Add heuristic prime sieves for cached divisor sequences
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Marek Lemańczyk committed
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@@ -1,5 +1,8 @@
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using System;
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using System.Buffers;
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using System.Collections.Concurrent;
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using Open.Numeric.Primes;
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using System.Collections.Generic;
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using System.Numerics;
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using System.Runtime.CompilerServices;
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using ILGPU;
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@@ -11,15 +14,96 @@ namespace PerfectNumbers.Core;
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public sealed class PrimeTester(bool useInternal = false)
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{
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public bool IsPrime(ulong n, CancellationToken ct) =>
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// TODO: Eliminate this wrapper once callers can reach IsPrimeInternal directly; the extra
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// indirection shows up when we sieve millions of candidates per second.
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IsPrimeInternal(n, ct);
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// TODO: Don't use these tiny arrays. Hard-code the values / checks instead
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private static readonly ulong[] GroupAConstantDivisors = [3UL, 7UL, 11UL, 13UL];
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private static readonly byte[] GroupAIncrementPattern = [20, 10];
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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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public static bool IsPrimeGpu(ulong n) => new PrimeTester().IsPrimeGpu(n, CancellationToken.None);
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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 static readonly ushort[] Wheel210ResiduesEnding1 = [1, 11, 31, 41, 61, 71, 101, 121, 131, 151, 181, 191];
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private static readonly ushort[] Wheel210ResiduesEnding7 = [17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 187, 197];
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private static readonly ushort[] Wheel210ResiduesEnding9 = [19, 29, 59, 79, 89, 109, 139, 149, 169, 179, 199, 209];
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private const ulong Wheel210 = 210UL;
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internal const int MaxGroupBSequences = 36;
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private const bool UseHeuristicGroupBTrialDivision = false; // Temporary fallback gate for Group B.
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private readonly bool _useLegacyPrimeTester = useInternal;
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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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public bool IsPrime(ulong n, CancellationToken ct)
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{
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if (_useLegacyPrimeTester)
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{
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return LegacyIsPrimeInternal(n, ct);
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}
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return IsPrimeInternal(n, ct);
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}
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[ThreadStatic]
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private static PrimeTester? _tester;
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public static PrimeTester Exclusive => _tester ??= new();
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public static bool IsPrimeGpu(ulong n)
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{
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return Exclusive.IsPrimeGpu(n, CancellationToken.None);
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}
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public static bool IsPrimeGpu(ulong n, ulong limit, byte nMod10)
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{
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return Exclusive.HeuristicIsPrimeGpu(n, limit, nMod10);
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}
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// Optional GPU-assisted primality: batched small-prime sieve on device.
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public bool IsPrimeGpu(ulong n, CancellationToken ct)
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{
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if (_useLegacyPrimeTester || !EnableHeuristicPrimeTesting)
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{
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return LegacyIsPrimeGpu(n, ct);
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}
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return HeuristicIsPrimeGpu(n);
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}
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public static bool LegacyIsPrimeGpu(ulong n, CancellationToken ct)
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{
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// EvenPerfectBitScanner never enqueues exponents <= 3 on the GPU path; keep the legacy guard commented out
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// so ad-hoc callers that expect that behavior must re-enable it intentionally.
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@@ -34,11 +118,11 @@ public sealed class PrimeTester(bool useInternal = false)
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// EvenPerfectBitScanner seeds p at 136,279,841 and advances monotonically, so production scans never hit the GPU with
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// exponents below 31. Leave this CPU redirect commented out to keep the wrapper branchless while documenting the guard.
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// The ternary fallback below still routes sub-31 values through IsPrimeInternal for correctness when ad-hoc callers bypass
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// The ternary fallback below still routes sub-31 values through LegacyIsPrimeInternal for correctness when ad-hoc callers bypass
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// the scanner pipeline.
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// if (n < 31UL)
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// {
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// return IsPrimeInternal(n, ct);
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// return LegacyIsPrimeInternal(n, ct);
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// }
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bool forceCpu = GpuContextPool.ForceCpu;
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@@ -58,16 +142,611 @@ public sealed class PrimeTester(bool useInternal = false)
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bool gpuReportedPrime = !forceCpu && !belowGpuRange && outFlags[0] != 0;
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bool requiresCpuFallback = forceCpu || belowGpuRange || !gpuReportedPrime;
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// Defensive fallback: GPU sieve produced a composite verdict or execution was skipped.
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// Confirm with CPU logic to prevent false negatives observed on some accelerators.
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return requiresCpuFallback ? IsPrimeInternal(n, ct) : true;
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return requiresCpuFallback ? LegacyIsPrimeInternal(n, ct) : true;
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}
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public bool HeuristicIsPrimeGpu(ulong n)
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{
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byte nMod10 = (byte)n.Mod10();
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ulong sqrtLimit = ComputeHeuristicSqrt(n);
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return HeuristicIsPrimeGpu(n, sqrtLimit, nMod10);
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}
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private bool HeuristicIsPrimeGpu(ulong n, ulong sqrtLimit, 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 (sqrtLimit < 3UL)
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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, sqrtLimit, nMod10, includeGroupB: false);
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}
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if (GpuContextPool.ForceCpu)
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{
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return HeuristicIsPrimeCpu(n, sqrtLimit, nMod10);
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}
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bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(n, sqrtLimit, nMod10);
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return !compositeDetected;
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}
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internal static bool HeuristicIsPrimeCpu(ulong n)
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{
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return HeuristicIsPrimeCpu(n, 0UL, (byte)n.Mod10());
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}
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internal static bool HeuristicIsPrimeCpu(ulong n, ulong sqrtLimit, byte nMod10)
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{
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if (sqrtLimit == 0UL)
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{
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sqrtLimit = ComputeHeuristicSqrt(n);
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}
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if (sqrtLimit < 3UL)
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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, sqrtLimit, nMod10, includeGroupB);
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}
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private static bool HeuristicTrialDivisionCpu(ulong n, ulong sqrtLimit, byte nMod10, bool includeGroupB)
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{
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Span<HeuristicGroupBSequenceState> groupBBuffer = stackalloc HeuristicGroupBSequenceState[MaxGroupBSequences];
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var enumerator = new HeuristicDivisorEnumerator(sqrtLimit, nMod10, groupBBuffer);
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while (enumerator.TryGetNext(out HeuristicDivisorCandidate candidate))
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{
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if (!includeGroupB && candidate.Group == HeuristicDivisorGroup.GroupB)
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{
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return EvaluateWithOpenNumericFallback(n);
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}
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ulong divisor = candidate.Value;
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if (divisor <= 1UL)
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{
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continue;
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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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}
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return includeGroupB ? true : EvaluateWithOpenNumericFallback(n);
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}
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private bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong sqrtLimit, byte nMod10)
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{
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Span<HeuristicGroupBSequenceState> groupBBuffer = stackalloc HeuristicGroupBSequenceState[MaxGroupBSequences];
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var enumerator = new HeuristicDivisorEnumerator(sqrtLimit, nMod10, groupBBuffer);
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int batchCapacity = Math.Max(1, HeuristicGpuDivisorBatchSize);
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var candidatePool = ArrayPool<HeuristicDivisorCandidate>.Shared;
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var divisorPool = ThreadStaticPools.UlongPool;
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var hitPool = ThreadStaticPools.BytePool;
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HeuristicDivisorCandidate[]? candidateArray = null;
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ulong[]? divisorArray = null;
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byte[]? hitFlags = null;
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var limiter = GpuPrimeWorkLimiter.Acquire();
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var gpu = PrimeTesterGpuContextPool.Rent();
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bool compositeDetected = false;
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try
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{
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candidateArray = candidatePool.Rent(batchCapacity);
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divisorArray = divisorPool.Rent(batchCapacity);
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hitFlags = hitPool.Rent(batchCapacity);
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var accelerator = gpu.Accelerator;
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var state = GpuKernelState.GetOrCreate(accelerator);
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lock (gpu.ExecutionLock)
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{
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var scratch = state.RentScratch(batchCapacity, accelerator);
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try
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{
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int count = 0;
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bool ProcessBatch(int length)
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{
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scratch.Input.View.CopyFromCPU(ref divisorArray![0], length);
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state.HeuristicTrialDivisionKernel(length, scratch.Input.View, n, scratch.Output.View);
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accelerator.Synchronize();
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scratch.Output.View.CopyToCPU(ref hitFlags![0], length);
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for (int i = 0; i < length; i++)
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{
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if (hitFlags![i] == 0)
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{
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continue;
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}
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ulong divisor = candidateArray![i].Value;
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if (divisor > 1UL && n % divisor == 0UL)
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{
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return true;
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}
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}
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return false;
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}
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while (enumerator.TryGetNext(out HeuristicDivisorCandidate candidate))
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{
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ulong divisor = candidate.Value;
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if (divisor <= 1UL)
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{
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continue;
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}
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candidateArray[count] = candidate;
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divisorArray[count] = divisor;
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count++;
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if (count == batchCapacity)
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{
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if (ProcessBatch(count))
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{
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compositeDetected = true;
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break;
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}
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count = 0;
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}
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}
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if (!compositeDetected && count > 0)
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{
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if (ProcessBatch(count))
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{
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compositeDetected = true;
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}
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}
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}
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finally
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{
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state.ReturnScratch(scratch);
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}
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}
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}
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finally
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{
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if (hitFlags is not null)
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{
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hitPool.Return(hitFlags);
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}
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if (divisorArray is not null)
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{
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divisorPool.Return(divisorArray);
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}
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if (candidateArray is not null)
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{
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candidatePool.Return(candidateArray);
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}
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gpu.Dispose();
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limiter.Dispose();
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}
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return compositeDetected;
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}
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private static bool EvaluateWithOpenNumericFallback(ulong n)
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{
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return Prime.Numbers.IsPrime(n);
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}
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internal static ulong ComputeHeuristicSqrt(ulong n)
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{
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ulong sqrt = (ulong)Math.Sqrt(n);
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UInt128 square = (UInt128)sqrt * sqrt;
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while (square > n)
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{
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sqrt--;
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square = (UInt128)sqrt * sqrt;
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}
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ulong next = sqrt + 1UL;
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UInt128 nextSquare = (UInt128)next * next;
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while (nextSquare <= n)
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{
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sqrt = next;
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next++;
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nextSquare = (UInt128)next * next;
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}
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return sqrt;
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}
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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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_ => ReadOnlySpan<byte>.Empty,
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};
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private static ReadOnlySpan<ushort> GetWheel210ResiduesForEnding(byte ending) => ending switch
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{
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1 => Wheel210ResiduesEnding1,
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7 => Wheel210ResiduesEnding7,
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9 => Wheel210ResiduesEnding9,
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_ => ReadOnlySpan<ushort>.Empty,
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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 = 0;
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for (int priorityIndex = 0; priorityIndex < endings.Length; priorityIndex++)
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{
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ReadOnlySpan<ushort> residues = GetWheel210ResiduesForEnding(endings[priorityIndex]);
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for (int residueIndex = 0; residueIndex < residues.Length; residueIndex++)
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{
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buffer[count++] = new HeuristicGroupBSequenceState(residues[residueIndex], endings[priorityIndex], (byte)priorityIndex);
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}
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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 sqrtLimit, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
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{
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return new HeuristicDivisorEnumerator(sqrtLimit, nMod10, groupBBuffer);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static MersenneHeuristicDivisorEnumerator CreateMersenneDivisorEnumerator(ulong exponent, ulong maxDivisor)
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{
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return new MersenneHeuristicDivisorEnumerator(exponent, maxDivisor);
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}
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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 = MontgomeryDivisorData.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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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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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(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 sqrtLimit;
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private int groupAConstantIndex;
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private ulong groupAWheelCandidate;
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private int groupAIncrementIndex;
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private bool groupAWheelActive;
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private Span<HeuristicGroupBSequenceState> groupBStates;
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public HeuristicDivisorEnumerator(ulong sqrtLimit, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
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{
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this.sqrtLimit = sqrtLimit;
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groupAConstantIndex = 0;
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groupAWheelCandidate = 23UL;
|
||||
groupAIncrementIndex = 0;
|
||||
groupAWheelActive = sqrtLimit >= 23UL;
|
||||
|
||||
int count = InitializeGroupBStates(nMod10, groupBBuffer);
|
||||
groupBStates = count == 0 ? Span<HeuristicGroupBSequenceState>.Empty : groupBBuffer[..count];
|
||||
|
||||
for (int i = 0; i < groupBStates.Length; i++)
|
||||
{
|
||||
groupBStates[i].TryNormalize();
|
||||
}
|
||||
}
|
||||
|
||||
public bool TryGetNext(out HeuristicDivisorCandidate candidate)
|
||||
{
|
||||
// TODO: Hard-code constant A divisor checks here instead of using an array
|
||||
while (groupAConstantIndex < GroupAConstantDivisors.Length)
|
||||
{
|
||||
ulong value = GroupAConstantDivisors[groupAConstantIndex++];
|
||||
if (value > sqrtLimit)
|
||||
{
|
||||
groupAConstantIndex = GroupAConstantDivisors.Length;
|
||||
break;
|
||||
}
|
||||
|
||||
// TODO: We're constantly dividing constants mod 10 which is constant too.
|
||||
candidate = new HeuristicDivisorCandidate(value, HeuristicDivisorGroup.GroupAConstant, (byte)(value % 10UL), 0, (ushort)value);
|
||||
return true;
|
||||
}
|
||||
|
||||
if (groupAWheelActive)
|
||||
{
|
||||
ulong value = groupAWheelCandidate;
|
||||
if (value <= sqrtLimit)
|
||||
{
|
||||
candidate = new HeuristicDivisorCandidate(value, HeuristicDivisorGroup.GroupAWheel, 3, 0, (ushort)(value % Wheel210));
|
||||
byte increment = GroupAIncrementPattern[groupAIncrementIndex];
|
||||
groupAIncrementIndex ^= 1;
|
||||
|
||||
ulong next = value + increment;
|
||||
if (next <= value)
|
||||
{
|
||||
groupAWheelActive = false;
|
||||
}
|
||||
else
|
||||
{
|
||||
groupAWheelCandidate = next;
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
groupAWheelActive = false;
|
||||
}
|
||||
|
||||
ulong bestCandidate = ulong.MaxValue;
|
||||
int bestIndex = -1;
|
||||
|
||||
for (int i = 0; i < groupBStates.Length; i++)
|
||||
{
|
||||
ref HeuristicGroupBSequenceState state = ref groupBStates[i];
|
||||
ulong value = state.Candidate;
|
||||
if (value == ulong.MaxValue)
|
||||
{
|
||||
continue;
|
||||
}
|
||||
|
||||
if (value > sqrtLimit)
|
||||
{
|
||||
state.Candidate = ulong.MaxValue;
|
||||
continue;
|
||||
}
|
||||
|
||||
if (bestIndex == -1 || value < bestCandidate ||
|
||||
(value == bestCandidate && state.PriorityIndex < groupBStates[bestIndex].PriorityIndex))
|
||||
{
|
||||
bestCandidate = value;
|
||||
bestIndex = i;
|
||||
}
|
||||
}
|
||||
|
||||
if (bestIndex == -1)
|
||||
{
|
||||
candidate = default;
|
||||
return false;
|
||||
}
|
||||
|
||||
ref HeuristicGroupBSequenceState bestState = ref groupBStates[bestIndex];
|
||||
var result = new HeuristicDivisorCandidate(bestState.Candidate, HeuristicDivisorGroup.GroupB, bestState.Ending, bestState.PriorityIndex, bestState.Residue);
|
||||
bestState.Advance();
|
||||
candidate = result;
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
internal struct HeuristicGroupBSequenceState(ushort residue, byte ending, byte priorityIndex)
|
||||
{
|
||||
public ulong Candidate = residue;
|
||||
public byte PriorityIndex = priorityIndex;
|
||||
public byte Ending = ending;
|
||||
public ushort Residue = residue;
|
||||
|
||||
public void TryNormalize()
|
||||
{
|
||||
ulong candidate = Candidate;
|
||||
if (candidate == ulong.MaxValue)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
while (candidate <= 13UL)
|
||||
{
|
||||
ulong next = candidate + Wheel210;
|
||||
if (next <= candidate)
|
||||
{
|
||||
Candidate = ulong.MaxValue;
|
||||
return;
|
||||
}
|
||||
|
||||
candidate = next;
|
||||
}
|
||||
|
||||
Candidate = candidate;
|
||||
}
|
||||
|
||||
public void Advance()
|
||||
{
|
||||
ulong candidate = Candidate;
|
||||
if (candidate == ulong.MaxValue)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
ulong next = candidate + Wheel210;
|
||||
Candidate = next > candidate ? next : ulong.MaxValue;
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
|
||||
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 ulong ProcessedCount => processedCount;
|
||||
|
||||
public ulong LastDivisor => lastDivisor;
|
||||
|
||||
public 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);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Note: GPU-backed primality path is implemented via IsPrimeGpu/IsPrimeBatchGpu and is routed
|
||||
// from EvenPerfectBitScanner based on --primes-device.
|
||||
|
||||
internal static bool IsPrimeInternal(ulong n, CancellationToken ct)
|
||||
{
|
||||
if (!EnableHeuristicPrimeTesting)
|
||||
{
|
||||
return LegacyIsPrimeInternal(n, ct);
|
||||
}
|
||||
|
||||
return HeuristicIsPrimeCpu(n);
|
||||
}
|
||||
|
||||
public static bool LegacyIsPrimeInternal(ulong n, CancellationToken ct)
|
||||
{
|
||||
// EvenPerfectBitScanner streams monotonically increasing odd exponents that start at 136,279,841 and already exclude
|
||||
// multiples of five. Factorization helpers (PrimeOrderCalculator, Pollard routines, and divisor-cycle warmups) reuse
|
||||
@@ -113,8 +792,13 @@ public sealed class PrimeTester(bool useInternal = false)
|
||||
return result;
|
||||
}
|
||||
|
||||
public static bool EnableHeuristicPrimeTesting { get; set; } = true;
|
||||
|
||||
public static int GpuBatchSize { get; set; } = 262_144;
|
||||
|
||||
public static int HeuristicGpuDivisorBatchSize { get; set; } = 4_096;
|
||||
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
public static void IsPrimeBatchGpu(ReadOnlySpan<ulong> values, Span<byte> results)
|
||||
{
|
||||
@@ -150,7 +834,7 @@ public sealed class PrimeTester(bool useInternal = false)
|
||||
int count = remaining > batchSize ? batchSize : remaining;
|
||||
|
||||
values.Slice(pos, count).CopyTo(temp);
|
||||
input.View.CopyFromCPU(ref temp[0], count);
|
||||
input.View.CopyFromCPU(ref temp[0], count);
|
||||
|
||||
state.Kernel(count, input.View, state.DevicePrimes.View, output.View);
|
||||
accelerator.Synchronize();
|
||||
@@ -263,6 +947,7 @@ public sealed class PrimeTester(bool useInternal = false)
|
||||
private sealed class KernelState
|
||||
{
|
||||
public Action<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>> Kernel { get; }
|
||||
public Action<Index1D, ArrayView<ulong>, ulong, ArrayView<byte>> HeuristicTrialDivisionKernel { get; }
|
||||
public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimes { get; }
|
||||
private readonly Accelerator _accel;
|
||||
private readonly System.Collections.Concurrent.ConcurrentBag<ScratchBuffers> _scratchPool = [];
|
||||
@@ -275,6 +960,7 @@ public sealed class PrimeTester(bool useInternal = false)
|
||||
_accel = accelerator;
|
||||
// Compile once per accelerator and upload primes once.
|
||||
Kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel);
|
||||
HeuristicTrialDivisionKernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ulong, ArrayView<byte>>(PrimeTesterKernels.HeuristicTrialDivisionKernel);
|
||||
|
||||
var primes = PrimesGenerator.SmallPrimes;
|
||||
DevicePrimes = accelerator.Allocate1D<uint>(primes.Length);
|
||||
|
||||
Reference in new issue
Block a user