Make MutableUInt128 a struct and reuse it in Pollard Rho

PerfectNumbers.Core/MutableUInt128.cs

@@ -1,5 +1,6 @@
 using System;
 using System.Numerics;
+using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core;
 
@@ -7,17 +8,14 @@ namespace PerfectNumbers.Core;
 /// Mutable helper for 128-bit arithmetic derived from the .NET runtime UInt128 implementation.
 /// Portions adapted from https://github.com/dotnet/runtime/blob/v8.0.0/src/libraries/System.Private.CoreLib/src/System/UInt128.cs.
 /// </summary>
-internal sealed class MutableUInt128
+internal struct MutableUInt128
 {
-    public ulong High { get; private set; }
-    public ulong Low { get; private set; }
-
-    public MutableUInt128()
-    {
-    }
+    public ulong High;
+    public ulong Low;
 
     public MutableUInt128(ulong value)
     {
+        High = 0UL;
         Low = value;
     }
 
@@ -29,23 +27,35 @@ internal sealed class MutableUInt128
 
     public MutableUInt128(UInt128 value)
     {
-        Set(value);
+        High = (ulong)(value >> 64);
+        Low = (ulong)value;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public void Set(ulong value)
+    {
+        High = 0UL;
+        Low = value;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Set(UInt128 value)
     {
         High = (ulong)(value >> 64);
         Low = (ulong)value;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Set(ulong high, ulong low)
     {
         High = high;
         Low = low;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public UInt128 ToUInt128() => ((UInt128)High << 64) | Low;
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Add(ulong value)
     {
         ulong low = Low + value;
@@ -57,6 +67,7 @@ internal sealed class MutableUInt128
         Low = low;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Add(in MutableUInt128 value)
     {
         ulong low = Low + value.Low;
@@ -67,6 +78,7 @@ internal sealed class MutableUInt128
         High = high;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Subtract(ulong value)
     {
         ulong low = Low;
@@ -77,6 +89,7 @@ internal sealed class MutableUInt128
         High -= borrow;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Subtract(in MutableUInt128 value)
     {
         ulong low = Low;
@@ -87,22 +100,62 @@ internal sealed class MutableUInt128
         High = High - value.High - borrow;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void Multiply(ulong value)
     {
-        ulong high = High;
-        ulong low = Low;
+        ulong currentHigh = High;
+        ulong currentLow = Low;
 
-        ulong highContribution = Math.BigMul(low, value, out ulong newLow);
-        Math.BigMul(high, value, out ulong shiftedHigh);
-        ulong newHigh = shiftedHigh + highContribution;
+        ulong carry = Multiply64(currentLow, value, out ulong newLow);
+        Multiply64(currentHigh, value, out ulong shiftedHigh);
+        ulong newHigh = shiftedHigh + carry;
 
         Low = newLow;
         High = newHigh;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static ulong Multiply64(ulong left, ulong right, out ulong low)
+    {
+        const ulong Mask32 = 0xFFFF_FFFFUL;
+
+        ulong leftLow = left & Mask32;
+        ulong leftHigh = left >> 32;
+        ulong rightLow = right & Mask32;
+        ulong rightHigh = right >> 32;
+
+        ulong lowLow = leftLow * rightLow;
+        ulong lowHigh = leftLow * rightHigh;
+        ulong highLow = leftHigh * rightLow;
+        ulong highHigh = leftHigh * rightHigh;
+
+        ulong carry = (lowLow >> 32) + (lowHigh & Mask32) + (highLow & Mask32);
+        ulong high = highHigh + (lowHigh >> 32) + (highLow >> 32) + (carry >> 32);
+
+        low = ((carry & Mask32) << 32) | (lowLow & Mask32);
+        return high;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void MultiplyAdd(ulong multiplier, ulong addend)
     {
         Multiply(multiplier);
         Add(addend);
     }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public ulong Mod(ulong modulus)
+    {
+        if (modulus == 0UL)
+        {
+            throw new DivideByZeroException();
+        }
+
+        if (High == 0UL)
+        {
+            return Low % modulus;
+        }
+
+        return (ulong)(ToUInt128() % modulus);
+    }
 }

PerfectNumbers.Core/PrimeOrderCalculator.cs

@@ -1,7 +1,6 @@
 using System.Buffers;
 using System.Buffers.Binary;
 using System.Diagnostics;
-using System.Numerics;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
 using PerfectNumbers.Core.Gpu;
@@ -73,6 +72,9 @@ internal static partial class PrimeOrderCalculator
     [ThreadStatic]
     private static int s_divisorCycleSuppressionDepth;
 
+    [ThreadStatic]
+    private static MutableUInt128 s_pollardRhoPolynomialBuffer;
+
     private static bool IsGpuHeuristicDevice => s_pow2ModeInitialized && s_deviceMode == PrimeOrderHeuristicDevice.Gpu;
 
     private readonly struct Pow2ModeScope
@@ -1326,8 +1328,11 @@ internal static partial class PrimeOrderCalculator
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static ulong AdvancePolynomial(ulong x, ulong c, ulong modulus)
     {
-        UInt128 value = (UInt128)x * x + c;
-        return (ulong)(value % modulus);
+        ref MutableUInt128 polynomial = ref s_pollardRhoPolynomialBuffer;
+        polynomial.Set(x);
+        polynomial.Multiply(x);
+        polynomial.Add(c);
+        return polynomial.Mod(modulus);
     }
 
     private static ulong BinaryGcd(ulong a, ulong b)