Merge branch 'codex/analyze-gc-instances-in-checkdivisors-method' of https://github.com/mlemanczyk/even-perfect-numbers-scanner into codex/analyze-gc-instances-in-checkdivisors-method
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@@ -16,6 +16,12 @@ internal static class DivisorGenerator
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public static readonly ulong[] SmallPrimesPow2LastThree;
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public static readonly uint[] SmallPrimesLastNine;
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public static readonly ulong[] SmallPrimesPow2LastNine;
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public static readonly uint[] SmallPrimesLastOneWithoutLastThree;
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public static readonly ulong[] SmallPrimesPow2LastOneWithoutLastThree;
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public static readonly uint[] SmallPrimesLastSevenWithoutLastThree;
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public static readonly ulong[] SmallPrimesPow2LastSevenWithoutLastThree;
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public static readonly uint[] SmallPrimesLastNineWithoutLastThree;
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public static readonly ulong[] SmallPrimesPow2LastNineWithoutLastThree;
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private const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
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private const ushort DecimalMaskWhenLastIsThree = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);
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@@ -34,7 +40,13 @@ internal static class DivisorGenerator
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out SmallPrimesLastThree,
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out SmallPrimesPow2LastThree,
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out SmallPrimesLastNine,
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out SmallPrimesPow2LastNine);
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out SmallPrimesPow2LastNine,
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out SmallPrimesLastOneWithoutLastThree,
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out SmallPrimesPow2LastOneWithoutLastThree,
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out SmallPrimesLastSevenWithoutLastThree,
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out SmallPrimesPow2LastSevenWithoutLastThree,
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out SmallPrimesLastNineWithoutLastThree,
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out SmallPrimesPow2LastNineWithoutLastThree);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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@@ -59,7 +71,13 @@ internal static class DivisorGenerator
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out uint[] lastThree,
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out ulong[] lastThreePow2,
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out uint[] lastNine,
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out ulong[] lastNinePow2)
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out ulong[] lastNinePow2,
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out uint[] lastOneWithoutThree,
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out ulong[] lastOneWithoutThreePow2,
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out uint[] lastSevenWithoutThree,
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out ulong[] lastSevenWithoutThreePow2,
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out uint[] lastNineWithoutThree,
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out ulong[] lastNineWithoutThreePow2)
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{
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uint target = PerfectNumberConstants.PrimesLimit;
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int targetInt = checked((int)target);
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@@ -75,6 +93,13 @@ internal static class DivisorGenerator
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lastNinePow2 = new ulong[targetInt];
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List<uint> primes = new(targetInt * 4 / 3 + 16);
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List<uint> lastOneWithoutThreeList = new(targetInt);
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List<ulong> lastOneWithoutThreePow2List = new(targetInt);
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List<uint> lastSevenWithoutThreeList = new(targetInt);
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List<ulong> lastSevenWithoutThreePow2List = new(targetInt);
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List<uint> lastNineWithoutThreeList = new(targetInt);
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List<ulong> lastNineWithoutThreePow2List = new(targetInt);
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uint candidate = 2U;
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int allCount = 0;
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int lastOneCount = 0;
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@@ -82,24 +107,22 @@ internal static class DivisorGenerator
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int lastThreeCount = 0;
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int lastNineCount = 0;
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while (allCount < targetInt || lastOneCount < targetInt || lastSevenCount < targetInt || lastThreeCount < targetInt || lastNineCount < targetInt)
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while (allCount < targetInt ||
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lastOneCount < targetInt ||
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lastSevenCount < targetInt ||
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lastThreeCount < targetInt ||
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lastNineCount < targetInt)
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{
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bool isPrime = true;
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int primesCount = primes.Count;
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for (int i = 0; i < primesCount; i++)
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{
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uint p = primes[i];
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// TODO: Reuse a single squared local for `p` within this loop so we avoid recalculating
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// `p * p` repeatedly without storing every squared prime globally (the cache must remain
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// limited to the small-divisor tables to honor the memory constraints).
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if (p * p > candidate)
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{
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break;
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}
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// TODO: Replace this trial-division `%` with the sieve-based generator that avoids
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// per-candidate modulo work so building the small-prime tables stops dominating
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// startup time for large scans.
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if (candidate % p == 0U)
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{
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isPrime = false;
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@@ -110,54 +133,80 @@ internal static class DivisorGenerator
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if (isPrime)
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{
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primes.Add(candidate);
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ulong candidateSquared = checked((ulong)candidate * candidate);
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if (allCount < targetInt)
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{
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// TODO: Reuse a single cached `candidateSquared` per iteration so we avoid issuing
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// three separate 64-bit multiplications when populating the pow2 arrays here and
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// in the last-one/last-seven branches below.
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all[allCount] = candidate;
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allPow2[allCount] = checked((ulong)candidate * candidate);
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allPow2[allCount] = candidateSquared;
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allCount++;
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}
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if (candidate != 2U)
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{
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LastDigit lastDigit = GetLastDigit(candidate);
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bool allowedForLastOne = IsAllowedForLastOne(candidate, lastDigit);
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bool allowedForLastSeven = IsAllowedForLastSeven(candidate, lastDigit);
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bool allowedForLastThree = IsAllowedForLastThree(candidate, lastDigit);
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bool allowedForLastNine = IsAllowedForLastNine(candidate, lastDigit);
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bool lastDigitIsThree = lastDigit == LastDigit.Three;
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if (lastOneCount < targetInt && IsAllowedForLastOne(candidate, lastDigit))
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if (allowedForLastOne && lastOneCount < targetInt)
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{
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lastOne[lastOneCount] = candidate;
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lastOnePow2[lastOneCount] = checked((ulong)candidate * candidate);
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lastOnePow2[lastOneCount] = candidateSquared;
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lastOneCount++;
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}
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if (lastSevenCount < targetInt && IsAllowedForLastSeven(candidate, lastDigit))
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if (allowedForLastSeven && lastSevenCount < targetInt)
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{
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lastSeven[lastSevenCount] = candidate;
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lastSevenPow2[lastSevenCount] = checked((ulong)candidate * candidate);
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lastSevenPow2[lastSevenCount] = candidateSquared;
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lastSevenCount++;
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}
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if (lastThreeCount < targetInt && IsAllowedForLastThree(candidate, lastDigit))
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if (allowedForLastThree && lastThreeCount < targetInt)
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{
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lastThree[lastThreeCount] = candidate;
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lastThreePow2[lastThreeCount] = checked((ulong)candidate * candidate);
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lastThreePow2[lastThreeCount] = candidateSquared;
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lastThreeCount++;
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}
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if (lastNineCount < targetInt && IsAllowedForLastNine(candidate, lastDigit))
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if (allowedForLastNine && lastNineCount < targetInt)
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{
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lastNine[lastNineCount] = candidate;
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lastNinePow2[lastNineCount] = checked((ulong)candidate * candidate);
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lastNinePow2[lastNineCount] = candidateSquared;
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lastNineCount++;
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}
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if (!lastDigitIsThree && allowedForLastOne)
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{
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lastOneWithoutThreeList.Add(candidate);
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lastOneWithoutThreePow2List.Add(candidateSquared);
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}
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if (!lastDigitIsThree && allowedForLastSeven)
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{
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lastSevenWithoutThreeList.Add(candidate);
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lastSevenWithoutThreePow2List.Add(candidateSquared);
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}
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if (!lastDigitIsThree && allowedForLastNine)
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{
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lastNineWithoutThreeList.Add(candidate);
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lastNineWithoutThreePow2List.Add(candidateSquared);
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}
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}
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}
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// TODO: Switch this increment to the Mod6 stepping table identified in the Mod6ComparisonBenchmarks
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// so we skip the composite residues without relying on per-iteration `%` checks.
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candidate = candidate == 2U ? 3U : candidate + 2U;
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}
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lastOneWithoutThree = lastOneWithoutThreeList.ToArray();
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lastOneWithoutThreePow2 = lastOneWithoutThreePow2List.ToArray();
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lastSevenWithoutThree = lastSevenWithoutThreeList.ToArray();
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lastSevenWithoutThreePow2 = lastSevenWithoutThreePow2List.ToArray();
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lastNineWithoutThree = lastNineWithoutThreeList.ToArray();
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lastNineWithoutThreePow2 = lastNineWithoutThreePow2List.ToArray();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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@@ -3,7 +3,6 @@ namespace PerfectNumbers.Core.Gpu;
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public static class GpuPrimeWorkLimiter
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{
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private static SemaphoreSlim _semaphore = new(1, int.MaxValue);
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private static readonly object _lock = new();
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private static int _currentLimit = 1;
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public static Lease Acquire()
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@@ -11,29 +10,21 @@ public static class GpuPrimeWorkLimiter
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// TODO: Inline the pooled limiter guard from the GpuLimiterThroughputBenchmarks so prime-sieve
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// GPU jobs stop allocating Lease instances on every acquisition.
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var sem = _semaphore;
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sem.Wait();
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// sem.Wait();
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return new Lease(sem);
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}
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public static void SetLimit(int value)
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{
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if (value < 1)
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{
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value = 1;
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}
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if (value == _currentLimit)
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{
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return;
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}
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lock (_lock)
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{
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if (value == _currentLimit)
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{
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return;
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}
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// TODO: Switch to a shared limiter implementation with GpuWorkLimiter so we can coordinate CPU/GPU prime work using
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// the same semaphore pool without reallocating per adjustment.
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_semaphore = new SemaphoreSlim(value, value);
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_currentLimit = value;
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}
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// TODO: Switch to a shared limiter implementation with GpuWorkLimiter so we can coordinate CPU/GPU prime work using
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// the same semaphore pool without reallocating per adjustment.
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_semaphore = new SemaphoreSlim(value, value);
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_currentLimit = value;
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}
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public sealed class Lease
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@@ -47,7 +38,7 @@ public static class GpuPrimeWorkLimiter
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public void Dispose()
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{
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_sem.Release();
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// _sem.Release();
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}
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}
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}
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@@ -94,7 +94,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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var gpuLease = RentAccelerator();
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var accelerator = gpuLease.Accelerator;
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Monitor.Enter(gpuLease.ExecutionLock);
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// Monitor.Enter(gpuLease.ExecutionLock);
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var kernel = GetKernel(accelerator);
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var resources = RentBatchResources(accelerator, batchCapacity);
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@@ -121,7 +121,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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out processedCount);
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ReturnBatchResources(resources);
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Monitor.Exit(gpuLease.ExecutionLock);
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// Monitor.Exit(gpuLease.ExecutionLock);
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ReturnAccelerator(gpuLease);
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if (composite)
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@@ -560,7 +560,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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}
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}
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Monitor.Enter(_lease.ExecutionLock);
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// Monitor.Enter(_lease.ExecutionLock);
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EnsureExecutionResourcesLocked(length);
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@@ -601,7 +601,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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ref byte hitRef = ref MemoryMarshal.GetReference(hitSlice);
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hitView.CopyToCPU(ref hitRef, length);
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Monitor.Exit(_lease.ExecutionLock);
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// Monitor.Exit(_lease.ExecutionLock);
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}
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public void Dispose()
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@@ -30,7 +30,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
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var gpuLease = RentAccelerator();
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var accelerator = gpuLease.Accelerator;
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Monitor.Enter(gpuLease.ExecutionLock);
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// Monitor.Enter(gpuLease.ExecutionLock);
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var stream = accelerator.CreateStream();
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var kernel = GetPow2ModKernel(accelerator);
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@@ -108,7 +108,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
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ReturnResources(accelerator, resources);
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stream.Dispose();
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Monitor.Exit(gpuLease.ExecutionLock);
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// Monitor.Exit(gpuLease.ExecutionLock);
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ReturnAccelerator(gpuLease);
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limiter.Dispose();
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}
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@@ -0,0 +1,667 @@
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using System;
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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 System.Threading;
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using ILGPU;
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using ILGPU.Algorithms;
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using ILGPU.Runtime;
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using PerfectNumbers.Core.Gpu;
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namespace PerfectNumbers.Core;
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public sealed class HeuristicCombinedPrimeTester
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{
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static HeuristicCombinedPrimeTester()
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{
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HeuristicPrimeSieves.EnsureInitialized();
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CombinedDivisorsEnding1TwoAOneB = BuildCombinedDivisors(1, CombinedDivisorPattern.TwoAOneB);
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CombinedDivisorsEnding3TwoAOneB = BuildCombinedDivisors(3, CombinedDivisorPattern.TwoAOneB);
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CombinedDivisorsEnding7TwoAOneB = BuildCombinedDivisors(7, CombinedDivisorPattern.TwoAOneB);
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CombinedDivisorsEnding9TwoAOneB = BuildCombinedDivisors(9, CombinedDivisorPattern.TwoAOneB);
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CombinedDivisorsEnding1OneAOneB = BuildCombinedDivisors(1, CombinedDivisorPattern.OneAOneB);
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CombinedDivisorsEnding3OneAOneB = BuildCombinedDivisors(3, CombinedDivisorPattern.OneAOneB);
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CombinedDivisorsEnding7OneAOneB = BuildCombinedDivisors(7, CombinedDivisorPattern.OneAOneB);
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CombinedDivisorsEnding9OneAOneB = BuildCombinedDivisors(9, CombinedDivisorPattern.OneAOneB);
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CombinedDivisorsEnding1ThreeAOneB = BuildCombinedDivisors(1, CombinedDivisorPattern.ThreeAOneB);
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CombinedDivisorsEnding3ThreeAOneB = BuildCombinedDivisors(3, CombinedDivisorPattern.ThreeAOneB);
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CombinedDivisorsEnding7ThreeAOneB = BuildCombinedDivisors(7, CombinedDivisorPattern.ThreeAOneB);
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CombinedDivisorsEnding9ThreeAOneB = BuildCombinedDivisors(9, CombinedDivisorPattern.ThreeAOneB);
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CombinedDivisorsEnding1ThreeATwoB = BuildCombinedDivisors(1, CombinedDivisorPattern.ThreeATwoB);
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CombinedDivisorsEnding3ThreeATwoB = BuildCombinedDivisors(3, CombinedDivisorPattern.ThreeATwoB);
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CombinedDivisorsEnding7ThreeATwoB = BuildCombinedDivisors(7, CombinedDivisorPattern.ThreeATwoB);
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CombinedDivisorsEnding9ThreeATwoB = BuildCombinedDivisors(9, CombinedDivisorPattern.ThreeATwoB);
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CombinedDivisorsEnding1 = CombinedDivisorsEnding1OneAOneB;
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CombinedDivisorsEnding3 = CombinedDivisorsEnding3OneAOneB;
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CombinedDivisorsEnding7 = CombinedDivisorsEnding7OneAOneB;
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CombinedDivisorsEnding9 = CombinedDivisorsEnding9OneAOneB;
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}
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private const ulong Wheel210 = 210UL;
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private static readonly bool UseHeuristicGroupBTrialDivision = false; // Temporary fallback gate for Group B.
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private static readonly uint[] CombinedDivisorsEnding1TwoAOneB;
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private static readonly uint[] CombinedDivisorsEnding3TwoAOneB;
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private static readonly uint[] CombinedDivisorsEnding7TwoAOneB;
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private static readonly uint[] CombinedDivisorsEnding9TwoAOneB;
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private static readonly uint[] CombinedDivisorsEnding1OneAOneB;
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private static readonly uint[] CombinedDivisorsEnding3OneAOneB;
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private static readonly uint[] CombinedDivisorsEnding7OneAOneB;
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private static readonly uint[] CombinedDivisorsEnding9OneAOneB;
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private static readonly uint[] CombinedDivisorsEnding1ThreeAOneB;
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private static readonly uint[] CombinedDivisorsEnding3ThreeAOneB;
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private static readonly uint[] CombinedDivisorsEnding7ThreeAOneB;
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private static readonly uint[] CombinedDivisorsEnding9ThreeAOneB;
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private static readonly uint[] CombinedDivisorsEnding1ThreeATwoB;
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private static readonly uint[] CombinedDivisorsEnding3ThreeATwoB;
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private static readonly uint[] CombinedDivisorsEnding7ThreeATwoB;
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private static readonly uint[] CombinedDivisorsEnding9ThreeATwoB;
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private static readonly uint[] CombinedDivisorsEnding1;
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private static readonly uint[] CombinedDivisorsEnding3;
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private static readonly uint[] CombinedDivisorsEnding7;
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private static readonly uint[] CombinedDivisorsEnding9;
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private static readonly ulong[] HeuristicSmallCycleSnapshot = MersenneDivisorCycles.Shared.ExportSmallCyclesSnapshot();
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internal enum CombinedDivisorPattern : byte
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{
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TwoAOneB = 0,
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OneAOneB = 1,
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ThreeAOneB = 2,
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ThreeATwoB = 3,
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}
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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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||||
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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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||||
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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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||||
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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||||
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internal static int HeuristicGpuDivisorBatchSize = 4_096;
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internal static int HeuristicDivisorInterleaveBatchSize = 64;
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||||
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||||
[ThreadStatic]
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private static HeuristicCombinedPrimeTester? _tester;
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||||
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||||
public static HeuristicCombinedPrimeTester Exclusive => _tester ??= new();
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||||
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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 sqrtLimit = ComputeHeuristicSqrt(n);
|
||||
|
||||
if (sqrtLimit < 3UL)
|
||||
{
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return EvaluateWithOpenNumericFallback(n);
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||||
}
|
||||
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||||
return HeuristicTrialDivisionCpu(n, sqrtLimit, nMod10);
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||||
}
|
||||
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||||
public static bool IsPrimeGpu(ulong n)
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||||
{
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||||
byte nMod10 = (byte)n.Mod10();
|
||||
ulong sqrtLimit = ComputeHeuristicSqrt(n);
|
||||
return IsPrimeGpu(n, sqrtLimit, nMod10);
|
||||
}
|
||||
|
||||
public static bool IsPrimeGpu(ulong n, ulong sqrtLimit, byte nMod10)
|
||||
{
|
||||
// TODO: Is this condition ever met on the execution path in EvenPerfectBitScanner?
|
||||
if (sqrtLimit < 3UL)
|
||||
{
|
||||
return EvaluateWithOpenNumericFallback(n);
|
||||
}
|
||||
|
||||
bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(n, sqrtLimit, nMod10);
|
||||
return !compositeDetected;
|
||||
}
|
||||
|
||||
private static bool HeuristicTrialDivisionCpu(ulong n, ulong sqrtLimit, byte nMod10)
|
||||
{
|
||||
ReadOnlySpan<uint> combinedDivisors = GetCombinedDivisors(nMod10);
|
||||
if (combinedDivisors.IsEmpty)
|
||||
{
|
||||
return EvaluateWithOpenNumericFallback(n);
|
||||
}
|
||||
|
||||
int length = combinedDivisors.Length;
|
||||
for (int i = 0; i < length; i++)
|
||||
{
|
||||
uint entry = combinedDivisors[i];
|
||||
if (entry > sqrtLimit)
|
||||
{
|
||||
break;
|
||||
}
|
||||
|
||||
if (n % entry == 0UL)
|
||||
{
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
return EvaluateWithOpenNumericFallback(n);
|
||||
}
|
||||
|
||||
private static bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong sqrtLimit, byte nMod10)
|
||||
{
|
||||
int batchCapacity = HeuristicGpuDivisorBatchSize;
|
||||
var divisorPool = ThreadStaticPools.UlongPool;
|
||||
var hitPool = ThreadStaticPools.BytePool;
|
||||
|
||||
ulong[] divisorArray = divisorPool.Rent(batchCapacity);
|
||||
byte[] hitFlags = hitPool.Rent(batchCapacity);
|
||||
|
||||
var limiter = GpuPrimeWorkLimiter.Acquire();
|
||||
var gpu = PrimeTester.PrimeTesterGpuContextPool.Rent();
|
||||
var accelerator = gpu.Accelerator;
|
||||
var state = PrimeTester.GpuKernelState.GetOrCreate(accelerator);
|
||||
var scratch = state.RentScratch(batchCapacity, accelerator);
|
||||
|
||||
bool compositeDetected = false;
|
||||
int count = 0;
|
||||
|
||||
var input = scratch.Input;
|
||||
var output = scratch.Output;
|
||||
|
||||
bool ProcessBatch(int length)
|
||||
{
|
||||
input.View.CopyFromCPU(ref divisorArray[0], length);
|
||||
state.HeuristicTrialDivisionKernel(length, input.View, n, output.View);
|
||||
accelerator.Synchronize();
|
||||
output.View.CopyToCPU(ref hitFlags[0], length);
|
||||
|
||||
for (int i = 0; i < length; i++)
|
||||
{
|
||||
if (hitFlags[i] == 0)
|
||||
{
|
||||
continue;
|
||||
}
|
||||
|
||||
return true;
|
||||
// ulong divisor = divisorArray[i];
|
||||
// if (divisor > 1UL && n % divisor == 0UL)
|
||||
// {
|
||||
// return true;
|
||||
// }
|
||||
}
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
ReadOnlySpan<uint> combinedDivisors = GetCombinedDivisors(nMod10);
|
||||
if (combinedDivisors.IsEmpty)
|
||||
{
|
||||
goto Cleanup;
|
||||
}
|
||||
|
||||
int length = combinedDivisors.Length;
|
||||
for (int i = 0; i < length; i++)
|
||||
{
|
||||
uint entry = combinedDivisors[i];
|
||||
if (entry > sqrtLimit)
|
||||
{
|
||||
break;
|
||||
}
|
||||
|
||||
divisorArray[count] = entry;
|
||||
count++;
|
||||
|
||||
if (count == batchCapacity)
|
||||
{
|
||||
if (ProcessBatch(count))
|
||||
{
|
||||
compositeDetected = true;
|
||||
goto Cleanup;
|
||||
}
|
||||
|
||||
count = 0;
|
||||
}
|
||||
}
|
||||
|
||||
if (!compositeDetected && count > 0)
|
||||
{
|
||||
if (ProcessBatch(count))
|
||||
{
|
||||
compositeDetected = true;
|
||||
goto Cleanup;
|
||||
}
|
||||
}
|
||||
|
||||
Cleanup:
|
||||
state.ReturnScratch(scratch);
|
||||
divisorPool.Return(divisorArray);
|
||||
hitPool.Return(hitFlags);
|
||||
gpu.Dispose();
|
||||
limiter.Dispose();
|
||||
return compositeDetected;
|
||||
}
|
||||
|
||||
private static bool EvaluateWithOpenNumericFallback(ulong n)
|
||||
{
|
||||
return Prime.Numbers.IsPrime(n);
|
||||
}
|
||||
|
||||
internal static ulong ComputeHeuristicSqrt(ulong n)
|
||||
{
|
||||
ulong sqrt = (ulong)Math.Sqrt(n);
|
||||
UInt128 square = (UInt128)sqrt * sqrt;
|
||||
|
||||
while (square > n)
|
||||
{
|
||||
sqrt--;
|
||||
square = (UInt128)sqrt * sqrt;
|
||||
}
|
||||
|
||||
ulong next = sqrt + 1UL;
|
||||
UInt128 nextSquare = (UInt128)next * next;
|
||||
while (nextSquare <= n)
|
||||
{
|
||||
sqrt = next;
|
||||
next++;
|
||||
nextSquare = (UInt128)next * next;
|
||||
}
|
||||
|
||||
return sqrt;
|
||||
}
|
||||
|
||||
private static ReadOnlySpan<uint> GetCombinedDivisors(byte nMod10)
|
||||
{
|
||||
return nMod10 switch
|
||||
{
|
||||
1 => CombinedDivisorsEnding1,
|
||||
3 => CombinedDivisorsEnding3,
|
||||
7 => CombinedDivisorsEnding7,
|
||||
9 => CombinedDivisorsEnding9,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
};
|
||||
}
|
||||
|
||||
internal static ReadOnlySpan<uint> GetCombinedDivisors(byte nMod10, CombinedDivisorPattern pattern)
|
||||
{
|
||||
return pattern switch
|
||||
{
|
||||
CombinedDivisorPattern.TwoAOneB => nMod10 switch
|
||||
{
|
||||
1 => CombinedDivisorsEnding1TwoAOneB,
|
||||
3 => CombinedDivisorsEnding3TwoAOneB,
|
||||
7 => CombinedDivisorsEnding7TwoAOneB,
|
||||
9 => CombinedDivisorsEnding9TwoAOneB,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
},
|
||||
CombinedDivisorPattern.OneAOneB => nMod10 switch
|
||||
{
|
||||
1 => CombinedDivisorsEnding1OneAOneB,
|
||||
3 => CombinedDivisorsEnding3OneAOneB,
|
||||
7 => CombinedDivisorsEnding7OneAOneB,
|
||||
9 => CombinedDivisorsEnding9OneAOneB,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
},
|
||||
CombinedDivisorPattern.ThreeAOneB => nMod10 switch
|
||||
{
|
||||
1 => CombinedDivisorsEnding1ThreeAOneB,
|
||||
3 => CombinedDivisorsEnding3ThreeAOneB,
|
||||
7 => CombinedDivisorsEnding7ThreeAOneB,
|
||||
9 => CombinedDivisorsEnding9ThreeAOneB,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
},
|
||||
CombinedDivisorPattern.ThreeATwoB => nMod10 switch
|
||||
{
|
||||
1 => CombinedDivisorsEnding1ThreeATwoB,
|
||||
3 => CombinedDivisorsEnding3ThreeATwoB,
|
||||
7 => CombinedDivisorsEnding7ThreeATwoB,
|
||||
9 => CombinedDivisorsEnding9ThreeATwoB,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
},
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
};
|
||||
}
|
||||
|
||||
private static uint[] BuildCombinedDivisors(byte nMod10, CombinedDivisorPattern pattern)
|
||||
{
|
||||
ReadOnlySpan<int> groupA = HeuristicPrimeSieves.GroupADivisors;
|
||||
ReadOnlySpan<uint> groupB = GetGroupBDivisors(nMod10);
|
||||
|
||||
var combined = new List<uint>(groupA.Length + groupB.Length);
|
||||
|
||||
int groupAIndex = 0;
|
||||
while (groupAIndex < groupA.Length && groupA[groupAIndex] <= 19)
|
||||
{
|
||||
combined.Add((uint)groupA[groupAIndex]);
|
||||
groupAIndex++;
|
||||
}
|
||||
|
||||
int groupBIndex = GetGroupBStartIndex(groupB);
|
||||
int groupAInterleaveCount;
|
||||
int groupBInterleaveCount;
|
||||
switch (pattern)
|
||||
{
|
||||
case CombinedDivisorPattern.OneAOneB:
|
||||
groupAInterleaveCount = 1;
|
||||
groupBInterleaveCount = 1;
|
||||
break;
|
||||
case CombinedDivisorPattern.TwoAOneB:
|
||||
groupAInterleaveCount = 2;
|
||||
groupBInterleaveCount = 1;
|
||||
break;
|
||||
case CombinedDivisorPattern.ThreeAOneB:
|
||||
groupAInterleaveCount = 3;
|
||||
groupBInterleaveCount = 1;
|
||||
break;
|
||||
case CombinedDivisorPattern.ThreeATwoB:
|
||||
groupAInterleaveCount = 3;
|
||||
groupBInterleaveCount = 2;
|
||||
break;
|
||||
default:
|
||||
groupAInterleaveCount = 2;
|
||||
groupBInterleaveCount = 1;
|
||||
break;
|
||||
}
|
||||
|
||||
while (groupAIndex < groupA.Length || groupBIndex < groupB.Length)
|
||||
{
|
||||
int addedA = 0;
|
||||
while (addedA < groupAInterleaveCount && groupAIndex < groupA.Length)
|
||||
{
|
||||
combined.Add((uint)groupA[groupAIndex]);
|
||||
groupAIndex++;
|
||||
addedA++;
|
||||
}
|
||||
|
||||
int addedB = 0;
|
||||
while (addedB < groupBInterleaveCount && groupBIndex < groupB.Length)
|
||||
{
|
||||
combined.Add(groupB[groupBIndex]);
|
||||
groupBIndex++;
|
||||
addedB++;
|
||||
}
|
||||
}
|
||||
|
||||
return combined.ToArray();
|
||||
}
|
||||
|
||||
|
||||
|
||||
private static int GetGroupBStartIndex(ReadOnlySpan<uint> divisors)
|
||||
{
|
||||
int index = 0;
|
||||
while (index < divisors.Length && IsGroupAPrefixValue(divisors[index]))
|
||||
{
|
||||
index++;
|
||||
}
|
||||
|
||||
return index;
|
||||
}
|
||||
|
||||
private static bool IsGroupAPrefixValue(uint value) => value is 3U or 7U or 11U or 13U;
|
||||
|
||||
private static HeuristicDivisorGroup ResolveGroup(uint value) => value switch
|
||||
{
|
||||
3U or 7U or 11U or 13U => HeuristicDivisorGroup.GroupAConstant,
|
||||
_ when value % 10U == 3U => HeuristicDivisorGroup.GroupAWheel,
|
||||
_ => HeuristicDivisorGroup.GroupB,
|
||||
};
|
||||
|
||||
private static ReadOnlySpan<uint> GetGroupBDivisors(byte ending) => ending switch
|
||||
{
|
||||
1 => DivisorGenerator.SmallPrimesLastOneWithoutLastThree,
|
||||
3 => ReadOnlySpan<uint>.Empty,
|
||||
7 => DivisorGenerator.SmallPrimesLastSevenWithoutLastThree,
|
||||
9 => DivisorGenerator.SmallPrimesLastNineWithoutLastThree,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
};
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong sqrtLimit, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
|
||||
{
|
||||
return new HeuristicDivisorEnumerator(sqrtLimit, nMod10, groupBBuffer);
|
||||
}
|
||||
|
||||
internal struct HeuristicGroupBSequenceState
|
||||
{
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
internal static MersenneHeuristicDivisorEnumerator CreateMersenneDivisorEnumerator(ulong exponent, ulong maxDivisor)
|
||||
{
|
||||
return new MersenneHeuristicDivisorEnumerator(exponent, maxDivisor);
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
internal static HeuristicDivisorPreparation PrepareHeuristicDivisor(in HeuristicDivisorCandidate candidate)
|
||||
{
|
||||
ulong divisor = candidate.Value;
|
||||
MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
|
||||
bool hasCycleHint = TryGetCycleLengthHint(divisor, out ulong cycleLength);
|
||||
return new HeuristicDivisorPreparation(candidate, divisorData, cycleLength, hasCycleHint);
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
internal static ulong ResolveHeuristicCycleLength(
|
||||
ulong exponent,
|
||||
in HeuristicDivisorPreparation preparation,
|
||||
out bool cycleFromHint,
|
||||
out bool cycleComputed,
|
||||
out bool primeOrderFailed)
|
||||
{
|
||||
if (preparation.HasCycleLengthHint && preparation.CycleLengthHint != 0UL)
|
||||
{
|
||||
cycleFromHint = true;
|
||||
cycleComputed = true;
|
||||
primeOrderFailed = false;
|
||||
return preparation.CycleLengthHint;
|
||||
}
|
||||
|
||||
ulong divisor = preparation.Candidate.Value;
|
||||
MontgomeryDivisorData divisorData = preparation.DivisorData;
|
||||
|
||||
bool trySuccess = MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
|
||||
divisor,
|
||||
exponent,
|
||||
divisorData,
|
||||
out ulong computedCycle,
|
||||
out bool primeOrderFailedLocal);
|
||||
|
||||
if (trySuccess && computedCycle != 0UL)
|
||||
{
|
||||
cycleFromHint = false;
|
||||
cycleComputed = true;
|
||||
primeOrderFailed = primeOrderFailedLocal;
|
||||
return computedCycle;
|
||||
}
|
||||
|
||||
primeOrderFailed = primeOrderFailedLocal || !trySuccess || computedCycle == 0UL;
|
||||
ulong resolvedCycle = MersenneDivisorCycles.CalculateCycleLength(divisor, divisorData, skipPrimeOrderHeuristic: primeOrderFailed);
|
||||
cycleFromHint = false;
|
||||
cycleComputed = resolvedCycle != 0UL;
|
||||
return resolvedCycle;
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
internal static bool TryGetCycleLengthHint(ulong divisor, out ulong cycleLength)
|
||||
{
|
||||
ulong[] snapshot = HeuristicSmallCycleSnapshot;
|
||||
if (divisor < (ulong)snapshot.Length)
|
||||
{
|
||||
cycleLength = snapshot[(int)divisor];
|
||||
if (cycleLength != 0UL)
|
||||
{
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
cycleLength = 0UL;
|
||||
return false;
|
||||
}
|
||||
|
||||
internal ref struct HeuristicDivisorEnumerator
|
||||
{
|
||||
private readonly ulong sqrtLimit;
|
||||
private readonly ReadOnlySpan<uint> combinedDivisors;
|
||||
private int index;
|
||||
|
||||
public HeuristicDivisorEnumerator(ulong sqrtLimit, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
|
||||
{
|
||||
this.sqrtLimit = sqrtLimit;
|
||||
_ = groupBBuffer;
|
||||
combinedDivisors = GetCombinedDivisors(nMod10);
|
||||
index = 0;
|
||||
}
|
||||
|
||||
public bool TryGetNext(out HeuristicDivisorCandidate candidate)
|
||||
{
|
||||
while (index < combinedDivisors.Length)
|
||||
{
|
||||
uint entry = combinedDivisors[index++];
|
||||
if (entry > sqrtLimit)
|
||||
{
|
||||
index = combinedDivisors.Length;
|
||||
break;
|
||||
}
|
||||
|
||||
HeuristicDivisorGroup group = ResolveGroup(entry);
|
||||
ulong value = entry;
|
||||
byte ending = (byte)(value % 10UL);
|
||||
ushort residue = (ushort)(value % Wheel210);
|
||||
candidate = new HeuristicDivisorCandidate(value, group, ending, 0, residue);
|
||||
return true;
|
||||
}
|
||||
|
||||
candidate = default;
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
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);
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -122,10 +122,10 @@ public sealed class HeuristicPrimeTester
|
||||
return EvaluateWithOpenNumericFallback(n);
|
||||
}
|
||||
|
||||
if (!UseHeuristicGroupBTrialDivision)
|
||||
{
|
||||
return HeuristicTrialDivisionCpu(n, sqrtLimit, nMod10, includeGroupB: false);
|
||||
}
|
||||
// if (!UseHeuristicGroupBTrialDivision)
|
||||
// {
|
||||
// return HeuristicTrialDivisionCpu(n, sqrtLimit, nMod10, includeGroupB: false);
|
||||
// }
|
||||
|
||||
bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(n, sqrtLimit, nMod10);
|
||||
return !compositeDetected;
|
||||
@@ -260,8 +260,8 @@ public sealed class HeuristicPrimeTester
|
||||
|
||||
private bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong sqrtLimit, byte nMod10)
|
||||
{
|
||||
int batchCapacity = Math.Max(1, HeuristicGpuDivisorBatchSize);
|
||||
int interleaveBatchSize = Math.Max(1, HeuristicDivisorInterleaveBatchSize);
|
||||
int batchCapacity = HeuristicGpuDivisorBatchSize;
|
||||
int interleaveBatchSize = HeuristicDivisorInterleaveBatchSize;
|
||||
var divisorPool = ThreadStaticPools.UlongPool;
|
||||
var hitPool = ThreadStaticPools.BytePool;
|
||||
|
||||
@@ -277,7 +277,7 @@ public sealed class HeuristicPrimeTester
|
||||
bool compositeDetected = false;
|
||||
int count = 0;
|
||||
|
||||
lock (gpu.ExecutionLock)
|
||||
// lock (gpu.ExecutionLock)
|
||||
{
|
||||
var input = scratch.Input;
|
||||
var output = scratch.Output;
|
||||
@@ -470,7 +470,7 @@ Cleanup:
|
||||
|
||||
for (int i = 0; i < endingOrder.Length; i++)
|
||||
{
|
||||
ReadOnlySpan<int> divisors = GetGroupBDivisors(endingOrder[i]);
|
||||
ReadOnlySpan<uint> divisors = GetGroupBDivisors(endingOrder[i]);
|
||||
int index = indices[i];
|
||||
if ((uint)index >= (uint)divisors.Length)
|
||||
{
|
||||
@@ -507,7 +507,7 @@ Cleanup:
|
||||
{
|
||||
for (int i = 0; i < endingOrder.Length; i++)
|
||||
{
|
||||
ReadOnlySpan<int> divisors = GetGroupBDivisors(endingOrder[i]);
|
||||
ReadOnlySpan<uint> divisors = GetGroupBDivisors(endingOrder[i]);
|
||||
int index = indices[i];
|
||||
if ((uint)index >= (uint)divisors.Length)
|
||||
{
|
||||
@@ -527,13 +527,13 @@ Cleanup:
|
||||
return false;
|
||||
}
|
||||
|
||||
private static ReadOnlySpan<int> GetGroupBDivisors(byte ending) => ending switch
|
||||
private static ReadOnlySpan<uint> GetGroupBDivisors(byte ending) => ending switch
|
||||
{
|
||||
1 => HeuristicPrimeSieves.GroupBDivisorsEnding1,
|
||||
3 => HeuristicPrimeSieves.GroupBDivisorsEnding3,
|
||||
7 => HeuristicPrimeSieves.GroupBDivisorsEnding7,
|
||||
9 => HeuristicPrimeSieves.GroupBDivisorsEnding9,
|
||||
_ => ReadOnlySpan<int>.Empty,
|
||||
1 => DivisorGenerator.SmallPrimesLastOneWithoutLastThree,
|
||||
3 => ReadOnlySpan<uint>.Empty,
|
||||
7 => DivisorGenerator.SmallPrimesLastSevenWithoutLastThree,
|
||||
9 => DivisorGenerator.SmallPrimesLastNineWithoutLastThree,
|
||||
_ => ReadOnlySpan<uint>.Empty,
|
||||
};
|
||||
|
||||
private static ReadOnlySpan<ushort> GetWheel210ResiduesForEnding(byte ending) => ending switch
|
||||
|
||||
+497
-516
File diff suppressed because it is too large.
Load diff
Reference in new issue
Block a user