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Marek Lemańczyk committed
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@@ -0,0 +1,9 @@
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namespace PerfectNumbers.Core.Cpu;
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public static class CpuConstants
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{
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// Allowed q mod 10 sets depending on last digit of M_p
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public const int LastSevenMask10 = (1 << 7) | (1 << 9);
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// For M_p ending with 1, restrict to {1,3,9}; 7 considered only for q == 7 (not possible for large p)
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public const int LastOneMask10 = (1 << 1) | (1 << 3) | (1 << 9);
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}
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@@ -0,0 +1,83 @@
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namespace PerfectNumbers.Core.Cpu;
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public class MersenneNumberIncrementalCpuTester(GpuKernelType kernelType)
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{
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private static readonly MersenneDivisorCycles _cycles = MersenneDivisorCycles.Shared;
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private readonly GpuKernelType _kernelType = kernelType;
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public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime)
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{
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UInt128 k, one = k = UInt128.One;
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ulong divMul = (ulong)((((UInt128)1 << 64) - UInt128.One) / exponent) + 1UL;
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// Use residue automaton always on CPU
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var auto = new MersenneResidueAutomaton(exponent);
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bool reject, shouldCheck;
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UInt128 q = auto.CurrentQ(),
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divPow, halfPow, phi, qCycle;
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ulong div, mod8, phi64;
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while (k <= maxK && Volatile.Read(ref isPrime))
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{
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qCycle = MersenneDivisorCycles.GetCycle(q);
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shouldCheck = lastIsSeven
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? (auto.Mod10R != 5UL)
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: (auto.Mod10R != 5UL);
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if (shouldCheck)
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{
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mod8 = auto.Mod8R;
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if (mod8 != 1UL && mod8 != 7UL)
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{
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shouldCheck = false;
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}
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else if (auto.Mod3R == 0UL || auto.Mod5R == 0UL)
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{
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shouldCheck = false;
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}
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}
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if (shouldCheck)
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{
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if (_kernelType == GpuKernelType.Pow2Mod)
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{
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reject = exponent.PowModWithCycle(q, qCycle) == UInt128.One;
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}
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else
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{
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phi = q - one;
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reject = false;
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if (phi <= ulong.MaxValue)
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{
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phi64 = (ulong)phi;
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if (phi64.PowModWithCycle(q, qCycle) == one)
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{
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halfPow = (phi64 >> 1).PowModWithCycle(q, qCycle) - one;
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if (halfPow.BinaryGcd(q) == one)
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{
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div = phi64.FastDiv64(exponent, divMul);
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divPow = div.PowModWithCycle(q, qCycle) - one;
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if (divPow.BinaryGcd(q) == one)
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{
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reject = true;
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}
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}
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}
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}
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}
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if (reject && q.IsPrimeCandidate())
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{
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Volatile.Write(ref isPrime, false);
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break;
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}
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}
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k += 1UL;
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auto.Next();
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q = auto.CurrentQ();
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}
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return;
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}
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}
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@@ -0,0 +1,43 @@
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using PeterO.Numbers;
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namespace PerfectNumbers.Core;
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public class MersenneNumberLucasLehmerCpuTester
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{
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public bool IsPrime(ulong exponent)
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{
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// Early rejections aligned with incremental/order sieves, but safe for small p:
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// - If 3 | p and p != 3, then 7 | M_p -> composite.
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// - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast.
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// - If p is divisible by divisors specific to numbers ending with 1 or 7, reject fast.
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if (
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((exponent % 3UL) == 0UL && exponent != 3UL) ||
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((exponent % 5UL) == 0UL && exponent != 5UL) ||
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((exponent % 7UL) == 0UL && exponent != 7UL) ||
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((exponent % 11UL) == 0UL && exponent != 11UL)
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)
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{
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return false;
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}
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if ((exponent & 3UL) == 1UL && exponent.SharesFactorWithExponentMinusOne())
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{
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return false;
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}
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UInt128 s = UInt128Numbers.Four, two = UInt128Numbers.Two,
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m = (UInt128.One << (int)exponent) - UInt128.One;
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UInt128 limit = exponent - UInt128Numbers.Two;
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for (UInt128 i = UInt128.Zero; i < limit; i++)
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{
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s = s.PowModWithCycle(two, MersenneDivisorCycles.GetCycle(m)) - two;
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if (s < UInt128.Zero)
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{
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s += m;
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}
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}
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return s == UInt128.Zero;
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}
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}
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@@ -0,0 +1,74 @@
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namespace PerfectNumbers.Core.Cpu;
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public class MersenneNumberOrderCpuTester(GpuKernelType kernelType)
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{
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private readonly GpuKernelType _kernelType = kernelType;
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public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime)
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{
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UInt128 k = 1UL;
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var auto = new MersenneResidueAutomaton(exponent);
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UInt128 qCycle,
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q = auto.CurrentQ();
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while (k <= maxK && Volatile.Read(ref isPrime))
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{
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qCycle = MersenneDivisorCycles.GetCycle(q);
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int allowMask2 = lastIsSeven ? CpuConstants.LastSevenMask10 : CpuConstants.LastOneMask10;
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bool shouldCheck = ((allowMask2 >> (int)auto.Mod10R) & 1) != 0;
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if (shouldCheck)
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{
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ulong mod8 = auto.Mod8R;
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if (mod8 != 1UL && mod8 != 7UL)
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{
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shouldCheck = false;
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}
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else if (auto.Mod3R == 0UL || auto.Mod5R == 0UL)
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{
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shouldCheck = false;
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}
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}
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if (shouldCheck)
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{
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if (_kernelType == GpuKernelType.Pow2Mod)
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{
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if (exponent.PowModWithCycle(q, qCycle) == 1UL)
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{
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Volatile.Write(ref isPrime, false);
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break;
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}
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}
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else
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{
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UInt128 phi = q - 1UL;
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if (phi <= ulong.MaxValue)
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{
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ulong phi64 = (ulong)phi;
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if (phi64.PowModWithCycle(q, qCycle) == 1UL)
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{
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UInt128 halfPow = (phi64 >> 1).PowModWithCycle(q, qCycle) - 1UL;
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if (halfPow.BinaryGcd(q) == 1UL)
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{
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ulong divMul = (ulong)((((UInt128)1 << 64) - 1UL) / exponent) + 1UL;
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ulong div = phi64.FastDiv64(exponent, divMul);
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UInt128 divPow = div.PowModWithCycle(q, qCycle) - 1UL;
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if (divPow.BinaryGcd(q) == 1UL)
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{
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Volatile.Write(ref isPrime, false);
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break;
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}
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}
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}
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}
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}
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}
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k += 1UL;
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auto.Next();
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q = auto.CurrentQ();
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}
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return;
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}
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}
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@@ -0,0 +1,169 @@
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namespace PerfectNumbers.Core.Cpu;
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public class MersenneNumberResidueCpuTester
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{
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private ModResidueTracker? _mersenneResidueTracker;
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// CPU residue variant using tracker + unrolled residue updates (no method calls in the loop).
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public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime)
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{
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// Initialize/update Mersenne residue tracker and start a merge walk for ascending q divisors
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_mersenneResidueTracker ??= new(ResidueModel.Mersenne);
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// For small divisors q <= 4,000,000 use cached cycle length to fast-path checks
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// and avoid per-q powmods when possible when scanning lanes.
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_mersenneResidueTracker.BeginMerge(exponent);
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// Start at k = 1: q0 = 2*p*1 + 1
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UInt128 k = UInt128.One;
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UInt128 q = twoP + UInt128.One;
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// Current residues
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q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3);
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// Step residues for q += 2*p
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ulong step10 = (ulong)(twoP % 10UL) % 10UL;
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ulong step8 = (ulong)(twoP % 8UL);
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ulong step3 = (ulong)(twoP % 3UL);
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ulong step5 = (ulong)(twoP % 5UL);
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// Allowed last-digit sets for q depending on last digit of M_p
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// lastIsSeven == true => allow {7,9}
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// lastIsSeven == false => allow {1,3,7,9}
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int allowMask = lastIsSeven ? CpuConstants.LastSevenMask10 : CpuConstants.LastOneMask10;
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// Predeclare temps to avoid redeclaration overhead in the loop
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UInt128 remaining;
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int i, lanes;
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// per-lane residues
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ulong r10_0, r10_1, r10_2, r10_3, r8_0, r8_1, r8_2, r8_3, r3_0, r3_1, r3_2, r3_3, r5_0, r5_1, r5_2, r5_3;
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// q lanes
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UInt128 twoP2 = twoP + twoP,
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twoP3 = twoP2 + twoP,
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twoP4 = twoP3 + twoP,
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qIncremental;
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bool localIsPrime, isDivider;
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maxK++;
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ModResidueTracker tracker = _mersenneResidueTracker!;
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while (k < maxK && (localIsPrime = Volatile.Read(ref isPrime)))
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{
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remaining = maxK - k;
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if (remaining == UInt128.Zero)
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{
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break;
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}
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lanes = remaining > 4UL ? 4 : (int)remaining;
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// Compute lane residues incrementally (avoid multiplications, minimize reductions)
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// r10
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r10_0 = r10;
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r10_1 = r10_0 + step10; if (r10_1 >= 20UL) r10_1 -= 20UL; if (r10_1 >= 10UL) r10_1 -= 10UL;
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r10_2 = r10_1 + step10; if (r10_2 >= 20UL) r10_2 -= 20UL; if (r10_2 >= 10UL) r10_2 -= 10UL;
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r10_3 = r10_2 + step10; if (r10_3 >= 20UL) r10_3 -= 20UL; if (r10_3 >= 10UL) r10_3 -= 10UL;
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// r8
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r8_0 = r8 & 7UL;
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r8_1 = (r8_0 + step8) & 7UL;
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r8_2 = (r8_1 + step8) & 7UL;
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r8_3 = (r8_2 + step8) & 7UL;
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// r3 (pattern 0,1,2,0)
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r3_0 = r3; if (r3_0 >= 3UL) r3_0 -= 3UL;
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r3_1 = r3_0 + step3; if (r3_1 >= 3UL) r3_1 -= 3UL;
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r3_2 = r3_1 + step3; if (r3_2 >= 3UL) r3_2 -= 3UL;
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r3_3 = r3; if (r3_3 >= 3UL) r3_3 -= 3UL;
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// r5 (pattern 0,1,2,3)
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r5_0 = r5; if (r5_0 >= 5UL) r5_0 -= 5UL;
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r5_1 = r5_0 + step5; if (r5_1 >= 10UL) r5_1 -= 10UL; if (r5_1 >= 5UL) r5_1 -= 5UL;
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r5_2 = r5_1 + step5; if (r5_2 >= 10UL) r5_2 -= 10UL; if (r5_2 >= 5UL) r5_2 -= 5UL;
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r5_3 = r5_2 + step5; if (r5_3 >= 10UL) r5_3 -= 10UL; if (r5_3 >= 5UL) r5_3 -= 5UL;
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// lane 0
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if (lanes >= 1 &&
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(((allowMask >> (int)r10_0) & 1) != 0 && (r8_0 == 1UL || r8_0 == 7UL) && r3_0 != 0UL && r5_0 != 0UL))
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{
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// cycle-based quick check for small q
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if (localIsPrime && tracker.MergeOrAppend(exponent, q, out isDivider) && isDivider &&
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(q <= ulong.MaxValue ? ((ulong)q).IsPrimeCandidate() : q.IsPrimeCandidate()))
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{
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localIsPrime = false;
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}
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}
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// lane 1
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qIncremental = q + twoP;
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if (lanes >= 2 &&
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((allowMask >> (int)r10_1) & 1) != 0 && (r8_1 == 1UL || r8_1 == 7UL) && r3_1 != 0UL && r5_1 != 0UL &&
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localIsPrime)
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{
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if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
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(qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
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{
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localIsPrime = false;
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}
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}
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// lane 2
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qIncremental += twoP;
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if (lanes >= 3 &&
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((allowMask >> (int)r10_2) & 1) != 0 && (r8_2 == 1UL || r8_2 == 7UL) && r3_2 != 0UL && r5_2 != 0UL &&
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localIsPrime)
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{
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if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
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(qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
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{
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localIsPrime = false;
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}
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}
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// lane 3
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qIncremental += twoP;
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if (lanes >= 4 &&
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((allowMask >> (int)r10_3) & 1) != 0 && (r8_3 == 1UL || r8_3 == 7UL) && r3_3 != 0UL && r5_3 != 0UL &&
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localIsPrime)
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{
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if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
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(qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
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{
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localIsPrime = false;
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}
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}
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if (!localIsPrime)
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{
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Volatile.Write(ref isPrime, false);
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return;
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}
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else if (!Volatile.Read(ref isPrime))
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{
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return;
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}
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// advance base by processed lanes
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k += (UInt128)lanes;
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q += lanes switch
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{
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0 => 0UL,
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1 => twoP,
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2 => twoP2,
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3 => twoP3,
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4 => twoP4,
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_ => throw new ArgumentException("Unsupproted value", nameof(twoP))
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};
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// advance residues by 'lanes' steps (consistent with base advance)
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for (i = 0; i < lanes; i++)
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{
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r10 += step10; if (r10 >= 20UL) r10 -= 20UL; if (r10 >= 10UL) r10 -= 10UL;
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r8 = (r8 + step8) & 7UL;
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r3 += step3; if (r3 >= 3UL) r3 -= 3UL;
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r5 += step5; if (r5 >= 10UL) r5 -= 10UL; if (r5 >= 5UL) r5 -= 5UL;
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}
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}
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return;
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}
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}
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