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

@@ -314,69 +314,84 @@ internal static partial class PrimeOrderCalculator
         return order;
     }
 
-	[ThreadStatic]
+    [ThreadStatic]
-	private static ArrayPool<FactorEntry>? _factorPool;
+    private static ArrayPool<FactorEntry>? _factorPool;
-	private static ArrayPool<FactorEntry> FactorPool => _factorPool ??= ArrayPool<FactorEntry>.Create();
+    private static ArrayPool<FactorEntry> FactorPool => _factorPool ??= ArrayPool<FactorEntry>.Create();
 
-	[ThreadStatic]
+    private const int FactorEntryStackThreshold = 32;
-	private static ArrayPool<ulong>? _ulongPool;
-	private static ArrayPool<ulong> ULongPool => _ulongPool ??= ArrayPool<ulong>.Create();
 
-	private static ulong ExponentLoweringCpu(ulong order, ulong prime, PartialFactorResult factors, in MontgomeryDivisorData divisorData)
+    [ThreadStatic]
-	{
+    private static ArrayPool<ulong>? _ulongPool;
-		ArrayPool<FactorEntry> factorPool = FactorPool;
+    private static ArrayPool<ulong> ULongPool => _ulongPool ??= ArrayPool<ulong>.Create();
 
-		FactorEntry[]? tempArray = null;
+    private static ulong ExponentLoweringCpu(ulong order, ulong prime, PartialFactorResult factors, in MontgomeryDivisorData divisorData)
-		try
+    {
-		{
+        ArrayPool<FactorEntry> factorPool = FactorPool;
-			ReadOnlySpan<FactorEntry> factorSpan = factors.Factors;
-			int length = factors.Count;
-			tempArray = factorPool.Rent(length + 1);
-			Span<FactorEntry> buffer = tempArray;
-			factorSpan.CopyTo(buffer);
 
-			bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(factors.Cofactor);
+        FactorEntry[]? tempArray = null;
-			// bool isPrime = PrimeTester.IsPrimeInternal(factors.Cofactor, CancellationToken.None);
+        try
-			if (!factors.FullyFactored && factors.Cofactor > 1UL && isPrime)
+        {
-			{
+            ReadOnlySpan<FactorEntry> factorSpan = factors.Factors;
-				buffer[length] = new FactorEntry(factors.Cofactor);
+            int length = factors.Count;
-				length++;
+            int capacity = length + 1;
-			}
 
-			buffer.Slice(0, length).Sort(static (a, b) => a.Value.CompareTo(b.Value));
+            Span<FactorEntry> buffer;
+            if (capacity <= FactorEntryStackThreshold)
+            {
+                buffer = stackalloc FactorEntry[capacity];
+            }
+            else
+            {
+                tempArray = factorPool.Rent(capacity);
+                buffer = tempArray.AsSpan(0, capacity);
+            }
 
-			for (int i = 0; i < length; i++)
+            factorSpan.CopyTo(buffer);
-			{
-				ulong primeFactor = buffer[i].Value;
-				int exponent = buffer[i].Exponent;
-				for (int iteration = 0; iteration < exponent; iteration++)
-				{
-					if ((order % primeFactor) != 0UL)
-					{
-						break;
-					}
 
-					ulong reduced = order / primeFactor;
+            bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(factors.Cofactor);
-					if (Pow2EqualsOneCpu(reduced, prime, divisorData))
+            // bool isPrime = PrimeTester.IsPrimeInternal(factors.Cofactor, CancellationToken.None);
-					{
+            if (!factors.FullyFactored && factors.Cofactor > 1UL && isPrime)
-						order = reduced;
+            {
-						continue;
+                buffer[length] = new FactorEntry(factors.Cofactor);
-					}
+                length++;
+            }
 
-					break;
+            buffer = buffer.Slice(0, length); // Reuse the same span restricted to populated entries.
-				}
+            buffer.Sort(static (a, b) => a.Value.CompareTo(b.Value));
-			}
 
-			return order;
+            for (int i = 0; i < buffer.Length; i++)
-		}
+            {
-		finally
+                FactorEntry entry = buffer[i];
-		{
+                ulong primeFactor = entry.Value;
-			if (tempArray is not null)
+                int exponent = entry.Exponent;
-			{
+                for (int iteration = 0; iteration < exponent; iteration++)
-				factorPool.Return(tempArray, clearArray: false);
+                {
-			}
+                    if ((order % primeFactor) != 0UL)
-		}
+                    {
-	}
+                        break;
+                    }
+
+                    ulong reduced = order / primeFactor;
+                    if (Pow2EqualsOneCpu(reduced, prime, divisorData))
+                    {
+                        order = reduced;
+                        continue;
+                    }
+
+                    break;
+                }
+            }
+
+            return order;
+        }
+        finally
+        {
+            if (tempArray is not null)
+            {
+                factorPool.Return(tempArray, clearArray: false);
+            }
+        }
+    }
 
     private static bool TryConfirmOrderCpu(ulong prime, ulong order, in MontgomeryDivisorData divisorData, ref PartialFactorResult orderFactors)
     {