극저온 방사광 X-선 나노회절 기반 위상 디락 반금속(Dirac Semimetal) 페르미 포켓 위상 변형(Lifshitz Transition) 능동 서보 아키텍처 (.NET 9 C# SIMD)

using System;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;

namespace ZeliDesk.Quantum.Synchrotron
{
    /// <summary>
    /// 위상 디락 반금속 립시츠 전이(Lifshitz Transition) 추적 및 극저온 피에조 서보
    /// GC 무할당 ref struct 및 AVX-256 SIMD 가속화
    /// </summary>
    public ref struct DiracLifshitzTransitionServo
    {
        private readonly ReadOnlySpan<float> _strainValues;       // 격자 변형률 epsilon_zz
        private readonly ReadOnlySpan<float> _fermiEnergies;     // 페르미 준위 E_F (meV)
        private readonly Span<float> _densityOfStates;           // 연산된 상태 밀도 DOS
        private readonly Span<float> _piezoCorrectionVoltages;   // 피에조 능동 제어 전압 (V)

        private readonly float _diracVelocity;   // 디락 페르미 속도 v_F (m/s)
        private readonly float _criticalStrain;  // 립시츠 전이 임계 변형률 epsilon_c
        private readonly float _piezoSensitivity;// 피에조 응답 감도 (V/microstrain)

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public DiracLifshitzTransitionServo(
            ReadOnlySpan<float> strainValues,
            ReadOnlySpan<float> fermiEnergies,
            Span<float> densityOfStates,
            Span<float> piezoCorrectionVoltages,
            float diracVelocity = 1.0e6f,
            float criticalStrain = 0.0125f,
            float piezoSensitivity = 0.45f)
        {
            _strainValues = strainValues;
            _fermiEnergies = fermiEnergies;
            _densityOfStates = densityOfStates;
            _piezoCorrectionVoltages = piezoCorrectionVoltages;
            _diracVelocity = diracVelocity;
            _criticalStrain = criticalStrain;
            _piezoSensitivity = piezoSensitivity;
        }

        /// <summary>
        /// 나노회절 변형률 어레이를 SIMD로 병렬 분석하여 립시츠 임계점 능동 피드백 산출
        /// </summary>
        [MethodImpl(MethodImplOptions.AggressiveOptimization)]
        public void ProcessLifshitzFeedbackLoop()
        {
            int length = _strainValues.Length;
            int simdLength = length - (length % 8);

            Vector256<float> vCritStrain = Vector256.Create(_criticalStrain);
            Vector256<float> vPiezoSens = Vector256.Create(_piezoSensitivity);
            Vector256<float> vZero = Vector256<float>.Zero;
            Vector256<float> vSmallEps = Vector256.Create(1e-5f);

            int i = 0;
            if (Avx2.IsSupported)
            {
                for (; i < simdLength; i += 8)
                {
                    Vector256<float> vStrain = Vector256.Create(MemoryMarshal.Cast<float, Vector256<float>>(_strainValues.Slice(i, 8))[0]);
                    Vector256<float> vEf = Vector256.Create(MemoryMarshal.Cast<float, Vector256<float>>(_fermiEnergies.Slice(i, 8))[0]);

                    // 임계 변형률과의 편차: DeltaEps = strain - criticalStrain
                    Vector256<float> vDeltaStrain = Avx.Subtract(vStrain, vCritStrain);

                    // 페르미 면 위상 변화 지표: DOS ~ sqrt(|DeltaEps|) * Ef^2
                    // 절대값 연산: andnot(sign_mask, x) 또는 max(-x, x)
                    Vector256<float> vAbsDelta = Avx.Max(vDeltaStrain, Avx.Subtract(vZero, vDeltaStrain));
                    Vector256<float> vSqrtAbs = Avx.Sqrt(Avx.Add(vAbsDelta, vSmallEps));
                    Vector256<float> vDos = Avx.Multiply(vSqrtAbs, Avx.Multiply(vEf, vEf));

                    // 피에조 능동 제어 전압 = -Sensitivity * DeltaStrain
                    Vector256<float> vVpiezo = Avx.Multiply(Avx.Subtract(vZero, vDeltaStrain), vPiezoSens);

                    vDos.CopyTo(_densityOfStates.Slice(i, 8));
                    vVpiezo.CopyTo(_piezoCorrectionVoltages.Slice(i, 8));
                }
            }

            for (; i < length; i++)
            {
                float deltaStrain = _strainValues[i] - _criticalStrain;
                float absDelta = MathF.Abs(deltaStrain);
                _densityOfStates[i] = MathF.Sqrt(absDelta + 1e-5f) * (_fermiEnergies[i] * _fermiEnergies[i]);
                _piezoCorrectionVoltages[i] = -_piezoSensitivity * deltaStrain;
            }
        }
    }
}