Accelerate by-divisor GPU tester with Montgomery math
This commit is contained in:
Marek Lemańczyk committed
1 parent
8ed8e56ec0
commit
a6571c2487
3 files changed
+611
-160
No files matched your search
@@ -1,9 +1,10 @@
|
||||
using System;
|
||||
using System.Buffers;
|
||||
using System.Collections.Concurrent;
|
||||
using System.Numerics;
|
||||
using System.Runtime.CompilerServices;
|
||||
using System.Runtime.InteropServices;
|
||||
using ILGPU;
|
||||
using ILGPU.Algorithms;
|
||||
using ILGPU.Runtime;
|
||||
|
||||
namespace PerfectNumbers.Core.Gpu;
|
||||
@@ -16,13 +17,29 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
private bool _isConfigured;
|
||||
private ulong _lastStatusDivisor;
|
||||
|
||||
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>>> _kernelCache = new();
|
||||
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>>> _kernelByPrimeCache = new();
|
||||
public readonly struct MontgomeryDivisorData
|
||||
{
|
||||
public readonly ulong Modulus;
|
||||
public readonly ulong NPrime;
|
||||
public readonly ulong MontgomeryOne;
|
||||
public readonly ulong MontgomeryTwo;
|
||||
|
||||
private Action<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>> GetKernel(Accelerator accelerator) =>
|
||||
_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>>(CheckKernel));
|
||||
private Action<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>> GetKernelByPrime(Accelerator accelerator) =>
|
||||
_kernelByPrimeCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>>(CheckKernelByPrime));
|
||||
public MontgomeryDivisorData(ulong modulus, ulong nPrime, ulong montgomeryOne, ulong montgomeryTwo)
|
||||
{
|
||||
Modulus = modulus;
|
||||
NPrime = nPrime;
|
||||
MontgomeryOne = montgomeryOne;
|
||||
MontgomeryTwo = montgomeryTwo;
|
||||
}
|
||||
}
|
||||
|
||||
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>> _kernelCache = new();
|
||||
private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>>> _kernelByPrimeCache = new();
|
||||
|
||||
private Action<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>> GetKernel(Accelerator accelerator) =>
|
||||
_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>(CheckKernel));
|
||||
private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>> GetKernelByPrime(Accelerator accelerator) =>
|
||||
_kernelByPrimeCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>>(CheckKernelByPrime));
|
||||
|
||||
public int GpuBatchSize
|
||||
{
|
||||
@@ -90,15 +107,16 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
var kernel = GetKernel(accelerator);
|
||||
|
||||
int batchCapacity = _gpuBatchSize;
|
||||
var divisorsBuffer = accelerator.Allocate1D<ulong>(batchCapacity);
|
||||
var hitsBuffer = accelerator.Allocate1D<byte>(batchCapacity);
|
||||
var divisorsBuffer = accelerator.Allocate1D<MontgomeryDivisorData>(batchCapacity);
|
||||
var hitsBuffer = accelerator.Allocate1D<byte>(batchCapacity);
|
||||
|
||||
ulong[] divisors = ArrayPool<ulong>.Shared.Rent(batchCapacity);
|
||||
byte[] hits = ArrayPool<byte>.Shared.Rent(batchCapacity);
|
||||
ulong[] divisors = ArrayPool<ulong>.Shared.Rent(batchCapacity);
|
||||
byte[] hits = ArrayPool<byte>.Shared.Rent(batchCapacity);
|
||||
MontgomeryDivisorData[] divisorData = ArrayPool<MontgomeryDivisorData>.Shared.Rent(batchCapacity);
|
||||
|
||||
bool composite = false;
|
||||
bool processedAll = false;
|
||||
ulong divisor = 3UL;
|
||||
bool composite = false;
|
||||
bool processedAll = false;
|
||||
ulong divisor = 3UL;
|
||||
|
||||
try
|
||||
{
|
||||
@@ -135,17 +153,23 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
break;
|
||||
}
|
||||
|
||||
var divisorView = divisorsBuffer.View.SubView(0, batchSize);
|
||||
var hitsView = hitsBuffer.View.SubView(0, batchSize);
|
||||
Span<MontgomeryDivisorData> divisorDataSpan = divisorData.AsSpan(0, batchSize);
|
||||
var divisorView = divisorsBuffer.View.SubView(0, batchSize);
|
||||
var hitsView = hitsBuffer.View.SubView(0, batchSize);
|
||||
|
||||
Span<ulong> divisorSpan = divisors.AsSpan(0, batchSize);
|
||||
Span<byte> hitsSpan = hits.AsSpan(0, batchSize);
|
||||
Span<ulong> divisorSpan = divisors.AsSpan(0, batchSize);
|
||||
Span<byte> hitsSpan = hits.AsSpan(0, batchSize);
|
||||
|
||||
divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(divisorSpan), batchSize);
|
||||
kernel(batchSize, prime, divisorView, hitsView);
|
||||
accelerator.Synchronize();
|
||||
for (int i = 0; i < batchSize; i++)
|
||||
{
|
||||
divisorDataSpan[i] = CreateMontgomeryDivisorData(divisorSpan[i]);
|
||||
}
|
||||
|
||||
hitsView.CopyToCPU(ref MemoryMarshal.GetReference(hitsSpan), batchSize);
|
||||
divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(divisorDataSpan), batchSize);
|
||||
kernel(batchSize, prime, divisorView, hitsView);
|
||||
accelerator.Synchronize();
|
||||
|
||||
hitsView.CopyToCPU(ref MemoryMarshal.GetReference(hitsSpan), batchSize);
|
||||
|
||||
for (int i = 0; i < batchSize; i++)
|
||||
{
|
||||
@@ -174,12 +198,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
}
|
||||
finally
|
||||
{
|
||||
ArrayPool<byte>.Shared.Return(hits, clearArray: true);
|
||||
ArrayPool<ulong>.Shared.Return(divisors, clearArray: true);
|
||||
hitsBuffer.Dispose();
|
||||
divisorsBuffer.Dispose();
|
||||
gpuLease.Dispose();
|
||||
}
|
||||
ArrayPool<byte>.Shared.Return(hits, clearArray: true);
|
||||
ArrayPool<ulong>.Shared.Return(divisors, clearArray: true);
|
||||
ArrayPool<MontgomeryDivisorData>.Shared.Return(divisorData, clearArray: true);
|
||||
hitsBuffer.Dispose();
|
||||
divisorsBuffer.Dispose();
|
||||
gpuLease.Dispose();
|
||||
}
|
||||
|
||||
return composite;
|
||||
}
|
||||
@@ -224,25 +249,25 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
return Math.Min(maxByPrime, _divisorLimit);
|
||||
}
|
||||
|
||||
private static void CheckKernel(Index1D index, ulong prime, ArrayView<ulong> divisors, ArrayView<byte> hits)
|
||||
{
|
||||
ulong divisor = divisors[index];
|
||||
if (divisor <= 1UL || (divisor & 1UL) == 0UL)
|
||||
{
|
||||
hits[index] = 0;
|
||||
return;
|
||||
}
|
||||
private static void CheckKernel(Index1D index, ulong prime, ArrayView<MontgomeryDivisorData> divisors, ArrayView<byte> hits)
|
||||
{
|
||||
MontgomeryDivisorData divisor = divisors[index];
|
||||
if (divisor.Modulus <= 1UL || (divisor.Modulus & 1UL) == 0UL)
|
||||
{
|
||||
hits[index] = 0;
|
||||
return;
|
||||
}
|
||||
|
||||
ulong pow = Pow2Mod(prime, divisor);
|
||||
hits[index] = pow == 1UL ? (byte)1 : (byte)0;
|
||||
}
|
||||
ulong pow = Pow2Mod(prime, divisor);
|
||||
hits[index] = pow == 1UL ? (byte)1 : (byte)0;
|
||||
}
|
||||
|
||||
public sealed class DivisorScanSession : IDisposable
|
||||
{
|
||||
private readonly MersenneNumberDivisorByDivisorGpuTester _owner;
|
||||
private readonly GpuContextPool.GpuContextLease _lease;
|
||||
private readonly Accelerator _accelerator;
|
||||
private readonly Action<Index1D, ulong, ArrayView<ulong>, ArrayView<byte>> _kernel;
|
||||
private readonly Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>> _kernel;
|
||||
private readonly MemoryBuffer1D<ulong, Stride1D.Dense> _primesBuffer;
|
||||
private readonly MemoryBuffer1D<byte, Stride1D.Dense> _hitsBuffer;
|
||||
private readonly ulong[] _primesHost;
|
||||
@@ -254,7 +279,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
_owner = owner;
|
||||
_lease = GpuContextPool.RentPreferred(preferCpu: false);
|
||||
_accelerator = _lease.Accelerator;
|
||||
_kernel = owner.GetKernelByPrime(_accelerator);
|
||||
_kernel = owner.GetKernelByPrime(_accelerator);
|
||||
_primesBuffer = _accelerator.Allocate1D<ulong>(owner._gpuBatchSize);
|
||||
_hitsBuffer = _accelerator.Allocate1D<byte>(owner._gpuBatchSize);
|
||||
_primesHost = ArrayPool<ulong>.Shared.Rent(owner._gpuBatchSize);
|
||||
@@ -275,8 +300,9 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
|
||||
int offset = 0;
|
||||
int consoleStatus = 0;
|
||||
while (offset < primes.Length)
|
||||
{
|
||||
MontgomeryDivisorData divisorData = CreateMontgomeryDivisorData(divisor);
|
||||
while (offset < primes.Length)
|
||||
{
|
||||
int batchSize = Math.Min(_owner._gpuBatchSize, primes.Length - offset);
|
||||
Span<ulong> primeSpan = _primesHost.AsSpan(0, batchSize);
|
||||
primes.Slice(offset, batchSize).CopyTo(primeSpan);
|
||||
@@ -291,7 +317,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
var hitsView = _hitsBuffer.View.SubView(0, batchSize);
|
||||
|
||||
primesView.CopyFromCPU(ref MemoryMarshal.GetReference(primeSpan), batchSize);
|
||||
_kernel(batchSize, divisor, primesView, hitsView);
|
||||
_kernel(batchSize, divisorData, primesView, hitsView);
|
||||
_accelerator.Synchronize();
|
||||
|
||||
Span<byte> hitSpan = _hitsHost.AsSpan(0, batchSize);
|
||||
@@ -317,80 +343,120 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester
|
||||
}
|
||||
}
|
||||
|
||||
private static ulong Pow2Mod(ulong exponent, ulong modulus)
|
||||
{
|
||||
if (modulus <= 1UL)
|
||||
{
|
||||
return 0UL;
|
||||
}
|
||||
private static ulong Pow2Mod(ulong exponent, MontgomeryDivisorData divisor)
|
||||
{
|
||||
ulong modulus = divisor.Modulus;
|
||||
if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
||||
{
|
||||
return 0UL;
|
||||
}
|
||||
|
||||
ulong result = 1UL % modulus;
|
||||
ulong baseVal = 2UL % modulus;
|
||||
ulong exp = exponent;
|
||||
while (exp > 0UL)
|
||||
{
|
||||
if ((exp & 1UL) != 0UL)
|
||||
{
|
||||
result = MulMod(result, baseVal, modulus);
|
||||
}
|
||||
ulong result = divisor.MontgomeryOne;
|
||||
ulong baseVal = divisor.MontgomeryTwo;
|
||||
ulong exp = exponent;
|
||||
while (exp > 0UL)
|
||||
{
|
||||
if ((exp & 1UL) != 0UL)
|
||||
{
|
||||
result = MontgomeryMultiply(result, baseVal, modulus, divisor.NPrime);
|
||||
}
|
||||
|
||||
exp >>= 1;
|
||||
if (exp == 0UL)
|
||||
{
|
||||
break;
|
||||
}
|
||||
exp >>= 1;
|
||||
if (exp == 0UL)
|
||||
{
|
||||
break;
|
||||
}
|
||||
|
||||
baseVal = MulMod(baseVal, baseVal, modulus);
|
||||
}
|
||||
baseVal = MontgomeryMultiply(baseVal, baseVal, modulus, divisor.NPrime);
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
return MontgomeryMultiply(result, 1UL, modulus, divisor.NPrime);
|
||||
}
|
||||
|
||||
private static ulong MulMod(ulong a, ulong b, ulong modulus)
|
||||
{
|
||||
if (modulus == 0UL)
|
||||
{
|
||||
return 0UL;
|
||||
}
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
private static ulong MontgomeryMultiply(ulong a, ulong b, ulong modulus, ulong nPrime)
|
||||
{
|
||||
ulong tLow = unchecked(a * b);
|
||||
ulong tHigh = MultiplyHigh(a, b);
|
||||
ulong m = unchecked(tLow * nPrime);
|
||||
ulong mnLow = unchecked(m * modulus);
|
||||
ulong mnHigh = MultiplyHigh(m, modulus);
|
||||
|
||||
ulong result = 0UL;
|
||||
ulong x = a % modulus;
|
||||
ulong y = b;
|
||||
while (y > 0UL)
|
||||
{
|
||||
if ((y & 1UL) != 0UL)
|
||||
{
|
||||
result += x;
|
||||
if (result >= modulus)
|
||||
{
|
||||
result -= modulus;
|
||||
}
|
||||
}
|
||||
ulong sumLow = unchecked(tLow + mnLow);
|
||||
ulong carry = sumLow < tLow ? 1UL : 0UL;
|
||||
ulong sumHigh = unchecked(tHigh + mnHigh + carry);
|
||||
|
||||
x <<= 1;
|
||||
if (x >= modulus)
|
||||
{
|
||||
x -= modulus;
|
||||
}
|
||||
ulong result = sumHigh;
|
||||
if (result >= modulus)
|
||||
{
|
||||
result -= modulus;
|
||||
}
|
||||
|
||||
y >>= 1;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
private static void CheckKernelByPrime(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> primes, ArrayView<byte> hits)
|
||||
{
|
||||
ulong prime = primes[index];
|
||||
if (divisor.Modulus <= 1UL || (divisor.Modulus & 1UL) == 0UL)
|
||||
{
|
||||
hits[index] = 0;
|
||||
return;
|
||||
}
|
||||
|
||||
private static void CheckKernelByPrime(Index1D index, ulong divisor, ArrayView<ulong> primes, ArrayView<byte> hits)
|
||||
{
|
||||
ulong prime = primes[index];
|
||||
if (divisor <= 1UL || (divisor & 1UL) == 0UL)
|
||||
{
|
||||
hits[index] = 0;
|
||||
return;
|
||||
}
|
||||
ulong pow = Pow2Mod(prime, divisor);
|
||||
hits[index] = pow == 1UL ? (byte)1 : (byte)0;
|
||||
}
|
||||
|
||||
ulong pow = Pow2Mod(prime, divisor);
|
||||
hits[index] = pow == 1UL ? (byte)1 : (byte)0;
|
||||
}
|
||||
private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
|
||||
{
|
||||
if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
||||
{
|
||||
return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL);
|
||||
}
|
||||
|
||||
ulong nPrime = ComputeMontgomeryNPrime(modulus);
|
||||
ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
|
||||
ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
|
||||
return new MontgomeryDivisorData(modulus, nPrime, montgomeryOne, montgomeryTwo);
|
||||
}
|
||||
|
||||
private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus)
|
||||
{
|
||||
UInt128 r = UInt128.One << 64;
|
||||
UInt128 result = ((UInt128)value * r) % modulus;
|
||||
return (ulong)result;
|
||||
}
|
||||
|
||||
private static ulong ComputeMontgomeryNPrime(ulong modulus)
|
||||
{
|
||||
ulong inv = modulus;
|
||||
inv *= unchecked(2UL - modulus * inv);
|
||||
inv *= unchecked(2UL - modulus * inv);
|
||||
inv *= unchecked(2UL - modulus * inv);
|
||||
inv *= unchecked(2UL - modulus * inv);
|
||||
inv *= unchecked(2UL - modulus * inv);
|
||||
inv *= unchecked(2UL - modulus * inv);
|
||||
return unchecked(0UL - inv);
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
private static ulong MultiplyHigh(ulong x, ulong y)
|
||||
{
|
||||
ulong xLow = (uint)x;
|
||||
ulong xHigh = x >> 32;
|
||||
ulong yLow = (uint)y;
|
||||
ulong yHigh = y >> 32;
|
||||
|
||||
ulong lowProduct = xLow * yLow;
|
||||
ulong mid = xHigh * yLow + (lowProduct >> 32);
|
||||
ulong midLow = mid & 0xFFFFFFFFUL;
|
||||
ulong midHigh = mid >> 32;
|
||||
midLow += xLow * yHigh;
|
||||
|
||||
ulong resultHigh = xHigh * yHigh + midHigh + (midLow >> 32);
|
||||
return resultHigh;
|
||||
}
|
||||
|
||||
public ulong DivisorLimit
|
||||
{
|
||||
|
||||
Reference in new issue
Block a user