222 lines
8.3 KiB
C#
222 lines
8.3 KiB
C#
using ILGPU;
|
|
using ILGPU.Algorithms;
|
|
using ILGPU.Runtime;
|
|
using PerfectNumbers.Core;
|
|
using PerfectNumbers.Core.Gpu;
|
|
|
|
namespace PerfectNumbers.Core.Gpu;
|
|
|
|
internal static class DivisorByDivisorKernels
|
|
{
|
|
public static void CheckKernel(Index1D index, ArrayView<MontgomeryDivisorData> divisors, ArrayView<ulong> exponents, ArrayView<byte> hits)
|
|
{
|
|
MontgomeryDivisorData divisor = divisors[index];
|
|
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 exponent = exponents[index];
|
|
ulong montgomeryResult = ULongExtensions.Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponent);
|
|
hits[index] = montgomeryResult == 1UL ? (byte)1 : (byte)0;
|
|
}
|
|
|
|
public static void EvaluateDivisorWithStepperKernel(
|
|
Index1D _,
|
|
MontgomeryDivisorData divisor,
|
|
ulong divisorCycle,
|
|
ulong firstCycleRemainder,
|
|
ArrayView<ulong> exponents,
|
|
ArrayView<byte> hits)
|
|
{
|
|
int length = (int)exponents.Length;
|
|
// EvenPerfectBitScanner always supplies at least one exponent per GPU divisor check,
|
|
// so the guard stays commented out to keep the kernel branch-free.
|
|
// if (length == 0)
|
|
// {
|
|
// return;
|
|
// }
|
|
|
|
var exponentStepper = new ExponentRemainderStepper(divisor);
|
|
ulong firstPrime = exponents[0];
|
|
bool firstUnity = exponentStepper.InitializeGpuIsUnity(firstPrime);
|
|
// EvenPerfectBitScanner only schedules divisors with non-zero cycle lengths (equal to the tested prime),
|
|
// so the no-cycle path remains commented out to keep the kernel branch-free.
|
|
// if (divisorCycle == 0UL)
|
|
// {
|
|
// hits[0] = firstUnity ? (byte)1 : (byte)0;
|
|
// for (int i = 1; i < length; i++)
|
|
// {
|
|
// ulong primeNoCycle = exponents[i];
|
|
// bool unityNoCycle = exponentStepper.ComputeNextGpuIsUnity(primeNoCycle);
|
|
// hits[i] = unityNoCycle ? (byte)1 : (byte)0;
|
|
// }
|
|
// return;
|
|
// }
|
|
|
|
ulong cycleLength = divisorCycle;
|
|
ulong previousPrime = firstPrime;
|
|
// The host precomputes the initial cycle remainder to keep the kernel free of modulo operations.
|
|
ulong cycleRemainder = firstCycleRemainder;
|
|
hits[0] = cycleRemainder == 0UL && firstUnity ? (byte)1 : (byte)0;
|
|
|
|
for (int i = 1; i < length; i++)
|
|
{
|
|
ulong prime = exponents[i];
|
|
ulong delta = prime - previousPrime;
|
|
previousPrime = prime;
|
|
|
|
var remainderValue = new GpuUInt128(cycleRemainder);
|
|
remainderValue.AddMod(delta, cycleLength);
|
|
cycleRemainder = remainderValue.Low;
|
|
|
|
hits[i] = cycleRemainder == 0UL
|
|
? (exponentStepper.ComputeNextGpuIsUnity(prime) ? (byte)1 : (byte)0)
|
|
: (byte)0;
|
|
}
|
|
}
|
|
|
|
public static void GenerateFilteredCandidatesKernel(
|
|
Index1D index,
|
|
ArrayView<ulong> candidates,
|
|
ArrayView<int> filteredCount,
|
|
ArrayView<GpuUInt128> nextStarts,
|
|
GpuUInt128 startValue,
|
|
GpuUInt128 stride,
|
|
byte lastIsSevenFlag)
|
|
{
|
|
int globalIndex = index;
|
|
int localIndex = Group.IdxX;
|
|
int groupSize = Group.Dimension.X;
|
|
|
|
ulong candidateOffset = (ulong)globalIndex;
|
|
GpuUInt128 candidateValue = stride;
|
|
candidateValue.Mul(candidateOffset);
|
|
candidateValue.Add(startValue);
|
|
ulong candidate = candidateValue.Low;
|
|
candidates[globalIndex] = candidate;
|
|
|
|
if (globalIndex == 0)
|
|
{
|
|
ulong candidateCount = (ulong)groupSize;
|
|
GpuUInt128 nextValue = stride;
|
|
nextValue.Mul(candidateCount);
|
|
nextValue.Add(startValue);
|
|
nextStarts[0] = nextValue;
|
|
}
|
|
|
|
bool lastIsSeven = lastIsSevenFlag != 0;
|
|
byte remainder10 = (byte)(candidate % 10UL);
|
|
bool acceptSeven = remainder10 == 3 || remainder10 == 7 || remainder10 == 9;
|
|
bool acceptNonSeven = remainder10 == 1 || remainder10 == 3 || remainder10 == 7 || remainder10 == 9;
|
|
bool accept10 = lastIsSeven ? acceptSeven : acceptNonSeven;
|
|
byte remainder8 = (byte)(candidate & 7UL);
|
|
bool accept8 = remainder8 == 1 || remainder8 == 7;
|
|
byte remainder5 = (byte)(candidate % 5UL);
|
|
bool accept5 = remainder5 != 0;
|
|
byte remainder3 = (byte)(candidate % 3UL);
|
|
bool accept3 = remainder3 != 0;
|
|
int accepted = (accept10 && accept8 && accept3 && accept5) ? 1 : 0;
|
|
|
|
var shared = SharedMemory.GetDynamic<int>();
|
|
int length = groupSize;
|
|
int prefixBase = 0;
|
|
int mappingBase = length;
|
|
int fallbackBase = length * 2;
|
|
|
|
shared[prefixBase + localIndex] = accepted;
|
|
shared[fallbackBase + localIndex] = globalIndex;
|
|
|
|
Group.Barrier();
|
|
|
|
int scanOffset = 1;
|
|
while (scanOffset < groupSize)
|
|
{
|
|
int addendIndex = prefixBase + localIndex - scanOffset;
|
|
int addend = localIndex >= scanOffset ? shared[addendIndex] : 0;
|
|
|
|
Group.Barrier();
|
|
|
|
int currentIndex = prefixBase + localIndex;
|
|
int current = shared[currentIndex];
|
|
int sum = current + addend;
|
|
int shouldUpdate = localIndex >= scanOffset ? 1 : 0;
|
|
shared[currentIndex] = shouldUpdate != 0 ? sum : current;
|
|
|
|
Group.Barrier();
|
|
|
|
scanOffset <<= 1;
|
|
}
|
|
|
|
int inclusivePrefix = shared[prefixBase + localIndex];
|
|
int exclusiveIndex = inclusivePrefix - accepted;
|
|
int targetBase = accepted != 0 ? mappingBase : fallbackBase;
|
|
int targetOffset = accepted != 0 ? exclusiveIndex : localIndex;
|
|
shared[targetBase + targetOffset] = globalIndex;
|
|
|
|
Group.Barrier();
|
|
|
|
int totalAccepted = shared[prefixBase + length - 1];
|
|
int writerMask = localIndex < totalAccepted ? 1 : 0;
|
|
int lookupBase = writerMask != 0 ? mappingBase : fallbackBase;
|
|
int sourceIndex = shared[lookupBase + localIndex];
|
|
|
|
ulong candidateValueToStore = candidates[sourceIndex];
|
|
if (writerMask != 0)
|
|
{
|
|
candidates[localIndex] = candidateValueToStore;
|
|
}
|
|
|
|
int lastLaneMask = globalIndex == length - 1 ? 1 : 0;
|
|
int countValue = shared[prefixBase + localIndex];
|
|
if (lastLaneMask != 0)
|
|
{
|
|
filteredCount[0] = countValue;
|
|
}
|
|
}
|
|
|
|
public static void PublishFirstHitKernel(
|
|
Index1D index,
|
|
ArrayView<byte> hits,
|
|
ArrayView<int> firstHit)
|
|
{
|
|
int globalIndex = index;
|
|
// EvenPerfectBitScanner launches this auto-grouped kernel with an extent matching the hit view length,
|
|
// so the defensive guard stays commented out to keep the hot path branch-free.
|
|
// int length = (int)hits.Length;
|
|
// if (globalIndex >= length)
|
|
// {
|
|
// return;
|
|
// }
|
|
|
|
byte hitValue = hits[globalIndex];
|
|
int candidate = hitValue != 0 ? globalIndex : int.MaxValue;
|
|
Atomic.Min(ref firstHit[0], candidate);
|
|
}
|
|
|
|
public static void ConvertMontgomeryResultsToHitsKernel(
|
|
Index1D index,
|
|
ArrayView<ulong> results,
|
|
ArrayView<byte> hits)
|
|
{
|
|
int globalIndex = index;
|
|
// EvenPerfectBitScanner launches this kernel with an extent matching the result and hit spans,
|
|
// so the defensive bounds guard stays commented out to keep the conversion branch-free.
|
|
// int length = (int)results.Length;
|
|
// if (globalIndex >= length)
|
|
// {
|
|
// return;
|
|
// }
|
|
|
|
ulong montgomeryResult = results[globalIndex];
|
|
hits[globalIndex] = montgomeryResult == 1UL ? (byte)1 : (byte)0;
|
|
}
|
|
|
|
public static void ComputeMontgomeryExponentKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> exponents, ArrayView<ulong> results)
|
|
{
|
|
ulong modulus = divisor.Modulus;
|
|
// Each divisor flowing through this kernel follows q = 2kp + 1 with k >= 1, so modulus is always odd and exceeds one.
|
|
ulong exponent = exponents[index];
|
|
ulong montgomeryResult = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(divisor, exponent);
|
|
results[index] = montgomeryResult;
|
|
}
|
|
}
|