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BitContradiction solvers improvements to increase early exclusions.

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mlemanczyk committed 2026-01-13 04:20:34 +01:00
1 parent c6dea4afcc
commit d0dbb8f92a
3 files changed
+469 -142
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PerfectNumbers.Core/ByDivisor/BitContradictionSolverWithAMultiplier.cs
+276 -9
View File
@@ -1,4 +1,5 @@
using System;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
namespace PerfectNumbers.Core.ByDivisor;
@@ -14,9 +15,85 @@ internal static class BitContradictionSolverWithAMultiplier
private const int TailCarryBatchColumns = 1024;
private const int TailCarryBatchRepeats = 1;
private const int ModLocalPrefilterMaxABits = 20;
private static readonly int[] ModLocalPrefilterModuli = { 65537, 65521 };
[ThreadStatic]
private static TopDownPruneFailure? _lastTopDownFailure;
private static bool _debugEnabled = true;
private const int TopDownCacheCapacity = 16;
private readonly struct TopDownCacheKey(long hash, int length, long maxAllowedA, long pLong)
{
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);
}
private readonly struct TopDownCacheValue(bool success, TopDownPruneFailure? failure)
{
public readonly bool Success = success;
public readonly TopDownPruneFailure? Failure = failure;
}
[ThreadStatic]
private static Dictionary<TopDownCacheKey, TopDownCacheValue>? _topDownCache;
[ThreadStatic]
private static List<TopDownCacheKey>? _topDownCacheOrder;
private static long ComputeQOffsetsHash(ReadOnlySpan<int> qOneOffsets)
{
const long fnvOffset = unchecked((long)1469598103934665603);
const long fnvPrime = 1099511628211;
long hash = fnvOffset;
for (int i = 0; i < qOneOffsets.Length; i++)
{
hash ^= qOneOffsets[i];
hash *= fnvPrime;
}
return hash;
}
private static bool TryGetTopDownCache(in TopDownCacheKey key, out TopDownCacheValue value)
{
if (_topDownCache == null)
{
value = default;
return false;
}
return _topDownCache.TryGetValue(key, out value);
}
private static void StoreTopDownCache(in TopDownCacheKey key, in TopDownCacheValue value)
{
_topDownCache ??= new Dictionary<TopDownCacheKey, TopDownCacheValue>();
_topDownCacheOrder ??= new List<TopDownCacheKey>(TopDownCacheCapacity + 1);
if (_topDownCache.ContainsKey(key))
{
_topDownCache[key] = value;
return;
}
if (_topDownCacheOrder.Count >= TopDownCacheCapacity)
{
var evict = _topDownCacheOrder[0];
_topDownCacheOrder.RemoveAt(0);
_topDownCache.Remove(evict);
}
_topDownCache[key] = value;
_topDownCacheOrder.Add(key);
}
private static int _parityZeroLogCount;
internal static TopDownPruneFailure? LastTopDownFailure => _lastTopDownFailure;
@@ -80,6 +157,109 @@ internal static class BitContradictionSolverWithAMultiplier
return true;
}
private static bool TryModularPrefilter(
ReadOnlySpan<int> qOneOffsets,
ulong p,
long maxAllowedA)
{
if (maxAllowedA < 0 || maxAllowedA > ModLocalPrefilterMaxABits)
{
return true;
}
int bitCount = (int)(maxAllowedA + 1);
if (bitCount <= 0 || bitCount >= 62)
{
return true;
}
long maxAValue = (1L << bitCount) - 1L;
for (int i = 0; i < ModLocalPrefilterModuli.Length; i++)
{
int mod = ModLocalPrefilterModuli[i];
int qMod = ComputeQMod(qOneOffsets, mod);
int target = ModPow2Minus1(p, mod);
if (qMod == 0)
{
if (target != 0)
{
return false;
}
continue;
}
int inverse = ModPow(qMod, mod - 2, mod);
long x = (long)((long)target * inverse % mod);
if (x > maxAValue)
{
return false;
}
}
return true;
}
private static int ComputeQMod(ReadOnlySpan<int> qOneOffsets, int mod)
{
long sum = 0;
for (int i = 0; i < qOneOffsets.Length; i++)
{
sum += PowMod2((ulong)qOneOffsets[i], mod);
if (sum >= mod)
{
sum %= mod;
}
}
return (int)(sum % mod);
}
private static int ModPow2Minus1(ulong p, int mod)
{
int pow = PowMod2(p, mod);
int result = pow - 1;
return result < 0 ? result + mod : result;
}
private static int PowMod2(ulong exp, int mod)
{
long result = 1 % mod;
long baseVal = 2 % mod;
ulong value = exp;
while (value > 0)
{
if ((value & 1) != 0)
{
result = (result * baseVal) % mod;
}
baseVal = (baseVal * baseVal) % mod;
value >>= 1;
}
return (int)result;
}
private static int ModPow(int value, int exp, int mod)
{
long result = 1 % mod;
long baseVal = value % mod;
int e = exp;
while (e > 0)
{
if ((e & 1) != 0)
{
result = (result * baseVal) % mod;
}
baseVal = (baseVal * baseVal) % mod;
e >>= 1;
}
return (int)result;
}
/// <summary>
/// Full column-wise propagation for a given set of q one-bit offsets (LSB=0) and exponent p.
/// Returns true if the solver could decide locally (divides or contradiction).
@@ -145,16 +325,44 @@ internal static class BitContradictionSolverWithAMultiplier
return true;
}
if (!TryTopDownCarryPrune(qOneOffsets, qOneOffsetsLength, pLong, maxAllowedA, out _lastTopDownFailure))
if (!TryModularPrefilter(qOneOffsets, p, maxAllowedA))
{
reason = ContradictionReason.ParityUnreachable;
return true;
}
long qHash = ComputeQOffsetsHash(qOneOffsets);
var cacheKey = new TopDownCacheKey(qHash, qOneOffsetsLength, maxAllowedA, pLong);
if (TryGetTopDownCache(in cacheKey, out var cached))
{
_lastTopDownFailure = cached.Failure;
if (!cached.Success)
{
reason = ContradictionReason.ParityUnreachable;
return true;
}
}
else
{
if (!TryTopDownCarryPrune(qOneOffsets, qOneOffsetsLength, pLong, maxAllowedA, out _lastTopDownFailure))
{
StoreTopDownCache(in cacheKey, new TopDownCacheValue(false, _lastTopDownFailure));
reason = ContradictionReason.ParityUnreachable;
return true;
}
StoreTopDownCache(in cacheKey, new TopDownCacheValue(true, null));
}
long lowColumn = 0;
long highColumn = pLong - 1;
CarryRange carryLow = CarryRange.Zero;
CarryRange carryHigh = CarryRange.Zero;
int bottomWindowStart = 0;
int bottomWindowEnd = 0;
int topWindowStart = qOneOffsetsLength;
int topWindowEnd = qOneOffsetsLength;
bool processTop = true;
while (lowColumn <= highColumn)
@@ -164,7 +372,7 @@ internal static class BitContradictionSolverWithAMultiplier
if (processTop)
{
if (!TryProcessTopDownBlock(qOneOffsets, qOneOffsetsLength, maxAllowedA, highColumn, blockSize, carryHigh, out carryHigh, out _lastTopDownFailure))
if (!TryProcessTopDownBlock(qOneOffsets, qOneOffsetsLength, maxAllowedA, highColumn, blockSize, carryHigh, ref topWindowStart, ref topWindowEnd, out carryHigh, out _lastTopDownFailure))
{
reason = ContradictionReason.ParityUnreachable;
return true;
@@ -174,7 +382,7 @@ internal static class BitContradictionSolverWithAMultiplier
}
else
{
if (!TryProcessBottomUpBlock(qOneOffsets, maxAllowedA, lowColumn, blockSize, ref carryLow, ref maxKnownA, ref segmentBase, segmentState0, segmentState1, out reason))
if (!TryProcessBottomUpBlock(qOneOffsets, maxAllowedA, lowColumn, blockSize, ref carryLow, ref maxKnownA, ref segmentBase, ref bottomWindowStart, ref bottomWindowEnd, segmentState0, segmentState1, out reason))
{
return true;
}
@@ -237,6 +445,8 @@ internal static class BitContradictionSolverWithAMultiplier
ref CarryRange carry,
ref long maxKnownA,
ref long segmentBase,
ref int windowStartIdx,
ref int windowEndIdx,
sbyte[] segmentState0,
sbyte[] segmentState1,
out ContradictionReason reason)
@@ -244,8 +454,53 @@ internal static class BitContradictionSolverWithAMultiplier
long endColumn = startColumn + columnCount;
int qOneOffsetsLength = qOneOffsets.Length;
int windowSize = segmentState0.Length;
for (long column = startColumn; column < endColumn; column++)
int maxOffset = qOneOffsets[qOneOffsetsLength - 1];
long stableUnknown = qOneOffsetsLength;
long column = startColumn;
while (column < endColumn)
{
if (column >= maxOffset && column <= maxAllowedA && maxKnownA < column - maxOffset)
{
long batchEnd = endColumn - 1;
if (batchEnd > maxAllowedA)
{
batchEnd = maxAllowedA;
}
long remaining = batchEnd - column + 1;
if (remaining > 0)
{
windowStartIdx = 0;
windowEndIdx = qOneOffsetsLength;
while (remaining > 0)
{
int step = remaining > TailCarryBatchColumns ? TailCarryBatchColumns : (int)remaining;
for (int i = 0; i < step; i++)
{
if (!TryPropagateCarry(carry, 0, stableUnknown, 1, out var next, out var propagateReason))
{
reason = propagateReason;
return false;
}
carry = next;
}
column += step;
remaining -= step;
}
long batchBase = (column / windowSize) * windowSize;
if (batchBase != segmentBase)
{
Array.Clear(segmentState0);
Array.Clear(segmentState1);
segmentBase = batchBase;
}
continue;
}
}
long forced = 0L;
long unknown = 0L;
long chosenIndex = -1L;
@@ -266,7 +521,18 @@ internal static class BitContradictionSolverWithAMultiplier
segmentBase = newBase;
}
for (int offsetIndex = 0; offsetIndex < qOneOffsetsLength; offsetIndex++)
while (windowEndIdx < qOneOffsetsLength && qOneOffsets[windowEndIdx] <= column)
{
windowEndIdx++;
}
long lowerBound = column - maxAllowedA;
while (windowStartIdx < windowEndIdx && qOneOffsets[windowStartIdx] < lowerBound)
{
windowStartIdx++;
}
for (int offsetIndex = windowStartIdx; offsetIndex < windowEndIdx; offsetIndex++)
{
int offset = qOneOffsets[offsetIndex];
long aIndex = column - offset;
@@ -418,6 +684,7 @@ internal static class BitContradictionSolverWithAMultiplier
carry = next;
}
column++;
}
reason = ContradictionReason.None;
@@ -431,6 +698,8 @@ internal static class BitContradictionSolverWithAMultiplier
long startHighColumn,
int columnCount,
CarryRange carryOut,
ref int windowStart,
ref int windowEnd,
out CarryRange nextCarryOut,
out TopDownPruneFailure? failure)
{
@@ -438,8 +707,6 @@ internal static class BitContradictionSolverWithAMultiplier
long carryOutMin = carryOut.Min,
carryOutMax = carryOut.Max,
value;
int windowStart = qOneOffsetsLength;
int windowEnd = qOneOffsetsLength;
long endColumn = startHighColumn - columnCount + 1;
long column = startHighColumn;
@@ -560,11 +827,11 @@ internal static class BitContradictionSolverWithAMultiplier
out TopDownPruneFailure? failure)
{
failure = null;
int windowStart = qOneOffsetsLength;
int windowEnd = qOneOffsetsLength;
long carryOutMin = 0,
carryOutMax = 0,
value;
int windowStart = qOneOffsetsLength;
int windowEnd = qOneOffsetsLength;
long column = pLong - 1;
while (column >= 0)
PerfectNumbers.Core/ByDivisor/BitContradictionSolverWithQMultiplier.cs
+119 -9
View File
@@ -52,6 +52,79 @@ internal static class BitContradictionSolverWithQMultiplier
[ThreadStatic]
private static bool _debugEnabled;
private const int TopDownCacheCapacity = 16;
private readonly struct TopDownCacheKey(long hash, int length, long maxAllowedA, long pLong)
{
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);
}
private readonly struct TopDownCacheValue(bool success, TopDownPruneFailure? failure)
{
public readonly bool Success = success;
public readonly TopDownPruneFailure? Failure = failure;
}
[ThreadStatic]
private static Dictionary<TopDownCacheKey, TopDownCacheValue>? _topDownCache;
[ThreadStatic]
private static List<TopDownCacheKey>? _topDownCacheOrder;
private static long ComputeQOffsetsHash(ReadOnlySpan<int> qOneOffsets)
{
const long fnvOffset = unchecked((long)1469598103934665603);
const long fnvPrime = 1099511628211;
long hash = fnvOffset;
for (int i = 0; i < qOneOffsets.Length; i++)
{
hash ^= qOneOffsets[i];
hash *= fnvPrime;
}
return hash;
}
private static bool TryGetTopDownCache(in TopDownCacheKey key, out TopDownCacheValue value)
{
if (_topDownCache == null)
{
value = default;
return false;
}
return _topDownCache.TryGetValue(key, out value);
}
private static void StoreTopDownCache(in TopDownCacheKey key, in TopDownCacheValue value)
{
_topDownCache ??= new Dictionary<TopDownCacheKey, TopDownCacheValue>();
_topDownCacheOrder ??= new List<TopDownCacheKey>(TopDownCacheCapacity + 1);
if (_topDownCache.ContainsKey(key))
{
_topDownCache[key] = value;
return;
}
if (_topDownCacheOrder.Count >= TopDownCacheCapacity)
{
var evict = _topDownCacheOrder[0];
_topDownCacheOrder.RemoveAt(0);
_topDownCache.Remove(evict);
}
_topDownCache[key] = value;
_topDownCacheOrder.Add(key);
}
internal static TopDownPruneFailure? LastTopDownFailure => _lastTopDownFailure;
internal static BottomUpFailure? LastBottomUpFailure => _lastBottomUpFailure;
@@ -188,17 +261,40 @@ internal static class BitContradictionSolverWithQMultiplier
return true;
}
if (!TryTopDownCarryPrune(qOneOffsets, qOneOffsetsLength, pLong, maxAllowedA, out _lastTopDownFailure))
long qHash = ComputeQOffsetsHash(qOneOffsets);
var cacheKey = new TopDownCacheKey(qHash, qOneOffsetsLength, maxAllowedA, pLong);
if (TryGetTopDownCache(in cacheKey, out var cached))
{
reason = ContradictionReason.ParityUnreachable;
Console.WriteLine($"[bit-contradiction] parity unreachable in top-down prune (failure={_lastTopDownFailure.HasValue})");
return true;
_lastTopDownFailure = cached.Failure;
if (!cached.Success)
{
reason = ContradictionReason.ParityUnreachable;
Console.WriteLine($"[bit-contradiction] parity unreachable in top-down prune (failure={_lastTopDownFailure.HasValue})");
return true;
}
}
else
{
if (!TryTopDownCarryPrune(qOneOffsets, qOneOffsetsLength, pLong, maxAllowedA, out _lastTopDownFailure))
{
StoreTopDownCache(in cacheKey, new TopDownCacheValue(false, _lastTopDownFailure));
reason = ContradictionReason.ParityUnreachable;
Console.WriteLine($"[bit-contradiction] parity unreachable in top-down prune (failure={_lastTopDownFailure.HasValue})");
return true;
}
StoreTopDownCache(in cacheKey, new TopDownCacheValue(true, null));
}
long lowColumn = 0;
long highColumn = pLong - 1;
CarryRange carryLow = CarryRange.Zero;
CarryRange carryHigh = CarryRange.Zero;
int bottomWindowStart = 0;
int bottomWindowEnd = 0;
int topWindowStart = qOneOffsetsLength;
int topWindowEnd = qOneOffsetsLength;
bool processTop = true;
while (lowColumn <= highColumn)
@@ -208,7 +304,7 @@ internal static class BitContradictionSolverWithQMultiplier
if (processTop)
{
if (!TryProcessTopDownBlock(qOneOffsets, qOneOffsetsLength, maxAllowedA, highColumn, blockSize, carryHigh, out carryHigh, out _lastTopDownFailure))
if (!TryProcessTopDownBlock(qOneOffsets, qOneOffsetsLength, maxAllowedA, highColumn, blockSize, carryHigh, ref topWindowStart, ref topWindowEnd, out carryHigh, out _lastTopDownFailure))
{
reason = ContradictionReason.ParityUnreachable;
return true;
@@ -218,7 +314,7 @@ internal static class BitContradictionSolverWithQMultiplier
}
else
{
if (!TryProcessBottomUpBlock(qOneOffsets, maxAllowedA, lowColumn, blockSize, ref carryLow, ref segmentBase, segmentState0, segmentState1, out reason))
if (!TryProcessBottomUpBlock(qOneOffsets, maxAllowedA, lowColumn, blockSize, ref carryLow, ref segmentBase, ref bottomWindowStart, ref bottomWindowEnd, segmentState0, segmentState1, out reason))
{
return true;
}
@@ -281,6 +377,8 @@ internal static class BitContradictionSolverWithQMultiplier
int columnCount,
ref CarryRange carry,
ref long segmentBase,
ref int windowStartIdx,
ref int windowEndIdx,
sbyte[] segmentState0,
sbyte[] segmentState1,
out ContradictionReason reason)
@@ -310,7 +408,18 @@ internal static class BitContradictionSolverWithQMultiplier
segmentBase = newBase;
}
for (int offsetIndex = 0; offsetIndex < qOneOffsetsLength; offsetIndex++)
while (windowEndIdx < qOneOffsetsLength && qOneOffsets[windowEndIdx] <= column)
{
windowEndIdx++;
}
long lowerBound = column - maxAllowedA;
while (windowStartIdx < windowEndIdx && qOneOffsets[windowStartIdx] < lowerBound)
{
windowStartIdx++;
}
for (int offsetIndex = windowStartIdx; offsetIndex < windowEndIdx; offsetIndex++)
{
int offset = qOneOffsets[offsetIndex];
long aIndex = column - offset;
@@ -480,6 +589,8 @@ internal static class BitContradictionSolverWithQMultiplier
long startHighColumn,
int columnCount,
CarryRange carryOut,
ref int windowStart,
ref int windowEnd,
out CarryRange nextCarryOut,
out TopDownPruneFailure? failure)
{
@@ -487,8 +598,6 @@ internal static class BitContradictionSolverWithQMultiplier
long carryOutMin = carryOut.Min,
carryOutMax = carryOut.Max,
value;
int windowStart = qOneOffsetsLength;
int windowEnd = qOneOffsetsLength;
long endColumn = startHighColumn - columnCount + 1;
long column = startHighColumn;
@@ -612,6 +721,7 @@ internal static class BitContradictionSolverWithQMultiplier
long carryOutMin = 0,
carryOutMax = 0,
value;
int windowStart = qOneOffsetsLength;
int windowEnd = qOneOffsetsLength;