mlemanczyk/even-perfect-numbers-scanner
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Replace small-modulo uses with optimized helpers

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Marek Lemańczyk committed 2025-09-22 19:54:50 +02:00
1 parent ca866ffc5b
commit 3598f88aaf
9 files changed
+41 -33
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EvenPerfectBitScanner/Program.cs
+2 -2
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@@ -519,7 +519,7 @@ internal static class Program
RleBlacklist.Load(_rleBlacklistPath!); RleBlacklist.Load(_rleBlacklistPath!);
} }
ulong remainder = currentP % 6UL; ulong remainder = currentP.Mod6();
if (currentP == InitialP && string.IsNullOrEmpty(filterFile)) if (currentP == InitialP && string.IsNullOrEmpty(filterFile))
{ {
// bool passedAllTests = IsEvenPerfectCandidate(InitialP, out bool searchedMersenne, out bool detailedCheck); // bool passedAllTests = IsEvenPerfectCandidate(InitialP, out bool searchedMersenne, out bool detailedCheck);
@@ -1595,7 +1595,7 @@ internal static class Program
// Optional: RLE blacklist and binary-threshold filters on p (safe only when configured) // Optional: RLE blacklist and binary-threshold filters on p (safe only when configured)
if (p <= _rleHardMaxP) if (p <= _rleHardMaxP)
{ {
if (!_rleOnlyLast7 || p % 10UL == 7UL) if (!_rleOnlyLast7 || p.Mod10() == 7UL)
{ {
if (RleBlacklist.IsLoaded() && RleBlacklist.Matches(p)) if (RleBlacklist.IsLoaded() && RleBlacklist.Matches(p))
{ {
PerfectNumbers.Core/Cpu/MersenneNumberResidueCpuTester.cs
+1 -1
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@@ -21,7 +21,7 @@ public class MersenneNumberResidueCpuTester
q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3); q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3);
// Step residues for q += 2*p // Step residues for q += 2*p
twoP.Mod10_8_5_3(out ulong step10, out ulong step8, out ulong step5, out ulong step3); twoP.Mod10_8_5_3(out ulong step10, out ulong step8, out ulong step5, out ulong step3);
step10 %= 10UL; step10 = step10.Mod10();
// Allowed last-digit sets for q depending on last digit of M_p // Allowed last-digit sets for q depending on last digit of M_p
// lastIsSeven == true => allow {7,9} // lastIsSeven == true => allow {7,9}
PerfectNumbers.Core/Gpu/GpuKernelPool.cs
+18 -10
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@@ -200,6 +200,8 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ArrayView1D<uint, Stride1D.Dense> smallCycles) ArrayView1D<uint, Stride1D.Dense> smallCycles)
{ {
ulong idx = (ulong)index.X; ulong idx = (ulong)index.X;
ulong idxMod3 = idx.Mod3();
ulong idxMod5 = idx.Mod5();
// residue automaton // residue automaton
ulong step10 = (exponent.Mod10() << 1).Mod10(); ulong step10 = (exponent.Mod10() << 1).Mod10();
ulong r10 = q0m10 + (step10 * idx).Mod10(); ulong r10 = q0m10 + (step10 * idx).Mod10();
@@ -215,16 +217,16 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong step3 = ((exponent % 3UL) << 1) % 3UL; ulong step3 = (exponent.Mod3() << 1).Mod3();
ulong r3 = q0m3 + (step3 * (idx % 3UL)); r3 -= (r3 >= 3UL) ? 3UL : 0UL; ulong r3 = q0m3 + (step3 * idxMod3); r3 -= (r3 >= 3UL) ? 3UL : 0UL;
if (r3 == 0UL) if (r3 == 0UL)
{ {
shouldCheck = false; shouldCheck = false;
} }
else else
{ {
ulong step5Loc = ((exponent % 5UL) << 1) % 5UL; ulong step5Loc = (exponent.Mod5() << 1).Mod5();
ulong r5 = q0m5 + (step5Loc * (idx % 5UL)); if (r5 >= 5UL) r5 -= 5UL; ulong r5 = q0m5 + (step5Loc * idxMod5); if (r5 >= 5UL) r5 -= 5UL;
if (r5 == 0UL) if (r5 == 0UL)
{ {
shouldCheck = false; shouldCheck = false;
@@ -358,6 +360,8 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastSeven) ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastSeven)
{ {
ulong idx = (ulong)index.X; ulong idx = (ulong)index.X;
ulong idxMod3 = idx.Mod3();
ulong idxMod5 = idx.Mod5();
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL; ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL; bool shouldCheck = r10 != 5UL;
if (shouldCheck) if (shouldCheck)
@@ -369,7 +373,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong r3 = ra.Q0M3 + (ra.Step3 * (idx % 3UL)); ulong r3 = ra.Q0M3 + (ra.Step3 * idxMod3);
if (r3 >= 6UL) r3 -= 6UL; if (r3 >= 6UL) r3 -= 6UL;
if (r3 >= 3UL) r3 -= 3UL; if (r3 >= 3UL) r3 -= 3UL;
if (r3 == 0UL) if (r3 == 0UL)
@@ -378,7 +382,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong r5 = ra.Q0M5 + (ra.Step5 * (idx % 5UL)); ulong r5 = ra.Q0M5 + (ra.Step5 * idxMod5);
if (r5 >= 15UL) r5 -= 15UL; if (r5 >= 15UL) r5 -= 15UL;
if (r5 >= 10UL) r5 -= 10UL; if (r5 >= 10UL) r5 -= 10UL;
if (r5 >= 5UL) r5 -= 5UL; if (r5 >= 5UL) r5 -= 5UL;
@@ -489,6 +493,8 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<uint, Stride1D.Dense> smallCycles) ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<uint, Stride1D.Dense> smallCycles)
{ {
ulong idx = (ulong)index.X; ulong idx = (ulong)index.X;
ulong idxMod3 = idx.Mod3();
ulong idxMod5 = idx.Mod5();
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL; ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL; bool shouldCheck = r10 != 5UL;
if (shouldCheck) if (shouldCheck)
@@ -500,7 +506,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong r3 = ra.Q0M3 + (ra.Step3 * (idx % 3UL)); ulong r3 = ra.Q0M3 + (ra.Step3 * idxMod3);
if (r3 >= 6UL) r3 -= 6UL; if (r3 >= 6UL) r3 -= 6UL;
if (r3 >= 3UL) r3 -= 3UL; if (r3 >= 3UL) r3 -= 3UL;
if (r3 == 0UL) if (r3 == 0UL)
@@ -509,7 +515,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong r5 = ra.Q0M5 + (ra.Step5 * (idx % 5UL)); ulong r5 = ra.Q0M5 + (ra.Step5 * idxMod5);
if (r5 >= 15UL) r5 -= 15UL; if (r5 >= 15UL) r5 -= 15UL;
if (r5 >= 10UL) r5 -= 10UL; if (r5 >= 10UL) r5 -= 10UL;
if (r5 >= 5UL) r5 -= 5UL; if (r5 >= 5UL) r5 -= 5UL;
@@ -573,6 +579,8 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<uint, Stride1D.Dense> smallCycles) ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<uint, Stride1D.Dense> smallCycles)
{ {
ulong idx = (ulong)index.X; ulong idx = (ulong)index.X;
ulong idxMod3 = idx.Mod3();
ulong idxMod5 = idx.Mod5();
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL; ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
bool shouldCheck = r10 != 5UL; bool shouldCheck = r10 != 5UL;
if (shouldCheck) if (shouldCheck)
@@ -584,7 +592,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong r3 = ra.Q0M3 + (ra.Step3 * (idx % 3UL)); ulong r3 = ra.Q0M3 + (ra.Step3 * idxMod3);
if (r3 >= 6UL) r3 -= 6UL; if (r3 >= 6UL) r3 -= 6UL;
if (r3 >= 3UL) r3 -= 3UL; if (r3 >= 3UL) r3 -= 3UL;
if (r3 == 0UL) if (r3 == 0UL)
@@ -593,7 +601,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
} }
else else
{ {
ulong r5 = ra.Q0M5 + (ra.Step5 * (idx % 5UL)); ulong r5 = ra.Q0M5 + (ra.Step5 * idxMod5);
if (r5 >= 15UL) r5 -= 15UL; if (r5 >= 15UL) r5 -= 15UL;
if (r5 >= 10UL) r5 -= 10UL; if (r5 >= 10UL) r5 -= 10UL;
if (r5 >= 5UL) r5 -= 5UL; if (r5 >= 5UL) r5 -= 5UL;
PerfectNumbers.Core/Gpu/MersenneNumberIncrementalGpuTester.cs
+2 -2
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@@ -25,8 +25,8 @@ public class MersenneNumberIncrementalGpuTester(GpuKernelType kernelType, bool u
var incKernel = gpuLease.IncrementalKernel; var incKernel = gpuLease.IncrementalKernel;
ulong step10 = (exponent.Mod10() << 1).Mod10(); ulong step10 = (exponent.Mod10() << 1).Mod10();
ulong step8 = ((exponent & 7UL) << 1) & 7UL; ulong step8 = ((exponent & 7UL) << 1) & 7UL;
ulong step3 = ((exponent % 3UL) << 1) % 3UL; ulong step3 = (exponent.Mod3() << 1).Mod3();
ulong step5 = ((exponent % 5UL) << 1) % 5UL; ulong step5 = (exponent.Mod5() << 1).Mod5();
GpuUInt128 twoPGpu = (GpuUInt128)twoP; GpuUInt128 twoPGpu = (GpuUInt128)twoP;
var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator); var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
ResiduePrimeViews primeViews = default; ResiduePrimeViews primeViews = default;
PerfectNumbers.Core/Gpu/MersenneNumberLucasLehmerGpuTester.cs
+1 -1
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@@ -51,7 +51,7 @@ public class MersenneNumberLucasLehmerGpuTester
// Early rejections aligned with incremental/order sieves, but safe for small p: // Early rejections aligned with incremental/order sieves, but safe for small p:
// - If 3 | p and p != 3, then 7 | M_p -> composite. // - If 3 | p and p != 3, then 7 | M_p -> composite.
// - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast. // - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast.
if (exponent % 3UL == 0UL && exponent != 3UL) if (exponent.Mod3() == 0UL && exponent != 3UL)
{ {
return false; return false;
} }
PerfectNumbers.Core/Gpu/MersenneNumberOrderGpuTester.cs
+3 -3
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@@ -27,10 +27,10 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
var foundBuffer = accelerator.Allocate1D<int>(1); var foundBuffer = accelerator.Allocate1D<int>(1);
UInt128 exponent128 = exponent; UInt128 exponent128 = exponent;
exponent128.Mod10_8_5_3(out ulong exponentMod10, out ulong exponentMod8, out ulong exponentMod5, out ulong exponentMod3); exponent128.Mod10_8_5_3(out ulong exponentMod10, out ulong exponentMod8, out ulong exponentMod5, out ulong exponentMod3);
ulong step10 = (exponentMod10 << 1) % 10UL; ulong step10 = (exponentMod10 << 1).Mod10();
ulong step8 = (exponentMod8 << 1) & 7UL; ulong step8 = (exponentMod8 << 1) & 7UL;
ulong step3 = (exponentMod3 << 1) % 3UL; ulong step3 = (exponentMod3 << 1).Mod3();
ulong step5 = (exponentMod5 << 1) % 5UL; ulong step5 = (exponentMod5 << 1).Mod5();
try try
{ {
UInt128 remaining; UInt128 remaining;
PerfectNumbers.Core/MersenneDivisorCycles.cs
+3 -3
View File
@@ -189,7 +189,7 @@ public class MersenneDivisorCycles
for (int i = 0; i < localCycleIndex; i++) for (int i = 0; i < localCycleIndex; i++)
{ {
(d, cycle) = localCycles[i]; (d, cycle) = localCycles[i];
if (d % 3UL == 0UL || d % 5UL == 0UL || d % 7UL == 0UL || d % 11UL == 0UL) if (d.Mod3() == 0UL || d.Mod5() == 0UL || d.Mod7() == 0UL || d.Mod11() == 0UL)
continue; continue;
writer.Write(d); writer.Write(d);
@@ -249,7 +249,7 @@ public class MersenneDivisorCycles
{ {
while (skipCount > 0L && start <= maxDivisor) while (skipCount > 0L && start <= maxDivisor)
{ {
if ((start & 1UL) == 0UL || start % 3UL == 0UL || start % 5UL == 0UL || start % 7UL == 0UL || start % 11UL == 0UL) if ((start & 1UL) == 0UL || start.Mod3() == 0UL || start.Mod5() == 0UL || start.Mod7() == 0UL || start.Mod11() == 0UL)
{ {
start++; start++;
continue; continue;
@@ -296,7 +296,7 @@ public class MersenneDivisorCycles
{ {
d = divisors[i]; d = divisors[i];
if (d % 3UL == 0UL || d % 5UL == 0UL || d % 7UL == 0UL || d % 11UL == 0UL) if (d.Mod3() == 0UL || d.Mod5() == 0UL || d.Mod7() == 0UL || d.Mod11() == 0UL)
continue; continue;
writer.Write(d); writer.Write(d);
PerfectNumbers.Core/MersenneNumberTester.cs
+7 -7
View File
@@ -67,7 +67,7 @@ public sealed class MersenneNumberTester(
for (; k <= limit; k++) for (; k <= limit; k++)
{ {
q = twoP * k + UInt128.One; q = twoP * k + UInt128.One;
remainder = (ulong)(q % 10UL); remainder = q.Mod10();
bool shouldCheck = lastIsSeven bool shouldCheck = lastIsSeven
? remainder == 7UL || remainder == 9UL || remainder == 3UL ? remainder == 7UL || remainder == 9UL || remainder == 3UL
: remainder == 1UL || remainder == 3UL || remainder == 9UL; : remainder == 1UL || remainder == 3UL || remainder == 9UL;
@@ -75,12 +75,12 @@ public sealed class MersenneNumberTester(
// Early modular filters for odd order and small-prime rejections // Early modular filters for odd order and small-prime rejections
if (shouldCheck) if (shouldCheck)
{ {
ulong mod8 = (ulong)(q % 8UL); ulong mod8 = q.Mod8();
if (mod8 != 1UL && mod8 != 7UL) if (mod8 != 1UL && mod8 != 7UL)
{ {
continue; continue;
} }
else if ((ulong)(q % 3UL) == 0UL || (ulong)(q % 5UL) == 0UL) else if (q.Mod3() == 0UL || q.Mod5() == 0UL)
{ {
continue; continue;
} }
@@ -106,7 +106,7 @@ public sealed class MersenneNumberTester(
for (; k2 <= limit; k2++) for (; k2 <= limit; k2++)
{ {
q2 = twoP * k2 + 1UL; q2 = twoP * k2 + 1UL;
remainder2 = (ulong)(q2 % 10UL); remainder2 = q2.Mod10();
bool shouldCheck2 = lastIsSeven bool shouldCheck2 = lastIsSeven
? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL ? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL
: remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL; : remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL;
@@ -114,12 +114,12 @@ public sealed class MersenneNumberTester(
// Early modular filters for odd order and small-prime rejections // Early modular filters for odd order and small-prime rejections
if (shouldCheck2) if (shouldCheck2)
{ {
ulong mod8 = (ulong)(q2 % 8UL); ulong mod8 = q2.Mod8();
if (mod8 != 1UL && mod8 != 7UL) if (mod8 != 1UL && mod8 != 7UL)
{ {
shouldCheck2 = false; shouldCheck2 = false;
} }
else if ((ulong)(q2 % 3UL) == 0UL || (ulong)(q2 % 5UL) == 0UL) else if (q2.Mod3() == 0UL || q2.Mod5() == 0UL)
{ {
shouldCheck2 = false; shouldCheck2 = false;
} }
@@ -203,7 +203,7 @@ public sealed class MersenneNumberTester(
{ {
// Safe early rejections using known orders for tiny primes: // 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. // 7 | M_p iff 3 | p. Avoid rejecting p == 3 where M_3 == 7 is prime.
if (exponent % 3UL == 0UL && exponent != 3UL) if (exponent.Mod3() == 0UL && exponent != 3UL)
{ {
return false; return false;
} }
PerfectNumbers.Core/PrimeTester.cs
+4 -4
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@@ -53,13 +53,13 @@ public sealed class PrimeTester(bool useInternal = false)
{ {
result = false; result = false;
} }
else if (n > 5UL && n % 5UL == 0UL) else if (n > 5UL && n.Mod5() == 0UL)
{ {
result = false; result = false;
} }
else else
{ {
if (n % 10UL == 1UL && SharesFactorWithMaxExponent(n)) if (n.Mod10() == 1UL && SharesFactorWithMaxExponent(n))
{ {
result = false; result = false;
} }
@@ -260,13 +260,13 @@ public sealed class PrimeTester(bool useInternal = false)
return; return;
} }
if ((n & 1UL) == 0UL || (n > 5UL && n % 5UL == 0UL)) if ((n & 1UL) == 0UL || (n > 5UL && n.Mod5() == 0UL))
{ {
results[index] = 0; results[index] = 0;
return; return;
} }
if (n % 10UL == 1UL) if (n.Mod10() == 1UL)
{ {
// Early reject special GCD heuristic with floor(log2 n) // Early reject special GCD heuristic with floor(log2 n)
ulong m = 63UL - (ulong)ILGPU.Algorithms.XMath.LeadingZeroCount(n); ulong m = 63UL - (ulong)ILGPU.Algorithms.XMath.LeadingZeroCount(n);