447 lines
14 KiB
C#
447 lines
14 KiB
C#
using System.Runtime.CompilerServices;
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using ILGPU;
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using ILGPU.Algorithms;
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using ILGPU.Runtime;
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namespace PerfectNumbers.Core.Gpu.Kernels;
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public static class Pow2MontgomeryKernels
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static GpuUInt128 AdvancePolynomialGpu(GpuUInt128 x, ulong c, ulong modulus)
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{
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x.Pow2();
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x.AddMod(c, modulus);
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return x;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong ComputeMontgomeryOddPowerGpu(ulong exponent, in MontgomeryDivisorDataGpu divisor, ulong modulus, ulong nPrime)
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{
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ulong baseValue = divisor.MontgomeryTwo;
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ulong power = divisor.MontgomeryOne;
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ulong remaining = exponent;
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while (remaining != 0UL)
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{
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ulong bit = remaining & 1UL;
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ulong multiplied = MontgomeryMultiplyGpu(power, baseValue, modulus, nPrime);
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ulong mask = (ulong)-(long)bit;
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power = (power & ~mask) | (multiplied & mask);
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remaining >>= 1;
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if (remaining == 0UL)
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{
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break;
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}
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baseValue = MontgomeryMultiplyGpu(baseValue, baseValue, modulus, nPrime);
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}
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return power;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetPortableBitLengthGpu(ulong value) => 64 - XMath.LeadingZeroCount(value);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetWindowSizeGpu(int n)
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{
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int w = PerfectNumberConstants.Pow2WindowSize;
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w = (n <= 671) ? 7 : w;
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w = (n <= 239) ? 6 : w;
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w = (n <= 79) ? 5 : w;
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w = (n <= 23) ? 4 : w;
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int m = (n >= 1) ? n : 1;
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w = (n <= 6) ? m : w;
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return w;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetNextSetBitIndexGpu(ulong exponent, int startIndex)
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{
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ulong guard = (ulong)(((long)startIndex - 64) >> 63);
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int shift = startIndex & 63;
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ulong mask = (~0UL << shift) & guard;
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ulong masked = exponent & mask;
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return XMath.TrailingZeroCount(masked);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void InitializeStandardOddPowers(ulong modulus, Span<ulong> oddPowers)
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{
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// oddPowers spans at least one entry for production workloads; keep the guard commented out to avoid redundant checks in the hot loop.
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// if (oddPowers.IsEmpty)
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// {
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// return;
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// }
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// EvenPerfectBitScanner feeds odd prime moduli (≥ 3) here, so the base value stays within range without a modulo reduction.
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ulong baseValue = 2UL;
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oddPowers[0] = baseValue;
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if (oddPowers.Length == 1)
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{
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return;
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}
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ulong square = baseValue.MulModGpu(baseValue, modulus);
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for (int i = 1; i < oddPowers.Length; i++)
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{
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ulong previous = oddPowers[i - 1];
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oddPowers[i] = previous.MulModGpu(square, modulus);
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static ulong MontgomeryMultiplyGpu(this ulong a, ulong b, ulong modulus, ulong nPrime)
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{
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// Mirror the struct-based MontMul64 helper measured as the second-fastest GPU-compatible
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// option in GpuUInt128Montgomery64Benchmarks so accelerator kernels reuse the validated path.
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MultiplyPartsGpu(a, b, out ulong productHigh, out ulong productLow);
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MultiplyPartsGpu(productLow, nPrime, out _, out ulong mLow);
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MultiplyPartsGpu(mLow, modulus, out ulong mTimesModulusHigh, out ulong mTimesModulusLow);
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ulong sumLow = unchecked(productLow + mTimesModulusLow);
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ulong carry = sumLow < productLow ? 1UL : 0UL;
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ulong sumHigh = unchecked(productHigh + mTimesModulusHigh + carry);
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if (sumHigh >= modulus)
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{
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sumHigh -= modulus;
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}
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return sumHigh;
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}
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[MethodImpl(MethodImplOptions.AggressiveOptimization | MethodImplOptions.AggressiveInlining)]
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private static void MultiplyPartsGpu(ulong left, ulong right, out ulong high, out ulong low)
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{
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ulong leftLow = (uint)left;
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ulong leftHigh = left >> 32;
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ulong rightLow = (uint)right;
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ulong rightHigh = right >> 32;
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ulong lowProduct = unchecked(leftLow * rightLow);
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ulong cross1 = unchecked(leftHigh * rightLow);
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ulong cross2 = unchecked(leftLow * rightHigh);
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ulong highProduct = unchecked(leftHigh * rightHigh);
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ulong carry = unchecked((lowProduct >> 32) + (uint)cross1 + (uint)cross2);
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low = unchecked((lowProduct & 0xFFFFFFFFUL) | (carry << 32));
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high = unchecked(highProduct + (cross1 >> 32) + (cross2 >> 32) + (carry >> 32));
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
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internal static ulong Pow2MontgomeryModWindowedGpuKeepMontgomery(in MontgomeryDivisorDataGpu divisor, ulong exponent)
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{
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return Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
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public static ulong Pow2MontgomeryModWindowedGpuKeepMontgomery(this MontgomeryDivisorDataGpu divisor, ulong exponent)
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{
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return Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
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public static ulong Pow2MontgomeryModWindowedGpuConvertToStandard(this MontgomeryDivisorDataGpu divisor, ulong exponent)
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{
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ulong modulus = divisor.Modulus;
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ulong nPrime = divisor.NPrime;
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ulong montgomeryResult = Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
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return MontgomeryMultiplyGpu(montgomeryResult, 1UL, modulus, nPrime);
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}
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[MethodImpl(MethodImplOptions.AggressiveOptimization)]
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private static ulong Pow2MontgomeryModWindowedGpuMontgomeryResult(in MontgomeryDivisorDataGpu divisor, ulong exponent)
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{
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ulong modulus = divisor.Modulus;
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// Reuse the GPU-compatible MontgomeryMultiply helper highlighted in MontgomeryMultiplyBenchmarks so the accelerator path
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// mirrors the fastest CPU reduction without relying on UInt128 intrinsics.
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// We shouldn't hit it in production code. If we do, we're doing something wrong.
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// if (exponent == 0UL)
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// {
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// return divisor.MontgomeryOne;
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// }
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// We barely ever hit it in production code. It's e.g. 772 calls out of billions
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// if (exponent <= Pow2WindowFallbackThreshold)
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// {
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// return Pow2MontgomeryModSingleBit(exponent, divisor);
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// }
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int bitLength = GetPortableBitLengthGpu(exponent);
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int windowSize = GetWindowSizeGpu(bitLength);
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ulong result = divisor.MontgomeryOne;
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ulong nPrime = divisor.NPrime;
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int index = bitLength - 1;
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while (index >= 0)
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{
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ulong currentBit = (exponent >> index) & 1UL;
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ulong squared = MontgomeryMultiplyGpu(result, result, modulus, nPrime);
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bool processWindow = currentBit != 0UL;
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result = processWindow ? result : squared;
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index -= (int)(currentBit ^ 1UL);
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int windowStartCandidate = index - windowSize + 1;
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// if (windowStartCandidate < 0)
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// {
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// windowStartCandidate = 0;
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// }
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// Clamp the negative offset without branching so the GPU loop stays divergence-free.
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// This still handles windows that would otherwise extend past the most significant bit.
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int negativeMask = windowStartCandidate >> 31;
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windowStartCandidate &= ~negativeMask;
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int windowStart = processWindow ? GetNextSetBitIndexGpu(exponent, windowStartCandidate) : windowStartCandidate;
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int windowLength = processWindow ? index - windowStart + 1 : 0;
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for (int square = 0; square < windowLength; square++)
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{
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result = MontgomeryMultiplyGpu(result, result, modulus, nPrime);
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}
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result = processWindow
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? MontgomeryMultiplyGpu(
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result,
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ComputeMontgomeryOddPowerGpu(
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(exponent >> windowStart) & ((1UL << windowLength) - 1UL),
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divisor,
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modulus,
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nPrime),
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modulus,
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nPrime)
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: result;
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index = processWindow ? windowStart - 1 : index;
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}
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Pow2ModWindowedGpu(this ulong exponent, ulong modulus)
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{
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// EvenPerfectBitScanner never routes moduli ≤ 1 through this path; keep the guard commented out so the hot loop stays branch-free.
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// if (modulus <= 1UL)
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// {
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// return 0UL;
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// }
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// EvenPerfectBitScanner always works with positive exponents here; leave the defensive check commented for future reference.
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// if (exponent == 0UL)
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// {
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// return 1UL % modulus;
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// }
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int bitLength = GetPortableBitLengthGpu(exponent);
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int windowSize = GetWindowSizeGpu(bitLength);
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int oddPowerCount = 1 << (windowSize - 1);
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// oddPowerCount is always ≥ 1 for the production workloads handled by EvenPerfectBitScanner.
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// if (oddPowerCount <= 0)
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// {
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// return 1UL;
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// }
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ulong[] oddPowersArray = ThreadStaticPools.UlongPool.Rent(oddPowerCount);
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Span<ulong> oddPowers = oddPowersArray.AsSpan(0, oddPowerCount);
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InitializeStandardOddPowers(modulus, oddPowers);
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ulong result = 1UL;
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int index = bitLength - 1;
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while (index >= 0)
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{
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ulong currentBit = (exponent >> index) & 1UL;
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ulong squared = result.MulModGpu(result, modulus);
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result = currentBit == 0UL ? squared : result;
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index = currentBit == 0UL ? index - 1 : index;
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if (currentBit == 0UL)
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{
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continue;
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}
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int windowStart = index - windowSize + 1;
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// EvenPerfectBitScanner guarantees windowStart stays non-negative for production exponents, so keep the guard commented out to avoid extra branching.
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// if (windowStart < 0)
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// {
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// windowStart = 0;
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// }
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windowStart = GetNextSetBitIndexGpu(exponent, windowStart);
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int windowLength = index - windowStart + 1;
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for (int square = 0; square < windowLength; square++)
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{
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result = result.MulModGpu(result, modulus);
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}
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ulong mask = (1UL << windowLength) - 1UL;
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ulong windowValue = (exponent >> windowStart) & mask;
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int tableIndex = (int)((windowValue - 1UL) >> 1);
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ulong multiplier = oddPowers[tableIndex];
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result = result.MulModGpu(multiplier, modulus);
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index = windowStart - 1;
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}
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ThreadStaticPools.UlongPool.Return(oddPowersArray);
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Pow2ModWindowedGpuKernel(this ulong exponent, ulong modulus)
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{
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int bitLength = GetPortableBitLengthGpu(exponent);
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int windowSize = GetWindowSizeGpu(bitLength);
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ReadOnlyGpuUInt128 modulusWide = new(modulus);
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GpuUInt128 result = new(1UL);
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int index = bitLength - 1;
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while (index >= 0)
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{
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ulong currentBit = (exponent >> index) & 1UL;
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if (currentBit == 0UL)
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{
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result.MulMod(result.AsReadOnly(), modulusWide);
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index--;
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continue;
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}
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int windowStartCandidate = index - windowSize + 1;
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int negativeMask = windowStartCandidate >> 31;
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windowStartCandidate &= ~negativeMask;
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int windowStart = GetNextSetBitIndexGpu(exponent, windowStartCandidate);
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int windowLength = index - windowStart + 1;
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for (int square = 0; square < windowLength; square++)
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{
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result.MulMod(result.AsReadOnly(), modulusWide);
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}
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ulong mask = (1UL << windowLength) - 1UL;
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ulong windowValue = (exponent >> windowStart) & mask;
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ulong multiplier = ComputeWindowedOddPowerGpuKernel(windowValue, modulusWide);
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result.MulMod(multiplier, modulusWide);
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index = windowStart - 1;
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}
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return result.Low;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong ComputeWindowedOddPowerGpuKernel(ulong windowValue, in ReadOnlyGpuUInt128 modulus)
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{
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GpuUInt128 result = new(2UL);
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if (windowValue == 1UL)
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{
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// Single-bit windows show up whenever the bit scan finds an isolated exponent bit,
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// which happens routinely on the GPU path, so keep the fast return enabled.
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return 2UL;
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}
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ulong remaining = (windowValue - 1UL) >> 1;
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GpuUInt128 squareBase = new(2UL);
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squareBase.MulMod(squareBase.AsReadOnly(), modulus);
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while (remaining != 0UL)
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{
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if ((remaining & 1UL) != 0UL)
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{
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result.MulMod(squareBase.AsReadOnly(), modulus);
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}
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remaining >>= 1;
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if (remaining != 0UL)
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{
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squareBase.MulMod(squareBase.AsReadOnly(), modulus);
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}
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}
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return result.Low;
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}
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public static void Pow2MontgomeryKernelKeepMontgomery(
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Index1D index,
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ArrayView1D<ulong, Stride1D.Dense> exponents,
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ulong divisorModulus,
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ulong divisorNPrime,
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ulong divisorMontgomeryOne,
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ulong divisorMontgomeryTwo,
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ulong divisorMontgomeryTwoSquared,
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ArrayView1D<ulong, Stride1D.Dense> results)
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{
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MontgomeryDivisorDataGpu divisor = new(divisorModulus, divisorNPrime, divisorMontgomeryOne, divisorMontgomeryTwo, divisorMontgomeryTwoSquared);
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results[0] = Pow2MontgomeryModWindowedGpuKeepMontgomery(divisor, exponents[0]);
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}
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public static void Pow2MontgomeryKernelConvertToStandard(
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Index1D index,
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ArrayView1D<ulong, Stride1D.Dense> exponents,
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ulong divisorModulus,
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ulong divisorNPrime,
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ulong divisorMontgomeryOne,
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ulong divisorMontgomeryTwo,
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ulong divisorMontgomeryTwoSquared,
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ArrayView1D<ulong, Stride1D.Dense> results)
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{
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MontgomeryDivisorDataGpu divisor = new(divisorModulus, divisorNPrime, divisorMontgomeryOne, divisorMontgomeryTwo, divisorMontgomeryTwoSquared);
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results[0] = Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponents[0]);
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}
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public static void TryPollardRhoKernel(ulong n, int limit, ArrayView1D<ulong, Stride1D.Dense> randomState, ArrayView1D<byte, Stride1D.Dense> factored, ArrayView1D<ulong, Stride1D.Dense> factor)
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{
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factored[0] = 0;
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if ((n & 1UL) == 0UL)
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{
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factor[0] = 2UL;
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factored[0] = 1;
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return;
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}
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int attempt = 0;
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GpuUInt128 nGpuUInt128 = (GpuUInt128)n;
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DeterministicRandomGpu random = new(randomState[0]);
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while (attempt < limit)
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{
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ulong c = (random.NextUInt64() % (n - 1UL)) + 1UL;
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GpuUInt128 x = (random.NextUInt64() % (n - 2UL)) + 2UL;
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GpuUInt128 y = x;
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GpuUInt128 d = GpuUInt128.One;
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while (d.CompareTo(GpuUInt128.One) == 0)
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{
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x = AdvancePolynomialGpu(x, c, modulus: n);
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y = AdvancePolynomialGpu(y, c, n);
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y = AdvancePolynomialGpu(y, c, n);
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GpuUInt128 diff = x.CompareTo(y) > 0 ? x - y : y - x;
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d = GpuUInt128.BinaryGcd(diff, nGpuUInt128);
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}
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if (d != n)
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{
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if (d.High == 0)
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{
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factor[0] = d.Low;
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factored[0] = 1;
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return;
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}
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}
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attempt++;
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}
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randomState[0] = random.State;
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}
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}
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