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Reuse divisor residues across prime candidates

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Marek Lemańczyk committed 2025-09-24 16:53:43 +02:00
1 parent a39f7dda59
commit 436d3856d6
1 file changed
+61 -34
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PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs
+61 -34
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@@ -27,14 +27,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
} }
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>> _kernelCache = new(); private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>> _kernelCache = new();
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>> _kernelDeltaCache = new(); private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>> _kernelExponentCache = new();
private readonly ConcurrentDictionary<Accelerator, ConcurrentBag<BatchResources>> _resourcePools = new(AcceleratorReferenceComparer.Instance); private readonly ConcurrentDictionary<Accelerator, ConcurrentBag<BatchResources>> _resourcePools = new(AcceleratorReferenceComparer.Instance);
private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new(); private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
private Action<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>> GetKernel(Accelerator accelerator) => private Action<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>> GetKernel(Accelerator accelerator) =>
_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>(CheckKernel)); _kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>(CheckKernel));
private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> GetKernelByPrimeDelta(Accelerator accelerator) => private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> GetKernelByPrimeExponent(Accelerator accelerator) =>
_kernelDeltaCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>(ComputePrimeDeltaKernel)); _kernelExponentCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>(ComputePrimeExponentKernel));
public int GpuBatchSize public int GpuBatchSize
{ {
@@ -344,6 +344,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
private MemoryBuffer1D<ulong, Stride1D.Dense> _exponentsBuffer; private MemoryBuffer1D<ulong, Stride1D.Dense> _exponentsBuffer;
private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer; private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer;
private ulong[] _hostBuffer; private ulong[] _hostBuffer;
private ulong[] _primeBuffer;
private int[] _positionBuffer; private int[] _positionBuffer;
private int _capacity; private int _capacity;
private bool _disposed; private bool _disposed;
@@ -353,11 +354,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
_owner = owner; _owner = owner;
_lease = GpuContextPool.RentPreferred(preferCpu: false); _lease = GpuContextPool.RentPreferred(preferCpu: false);
_accelerator = _lease.Accelerator; _accelerator = _lease.Accelerator;
_kernel = owner.GetKernelByPrimeDelta(_accelerator); _kernel = owner.GetKernelByPrimeExponent(_accelerator);
_capacity = Math.Max(1, owner._gpuBatchSize); _capacity = Math.Max(1, owner._gpuBatchSize);
_exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity); _exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
_resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity); _resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity); _hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
_primeBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity); _positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
} }
@@ -376,12 +378,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
_exponentsBuffer.Dispose(); _exponentsBuffer.Dispose();
_resultsBuffer.Dispose(); _resultsBuffer.Dispose();
ArrayPool<ulong>.Shared.Return(_hostBuffer, clearArray: false); ArrayPool<ulong>.Shared.Return(_hostBuffer, clearArray: false);
ArrayPool<ulong>.Shared.Return(_primeBuffer, clearArray: false);
ArrayPool<int>.Shared.Return(_positionBuffer, clearArray: false); ArrayPool<int>.Shared.Return(_positionBuffer, clearArray: false);
_capacity = requiredCapacity; _capacity = requiredCapacity;
_exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity); _exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
_resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity); _resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity); _hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
_primeBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity); _positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
} }
@@ -428,11 +432,11 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
ReadOnlySpan<ulong> primesSlice; ReadOnlySpan<ulong> primesSlice;
Span<byte> hitsSlice; Span<byte> hitsSlice;
Span<ulong> hostSpan = _hostBuffer.AsSpan(); Span<ulong> hostSpan = _hostBuffer.AsSpan();
Span<ulong> primeSpan = _primeBuffer.AsSpan();
Span<int> positionSpan = _positionBuffer.AsSpan(); Span<int> positionSpan = _positionBuffer.AsSpan();
bool hasResidue = false; bool hasPreviousResidue = false;
ulong lastPrimeWithResidue = 0UL; ulong previousResidue = 0UL;
ulong lastResidue = 0UL; ulong previousPrime = 0UL;
while (offset < primesLength) while (offset < primesLength)
{ {
batchSize = Math.Min(gpuBatchSize, primesLength - offset); batchSize = Math.Min(gpuBatchSize, primesLength - offset);
@@ -440,8 +444,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
hitsSlice = hits.Slice(offset, batchSize); hitsSlice = hits.Slice(offset, batchSize);
int computeCount = 0; int computeCount = 0;
ulong deltaBasePrime = lastPrimeWithResidue;
bool deltaHasResidue = hasResidue;
for (int i = 0; i < batchSize; i++) for (int i = 0; i < batchSize; i++)
{ {
@@ -452,25 +454,32 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
continue; continue;
} }
ulong delta; primeSpan[computeCount] = prime;
if (deltaHasResidue)
{
delta = prime >= deltaBasePrime ? prime - deltaBasePrime : prime;
}
else
{
delta = prime;
}
hostSpan[computeCount] = delta;
positionSpan[computeCount] = i; positionSpan[computeCount] = i;
computeCount++; computeCount++;
deltaBasePrime = prime;
deltaHasResidue = true;
} }
if (computeCount > 0) if (computeCount > 0)
{ {
Span<ulong> exponentSlice = hostSpan.Slice(0, computeCount); Span<ulong> exponentSlice = hostSpan.Slice(0, computeCount);
ulong currentPrime = hasPreviousResidue ? previousPrime : 0UL;
bool hasDeltaSource = hasPreviousResidue;
for (int i = 0; i < computeCount; i++)
{
ulong prime = primeSpan[i];
if (hasDeltaSource)
{
exponentSlice[i] = prime - currentPrime;
}
else
{
exponentSlice[i] = prime;
hasDeltaSource = true;
}
currentPrime = prime;
}
ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentsView.SubView(0, computeCount); ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentsView.SubView(0, computeCount);
exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount); exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
ArrayView1D<ulong, Stride1D.Dense> resultView = resultsView.SubView(0, computeCount); ArrayView1D<ulong, Stride1D.Dense> resultView = resultsView.SubView(0, computeCount);
@@ -478,20 +487,27 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
accelerator.Synchronize(); accelerator.Synchronize();
resultView.CopyToCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount); resultView.CopyToCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
// TODO: Can we move this somehow to GPU? MulMod64 takes half of the time in CheckDivisor ulong lastPrime = previousPrime;
ulong residueAccumulator = previousResidue;
bool hasAccumulator = hasPreviousResidue;
for (int i = 0; i < computeCount; i++) for (int i = 0; i < computeCount; i++)
{ {
int position = positionSpan[i]; int position = positionSpan[i];
ulong prime = primesSlice[position]; ulong stepResidue = exponentSlice[i];
ulong deltaResult = exponentSlice[i]; ulong prime = primeSpan[i];
ulong residue = hasResidue ulong residue = hasAccumulator ? MultiplyMod(residueAccumulator, stepResidue, modulus) : stepResidue;
? lastResidue.MulMod64(deltaResult, modulus)
: deltaResult % modulus;
hitsSlice[position] = residue == 1UL ? (byte)1 : (byte)0; hitsSlice[position] = residue == 1UL ? (byte)1 : (byte)0;
hasResidue = true; exponentSlice[i] = residue;
lastResidue = residue; residueAccumulator = residue;
lastPrimeWithResidue = prime; lastPrime = prime;
hasAccumulator = true;
}
if (hasAccumulator)
{
previousResidue = residueAccumulator;
previousPrime = lastPrime;
hasPreviousResidue = true;
} }
} }
@@ -510,6 +526,17 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
_owner.ReturnSession(this); _owner.ReturnSession(this);
} }
private static ulong MultiplyMod(ulong left, ulong right, ulong modulus)
{
if (modulus == 0UL)
{
return 0UL;
}
UInt128 product = (UInt128)left * right;
return (ulong)(product % modulus);
}
} }
internal void ReturnSession(DivisorScanSession session) internal void ReturnSession(DivisorScanSession session)
@@ -517,7 +544,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
_sessionPool.Add(session); _sessionPool.Add(session);
} }
private static void ComputePrimeDeltaKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> deltas, ArrayView<ulong> results) private static void ComputePrimeExponentKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> exponents, ArrayView<ulong> results)
{ {
ulong modulus = divisor.Modulus; ulong modulus = divisor.Modulus;
if (modulus <= 1UL || (modulus & 1UL) == 0UL) if (modulus <= 1UL || (modulus & 1UL) == 0UL)
@@ -526,7 +553,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
return; return;
} }
ulong exponent = deltas[index]; ulong exponent = exponents[index];
results[index] = exponent.Pow2MontgomeryMod(divisor); results[index] = exponent.Pow2MontgomeryMod(divisor);
} }