BitContradiction improvements - 0.043s, p=138000001+

This commit is contained in:
mlemanczyk committed 2026-01-17 15:37:43 +01:00
1 parent e97ea151e1
commit 41e421e1eb
9 files changed
+5227 -1971

No files matched your search

@@ -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