643 lines
19 KiB
C#
643 lines
19 KiB
C#
using System.Runtime.CompilerServices;
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using System.Collections.Concurrent;
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using System.Buffers;
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using ILGPU;
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using ILGPU.Runtime;
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using PerfectNumbers.Core.Cpu;
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using PerfectNumbers.Core.Gpu;
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using UInt128 = System.UInt128;
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using PerfectNumbers.Core.Gpu.Accelerators;
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namespace PerfectNumbers.Core;
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public enum GpuKernelType
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{
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Incremental,
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Pow2Mod,
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}
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public sealed class MersenneNumberTester(
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bool useIncremental = true,
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bool useOrderCache = false,
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GpuKernelType kernelType = GpuKernelType.Incremental,
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bool useOrder = false,
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bool useGpuLucas = true,
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bool useGpuScan = true,
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bool useGpuOrder = true,
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bool useResidue = true,
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ulong maxK = 5_000_000UL,
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ComputationDevice orderDevice = ComputationDevice.Gpu)
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{
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private readonly bool _useResidue = useResidue;
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private readonly bool _useIncremental = useIncremental && !useResidue;
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private readonly ulong _maxK = maxK;
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private readonly Func<PrimeOrderCalculatorAccelerator, ulong, bool> _sharesFactorWithExponentMinusOne = orderDevice switch
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{
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ComputationDevice.Hybrid => static (gpu, exponent) => exponent.SharesFactorWithExponentMinusOneHybrid(gpu),
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_ when useGpuScan => static (gpu, exponent) => exponent.SharesFactorWithExponentMinusOneGpu(gpu),
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_ => static (_, exponent) => exponent.SharesFactorWithExponentMinusOneCpu(),
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};
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private static readonly ConcurrentDictionary<UInt128, ulong> _orderCache = [];
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// TODO: Swap this ConcurrentDictionary for the pooled dictionary variant highlighted in
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// Pow2MontgomeryModBenchmarks once order warmups reuse deterministic divisor-cycle snapshots; the pooled approach removed
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// the locking overhead when scanning p >= 138M in those benchmarks.
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private readonly MersenneNumberIncrementalGpuTester _incrementalGpuTester = new(kernelType, useGpuOrder);
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private readonly MersenneNumberIncrementalCpuTester _incrementalCpuTester = new(kernelType);
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private readonly MersenneNumberOrderGpuTester _orderGpuTester = new(kernelType, useGpuOrder);
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private readonly MersenneNumberOrderCpuTester _orderCpuTester = new(kernelType);
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private readonly MersenneNumberLucasLehmerGpuTester _lucasLehmerGpuTester = new();
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private readonly MersenneNumberLucasLehmerCpuTester _lucasLehmerCpuTester = new();
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private readonly MersenneNumberResidueGpuTester? _residueGpuTester = useResidue ? new(useGpuOrder) : null;
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private readonly MersenneNumberResidueCpuTester? _residueCpuTester = useResidue ? new() : null;
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// TODO: Ensure Program passes useResidue correctly and that residue-vs-incremental-vs-LL selection respects CLI flags.
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// Also consider injecting a shared cycles cache (MersenneDivisorCycles.Shared) to both CPU and GPU testers.
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private static readonly Accelerator[] _accelerators = AcceleratorPool.Shared.Accelerators;
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public void WarmUpOrdersHybrid(ulong exponent, ulong limit = 5_000_000UL)
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{
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bool cacheEnabled = useOrderCache;
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if (!cacheEnabled)
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{
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return;
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}
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UInt128 twoP = (UInt128)exponent << 1; // 2 * p
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LastDigit lastDigit = (exponent & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
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var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
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if (!useGpuOrder)
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{
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UInt128 k = UInt128.One;
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UInt128 q;
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ulong remainder;
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for (; k <= limit; k++)
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{
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q = twoP * k + UInt128.One;
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remainder = q.Mod10();
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bool shouldCheck = lastDigit == LastDigit.Seven
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? remainder == 7UL || remainder == 9UL || remainder == 3UL
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: remainder == 1UL || remainder == 3UL || remainder == 9UL;
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if (shouldCheck)
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{
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ulong mod8 = q.Mod8();
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if (mod8 != 1UL && mod8 != 7UL)
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{
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continue;
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}
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else if (q.Mod3() == 0UL || q.Mod5() == 0UL)
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{
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continue;
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}
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}
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if (!shouldCheck || !cacheEnabled || (cacheEnabled && _orderCache.ContainsKey(q)))
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{
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continue;
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}
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ulong ord = q.CalculateOrderHybrid(gpu);
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_orderCache[q] = ord;
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}
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PrimeOrderCalculatorAccelerator.Return(gpu);
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return;
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}
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ArrayPool<UInt128> uInt128Pool = ThreadStaticPools.UInt128Pool;
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UInt128[] qsBuffer = uInt128Pool.Rent((int)limit);
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int idx = 0;
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UInt128 k2 = 1UL;
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UInt128 q2;
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ulong remainder2;
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for (; k2 <= limit; k2++)
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{
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q2 = twoP * k2 + 1UL;
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remainder2 = q2.Mod10();
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bool shouldCheck2 = lastDigit == LastDigit.Seven
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? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL
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: remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL;
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if (shouldCheck2)
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{
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ulong mod8 = q2.Mod8();
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if (mod8 != 1UL && mod8 != 7UL)
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{
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shouldCheck2 = false;
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}
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else if (q2.Mod3() == 0UL || q2.Mod5() == 0UL)
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{
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shouldCheck2 = false;
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}
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}
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if (!shouldCheck2 || (cacheEnabled && _orderCache.ContainsKey(q2)))
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{
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continue;
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}
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qsBuffer[idx++] = q2;
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}
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if (idx == 0)
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{
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PrimeOrderCalculatorAccelerator.Return(gpu);
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ThreadStaticPools.UInt128Pool.Return(qsBuffer);
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return;
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}
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UInt128[] qs = qsBuffer;
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var acceleratorIndex = AcceleratorPool.Shared.Rent();
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var accelerator = _accelerators[acceleratorIndex];
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var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
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var orderKernel = GpuKernelPool.GetOrAddKernels(acceleratorIndex, stream, KernelType.OrderKernelScan).Order!;
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int batchSize = GpuConstants.ScanBatchSize;
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ulong divMul = (ulong)((((UInt128)1 << 64) - 1UL) / exponent) + 1UL;
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int offset = 0;
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var gpuUInt128Pool = ThreadStaticPools.GpuUInt128Pool;
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MemoryBuffer1D<GpuUInt128, Stride1D.Dense>? qBuffer;
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MemoryBuffer1D<ulong, Stride1D.Dense>? orderBuffer;
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while (offset < idx)
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{
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int count = Math.Min(batchSize, idx - offset);
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qBuffer = accelerator.Allocate1D<GpuUInt128>(count);
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orderBuffer = accelerator.Allocate1D<ulong>(count);
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var tmp = gpuUInt128Pool.Rent(count);
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for (int i = 0; i < count; i++)
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{
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tmp[i] = (GpuUInt128)qs[offset + i];
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}
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qBuffer.View.CopyFromCPU(stream, ref tmp[0], count);
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gpuUInt128Pool.Return(tmp);
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orderKernel(stream, count, exponent, divMul, qBuffer.View, orderBuffer.View);
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stream.Synchronize();
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ulong[] orders = orderBuffer.GetAsArray1D();
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for (int i = 0; i < count; i++)
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{
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ulong order = orders[i];
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if (order == 0UL)
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{
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order = qs[offset + i].CalculateOrderHybrid(gpu);
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}
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if (useOrderCache)
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{
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_orderCache[qs[offset + i]] = order;
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}
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}
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offset += count;
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orderBuffer.Dispose();
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qBuffer.Dispose();
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}
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AcceleratorStreamPool.Return(acceleratorIndex,stream);
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PrimeOrderCalculatorAccelerator.Return(gpu);
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ThreadStaticPools.UInt128Pool.Return(qs);
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}
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public void WarmUpOrdersCpu(ulong exponent, ulong limit = 5_000_000UL)
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{
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bool cacheEnabled = useOrderCache;
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if (!cacheEnabled)
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{
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return;
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}
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UInt128 twoP = (UInt128)exponent << 1; // 2 * p
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LastDigit lastDigit = (exponent & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
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// CPU path: compute orders directly and cache
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if (!useGpuOrder)
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{
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UInt128 k = UInt128.One;
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UInt128 q;
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ulong remainder;
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for (; k <= limit; k++)
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{
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q = twoP * k + UInt128.One;
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remainder = q.Mod10();
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// TODO: Replace these repeated Mod10/Mod8/Mod3/Mod5 calls with a residue automaton walk so
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// order warmups reuse the optimized cycle stepping validated in the residue benchmarks.
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bool shouldCheck = lastDigit == LastDigit.Seven
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? remainder == 7UL || remainder == 9UL || remainder == 3UL
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: remainder == 1UL || remainder == 3UL || remainder == 9UL;
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// Early modular filters for odd order and small-prime rejections
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if (shouldCheck)
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{
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ulong mod8 = q.Mod8();
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if (mod8 != 1UL && mod8 != 7UL)
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{
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continue;
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}
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else if (q.Mod3() == 0UL || q.Mod5() == 0UL)
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{
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continue;
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}
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}
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if (!shouldCheck || !cacheEnabled || (cacheEnabled && _orderCache.ContainsKey(q)))
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{
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continue;
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}
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ulong ord = q.CalculateOrderCpu();
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_orderCache[q] = ord;
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}
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return;
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}
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ArrayPool<UInt128> uInt128Pool = ThreadStaticPools.UInt128Pool;
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UInt128[] qsBuffer = uInt128Pool.Rent((int)limit);
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int idx = 0;
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UInt128 k2 = 1UL;
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UInt128 q2;
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ulong remainder2;
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for (; k2 <= limit; k2++)
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{
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q2 = twoP * k2 + 1UL;
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remainder2 = q2.Mod10();
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// TODO: Reuse the same residue-automaton fast path here so the GPU warmup staging avoids `%` and
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// branches the benchmarks showed slower than the tracked stepping helper.
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bool shouldCheck2 = lastDigit == LastDigit.Seven
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? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL
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: remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL;
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// Early modular filters for odd order and small-prime rejections
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if (shouldCheck2)
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{
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ulong mod8 = q2.Mod8();
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if (mod8 != 1UL && mod8 != 7UL)
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{
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shouldCheck2 = false;
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}
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else if (q2.Mod3() == 0UL || q2.Mod5() == 0UL)
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{
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shouldCheck2 = false;
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}
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}
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if (!shouldCheck2 || (cacheEnabled && _orderCache.ContainsKey(q2)))
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{
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continue;
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}
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qsBuffer[idx++] = q2;
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}
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if (idx == 0)
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{
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ThreadStaticPools.UInt128Pool.Return(qsBuffer);
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return;
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}
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UInt128[] qs = qsBuffer;
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var acceleratorIndex = AcceleratorPool.Shared.Rent();
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var accelerator = _accelerators[acceleratorIndex];
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var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
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var orderKernel = GpuKernelPool.GetOrAddKernels(acceleratorIndex, stream, KernelType.OrderKernelScan).Order!;
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// Guard long-running kernels by chunking the warm-up across batches.
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// Reuse the same ScanBatchSize knob used for scanning.
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int batchSize = GpuConstants.ScanBatchSize;
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ulong divMul = (ulong)((((UInt128)1 << 64) - 1UL) / exponent) + 1UL;
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int offset = 0;
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var gpuUInt128Pool = ThreadStaticPools.GpuUInt128Pool;
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MemoryBuffer1D<GpuUInt128, Stride1D.Dense>? qBuffer;
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MemoryBuffer1D<ulong, Stride1D.Dense>? orderBuffer;
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while (offset < idx)
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{
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int count = Math.Min(batchSize, idx - offset);
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qBuffer = accelerator.Allocate1D<GpuUInt128>(count);
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orderBuffer = accelerator.Allocate1D<ulong>(count);
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// Convert to device-friendly GpuUInt128 on the fly
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var tmp = gpuUInt128Pool.Rent(count);
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for (int i = 0; i < count; i++)
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{
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tmp[i] = (GpuUInt128)qs[offset + i];
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}
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// Copy only the populated elements to the device buffer to avoid overrun on pooled arrays.
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qBuffer.View.CopyFromCPU(stream, ref tmp[0], count);
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gpuUInt128Pool.Return(tmp);
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orderKernel(stream, count, exponent, divMul, qBuffer.View, orderBuffer.View);
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stream.Synchronize();
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// TODO: Change this to .CopyToCPU and use pre-allocated buffer with fixed, max capacity, using stream. Synchronize on the stream after copy.
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ulong[] orders = orderBuffer.GetAsArray1D();
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for (int i = 0; i < count; i++)
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{
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ulong order = orders[i];
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if (order == 0UL)
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{
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order = qs[offset + i].CalculateOrderCpu();
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}
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if (useOrderCache)
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{
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_orderCache[qs[offset + i]] = order;
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}
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}
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offset += count;
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orderBuffer.Dispose();
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qBuffer.Dispose();
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}
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AcceleratorStreamPool.Return(acceleratorIndex,stream);
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uInt128Pool.Return(qs);
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}
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public void WarmUpOrdersGpu(ulong exponent, ulong limit = 5_000_000UL)
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{
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bool cacheEnabled = useOrderCache;
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if (!cacheEnabled)
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{
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return;
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}
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UInt128 twoP = (UInt128)exponent << 1; // 2 * p
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LastDigit lastDigit = (exponent & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
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// CPU path: compute orders directly and cache
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var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
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if (!useGpuOrder)
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{
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UInt128 k = UInt128.One;
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UInt128 q;
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ulong remainder;
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for (; k <= limit; k++)
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{
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q = twoP * k + UInt128.One;
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remainder = q.Mod10();
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// TODO: Replace these repeated Mod10/Mod8/Mod3/Mod5 calls with a residue automaton walk so
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// order warmups reuse the optimized cycle stepping validated in the residue benchmarks.
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bool shouldCheck = lastDigit == LastDigit.Seven
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? remainder == 7UL || remainder == 9UL || remainder == 3UL
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: remainder == 1UL || remainder == 3UL || remainder == 9UL;
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// Early modular filters for odd order and small-prime rejections
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if (shouldCheck)
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{
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ulong mod8 = q.Mod8();
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if (mod8 != 1UL && mod8 != 7UL)
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{
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continue;
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}
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else if (q.Mod3() == 0UL || q.Mod5() == 0UL)
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{
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continue;
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}
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}
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if (!shouldCheck || !cacheEnabled || (cacheEnabled && _orderCache.ContainsKey(q)))
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{
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continue;
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}
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ulong ord = q.CalculateOrderGpu(gpu);
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_orderCache[q] = ord;
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}
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PrimeOrderCalculatorAccelerator.Return(gpu);
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return;
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}
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ArrayPool<UInt128> uInt128Pool = ThreadStaticPools.UInt128Pool;
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UInt128[] qsBuffer = uInt128Pool.Rent((int)limit);
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int idx = 0;
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UInt128 k2 = 1UL;
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UInt128 q2;
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ulong remainder2;
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for (; k2 <= limit; k2++)
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{
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q2 = twoP * k2 + 1UL;
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remainder2 = q2.Mod10();
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// TODO: Reuse the same residue-automaton fast path here so the GPU warmup staging avoids `%` and
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// branches the benchmarks showed slower than the tracked stepping helper.
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bool shouldCheck2 = lastDigit == LastDigit.Seven
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? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL
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: remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL;
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// Early modular filters for odd order and small-prime rejections
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if (shouldCheck2)
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{
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ulong mod8 = q2.Mod8();
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if (mod8 != 1UL && mod8 != 7UL)
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{
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shouldCheck2 = false;
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}
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else if (q2.Mod3() == 0UL || q2.Mod5() == 0UL)
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{
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shouldCheck2 = false;
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}
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}
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if (!shouldCheck2 || (cacheEnabled && _orderCache.ContainsKey(q2)))
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{
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continue;
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}
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qsBuffer[idx++] = q2;
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}
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if (idx == 0)
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{
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PrimeOrderCalculatorAccelerator.Return(gpu);
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ThreadStaticPools.UInt128Pool.Return(qsBuffer);
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return;
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}
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UInt128[] qs = qsBuffer;
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// GpuPrimeWorkLimiter.Acquire();
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var acceleratorIndex = AcceleratorPool.Shared.Rent();
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var accelerator = _accelerators[acceleratorIndex];
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var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
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var orderKernel = GpuKernelPool.GetOrAddKernels(acceleratorIndex, stream, KernelType.OrderKernelScan).Order!;
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// Guard long-running kernels by chunking the warm-up across batches.
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// Reuse the same ScanBatchSize knob used for scanning.
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int batchSize = GpuConstants.ScanBatchSize;
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ulong divMul = (ulong)((((UInt128)1 << 64) - 1UL) / exponent) + 1UL;
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int offset = 0;
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var gpuUInt128Pool = ThreadStaticPools.GpuUInt128Pool;
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MemoryBuffer1D<GpuUInt128, Stride1D.Dense>? qBuffer;
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MemoryBuffer1D<ulong, Stride1D.Dense>? orderBuffer;
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while (offset < idx)
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{
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int count = Math.Min(batchSize, idx - offset);
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qBuffer = accelerator.Allocate1D<GpuUInt128>(count);
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orderBuffer = accelerator.Allocate1D<ulong>(count);
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// Convert to device-friendly GpuUInt128 on the fly
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var tmp = gpuUInt128Pool.Rent(count);
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for (int i = 0; i < count; i++)
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{
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tmp[i] = (GpuUInt128)qs[offset + i];
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}
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// Copy only the populated elements to the device buffer to avoid overrun on pooled arrays.
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qBuffer.View.CopyFromCPU(stream, ref tmp[0], count);
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gpuUInt128Pool.Return(tmp);
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orderKernel(stream, count, exponent, divMul, qBuffer.View, orderBuffer.View);
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stream.Synchronize();
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// TODO: Change this to .CopyToCPU and use pre-allocated buffer with fixed, max capacity, using stream. Synchronize on the stream after copy.
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ulong[] orders = orderBuffer.GetAsArray1D();
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for (int i = 0; i < count; i++)
|
||
{
|
||
ulong order = orders[i];
|
||
if (order == 0UL)
|
||
{
|
||
order = qs[offset + i].CalculateOrderGpu(gpu);
|
||
}
|
||
|
||
if (useOrderCache)
|
||
{
|
||
_orderCache[qs[offset + i]] = order;
|
||
}
|
||
}
|
||
|
||
offset += count;
|
||
orderBuffer.Dispose();
|
||
qBuffer.Dispose();
|
||
}
|
||
|
||
AcceleratorStreamPool.Return(acceleratorIndex,stream);
|
||
PrimeOrderCalculatorAccelerator.Return(gpu);
|
||
// GpuPrimeWorkLimiter.Release();
|
||
uInt128Pool.Return(qs);
|
||
}
|
||
|
||
public bool IsMersennePrime(PrimeOrderCalculatorAccelerator gpu, ulong exponent)
|
||
{
|
||
// Safe early rejections using known orders for tiny primes:
|
||
// 7 | M_p iff 3 | p. Avoid rejecting p == 3 where M_3 == 7 is prime.
|
||
if ((exponent % 3UL) == 0UL && exponent != 3UL)
|
||
{
|
||
// TODO: Replace this `% 3` check with ULongExtensions.Mod3 to align the early rejection with
|
||
// the benchmarked bitmask helper instead of generic modulo for CPU workloads.
|
||
return false;
|
||
}
|
||
|
||
if ((exponent & 3UL) == 1UL && _sharesFactorWithExponentMinusOne(gpu, exponent))
|
||
{
|
||
return false;
|
||
}
|
||
|
||
// Skip even exponents: for even p > 2, M_p is composite; here p is large.
|
||
if ((exponent & 1UL) == 0UL)
|
||
{
|
||
return false;
|
||
}
|
||
|
||
bool prePrime = true;
|
||
UInt128 twoP = (UInt128)exponent << 1; // 2 * p
|
||
// UInt128 maxDivisor = new(ulong.MaxValue, ulong.MaxValue);
|
||
UInt128 maxK = UInt128Numbers.Two.Pow(exponent) / 2 + 1;
|
||
LastDigit lastDigit = (exponent & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
|
||
|
||
// In residue mode the residue scan is the final primality check.
|
||
if (_useResidue)
|
||
{
|
||
if (_maxK < maxK)
|
||
{
|
||
maxK = _maxK;
|
||
}
|
||
|
||
if (useGpuScan)
|
||
{
|
||
_residueGpuTester!.Scan(gpu, exponent, twoP, lastDigit, maxK, ref prePrime);
|
||
}
|
||
else
|
||
{
|
||
_residueCpuTester!.Scan(exponent, twoP, lastDigit, maxK, ref prePrime);
|
||
}
|
||
|
||
return prePrime;
|
||
}
|
||
|
||
if (!_useIncremental)
|
||
{
|
||
// Optional prefilter before Lucas–Lehmer using the same GPU/CPU scan path.
|
||
// Scan a limited range of k to quickly reject obvious cases.
|
||
UInt128 twoPPre = (UInt128)exponent << 1;
|
||
UInt128 maxKPre = (UInt128)PreLucasPreScanK;
|
||
LastDigit lastDigitPre = (exponent & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
|
||
if (useGpuScan)
|
||
{
|
||
_incrementalGpuTester.Scan(exponent, twoPPre, lastDigitPre, maxKPre, ref prePrime);
|
||
}
|
||
else
|
||
{
|
||
_incrementalCpuTester.Scan(gpu, exponent, twoPPre, lastDigitPre, maxKPre, ref prePrime);
|
||
}
|
||
|
||
if (!prePrime)
|
||
{
|
||
return false;
|
||
}
|
||
|
||
return useGpuLucas
|
||
? _lucasLehmerGpuTester.IsPrime(gpu, exponent, runOnGpu: true)
|
||
: _lucasLehmerCpuTester.IsPrime(gpu, exponent);
|
||
}
|
||
|
||
bool isPrime = true;
|
||
|
||
if (useOrder)
|
||
{
|
||
if (useGpuOrder)
|
||
{
|
||
_orderGpuTester.Scan(exponent, twoP, lastDigit, maxK, ref isPrime);
|
||
}
|
||
else
|
||
{
|
||
_orderCpuTester.Scan(gpu, exponent, twoP, lastDigit, maxK, ref isPrime);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
if (useGpuScan)
|
||
{
|
||
_incrementalGpuTester.Scan(exponent, twoP, lastDigit, maxK, ref isPrime);
|
||
}
|
||
else
|
||
{
|
||
_incrementalCpuTester.Scan(gpu, exponent, twoP, lastDigit, maxK, ref isPrime);
|
||
}
|
||
}
|
||
|
||
return isPrime;
|
||
}
|
||
|
||
// Limit of k to scan in the pre-Lucas prescan
|
||
public const int PreLucasPreScanK = 5_000_000;
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static bool DividesMersenne(ulong exponent, ulong prime)
|
||
{
|
||
return 2UL.ModPow64(exponent, prime) == 1UL;
|
||
}
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static void LegacyOrderKernel(Index1D index, ulong exponent, ArrayView<UInt128> qs, ArrayView<ulong> orders)
|
||
{
|
||
UInt128 q = qs[index];
|
||
UInt128 pow = exponent.PowMod(q);
|
||
orders[index] = pow == 1UL ? exponent : 0UL;
|
||
}
|
||
}
|