740 lines
20 KiB
C#
740 lines
20 KiB
C#
using Open.Numeric.Primes;
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using System.Runtime.CompilerServices;
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using ILGPU.Runtime;
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using PerfectNumbers.Core.Gpu;
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using PerfectNumbers.Core.Gpu.Accelerators;
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namespace PerfectNumbers.Core;
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public sealed class HeuristicPrimeTester
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{
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static HeuristicPrimeTester()
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{
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HeuristicPrimeSieves.EnsureInitialized();
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}
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// TODO: Don't use these tiny arrays. Hard-code the values / checks instead
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private static readonly byte[] GroupBEndingOrderMod1 = [9, 1];
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private static readonly byte[] GroupBEndingOrderMod3 = [9, 7];
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private static readonly byte[] GroupBEndingOrderMod7 = [7, 1];
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private static readonly byte[] GroupBEndingOrderMod9 = [9, 7, 1];
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// TODO: Would it speed up things if we implement something like ExponentRemainderStepper,
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// MersenneDivisorResidueStepper, or CycleRemainderStepper work with these?
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private const ulong Wheel210 = 210UL;
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private const int GroupAConstantCount = 4;
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internal const int MaxGroupBSequences = 36;
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private static readonly bool UseHeuristicGroupBTrialDivision = false; // Temporary fallback gate for Group B.
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private static readonly ulong[] HeuristicSmallCycleSnapshot = MersenneDivisorCycles.Shared.ExportSmallCyclesSnapshot();
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internal enum HeuristicDivisorGroup : byte
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{
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None = 0,
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GroupAConstant = 1,
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GroupAWheel = 2,
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GroupB = 3,
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}
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internal readonly struct HeuristicDivisorCandidate(ulong value, HeuristicDivisorGroup group, byte ending, byte priorityIndex, ushort wheelResidue)
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{
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public readonly ulong Value = value;
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public readonly HeuristicDivisorGroup Group = group;
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public readonly byte Ending = ending;
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public readonly byte PriorityIndex = priorityIndex;
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public readonly ushort WheelResidue = wheelResidue;
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}
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internal readonly struct HeuristicDivisorPreparation(
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in HeuristicDivisorCandidate candidate,
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in MontgomeryDivisorData divisorData,
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ulong cycleLengthHint,
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bool hasCycleLengthHint)
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{
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public readonly HeuristicDivisorCandidate Candidate = candidate;
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public readonly MontgomeryDivisorData DivisorData = divisorData;
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public readonly ulong CycleLengthHint = cycleLengthHint;
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public readonly bool HasCycleLengthHint = hasCycleLengthHint;
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public readonly bool RequiresCycleComputation = !hasCycleLengthHint;
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}
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[ThreadStatic]
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private static HeuristicPrimeTester? _tester;
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public static HeuristicPrimeTester Exclusive => _tester ??= new();
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool IsPrimeCpu(ulong n)
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{
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byte nMod10 = (byte)n.Mod10();
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ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
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if (maxDivisorSquare < 9UL)
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{
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return EvaluateWithOpenNumericFallback(n);
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}
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bool includeGroupB = UseHeuristicGroupBTrialDivision;
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return HeuristicTrialDivisionCpu(n, maxDivisorSquare, nMod10, includeGroupB);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool IsPrimeGpu(PrimeOrderCalculatorAccelerator gpu, ulong n)
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{
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byte nMod10 = (byte)n.Mod10();
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ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
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return IsPrimeGpu(gpu, n, maxDivisorSquare, nMod10);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool IsPrimeGpu(PrimeOrderCalculatorAccelerator gpu, ulong n, ulong maxDivisorSquare, byte nMod10) => HeuristicIsPrimeGpuCore(gpu, n, maxDivisorSquare, nMod10);
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private static bool HeuristicIsPrimeGpuCore(PrimeOrderCalculatorAccelerator gpu, ulong n, ulong maxDivisorSquare, byte nMod10)
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{
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// TODO: Is this condition ever met on the execution path in EvenPerfectBitScanner?
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if (maxDivisorSquare < 9UL)
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{
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return EvaluateWithOpenNumericFallback(n);
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}
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// if (!UseHeuristicGroupBTrialDivision)
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// {
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// return HeuristicTrialDivisionCpu(n, maxDivisorSquare, nMod10, includeGroupB: false);
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// }
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bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(gpu, n, maxDivisorSquare, nMod10);
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return !compositeDetected;
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}
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private static bool HeuristicTrialDivisionCpu(ulong n, ulong maxDivisorSquare, byte nMod10, bool includeGroupB)
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{
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ReadOnlySpan<ulong> groupADivisors = HeuristicPrimeSieves.GroupADivisors;
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ReadOnlySpan<ulong> groupADivisorSquares = HeuristicPrimeSieves.GroupADivisorSquares;
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int interleaveBatchSize = HeuristicCombinedPrimeTester.GetBatchSize(n);
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int groupAIndex = 0;
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if (!includeGroupB)
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{
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int groupALength = groupADivisors.Length;
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while (groupAIndex < groupALength)
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{
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int processed = 0;
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while (processed < interleaveBatchSize && groupAIndex < groupALength)
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{
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ulong divisorSquare = groupADivisorSquares[groupAIndex];
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if (divisorSquare > maxDivisorSquare)
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{
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groupAIndex = groupALength;
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break;
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}
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ulong divisor = groupADivisors[groupAIndex];
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if (n % divisor == 0UL)
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{
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return false;
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}
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groupAIndex++;
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processed++;
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}
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if (groupAIndex >= groupALength)
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{
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break;
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}
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if (groupADivisorSquares[groupAIndex] > maxDivisorSquare)
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{
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groupAIndex = groupALength;
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break;
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}
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}
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return EvaluateWithOpenNumericFallback(n);
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}
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ReadOnlySpan<byte> endingOrder = GetGroupBEndingOrder(nMod10);
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if (endingOrder.IsEmpty)
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{
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return EvaluateWithOpenNumericFallback(n);
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}
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Span<int> indices = endingOrder.Length <= 8
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? stackalloc int[endingOrder.Length]
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: new int[endingOrder.Length];
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bool groupAHasMore = groupAIndex < groupADivisors.Length && groupADivisorSquares[groupAIndex] <= maxDivisorSquare;
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bool groupBHasMore = HasGroupBCandidates(endingOrder, indices, maxDivisorSquare);
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while (groupAHasMore || groupBHasMore)
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{
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if (groupAHasMore)
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{
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int processed = 0;
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while (processed < interleaveBatchSize && groupAIndex < groupADivisors.Length)
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{
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ulong divisorSquare = groupADivisorSquares[groupAIndex];
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if (divisorSquare > maxDivisorSquare)
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{
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groupAIndex = groupADivisors.Length;
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groupAHasMore = false;
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break;
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}
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ulong divisor = groupADivisors[groupAIndex];
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if (n % divisor == 0UL)
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{
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return false;
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}
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groupAIndex++;
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processed++;
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}
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if (groupAIndex >= groupADivisors.Length)
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{
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groupAHasMore = false;
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}
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else
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{
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groupAHasMore = groupADivisorSquares[groupAIndex] <= maxDivisorSquare;
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if (!groupAHasMore)
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{
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groupAIndex = groupADivisors.Length;
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}
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}
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}
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if (groupBHasMore)
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{
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int processed = 0;
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while (processed < interleaveBatchSize)
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{
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if (!TrySelectNextGroupBDivisor(endingOrder, indices, maxDivisorSquare, out ulong divisor))
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{
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groupBHasMore = false;
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break;
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}
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if (n % divisor == 0UL)
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{
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return false;
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}
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processed++;
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}
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if (groupBHasMore)
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{
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groupBHasMore = HasGroupBCandidates(endingOrder, indices, maxDivisorSquare);
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}
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}
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}
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return true;
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}
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private static bool HeuristicTrialDivisionGpuDetectsDivisor(PrimeOrderCalculatorAccelerator gpu, ulong n, ulong maxDivisorSquare, byte nMod10)
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{
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// GpuPrimeWorkLimiter.Acquire();
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int acceleratorIndex = gpu.AcceleratorIndex;
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var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
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var flagView1D = gpu.OutputInt!.View;
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bool compositeDetected;
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int compositeFlag = 0;
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flagView1D.CopyFromCPU(stream, ref compositeFlag, 1);
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// Index1D index,
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// ArrayView<int> resultFlag,
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// ulong n,
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// ulong maxDivisorSquare,
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// HeuristicGpuDivisorTableKind tableKind,
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// HeuristicGpuDivisorTables tables)
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var kernelLauncher = gpu.HeuristicCombinedTrialDivisionKernelLauncher;
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kernelLauncher(
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stream,
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1,
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nMod10,
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flagView1D,
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n,
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maxDivisorSquare,
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gpu.DivisorTables);
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flagView1D.CopyToCPU(stream, ref compositeFlag, 1);
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stream!.Synchronize();
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compositeDetected = compositeFlag != 0;
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// compositeDetected = compositeFlag != 0;
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// if (!compositeDetected)
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// {
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// ReadOnlySpan<byte> endingOrder = GetGroupBEndingOrder(nMod10);
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// for (int i = 0; i < endingOrder.Length && !compositeDetected; i++)
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// {
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// byte ending = endingOrder[i];
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// HeuristicGpuDivisorTableKind tableKind = ending switch
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// {
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// 1 => HeuristicGpuDivisorTableKind.GroupBEnding1,
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// 7 => HeuristicGpuDivisorTableKind.GroupBEnding7,
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// 9 => HeuristicGpuDivisorTableKind.GroupBEnding9,
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// _ => HeuristicGpuDivisorTableKind.GroupA,
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// };
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// if (tableKind == HeuristicGpuDivisorTableKind.GroupA)
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// {
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// continue;
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// }
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// int divisorLength = GetGroupBDivisors(ending).Length;
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// compositeFlag = 0;
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// flagView1D.CopyFromCPU(stream, ref compositeFlag, 1);
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// kernelLauncher(
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// stream,
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// 1,
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// flagView1D,
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// n,
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// maxDivisorSquare,
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// tableKind,
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// gpu.HeuristicGpuTables);
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// flagView1D.CopyToCPU(stream, ref compositeFlag, 1);
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// stream.Synchronize();
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// compositeDetected = compositeFlag != 0;
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// }
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// }
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AcceleratorStreamPool.Return(acceleratorIndex, stream);
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// GpuPrimeWorkLimiter.Release();
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return compositeDetected;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static bool EvaluateWithOpenNumericFallback(ulong n) => Prime.Numbers.IsPrime(n);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n) => n;
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private static ReadOnlySpan<byte> GetGroupBEndingOrder(byte nMod10) => nMod10 switch
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{
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1 => GroupBEndingOrderMod1,
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3 => GroupBEndingOrderMod3,
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7 => GroupBEndingOrderMod7,
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9 => GroupBEndingOrderMod9,
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_ => [],
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};
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static bool TrySelectNextGroupBDivisor(ReadOnlySpan<byte> endingOrder, Span<int> indices, ulong maxDivisorSquare, out ulong divisor)
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{
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ulong bestCandidate = ulong.MaxValue;
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int bestEndingIndex = -1;
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for (int i = 0; i < endingOrder.Length; i++)
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{
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ReadOnlySpan<uint> divisors = GetGroupBDivisors(endingOrder[i]);
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ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(endingOrder[i]);
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int index = indices[i];
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if ((uint)index >= (uint)divisors.Length)
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{
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continue;
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}
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ulong candidateSquare = squares[index];
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if (candidateSquare > maxDivisorSquare)
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{
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indices[i] = divisors.Length;
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continue;
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}
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ulong candidate = divisors[index];
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if (bestEndingIndex == -1 || candidate < bestCandidate)
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{
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bestCandidate = candidate;
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bestEndingIndex = i;
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}
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}
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if (bestEndingIndex == -1)
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{
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divisor = 0UL;
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return false;
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}
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ReadOnlySpan<uint> selectedDivisors = GetGroupBDivisors(endingOrder[bestEndingIndex]);
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divisor = selectedDivisors[indices[bestEndingIndex]];
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indices[bestEndingIndex]++;
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return true;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static bool HasGroupBCandidates(ReadOnlySpan<byte> endingOrder, Span<int> indices, ulong maxDivisorSquare)
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{
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for (int i = 0; i < endingOrder.Length; i++)
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{
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ReadOnlySpan<uint> divisors = GetGroupBDivisors(endingOrder[i]);
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ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(endingOrder[i]);
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int index = indices[i];
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if ((uint)index >= (uint)divisors.Length)
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{
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continue;
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}
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if (squares[index] > maxDivisorSquare)
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{
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indices[i] = divisors.Length;
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continue;
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}
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return true;
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}
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return false;
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}
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private static ReadOnlySpan<uint> GetGroupBDivisors(byte ending) => ending switch
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{
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1 => DivisorGenerator.SmallPrimesLastOneWithoutLastThree,
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3 => [],
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7 => DivisorGenerator.SmallPrimesLastSevenWithoutLastThree,
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9 => DivisorGenerator.SmallPrimesLastNineWithoutLastThree,
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_ => [],
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};
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private static ReadOnlySpan<ulong> GetGroupBDivisorSquares(byte ending) => ending switch
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{
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1 => DivisorGenerator.SmallPrimesPow2LastOneWithoutLastThree,
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3 => [],
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7 => DivisorGenerator.SmallPrimesPow2LastSevenWithoutLastThree,
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9 => DivisorGenerator.SmallPrimesPow2LastNineWithoutLastThree,
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_ => [],
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};
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private static int InitializeGroupBStates(byte nMod10, Span<HeuristicGroupBSequenceState> buffer)
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{
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ReadOnlySpan<byte> endings = GetGroupBEndingOrder(nMod10);
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int count = endings.Length;
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for (int i = 0; i < count; i++)
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{
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buffer[i] = new HeuristicGroupBSequenceState(endings[i], (byte)i);
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}
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return count;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer) => new(maxDivisorSquare, nMod10, groupBBuffer);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static MersenneHeuristicDivisorEnumerator CreateMersenneDivisorEnumerator(ulong exponent, ulong maxDivisor)
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=> new(exponent, maxDivisor);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static HeuristicDivisorPreparation PrepareHeuristicDivisor(in HeuristicDivisorCandidate candidate)
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{
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ulong divisor = candidate.Value;
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MontgomeryDivisorData divisorData = MontgomeryDivisorDataPool.Shared.FromModulus(divisor);
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bool hasCycleHint = TryGetCycleLengthHint(divisor, out ulong cycleLength);
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return new HeuristicDivisorPreparation(candidate, divisorData, cycleLength, hasCycleHint);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static ulong ResolveHeuristicCycleLength(
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PrimeOrderCalculatorAccelerator gpu,
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ulong exponent,
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in HeuristicDivisorPreparation preparation,
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out bool cycleFromHint,
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out bool cycleComputed,
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out bool primeOrderFailed)
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{
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if (preparation.HasCycleLengthHint && preparation.CycleLengthHint != 0UL)
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{
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cycleFromHint = true;
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cycleComputed = true;
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primeOrderFailed = false;
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return preparation.CycleLengthHint;
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}
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ulong divisor = preparation.Candidate.Value;
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MontgomeryDivisorData divisorData = preparation.DivisorData;
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bool trySuccess = MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
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gpu,
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divisor,
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exponent,
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divisorData,
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out ulong computedCycle,
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out bool primeOrderFailedLocal);
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if (trySuccess && computedCycle != 0UL)
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{
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cycleFromHint = false;
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cycleComputed = true;
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primeOrderFailed = primeOrderFailedLocal;
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return computedCycle;
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}
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primeOrderFailed = primeOrderFailedLocal || !trySuccess || computedCycle == 0UL;
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ulong resolvedCycle = MersenneDivisorCycles.CalculateCycleLength(gpu, divisor, divisorData, skipPrimeOrderHeuristic: primeOrderFailed);
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cycleFromHint = false;
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cycleComputed = resolvedCycle != 0UL;
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return resolvedCycle;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static bool TryGetCycleLengthHint(ulong divisor, out ulong cycleLength)
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{
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ulong[] snapshot = HeuristicSmallCycleSnapshot;
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if (divisor < (ulong)snapshot.Length)
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{
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cycleLength = snapshot[(int)divisor];
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if (cycleLength != 0UL)
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{
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return true;
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}
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}
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cycleLength = 0UL;
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return false;
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}
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internal ref struct HeuristicDivisorEnumerator
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{
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private readonly ulong maxDivisorSquare;
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private readonly ReadOnlySpan<ulong> groupADivisors;
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private readonly ReadOnlySpan<ulong> groupADivisorSquares;
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private int groupAIndex;
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private Span<HeuristicGroupBSequenceState> groupBStates;
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public HeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
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{
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this.maxDivisorSquare = maxDivisorSquare;
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groupADivisors = HeuristicPrimeSieves.GroupADivisors;
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groupADivisorSquares = HeuristicPrimeSieves.GroupADivisorSquares;
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groupAIndex = 0;
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int count = InitializeGroupBStates(nMod10, groupBBuffer);
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groupBStates = count == 0 ? Span<HeuristicGroupBSequenceState>.Empty : groupBBuffer[..count];
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}
|
|
|
|
public bool TryGetNext(out HeuristicDivisorCandidate candidate)
|
|
{
|
|
while (groupAIndex < groupADivisors.Length)
|
|
{
|
|
ulong divisorSquare = groupADivisorSquares[groupAIndex];
|
|
if (divisorSquare > maxDivisorSquare)
|
|
{
|
|
groupAIndex = groupADivisors.Length;
|
|
break;
|
|
}
|
|
|
|
int currentIndex = groupAIndex;
|
|
ulong divisor = groupADivisors[currentIndex];
|
|
groupAIndex++;
|
|
|
|
HeuristicDivisorGroup group = currentIndex < GroupAConstantCount
|
|
? HeuristicDivisorGroup.GroupAConstant
|
|
: HeuristicDivisorGroup.GroupAWheel;
|
|
|
|
candidate = new HeuristicDivisorCandidate(
|
|
divisor,
|
|
group,
|
|
(byte)(divisor % 10UL),
|
|
0,
|
|
(ushort)(divisor % Wheel210));
|
|
return true;
|
|
}
|
|
|
|
ulong bestCandidate = ulong.MaxValue;
|
|
int bestIndex = -1;
|
|
|
|
for (int i = 0; i < groupBStates.Length; i++)
|
|
{
|
|
ref HeuristicGroupBSequenceState state = ref groupBStates[i];
|
|
if (!state.TryPeek(maxDivisorSquare, out ulong candidateValue))
|
|
{
|
|
continue;
|
|
}
|
|
|
|
if (bestIndex == -1 || candidateValue < bestCandidate ||
|
|
(candidateValue == bestCandidate && state.PriorityIndex < groupBStates[bestIndex].PriorityIndex))
|
|
{
|
|
bestCandidate = candidateValue;
|
|
bestIndex = i;
|
|
}
|
|
}
|
|
|
|
if (bestIndex == -1)
|
|
{
|
|
candidate = default;
|
|
return false;
|
|
}
|
|
|
|
ref HeuristicGroupBSequenceState bestState = ref groupBStates[bestIndex];
|
|
bestState.Advance();
|
|
candidate = new HeuristicDivisorCandidate(
|
|
bestCandidate,
|
|
HeuristicDivisorGroup.GroupB,
|
|
bestState.Ending,
|
|
bestState.PriorityIndex,
|
|
(ushort)(bestCandidate % Wheel210));
|
|
return true;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
internal struct HeuristicGroupBSequenceState(byte ending, byte priorityIndex)
|
|
{
|
|
public byte Ending = ending;
|
|
public byte PriorityIndex = priorityIndex;
|
|
public int Index = 0;
|
|
|
|
public bool TryPeek(ulong maxDivisorSquare, out ulong divisor)
|
|
{
|
|
ReadOnlySpan<uint> divisors = GetGroupBDivisors(Ending);
|
|
ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(Ending);
|
|
int index = Index;
|
|
if (index >= divisors.Length)
|
|
{
|
|
divisor = 0UL;
|
|
return false;
|
|
}
|
|
|
|
if (squares[index] > maxDivisorSquare)
|
|
{
|
|
Index = divisors.Length;
|
|
divisor = 0UL;
|
|
return false;
|
|
}
|
|
|
|
divisor = divisors[index];
|
|
return true;
|
|
}
|
|
|
|
public void Advance()
|
|
{
|
|
int next = Index + 1;
|
|
ReadOnlySpan<uint> divisors = GetGroupBDivisors(Ending);
|
|
if ((uint)next >= (uint)divisors.Length)
|
|
{
|
|
Index = divisors.Length;
|
|
}
|
|
else
|
|
{
|
|
Index = next;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
internal ref struct MersenneHeuristicDivisorEnumerator
|
|
{
|
|
private readonly GpuUInt128 step;
|
|
private readonly GpuUInt128 limit;
|
|
private GpuUInt128 current;
|
|
private MersenneDivisorResidueStepper residueStepper;
|
|
private bool active;
|
|
private ulong processedCount;
|
|
private ulong lastDivisor;
|
|
|
|
public MersenneHeuristicDivisorEnumerator(ulong exponent, ulong maxDivisor)
|
|
{
|
|
var stepLocal = new GpuUInt128(exponent);
|
|
stepLocal.ShiftLeft(1);
|
|
step = stepLocal;
|
|
|
|
var limitLocal = new GpuUInt128(maxDivisor);
|
|
limit = limitLocal;
|
|
|
|
var firstDivisor = stepLocal;
|
|
firstDivisor.Add(1UL);
|
|
|
|
bool hasCandidates = !stepLocal.IsZero && firstDivisor.CompareTo(limitLocal) <= 0;
|
|
|
|
current = hasCandidates ? firstDivisor : GpuUInt128.Zero;
|
|
residueStepper = hasCandidates ? new MersenneDivisorResidueStepper(exponent, stepLocal, firstDivisor) : default;
|
|
active = hasCandidates;
|
|
processedCount = 0UL;
|
|
lastDivisor = 0UL;
|
|
}
|
|
|
|
public bool TryGetNext(out HeuristicDivisorCandidate candidate)
|
|
{
|
|
while (active)
|
|
{
|
|
ulong value = current.Low;
|
|
processedCount++;
|
|
lastDivisor = value;
|
|
|
|
bool admissible = residueStepper.IsAdmissible();
|
|
|
|
Advance();
|
|
|
|
if (admissible)
|
|
{
|
|
candidate = CreateCandidate(value);
|
|
return true;
|
|
}
|
|
}
|
|
|
|
candidate = default;
|
|
return false;
|
|
}
|
|
|
|
private void Advance()
|
|
{
|
|
GpuUInt128 next = current;
|
|
next.Add(step);
|
|
|
|
if (next.CompareTo(limit) > 0 || next.CompareTo(current) <= 0)
|
|
{
|
|
active = false;
|
|
return;
|
|
}
|
|
|
|
current = next;
|
|
residueStepper.Advance();
|
|
}
|
|
|
|
public readonly ulong ProcessedCount => processedCount;
|
|
|
|
public readonly ulong LastDivisor => lastDivisor;
|
|
|
|
public readonly bool Exhausted => !active;
|
|
|
|
private static HeuristicDivisorCandidate CreateCandidate(ulong value)
|
|
{
|
|
byte ending = (byte)(value % 10UL);
|
|
HeuristicDivisorGroup group;
|
|
|
|
if (value == 3UL || value == 7UL || value == 11UL || value == 13UL)
|
|
{
|
|
group = HeuristicDivisorGroup.GroupAConstant;
|
|
}
|
|
else if (ending == 3)
|
|
{
|
|
group = HeuristicDivisorGroup.GroupAWheel;
|
|
}
|
|
else
|
|
{
|
|
group = HeuristicDivisorGroup.GroupB;
|
|
}
|
|
|
|
ushort residue = (ushort)(value % Wheel210);
|
|
return new HeuristicDivisorCandidate(value, group, ending, 0, residue);
|
|
}
|
|
}
|
|
}
|