401 lines
11 KiB
C#
401 lines
11 KiB
C#
using System.Runtime.CompilerServices;
|
||
using System.Collections.Concurrent;
|
||
using System.Buffers;
|
||
using ILGPU;
|
||
using ILGPU.Runtime;
|
||
using PerfectNumbers.Core.Cpu;
|
||
using PerfectNumbers.Core.Gpu;
|
||
using UInt128 = System.UInt128;
|
||
|
||
namespace PerfectNumbers.Core;
|
||
|
||
public enum GpuKernelType
|
||
{
|
||
Incremental,
|
||
Pow2Mod,
|
||
}
|
||
|
||
public sealed class MersenneNumberTester(
|
||
bool useIncremental = true,
|
||
bool useOrderCache = false,
|
||
GpuKernelType kernelType = GpuKernelType.Incremental,
|
||
bool useModuloWorkaround = false,
|
||
bool useOrder = false,
|
||
bool useGpuLucas = true,
|
||
bool useGpuScan = true,
|
||
bool useGpuOrder = true,
|
||
bool useResidue = true,
|
||
UInt128? maxK = null,
|
||
UInt128? residueDivisorSets = null)
|
||
{
|
||
private readonly bool _useResidue = useResidue;
|
||
private readonly bool _useIncremental = useIncremental && !useResidue;
|
||
private readonly UInt128 _maxK = maxK ?? (UInt128)5_000_000UL;
|
||
private readonly UInt128 _residueDivisorSetCount = residueDivisorSets ?? (UInt128)PerfectNumberConstants.ExtraDivisorCycleSearchLimit;
|
||
private readonly GpuKernelType _kernelType = kernelType;
|
||
private readonly bool _useModuloWorkaround = useModuloWorkaround;
|
||
private readonly bool _useGpuLucas = useGpuLucas;
|
||
private readonly bool _useGpuScan = useGpuScan; // device for pow2mod/incremental scanning
|
||
private readonly bool _useGpuOrder = useGpuOrder; // device for order computations
|
||
private static readonly ConcurrentDictionary<UInt128, ulong> OrderCache = new();
|
||
private readonly MersenneNumberIncrementalGpuTester _incrementalGpuTester = new(kernelType, useGpuOrder);
|
||
private readonly MersenneNumberIncrementalCpuTester _incrementalCpuTester = new(kernelType);
|
||
private readonly MersenneNumberOrderGpuTester _orderGpuTester = new(kernelType, useGpuOrder);
|
||
private readonly MersenneNumberOrderCpuTester _orderCpuTester = new(kernelType);
|
||
private readonly MersenneNumberLucasLehmerGpuTester _lucasLehmerGpuTester = new();
|
||
private readonly MersenneNumberLucasLehmerCpuTester _lucasLehmerCpuTester = new();
|
||
private readonly MersenneNumberResidueGpuTester? _residueGpuTester = useResidue ? new(useGpuOrder) : null;
|
||
private readonly MersenneNumberResidueCpuTester? _residueCpuTester = useResidue ? new() : null;
|
||
|
||
// TODO: Ensure Program passes useResidue correctly and that residue-vs-incremental-vs-LL selection respects CLI flags.
|
||
// Also consider injecting a shared cycles cache (MersenneDivisorCycles.Shared) to both CPU and GPU testers.
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static UInt128 DivideRoundUp(UInt128 value, UInt128 divisor)
|
||
{
|
||
if (divisor == UInt128.Zero)
|
||
{
|
||
return UInt128.Zero;
|
||
}
|
||
|
||
UInt128 result = value / divisor;
|
||
if (result * divisor == value)
|
||
{
|
||
return result;
|
||
}
|
||
|
||
return result + UInt128.One;
|
||
}
|
||
|
||
public void WarmUpOrders(ulong exponent, ulong limit = 5_000_000UL)
|
||
{
|
||
bool cacheEnabled = useOrderCache;
|
||
if (!cacheEnabled)
|
||
{
|
||
return;
|
||
}
|
||
|
||
UInt128 twoP = (UInt128)exponent << 1; // 2 * p
|
||
bool lastIsSeven = (exponent & 3UL) == 3UL;
|
||
// CPU path: compute orders directly and cache
|
||
if (!_useGpuOrder)
|
||
{
|
||
UInt128 k = UInt128.One;
|
||
UInt128 q;
|
||
ulong remainder;
|
||
for (; k <= limit; k++)
|
||
{
|
||
q = twoP * k + UInt128.One;
|
||
remainder = q.Mod10();
|
||
bool shouldCheck = lastIsSeven
|
||
? remainder == 7UL || remainder == 9UL || remainder == 3UL
|
||
: remainder == 1UL || remainder == 3UL || remainder == 9UL;
|
||
|
||
// Early modular filters for odd order and small-prime rejections
|
||
if (shouldCheck)
|
||
{
|
||
ulong mod8 = q.Mod8();
|
||
if (mod8 != 1UL && mod8 != 7UL)
|
||
{
|
||
continue;
|
||
}
|
||
else if (q.Mod3() == 0UL || q.Mod5() == 0UL)
|
||
{
|
||
continue;
|
||
}
|
||
}
|
||
|
||
if (!shouldCheck || !cacheEnabled || (cacheEnabled && OrderCache.ContainsKey(q)))
|
||
{
|
||
continue;
|
||
}
|
||
|
||
ulong ord = q.CalculateOrder();
|
||
OrderCache[q] = ord;
|
||
}
|
||
|
||
return;
|
||
}
|
||
|
||
UInt128[] qsBuffer = ArrayPool<UInt128>.Shared.Rent((int)limit);
|
||
int idx = 0;
|
||
UInt128 k2 = 1UL;
|
||
UInt128 q2;
|
||
ulong remainder2;
|
||
for (; k2 <= limit; k2++)
|
||
{
|
||
q2 = twoP * k2 + 1UL;
|
||
remainder2 = q2.Mod10();
|
||
bool shouldCheck2 = lastIsSeven
|
||
? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL
|
||
: remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL;
|
||
|
||
// Early modular filters for odd order and small-prime rejections
|
||
if (shouldCheck2)
|
||
{
|
||
ulong mod8 = q2.Mod8();
|
||
if (mod8 != 1UL && mod8 != 7UL)
|
||
{
|
||
shouldCheck2 = false;
|
||
}
|
||
else if (q2.Mod3() == 0UL || q2.Mod5() == 0UL)
|
||
{
|
||
shouldCheck2 = false;
|
||
}
|
||
}
|
||
|
||
if (!shouldCheck2 || (cacheEnabled && OrderCache.ContainsKey(q2)))
|
||
{
|
||
continue;
|
||
}
|
||
|
||
qsBuffer[idx++] = q2;
|
||
}
|
||
|
||
if (idx == 0)
|
||
{
|
||
ArrayPool<UInt128>.Shared.Return(qsBuffer);
|
||
return;
|
||
}
|
||
|
||
UInt128[] qs = qsBuffer;
|
||
|
||
var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
|
||
var accelerator = gpuLease.Accelerator;
|
||
var orderKernel = gpuLease.OrderKernel!;
|
||
|
||
// Guard long-running kernels by chunking the warm-up across batches.
|
||
// Reuse the same ScanBatchSize knob used for scanning.
|
||
int batchSize = GpuConstants.ScanBatchSize;
|
||
ulong divMul = (ulong)((((UInt128)1 << 64) - 1UL) / exponent) + 1UL;
|
||
int offset = 0;
|
||
while (offset < idx)
|
||
{
|
||
int count = Math.Min(batchSize, idx - offset);
|
||
var qBuffer = accelerator.Allocate1D<PerfectNumbers.Core.Gpu.GpuUInt128>(count);
|
||
var orderBuffer = accelerator.Allocate1D<ulong>(count);
|
||
// Convert to device-friendly GpuUInt128 on the fly
|
||
var tmp = System.Buffers.ArrayPool<PerfectNumbers.Core.Gpu.GpuUInt128>.Shared.Rent(count);
|
||
for (int i = 0; i < count; i++)
|
||
{
|
||
tmp[i] = (PerfectNumbers.Core.Gpu.GpuUInt128)qs[offset + i];
|
||
}
|
||
// Copy only the populated elements to the device buffer to avoid overrun on pooled arrays.
|
||
qBuffer.View.CopyFromCPU(ref tmp[0], count);
|
||
System.Buffers.ArrayPool<PerfectNumbers.Core.Gpu.GpuUInt128>.Shared.Return(tmp);
|
||
orderKernel(count, exponent, divMul, qBuffer.View, orderBuffer.View);
|
||
accelerator.Synchronize();
|
||
|
||
ulong[] orders = orderBuffer.GetAsArray1D();
|
||
for (int i = 0; i < count; i++)
|
||
{
|
||
ulong order = orders[i];
|
||
if (order == 0UL)
|
||
{
|
||
order = qs[offset + i].CalculateOrder();
|
||
}
|
||
|
||
if (useOrderCache)
|
||
{
|
||
OrderCache[qs[offset + i]] = order;
|
||
}
|
||
}
|
||
|
||
offset += count;
|
||
orderBuffer.Dispose();
|
||
qBuffer.Dispose();
|
||
}
|
||
|
||
gpuLease.Dispose();
|
||
ArrayPool<UInt128>.Shared.Return(qs);
|
||
}
|
||
|
||
public bool IsMersennePrime(ulong exponent) => IsMersennePrime(exponent, out _);
|
||
|
||
public bool IsMersennePrime(ulong exponent, out bool divisorsExhausted)
|
||
{
|
||
divisorsExhausted = false;
|
||
|
||
// Safe early rejections using known orders for tiny primes:
|
||
// 7 | M_p iff 3 | p. Avoid rejecting p == 3 where M_3 == 7 is prime.
|
||
if ((exponent % 3UL) == 0UL && exponent != 3UL)
|
||
{
|
||
divisorsExhausted = true;
|
||
return false;
|
||
}
|
||
|
||
if ((exponent & 3UL) == 1UL && exponent.SharesFactorWithExponentMinusOne())
|
||
{
|
||
divisorsExhausted = true;
|
||
return false;
|
||
}
|
||
|
||
// Skip even exponents: for even p > 2, M_p is composite; here p is large.
|
||
if ((exponent & 1UL) == 0UL)
|
||
{
|
||
divisorsExhausted = true;
|
||
return false;
|
||
}
|
||
|
||
bool prePrime = true;
|
||
UInt128 twoP = (UInt128)exponent << 1; // 2 * p
|
||
// UInt128 maxDivisor = new(ulong.MaxValue, ulong.MaxValue);
|
||
UInt128 maxK = UInt128Numbers.Two.Pow(exponent) / 2 + 1;
|
||
bool lastIsSeven = (exponent & 3UL) == 3UL;
|
||
|
||
// In residue mode the residue scan is the final primality check.
|
||
if (_useResidue)
|
||
{
|
||
if (_maxK < maxK)
|
||
{
|
||
maxK = _maxK;
|
||
}
|
||
|
||
if (_maxK == UInt128.Zero || _residueDivisorSetCount == UInt128.Zero)
|
||
{
|
||
return prePrime;
|
||
}
|
||
|
||
UInt128 totalLimit = _maxK;
|
||
if (totalLimit > maxK)
|
||
{
|
||
totalLimit = maxK;
|
||
}
|
||
|
||
if (totalLimit == UInt128.Zero)
|
||
{
|
||
return true;
|
||
}
|
||
|
||
UInt128 requestedSets = _residueDivisorSetCount;
|
||
if (_useGpuScan)
|
||
{
|
||
UInt128 maxUsefulSets = DivideRoundUp(totalLimit, (UInt128)GpuConstants.ScanBatchSize);
|
||
if (maxUsefulSets == UInt128.Zero)
|
||
{
|
||
maxUsefulSets = UInt128.One;
|
||
}
|
||
|
||
if (requestedSets == UInt128.Zero || requestedSets > maxUsefulSets)
|
||
{
|
||
requestedSets = maxUsefulSets;
|
||
}
|
||
}
|
||
|
||
if (requestedSets == UInt128.Zero)
|
||
{
|
||
requestedSets = UInt128.One;
|
||
}
|
||
|
||
UInt128 perSetLimit = DivideRoundUp(totalLimit, requestedSets);
|
||
if (perSetLimit == UInt128.Zero)
|
||
{
|
||
perSetLimit = UInt128.One;
|
||
}
|
||
|
||
UInt128 setsNeeded = DivideRoundUp(totalLimit, perSetLimit);
|
||
UInt128 effectiveSets = requestedSets;
|
||
if (setsNeeded < effectiveSets)
|
||
{
|
||
effectiveSets = setsNeeded;
|
||
}
|
||
|
||
bool scanCompleted = false;
|
||
|
||
if (_useGpuScan)
|
||
{
|
||
_residueGpuTester!.Scan(exponent, twoP, lastIsSeven, perSetLimit, effectiveSets, totalLimit, ref prePrime, ref scanCompleted);
|
||
}
|
||
else
|
||
{
|
||
_residueCpuTester!.Scan(exponent, twoP, lastIsSeven, perSetLimit, effectiveSets, totalLimit, ref prePrime, ref scanCompleted);
|
||
}
|
||
|
||
if (!prePrime)
|
||
{
|
||
divisorsExhausted = true;
|
||
return false;
|
||
}
|
||
|
||
divisorsExhausted = scanCompleted;
|
||
return true;
|
||
}
|
||
|
||
if (!_useIncremental)
|
||
{
|
||
// Optional prefilter before Lucas–Lehmer using the same GPU/CPU scan path.
|
||
// Scan a limited range of k to quickly reject obvious cases.
|
||
UInt128 twoPPre = (UInt128)exponent << 1;
|
||
UInt128 maxKPre = (UInt128)PreLucasPreScanK;
|
||
bool lastIsSevenPre = (exponent & 3UL) == 3UL;
|
||
if (_useGpuScan)
|
||
{
|
||
_incrementalGpuTester.Scan(exponent, twoPPre, lastIsSevenPre, maxKPre, ref prePrime);
|
||
}
|
||
else
|
||
{
|
||
_incrementalCpuTester.Scan(exponent, twoPPre, lastIsSevenPre, maxKPre, ref prePrime);
|
||
}
|
||
|
||
if (!prePrime)
|
||
{
|
||
divisorsExhausted = true;
|
||
return false;
|
||
}
|
||
|
||
bool lucasPrime = _useGpuLucas
|
||
? _lucasLehmerGpuTester.IsPrime(exponent, runOnGpu: true)
|
||
: _lucasLehmerCpuTester.IsPrime(exponent);
|
||
divisorsExhausted = true;
|
||
return lucasPrime;
|
||
}
|
||
|
||
bool isPrime = true;
|
||
|
||
if (useOrder)
|
||
{
|
||
if (_useGpuOrder)
|
||
{
|
||
_orderGpuTester.Scan(exponent, twoP, lastIsSeven, maxK, ref isPrime);
|
||
}
|
||
else
|
||
{
|
||
_orderCpuTester.Scan(exponent, twoP, lastIsSeven, maxK, ref isPrime);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
if (_useGpuScan)
|
||
{
|
||
_incrementalGpuTester.Scan(exponent, twoP, lastIsSeven, maxK, ref isPrime);
|
||
}
|
||
else
|
||
{
|
||
_incrementalCpuTester.Scan(exponent, twoP, lastIsSeven, maxK, ref isPrime);
|
||
}
|
||
}
|
||
|
||
divisorsExhausted = true;
|
||
return isPrime;
|
||
}
|
||
|
||
// Limit of k to scan in the pre-Lucas prescan
|
||
public const int PreLucasPreScanK = 5_000_000;
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static bool DividesMersenne(ulong exponent, ulong prime)
|
||
{
|
||
return 2UL.ModPow64(exponent, prime) == 1UL;
|
||
}
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static void LegacyOrderKernel(Index1D index, ulong exponent, ArrayView<UInt128> qs, ArrayView<ulong> orders)
|
||
{
|
||
UInt128 q = qs[index];
|
||
UInt128 pow = exponent.PowMod(q);
|
||
orders[index] = pow == 1UL ? exponent : 0UL;
|
||
}
|
||
|
||
|
||
}
|