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Pow2MontgomeryModWindowedConvertToStandardCpu usages replaced with a comparison to MontgomeryOne avoiding unnecessary conversions. Results updated.

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mlemanczyk committed 2026-01-03 01:37:40 +01:00
1 parent 3f59cdc14b
commit 6b80e31e6c
7 files changed
+57 -34
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PerfectNumbers.Core/Gpu/Kernels/Pow2MontgomeryKernels.cs
+6
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@@ -141,6 +141,12 @@ public static class Pow2MontgomeryKernels
return Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent); return Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
} }
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong Pow2MontgomeryModWindowedGpuKeepMontgomery(this MontgomeryDivisorDataGpu divisor, ulong exponent)
{
return Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong Pow2MontgomeryModWindowedGpuConvertToStandard(this MontgomeryDivisorDataGpu divisor, ulong exponent) public static ulong Pow2MontgomeryModWindowedGpuConvertToStandard(this MontgomeryDivisorDataGpu divisor, ulong exponent)
{ {
PerfectNumbers.Core/Gpu/Kernels/PrimeOrderKernels.cs
+3 -3
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@@ -39,7 +39,7 @@ internal static partial class PrimeOrderKernels
} }
// ulong candidate = order / primeFactor; // ulong candidate = order / primeFactor;
if (divisorData.Pow2MontgomeryModWindowedGpuConvertToStandard(candidate) == 1UL) if (divisorData.Pow2MontgomeryModWindowedGpuKeepMontgomery(candidate) == divisorData.MontgomeryOne)
{ {
order = candidate; order = candidate;
continue; continue;
@@ -395,7 +395,7 @@ internal static partial class PrimeOrderKernels
} }
ulong reduced = phi / factor; ulong reduced = phi / factor;
if (divisor.Pow2MontgomeryModWindowedGpuConvertToStandard(reduced) == 1UL) if (divisor.Pow2MontgomeryModWindowedGpuKeepMontgomery(reduced) == divisor.MontgomeryOne)
{ {
return false; return false;
} }
@@ -1179,7 +1179,7 @@ internal static partial class PrimeOrderKernels
private static bool Pow2EqualsOneKernel(ulong exponent, in MontgomeryDivisorDataGpu divisor) private static bool Pow2EqualsOneKernel(ulong exponent, in MontgomeryDivisorDataGpu divisor)
{ {
return divisor.Pow2MontgomeryModWindowedGpuConvertToStandard(exponent) == 1UL; return divisor.Pow2MontgomeryModWindowedGpuKeepMontgomery(exponent) == divisor.MontgomeryOne;
} }
[MethodImpl(MethodImplOptions.AggressiveOptimization)] [MethodImpl(MethodImplOptions.AggressiveOptimization)]
PerfectNumbers.Core/MersenneDivisorCyclesTemplate.cs
+2 -2
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@@ -99,7 +99,7 @@ public struct MersenneDivisorCyclesTemplate
return cycleLength == exponent; return cycleLength == exponent;
} }
return exponent.Pow2MontgomeryModWindowedConvertToStandardCpu(divisorData) == 1UL; return exponent.Pow2MontgomeryModWindowedKeepMontgomeryCpu(divisorData) == divisorData.MontgomeryOne;
} }
public static bool CycleEqualsExponentForMersenneCandidate(ulong divisor, in MontgomeryDivisorData divisorData, ulong exponent) public static bool CycleEqualsExponentForMersenneCandidate(ulong divisor, in MontgomeryDivisorData divisorData, ulong exponent)
@@ -125,7 +125,7 @@ public struct MersenneDivisorCyclesTemplate
} }
} }
return exponent.Pow2MontgomeryModWindowedConvertToStandardCpu(divisorData) == 1UL; return exponent.Pow2MontgomeryModWindowedKeepMontgomeryCpu(divisorData) == divisorData.MontgomeryOne;
} }
private static bool IsValidMersenneDivisorCandidate(ulong divisor, ulong exponent) private static bool IsValidMersenneDivisorCandidate(ulong divisor, ulong exponent)
PerfectNumbers.Core/PrimeOrderCalculatorTemplate.cs
+4 -4
View File
@@ -938,7 +938,7 @@ public static partial class PrimeOrderCalculatorTemplate
ulong candidate = order - primeFactor * remainder; ulong candidate = order - primeFactor * remainder;
// ulong candidate = order / primeFactor; // ulong candidate = order / primeFactor;
if (candidate.Pow2MontgomeryModWindowedConvertToStandardCpu(divisorData) == 1UL) if (candidate.Pow2MontgomeryModWindowedKeepMontgomeryCpu(divisorData) == divisorData.MontgomeryOne)
{ {
order = candidate; order = candidate;
continue; continue;
@@ -1674,7 +1674,7 @@ public static partial class PrimeOrderCalculatorTemplate
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static bool Pow2EqualsOne(ulong exponent, in MontgomeryDivisorData divisorData) private static bool Pow2EqualsOne(ulong exponent, in MontgomeryDivisorData divisorData)
{ {
return exponent.Pow2MontgomeryModWindowedConvertToStandardCpu(divisorData) == 1UL; return exponent.Pow2MontgomeryModWindowedKeepMontgomeryCpu(divisorData) == divisorData.MontgomeryOne;
} }
#if DEVICE_HYBRID || DEVICE_GPU #if DEVICE_HYBRID || DEVICE_GPU
@@ -1685,7 +1685,7 @@ public static partial class PrimeOrderCalculatorTemplate
in MontgomeryDivisorData divisorData) in MontgomeryDivisorData divisorData)
{ {
// TODO: swap to GPU pow2 when available; fallback to CPU for now. // TODO: swap to GPU pow2 when available; fallback to CPU for now.
return exponent.Pow2MontgomeryModWindowedConvertToStandardCpu(divisorData) == 1UL; return exponent.Pow2MontgomeryModWindowedKeepMontgomeryCpu(divisorData) == divisorData.MontgomeryOne;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
@@ -1695,7 +1695,7 @@ public static partial class PrimeOrderCalculatorTemplate
ulong prime, ulong prime,
in MontgomeryDivisorData divisorData) in MontgomeryDivisorData divisorData)
{ {
return exponent.Pow2MontgomeryModWindowedConvertToStandardCpu(divisorData) == 1UL; return exponent.Pow2MontgomeryModWindowedKeepMontgomeryCpu(divisorData) == divisorData.MontgomeryOne;
} }
#endif #endif
PerfectNumbers.Core/ULongExtensions.Cpu.cs
+3 -3
View File
@@ -18,7 +18,7 @@ public static partial class ULongExtensions
// Small divisors come from the precomputed <= 4,000,000 snapshot and tiny rotation counts // Small divisors come from the precomputed <= 4,000,000 snapshot and tiny rotation counts
// appear when cycle reductions trigger. Route both cases through the single-bit ladder so the // appear when cycle reductions trigger. Route both cases through the single-bit ladder so the
// CPU path avoids renting the window tables when a cheaper method is available. // CPU path avoids renting the window tables when a cheaper method is available.
if (exponent <= Pow2WindowFallbackThreshold || modulus <= (ulong)PerfectNumberConstants.MaxQForDivisorCycles) if (exponent <= Pow2WindowFallbackThreshold || modulus <= PerfectNumberConstants.MaxQForDivisorCycles)
{ {
return Pow2MontgomeryModSingleBitKeepMontgomery(exponent, divisor); return Pow2MontgomeryModSingleBitKeepMontgomery(exponent, divisor);
} }
@@ -88,7 +88,7 @@ public static partial class ULongExtensions
// Small divisors come from the precomputed <= 4,000,000 snapshot and tiny rotation counts // Small divisors come from the precomputed <= 4,000,000 snapshot and tiny rotation counts
// appear when cycle reductions trigger. Route both cases through the single-bit ladder so the // appear when cycle reductions trigger. Route both cases through the single-bit ladder so the
// CPU path avoids renting the window tables when a cheaper method is available. // CPU path avoids renting the window tables when a cheaper method is available.
if (exponent <= Pow2WindowFallbackThreshold || modulus <= (ulong)PerfectNumberConstants.MaxQForDivisorCycles) if (exponent <= Pow2WindowFallbackThreshold || modulus <= PerfectNumberConstants.MaxQForDivisorCycles)
{ {
return Pow2MontgomeryModSingleBitConvertToStandard(exponent, divisor); return Pow2MontgomeryModSingleBitConvertToStandard(exponent, divisor);
} }
@@ -274,7 +274,7 @@ public static partial class ULongExtensions
} }
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static bool AdvanceMersenneDivisorCycleStepCpu(ref ulong pow, ulong divisor, ref ulong order) private static bool AdvanceMersenneDivisorCycleStepCpu(ref ulong pow, ulong divisor, ref ulong order)
{ {
pow += pow; pow += pow;
PerfectNumbers.Core/ULongExtensions.cs
+19 -22
View File
@@ -390,7 +390,7 @@ public static partial class ULongExtensions
return value.BinaryGcd(exponentLog) > 1UL; return value.BinaryGcd(exponentLog) > 1UL;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong BinaryGcd(this ulong a, ulong b) public static ulong BinaryGcd(this ulong a, ulong b)
{ {
if (a == 0UL) if (a == 0UL)
@@ -423,7 +423,7 @@ public static partial class ULongExtensions
} }
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static ulong Select(ulong left, ulong right, bool useRight) private static ulong Select(ulong left, ulong right, bool useRight)
{ {
ulong mask = useRight ? ulong.MaxValue : 0UL; ulong mask = useRight ? ulong.MaxValue : 0UL;
@@ -432,7 +432,7 @@ public static partial class ULongExtensions
// Benchmarks (Mod5ULongBenchmarks) show the direct `% 5` is still cheaper (~0.26 ns vs 0.43 ns), so keep the modulo until a faster lookup is proven. // Benchmarks (Mod5ULongBenchmarks) show the direct `% 5` is still cheaper (~0.26 ns vs 0.43 ns), so keep the modulo until a faster lookup is proven.
// (Mod8/Mod10 stay masked because they win; Mod5 currently does not.) // (Mod8/Mod10 stay masked because they win; Mod5 currently does not.)
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static byte Mod10(this ulong value) => (byte)(value % 5UL) switch public static byte Mod10(this ulong value) => (byte)(value % 5UL) switch
{ {
0 => 0, 0 => 0,
@@ -446,7 +446,7 @@ public static partial class ULongExtensions
public static ulong Mod128(this ulong value) => value & 127UL; public static ulong Mod128(this ulong value) => value & 127UL;
// Benchmarks confirm `%` beats our current Mod5/Mod3 helpers for 64-bit inputs, so leave these modulo operations in place until a superior lookup is available. // Benchmarks confirm `%` beats our current Mod5/Mod3 helpers for 64-bit inputs, so leave these modulo operations in place until a superior lookup is available.
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static void Mod10_8_5_3(this ulong value, out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3) public static void Mod10_8_5_3(this ulong value, out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3)
{ {
mod8 = value & 7UL; mod8 = value & 7UL;
@@ -474,7 +474,7 @@ public static partial class ULongExtensions
} }
// Mod5/Mod3 lookup tables are currently slower on 64-bit operands; keep the direct modulo until benchmarks flip. // Mod5/Mod3 lookup tables are currently slower on 64-bit operands; keep the direct modulo until benchmarks flip.
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static void Mod10_8_5_3Steps(this ulong value, out ulong step10, out ulong step8, out ulong step5, out ulong step3) public static void Mod10_8_5_3Steps(this ulong value, out ulong step10, out ulong step8, out ulong step5, out ulong step3)
{ {
ulong mod8 = value & 7UL; ulong mod8 = value & 7UL;
@@ -520,16 +520,16 @@ public static partial class ULongExtensions
} }
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static UInt128 Mul64(this ulong a, ulong b) => ((UInt128)a.MulHighCpu(b) << 64) | (UInt128)(a * b); public static UInt128 Mul64(this ulong a, ulong b) => ((UInt128)a.MulHighCpu(b) << 64) | (UInt128)(a * b);
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong MulHighCpu(this ulong x, ulong y) public static ulong MulHighCpu(this ulong x, ulong y)
{ {
return (ulong)(((UInt128)x * y) >> 64); return (ulong)(((UInt128)x * y) >> 64);
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong MulHighGpu(this ulong x, ulong y) public static ulong MulHighGpu(this ulong x, ulong y)
{ {
// Retain this manual decomposition for GPU-style arithmetic so callers staging accelerator work // Retain this manual decomposition for GPU-style arithmetic so callers staging accelerator work
@@ -553,7 +553,7 @@ public static partial class ULongExtensions
return result; return result;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong AddMod64(this ulong value, ulong addend, ulong modulus) public static ulong AddMod64(this ulong value, ulong addend, ulong modulus)
{ {
// Every CPU caller (Pollard Rho and the ModPow64 ladder) supplies moduli of at least three, so leave this guard // Every CPU caller (Pollard Rho and the ModPow64 ladder) supplies moduli of at least three, so leave this guard
@@ -580,7 +580,7 @@ public static partial class ULongExtensions
return (ulong)sum; return (ulong)sum;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static ulong FoldMontgomery(ulong value, ulong modulus) private static ulong FoldMontgomery(ulong value, ulong modulus)
{ {
// Pollard Rho and ModPow64 both feed moduli of at least three, so retain the documentation and skip the runtime guard. // Pollard Rho and ModPow64 both feed moduli of at least three, so retain the documentation and skip the runtime guard.
@@ -609,7 +609,7 @@ public static partial class ULongExtensions
return folded; return folded;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong ModPow64(this ulong value, ulong exponent, ulong modulus) public static ulong ModPow64(this ulong value, ulong exponent, ulong modulus)
{ {
// Pollard Rho and the Mersenne testers never pass moduli below two, so keep the guard commented for clarity. // Pollard Rho and the Mersenne testers never pass moduli below two, so keep the guard commented for clarity.
@@ -635,13 +635,10 @@ public static partial class ULongExtensions
return result; return result;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
// Reuse the direct UInt128 reduction path that dominated MulMod64Benchmarks to avoid // Reuse the direct UInt128 reduction path that dominated MulMod64Benchmarks to avoid
// the redundant operand modulo operations in the older fallback. // the redundant operand modulo operations in the older fallback.
public static ulong MulMod64(this ulong a, ulong b, ulong modulus) public static ulong MulMod64(this ulong a, ulong b, ulong modulus) => (ulong)(((UInt128)a * b) % modulus);
{
return (ulong)(((UInt128)a * b) % modulus);
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static ulong MontgomeryMultiplyCpu(this ulong a, ulong b, ulong modulus, ulong nPrime) public static ulong MontgomeryMultiplyCpu(this ulong a, ulong b, ulong modulus, ulong nPrime)
@@ -658,7 +655,7 @@ public static partial class ULongExtensions
return result; return result;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static ulong Pow2MontgomeryModSingleBitKeepMontgomery(ulong exponent, in MontgomeryDivisorData divisor) private static ulong Pow2MontgomeryModSingleBitKeepMontgomery(ulong exponent, in MontgomeryDivisorData divisor)
{ {
ulong modulus = divisor.Modulus; ulong modulus = divisor.Modulus;
@@ -686,7 +683,7 @@ public static partial class ULongExtensions
return result; return result;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static ulong Pow2MontgomeryModSingleBitConvertToStandard(ulong exponent, in MontgomeryDivisorData divisor) private static ulong Pow2MontgomeryModSingleBitConvertToStandard(ulong exponent, in MontgomeryDivisorData divisor)
{ {
ulong modulus = divisor.Modulus; ulong modulus = divisor.Modulus;
@@ -714,7 +711,7 @@ public static partial class ULongExtensions
return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime); return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static UInt128 PowMod(this ulong exponent, UInt128 modulus) public static UInt128 PowMod(this ulong exponent, UInt128 modulus)
{ {
// EvenPerfectBitScanner starts CPU scans at p >= 138,000,000 (Program.cs), // EvenPerfectBitScanner starts CPU scans at p >= 138,000,000 (Program.cs),
@@ -1198,7 +1195,7 @@ public static partial class ULongExtensions
return value % modulus; return value % modulus;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static bool SharesFactorWithExponentMinusOneCpu(this ulong exponent) public static bool SharesFactorWithExponentMinusOneCpu(this ulong exponent)
{ {
ulong prime, value = exponent - 1UL; ulong prime, value = exponent - 1UL;
@@ -1235,7 +1232,7 @@ public static partial class ULongExtensions
return false; return false;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static bool SharesFactorWithExponentMinusOneGpu(this ulong exponent, PrimeOrderCalculatorAccelerator gpu) public static bool SharesFactorWithExponentMinusOneGpu(this ulong exponent, PrimeOrderCalculatorAccelerator gpu)
{ {
ulong prime, value = exponent - 1UL; ulong prime, value = exponent - 1UL;
@@ -1272,7 +1269,7 @@ public static partial class ULongExtensions
return false; return false;
} }
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
public static bool SharesFactorWithExponentMinusOneHybrid(this ulong exponent, PrimeOrderCalculatorAccelerator gpu) public static bool SharesFactorWithExponentMinusOneHybrid(this ulong exponent, PrimeOrderCalculatorAccelerator gpu)
{ {
ulong prime, value = exponent - 1UL; ulong prime, value = exponent - 1UL;
excluded-138m.csv
+20
View File
@@ -34510,3 +34510,23 @@ p,divisor,searchedMersenne,detailedCheck,passedAllTests
10639,427251792503,True,True,False 10639,427251792503,True,True,False
20023,1235434157297,True,True,False 20023,1235434157297,True,True,False
12497,347432096281,True,True,False 12497,347432096281,True,True,False
17539,1434748148857,True,True,False
5669,122398868791,True,True,False
12721,338895581441,True,True,False
15773,344578472209,True,True,False
16573,588828580471,True,True,False
5581,129359320121,True,True,False
17477,606383809609,True,True,False
19571,2844272257303,True,True,False
9433,444094320401,True,True,False
9769,296887940119,True,True,False
15629,284749721023,True,True,False
16519,2418552373423,True,True,False
7603,918910927273,True,True,False
20399,167108609,True,True,False
10729,290280712591,True,True,False
20411,40823,True,True,False
20441,406981291169,True,True,False
9511,1366035502967,True,True,False
2789,128664552119,True,True,False
20479,2948977,True,True,False
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