49 lines
1.8 KiB
C#
49 lines
1.8 KiB
C#
using System;
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using System.Numerics;
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core;
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public readonly struct MontgomeryDivisorData(ulong modulus, ulong nPrime, ulong montgomeryOne, ulong montgomeryTwo, ulong montgomeryTwoSquared)
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{
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public readonly ulong Modulus = modulus;
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public readonly ulong NPrime = nPrime;
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public readonly ulong MontgomeryOne = montgomeryOne;
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public readonly ulong MontgomeryTwo = montgomeryTwo;
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public readonly ulong MontgomeryTwoSquared = montgomeryTwoSquared;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong ComputeMontgomeryResidue(UInt128 value, ulong modulus) => (ulong)(value % modulus);
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private static ulong ComputeMontgomeryNPrime(ulong modulus)
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{
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ulong inv = modulus;
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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return unchecked(0UL - inv);
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}
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public static MontgomeryDivisorData FromModulus(ulong modulus)
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{
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ulong nPrime = ComputeMontgomeryNPrime(modulus);
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ulong montgomeryOne = ComputeMontgomeryResidue(UInt128Numbers.OneShiftedLeft64, modulus);
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ulong montgomeryTwo = ComputeMontgomeryResidue(UInt128Numbers.OneShiftedLeft64x2, modulus);
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ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
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return new MontgomeryDivisorData(
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modulus,
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nPrime,
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montgomeryOne,
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montgomeryTwo,
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montgomeryTwoSquared);
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}
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}
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