BitContradiction improvements - 0.043s, p=138000001+

2026-01-17 15:37:43 +01:00
1 parent e97ea151e1
commit 41e421e1eb
@@ -22,34 +22,30 @@ public class BitContradictionSolverTests
    [Fact]
    public void TryPropagateCarry_FailsWhenParityUnreachable()
    {
+		CarryRange carry = CarryRange.Single(0);
        bool success = TryPropagateCarry(
-            currentCarry: CarryRange.Single(0),
+            currentCarry: ref carry,
            forcedOnes: 0,
            possibleOnes: 0,
-            requiredResultBit: 1,
-            out var nextCarry,
-            out ContradictionReason reason);
+            requiredResultBit: 1);

        success.Should().BeFalse();
-        reason.Should().Be(ContradictionReason.ParityUnreachable);
-        nextCarry.Min.Should().Be(0);
-        nextCarry.Max.Should().Be(0);
+        carry.Min.Should().Be(0);
+        carry.Max.Should().Be(0);
    }

    [Fact]
    public void TryPropagateCarry_ComputesNextCarryRange()
    {
+		CarryRange carry = new(0, 1);
        bool success = TryPropagateCarry(
-            currentCarry: new CarryRange(0, 1),
+            currentCarry: ref carry,
            forcedOnes: 1,
            possibleOnes: 3,
-            requiredResultBit: 1,
-            out var nextCarry,
-            out ContradictionReason reason);
+            requiredResultBit: 1);

        success.Should().BeTrue();
-        reason.Should().Be(ContradictionReason.None);
-        nextCarry.Min.Should().Be(0);
-        nextCarry.Max.Should().Be(1);
+        carry.Min.Should().Be(0);
+        carry.Max.Should().Be(1);
    }
 }
@@ -3,36 +3,28 @@ using System.Runtime.CompilerServices;

 namespace PerfectNumbers.Core.ByDivisor;

-    public readonly struct TopDownPruneFailure(long column, long carryMin, long carryMax, long unknown)
-    {
-        public readonly long Column = column;
-        public readonly long CarryMin = carryMin;
-        public readonly long CarryMax = carryMax;
-        public readonly long Unknown = unknown;
-    }
+public readonly struct ColumnBounds(int forcedOnes, int possibleOnes)
+{
+	public readonly int ForcedOnes = forcedOnes;
+	public readonly int PossibleOnes = possibleOnes;
+}

-    public readonly struct ColumnBounds(long forcedOnes, long possibleOnes)
-	{
-        public readonly long ForcedOnes = forcedOnes;
-        public readonly long PossibleOnes = possibleOnes;
-	}
-
-    public readonly struct CarryRange(long min, long max)
-	{
+public readonly struct CarryRange(long min, long max)
+{
 	public readonly long Min = min;
 	public readonly long Max = max;

 	public static CarryRange Single(long value) => new(value, value);
 	public static readonly CarryRange Zero = Single(0);
-    }
+}

-    public enum ContradictionReason
-    {
+public enum ContradictionReason
+{
 	None,
 	ParityUnreachable,
 	TruncatedLength,
 	TailNotZero,
-    }
+}

 /// <summary>
 /// Helper utilities for the BitContradiction divisor search. These methods implement the
@@ -44,26 +36,15 @@ internal static class BitContradictionSolverWithQMultiplier
 	private const int PingPongBlockColumns = 64;
 	private const int TailCarryBatchColumns = 1024;
 	private const int TailCarryBatchRepeats = 1;
-
-    [ThreadStatic]
-    private static TopDownPruneFailure? _lastTopDownFailure;
-    [ThreadStatic]
-    private static BottomUpFailure? _lastBottomUpFailure;
-    [ThreadStatic]
-    private static bool _debugEnabled;
-
 	private const int TopDownCacheCapacity = 16;

-    private readonly struct TopDownCacheKey(long hash, int length, long maxAllowedA, long pLong)
+#if DETAILED_LOG
+    public readonly struct TopDownPruneFailure(int column, int carryMin, int carryMax, int unknown)
    {
-        public readonly long Hash = hash;
-        public readonly int Length = length;
-        public readonly long MaxAllowedA = maxAllowedA;
-        public readonly long PLong = pLong;
-
-        public bool Equals(TopDownCacheKey other) => Hash == other.Hash && Length == other.Length && MaxAllowedA == other.MaxAllowedA && PLong == other.PLong;
-        public override bool Equals(object? obj) => obj is TopDownCacheKey other && Equals(other);
-        public override int GetHashCode() => HashCode.Combine(Hash, Length, MaxAllowedA, PLong);
+        public readonly int Column = column;
+        public readonly int CarryMin = carryMin;
+        public readonly int CarryMax = carryMax;
+        public readonly int Unknown = unknown;
    }

    private readonly struct TopDownCacheValue(bool success, TopDownPruneFailure? failure)
@@ -72,11 +53,44 @@ internal static class BitContradictionSolverWithQMultiplier
        public readonly TopDownPruneFailure? Failure = failure;
    }

+    internal readonly struct BottomUpFailure(int column, int carryMin, int carryMax, int forced, int unknown)
+    {
+        public readonly int Column = column;
+        public readonly int CarryMin = carryMin;
+        public readonly int CarryMax = carryMax;
+        public readonly int Forced = forced;
+        public readonly int Unknown = unknown;
+    }
+
+    [ThreadStatic]
+    private static TopDownPruneFailure? _lastTopDownFailure;
+    [ThreadStatic]
+    private static BottomUpFailure? _lastBottomUpFailure;
    [ThreadStatic]
    private static Dictionary<TopDownCacheKey, TopDownCacheValue>? _topDownCache;
+
+    internal static TopDownPruneFailure? LastTopDownFailure => _lastTopDownFailure;
+    internal static BottomUpFailure? LastBottomUpFailure => _lastBottomUpFailure;
+#else
+	[ThreadStatic]
+	private static Dictionary<TopDownCacheKey, bool>? _topDownCache;
+#endif
+
 	[ThreadStatic]
 	private static List<TopDownCacheKey>? _topDownCacheOrder;

+	private readonly struct TopDownCacheKey(long hash, int length, int maxAllowedA, int pLong)
+	{
+		public readonly long Hash = hash;
+		public readonly int Length = length;
+		public readonly int MaxAllowedA = maxAllowedA;
+		public readonly int PLong = pLong;
+
+		public bool Equals(TopDownCacheKey other) => Hash == other.Hash && Length == other.Length && MaxAllowedA == other.MaxAllowedA && PLong == other.PLong;
+		public override bool Equals(object? obj) => obj is TopDownCacheKey other && Equals(other);
+		public override int GetHashCode() => HashCode.Combine(Hash, Length, MaxAllowedA, PLong);
+	}
+
 	private static long ComputeQOffsetsHash(ReadOnlySpan<int> qOneOffsets)
 	{
 		const long fnvOffset = unchecked((long)1469598103934665603);
@@ -91,61 +105,62 @@ internal static class BitContradictionSolverWithQMultiplier
 		return hash;
 	}

+#if DETAILED_LOG
    private static bool TryGetTopDownCache(in TopDownCacheKey key, out TopDownCacheValue value)
+#else
+	private static bool TryGetTopDownCache(in TopDownCacheKey key, out bool value)
+#endif
 	{
-        if (_topDownCache == null)
+		var cache = _topDownCache;
+		if (cache == null)
 		{
+			cache = [];
+			_topDownCache = cache;
 			value = default;
 			return false;
 		}

-        return _topDownCache.TryGetValue(key, out value);
+		return cache.TryGetValue(key, out value);
 	}

+#if DETAILED_LOG
    private static void StoreTopDownCache(in TopDownCacheKey key, in TopDownCacheValue value)
+#else
+	private static void StoreTopDownCache(in TopDownCacheKey key, bool value)
+#endif
 	{
-        _topDownCache ??= new Dictionary<TopDownCacheKey, TopDownCacheValue>();
-        _topDownCacheOrder ??= new List<TopDownCacheKey>(TopDownCacheCapacity + 1);
-
-        if (_topDownCache.ContainsKey(key))
+		// _topDownCache is always non-null here on EvenPerfectBitScanner execution path.
+		var topDownCache = _topDownCache!;
+		if (topDownCache.ContainsKey(key))
 		{
-            _topDownCache[key] = value;
+			topDownCache[key] = value;
 			return;
 		}

-        if (_topDownCacheOrder.Count >= TopDownCacheCapacity)
+		List<TopDownCacheKey>? topDownCacheOrder = _topDownCacheOrder;
+		if (topDownCacheOrder == null)
 		{
-            var evict = _topDownCacheOrder[0];
-            _topDownCacheOrder.RemoveAt(0);
-            _topDownCache.Remove(evict);
+			topDownCacheOrder = new List<TopDownCacheKey>(TopDownCacheCapacity + 1);
+			_topDownCacheOrder = topDownCacheOrder;
 		}
-
-        _topDownCache[key] = value;
-        _topDownCacheOrder.Add(key);
-    }
-
-
-    internal static TopDownPruneFailure? LastTopDownFailure => _lastTopDownFailure;
-    internal static BottomUpFailure? LastBottomUpFailure => _lastBottomUpFailure;
-
-    internal readonly struct BottomUpFailure(long column, long carryMin, long carryMax, long forced, long unknown)
+		else if (topDownCacheOrder.Count >= TopDownCacheCapacity)
 		{
-        public readonly long Column = column;
-        public readonly long CarryMin = carryMin;
-        public readonly long CarryMax = carryMax;
-        public readonly long Forced = forced;
-        public readonly long Unknown = unknown;
+			var evict = topDownCacheOrder[0];
+			topDownCacheOrder.RemoveAt(0);
+			topDownCache.Remove(evict);
 		}

-    internal static void SetDebugEnabled(bool enabled) => _debugEnabled = enabled;
+		topDownCache[key] = value;
+		topDownCacheOrder.Add(key);
+	}

 	internal static ColumnBounds ComputeColumnBounds(
-        ReadOnlySpan<bool> multiplicand,
-        ReadOnlySpan<bool> multiplier,
+		in ReadOnlySpan<bool> multiplicand,
+		in ReadOnlySpan<bool> multiplier,
 		int columnIndex)
 	{
-        long forced = 0;
-        long possible = 0;
+		int forced = 0;
+		int possible = 0;

 		int multiplicandLength = multiplicand.Length;
 		int multiplierLength = multiplier.Length;
@@ -169,6 +184,7 @@ internal static class BitContradictionSolverWithQMultiplier
 		return new ColumnBounds(forced, possible);
 	}

+#if DETAILED_LOG
    internal static bool TryPropagateCarry(
        CarryRange currentCarry,
        long forcedOnes,
@@ -176,6 +192,14 @@ internal static class BitContradictionSolverWithQMultiplier
        int requiredResultBit,
        out CarryRange nextCarry,
        out ContradictionReason reason)
+#else
+	internal static bool TryPropagateCarry(
+		CarryRange currentCarry,
+		int forcedOnes,
+		int possibleOnes,
+		int requiredResultBit,
+		out CarryRange nextCarry)
+#endif
 	{
 		long minSum = currentCarry.Min + forcedOnes;
 		long maxSum = currentCarry.Max + possibleOnes;
@@ -187,12 +211,16 @@ internal static class BitContradictionSolverWithQMultiplier
 		if (minSum > maxSum)
 		{
 			nextCarry = default;
+#if DETAILED_LOG
            reason = ContradictionReason.ParityUnreachable;
+#endif
 			return false;
 		}

 		nextCarry = new CarryRange((minSum - requiredResultBit) >> 1, (maxSum - requiredResultBit) >> 1);
+#if DETAILED_LOG
        reason = ContradictionReason.None;
+#endif
 		return true;
 	}

@@ -207,8 +235,10 @@ internal static class BitContradictionSolverWithQMultiplier
 		out ContradictionReason reason)
 	{
 		divides = false;
+#if DETAILED_LOG
 		_lastTopDownFailure = null;
 		_lastBottomUpFailure = null;
+#endif

 		// These conditions will never be true on EvenPerfectBitScanner execution path.
 		// if (p == 0 || qOneOffsets.Length == 0)
@@ -253,8 +283,8 @@ internal static class BitContradictionSolverWithQMultiplier
 		var segmentState0 = new sbyte[windowSize];
 		var segmentState1 = new sbyte[windowSize];
 		long segmentBase = 0;
-		long pLong = (long)p;
-		long maxAllowedA = pLong - (maxOffset + 1L);
+		int pLong = (int)p;
+		int maxAllowedA = pLong - (maxOffset + 1);
 		if (maxAllowedA < 0)
 		{
 			reason = ContradictionReason.TruncatedLength;
@@ -265,29 +295,47 @@ internal static class BitContradictionSolverWithQMultiplier
 		var cacheKey = new TopDownCacheKey(qHash, qOneOffsetsLength, maxAllowedA, pLong);
 		if (TryGetTopDownCache(in cacheKey, out var cached))
 		{
+#if DETAILED_LOG
 			_lastTopDownFailure = cached.Failure;
 			if (!cached.Success)
+#else
+			if (!cached)
+#endif
 			{
 				reason = ContradictionReason.ParityUnreachable;
+#if DETAILED_LOG
 				Console.WriteLine($"[bit-contradiction] parity unreachable in top-down prune (failure={_lastTopDownFailure.HasValue})");
+#endif
 				return true;
 			}
 		}
 		else
 		{
+#if DETAILED_LOG
 			if (!TryTopDownCarryPrune(qOneOffsets, qOneOffsetsLength, pLong, maxAllowedA, out _lastTopDownFailure))
+#else
+			if (!TryTopDownCarryPrune(qOneOffsets, qOneOffsetsLength, pLong, maxAllowedA))
+#endif
 			{
+#if DETAILED_LOG
 				StoreTopDownCache(in cacheKey, new TopDownCacheValue(false, _lastTopDownFailure));
-                reason = ContradictionReason.ParityUnreachable;
 				Console.WriteLine($"[bit-contradiction] parity unreachable in top-down prune (failure={_lastTopDownFailure.HasValue})");
+#else
+				StoreTopDownCache(in cacheKey, false);
+#endif
+				reason = ContradictionReason.ParityUnreachable;
 				return true;
 			}

+#if DETAILED_LOG
 			StoreTopDownCache(in cacheKey, new TopDownCacheValue(true, null));
+#else
+			StoreTopDownCache(in cacheKey, true);
+#endif
 		}

-        long lowColumn = 0;
-        long highColumn = pLong - 1;
+		int lowColumn = 0;
+		int highColumn = pLong - 1;
 		CarryRange carryLow = CarryRange.Zero;
 		CarryRange carryHigh = CarryRange.Zero;
 		int bottomWindowStart = 0;
@@ -304,7 +352,11 @@ internal static class BitContradictionSolverWithQMultiplier

 			if (processTop)
 			{
+#if DETAILED_LOG
 				if (!TryProcessTopDownBlock(qOneOffsets, qOneOffsetsLength, maxAllowedA, highColumn, blockSize, carryHigh, ref topWindowStart, ref topWindowEnd, out carryHigh, out _lastTopDownFailure))
+#else
+				if (!TryProcessTopDownBlock(qOneOffsets, qOneOffsetsLength, maxAllowedA, highColumn, blockSize, carryHigh, ref topWindowStart, ref topWindowEnd, out carryHigh))
+#endif
 				{
 					reason = ContradictionReason.ParityUnreachable;
 					return true;
@@ -329,7 +381,9 @@ internal static class BitContradictionSolverWithQMultiplier
 		long carryMax = carryLow.Max < carryHigh.Max ? carryLow.Max : carryHigh.Max;
 		if (carryMin > carryMax)
 		{
+#if DETAILED_LOG
 			Console.WriteLine($"[bit-contradiction] parity unreachable after ping-pong carry merge (low=[{carryLow.Min},{carryLow.Max}] high=[{carryHigh.Min},{carryHigh.Max}])");
+#endif
 			reason = ContradictionReason.ParityUnreachable;
 			divides = false;
 			return true;
@@ -352,8 +406,8 @@ internal static class BitContradictionSolverWithQMultiplier
 		long carryMax = carry.Max;
 		while (columnCount > 0)
 		{
-            int step = columnCount > 62 ? 62 : columnCount;
-            long add = (1L << step) - 1L;
+			int step = columnCount > 30 ? 30 : columnCount;
+			int add = (1 << step) - 1;
 			long nextMin = (carryMin + add) >> step;
 			long nextMax = carryMax >> step;
 			if (nextMin > nextMax)
@@ -372,8 +426,8 @@ internal static class BitContradictionSolverWithQMultiplier

 	private static bool TryProcessBottomUpBlock(
 		ReadOnlySpan<int> qOneOffsets,
-        long maxAllowedA,
-        long startColumn,
+		int maxAllowedA,
+		int startColumn,
 		int columnCount,
 		ref CarryRange carry,
 		ref long segmentBase,
@@ -386,12 +440,12 @@ internal static class BitContradictionSolverWithQMultiplier
 		long endColumn = startColumn + columnCount;
 		int qOneOffsetsLength = qOneOffsets.Length;
 		int windowSize = segmentState0.Length;
-        for (long column = startColumn; column < endColumn; column++)
+		for (int column = startColumn; column < endColumn; column++)
 		{
-            long forced = 0L;
-            long unknown = 0L;
-            long chosenIndex = -1L;
-            long newBase = (column / windowSize) * windowSize;
+			int forced = 0;
+			int unknown = 0;
+			int chosenIndex = -1;
+			int newBase = (column / windowSize) * windowSize;
 			if (newBase != segmentBase)
 			{
 				if (newBase == segmentBase + windowSize)
@@ -413,7 +467,7 @@ internal static class BitContradictionSolverWithQMultiplier
 				windowEndIdx++;
 			}

-            long lowerBound = column - maxAllowedA;
+			int lowerBound = column - maxAllowedA;
 			while (windowStartIdx < windowEndIdx && qOneOffsets[windowStartIdx] < lowerBound)
 			{
 				windowStartIdx++;
@@ -422,7 +476,7 @@ internal static class BitContradictionSolverWithQMultiplier
 			for (int offsetIndex = windowStartIdx; offsetIndex < windowEndIdx; offsetIndex++)
 			{
 				int offset = qOneOffsets[offsetIndex];
-                long aIndex = column - offset;
+				int aIndex = column - offset;
 				if (aIndex < 0)
 				{
 					break;
@@ -513,10 +567,9 @@ internal static class BitContradictionSolverWithQMultiplier
 				long carryMax = AlignDownToParity(carry.Max, requiredCarryParity);
 				if (carryMin > carryMax)
 				{
-					if (_debugEnabled)
-					{
+#if DETAILED_LOG
 					_lastBottomUpFailure = new BottomUpFailure(column, carryMin, carryMax, forced, unknown);
-					}
+#endif
 					reason = ContradictionReason.ParityUnreachable;
 					return false;
 				}
@@ -534,10 +587,9 @@ internal static class BitContradictionSolverWithQMultiplier
 			{
 				if ((minSum & 1) != requiredParity)
 				{
-                    if (_debugEnabled)
-                    {
+#if DETAILED_LOG
 					_lastBottomUpFailure = new BottomUpFailure(column, carry.Min, carry.Max, forced, unknown);
-                    }
+#endif
 					reason = ContradictionReason.ParityUnreachable;
 					return false;
 				}
@@ -549,14 +601,14 @@ internal static class BitContradictionSolverWithQMultiplier
 			{
 				if ((minSum & 1) != requiredParity && unknown == 0)
 				{
-                    if (_debugEnabled)
-                    {
+#if DETAILED_LOG
 					_lastBottomUpFailure = new BottomUpFailure(column, carry.Min, carry.Max, forced, unknown);
-                    }
+#endif
 					reason = ContradictionReason.ParityUnreachable;
 					return false;
 				}

+#if DETAILED_LOG
 				if (!TryPropagateCarry(
 						carry,
 						forced,
@@ -564,12 +616,21 @@ internal static class BitContradictionSolverWithQMultiplier
 						requiredParity,
 						out var next,
 						out var propagateReason))
+#else
+				if (!TryPropagateCarry(
+						carry,
+						forced,
+						forced + unknown,
+						requiredParity,
+						out var next))
+#endif
 				{
-                    if (_debugEnabled)
-                    {
+#if DETAILED_LOG
 					_lastBottomUpFailure = new BottomUpFailure(column, carry.Min, carry.Max, forced, unknown);
-                    }
 					reason = propagateReason;
+#else
+					reason = ContradictionReason.ParityUnreachable;
+#endif
 					return false;
 				}

@@ -582,6 +643,7 @@ internal static class BitContradictionSolverWithQMultiplier
 		return true;
 	}

+#if DETAILED_LOG
 	private static bool TryProcessTopDownBlock(
 		ReadOnlySpan<int> qOneOffsets,
 		int qOneOffsetsLength,
@@ -593,14 +655,28 @@ internal static class BitContradictionSolverWithQMultiplier
 		ref int windowEnd,
 		out CarryRange nextCarryOut,
 		out TopDownPruneFailure? failure)
+#else
+	private static bool TryProcessTopDownBlock(
+		ReadOnlySpan<int> qOneOffsets,
+		int qOneOffsetsLength,
+		int maxAllowedA,
+		int startHighColumn,
+		int columnCount,
+		CarryRange carryOut,
+		ref int windowStart,
+		ref int windowEnd,
+		out CarryRange nextCarryOut)
+#endif
 	{
+#if DETAILED_LOG
 		failure = null;
+#endif
 		long carryOutMin = carryOut.Min,
-			 carryOutMax = carryOut.Max,
-			 value;
-        long endColumn = startHighColumn - columnCount + 1;
+			 carryOutMax = carryOut.Max;
+		int value;
+		int endColumn = startHighColumn - columnCount + 1;

-        long column = startHighColumn;
+		int column = startHighColumn;
 		while (column >= endColumn)
 		{
 			// value is used as high column index
@@ -631,9 +707,9 @@ internal static class BitContradictionSolverWithQMultiplier
 			value = windowEnd - windowStart;
 			if (value == 0)
 			{
-                long lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : long.MinValue;
-                long lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : long.MinValue;
-                long chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
+				int lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : int.MinValue;
+				int lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : int.MinValue;
+				int chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
 				if (chunkEnd < endColumn)
 				{
 					chunkEnd = endColumn;
@@ -644,7 +720,9 @@ internal static class BitContradictionSolverWithQMultiplier
 				{
 					if (!AdvanceTopDownUnknown0(ref carryOutMin, ref carryOutMax, steps))
 					{
+#if DETAILED_LOG
 						failure = new TopDownPruneFailure(column, carryOutMin, carryOutMax, value);
+#endif
 						nextCarryOut = default;
 						return false;
 					}
@@ -655,9 +733,9 @@ internal static class BitContradictionSolverWithQMultiplier
 			}
 			else if (value == 1)
 			{
-                long lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : long.MinValue;
-                long lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : long.MinValue;
-                long chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
+				int lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : int.MinValue;
+				int lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : int.MinValue;
+				int chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
 				if (chunkEnd < endColumn)
 				{
 					chunkEnd = endColumn;
@@ -668,7 +746,9 @@ internal static class BitContradictionSolverWithQMultiplier
 				{
 					if (!AdvanceTopDownUnknown1(ref carryOutMin, ref carryOutMax, steps))
 					{
+#if DETAILED_LOG
 						failure = new TopDownPruneFailure(column, carryOutMin, carryOutMax, value);
+#endif
 						nextCarryOut = default;
 						return false;
 					}
@@ -694,7 +774,9 @@ internal static class BitContradictionSolverWithQMultiplier

 			if (carryOutMin > carryOutMax)
 			{
+#if DETAILED_LOG
 				failure = new TopDownPruneFailure(column, carryOutMin, carryOutMax, value);
+#endif
 				nextCarryOut = default;
 				return false;
 			}
@@ -706,26 +788,35 @@ internal static class BitContradictionSolverWithQMultiplier
 		return true;
 	}

-    private static long AlignUpToParity(long value, int parity) => (value & 1) == parity ? value : value + 1;
-
-	private static long AlignDownToParity(long value, int parity) => (value & 1) == parity ? value : value - 1;
+	private static long AlignUpToParity(long value, int parity) => (value & 1L) == parity ? value : value + 1L;
+	private static long AlignDownToParity(long value, int parity) => (value & 1L) == parity ? value : value - 1L;

+#if DETAILED_LOG
 	private static bool TryTopDownCarryPrune(
 		ReadOnlySpan<int> qOneOffsets,
 		int qOneOffsetsLength,
 		long pLong,
 		long maxAllowedA,
 		out TopDownPruneFailure? failure)
+#else
+	private static bool TryTopDownCarryPrune(
+		ReadOnlySpan<int> qOneOffsets,
+		int qOneOffsetsLength,
+		int pLong,
+		int maxAllowedA)
+#endif
 	{
+#if DETAILED_LOG
 		failure = null;
+#endif
 		long carryOutMin = 0,
-			 carryOutMax = 0,
-			 value;
+			 carryOutMax = 0;
+		int value;

 		int windowStart = qOneOffsetsLength;
 		int windowEnd = qOneOffsetsLength;

-        long column = pLong - 1;
+		int column = pLong - 1;
 		while (column >= 0)
 		{
 			// value is used as high column index
@@ -756,9 +847,9 @@ internal static class BitContradictionSolverWithQMultiplier
 			value = windowEnd - windowStart;
 			if (value == 0)
 			{
-                long lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : long.MinValue;
-                long lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : long.MinValue;
-                long chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
+				int lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : int.MinValue;
+				int lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : int.MinValue;
+				int chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
 				if (chunkEnd < 0)
 				{
 					chunkEnd = 0;
@@ -769,7 +860,9 @@ internal static class BitContradictionSolverWithQMultiplier
 				{
 					if (!AdvanceTopDownUnknown0(ref carryOutMin, ref carryOutMax, steps))
 					{
+#if DETAILED_LOG
 						failure = new TopDownPruneFailure(column, carryOutMin, carryOutMax, value);
+#endif
 						return false;
 					}

@@ -779,9 +872,9 @@ internal static class BitContradictionSolverWithQMultiplier
 			}
 			else if (value == 1)
 			{
-                long lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : long.MinValue;
-                long lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : long.MinValue;
-                long chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
+				int lastEnd = windowEnd > 0 ? qOneOffsets[windowEnd - 1] : int.MinValue;
+				int lastStart = windowStart > 0 ? qOneOffsets[windowStart - 1] + maxAllowedA : int.MinValue;
+				int chunkEnd = lastEnd > lastStart ? lastEnd : lastStart;
 				if (chunkEnd < 0)
 				{
 					chunkEnd = 0;
@@ -792,7 +885,9 @@ internal static class BitContradictionSolverWithQMultiplier
 				{
 					if (!AdvanceTopDownUnknown1(ref carryOutMin, ref carryOutMax, steps))
 					{
+#if DETAILED_LOG
 						failure = new TopDownPruneFailure(column, carryOutMin, carryOutMax, value);
+#endif
 						return false;
 					}

@@ -817,7 +912,9 @@ internal static class BitContradictionSolverWithQMultiplier

 			if (carryOutMin > carryOutMax)
 			{
+#if DETAILED_LOG
 				failure = new TopDownPruneFailure(column, carryOutMin, carryOutMax, value);
+#endif
 				return false;
 			}

@@ -826,7 +923,9 @@ internal static class BitContradictionSolverWithQMultiplier

 		if (carryOutMin > 0)
 		{
+#if DETAILED_LOG
 			failure = new TopDownPruneFailure(0, carryOutMin, carryOutMax, 0);
+#endif
 			return false;
 		}

@@ -837,13 +936,13 @@ internal static class BitContradictionSolverWithQMultiplier
 	{
 		while (steps > 0)
 		{
-            int step = steps > 62 ? 62 : steps;
-            long pow = 1L << step;
+			int step = steps > 30 ? 30 : steps;
+			int pow = 1 << step;

 			if (carryOutMin > (long.MaxValue >> step) || carryOutMax > ((long.MaxValue - (pow - 1)) >> step))
 			{
 				carryOutMin = 0;
-                carryOutMax = long.MaxValue;
+				carryOutMax = int.MaxValue;
 				return true;
 			}

@@ -859,12 +958,12 @@ internal static class BitContradictionSolverWithQMultiplier
 	{
 		while (steps > 0)
 		{
-            int step = steps > 62 ? 62 : steps;
-            long add = (1L << step) - 1L;
-            if (carryOutMin > ((long.MaxValue - add) >> step) || carryOutMax > ((long.MaxValue - add) >> step))
+			int step = steps > 30 ? 30 : steps;
+			int add = (1 << step) - 1;
+			if (carryOutMin > ((int.MaxValue - add) >> step) || carryOutMax > ((int.MaxValue - add) >> step))
 			{
 				carryOutMin = 0;
-                carryOutMax = long.MaxValue;
+				carryOutMax = int.MaxValue;
 				return true;
 			}

@@ -0,0 +1,452 @@
+
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core.Cpu;
+
+/// <summary>
+/// Block-ordered streaming divisor scan for M_p = 2^p - 1 in the family q = (2p)k + 1,
+/// using a 4-bit (base-16) residue automaton.
+///
+/// Key design change vs column-wise branching:
+/// - We always assign an a-nibble (4 planned a-bits) before stepping the 4 columns.
+/// - With planned bits present, each of the 4 columns becomes deterministic (no 0/1 branching),
+///   so we can test each a-nibble in O(1) per column and cache allowed masks by signatures.
+///
+/// This makes the "residue per block" perspective operational while staying exact for the explored tree.
+/// </summary>
+public static class MersenneResidueNibbleAutomatonScanner
+{
+    public enum ScanResult
+    {
+        RuledOut = 0,
+        Candidate = 1,
+        FoundDivisor = 2
+    }
+
+    public const int MaxSupportedQBits = 8192;
+
+    // Cache allowed a-nibble masks only for moderate carry values.
+    // For larger carry we compute directly to avoid any risk of false pruning.
+    private const int CarryCacheMax = 511;
+
+    // Reuse the same block-0 filter as the original scanner: q odd and q mod 8 in {1,7}.
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static bool IsAllowedQ0Nibble(byte q0)
+    {
+        if ((q0 & 0x1) == 0) return false;
+        int mod8 = q0 & 0x7;
+        return mod8 == 0x1 || mod8 == 0x7;
+    }
+
+    private readonly struct AllowedMaskKey(
+        int pBits,
+        int maxQBits,
+        int block,
+        int carry,
+        byte qNibble,
+        ulong qSig,
+        ulong aSig) : IEquatable<AllowedMaskKey>
+    {
+        public readonly int PBits = pBits;
+        public readonly int MaxQBits = maxQBits;
+        public readonly int Block = block;
+        public readonly int Carry = carry;
+        public readonly byte QNibble = qNibble;
+        public readonly ulong QSig = qSig;
+        public readonly ulong ASig = aSig;
+
+        public bool Equals(AllowedMaskKey other)
+            => PBits == other.PBits
+               && MaxQBits == other.MaxQBits
+               && Block == other.Block
+               && Carry == other.Carry
+               && QNibble == other.QNibble
+               && QSig == other.QSig
+               && ASig == other.ASig;
+
+        public override bool Equals(object? obj) => obj is AllowedMaskKey k && Equals(k);
+        public override int GetHashCode() => HashCode.Combine(PBits, MaxQBits, Block, Carry, QNibble, QSig, ASig);
+    }
+
+    private struct State
+    {
+        public int Block;
+        public int BitIndex;
+        public int Carry;
+
+        public bool KTerminated;
+        public byte KFlushRemaining;
+        public byte PostTermZeroQNibbles;
+
+        public MersenneCombinedDivisorScannerFullStreamExtended.DynamicBitset QBits;
+        public MersenneCombinedDivisorScannerFullStreamExtended.ABitsWindow AWindow;
+        public MersenneCombinedDivisorScannerFullStreamExtended.QGenState16 QState;
+
+        public State CloneShallow() => new()
+        {
+            Block = Block,
+            BitIndex = BitIndex,
+            Carry = Carry,
+            KTerminated = KTerminated,
+            KFlushRemaining = KFlushRemaining,
+            PostTermZeroQNibbles = PostTermZeroQNibbles,
+            QBits = QBits.CloneShared(),
+            AWindow = AWindow.Clone(),
+            QState = QState
+        };
+
+        public static State CreateInitial(MersenneCombinedDivisorScannerFullStreamExtended.QGenState16 initQ, int maxQBits)
+        {
+            var s = new State
+            {
+                Block = initQ.NibbleIndex,
+                BitIndex = 0,
+                Carry = 0,
+                QBits = new MersenneCombinedDivisorScannerFullStreamExtended.DynamicBitset(maxQBits),
+                AWindow = new MersenneCombinedDivisorScannerFullStreamExtended.ABitsWindow(maxQBits),
+                QState = initQ,
+                KTerminated = false,
+                KFlushRemaining = 0,
+                PostTermZeroQNibbles = 0
+            };
+
+            s.QBits.Set(0);      // q0 = 1
+            s.AWindow.SetPlanned(0, 1); // a0 = 1
+            return s;
+        }
+    }
+
+    /// <summary>
+    /// Try to find a divisor q (within maxQBits) for M_p by streaming q via QNibbleGenerator16 and
+    /// validating with the deterministic planned-nibble automaton.
+    /// </summary>
+    public static ScanResult TryFindDivisorByResidueAutomaton(
+        ulong prime,
+        int maxQBits,
+        bool verifyWithModPow,
+        out BigInteger foundQ)
+    {
+        foundQ = BigInteger.Zero;
+
+        if (prime == 0) return ScanResult.RuledOut;
+        if (maxQBits < 2) throw new ArgumentOutOfRangeException(nameof(maxQBits));
+        if (maxQBits > MaxSupportedQBits) return ScanResult.Candidate;
+
+        int pBits = checked((int)prime);
+        int maxBlocks = (maxQBits + 3) / 4;
+
+        var qGen = new MersenneCombinedDivisorScannerFullStreamExtended.QNibbleGenerator16(prime);
+
+        // Block-ordered exploration (BFS by block index).
+        var openByBlock = new Dictionary<int, Queue<State>>(capacity: 4096);
+        var termByBlock = new Dictionary<int, Queue<State>>(capacity: 4096);
+        var activeBlocks = new SortedSet<int>();
+
+        void Enqueue(State s)
+        {
+            var dict = s.KTerminated ? termByBlock : openByBlock;
+            if (!dict.TryGetValue(s.Block, out var q))
+            {
+                q = new Queue<State>();
+                dict[s.Block] = q;
+            }
+            q.Enqueue(s);
+            activeBlocks.Add(s.Block);
+        }
+
+        bool TryDequeue(out State s)
+        {
+            s = default;
+            if (activeBlocks.Count == 0) return false;
+            int b = activeBlocks.Min;
+
+            if (termByBlock.TryGetValue(b, out var tq) && tq.Count > 0) s = tq.Dequeue();
+            else if (openByBlock.TryGetValue(b, out var oq) && oq.Count > 0) s = oq.Dequeue();
+            else
+            {
+                activeBlocks.Remove(b);
+                return false;
+            }
+
+            bool termEmpty = !termByBlock.TryGetValue(b, out var tq2) || tq2.Count == 0;
+            bool openEmpty = !openByBlock.TryGetValue(b, out var oq2) || oq2.Count == 0;
+            if (termEmpty && openEmpty) activeBlocks.Remove(b);
+
+            return true;
+        }
+
+        // Cache of allowed a-nibble masks for (state signature, qNibble, carry).
+        var allowedMaskCache = new Dictionary<AllowedMaskKey, ushort>(capacity: 1 << 16);
+
+        // Reusable buffers.
+        Span<byte> qNibByKn = stackalloc byte[16];
+        Span<MersenneCombinedDivisorScannerFullStreamExtended.QGenState16> nextByKn = stackalloc MersenneCombinedDivisorScannerFullStreamExtended.QGenState16[16];
+        Span<int> countsByQn = stackalloc int[16];
+
+        var init = State.CreateInitial(MersenneCombinedDivisorScannerFullStreamExtended.QNibbleGenerator16.InitialState, maxQBits);
+        Enqueue(init);
+
+        while (TryDequeue(out var st))
+        {
+            if (st.Block >= maxBlocks)
+            {
+                if (FinishScanToEndDeterministic(pBits, maxQBits, ref st) && st.Carry == 0)
+                {
+                    BigInteger qVal = st.QBits.ToBigInteger();
+                    if (qVal > BigInteger.One)
+                    {
+                        foundQ = qVal;
+                        if (verifyWithModPow)
+                        {
+                            bool ok = BigInteger.ModPow(2, prime, foundQ) == BigInteger.One;
+                            if (!ok) return ScanResult.Candidate;
+                        }
+                        return ScanResult.FoundDivisor;
+                    }
+                }
+                continue;
+            }
+
+            int startBit = st.Block << 2;
+
+            // Reset buffers
+            for (int i = 0; i < 16; i++) { qNibByKn[i] = 0xFF; nextByKn[i] = default; countsByQn[i] = 0; }
+
+            if (st.KTerminated)
+            {
+                byte kn = 0;
+                qGen.ComputeNext(st.QState, kn, out byte qn, out var ns);
+
+                // Advance generator state and post-termination flushing
+                st.QState = ns;
+                if (st.KFlushRemaining > 0) st.KFlushRemaining--;
+
+                ApplyQNibble(ref st, startBit, qn, maxQBits);
+
+                if (qn == 0) st.PostTermZeroQNibbles++;
+                else st.PostTermZeroQNibbles = 0;
+
+                int requiredZeroRun = qGen.KWinLen + 1;
+                if (st.KFlushRemaining == 0 && st.QState.Carry16 == 0 && st.PostTermZeroQNibbles >= requiredZeroRun)
+                {
+                    // Freeze q and finish
+                    var done = st.CloneShallow();
+                    done.Block = maxBlocks;
+                    Enqueue(done);
+                    continue;
+                }
+
+                qNibByKn[kn] = qn;
+                nextByKn[kn] = ns;
+                countsByQn[qn] = 1;
+            }
+            else
+            {
+                qGen.ComputeAllNext(st.QState, qNibByKn, nextByKn, countsByQn);
+            }
+
+            for (int qnVal = 0; qnVal < 16; qnVal++)
+            {
+                if (countsByQn[qnVal] == 0) continue;
+                byte qn = (byte)qnVal;
+
+                if (st.Block == 0 && !IsAllowedQ0Nibble(qn))
+                    continue;
+
+                // Compute allowed a-nibbles deterministically for this (state, qn).
+                int sigEndBit = Math.Min(startBit + 3, pBits + maxQBits);
+                ulong qSig = st.QBits.Signature64WithNibbleUpTo(sigEndBit, startBit, qn, maxQBits);
+                ulong aSig = st.AWindow.Signature64();
+
+                ushort allowedMask;
+                int carryForCache = st.Carry;
+                if ((uint)carryForCache <= (uint)CarryCacheMax)
+                {
+                    var key = new AllowedMaskKey(pBits, maxQBits, st.Block, carryForCache, qn, qSig, aSig);
+                    if (!allowedMaskCache.TryGetValue(key, out allowedMask))
+                    {
+                        allowedMask = ComputeAllowedANibbleMaskDeterministic(pBits, maxQBits, st, startBit, qn);
+                        allowedMaskCache[key] = allowedMask;
+                    }
+                }
+                else
+                {
+                    // Large carry: compute without caching.
+                    allowedMask = ComputeAllowedANibbleMaskDeterministic(pBits, maxQBits, st, startBit, qn);
+                }
+
+                if (allowedMask == 0)
+                    continue;
+
+                // Expand k-nibbles mapping to this q-nibble.
+                for (int kn = 0; kn < 16; kn++)
+                {
+                    if (qNibByKn[kn] != qn) continue;
+                    if (st.Block == 0 && kn == 0) continue; // keep k>=1 (so q>1)
+
+                    var child = st.CloneShallow();
+                    child.QState = nextByKn[kn];
+
+                    bool canTerminateHere = !st.KTerminated && kn == 0 && st.Block > 0;
+
+                    ApplyQNibble(ref child, startBit, qn, maxQBits);
+
+                    // normal branch
+                    ExpandANibbles(pBits, maxQBits, maxQBits, ref child, startBit, allowedMask, Enqueue);
+
+                    // terminated branch
+                    if (canTerminateHere)
+                    {
+                        var termChild = st.CloneShallow();
+                        termChild.QState = nextByKn[kn];
+                        termChild.KTerminated = true;
+                        termChild.KFlushRemaining = (byte)qGen.KWinLen;
+                        termChild.PostTermZeroQNibbles = 0;
+
+                        ApplyQNibble(ref termChild, startBit, qn, maxQBits);
+
+                        ExpandANibbles(pBits, maxQBits, maxQBits, ref termChild, startBit, allowedMask, Enqueue);
+                    }
+                }
+            }
+        }
+
+        return ScanResult.RuledOut;
+    }
+
+    private static void ExpandANibbles(
+        int pBits,
+        int maxQBits,
+        int windowBits,
+        ref State baseState,
+        int startBit,
+        ushort allowedMask,
+        Action<State> push)
+    {
+        // Iterate allowed a-nibbles.
+        for (int aNib = 0; aNib < 16; aNib++)
+        {
+            if ((allowedMask & (1 << aNib)) == 0) continue;
+            if (startBit == 0 && (aNib & 1) == 0) continue; // enforce a0=1
+
+            var st = baseState.CloneShallow();
+            ApplyANibblePlanned(ref st, startBit, (byte)aNib);
+
+            // Deterministically step the 4 columns (planned bits remove branching).
+            if (!StepColumnsForBlockDeterministic(pBits, maxQBits, ref st, startBit))
+                continue;
+
+            st.Block = st.QState.NibbleIndex;
+            push(st);
+        }
+    }
+
+    private static ushort ComputeAllowedANibbleMaskDeterministic(int pBits, int maxQBits, State st, int startBit, byte qNibble)
+    {
+        // Ensure qNibble is applied to the state for reading q bits within this block.
+        var baseState = st.CloneShallow();
+        ApplyQNibble(ref baseState, startBit, qNibble, maxQBits);
+
+        ushort mask = 0;
+        for (int aNib = 0; aNib < 16; aNib++)
+        {
+            if (startBit == 0 && (aNib & 1) == 0) continue;
+
+            var tmp = baseState.CloneShallow();
+            ApplyANibblePlanned(ref tmp, startBit, (byte)aNib);
+
+            // Only test the 4 columns deterministically.
+            if (StepColumnsForBlockDeterministic(pBits, maxQBits, ref tmp, startBit))
+                mask |= (ushort)(1 << aNib);
+        }
+
+        return mask;
+    }
+
+    private static bool StepColumnsForBlockDeterministic(int pBits, int maxQBits, ref State st, int startBit)
+    {
+        int endBit = Math.Min(startBit + 3, pBits + maxQBits);
+        while (st.BitIndex <= endBit)
+        {
+            if (!StepSingleColumnDeterministic(pBits, maxQBits, ref st))
+                return false;
+            st.BitIndex++;
+        }
+        return true;
+    }
+
+    private static bool FinishScanToEndDeterministic(int pBits, int maxQBits, ref State st)
+    {
+        int end = pBits + 1;
+        while (st.BitIndex <= end)
+        {
+            int startBit = (st.BitIndex >> 2) << 2;
+            if (!StepColumnsForBlockDeterministic(pBits, maxQBits, ref st, startBit))
+                return false;
+        }
+        return true;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static bool StepSingleColumnDeterministic(int pBits, int maxQBits, ref State st)
+    {
+        int j = st.BitIndex;
+        int requiredBit = (j < pBits) ? 1 : 0;
+
+        int sumOther = st.Carry;
+
+        int maxT = Math.Min(j, maxQBits - 1);
+
+        // Contributions from q_t=1 for t>0: add a_{j-t}
+        foreach (int t in st.QBits.EnumerateSetBitsUpTo(maxT))
+        {
+            if (t == 0) continue;
+            int aIndex = j - t;
+            if (aIndex < 0) continue;
+            if (st.AWindow.GetBitRelative(aIndex) != 0)
+                sumOther++;
+        }
+
+        // Deterministic a_j: must be planned or already committed; if missing, treat as unknown => not deterministic
+        if (!st.AWindow.TryGetKnownBit(j, out int aJ))
+            return false;
+
+        int sum = sumOther + aJ;
+        if ((sum & 1) != requiredBit)
+            return false;
+
+        int newCarry = (requiredBit == 1) ? ((sum - 1) >> 1) : (sum >> 1);
+        st.Carry = newCarry;
+
+        // Commit bit into window (PushBit also clears planned for j).
+        st.AWindow.PushBit(j, aJ);
+        return true;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static void ApplyQNibble(ref State st, int startBit, byte qNibble, int maxQBits)
+    {
+        for (int b = 0; b < 4; b++)
+        {
+            int bitPos = startBit + b;
+            if (bitPos >= maxQBits) continue;
+            int bit = (qNibble >> b) & 1;
+            if (bit != 0) st.QBits.Set(bitPos);
+        }
+        st.QBits.Set(0); // enforce q0=1
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static void ApplyANibblePlanned(ref State st, int startBit, byte aNibble)
+    {
+        for (int b = 0; b < 4; b++)
+        {
+            int bitPos = startBit + b;
+            int bit = (aNibble >> b) & 1;
+            st.AWindow.SetPlanned(bitPos, bit);
+        }
+    }
+}
@@ -0,0 +1,465 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core.Cpu;
+
+/// <summary>
+/// Jump-capable (power-of-two composition) residue automaton for M_p = 2^p - 1.
+///
+/// For a fixed candidate divisor q (bit-length <= maxQBits), this is an exact decision procedure:
+/// it checks whether there exists an a-bitstream such that a*q equals 2^p-1, i.e. the output bits are
+///   - 1 for columns j = 0..p-1
+///   - 0 for columns j >= p (and the multiplication "drains" to zero).
+///
+/// No powmod2 is used.
+///
+/// NOTE: This algorithm is intended for your "sparse shifted-p" family:
+///   q = 1 + Σ_{u in U} (p << u)
+/// with small |U|, where q itself is not supplied as ulong but can be materialized as BigInteger at the end.
+///
+/// IMPORTANT: This implementation supports q of arbitrary size (bounded by maxQBits for the run), but
+/// the state space can still be large for big maxQBits.
+/// </summary>
+public static class MersenneShiftedPJumpResidueScanner64
+{
+    public enum ScanResult
+    {
+        RuledOut = 0,
+        FoundDivisor = 1,
+    }
+
+    // --------------------------- Bit window (immutable) ---------------------------
+
+    private sealed class BitWindow : IEquatable<BitWindow>
+    {
+        private readonly ulong[] _words; // little endian words; bit i in word i>>6
+        private readonly ulong _lastMask;
+        private readonly int _hash;
+
+        public int Bits { get; }
+        public int WordCount => _words.Length;
+
+        public BitWindow(int bits, bool setBit0)
+        {
+            if (bits <= 0) throw new ArgumentOutOfRangeException(nameof(bits));
+            Bits = bits;
+            _words = new ulong[(bits + 63) >> 6];
+            int lastBits = bits - ((_words.Length - 1) << 6);
+            _lastMask = lastBits == 64 ? ulong.MaxValue : ((1UL << lastBits) - 1UL);
+            if (setBit0) _words[0] = 1UL;
+            _words[^1] &= _lastMask;
+            _hash = ComputeHash(_words);
+        }
+
+        private BitWindow(int bits, ulong[] words, ulong lastMask, int hash)
+        {
+            Bits = bits;
+            _words = words;
+            _lastMask = lastMask;
+            _hash = hash;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public int GetBit(int idx)
+        {
+            if ((uint)idx >= (uint)Bits) return 0;
+            return (int)((_words[idx >> 6] >> (idx & 63)) & 1UL);
+        }
+
+        /// <summary>
+        /// Shift left by 1 within the fixed width and OR-in nextBit at position 0 (i.e. new a_j at LSB).
+        /// This matches the representation: bit0 = a_j, bit i = a_{j-i}.
+        /// </summary>
+        public BitWindow ShiftAddBit(int nextBit)
+        {
+            ulong carry = (uint)nextBit & 1U;
+            var nw = new ulong[_words.Length];
+
+            for (int i = 0; i < _words.Length; i++)
+            {
+                ulong w = _words[i];
+                ulong nextCarry = w >> 63;
+                ulong shifted = (w << 1) | carry;
+                nw[i] = shifted;
+                carry = nextCarry;
+            }
+
+            nw[^1] &= _lastMask;
+            int h = ComputeHash(nw);
+            return new BitWindow(Bits, nw, _lastMask, h);
+        }
+
+        public bool IsZero()
+        {
+            for (int i = 0; i < _words.Length; i++)
+                if (_words[i] != 0) return false;
+            return true;
+        }
+
+        public bool Equals(BitWindow? other)
+        {
+            if (ReferenceEquals(this, other)) return true;
+            if (other is null) return false;
+            if (Bits != other.Bits) return false;
+            if (_hash != other._hash) return false;
+            if (_words.Length != other._words.Length) return false;
+            for (int i = 0; i < _words.Length; i++)
+                if (_words[i] != other._words[i]) return false;
+            return true;
+        }
+
+        public override bool Equals(object? obj) => obj is BitWindow bw && Equals(bw);
+        public override int GetHashCode() => _hash;
+
+        private static int ComputeHash(ulong[] words)
+        {
+            // FNV-1a-ish
+            const ulong FnvOffset = 1469598103934665603UL;
+            const ulong FnvPrime = 1099511628211UL;
+            ulong h = FnvOffset;
+            for (int i = 0; i < words.Length; i++)
+            {
+                h ^= words[i];
+                h *= FnvPrime;
+            }
+            return unchecked((int)(h ^ (h >> 32)));
+        }
+    }
+
+    // ------------------------------ DP state ------------------------------
+
+    private readonly struct State : IEquatable<State>
+    {
+        public readonly int Carry;
+        public readonly BitWindow AWin;
+
+        public State(int carry, BitWindow aWin)
+        {
+            Carry = carry;
+            AWin = aWin;
+        }
+
+        public bool Equals(State other) => Carry == other.Carry && AWin.Equals(other.AWin);
+        public override bool Equals(object? obj) => obj is State s && Equals(s);
+        public override int GetHashCode() => HashCode.Combine(Carry, AWin);
+    }
+
+    // ------------------------------ q representation ------------------------------
+
+    private sealed class QBits
+    {
+        private readonly ulong[] _words;
+        public int Bits { get; }
+        public int PopCount { get; }
+
+        public QBits(BigInteger q, int maxQBits)
+        {
+            if (maxQBits <= 0) throw new ArgumentOutOfRangeException(nameof(maxQBits));
+            Bits = maxQBits;
+            int wc = (maxQBits + 63) >> 6;
+            _words = new ulong[wc];
+
+            BigInteger tmp = q;
+            for (int i = 0; i < wc; i++)
+            {
+                _words[i] = (ulong)(tmp & ulong.MaxValue);
+                tmp >>= 64;
+            }
+
+            // mask out bits above maxQBits
+            int lastBits = maxQBits - ((wc - 1) << 6);
+            ulong lastMask = lastBits == 64 ? ulong.MaxValue : ((1UL << lastBits) - 1UL);
+            _words[^1] &= lastMask;
+
+            int pc = 0;
+            for (int i = 0; i < wc; i++) pc += BitOperations.PopCount(_words[i]);
+            PopCount = pc;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public int GetBit(int idx)
+        {
+            if ((uint)idx >= (uint)Bits) return 0;
+            return (int)((_words[idx >> 6] >> (idx & 63)) & 1UL);
+        }
+
+        /// <summary>Enumerate indices of set bits (0..Bits-1).</summary>
+        public IEnumerable<int> EnumerateOnes()
+        {
+            for (int wi = 0; wi < _words.Length; wi++)
+            {
+                ulong w = _words[wi];
+                while (w != 0)
+                {
+                    int tz = BitOperations.TrailingZeroCount(w);
+                    int bit = (wi << 6) + tz;
+                    if (bit >= Bits) yield break;
+                    yield return bit;
+                    w &= w - 1;
+                }
+            }
+        }
+    }
+
+    // -------------------------- One-step transition --------------------------
+
+    private static void NextStatesOneStep(
+        QBits qBits,
+        int maxOnes,
+        int targetBit,
+        in State s,
+        List<State> dst)
+    {
+        int sum = s.Carry;
+
+        // Σ_{i where q_i=1} a_{j-i}  -- note: AWin bit i is a_{j-i}
+        foreach (int i in qBits.EnumerateOnes())
+        {
+            sum += s.AWin.GetBit(i);
+        }
+
+        if ((sum & 1) != targetBit) return;
+
+        int newCarry = sum >> 1;
+
+        // Very conservative ceiling to avoid runaway state blow-up on junk candidates.
+        // For your sparse q, maxOnes is typically small.
+        if (newCarry > (maxOnes + 256)) return;
+
+        // branch on next a-bit (a_{j+1} ∈ {0,1})
+        dst.Add(new State(newCarry, s.AWin.ShiftAddBit(0)));
+        dst.Add(new State(newCarry, s.AWin.ShiftAddBit(1)));
+    }
+
+    // -------------------------- Jump table (targetBit=1) --------------------------
+
+    private sealed class JumpTable
+    {
+        private readonly QBits _qBits;
+        private readonly int _maxOnes;
+        private readonly List<Dictionary<State, HashSet<State>>> _pow = new();
+
+        public JumpTable(QBits qBits)
+        {
+            _qBits = qBits;
+            _maxOnes = qBits.PopCount;
+            _pow.Add(new Dictionary<State, HashSet<State>>(capacity: 1024)); // k=0
+        }
+
+        private HashSet<State> GetPow0(in State s)
+        {
+            var d0 = _pow[0];
+            if (d0.TryGetValue(s, out var set)) return set;
+
+            var tmp = new List<State>(2);
+            NextStatesOneStep(_qBits, _maxOnes, targetBit: 1, s, tmp);
+
+            set = new HashSet<State>(tmp);
+            d0[s] = set;
+            return set;
+        }
+
+        private HashSet<State> GetPowK(int k, in State s)
+        {
+            EnsurePow(k);
+            var dk = _pow[k];
+            if (dk.TryGetValue(s, out var set)) return set;
+
+            if (k == 0) return GetPow0(s);
+
+            var mid = GetPowK(k - 1, s);
+            var outSet = new HashSet<State>();
+            foreach (var m in mid)
+            {
+                foreach (var e in GetPowK(k - 1, m))
+                    outSet.Add(e);
+            }
+            dk[s] = outSet;
+            return outSet;
+        }
+
+        private void EnsurePow(int k)
+        {
+            while (_pow.Count <= k)
+                _pow.Add(new Dictionary<State, HashSet<State>>(capacity: 1024));
+        }
+
+        public HashSet<State> Advance(HashSet<State> start, ulong steps)
+        {
+            if (steps == 0) return start;
+
+            int hi = 63 - BitOperations.LeadingZeroCount(steps);
+
+            var cur = start;
+            for (int k = 0; k <= hi; k++)
+            {
+                if (((steps >> k) & 1UL) == 0) continue;
+
+                var next = new HashSet<State>();
+                foreach (var s in cur)
+                {
+                    foreach (var e in GetPowK(k, s))
+                        next.Add(e);
+                }
+
+                cur = next;
+                if (cur.Count == 0) break;
+            }
+
+            return cur;
+        }
+
+        public int MaxOnes => _maxOnes;
+        public QBits QBits => _qBits;
+    }
+
+    // ------------------------------ Tail drain (targetBit=0) ------------------------------
+
+    private static bool CanDrainToZero(QBits qBits, int maxOnes, HashSet<State> afterMain)
+    {
+        var frontier = new HashSet<State>(afterMain);
+        var seen = new HashSet<State>(afterMain);
+
+        int maxSteps = qBits.Bits + 256; // conservative
+
+        for (int step = 0; step < maxSteps; step++)
+        {
+            if (frontier.Count == 0) break;
+
+            var nextFrontier = new HashSet<State>();
+
+            foreach (var s in frontier)
+            {
+                if (s.Carry == 0 && s.AWin.IsZero())
+                    return true;
+
+                var tmp = new List<State>(2);
+                NextStatesOneStep(qBits, maxOnes, targetBit: 0, s, tmp);
+                foreach (var ns in tmp)
+                    if (seen.Add(ns))
+                        nextFrontier.Add(ns);
+            }
+
+            frontier = nextFrontier;
+        }
+
+        return false;
+    }
+
+    // ------------------------------ Public API ------------------------------
+
+    /// <summary>
+    /// Exact decision: does there exist an a-bitstream such that a*q == 2^p-1 and no higher bits,
+    /// using only the automaton (no powmod2)?
+    /// </summary>
+    public static bool IsDivisorByJumpAutomaton(ulong primeP, BigInteger q, int maxQBits)
+    {
+        if (maxQBits <= 0) throw new ArgumentOutOfRangeException(nameof(maxQBits));
+        if (q.Sign <= 0) return false;
+        if ((q & 1) == 0) return false;
+        if (q == BigInteger.One) return false;
+
+        // Require q to fit within maxQBits.
+        if (BitLength(q) > maxQBits) return false;
+
+        // quick low-bit filter: q mod 8 in {1,7} (necessary in your current search family)
+        int mod8 = (int)(q & 7);
+        if (mod8 != 1 && mod8 != 7) return false;
+
+        var qb = new QBits(q, maxQBits);
+
+        // Initial state at j=0: a0=1 => AWin bit0=1; carry=0
+        var initA = new BitWindow(maxQBits, setBit0: true);
+        var initSet = new HashSet<State> { new State(0, initA) };
+
+        var jt = new JumpTable(qb);
+        var afterMain = jt.Advance(initSet, primeP);
+        if (afterMain.Count == 0) return false;
+
+        return CanDrainToZero(qb, jt.MaxOnes, afterMain);
+    }
+
+    /// <summary>
+    /// Enumerate sparse U combinations and test q via the jump automaton.
+    /// Returns the found q as BigInteger (materialized) with no 64-bit limit.
+    /// </summary>
+    public static ScanResult TryFindDivisorBySparseShiftU(
+        ulong primeP,
+        int maxQBits,
+        int maxShiftTerms,
+        out BigInteger foundQ)
+    {
+        foundQ = BigInteger.Zero;
+
+        if (maxQBits <= 0) throw new ArgumentOutOfRangeException(nameof(maxQBits));
+        if (maxShiftTerms <= 0) throw new ArgumentOutOfRangeException(nameof(maxShiftTerms));
+
+        // Candidate shifts u are in [1, maxQBits-1]
+        int maxU = maxQBits - 1;
+        if (maxU <= 0) return ScanResult.RuledOut;
+
+        BigInteger pBI = new BigInteger(primeP);
+
+        for (int terms = 1; terms <= maxShiftTerms; terms++)
+        {
+            if (terms > maxU) break;
+
+            var comb = new int[terms];
+            for (int i = 0; i < terms; i++) comb[i] = i + 1;
+
+            while (true)
+            {
+                BigInteger q = BigInteger.One;
+                for (int i = 0; i < comb.Length; i++)
+                {
+                    int u = comb[i];
+                    q += (pBI << u);
+
+                    // Early cut: if already exceeds bit budget, skip building further.
+                    if (BitLength(q) > maxQBits)
+                        break;
+                }
+
+                if (BitLength(q) <= maxQBits)
+                {
+                    if (IsDivisorByJumpAutomaton(primeP, q, maxQBits))
+                    {
+                        foundQ = q;
+                        return ScanResult.FoundDivisor;
+                    }
+                }
+
+                // next combination
+                int pos = terms - 1;
+                while (pos >= 0 && comb[pos] == maxU - (terms - 1 - pos)) pos--;
+                if (pos < 0) break;
+                comb[pos]++;
+                for (int j = pos + 1; j < terms; j++)
+                    comb[j] = comb[j - 1] + 1;
+            }
+        }
+
+        return ScanResult.RuledOut;
+    }
+
+    // ------------------------------ Helpers ------------------------------
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static int BitLength(in BigInteger x)
+    {
+        if (x.Sign == 0) return 0;
+        // BigInteger uses two's complement; for positive numbers this is OK.
+        byte[] bytes = x.ToByteArray(isUnsigned: true, isBigEndian: true);
+        if (bytes.Length == 0) return 0;
+        byte msb = bytes[0];
+        int lz = 0;
+        for (int b = 7; b >= 0; b--)
+        {
+            if (((msb >> b) & 1) != 0) break;
+            lz++;
+        }
+        return bytes.Length * 8 - lz;
+    }
+}
@@ -58,6 +58,30 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 	private GpuUInt128WorkSet _divisorScanGpuWorkSet;
 	private static readonly ConcurrentDictionary<ulong, byte> _checkedPow2MinusOne = new();
 	private ulong _currentPrime;
+	[ThreadStatic]
+	private static Dictionary<ulong, ulong>? _pow2DivisorPowModCache;
+#if DETAILED_LOG
+	[ThreadStatic]
+	private static long _pow2CacheHits;
+	[ThreadStatic]
+	private static long _pow2CacheMisses;
+	[ThreadStatic]
+	private static long _pow2CacheLookups;
+	[ThreadStatic]
+	private static long _pow2CacheEligible;
+#endif
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static void ResetPow2Cache()
+	{
+		_pow2DivisorPowModCache?.Clear();
+#if DETAILED_LOG
+		_pow2CacheHits = 0;
+		_pow2CacheMisses = 0;
+		_pow2CacheLookups = 0;
+		_pow2CacheEligible = 0;
+#endif
+	}
+
 #if DivisorSet_BitContradiction
 	private static Persistence.BitContradictionStateRepository? _bitContradictionStateRepository;
 #endif
@@ -125,14 +149,15 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	private static int GetBitLengthPortable(in BigInteger value)
 	{
-		if (value.IsZero)
-		{
-			return 0;
-		}
+		// if (value.IsZero)
+		// {
+		// 	return 0;
+		// }

-		byte[] bytes = value.ToByteArray(isUnsigned: true, isBigEndian: false);
-		byte msb = bytes[^1];
-		return ((bytes.Length - 1) * 8) + (BitOperations.Log2(msb) + 1);
+		// byte[] bytes = value.ToByteArray(isUnsigned: true, isBigEndian: false);
+		// byte msb = bytes[^1];
+		// return ((bytes.Length - 1) * 8) + (BitOperations.Log2(msb) + 1);
+		return (int)(value.GetBitLength());
 	}

 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -152,25 +177,8 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 			return false;
 		}

-		int bits;
-		try
-		{
-			bits = checked((int)prime);
-		}
-		catch (OverflowException)
-		{
-			throw;
-		}
-
-		BigInteger mersenne;
-		try
-		{
-			mersenne = (BigInteger.One << bits) - BigInteger.One;
-		}
-		catch (OutOfMemoryException)
-		{
-			throw;
-		}
+		int bits = checked((int)prime);
+		BigInteger mersenne = (BigInteger.One << bits) - BigInteger.One;
 		BigInteger denominator = step;
 		if (denominator <= BigInteger.Zero)
 		{
@@ -271,6 +279,7 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 	[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
 	public void ResetStateTracking()
 	{
+		ResetPow2Cache();
 		_stateCounter = 0;
 		_pow2MinusOneChecked = false;
 		_currentPrime = 0UL;
@@ -290,6 +299,7 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 	[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
 	public void ResumeFromState(in string stateFile, in BigInteger lastSavedK, in BigInteger minK)
 	{
+		ResetPow2Cache();
 		StateFilePath = stateFile;
 		_lastSavedK = lastSavedK;
 		MinK = minK;
@@ -356,6 +366,7 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 	public bool IsPrime(ulong prime, out bool divisorsExhausted, out BigInteger divisor)
 	{
 		_currentPrime = prime;
+		ResetPow2Cache();
 		BigInteger allowedMax = MersenneNumberDivisorByDivisorTester.ComputeAllowedMaxDivisorBig(prime, DivisorLimit);

 		// if (TryFindPowerOfTwoMinusOneDivisor(prime, allowedMax, out divisor))
@@ -454,6 +465,7 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 			return compositePow2;
 #else
 #if DivisorSet_BitContradiction
+		BitContradictionSolverWithAMultiplier.Initialize();
 		bool compositeBitContradiction = CheckDivisorsBitContradiction(
 			prime,
 			primeDecimalMask,
@@ -514,7 +526,14 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		if (fits64 && composite64)
 		{
 			allowedMax64 = unlimited ? ulong.MaxValue : (ulong)allowedMax;
-			composite64 = CheckDivisors64Bit(
+			// composite64 = CheckDivisors64Bit(
+			// 	prime,
+			// 	primeDecimalMask,
+			// 	allowedMax64,
+			// 	(ulong)normalizedMinK,
+			// 	out processedAll,
+			// 	out foundDivisor64);
+			composite64 = CheckDivisorsSequentialPow2Cache64(
 				prime,
 				primeDecimalMask,
 				allowedMax64,
@@ -528,7 +547,14 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		if (fits64 && allowedMax > ulong.MaxValue)
 		{
 			allowedMax64 = ulong.MaxValue;
-			composite64 = CheckDivisors64Bit(
+			// composite64 = CheckDivisors64Bit(
+			// 	prime,
+			// 	primeDecimalMask,
+			// 	allowedMax64,
+			// 	(ulong)normalizedMinK,
+			// 	out processedAll,
+			// 	out foundDivisor64);
+			composite64 = CheckDivisorsSequentialPow2Cache64(
 				prime,
 				primeDecimalMask,
 				allowedMax64,
@@ -554,7 +580,15 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		}
 #endif

-		return CheckDivisorsLarge(
+		// return CheckDivisorsLarge(
+		// 	prime,
+		// 	primeDecimalMask,
+		// 	allowedMax,
+		// 	normalizedMinK,
+		// 	step,
+		// 	out processedAll,
+		// 	out foundDivisor);
+		return CheckDivisorsSequentialPow2CacheBig(
 			prime,
 			primeDecimalMask,
 			allowedMax,
@@ -750,16 +784,23 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		// Default: frontier/windowed scan over (q,a) space.
 		MersenneCombinedDivisorScannerFullStreamExtended.QNibbleGenerator16.SelfTest(138000001);
 		// MersenneBitTreeDivisorScannerWithAMultiplier.ScanResult scanResult = MersenneBitTreeDivisorScannerWithAMultiplier.TryFindDivisorByStreamingScan(prime, 128, false, out BigInteger branchDivisor);
-		MersenneCombinedDivisorScannerFullStreamExtended.ScanResult scanResult = MersenneCombinedDivisorScannerFullStreamExtended.TryFindDivisorByStreamingScan(prime, 128, false, out BigInteger branchDivisor);
+		// MersenneCombinedDivisorScannerFullStreamExtended.ScanResult scanResult = MersenneCombinedDivisorScannerFullStreamExtended.TryFindDivisorByStreamingScan(prime, 128, false, out BigInteger branchDivisor);
+		// MersenneResidueNibbleAutomatonScanner.ScanResult scanResult = MersenneResidueNibbleAutomatonScanner.TryFindDivisorByResidueAutomaton(prime, 4096, false, out BigInteger branchDivisor);
+		MersenneShiftedPJumpResidueScanner64.ScanResult scanResult = MersenneShiftedPJumpResidueScanner64.TryFindDivisorBySparseShiftU(prime, 4096, 10, out BigInteger branchDivisor);
+
 		// if (TryExactBitTreeCheck(prime, allowedMax, minK, step, out BigInteger branchDivisor))
-		if (scanResult == MersenneCombinedDivisorScannerFullStreamExtended.ScanResult.FoundDivisor)
+		// if (scanResult == MersenneCombinedDivisorScannerFullStreamExtended.ScanResult.FoundDivisor)
+		// if (scanResult == MersenneResidueNibbleAutomatonScanner.ScanResult.FoundDivisor)
+		if (scanResult == MersenneShiftedPJumpResidueScanner64.ScanResult.FoundDivisor)
 		{
 			foundDivisor = branchDivisor;
 			return true;
 		}
-		else if (scanResult == MersenneCombinedDivisorScannerFullStreamExtended.ScanResult.Candidate)
+		else if (scanResult == MersenneShiftedPJumpResidueScanner64.ScanResult.RuledOut)
+		// else if (scanResult == MersenneResidueNibbleAutomatonScanner.ScanResult.Candidate)
+		// else if (scanResult == MersenneCombinedDivisorScannerFullStreamExtended.ScanResult.Candidate)
 		{
-			processedAll = false;
+			processedAll = true;
 		}

 		return false;
@@ -1552,7 +1593,7 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 	// 		return true;
 	// 	}

-	// 	ulong exponent = effectiveExponent > 0UL ? effectiveExponent : prime;
+	// 	ulong exponent64 = effectiveExponent > 0UL ? effectiveExponent : prime;
 	// 	int pBits;
 	// 	try
 	// 	{
@@ -2744,6 +2785,227 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 #endif
 	}

+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static bool IsPowerOfTwo(ulong value) => value != 0 && (value & (value - 1)) == 0;
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static ulong PowModUlong(ulong exponent, ulong modulus)
+	{
+		ulong result = 1 % modulus;
+		ulong baseVal = 2 % modulus;
+		ulong exp = exponent;
+		while (exp > 0)
+		{
+			if ((exp & 1UL) != 0)
+			{
+				result = (ulong)(((UInt128)result * baseVal) % modulus);
+			}
+
+			baseVal = (ulong)(((UInt128)baseVal * baseVal) % modulus);
+			exp >>= 1;
+		}
+
+		return result;
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static bool TryGetPow2PowModCached(ulong divisor, out ulong powMod)
+	{
+#if DETAILED_LOG
+		_pow2CacheLookups++;
+#endif
+		_pow2DivisorPowModCache ??= new Dictionary<ulong, ulong>(64);
+		if (_pow2DivisorPowModCache.TryGetValue(divisor, out powMod))
+		{
+#if DETAILED_LOG
+			_pow2CacheHits++;
+#endif
+			return true;
+		}
+
+#if DETAILED_LOG
+		_pow2CacheMisses++;
+#endif
+		return false;
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static void StorePow2PowModCached(ulong divisor, ulong powMod)
+	{
+		// EvenPerfectBitScanner's logic forces the divisor to be initialized here. We first get, then store.
+		_pow2DivisorPowModCache![divisor] = powMod;
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveOptimization)]
+	private bool CheckDivisorsSequentialPow2Cache64(
+			ulong prime,
+			ushort primeDecimalMask,
+			ulong allowedMax,
+			ulong minK,
+			out bool processedAll,
+			out ulong foundDivisor)
+	{
+		processedAll = true;
+		foundDivisor = 0UL;
+
+		ulong step = prime << 1;
+		if (step == 0UL)
+		{
+			return false;
+		}
+
+		ulong effectiveMax = allowedMax == 0UL ? ulong.MaxValue : allowedMax;
+		ulong maxKAllowed = (effectiveMax - 1UL) / step;
+		if (maxKAllowed < 1UL || minK > maxKAllowed)
+		{
+			return false;
+		}
+
+		UInt128 step128 = step;
+		UInt128 divisor128 = (step128 * minK) + UInt128.One;
+		if (divisor128 > effectiveMax)
+		{
+			return false;
+		}
+
+		ulong divisor = (ulong)divisor128;
+		ulong currentK = minK;
+		var residueStepper = new MersenneDivisorResidueStepper(prime, new GpuUInt128(step), new GpuUInt128(divisor));
+
+		while (divisor <= effectiveMax)
+		{
+			if (residueStepper.IsAdmissible())
+			{
+				// Stopwatch sw = Stopwatch.StartNew();
+				RecordState(currentK);
+				ulong powMod;
+				bool isPow2 = IsPowerOfTwo(currentK);
+#if DETAILED_LOG
+				if (isPow2)
+				{
+					_pow2CacheEligible++;
+				}
+#endif
+				if (!isPow2 || !TryGetPow2PowModCached(divisor, out powMod))
+				{
+					powMod = PowModUlong(prime, divisor);
+					if (isPow2)
+					{
+						StorePow2PowModCached(divisor, powMod);
+					}
+				}
+
+				if (powMod == 1UL)
+				{
+					// sw.Stop();
+					foundDivisor = divisor;
+					return true;
+				}
+
+				// sw.Stop();
+				// Console.WriteLine($"[sequential-pow2] p={prime} divisor={divisor} powmod={powMod} isPow2={isPow2} pow2Eligible={_pow2CacheEligible} lookups={_pow2CacheLookups} cacheHits={_pow2CacheHits} cacheMisses={_pow2CacheMisses} elapsed={sw.Elapsed}");
+			}
+
+			if (currentK == maxKAllowed)
+			{
+				break;
+			}
+
+			divisor += step;
+			currentK++;
+			residueStepper.Advance();
+		}
+
+		return false;
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveOptimization)]
+	private bool CheckDivisorsSequentialPow2CacheBig(
+		ulong prime,
+		ushort primeDecimalMask,
+		BigInteger allowedMax,
+		BigInteger currentK,
+		BigInteger step,
+		out bool processedAll,
+		out BigInteger foundDivisor)
+	{
+		foundDivisor = BigInteger.Zero;
+		if (allowedMax.IsZero)
+		{
+			processedAll = false;
+			return false;
+		}
+
+		processedAll = true;
+		BigInteger divisor = (step * currentK) + BigInteger.One;
+		if (divisor > allowedMax)
+		{
+			return false;
+		}
+
+		BigInteger maxKAllowed = (allowedMax - BigInteger.One) / step;
+		TryClampMaxKForMersenneTail(prime, step, ref maxKAllowed);
+		if (currentK > maxKAllowed)
+		{
+			return false;
+		}
+
+		BigInteger remainingIterationsBig = maxKAllowed - currentK + BigInteger.One;
+
+		var rem10 = new BigIntegerCycleRemainderStepper(10);
+		var rem8 = new BigIntegerCycleRemainderStepper(8);
+		var rem3 = new BigIntegerCycleRemainderStepper(3);
+		var rem7 = new BigIntegerCycleRemainderStepper(7);
+		var rem11 = new BigIntegerCycleRemainderStepper(11);
+		var rem13 = new BigIntegerCycleRemainderStepper(13);
+		var rem17 = new BigIntegerCycleRemainderStepper(17);
+		var rem19 = new BigIntegerCycleRemainderStepper(19);
+
+		byte remainder10 = rem10.Initialize(divisor);
+		BigInteger primeBig = (BigInteger)prime;
+		while (remainingIterationsBig.Sign > 0)
+		{
+			bool passesSmallModuli = remainder10 == 1 || remainder10 == 7;
+			if (passesSmallModuli && ((primeDecimalMask >> remainder10) & 1) != 0)
+			{
+				if (rem3.NextIsNotDivisible(divisor) &&
+					rem7.NextIsNotDivisible(divisor) &&
+					rem11.NextIsNotDivisible(divisor) &&
+					rem13.NextIsNotDivisible(divisor) &&
+					rem17.NextIsNotDivisible(divisor) &&
+					rem19.NextIsNotDivisible(divisor))
+				{
+					byte remainder8 = rem8.ComputeNext(divisor);
+					if (remainder8 == 1 || remainder8 == 7)
+					{
+						RecordState(currentK);
+						BigInteger powResult = BigInteger.ModPow(BigIntegerNumbers.Two, primeBig, divisor);
+						if (powResult.IsOne)
+						{
+							foundDivisor = divisor;
+							processedAll = true;
+							return true;
+						}
+					}
+				}
+			}
+
+			currentK++;
+			divisor += step;
+			remainder10 = rem10.ComputeNext(divisor);
+
+			remainingIterationsBig--;
+			if (remainingIterationsBig.IsZero)
+			{
+				break;
+			}
+		}
+
+		processedAll = true;
+		foundDivisor = BigInteger.Zero;
+		return false;
+	}
+
 #if DivisorSet_Pow2Groups
 	[MethodImpl(MethodImplOptions.AggressiveOptimization)]
 	private bool ProcessPow2Phase(
@@ -4311,6 +4573,7 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN

 #if DivisorSet_BitContradiction
 	private static readonly BigInteger Five = (BigInteger)5;
+	private static int _consolePrintOut;

 	[MethodImpl(MethodImplOptions.AggressiveOptimization)]
 	private bool CheckDivisorsBitContradiction(
@@ -4332,7 +4595,9 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		int kRem8 = (int)(currentK % 8);

 		BigInteger divisor = (step * currentK) + BigInteger.One;
+		_qBits = new int[(int)prime];
 		Stopwatch sw = new Stopwatch();
+		// sw.Start();
 		while (true)
 		{
 			int remainder8 = (stepMod8 * kRem8 + 1) & 7;
@@ -4341,21 +4606,20 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 				goto MOVE_NEXT;
 			}

-			if (
-					divisor <= ulong.MaxValue &&
-					!PrimeTesterByLastDigit.IsPrimeCpu((ulong)divisor)
-				)
-			{
-				goto MOVE_NEXT;
-			}
+			// if (
+			// 		divisor <= ulong.MaxValue &&
+			// 		!PrimeTesterByLastDigit.IsPrimeCpu((ulong)divisor)
+			// 	)
+			// {
+			// 	goto MOVE_NEXT;
+			// }

 			bool divides;
 			// divides = BigInteger.ModPow(BigIntegerNumbers.Two, prime, divisor) == 1;

-			ulong effectiveExponent = 0UL;
 			sw.Reset();
 			sw.Start();
-			bool decided = TryExactBitContradictionCheck(prime, divisor, effectiveExponent, out divides);
+			bool decided = TryExactBitContradictionCheck(prime, divisor, out divides);
 			sw.Stop();
 			if (!decided)
 			{
@@ -4367,18 +4631,27 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 				foundDivisor = divisor;
 				return true;
 			}
-			else {
-				Console.WriteLine($"Prime {prime} ({sw.Elapsed}), excluded {divisor}");
-			}
-
-			RecordState(currentK);
-		MOVE_NEXT:
-			if (hasLimit && currentK >= maxK)
+			else
 			{
-				break;
+				// var printToConsole = (_consolePrintOut++) == 1;
+				// if (printToConsole)
+				// {
+					// sw.Stop();
+					Console.WriteLine($"Prime {prime} ({sw.Elapsed}: {divisor})");
+					_consolePrintOut = 0;
+					// sw.Reset();
+					// sw.Start();
+				// }
 			}

-			currentK += BigInteger.One;
+			// RecordState(currentK);
+		MOVE_NEXT:
+			// if (hasLimit && currentK >= maxK)
+			// {
+			// 	break;
+			// }
+
+			// currentK += BigInteger.One;
 			divisor += step;
 			kRem8 = (kRem8 + 1) & 7;
 		}
@@ -4438,12 +4711,12 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		// 	out foundDivisor);
 	}

+	[ThreadStatic]
+	private static int[]? _qBits;
+
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	private static bool TryExactBitContradictionCheck(ulong prime, BigInteger divisor, ulong effectiveExponent, out bool divides)
+	private static bool TryExactBitContradictionCheck(ulong prime, BigInteger divisor, out bool divides)
 	{
-#if DETAILED_LOG
-		Stopwatch sw = Stopwatch.StartNew();
-#endif
 		divides = false;
 		// const ulong DebugTopDownDivisor = 1209708008767UL;
 		// const ulong DebugTopDownDivisor = 1007991562955719UL;
@@ -4477,8 +4750,31 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 			return true;
 		}

+		// if (divisor <= ulong.MaxValue)
+		// {
+		// 	// ulong exponent64 = effectiveExponent > 0UL ? effectiveExponent : prime;
+		// 	// ContradictionReason reason64;
+		// 	// bool decided64 = BitContradictionSolverWithAMultiplier.TryCheckDivisibilityFromDivisor((ulong)divisor, exponent64, out divides, out reason64);
+		// 	// if (decided64 && divides)
+		// 	// {
+		// 	// 	bool structuralOk = ((divisor - BigInteger.One) % (((BigInteger)prime) << 1)) == BigInteger.Zero;
+		// 		// bool dividesExact = structuralOk && BigInteger.ModPow(2, prime, divisor) == BigInteger.One;
+		// 		divides = BigInteger.ModPow(2, prime, divisor) == BigInteger.One;
+		// 		return true;
+		// 		// if (!dividesExact)
+		// 		// {
+		// 		// 	divides = false;
+		// 		// 	reason64 = ContradictionReason.ParityUnreachable;
+		// 		// }
+		// 	// }
+
+		// 	// return decided64;
+		// }
+
+		// Console.WriteLine($"Switching to bit-contradiction mode for {prime}");
 		// Iterative column-wise propagation without storing all columns; we only keep assigned bits of 'a'.
-		Span<int> oneOffsets = stackalloc int[qBitLength];
+		int[] oneOffsets = _qBits;
+		// Span<int> oneOffsets = stackalloc int[qBitLength];
 		int oneCount = 0;
 		for (int i = 0; i < qBitLength; i++)
 		{
@@ -4495,9 +4791,8 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 		}

 		ReadOnlySpan<int> oneOffsetsSlice = oneOffsets[..oneCount];
-		ulong exponent = effectiveExponent > 0UL ? effectiveExponent : prime;
 		// BitContradictionSolverWithQMultiplier.SetDebugEnabled(true);
-		bool decided = BitContradictionSolverWithAMultiplier.TryCheckDivisibilityFromOneOffsets(oneOffsetsSlice, exponent, out divides, out var reason);
+		bool decided = BitContradictionSolverWithAMultiplier.TryCheckDivisibilityFromOneOffsets(oneOffsetsSlice, prime, out divides, out var reason);
 		// BitContradictionSolverWithQMultiplier.SetDebugEnabled(false);
 		// bool decided = BitContradictionSolverBaseline.TryCheckDivisibilityFromOneOffsets(oneOffsetsSlice, exponent, out divides, out var reason);
 		if (decided && divides)
@@ -4511,32 +4806,28 @@ public struct MersenneNumberDivisorByDivisorCpuTesterWithTemplate() : IMersenneN
 				reason = ContradictionReason.ParityUnreachable;
 			}
 		}
-
-#if DETAILED_LOG
-		sw.Stop();
-#endif
 		if (decided && !divides)
 		{
 #if DETAILED_LOG
 			if (reason == ContradictionReason.ParityUnreachable)
 			{
-				var failure = BitContradictionSolverWithQMultiplier.LastTopDownFailure;
-				if (failure.HasValue)
-				{
-					var info = failure.Value;
-					Console.WriteLine($"[bit-contradiction] top-down prune failed at column={info.Column} carry=[{info.CarryMin},{info.CarryMax}] unknown={info.Unknown}");
-				}
+				// var failure = BitContradictionSolverWithQMultiplier.LastTopDownFailure;
+				// if (failure.HasValue)
+				// {
+				// 	var info = failure.Value;
+				// 	Console.WriteLine($"[bit-contradiction] top-down prune failed at column={info.Column} carry=[{info.CarryMin},{info.CarryMax}] unknown={info.Unknown}");
+				// }

-				var bottomUp = BitContradictionSolverWithQMultiplier.LastBottomUpFailure;
-				if (bottomUp.HasValue)
-				{
-					var info = bottomUp.Value;
-					Console.WriteLine($"[bit-contradiction] bottom-up failed at column={info.Column} carry=[{info.CarryMin},{info.CarryMax}] forced={info.Forced} unknown={info.Unknown}");
-				}
+				// var bottomUp = BitContradictionSolverWithQMultiplier.LastBottomUpFailure;
+				// if (bottomUp.HasValue)
+				// {
+				// 	var info = bottomUp.Value;
+				// 	Console.WriteLine($"[bit-contradiction] bottom-up failed at column={info.Column} carry=[{info.CarryMin},{info.CarryMax}] forced={info.Forced} unknown={info.Unknown}");
+				// }
 			}
 #endif

-			_bitContradictionStateRepository?.Upsert(prime, "excluded");
+			// _bitContradictionStateRepository?.Upsert(prime, "excluded");
 		}

 #if DETAILED_LOG
@@ -24,7 +24,7 @@ internal static class DivisorGenerator
    private const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
    private const ushort DecimalMaskWhenLastIsThree = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);
    private const ushort DecimalMaskWhenLastIsNine = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);
-    private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
+    private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);

    static DivisorGenerator()
    {
@@ -7,7 +7,7 @@ namespace PerfectNumbers.Core;
 internal struct MersenneDivisorResidueStepper(ulong prime, in GpuUInt128 step, in GpuUInt128 firstDivisor)
 {
    private const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
-    private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
+    private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);

    private readonly ushort decimalMask = (prime & 3UL) == 3UL ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
    private readonly byte step10 = ComputeModulo(step, 10, multiplier: 6);
@@ -92,7 +92,7 @@ internal struct MersenneDivisorResidueStepper(ulong prime, in GpuUInt128 step, i
 internal struct MersenneDivisorResidueStepperDescending(ulong prime, in GpuUInt128 step, in GpuUInt128 firstDivisor)
 {
    private const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
-    private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
+    private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);

    private readonly ushort decimalMask = (prime & 3UL) == 3UL ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
    private readonly byte step10 = ComputeModulo(step, 10, multiplier: 6);
@@ -8,10 +8,13 @@
    <DefineConstants>$(DefineConstants);DEVICE_CPU</DefineConstants>
    <EmitCompilerGeneratedFiles>true</EmitCompilerGeneratedFiles>
    <CompilerGeneratedFilesOutputPath>$(IntermediateOutputPath)generated</CompilerGeneratedFilesOutputPath>
+	<!-- <DefineConstants>$(DefineConstants);DETAILED_LOG</DefineConstants> -->
  </PropertyGroup>

  <ItemGroup>
    <Compile Remove="**/*.generated.cs" />
+    <Compile Remove="**/*.temp..cs" />
+    <Compile Remove="**/*.temp.cs" />
  </ItemGroup>	

  <ItemGroup>