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% 10 operations replaces with UInt128/ulong.Mod10 methods

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Marek Lemańczyk committed 2025-09-21 07:42:25 +02:00
1 parent 3e0102a404
commit 412ce4fd50
13 files changed
+256 -195
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PerfectNumbers.Core/Cpu/MersenneNumberResidueCpuTester.cs
+2 -4
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@@ -20,10 +20,8 @@ public class MersenneNumberResidueCpuTester
// Current residues
q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3);
// Step residues for q += 2*p
ulong step10 = (ulong)(twoP % 10UL) % 10UL;
ulong step8 = (ulong)(twoP % 8UL);
ulong step3 = (ulong)(twoP % 3UL);
ulong step5 = (ulong)(twoP % 5UL);
twoP.Mod10_8_5_3(out ulong step10, out ulong step8, out ulong step5, out ulong step3);
step10 = step10.Mod10();
// Allowed last-digit sets for q depending on last digit of M_p
// lastIsSeven == true => allow {7,9}
PerfectNumbers.Core/Gpu/GpuKernelPool.cs
+5 -5
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@@ -201,8 +201,8 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
{
ulong idx = (ulong)index.X;
// residue automaton
ulong step10 = ((exponent % 10UL) << 1) % 10UL;
ulong r10 = q0m10 + (step10 * idx) % 10UL;
ulong step10 = (exponent.Mod10() << 1).Mod10();
ulong r10 = q0m10 + (step10 * idx).Mod10();
r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL; // skip q ≡ 5 (mod 10); other residues handled by r8/r3/r5
if (shouldCheck)
@@ -358,7 +358,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastSeven)
{
ulong idx = (ulong)index.X;
ulong r10 = ra.Q0M10 + (ra.Step10 * idx) % 10UL; r10 -= (r10 >= 10UL) ? 10UL : 0UL;
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL;
if (shouldCheck)
{
@@ -489,7 +489,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<uint, Stride1D.Dense> smallCycles)
{
ulong idx = (ulong)index.X;
ulong r10 = ra.Q0M10 + (ra.Step10 * idx) % 10UL; r10 -= (r10 >= 10UL) ? 10UL : 0UL;
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL;
if (shouldCheck)
{
@@ -573,7 +573,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<uint, Stride1D.Dense> smallCycles)
{
ulong idx = (ulong)index.X;
ulong r10 = ra.Q0M10 + (ra.Step10 * idx) % 10UL; r10 -= (r10 >= 10UL) ? 10UL : 0UL;
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL;
if (shouldCheck)
{
PerfectNumbers.Core/Gpu/MersenneNumberIncrementalGpuTester.cs
+1 -1
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@@ -23,7 +23,7 @@ public class MersenneNumberIncrementalGpuTester(GpuKernelType kernelType, bool u
var pow2Kernel = gpuLease.Pow2ModKernel;
var incKernel = gpuLease.IncrementalKernel;
ulong step10 = ((exponent % 10UL) << 1) % 10UL;
ulong step10 = (exponent.Mod10() << 1).Mod10();
ulong step8 = ((exponent & 7UL) << 1) & 7UL;
ulong step3 = ((exponent % 3UL) << 1) % 3UL;
ulong step5 = ((exponent % 5UL) << 1) % 5UL;
PerfectNumbers.Core/Gpu/MersenneNumberOrderGpuTester.cs
+57 -57
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@@ -7,68 +7,68 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
private readonly GpuKernelType _kernelType = kernelType;
private readonly bool _useGpuOrder = useGpuOrder;
public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime)
{
var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
var execution = gpuLease.EnterExecutionScope();
var accelerator = gpuLease.Accelerator;
var stream = gpuLease.Stream;
int batchSize = GpuConstants.ScanBatchSize; // large batch improves GPU occupancy and avoids TDR
UInt128 kStart = UInt128.One;
ulong divMul = (ulong)((((UInt128)1 << 64) - UInt128.One) / exponent) + 1UL;
byte last = lastIsSeven ? (byte)1 : (byte)0; // ILGPU kernels do not support bool parameters
public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime)
{
var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
var execution = gpuLease.EnterExecutionScope();
var accelerator = gpuLease.Accelerator;
var stream = gpuLease.Stream;
int batchSize = GpuConstants.ScanBatchSize; // large batch improves GPU occupancy and avoids TDR
UInt128 kStart = UInt128.One;
ulong divMul = (ulong)((((UInt128)1 << 64) - UInt128.One) / exponent) + 1UL;
byte last = lastIsSeven ? (byte)1 : (byte)0; // ILGPU kernels do not support bool parameters
var kernel = _kernelType switch
{
GpuKernelType.Pow2Mod => gpuLease.Pow2ModOrderKernel,
_ => gpuLease.IncrementalOrderKernel,
};
var kernel = _kernelType switch
{
GpuKernelType.Pow2Mod => gpuLease.Pow2ModOrderKernel,
_ => gpuLease.IncrementalOrderKernel,
};
var foundBuffer = accelerator.Allocate1D<int>(1);
UInt128 exponent128 = exponent;
exponent128.Mod10_8_5_3(out ulong exponentMod10, out ulong exponentMod8, out ulong exponentMod5, out ulong exponentMod3);
ulong step10 = (exponentMod10 << 1) % 10UL;
ulong step8 = (exponentMod8 << 1) & 7UL;
ulong step3 = (exponentMod3 << 1) % 3UL;
ulong step5 = (exponentMod5 << 1) % 5UL;
try
{
UInt128 remaining;
int currentSize;
int found = 0;
while (kStart <= maxK && Volatile.Read(ref isPrime))
{
remaining = maxK - kStart + 1UL;
currentSize = remaining > (UInt128)batchSize ? batchSize : (int)remaining;
foundBuffer.MemSetToZero();
// Precompute residue automaton bases for this batch
UInt128 q0 = twoP * kStart + 1UL;
q0.Mod10_8_5_3(out ulong q0m10, out ulong q0m8, out ulong q0m5, out ulong q0m3);
var kernelArgs = new ResidueAutomatonArgs(q0m10, step10, q0m8, step8, q0m3, step3, q0m5, step5);
var foundBuffer = accelerator.Allocate1D<int>(1);
UInt128 exponent128 = exponent;
exponent128.Mod10_8_5_3(out ulong exponentMod10, out ulong exponentMod8, out ulong exponentMod5, out ulong exponentMod3);
ulong step10 = (exponentMod10 << 1).Mod10();
ulong step8 = (exponentMod8 << 1) & 7UL;
ulong step3 = (exponentMod3 << 1) % 3UL;
ulong step5 = (exponentMod5 << 1) % 5UL;
try
{
UInt128 remaining;
int currentSize;
int found = 0;
while (kStart <= maxK && Volatile.Read(ref isPrime))
{
remaining = maxK - kStart + 1UL;
currentSize = remaining > (UInt128)batchSize ? batchSize : (int)remaining;
foundBuffer.MemSetToZero();
// Precompute residue automaton bases for this batch
UInt128 q0 = twoP * kStart + 1UL;
q0.Mod10_8_5_3(out ulong q0m10, out ulong q0m8, out ulong q0m5, out ulong q0m3);
var kernelArgs = new ResidueAutomatonArgs(q0m10, step10, q0m8, step8, q0m3, step3, q0m5, step5);
// Ensure device has small cycles table for early rejections in order kernels
var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
kernel(stream, currentSize, exponent, (GpuUInt128)twoP, (GpuUInt128)kStart, last, divMul,
kernelArgs, foundBuffer.View, smallCyclesView);
// Ensure device has small cycles table for early rejections in order kernels
var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
kernel(stream, currentSize, exponent, (GpuUInt128)twoP, (GpuUInt128)kStart, last, divMul,
kernelArgs, foundBuffer.View, smallCyclesView);
stream.Synchronize();
foundBuffer.View.CopyToCPU(ref found, 1);
if (found != 0)
{
Volatile.Write(ref isPrime, false);
break;
}
stream.Synchronize();
foundBuffer.View.CopyToCPU(ref found, 1);
if (found != 0)
{
Volatile.Write(ref isPrime, false);
break;
}
kStart += (UInt128)currentSize;
}
}
finally
{
foundBuffer.Dispose();
execution.Dispose();
gpuLease.Dispose();
}
kStart += (UInt128)currentSize;
}
}
finally
{
foundBuffer.Dispose();
execution.Dispose();
gpuLease.Dispose();
}
}
}
}
PerfectNumbers.Core/Gpu/MersenneNumberResidueGpuTester.cs
+1 -1
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@@ -24,7 +24,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
UInt128 kStart = 1UL;
byte last = lastIsSeven ? (byte)1 : (byte)0;
var kernel = gpuLease.Pow2ModKernel;
ulong step10 = ((exponent % 10UL) << 1) % 10UL;
ulong step10 = (exponent.Mod10() << 1).Mod10();
ulong step8 = ((exponent & 7UL) << 1) & 7UL;
ulong step3 = ((exponent % 3UL) << 1) % 3UL;
ulong step5 = ((exponent % 5UL) << 1) % 5UL;
PerfectNumbers.Core/ModuloAutomata.cs
+4 -19
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@@ -30,12 +30,12 @@ public sealed class MersenneResidueAutomaton
_currentQ = _step + 1UL; // start at k = 1
// init residues
Mod10R = Mod10(_currentQ);
Mod10R = _currentQ.Mod10();
Mod8R = Mod8(_currentQ);
Mod3R = Mod3(_currentQ);
Mod5R = Mod5(_currentQ);
_step10 = Mod10((ulong)(_step % 10UL));
_step10 = _step.Mod10().Mod10();
_step8 = (ulong)(_step & 7UL); // % 8
_step3 = Mod3(_step);
_step5 = Mod5(_step);
@@ -72,21 +72,6 @@ public sealed class MersenneResidueAutomaton
Mod5R = r5;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong Mod10(UInt128 value)
{
// Split and fold under mod 10: 2^64 ≡ 6 (mod 10)
ulong high = (ulong)(value >> 64);
ulong low = (ulong)value;
ulong highRem = Mod10(high);
ulong lowRem = Mod10(low);
ulong combined = lowRem + highRem * 6UL;
return Mod10(combined);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong Mod10(ulong value) => value % 10UL;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong Mod8(UInt128 value) => (ulong)value & 7UL;
@@ -196,8 +181,8 @@ public sealed class Ending7Automaton
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong AlignTo7(ulong start)
{
ulong r = start % 10UL;
ulong add = (7UL + 10UL - r) % 10UL;
ulong r = start.Mod10();
ulong add = (7UL + 10UL - r).Mod10();
return start + add;
}
PerfectNumbers.Core/PrimeTester.cs
+2 -2
View File
@@ -59,7 +59,7 @@ public sealed class PrimeTester(bool useInternal = false)
}
else
{
if ((n % 10UL) == 1UL && SharesFactorWithMaxExponent(n))
if (n.Mod10() == 1UL && SharesFactorWithMaxExponent(n))
{
result = false;
}
@@ -266,7 +266,7 @@ public sealed class PrimeTester(bool useInternal = false)
return;
}
if ((n % 10UL) == 1UL)
if (n.Mod10() == 1UL)
{
// Early reject special GCD heuristic with floor(log2 n)
ulong m = 63UL - (ulong)ILGPU.Algorithms.XMath.LeadingZeroCount(n);
PerfectNumbers.Core/PrimesGenerator.cs
+94 -94
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@@ -5,109 +5,109 @@ namespace PerfectNumbers.Core;
public static class PrimesGenerator
{
public static readonly uint[] SmallPrimes;
public static readonly ulong[] SmallPrimesPow2;
public static readonly uint[] SmallPrimesLastOne;
public static readonly ulong[] SmallPrimesPow2LastOne;
public static readonly uint[] SmallPrimesLastSeven;
public static readonly ulong[] SmallPrimesPow2LastSeven;
public static readonly uint[] SmallPrimes;
public static readonly ulong[] SmallPrimesPow2;
public static readonly uint[] SmallPrimesLastOne;
public static readonly ulong[] SmallPrimesPow2LastOne;
public static readonly uint[] SmallPrimesLastSeven;
public static readonly ulong[] SmallPrimesPow2LastSeven;
static PrimesGenerator()
{
BuildSmallPrimes(
out SmallPrimes,
out SmallPrimesPow2,
out SmallPrimesLastOne,
out SmallPrimesPow2LastOne,
out SmallPrimesLastSeven,
out SmallPrimesPow2LastSeven);
}
static PrimesGenerator()
{
BuildSmallPrimes(
out SmallPrimes,
out SmallPrimesPow2,
out SmallPrimesLastOne,
out SmallPrimesPow2LastOne,
out SmallPrimesLastSeven,
out SmallPrimesPow2LastSeven);
}
private static void BuildSmallPrimes(
out uint[] all,
out ulong[] allPow2,
out uint[] lastOne,
out ulong[] lastOnePow2,
out uint[] lastSeven,
out ulong[] lastSevenPow2)
{
uint target = PerfectNumberConstants.PrimesLimit;
int targetInt = checked((int)target);
all = new uint[targetInt];
allPow2 = new ulong[targetInt];
lastOne = new uint[targetInt];
lastOnePow2 = new ulong[targetInt];
lastSeven = new uint[targetInt];
lastSevenPow2 = new ulong[targetInt];
private static void BuildSmallPrimes(
out uint[] all,
out ulong[] allPow2,
out uint[] lastOne,
out ulong[] lastOnePow2,
out uint[] lastSeven,
out ulong[] lastSevenPow2)
{
uint target = PerfectNumberConstants.PrimesLimit;
int targetInt = checked((int)target);
all = new uint[targetInt];
allPow2 = new ulong[targetInt];
lastOne = new uint[targetInt];
lastOnePow2 = new ulong[targetInt];
lastSeven = new uint[targetInt];
lastSevenPow2 = new ulong[targetInt];
List<uint> primes = new(targetInt * 4 / 3 + 16);
uint candidate = 2U;
int allCount = 0;
int lastOneCount = 0;
int lastSevenCount = 0;
List<uint> primes = new(targetInt * 4 / 3 + 16);
uint candidate = 2U;
int allCount = 0;
int lastOneCount = 0;
int lastSevenCount = 0;
while (allCount < targetInt || lastOneCount < targetInt || lastSevenCount < targetInt)
{
bool isPrime = true;
int primesCount = primes.Count;
for (int i = 0; i < primesCount; i++)
{
uint p = primes[i];
if (p * p > candidate)
{
break;
}
while (allCount < targetInt || lastOneCount < targetInt || lastSevenCount < targetInt)
{
bool isPrime = true;
int primesCount = primes.Count;
for (int i = 0; i < primesCount; i++)
{
uint p = primes[i];
if (p * p > candidate)
{
break;
}
if (candidate % p == 0U)
{
isPrime = false;
break;
}
}
if (candidate % p == 0U)
{
isPrime = false;
break;
}
}
if (isPrime)
{
primes.Add(candidate);
if (allCount < targetInt)
{
all[allCount] = candidate;
allPow2[allCount] = checked((ulong)candidate * candidate);
allCount++;
}
if (isPrime)
{
primes.Add(candidate);
if (allCount < targetInt)
{
all[allCount] = candidate;
allPow2[allCount] = checked((ulong)candidate * candidate);
allCount++;
}
if (candidate != 2U)
{
if (lastOneCount < targetInt && IsAllowedForLastOne(candidate))
{
lastOne[lastOneCount] = candidate;
lastOnePow2[lastOneCount] = checked((ulong)candidate * candidate);
lastOneCount++;
}
if (candidate != 2U)
{
if (lastOneCount < targetInt && IsAllowedForLastOne(candidate))
{
lastOne[lastOneCount] = candidate;
lastOnePow2[lastOneCount] = checked((ulong)candidate * candidate);
lastOneCount++;
}
if (lastSevenCount < targetInt && IsAllowedForLastSeven(candidate))
{
lastSeven[lastSevenCount] = candidate;
lastSevenPow2[lastSevenCount] = checked((ulong)candidate * candidate);
lastSevenCount++;
}
}
}
if (lastSevenCount < targetInt && IsAllowedForLastSeven(candidate))
{
lastSeven[lastSevenCount] = candidate;
lastSevenPow2[lastSevenCount] = checked((ulong)candidate * candidate);
lastSevenCount++;
}
}
}
candidate = candidate == 2U ? 3U : candidate + 2U;
}
}
candidate = candidate == 2U ? 3U : candidate + 2U;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsAllowedForLastOne(uint prime)
{
uint mod10 = prime % 10U;
return mod10 == 1U || mod10 == 3U || mod10 == 9U || prime == 7U || prime == 11U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsAllowedForLastOne(uint prime)
{
uint mod10 = prime % 10U;
return mod10 == 1U || mod10 == 3U || mod10 == 9U || prime == 7U || prime == 11U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsAllowedForLastSeven(uint prime)
{
uint mod10 = prime % 10U;
return mod10 == 3U || mod10 == 7U || mod10 == 9U || prime == 11U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsAllowedForLastSeven(uint prime)
{
uint mod10 = prime % 10U;
return mod10 == 3U || mod10 == 7U || mod10 == 9U || prime == 11U;
}
}
PerfectNumbers.Core/UInt128Extensions.cs
+2 -2
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@@ -215,11 +215,11 @@ public static class UInt128Extensions
while (high != zero)
{
// 2^64 ≡ 6 (mod 10)
result = (result + (ulong)high * 6UL) % 10UL;
result = (result + (ulong)high * 6UL).Mod10();
high >>= 64;
}
return result % 10UL;
return result.Mod10();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]