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Reuse Pollard rho reciprocals for fast Montgomery stepping

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Marek Lemańczyk committed 2025-10-10 13:44:23 +02:00
1 parent 01ac80466b
commit 645969309c
5 files changed
+352 -43
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PerfectNumbers.Core/MersenneDivisorCycles.cs
+18 -14
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@@ -527,20 +527,31 @@ public class MersenneDivisorCycles
return 2UL;
}
PollardRhoMontgomeryReducer reducer = PollardRhoMontgomeryReducer.Create(n);
ulong diff = 0UL;
ulong d = 0UL;
while (true)
{
ulong c = (DeterministicRandom.NextUInt64() % (n - 1UL)) + 1UL;
ulong x = (DeterministicRandom.NextUInt64() % (n - 2UL)) + 2UL;
ulong y = x;
ulong d = 1UL;
ulong xStandard = (DeterministicRandom.NextUInt64() % (n - 2UL)) + 2UL;
ulong yStandard = xStandard;
ulong cMontgomery = reducer.ConvertToMontgomery(c);
ulong xMontgomery = reducer.ConvertToMontgomery(xStandard);
ulong yMontgomery = xMontgomery;
d = 1UL;
while (d == 1UL)
{
x = AdvancePolynomial(x, c, n);
y = AdvancePolynomial(y, c, n);
y = AdvancePolynomial(y, c, n);
xMontgomery = reducer.Advance(xMontgomery, cMontgomery);
xStandard = reducer.AdvanceStandard(xStandard, c);
ulong diff = x > y ? x - y : y - x;
yMontgomery = reducer.Advance(yMontgomery, cMontgomery);
yStandard = reducer.AdvanceStandard(yStandard, c);
yMontgomery = reducer.Advance(yMontgomery, cMontgomery);
yStandard = reducer.AdvanceStandard(yStandard, c);
diff = xStandard > yStandard ? xStandard - yStandard : yStandard - xStandard;
d = BinaryGcd(diff, n);
}
@@ -551,13 +562,6 @@ public class MersenneDivisorCycles
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong AdvancePolynomial(ulong x, ulong c, ulong modulus)
{
UInt128 value = (UInt128)x * x + c;
return (ulong)(value % modulus);
}
private static ulong BinaryGcd(ulong a, ulong b)
{
if (a == 0UL)