1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 /// @file 9 /// Internal header for CUDA tensor product basis with AtPoints evaluation 10 11 #include <ceed.h> 12 13 //------------------------------------------------------------------------------ 14 // Chebyshev values 15 //------------------------------------------------------------------------------ 16 template <int Q_1D> 17 inline __device__ void ChebyshevPolynomialsAtPoint(const CeedScalar x, CeedScalar *chebyshev_x) { 18 chebyshev_x[0] = 1.0; 19 chebyshev_x[1] = 2 * x; 20 for (CeedInt i = 2; i < Q_1D; i++) chebyshev_x[i] = 2 * x * chebyshev_x[i - 1] - chebyshev_x[i - 2]; 21 } 22 23 template <int Q_1D> 24 inline __device__ void ChebyshevDerivativeAtPoint(const CeedScalar x, CeedScalar *chebyshev_dx) { 25 CeedScalar chebyshev_x[3]; 26 27 chebyshev_x[1] = 1.0; 28 chebyshev_x[2] = 2 * x; 29 chebyshev_dx[0] = 0.0; 30 chebyshev_dx[1] = 2.0; 31 for (CeedInt i = 2; i < Q_1D; i++) { 32 chebyshev_x[0] = chebyshev_x[1]; 33 chebyshev_x[1] = chebyshev_x[2]; 34 chebyshev_x[2] = 2 * x * chebyshev_x[1] - chebyshev_x[0]; 35 chebyshev_dx[i] = 2 * x * chebyshev_dx[i - 1] + 2 * chebyshev_x[1] - chebyshev_dx[i - 2]; 36 } 37 } 38 39 //------------------------------------------------------------------------------ 40 // Tensor Basis Kernels AtPoints 41 //------------------------------------------------------------------------------ 42 43 //------------------------------------------------------------------------------ 44 // Interp 45 //------------------------------------------------------------------------------ 46 extern "C" __global__ void InterpAtPoints(const CeedInt num_elem, const CeedInt is_transpose, const CeedScalar *__restrict__ chebyshev_interp_1d, 47 const CeedScalar *__restrict__ coords, const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) { 48 const CeedInt i = threadIdx.x; 49 50 __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 3 * BASIS_BUF_LEN]; 51 CeedScalar *s_chebyshev_interp_1d = s_mem; 52 CeedScalar *s_buffer_1 = s_mem + BASIS_Q_1D * BASIS_P_1D; 53 CeedScalar *s_buffer_2 = s_buffer_1 + BASIS_BUF_LEN; 54 CeedScalar *s_chebyshev_coeffs = s_buffer_2 + BASIS_BUF_LEN; 55 CeedScalar chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN]; 56 for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) { 57 s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k]; 58 } 59 60 const CeedInt P = BASIS_P_1D; 61 const CeedInt Q = BASIS_Q_1D; 62 const CeedInt u_stride = is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES; 63 const CeedInt v_stride = is_transpose ? BASIS_NUM_NODES : BASIS_NUM_PTS; 64 const CeedInt u_comp_stride = num_elem * (is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES); 65 const CeedInt v_comp_stride = num_elem * (is_transpose ? BASIS_NUM_NODES : BASIS_NUM_PTS); 66 const CeedInt u_size = is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES; 67 68 // Apply basis element by element 69 if (is_transpose) { 70 for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) { 71 for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) { 72 const CeedScalar *cur_u = u + elem * u_stride + comp * u_comp_stride; 73 CeedScalar *cur_v = v + elem * v_stride + comp * v_comp_stride; 74 CeedInt pre = 1; 75 CeedInt post = 1; 76 77 // Clear Chebyshev coeffs 78 for (CeedInt k = i; k < BASIS_NUM_QPTS; k += blockDim.x) { 79 s_chebyshev_coeffs[k] = 0.0; 80 } 81 82 // Map from point 83 for (CeedInt p = blockIdx.x; p < BASIS_NUM_PTS; p += gridDim.x) { 84 pre = 1; 85 post = 1; 86 for (CeedInt d = 0; d < BASIS_DIM; d++) { 87 // Update buffers used 88 pre /= 1; 89 const CeedScalar *in = d == 0 ? (cur_u + p) : (d % 2 ? buffer_2 : buffer_1); 90 CeedScalar *out = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? buffer_1 : buffer_2); 91 92 // Build Chebyshev polynomial values 93 ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * u_stride + d * u_comp_stride + p], chebyshev_x); 94 95 // Contract along middle index 96 for (CeedInt a = 0; a < pre; a++) { 97 for (CeedInt c = 0; c < post; c++) { 98 if (d == BASIS_DIM - 1) { 99 for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] += chebyshev_x[j] * in[a * post + c]; 100 } else { 101 for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] = chebyshev_x[j] * in[a * post + c]; 102 } 103 } 104 } 105 post *= Q; 106 } 107 } 108 109 // Map from coefficients 110 pre = BASIS_NUM_QPTS; 111 post = 1; 112 for (CeedInt d = 0; d < BASIS_DIM; d++) { 113 __syncthreads(); 114 // Update buffers used 115 pre /= Q; 116 const CeedScalar *in = d == 0 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_2 : s_buffer_1); 117 CeedScalar *out = d == BASIS_DIM - 1 ? cur_v : (d % 2 ? s_buffer_1 : s_buffer_2); 118 const CeedInt writeLen = pre * post * P; 119 120 // Contract along middle index 121 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 122 const CeedInt c = k % post; 123 const CeedInt j = (k / post) % P; 124 const CeedInt a = k / (post * P); 125 CeedScalar v_k = 0; 126 127 for (CeedInt b = 0; b < Q; b++) v_k += s_chebyshev_interp_1d[j + b * BASIS_P_1D] * in[(a * Q + b) * post + c]; 128 out[k] = v_k; 129 } 130 post *= P; 131 } 132 } 133 } 134 } else { 135 for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) { 136 for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) { 137 const CeedScalar *cur_u = u + elem * u_stride + comp * u_comp_stride; 138 CeedScalar *cur_v = v + elem * v_stride + comp * v_comp_stride; 139 CeedInt pre = u_size; 140 CeedInt post = 1; 141 142 // Map to coefficients 143 for (CeedInt d = 0; d < BASIS_DIM; d++) { 144 __syncthreads(); 145 // Update buffers used 146 pre /= P; 147 const CeedScalar *in = d == 0 ? cur_u : (d % 2 ? s_buffer_2 : s_buffer_1); 148 CeedScalar *out = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_1 : s_buffer_2); 149 const CeedInt writeLen = pre * post * Q; 150 151 // Contract along middle index 152 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 153 const CeedInt c = k % post; 154 const CeedInt j = (k / post) % Q; 155 const CeedInt a = k / (post * Q); 156 CeedScalar v_k = 0; 157 158 for (CeedInt b = 0; b < P; b++) v_k += s_chebyshev_interp_1d[j * BASIS_P_1D + b] * in[(a * P + b) * post + c]; 159 out[k] = v_k; 160 } 161 post *= Q; 162 } 163 164 // Map to point 165 __syncthreads(); 166 for (CeedInt p = blockIdx.x; p < BASIS_NUM_PTS; p += gridDim.x) { 167 pre = BASIS_NUM_QPTS; 168 post = 1; 169 for (CeedInt d = 0; d < BASIS_DIM; d++) { 170 // Update buffers used 171 pre /= Q; 172 const CeedScalar *in = d == 0 ? s_chebyshev_coeffs : (d % 2 ? buffer_2 : buffer_1); 173 CeedScalar *out = d == BASIS_DIM - 1 ? (cur_v + p) : (d % 2 ? buffer_1 : buffer_2); 174 175 // Build Chebyshev polynomial values 176 ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * v_stride + d * v_comp_stride + p], chebyshev_x); 177 178 // Contract along middle index 179 for (CeedInt a = 0; a < pre; a++) { 180 for (CeedInt c = 0; c < post; c++) { 181 CeedScalar v_k = 0; 182 183 for (CeedInt b = 0; b < Q; b++) v_k += chebyshev_x[b] * in[(a * Q + b) * post + c]; 184 out[a * post + c] = v_k; 185 } 186 } 187 post *= 1; 188 } 189 } 190 } 191 } 192 } 193 } 194 195 //------------------------------------------------------------------------------ 196 // Grad 197 //------------------------------------------------------------------------------ 198 extern "C" __global__ void GradAtPoints(const CeedInt num_elem, const CeedInt is_transpose, const CeedScalar *__restrict__ chebyshev_interp_1d, 199 const CeedScalar *__restrict__ coords, const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) { 200 const CeedInt i = threadIdx.x; 201 202 __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 3 * BASIS_BUF_LEN]; 203 CeedScalar *s_chebyshev_interp_1d = s_mem; 204 CeedScalar *s_buffer_1 = s_mem + BASIS_Q_1D * BASIS_P_1D; 205 CeedScalar *s_buffer_2 = s_buffer_1 + BASIS_BUF_LEN; 206 CeedScalar *s_chebyshev_coeffs = s_buffer_2 + BASIS_BUF_LEN; 207 CeedScalar chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN]; 208 for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) { 209 s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k]; 210 } 211 212 const CeedInt P = BASIS_P_1D; 213 const CeedInt Q = BASIS_Q_1D; 214 const CeedInt u_stride = is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES; 215 const CeedInt v_stride = is_transpose ? BASIS_NUM_NODES : BASIS_NUM_PTS; 216 const CeedInt u_comp_stride = num_elem * (is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES); 217 const CeedInt v_comp_stride = num_elem * (is_transpose ? BASIS_NUM_NODES : BASIS_NUM_PTS); 218 const CeedInt u_size = is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES; 219 const CeedInt u_dim_stride = is_transpose ? num_elem * BASIS_NUM_PTS * BASIS_NUM_COMP : 0; 220 const CeedInt v_dim_stride = is_transpose ? 0 : num_elem * BASIS_NUM_PTS * BASIS_NUM_COMP; 221 222 // Apply basis element by element 223 if (is_transpose) { 224 for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) { 225 for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) { 226 CeedScalar *cur_v = v + elem * v_stride + comp * v_comp_stride; 227 CeedInt pre = 1; 228 CeedInt post = 1; 229 230 // Clear Chebyshev coeffs 231 for (CeedInt k = i; k < BASIS_NUM_QPTS; k += blockDim.x) { 232 s_chebyshev_coeffs[k] = 0.0; 233 } 234 235 // Map from point 236 for (CeedInt p = blockIdx.x; p < BASIS_NUM_PTS; p += gridDim.x) { 237 for (CeedInt dim_1 = 0; dim_1 < BASIS_DIM; dim_1++) { 238 const CeedScalar *cur_u = u + elem * u_stride + dim_1 * u_dim_stride + comp * u_comp_stride; 239 240 pre = 1; 241 post = 1; 242 for (CeedInt dim_2 = 0; dim_2 < BASIS_DIM; dim_2++) { 243 // Update buffers used 244 pre /= 1; 245 const CeedScalar *in = dim_2 == 0 ? (cur_u + p) : (dim_2 % 2 ? buffer_2 : buffer_1); 246 CeedScalar *out = dim_2 == BASIS_DIM - 1 ? s_chebyshev_coeffs : (dim_2 % 2 ? buffer_1 : buffer_2); 247 248 // Build Chebyshev polynomial values 249 if (dim_1 == dim_2) ChebyshevDerivativeAtPoint<BASIS_Q_1D>(coords[elem * u_stride + dim_2 * u_comp_stride + p], chebyshev_x); 250 else ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * u_stride + dim_2 * u_comp_stride + p], chebyshev_x); 251 252 // Contract along middle index 253 for (CeedInt a = 0; a < pre; a++) { 254 for (CeedInt c = 0; c < post; c++) { 255 if (dim_2 == BASIS_DIM - 1) { 256 for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] += chebyshev_x[j] * in[a * post + c]; 257 } else { 258 for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] = chebyshev_x[j] * in[a * post + c]; 259 } 260 } 261 } 262 post *= Q; 263 } 264 } 265 } 266 267 // Map from coefficients 268 pre = BASIS_NUM_QPTS; 269 post = 1; 270 for (CeedInt d = 0; d < BASIS_DIM; d++) { 271 __syncthreads(); 272 // Update buffers used 273 pre /= Q; 274 const CeedScalar *in = d == 0 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_2 : s_buffer_1); 275 CeedScalar *out = d == BASIS_DIM - 1 ? cur_v : (d % 2 ? s_buffer_1 : s_buffer_2); 276 const CeedInt writeLen = pre * post * P; 277 278 // Contract along middle index 279 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 280 const CeedInt c = k % post; 281 const CeedInt j = (k / post) % P; 282 const CeedInt a = k / (post * P); 283 CeedScalar v_k = 0; 284 285 for (CeedInt b = 0; b < Q; b++) v_k += s_chebyshev_interp_1d[j + b * BASIS_P_1D] * in[(a * Q + b) * post + c]; 286 out[k] = v_k; 287 } 288 post *= P; 289 } 290 } 291 } 292 } else { 293 for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) { 294 for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) { 295 const CeedScalar *cur_u = u + elem * u_stride + comp * u_comp_stride; 296 CeedInt pre = u_size; 297 CeedInt post = 1; 298 299 // Map to coefficients 300 for (CeedInt d = 0; d < BASIS_DIM; d++) { 301 __syncthreads(); 302 // Update buffers used 303 pre /= P; 304 const CeedScalar *in = d == 0 ? cur_u : (d % 2 ? s_buffer_2 : s_buffer_1); 305 CeedScalar *out = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_1 : s_buffer_2); 306 const CeedInt writeLen = pre * post * Q; 307 308 // Contract along middle index 309 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 310 const CeedInt c = k % post; 311 const CeedInt j = (k / post) % Q; 312 const CeedInt a = k / (post * Q); 313 CeedScalar v_k = 0; 314 315 for (CeedInt b = 0; b < P; b++) v_k += s_chebyshev_interp_1d[j * BASIS_P_1D + b] * in[(a * P + b) * post + c]; 316 out[k] = v_k; 317 } 318 post *= Q; 319 } 320 321 // Map to point 322 __syncthreads(); 323 for (CeedInt p = blockIdx.x; p < BASIS_NUM_PTS; p += gridDim.x) { 324 for (CeedInt dim_1 = 0; dim_1 < BASIS_DIM; dim_1++) { 325 CeedScalar *cur_v = v + elem * v_stride + dim_1 * v_dim_stride + comp * v_comp_stride; 326 327 pre = BASIS_NUM_QPTS; 328 post = 1; 329 for (CeedInt dim_2 = 0; dim_2 < BASIS_DIM; dim_2++) { 330 // Update buffers used 331 pre /= Q; 332 const CeedScalar *in = dim_2 == 0 ? s_chebyshev_coeffs : (dim_2 % 2 ? buffer_2 : buffer_1); 333 CeedScalar *out = dim_2 == BASIS_DIM - 1 ? (cur_v + p) : (dim_2 % 2 ? buffer_1 : buffer_2); 334 335 // Build Chebyshev polynomial values 336 if (dim_1 == dim_2) ChebyshevDerivativeAtPoint<BASIS_Q_1D>(coords[elem * v_stride + dim_2 * v_comp_stride + p], chebyshev_x); 337 else ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * v_stride + dim_2 * v_comp_stride + p], chebyshev_x); 338 339 // Contract along middle index 340 for (CeedInt a = 0; a < pre; a++) { 341 for (CeedInt c = 0; c < post; c++) { 342 CeedScalar v_k = 0; 343 344 for (CeedInt b = 0; b < Q; b++) v_k += chebyshev_x[b] * in[(a * Q + b) * post + c]; 345 out[a * post + c] = v_k; 346 } 347 } 348 post *= 1; 349 } 350 } 351 } 352 } 353 } 354 } 355 } 356