Replace GPU by-divisor kernel with standard modular exponentiation

This commit is contained in:
Marek Lemańczyk committed 2025-10-24 08:49:48 +02:00
1 parent fbd6235316
commit 035956cdb6
2 files changed
+109 -27

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@@ -1,3 +1,4 @@
using System.Runtime.CompilerServices;
using ILGPU;
using ILGPU.Algorithms;
using ILGPU.Runtime;
@@ -8,21 +9,19 @@ namespace PerfectNumbers.Core.Gpu;
internal static class DivisorByDivisorKernels
{
private const int WindowSizeMax = 8;
public static void CheckKernel(
Index1D index,
ArrayView<MontgomeryDivisorData> divisors,
ArrayView<ulong> divisors,
ArrayView<ulong> exponents,
ArrayView<byte> hits,
ArrayView<int> firstHit)
{
int globalIndex = index;
MontgomeryDivisorData divisor = divisors[globalIndex];
ulong modulus = divisor.Modulus;
// The GPU by-divisor pipeline only materializes odd moduli greater than one (q = 2kp + 1),
// so the defensive guard for invalid values stays disabled here to keep the kernel branch-free.
ulong modulus = divisors[globalIndex];
ulong exponent = exponents[globalIndex];
ulong montgomeryResult = ULongExtensions.Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponent);
byte hit = montgomeryResult == 1UL ? (byte)1 : (byte)0;
ulong result = Pow2ModWindowedKernel(exponent, modulus);
byte hit = result == 1UL ? (byte)1 : (byte)0;
hits[globalIndex] = hit;
if (hit != 0)
@@ -31,6 +30,100 @@ internal static class DivisorByDivisorKernels
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong Pow2ModWindowedKernel(ulong exponent, ulong modulus)
{
int bitLength = GetBitLength(exponent);
int windowSize = GetWindowSize(bitLength);
ulong result = 1UL;
int index = bitLength - 1;
while (index >= 0)
{
result = ULongExtensions.MulMod64Gpu(result, result, modulus);
if (((exponent >> index) & 1UL) == 0UL)
{
index--;
continue;
}
int windowStart = index - windowSize + 1;
if (windowStart < 0)
{
windowStart = 0;
}
while (((exponent >> windowStart) & 1UL) == 0UL)
{
windowStart++;
}
int windowLength = index - windowStart + 1;
for (int square = 1; square < windowLength; square++)
{
result = ULongExtensions.MulMod64Gpu(result, result, modulus);
}
ulong mask = (1UL << windowLength) - 1UL;
ulong windowValue = (exponent >> windowStart) & mask;
ulong multiplier = ComputeWindowedOddPower(windowValue, modulus);
result = ULongExtensions.MulMod64Gpu(result, multiplier, modulus);
index = windowStart - 1;
}
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong ComputeWindowedOddPower(ulong windowValue, ulong modulus)
{
ulong baseValue = 2UL % modulus;
ulong result = baseValue;
ulong remaining = (windowValue - 1UL) >> 1;
ulong squareBase = ULongExtensions.MulMod64Gpu(baseValue, baseValue, modulus);
while (remaining != 0UL)
{
if ((remaining & 1UL) != 0UL)
{
result = ULongExtensions.MulMod64Gpu(result, squareBase, modulus);
}
remaining >>= 1;
if (remaining == 0UL)
{
break;
}
squareBase = ULongExtensions.MulMod64Gpu(squareBase, squareBase, modulus);
}
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static int GetBitLength(ulong value)
{
return 64 - XMath.LeadingZeroCount(value);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static int GetWindowSize(int bitLength)
{
int window = WindowSizeMax;
window = bitLength <= 671 ? 7 : window;
window = bitLength <= 239 ? 6 : window;
window = bitLength <= 79 ? 5 : window;
window = bitLength <= 23 ? 4 : window;
int clamped = bitLength >= 1 ? bitLength : 1;
window = bitLength <= 6 ? clamped : window;
return window;
}
public static void EvaluateDivisorWithStepperKernel(
Index1D _,
MontgomeryDivisorData divisor,
@@ -23,14 +23,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
private ulong _divisorLimit;
// private bool _isConfigured;
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>> _kernelCache = new();
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>> _kernelCache = new();
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ulong, ulong, ArrayView<ulong>, ArrayView<byte>>> _stepperKernelCache = new(AcceleratorReferenceComparer.Instance);
private readonly ConcurrentDictionary<Accelerator, ConcurrentBag<BatchResources>> _resourcePools = new(AcceleratorReferenceComparer.Instance);
private readonly ConcurrentBag<GpuContextPool.GpuContextLease> _acceleratorPool = new();
private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
private Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> GetKernel(Accelerator accelerator) =>
_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>(DivisorByDivisorKernels.CheckKernel));
private Action<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> GetKernel(Accelerator accelerator) =>
_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>(DivisorByDivisorKernels.CheckKernel));
private Action<Index1D, MontgomeryDivisorData, ulong, ulong, ArrayView<ulong>, ArrayView<byte>> GetStepperKernel(Accelerator accelerator) =>
_stepperKernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ulong, ulong, ArrayView<ulong>, ArrayView<byte>>(DivisorByDivisorKernels.EvaluateDivisorWithStepperKernel));
@@ -112,7 +112,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
resources.HitIndexBuffer,
resources.Divisors,
resources.Exponents,
resources.DivisorData,
out lastProcessed,
out coveredRange,
out processedCount);
@@ -163,14 +162,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
private static bool CheckDivisors(
ulong prime,
ulong allowedMax,
Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> kernel,
MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> divisorsBuffer,
Action<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> kernel,
MemoryBuffer1D<ulong, Stride1D.Dense> divisorsBuffer,
MemoryBuffer1D<ulong, Stride1D.Dense> exponentBuffer,
MemoryBuffer1D<byte, Stride1D.Dense> hitsBuffer,
MemoryBuffer1D<int, Stride1D.Dense> hitIndexBuffer,
in ulong[] divisors,
ulong[] exponents,
MontgomeryDivisorData[] divisorData,
out ulong lastProcessed,
out bool coveredRange,
out ulong processedCount)
@@ -205,7 +203,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
ArrayPool<ulong> ulongPool = ThreadStaticPools.UlongPool;
ulong[] filteredDivisors = ulongPool.Rent(chunkCapacity);
Span<ulong> filteredStorage = filteredDivisors.AsSpan();
Span<MontgomeryDivisorData> divisorDataStorage = divisorData.AsSpan();
Span<ulong> divisorStorage = divisors.AsSpan();
Span<ulong> exponentStorage = exponents.AsSpan();
@@ -254,7 +251,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
Span<ulong> filteredDivisorsSpan = filteredStorage[..filteredCount];
Span<MontgomeryDivisorData> divisorDataSpan = divisorDataStorage;
Span<ulong> divisorSpan = divisorStorage;
Span<ulong> exponentSpan = exponentStorage;
@@ -271,7 +267,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
divisorSpan[admissibleCount] = divisorValue;
exponentSpan[admissibleCount] = prime;
divisorDataSpan[admissibleCount] = divisorDataValue;
admissibleCount++;
}
@@ -281,14 +276,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
}
Span<ulong> activeDivisors = divisorSpan[..admissibleCount];
Span<MontgomeryDivisorData> activeDivisorData = divisorDataSpan[..admissibleCount];
Span<ulong> activeExponents = exponentSpan[..admissibleCount];
ArrayView1D<MontgomeryDivisorData, Stride1D.Dense> divisorView = divisorsBuffer.View.SubView(0, admissibleCount);
ArrayView1D<ulong, Stride1D.Dense> divisorView = divisorsBuffer.View.SubView(0, admissibleCount);
ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentBuffer.View.SubView(0, admissibleCount);
ArrayView1D<byte, Stride1D.Dense> hitsView = hitsBuffer.View.SubView(0, admissibleCount);
ArrayView1D<int, Stride1D.Dense> hitIndexView = hitIndexBuffer.View.SubView(0, 1);
divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(activeDivisorData), admissibleCount);
divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(activeDivisors), admissibleCount);
exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(activeExponents), admissibleCount);
int sentinel = int.MaxValue;
hitIndexView.SubView(0, 1).CopyFromCPU(ref sentinel, 1);
@@ -586,18 +580,17 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
{
int actualCapacity = Math.Max(1, capacity);
DivisorsBuffer = accelerator.Allocate1D<MontgomeryDivisorData>(actualCapacity);
DivisorsBuffer = accelerator.Allocate1D<ulong>(actualCapacity);
ExponentBuffer = accelerator.Allocate1D<ulong>(actualCapacity);
HitsBuffer = accelerator.Allocate1D<byte>(actualCapacity);
HitIndexBuffer = accelerator.Allocate1D<int>(1);
ArrayPool<ulong> ulongPool = ThreadStaticPools.UlongPool;
Divisors = ulongPool.Rent(actualCapacity);
Exponents = ulongPool.Rent(actualCapacity);
DivisorData = ThreadStaticPools.MontgomeryDivisorDataPool.Rent(actualCapacity);
Capacity = actualCapacity;
}
internal readonly MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> DivisorsBuffer;
internal readonly MemoryBuffer1D<ulong, Stride1D.Dense> DivisorsBuffer;
internal readonly MemoryBuffer1D<ulong, Stride1D.Dense> ExponentBuffer;
@@ -609,8 +602,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
internal readonly ulong[] Exponents;
internal readonly MontgomeryDivisorData[] DivisorData;
internal readonly int Capacity;
public void Dispose()
@@ -620,10 +611,8 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
HitsBuffer.Dispose();
HitIndexBuffer.Dispose();
ArrayPool<ulong> ulongPool = ThreadStaticPools.UlongPool;
ArrayPool<MontgomeryDivisorData> divisorPool = ThreadStaticPools.MontgomeryDivisorDataPool;
ulongPool.Return(Divisors, clearArray: false);
ulongPool.Return(Exponents, clearArray: false);
divisorPool.Return(DivisorData, clearArray: false);
}
}