#include "xh_tool.h" void fdderivs(const int ex[3], const double *f, double *fxx, double *fxy, double *fxz, double *fyy, double *fyz, double *fzz, const double *X, const double *Y, const double *Z, double SYM1, double SYM2, double SYM3, int Symmetry, int onoff) { (void)onoff; const int NO_SYMM = 0, EQ_SYMM = 1; const double ZEO = 0.0, ONE = 1.0, TWO = 2.0; const double F1o4 = 2.5e-1; // 1/4 const double F8 = 8.0; const double F16 = 16.0; const double F30 = 30.0; const double F1o12 = ONE / 12.0; const double F1o144 = ONE / 144.0; const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2]; const double dX = X[1] - X[0]; const double dY = Y[1] - Y[0]; const double dZ = Z[1] - Z[0]; const int imaxF = ex1; const int jmaxF = ex2; const int kmaxF = ex3; int iminF = 1, jminF = 1, kminF = 1; if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1; if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1; if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1; /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */ const size_t nx = (size_t)ex1 + 2; const size_t ny = (size_t)ex2 + 2; const size_t nz = (size_t)ex3 + 2; const size_t fh_size = nx * ny * nz; /* 系数：按 Fortran 原式 */ const double Sdxdx = ONE / (dX * dX); const double Sdydy = ONE / (dY * dY); const double Sdzdz = ONE / (dZ * dZ); const double Fdxdx = F1o12 / (dX * dX); const double Fdydy = F1o12 / (dY * dY); const double Fdzdz = F1o12 / (dZ * dZ); const double Sdxdy = F1o4 / (dX * dY); const double Sdxdz = F1o4 / (dX * dZ); const double Sdydz = F1o4 / (dY * dZ); const double Fdxdy = F1o144 / (dX * dY); const double Fdxdz = F1o144 / (dX * dZ); const double Fdydz = F1o144 / (dY * dZ); static thread_local double *fh = NULL; static thread_local size_t cap = 0; if (fh_size > cap) { free(fh); fh = (double*)aligned_alloc(64, fh_size * sizeof(double)); cap = fh_size; } // double *fh = (double*)malloc(fh_size * sizeof(double)); if (!fh) return; // symmetry_bd(2, ex, f, fh, SoA); const double SoA[3] = { SYM1, SYM2, SYM3 }; for (int k0 = 0; k0 < ex[2]; ++k0) { for (int j0 = 0; j0 < ex[1]; ++j0) { for (int i0 = 0; i0 < ex[0]; ++i0) { const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)]; } } } // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1) for (int ii = 0; ii <= 2 - 1; ++ii) { const int iF_dst = -ii; // 0, -1, -2, ... const int iF_src = ii + 1; // 1, 2, 3, ... for (int kF = 1; kF <= ex[2]; ++kF) { for (int jF = 1; jF <= ex[1]; ++jF) { fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0]; } } } // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2) // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖 for (int jj = 0; jj <= 2 - 1; ++jj) { const int jF_dst = -jj; const int jF_src = jj + 1; for (int kF = 1; kF <= ex[2]; ++kF) { for (int iF = -2 + 1; iF <= ex[0]; ++iF) { fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] = fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1]; } } } // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3) for (int kk = 0; kk <= 2 - 1; ++kk) { const int kF_dst = -kk; const int kF_src = kk + 1; for (int jF = -2 + 1; jF <= ex[1]; ++jF) { for (int iF = -2 + 1; iF <= ex[0]; ++iF) { fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] = fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2]; } } } /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */ // const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3; // for (size_t p = 0; p < all; ++p) { // fxx[p] = ZEO; fyy[p] = ZEO; fzz[p] = ZEO; // fxy[p] = ZEO; fxz[p] = ZEO; fyz[p] = ZEO; // } /* * Fortran: * do k=1,ex3-1 * do j=1,ex2-1 * do i=1,ex1-1 */ for (int k0 = 0; k0 <= ex3 - 2; ++k0) { const int kF = k0 + 1; for (int j0 = 0; j0 <= ex2 - 2; ++j0) { const int jF = j0 + 1; for (int i0 = 0; i0 <= ex1 - 2; ++i0) { const int iF = i0 + 1; const size_t p = idx_ex(i0, j0, k0, ex); /* 高阶分支：i±2,j±2,k±2 都在范围内 */ if ((iF + 2) <= imaxF && (iF - 2) >= iminF && (jF + 2) <= jmaxF && (jF - 2) >= jminF && (kF + 2) <= kmaxF && (kF - 2) >= kminF) { fxx[p] = Fdxdx * ( -fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] - F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)] ); fyy[p] = Fdydy * ( -fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] - F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)] ); fzz[p] = Fdzdz * ( -fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] - F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] - fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)] ); /* fxy 高阶：完全照搬 Fortran 的括号结构 */ { const double t_jm2 = ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] ); const double t_jm1 = ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] ); const double t_jp1 = ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] ); const double t_jp2 = ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] ); fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 ); } /* fxz 高阶 */ { const double t_km2 = ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] ); const double t_km1 = ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] ); const double t_kp1 = ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] ); const double t_kp2 = ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)] -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)] +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] ); fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 ); } /* fyz 高阶 */ { const double t_km2 = ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)] -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)] +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] ); const double t_km1 = ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)] -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] ); const double t_kp1 = ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)] -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] ); const double t_kp2 = ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)] -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)] +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] ); fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 ); } } /* 二阶分支：i±1,j±1,k±1 在范围内 */ else if ((iF + 1) <= imaxF && (iF - 1) >= iminF && (jF + 1) <= jmaxF && (jF - 1) >= jminF && (kF + 1) <= kmaxF && (kF - 1) >= kminF) { fxx[p] = Sdxdx * ( fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] - TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] + fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)] ); fyy[p] = Sdydy * ( fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] - TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] + fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)] ); fzz[p] = Sdzdz * ( fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] - TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] + fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)] ); fxy[p] = Sdxdy * ( fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] + fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] ); fxz[p] = Sdxdz * ( fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] + fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] ); fyz[p] = Sdydz * ( fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] + fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] ); }else{ fxx[p] = 0.0; fyy[p] = 0.0; fzz[p] = 0.0; fxy[p] = 0.0; fxz[p] = 0.0; fyz[p] = 0.0; } } } } // free(fh); }