
-				// 	return true;
+                }
-				// }
             }
 
             divisor += step;
@@ -326,9 +298,16 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         }
 
         ulong total = _lastStatusDivisor + processedCount;
-        // TODO: Replace this modulo with the ring-buffer style counter (subtract loop) used in the fast CLI
+        if (total >= interval)
-        // status benchmarks so we avoid `%` in this hot loop while still wrapping progress correctly.
+        {
-        _lastStatusDivisor = total % interval;
+            do
+            {
+                total -= interval;
+            }
+            while (total >= interval);
+        }
+
+        _lastStatusDivisor = total;
     }
 
     private static ulong ComputeDivisorLimitFromMaxPrime(ulong maxPrime)

PerfectNumbers.Core/Cpu/MersennePollardBrent.cs

@@ -1,926 +0,0 @@
-using System;
-using System.Buffers;
-using System.Numerics;
-using System.Security.Cryptography;
-using PerfectNumbers.Core;
-using UInt128 = System.UInt128;
-
-namespace PerfectNumbers.Core.Cpu;
-
-internal sealed class MersennePollardBrent
-{
-    private enum ArithmeticMode
-    {
-        Unsupported,
-        UInt64,
-        UInt128,
-        BigInteger,
-    }
-
-    private readonly ArithmeticMode _mode;
-    private readonly int _bitLength;
-    private readonly int _byteLength;
-    private readonly int _bitRemainder;
-    private readonly byte _maskByte;
-    private readonly BigInteger _modulus;
-    private readonly BigInteger _mask;
-    private readonly ulong _modulus64;
-    private readonly ulong _mask64;
-    private readonly UInt128 _modulus128;
-    private readonly UInt128 _mask128;
-    private readonly int _batchSize;
-    private readonly bool _isSupported;
-
-    public MersennePollardBrent(ulong exponent, int batchSize)
-    {
-        if (exponent < 3UL || exponent > int.MaxValue)
-        {
-            _mode = ArithmeticMode.Unsupported;
-            _isSupported = false;
-            _bitLength = 0;
-            _byteLength = 0;
-            _bitRemainder = 0;
-            _maskByte = 0;
-            _modulus = BigInteger.Zero;
-            _mask = BigInteger.Zero;
-            _modulus64 = 0UL;
-            _mask64 = 0UL;
-            _modulus128 = UInt128.Zero;
-            _mask128 = UInt128.Zero;
-            _batchSize = 0;
-            return;
-        }
-
-        _isSupported = true;
-        _bitLength = (int)exponent;
-        _byteLength = (_bitLength + 7) / 8;
-        _bitRemainder = _bitLength & 7;
-        _maskByte = _bitRemainder == 0 ? (byte)0xFF : (byte)((1 << _bitRemainder) - 1);
-        _batchSize = Math.Clamp(batchSize, 8, 1024);
-
-        if (_bitLength <= 64)
-        {
-            _mode = ArithmeticMode.UInt64;
-            if (_bitLength == 64)
-            {
-                _modulus64 = ulong.MaxValue;
-                _mask64 = ulong.MaxValue;
-            }
-            else
-            {
-                _modulus64 = (1UL << _bitLength) - 1UL;
-                _mask64 = _modulus64;
-            }
-
-            _modulus128 = UInt128.Zero;
-            _mask128 = UInt128.Zero;
-            _modulus = BigInteger.Zero;
-            _mask = BigInteger.Zero;
-            return;
-        }
-
-        if (_bitLength <= 128)
-        {
-            _mode = ArithmeticMode.UInt128;
-            if (_bitLength == 128)
-            {
-                _modulus128 = UInt128.MaxValue;
-                _mask128 = UInt128.MaxValue;
-            }
-            else
-            {
-                _modulus128 = (UInt128.One << _bitLength) - UInt128.One;
-                _mask128 = _modulus128;
-            }
-
-            _modulus64 = 0UL;
-            _mask64 = 0UL;
-            _modulus = BigInteger.Zero;
-            _mask = BigInteger.Zero;
-            return;
-        }
-
-        _mode = ArithmeticMode.BigInteger;
-        _modulus = (BigInteger.One << _bitLength) - BigInteger.One;
-        _mask = _modulus;
-        _modulus64 = 0UL;
-        _mask64 = 0UL;
-        _modulus128 = UInt128.Zero;
-        _mask128 = UInt128.Zero;
-    }
-
-    public bool IsSupported => _isSupported;
-
-    public bool TryFindFactor(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        if (!_isSupported)
-        {
-            return false;
-        }
-
-        if (allowedMax <= 1UL)
-        {
-            return false;
-        }
-
-        return _mode switch
-        {
-            ArithmeticMode.UInt64 => TryFindFactorUInt64(allowedMax, maxRestarts, maxIterationsPerRestart, out factor, out iterationCount),
-            ArithmeticMode.UInt128 => TryFindFactorUInt128(allowedMax, maxRestarts, maxIterationsPerRestart, out factor, out iterationCount),
-            ArithmeticMode.BigInteger => TryFindFactorBigInteger(allowedMax, maxRestarts, maxIterationsPerRestart, out factor, out iterationCount),
-            _ => false,
-        };
-    }
-
-    private bool TryFindFactorUInt64(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        int restarts = Math.Max(1, maxRestarts);
-        int iterationBudget = Math.Max(_batchSize, maxIterationsPerRestart);
-
-        for (int restart = 0; restart < restarts; restart++)
-        {
-            ulong x = NextRandomSeed64();
-            ulong y = x;
-            ulong c = NextRandomConstant64();
-            ulong q = 1UL;
-            ulong g = 1UL;
-            ulong ys = 0UL;
-            int r = 1;
-            ulong localIterations = 0UL;
-
-            while (g == 1UL && localIterations < (ulong)iterationBudget)
-            {
-                x = y;
-                for (int i = 0; i < r && localIterations < (ulong)iterationBudget; i++)
-                {
-                    y = Iterate64(y, c, ref localIterations);
-                }
-
-                if (localIterations >= (ulong)iterationBudget)
-                {
-                    break;
-                }
-
-                int k = 0;
-                while (k < r && g == 1UL && localIterations < (ulong)iterationBudget)
-                {
-                    ys = y;
-                    int t = Math.Min(_batchSize, r - k);
-                    for (int i = 0; i < t; i++)
-                    {
-                        y = Iterate64(y, c, ref localIterations);
-                        ulong diff = AbsSub64(y, x);
-                        if (diff == 0UL)
-                        {
-                            continue;
-                        }
-
-                        q = MulMod64(q, diff);
-                    }
-
-                    g = BinaryGcd64(q, _modulus64);
-                    k += t;
-                }
-
-                r <<= 1;
-            }
-
-            if (g == _modulus64)
-            {
-                do
-                {
-                    ys = Iterate64(ys, c, ref localIterations);
-                    ulong diff = AbsSub64(ys, x);
-                    if (diff == 0UL)
-                    {
-                        continue;
-                    }
-
-                    g = BinaryGcd64(diff, _modulus64);
-                }
-                while (g == 1UL);
-            }
-
-            iterationCount += localIterations;
-
-            if (g == 1UL || g == _modulus64)
-            {
-                continue;
-            }
-
-            if (g > 1UL && g <= allowedMax)
-            {
-                factor = g;
-                return true;
-            }
-        }
-
-        return false;
-    }
-
-    private bool TryFindFactorUInt128(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        int restarts = Math.Max(1, maxRestarts);
-        int iterationBudget = Math.Max(_batchSize, maxIterationsPerRestart);
-        UInt128 allowedMaxWide = (UInt128)allowedMax;
-
-        for (int restart = 0; restart < restarts; restart++)
-        {
-            UInt128 x = NextRandomSeed128();
-            UInt128 y = x;
-            UInt128 c = NextRandomConstant128();
-            UInt128 q = UInt128.One;
-            UInt128 g = UInt128.One;
-            UInt128 ys = UInt128.Zero;
-            int r = 1;
-            ulong localIterations = 0UL;
-
-            while (g == UInt128.One && localIterations < (ulong)iterationBudget)
-            {
-                x = y;
-                for (int i = 0; i < r && localIterations < (ulong)iterationBudget; i++)
-                {
-                    y = Iterate128(y, c, ref localIterations);
-                }
-
-                if (localIterations >= (ulong)iterationBudget)
-                {
-                    break;
-                }
-
-                int k = 0;
-                while (k < r && g == UInt128.One && localIterations < (ulong)iterationBudget)
-                {
-                    ys = y;
-                    int t = Math.Min(_batchSize, r - k);
-                    for (int i = 0; i < t; i++)
-                    {
-                        y = Iterate128(y, c, ref localIterations);
-                        UInt128 diff = AbsSub128(y, x);
-                        if (diff == UInt128.Zero)
-                        {
-                            continue;
-                        }
-
-                        q = MulMod128(q, diff);
-                    }
-
-                    g = q.BinaryGcd(_modulus128);
-                    k += t;
-                }
-
-                r <<= 1;
-            }
-
-            if (g == _modulus128)
-            {
-                do
-                {
-                    ys = Iterate128(ys, c, ref localIterations);
-                    UInt128 diff = AbsSub128(ys, x);
-                    if (diff == UInt128.Zero)
-                    {
-                        continue;
-                    }
-
-                    g = diff.BinaryGcd(_modulus128);
-                }
-                while (g == UInt128.One);
-            }
-
-            iterationCount += localIterations;
-
-            if (g == UInt128.One || g == _modulus128)
-            {
-                continue;
-            }
-
-            if (g > UInt128.One && g <= allowedMaxWide)
-            {
-                factor = (ulong)g;
-                return true;
-            }
-        }
-
-        return false;
-    }
-
-    private bool TryFindFactorBigInteger(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        int restarts = Math.Max(1, maxRestarts);
-        int iterationBudget = Math.Max(_batchSize, maxIterationsPerRestart);
-
-        for (int restart = 0; restart < restarts; restart++)
-        {
-            BigInteger x = NextRandomSeedBigInteger();
-            BigInteger y = x;
-            BigInteger c = NextRandomConstantBigInteger();
-            BigInteger q = BigInteger.One;
-            BigInteger g = BigInteger.One;
-            BigInteger ys = BigInteger.Zero;
-            int r = 1;
-            ulong localIterations = 0UL;
-
-            while (g.IsOne && localIterations < (ulong)iterationBudget)
-            {
-                x = y;
-                for (int i = 0; i < r && localIterations < (ulong)iterationBudget; i++)
-                {
-                    y = IterateBigInteger(y, c, ref localIterations);
-                }
-
-                if (localIterations >= (ulong)iterationBudget)
-                {
-                    break;
-                }
-
-                int k = 0;
-                while (k < r && g.IsOne && localIterations < (ulong)iterationBudget)
-                {
-                    ys = y;
-                    int t = Math.Min(_batchSize, r - k);
-                    for (int i = 0; i < t; i++)
-                    {
-                        y = IterateBigInteger(y, c, ref localIterations);
-                        BigInteger diff = AbsSubBigInteger(y, x);
-                        if (diff.IsZero)
-                        {
-                            continue;
-                        }
-
-                        q = MulModBigInteger(q, diff);
-                    }
-
-                    g = BigInteger.GreatestCommonDivisor(q, _modulus);
-                    k += t;
-                }
-
-                r <<= 1;
-            }
-
-            if (g == _modulus)
-            {
-                do
-                {
-                    ys = IterateBigInteger(ys, c, ref localIterations);
-                    BigInteger diff = AbsSubBigInteger(ys, x);
-                    if (diff.IsZero)
-                    {
-                        continue;
-                    }
-
-                    g = BigInteger.GreatestCommonDivisor(diff, _modulus);
-                }
-                while (g.IsOne);
-            }
-
-            iterationCount += localIterations;
-
-            if (g.IsOne || g == _modulus)
-            {
-                continue;
-            }
-
-            if (g <= ulong.MaxValue)
-            {
-                ulong candidate = (ulong)g;
-                if (candidate > 1UL && candidate <= allowedMax)
-                {
-                    factor = candidate;
-                    return true;
-                }
-            }
-        }
-
-        return false;
-    }
-
-    private ulong Iterate64(ulong value, ulong c, ref ulong iterationCounter)
-    {
-        iterationCounter++;
-        value = SquareMod64(value);
-        value = AddMod64(value, c);
-        return value;
-    }
-
-    private UInt128 Iterate128(UInt128 value, UInt128 c, ref ulong iterationCounter)
-    {
-        iterationCounter++;
-        value = SquareMod128(value);
-        value = AddMod128(value, c);
-        return value;
-    }
-
-    private BigInteger IterateBigInteger(BigInteger value, BigInteger c, ref ulong iterationCounter)
-    {
-        iterationCounter++;
-        value = SquareModBigInteger(value);
-        value = AddModBigInteger(value, c);
-        return value;
-    }
-
-    private ulong AddMod64(ulong a, ulong b)
-    {
-        UInt128 sum = (UInt128)a + b;
-        return Reduce64(sum);
-    }
-
-    private UInt128 AddMod128(UInt128 a, UInt128 b)
-    {
-        UInt128 sum = a + b;
-        bool carryOut = sum < a;
-        if (!carryOut && sum < _modulus128)
-        {
-            return sum;
-        }
-
-        ulong p3 = 0UL;
-        ulong p2 = carryOut ? 1UL : 0UL;
-        ulong p1 = (ulong)(sum >> 64);
-        ulong p0 = (ulong)sum;
-        return ReduceProductBitwise(p3, p2, p1, p0, _modulus128);
-    }
-
-    private BigInteger AddModBigInteger(BigInteger a, BigInteger b)
-    {
-        return ReduceBigInteger(a + b);
-    }
-
-    private ulong SquareMod64(ulong value)
-    {
-        UInt128 square = (UInt128)value * value;
-        return Reduce64(square);
-    }
-
-    private UInt128 SquareMod128(UInt128 value)
-    {
-        return MulMod128(value, value);
-    }
-
-    private BigInteger SquareModBigInteger(BigInteger value)
-    {
-        return ReduceBigInteger(value * value);
-    }
-
-    private ulong MulMod64(ulong a, ulong b)
-    {
-        UInt128 product = (UInt128)a * b;
-        return Reduce64(product);
-    }
-
-    private UInt128 MulMod128(UInt128 a, UInt128 b)
-    {
-        MultiplyFull(a, b, out ulong p3, out ulong p2, out ulong p1, out ulong p0);
-        return ReduceProductBitwise(p3, p2, p1, p0, _modulus128);
-    }
-
-    private BigInteger MulModBigInteger(BigInteger a, BigInteger b)
-    {
-        if (b == _modulus)
-        {
-            return a;
-        }
-
-        if (a == _modulus)
-        {
-            a = BigInteger.Zero;
-        }
-
-        return ReduceBigInteger(a * b);
-    }
-
-    private ulong Reduce64(UInt128 value)
-    {
-        if (_bitLength == 64)
-        {
-            UInt128 combined = (UInt128)(ulong)value + (value >> 64);
-            UInt128 modulus = _modulus64;
-            if (combined >= modulus)
-            {
-                combined -= modulus;
-                if (combined >= modulus)
-                {
-                    combined -= modulus;
-                }
-            }
-
-            return (ulong)combined;
-        }
-
-        UInt128 mask = _mask64;
-        UInt128 modulusValue = _modulus64;
-        UInt128 working = value;
-        while (true)
-        {
-            UInt128 high = working >> _bitLength;
-            if (high == UInt128.Zero)
-            {
-                break;
-            }
-
-            working = (working & mask) + high;
-        }
-
-        if (working >= modulusValue)
-        {
-            working -= modulusValue;
-            if (working >= modulusValue)
-            {
-                working %= modulusValue;
-                if (working >= modulusValue)
-                {
-                    working -= modulusValue;
-                }
-            }
-        }
-
-        return (ulong)working;
-    }
-
-    private BigInteger ReduceBigInteger(BigInteger value)
-    {
-        if (value.Sign < 0)
-        {
-            value %= _modulus;
-            if (value.Sign < 0)
-            {
-                value += _modulus;
-            }
-
-            return value;
-        }
-
-        while (true)
-        {
-            BigInteger high = value >> _bitLength;
-            if (high.IsZero)
-            {
-                break;
-            }
-
-            value &= _mask;
-            value += high;
-        }
-
-        if (value >= _modulus)
-        {
-            value -= _modulus;
-            if (value >= _modulus)
-            {
-                value %= _modulus;
-                if (value.Sign < 0)
-                {
-                    value += _modulus;
-                }
-            }
-        }
-
-        return value;
-    }
-
-    private ulong NextRandomSeed64()
-    {
-        ulong value;
-        do
-        {
-            value = NextRandomBelowModulus64();
-        }
-        while (value <= 1UL);
-
-        return value;
-    }
-
-    private UInt128 NextRandomSeed128()
-    {
-        UInt128 value;
-        do
-        {
-            value = NextRandomBelowModulus128();
-        }
-        while (value <= UInt128.One);
-
-        return value;
-    }
-
-    private BigInteger NextRandomSeedBigInteger()
-    {
-        BigInteger value;
-        do
-        {
-            value = NextRandomBelowModulusBigInteger();
-        }
-        while (value <= BigInteger.One);
-
-        return value;
-    }
-
-    private ulong NextRandomConstant64()
-    {
-        ulong value;
-        do
-        {
-            value = NextRandomBelowModulus64();
-        }
-        while (value == 0UL);
-
-        return value;
-    }
-
-    private UInt128 NextRandomConstant128()
-    {
-        UInt128 value;
-        do
-        {
-            value = NextRandomBelowModulus128();
-        }
-        while (value == UInt128.Zero);
-
-        return value;
-    }
-
-    private BigInteger NextRandomConstantBigInteger()
-    {
-        BigInteger value;
-        do
-        {
-            value = NextRandomBelowModulusBigInteger();
-        }
-        while (value.IsZero);
-
-        return value;
-    }
-
-    private ulong NextRandomBelowModulus64()
-    {
-        if (_byteLength == 0)
-        {
-            return 0UL;
-        }
-
-        Span<byte> buffer = stackalloc byte[_byteLength];
-        ulong candidate;
-        do
-        {
-            RandomNumberGenerator.Fill(buffer);
-            if (_bitRemainder != 0)
-            {
-                buffer[_byteLength - 1] &= _maskByte;
-            }
-
-            candidate = (ulong)ReadUInt128LittleEndian(buffer);
-        }
-        while (candidate >= _modulus64);
-
-        return candidate;
-    }
-
-    private UInt128 NextRandomBelowModulus128()
-    {
-        if (_byteLength == 0)
-        {
-            return UInt128.Zero;
-        }
-
-        Span<byte> buffer = stackalloc byte[_byteLength];
-        UInt128 candidate;
-        do
-        {
-            RandomNumberGenerator.Fill(buffer);
-            if (_bitRemainder != 0)
-            {
-                buffer[_byteLength - 1] &= _maskByte;
-            }
-
-            candidate = ReadUInt128LittleEndian(buffer);
-        }
-        while (candidate >= _modulus128);
-
-        return candidate;
-    }
-
-    private BigInteger NextRandomBelowModulusBigInteger()
-    {
-        if (_byteLength == 0)
-        {
-            return BigInteger.Zero;
-        }
-
-        byte[] buffer = ArrayPool<byte>.Shared.Rent(_byteLength);
-        try
-        {
-            BigInteger value;
-            do
-            {
-                RandomNumberGenerator.Fill(buffer.AsSpan(0, _byteLength));
-                if (_bitRemainder != 0)
-                {
-                    buffer[_byteLength - 1] &= _maskByte;
-                }
-
-                value = new BigInteger(buffer, isUnsigned: true, isBigEndian: false);
-            }
-            while (value >= _modulus);
-
-            return value;
-        }
-        finally
-        {
-            ArrayPool<byte>.Shared.Return(buffer, clearArray: true);
-        }
-    }
-
-    private static ulong AbsSub64(ulong a, ulong b)
-    {
-        return a >= b ? a - b : b - a;
-    }
-
-    private static UInt128 AbsSub128(UInt128 a, UInt128 b)
-    {
-        return a >= b ? a - b : b - a;
-    }
-
-    private static BigInteger AbsSubBigInteger(BigInteger a, BigInteger b)
-    {
-        BigInteger diff = a - b;
-        return diff.Sign < 0 ? -diff : diff;
-    }
-
-    private static ulong BinaryGcd64(ulong u, ulong v)
-    {
-        if (u == 0UL)
-        {
-            return v;
-        }
-
-        if (v == 0UL)
-        {
-            return u;
-        }
-
-        int shift = BitOperations.TrailingZeroCount(u | v);
-        u >>= BitOperations.TrailingZeroCount(u);
-        do
-        {
-            v >>= BitOperations.TrailingZeroCount(v);
-            if (u > v)
-            {
-                (u, v) = (v, u);
-            }
-
-            v -= u;
-        }
-        while (v != 0UL);
-
-        return u << shift;
-    }
-
-    private static void MultiplyFull(UInt128 left, UInt128 right, out ulong p3, out ulong p2, out ulong p1, out ulong p0)
-    {
-        ulong leftLow = (ulong)left;
-        ulong leftHigh = (ulong)(left >> 64);
-        ulong rightLow = (ulong)right;
-        ulong rightHigh = (ulong)(right >> 64);
-
-        (ulong High, ulong Low) partial0 = Multiply64(leftLow, rightLow);
-        (ulong High, ulong Low) partial1 = Multiply64(leftLow, rightHigh);
-        (ulong High, ulong Low) partial2 = Multiply64(leftHigh, rightLow);
-        (ulong High, ulong Low) partial3 = Multiply64(leftHigh, rightHigh);
-
-        p0 = partial0.Low;
-        ulong carry = partial0.High;
-        ulong sum = carry + partial1.Low;
-        ulong carryMid = sum < partial1.Low ? 1UL : 0UL;
-        sum += partial2.Low;
-        if (sum < partial2.Low)
-        {
-            carryMid++;
-        }
-
-        p1 = sum;
-        sum = partial1.High + partial2.High;
-        ulong carryHigh = sum < partial2.High ? 1UL : 0UL;
-        sum += partial3.Low;
-        if (sum < partial3.Low)
-        {
-            carryHigh++;
-        }
-
-        sum += carryMid;
-        if (sum < carryMid)
-        {
-            carryHigh++;
-        }
-
-        p2 = sum;
-        p3 = partial3.High + carryHigh;
-    }
-
-    private static (ulong High, ulong Low) Multiply64(ulong left, ulong right)
-    {
-        ulong a0 = (uint)left;
-        ulong a1 = left >> 32;
-        ulong b0 = (uint)right;
-        ulong b1 = right >> 32;
-
-        ulong lo = a0 * b0;
-        ulong mid1 = a1 * b0;
-        b0 = a0 * b1;
-        b1 *= a1;
-
-        a0 = (lo >> 32) + (uint)mid1 + (uint)b0;
-        a1 = (lo & 0xFFFFFFFFUL) | (a0 << 32);
-        b1 += (mid1 >> 32) + (b0 >> 32) + (a0 >> 32);
-
-        return (b1, a1);
-    }
-
-    private static UInt128 ReduceProductBitwise(ulong p3, ulong p2, ulong p1, ulong p0, UInt128 modulus)
-    {
-        UInt128 remainder = UInt128.Zero;
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p3 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p2 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p1 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p0 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        return remainder;
-    }
-
-    private static UInt128 ReadUInt128LittleEndian(ReadOnlySpan<byte> buffer)
-    {
-        UInt128 value = UInt128.Zero;
-        for (int i = buffer.Length - 1; i >= 0; i--)
-        {
-            value <<= 8;
-            value |= buffer[i];
-        }
-
-        return value;
-    }
-}