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Merge pull request #159 from mlemanczyk/codex/update-pow2mod-to-use-montgomery

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Switch Pow2Mod kernel to non-windowed Montgomery exponentiation
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Marek Lemańczyk authored and GitHub committed 2025-10-12 05:44:53 +02:00
2 parents e5dc688865 86989d0502
commit 808bf64fab
1 file changed
+51 -1
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PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs
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@@ -1811,7 +1811,57 @@ internal static partial class PrimeOrderGpuHeuristics
private static void Pow2ModKernel(Index1D index, ArrayView1D<ulong, Stride1D.Dense> exponents, MontgomeryDivisorData divisor, ArrayView1D<ulong, Stride1D.Dense> remainders)
{
ulong exponent = exponents[index];
remainders[index] = exponent.Pow2MontgomeryModWindowedGpu(divisor, keepMontgomery: false);
ulong modulus = divisor.Modulus;
ulong nPrime = divisor.NPrime;
ulong result = divisor.MontgomeryOne;
ulong baseValue = divisor.MontgomeryTwo;
ulong remainingExponent = exponent;
if (remainingExponent == 0UL)
{
remainders[index] = result.MontgomeryMultiply(1UL, modulus, nPrime);
return;
}
while (remainingExponent != 0UL)
{
if ((remainingExponent & 1UL) != 0UL)
{
result = result.MontgomeryMultiply(baseValue, modulus, nPrime);
}
remainingExponent >>= 1;
if (remainingExponent == 0UL)
{
break;
}
// Reusing baseValue to hold base^2 so we avoid allocating another register for the squared term.
baseValue = baseValue.MontgomeryMultiply(baseValue, modulus, nPrime);
}
remainders[index] = result.MontgomeryMultiply(1UL, modulus, nPrime);
// Plain modular exponentiation without Montgomery reduction kept for reference.
// ulong plainResult = 1UL % modulus;
// ulong plainBase = 2UL % modulus;
// ulong plainExponent = exponent;
// while (plainExponent != 0UL)
// {
// if ((plainExponent & 1UL) != 0UL)
// {
// plainResult = (plainResult * plainBase) % modulus;
// }
//
// plainExponent >>= 1;
// if (plainExponent == 0UL)
// {
// break;
// }
//
// plainBase = (plainBase * plainBase) % modulus;
// }
// remainders[index] = plainResult;
}
private static Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>> GetPow2ModWideKernel(Accelerator accelerator)