Reduce GC pressure in divisor checking pipeline

PerfectNumbers.Core/PrimeOrderCalculator.cs

@@ -1,4 +1,5 @@
 using System.Buffers;
+using System.Collections.Generic;
 using System.Buffers.Binary;
 using System.Diagnostics;
 using System.Numerics;
@@ -56,6 +57,9 @@ internal static partial class PrimeOrderCalculator
 	[ThreadStatic]
 	private static Dictionary<ulong, int>? s_partialFactorCounts;
 
+	[ThreadStatic]
+	private static List<ulong>? s_heuristicCandidateList;
+
 	private static bool IsGpuHeuristicDevice => s_pow2ModeInitialized && s_deviceMode == PrimeOrderHeuristicDevice.Gpu;
 
 	private readonly struct Pow2ModeScope
@@ -402,7 +406,9 @@ internal static partial class PrimeOrderCalculator
 			}
 
 			int capacity = config.MaxPowChecks <= 0 ? 64 : config.MaxPowChecks * 4;
-			List<ulong> candidates = new(capacity);
+			List<ulong> candidates = AcquireHeuristicCandidateList(capacity);
+			try
+			{
 				FactorEntry[] factorArray = orderFactors.Factors!;
 				// DebugLog("Building candidates list");
 				BuildCandidates(order, factorArray, orderFactors.Count, candidates, capacity);
@@ -520,6 +526,11 @@ internal static partial class PrimeOrderCalculator
 					index += batchSize;
 				}
 	
+			}
+			finally
+			{
+				candidates.Clear();
+			}
 			// DebugLog("No candidate confirmed");
 			return false;
 		}
@@ -823,6 +834,21 @@ internal static partial class PrimeOrderCalculator
 		return dictionary;
 	}
 
+	private static List<ulong> AcquireHeuristicCandidateList(int capacityHint)
+	{
+		List<ulong>? list = s_heuristicCandidateList;
+		if (list is null)
+		{
+			list = new List<ulong>(capacityHint);
+			s_heuristicCandidateList = list;
+			return list;
+		}
+
+		list.Clear();
+		list.EnsureCapacity(capacityHint);
+		return list;
+	}
+
 	private static PartialFactorResult PartialFactor(ulong value, in PrimeOrderSearchConfig config)
 	{
 		if (value <= 1UL)

PerfectNumbers.Core/ULongExtensions.cs

@@ -346,7 +346,26 @@ public static class ULongExtensions
 
         ulong result = divisor.MontgomeryOne;
         ulong nPrime = divisor.NPrime;
-        ulong[] oddPowers = InitializeMontgomeryOddPowersCpu(divisor, modulus, nPrime, oddPowerCount);
+
+        const int StackOddPowerThreshold = PerfectNumberConstants.PooledArrayThreshold;
+        Span<ulong> oddPowersSpan = oddPowerCount <= StackOddPowerThreshold
+            ? stackalloc ulong[StackOddPowerThreshold]
+            : default;
+
+        Span<ulong> oddPowers;
+        ulong[]? oddPowersArray = null;
+
+        if (!oddPowersSpan.IsEmpty)
+        {
+            oddPowers = oddPowersSpan.Slice(0, oddPowerCount);
+        }
+        else
+        {
+            oddPowersArray = ThreadStaticPools.UlongPool.Rent(oddPowerCount);
+            oddPowers = oddPowersArray.AsSpan(0, oddPowerCount);
+        }
+
+        InitializeMontgomeryOddPowersCpu(divisor, modulus, nPrime, oddPowers);
 
         int index = bitLength - 1;
         while (index >= 0)
@@ -384,9 +403,9 @@ public static class ULongExtensions
             index = windowStart - 1;
         }
 
-		if (oddPowerCount >= PerfectNumberConstants.PooledArrayThreshold)
+        if (oddPowersArray is not null)
         {
-			ArrayPool<ulong>.Shared.Return(oddPowers);
+            ThreadStaticPools.UlongPool.Return(oddPowersArray, clearArray: false);
         }
 
         if (keepMontgomery)
@@ -533,26 +552,22 @@ public static class ULongExtensions
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static ulong[] InitializeMontgomeryOddPowersCpu(in MontgomeryDivisorData divisor, ulong modulus, ulong nPrime, int oddPowerCount)
+    private static void InitializeMontgomeryOddPowersCpu(in MontgomeryDivisorData divisor, ulong modulus, ulong nPrime, Span<ulong> oddPowers)
     {
-		ulong[] oddPowers = oddPowerCount < PerfectNumberConstants.PooledArrayThreshold ? new ulong[oddPowerCount] : ArrayPool<ulong>.Shared.Rent(oddPowerCount);
-		
         oddPowers[0] = divisor.MontgomeryTwo;
-        if (oddPowerCount == 1)
+        if (oddPowers.Length == 1)
         {
-            return oddPowers;
+            return;
         }
 
-        ulong previous,
-			  square = divisor.MontgomeryTwoSquared;
+        ulong previous;
+        ulong square = divisor.MontgomeryTwoSquared;
 
-        for (int i = 1; i < oddPowerCount; i++)
+        for (int i = 1; i < oddPowers.Length; i++)
         {
             previous = oddPowers[i - 1];
             oddPowers[i] = previous.MontgomeryMultiply(square, modulus, nPrime);
         }
-
-        return oddPowers;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]