Use stack buffers for CPU exponent lowering and add MutableUInt128

PerfectNumbers.Core/MutableUInt128.cs

@@ -0,0 +1,108 @@
+using System;
+using System.Numerics;
+
+namespace PerfectNumbers.Core;
+
+/// <summary>
+/// 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
+{
+    public ulong High { get; private set; }
+    public ulong Low { get; private set; }
+
+    public MutableUInt128()
+    {
+    }
+
+    public MutableUInt128(ulong value)
+    {
+        Low = value;
+    }
+
+    public MutableUInt128(ulong high, ulong low)
+    {
+        High = high;
+        Low = low;
+    }
+
+    public MutableUInt128(UInt128 value)
+    {
+        Set(value);
+    }
+
+    public void Set(UInt128 value)
+    {
+        High = (ulong)(value >> 64);
+        Low = (ulong)value;
+    }
+
+    public void Set(ulong high, ulong low)
+    {
+        High = high;
+        Low = low;
+    }
+
+    public UInt128 ToUInt128() => ((UInt128)High << 64) | Low;
+
+    public void Add(ulong value)
+    {
+        ulong low = Low + value;
+        if (low < value)
+        {
+            High++;
+        }
+
+        Low = low;
+    }
+
+    public void Add(in MutableUInt128 value)
+    {
+        ulong low = Low + value.Low;
+        ulong carry = low < Low ? 1UL : 0UL;
+        ulong high = High + value.High + carry;
+
+        Low = low;
+        High = high;
+    }
+
+    public void Subtract(ulong value)
+    {
+        ulong low = Low;
+        ulong result = low - value;
+        ulong borrow = result > low ? 1UL : 0UL;
+
+        Low = result;
+        High -= borrow;
+    }
+
+    public void Subtract(in MutableUInt128 value)
+    {
+        ulong low = Low;
+        ulong result = low - value.Low;
+        ulong borrow = low < value.Low ? 1UL : 0UL;
+
+        Low = result;
+        High = High - value.High - borrow;
+    }
+
+    public void Multiply(ulong value)
+    {
+        ulong high = High;
+        ulong low = Low;
+
+        ulong highContribution = Math.BigMul(low, value, out ulong newLow);
+        Math.BigMul(high, value, out ulong shiftedHigh);
+        ulong newHigh = shiftedHigh + highContribution;
+
+        Low = newLow;
+        High = newHigh;
+    }
+
+    public void MultiplyAdd(ulong multiplier, ulong addend)
+    {
+        Multiply(multiplier);
+        Add(addend);
+    }
+}

PerfectNumbers.Core/PrimeOrderCalculator.cs

@@ -318,6 +318,8 @@ internal static partial class PrimeOrderCalculator
     private static ArrayPool<FactorEntry>? _factorPool;
     private static ArrayPool<FactorEntry> FactorPool => _factorPool ??= ArrayPool<FactorEntry>.Create();
 
+    private const int FactorEntryStackThreshold = 32;
+
     [ThreadStatic]
     private static ArrayPool<ulong>? _ulongPool;
     private static ArrayPool<ulong> ULongPool => _ulongPool ??= ArrayPool<ulong>.Create();
@@ -331,8 +333,19 @@ internal static partial class PrimeOrderCalculator
         {
             ReadOnlySpan<FactorEntry> factorSpan = factors.Factors;
             int length = factors.Count;
-			tempArray = factorPool.Rent(length + 1);
+            int capacity = length + 1;
-			Span<FactorEntry> buffer = tempArray;
+
+            Span<FactorEntry> buffer;
+            if (capacity <= FactorEntryStackThreshold)
+            {
+                buffer = stackalloc FactorEntry[capacity];
+            }
+            else
+            {
+                tempArray = factorPool.Rent(capacity);
+                buffer = tempArray.AsSpan(0, capacity);
+            }
+
             factorSpan.CopyTo(buffer);
 
             bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(factors.Cofactor);
@@ -343,12 +356,14 @@ internal static partial class PrimeOrderCalculator
                 length++;
             }
 
-			buffer.Slice(0, length).Sort(static (a, b) => a.Value.CompareTo(b.Value));
+            buffer = buffer.Slice(0, length); // Reuse the same span restricted to populated entries.
+            buffer.Sort(static (a, b) => a.Value.CompareTo(b.Value));
 
-			for (int i = 0; i < length; i++)
+            for (int i = 0; i < buffer.Length; i++)
             {
-				ulong primeFactor = buffer[i].Value;
+                FactorEntry entry = buffer[i];
-				int exponent = buffer[i].Exponent;
+                ulong primeFactor = entry.Value;
+                int exponent = entry.Exponent;
                 for (int iteration = 0; iteration < exponent; iteration++)
                 {
                     if ((order % primeFactor) != 0UL)