Reuse divisor residues across prime candidates
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Marek Lemańczyk committed
1 parent
a39f7dda59
commit
436d3856d6
1 file changed
+136
-109
@@ -27,14 +27,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
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}
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>> _kernelCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>> _kernelDeltaCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>> _kernelExponentCache = new();
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private readonly ConcurrentDictionary<Accelerator, ConcurrentBag<BatchResources>> _resourcePools = new(AcceleratorReferenceComparer.Instance);
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private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
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private Action<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>> GetKernel(Accelerator accelerator) =>
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_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, byte, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>(CheckKernel));
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private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> GetKernelByPrimeDelta(Accelerator accelerator) =>
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_kernelDeltaCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>(ComputePrimeDeltaKernel));
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private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> GetKernelByPrimeExponent(Accelerator accelerator) =>
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_kernelExponentCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>(ComputePrimeExponentKernel));
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public int GpuBatchSize
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{
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@@ -341,10 +341,11 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
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private readonly GpuContextPool.GpuContextLease _lease;
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private readonly Accelerator _accelerator;
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private readonly Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> _kernel;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _exponentsBuffer;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer;
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private ulong[] _hostBuffer;
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private int[] _positionBuffer;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _exponentsBuffer;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer;
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private ulong[] _hostBuffer;
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private ulong[] _primeBuffer;
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private int[] _positionBuffer;
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private int _capacity;
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private bool _disposed;
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@@ -353,13 +354,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
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_owner = owner;
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_lease = GpuContextPool.RentPreferred(preferCpu: false);
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_accelerator = _lease.Accelerator;
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_kernel = owner.GetKernelByPrimeDelta(_accelerator);
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_kernel = owner.GetKernelByPrimeExponent(_accelerator);
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_capacity = Math.Max(1, owner._gpuBatchSize);
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_exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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}
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_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_primeBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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}
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internal void Reset()
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{
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@@ -374,16 +376,18 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
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}
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_exponentsBuffer.Dispose();
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_resultsBuffer.Dispose();
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ArrayPool<ulong>.Shared.Return(_hostBuffer, clearArray: false);
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ArrayPool<int>.Shared.Return(_positionBuffer, clearArray: false);
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_resultsBuffer.Dispose();
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ArrayPool<ulong>.Shared.Return(_hostBuffer, clearArray: false);
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ArrayPool<ulong>.Shared.Return(_primeBuffer, clearArray: false);
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ArrayPool<int>.Shared.Return(_positionBuffer, clearArray: false);
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_capacity = requiredCapacity;
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_exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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}
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_capacity = requiredCapacity;
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_exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_primeBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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}
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public void CheckDivisor(ulong divisor, ReadOnlySpan<ulong> primes, Span<byte> hits)
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{
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@@ -409,14 +413,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
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return;
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}
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bool useCycles = owner._useDivisorCycles;
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ulong cycle = 0UL;
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bool cycleEnabled = false;
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if (useCycles)
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{
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cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(modulus);
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cycleEnabled = cycle != 0UL;
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}
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bool useCycles = owner._useDivisorCycles;
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ulong cycle = 0UL;
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bool cycleEnabled = false;
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if (useCycles)
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{
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cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(modulus);
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cycleEnabled = cycle != 0UL;
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}
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Accelerator accelerator = _accelerator;
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Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> kernel = _kernel;
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@@ -427,108 +431,131 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
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int batchSize;
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ReadOnlySpan<ulong> primesSlice;
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Span<byte> hitsSlice;
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Span<ulong> hostSpan = _hostBuffer.AsSpan();
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Span<int> positionSpan = _positionBuffer.AsSpan();
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bool hasResidue = false;
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ulong lastPrimeWithResidue = 0UL;
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ulong lastResidue = 0UL;
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Span<ulong> hostSpan = _hostBuffer.AsSpan();
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Span<ulong> primeSpan = _primeBuffer.AsSpan();
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Span<int> positionSpan = _positionBuffer.AsSpan();
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bool hasPreviousResidue = false;
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ulong previousResidue = 0UL;
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ulong previousPrime = 0UL;
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while (offset < primesLength)
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{
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batchSize = Math.Min(gpuBatchSize, primesLength - offset);
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primesSlice = primes.Slice(offset, batchSize);
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hitsSlice = hits.Slice(offset, batchSize);
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while (offset < primesLength)
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{
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batchSize = Math.Min(gpuBatchSize, primesLength - offset);
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primesSlice = primes.Slice(offset, batchSize);
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hitsSlice = hits.Slice(offset, batchSize);
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int computeCount = 0;
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int computeCount = 0;
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ulong deltaBasePrime = lastPrimeWithResidue;
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bool deltaHasResidue = hasResidue;
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for (int i = 0; i < batchSize; i++)
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{
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ulong prime = primesSlice[i];
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if (cycleEnabled && prime % cycle != 0UL)
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for (int i = 0; i < batchSize; i++)
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{
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ulong prime = primesSlice[i];
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if (cycleEnabled && prime % cycle != 0UL)
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{
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hitsSlice[i] = 0;
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continue;
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}
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ulong delta;
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if (deltaHasResidue)
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{
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delta = prime >= deltaBasePrime ? prime - deltaBasePrime : prime;
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}
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else
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{
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delta = prime;
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}
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hostSpan[computeCount] = delta;
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positionSpan[computeCount] = i;
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computeCount++;
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deltaBasePrime = prime;
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deltaHasResidue = true;
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}
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primeSpan[computeCount] = prime;
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positionSpan[computeCount] = i;
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computeCount++;
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}
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if (computeCount > 0)
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{
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Span<ulong> exponentSlice = hostSpan.Slice(0, computeCount);
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ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentsView.SubView(0, computeCount);
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exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
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ArrayView1D<ulong, Stride1D.Dense> resultView = resultsView.SubView(0, computeCount);
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kernel(computeCount, divisorData, exponentView, resultView);
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accelerator.Synchronize();
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resultView.CopyToCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
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if (computeCount > 0)
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{
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Span<ulong> exponentSlice = hostSpan.Slice(0, computeCount);
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ulong currentPrime = hasPreviousResidue ? previousPrime : 0UL;
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bool hasDeltaSource = hasPreviousResidue;
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for (int i = 0; i < computeCount; i++)
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{
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ulong prime = primeSpan[i];
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if (hasDeltaSource)
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{
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exponentSlice[i] = prime - currentPrime;
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}
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else
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{
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exponentSlice[i] = prime;
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hasDeltaSource = true;
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}
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// TODO: Can we move this somehow to GPU? MulMod64 takes half of the time in CheckDivisor
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for (int i = 0; i < computeCount; i++)
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{
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int position = positionSpan[i];
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ulong prime = primesSlice[position];
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ulong deltaResult = exponentSlice[i];
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ulong residue = hasResidue
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? lastResidue.MulMod64(deltaResult, modulus)
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: deltaResult % modulus;
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currentPrime = prime;
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}
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hitsSlice[position] = residue == 1UL ? (byte)1 : (byte)0;
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hasResidue = true;
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lastResidue = residue;
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lastPrimeWithResidue = prime;
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}
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}
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ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentsView.SubView(0, computeCount);
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exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
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ArrayView1D<ulong, Stride1D.Dense> resultView = resultsView.SubView(0, computeCount);
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kernel(computeCount, divisorData, exponentView, resultView);
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accelerator.Synchronize();
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resultView.CopyToCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
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offset += batchSize;
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}
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}
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ulong lastPrime = previousPrime;
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ulong residueAccumulator = previousResidue;
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bool hasAccumulator = hasPreviousResidue;
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for (int i = 0; i < computeCount; i++)
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{
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int position = positionSpan[i];
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ulong stepResidue = exponentSlice[i];
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ulong prime = primeSpan[i];
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ulong residue = hasAccumulator ? MultiplyMod(residueAccumulator, stepResidue, modulus) : stepResidue;
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hitsSlice[position] = residue == 1UL ? (byte)1 : (byte)0;
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exponentSlice[i] = residue;
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residueAccumulator = residue;
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lastPrime = prime;
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hasAccumulator = true;
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}
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public void Dispose()
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{
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if (_disposed)
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{
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return;
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}
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if (hasAccumulator)
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{
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previousResidue = residueAccumulator;
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previousPrime = lastPrime;
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hasPreviousResidue = true;
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}
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}
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_disposed = true;
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_owner.ReturnSession(this);
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}
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offset += batchSize;
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}
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}
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}
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public void Dispose()
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{
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if (_disposed)
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{
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return;
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}
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_disposed = true;
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_owner.ReturnSession(this);
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}
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private static ulong MultiplyMod(ulong left, ulong right, ulong modulus)
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{
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if (modulus == 0UL)
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{
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return 0UL;
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}
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UInt128 product = (UInt128)left * right;
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return (ulong)(product % modulus);
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}
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}
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internal void ReturnSession(DivisorScanSession session)
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{
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_sessionPool.Add(session);
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}
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private static void ComputePrimeDeltaKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> deltas, ArrayView<ulong> results)
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{
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ulong modulus = divisor.Modulus;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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results[index] = 0UL;
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return;
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}
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private static void ComputePrimeExponentKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> exponents, ArrayView<ulong> results)
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{
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ulong modulus = divisor.Modulus;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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results[index] = 0UL;
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return;
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}
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ulong exponent = deltas[index];
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results[index] = exponent.Pow2MontgomeryMod(divisor);
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}
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ulong exponent = exponents[index];
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results[index] = exponent.Pow2MontgomeryMod(divisor);
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}
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private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
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{
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