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[(i + 1) % 3] = 2 * x * chebyshev_x[(i + 0) % 3] - chebyshev_x[(i + 2) % 3]; 33 chebyshev_dx[i] = 2 * x * chebyshev_dx[i - 1] + 2 * chebyshev_x[(i + 0) % 3] - chebyshev_dx[i - 2]; 34 } 35 } 36 37 //------------------------------------------------------------------------------ 38 // Tensor Basis Kernels AtPoints 39 //------------------------------------------------------------------------------ 40 41 //------------------------------------------------------------------------------ 42 // Interp 43 //------------------------------------------------------------------------------ 44 extern "C" __global__ void InterpAtPoints(const CeedInt num_elem, const CeedInt is_transpose, const CeedScalar *__restrict__ chebyshev_interp_1d, 45 const CeedScalar *__restrict__ coords, const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) { 46 const CeedInt i = threadIdx.x; 47 48 __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 2 * BASIS_BUF_LEN + POINTS_BUFF_LEN * BASIS_Q_1D]; 49 CeedScalar *s_chebyshev_interp_1d = s_mem; 50 CeedScalar *s_buffer_1 = s_mem + BASIS_Q_1D * BASIS_P_1D; 51 CeedScalar *s_buffer_2 = s_buffer_1 + BASIS_BUF_LEN; 52 CeedScalar *s_chebyshev_coeffs = s_buffer_2 + BASIS_BUF_LEN; 53 CeedScalar chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN]; 54 for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) { 55 s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k]; 56 } 57 58 const CeedInt P = BASIS_P_1D; 59 const CeedInt Q = BASIS_Q_1D; 60 const CeedInt u_stride = is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES; 61 const CeedInt v_stride = is_transpose ? BASIS_NUM_NODES : BASIS_NUM_PTS; 62 const CeedInt u_comp_stride = num_elem * (is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES); 63 const CeedInt v_comp_stride = num_elem * (is_transpose ? BASIS_NUM_NODES : BASIS_NUM_PTS); 64 const CeedInt u_size = is_transpose ? BASIS_NUM_PTS : BASIS_NUM_NODES; 65 66 // Apply basis element by element 67 if (is_transpose) { 68 for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) { 69 for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) { 70 const CeedScalar *cur_u = &u[elem * u_stride + comp * u_comp_stride]; 71 CeedScalar *cur_v = &v[elem * v_stride + comp * v_comp_stride]; 72 CeedInt pre = 1; 73 CeedInt post = 1; 74 75 // Clear Chebyshev coeffs 76 for (CeedInt k = i; k < BASIS_NUM_QPTS; k += blockDim.x) { 77 s_chebyshev_coeffs[k] = 0.0; 78 } 79 80 // Map from point 81 __syncthreads(); 82 for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) { 83 pre = 1; 84 post = 1; 85 for (CeedInt d = 0; d < BASIS_DIM; d++) { 86 // Update buffers used 87 pre /= 1; 88 const CeedScalar *in = d == 0 ? (&cur_u[p]) : (d % 2 ? buffer_2 : buffer_1); 89 CeedScalar *out = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? buffer_1 : buffer_2); 90 91 // Build Chebyshev polynomial values 92 ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * u_stride + d * u_comp_stride + p], chebyshev_x); 93 94 // Contract along middle index 95 for (CeedInt a = 0; a < pre; a++) { 96 for (CeedInt c = 0; c < post; c++) { 97 if (d == BASIS_DIM - 1) { 98 for (CeedInt j = 0; j < Q; j++) atomicAdd(&out[(a * Q + (j + p) % Q) * post + c], chebyshev_x[(j + p) % Q] * in[a * post + c]); 99 } else { 100 for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] = chebyshev_x[j] * in[a * post + c]; 101 } 102 } 103 } 104 post *= Q; 105 } 106 } 107 108 // Map from coefficients 109 pre = BASIS_NUM_QPTS; 110 post = 1; 111 for (CeedInt d = 0; d < BASIS_DIM; d++) { 112 __syncthreads(); 113 // Update buffers used 114 pre /= Q; 115 const CeedScalar *in = d == 0 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_2 : s_buffer_1); 116 CeedScalar *out = d == BASIS_DIM - 1 ? cur_v : (d % 2 ? s_buffer_1 : s_buffer_2); 117 const CeedInt writeLen = pre * post * P; 118 119 // Contract along middle index 120 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 121 const CeedInt c = k % post; 122 const CeedInt j = (k / post) % P; 123 const CeedInt a = k / (post * P); 124 CeedScalar v_k = 0; 125 126 for (CeedInt b = 0; b < Q; b++) v_k += s_chebyshev_interp_1d[j + b * BASIS_P_1D] * in[(a * Q + b) * post + c]; 127 if (d == BASIS_DIM - 1) out[k] += v_k; 128 else 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 = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.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 + 2 * BASIS_BUF_LEN + POINTS_BUFF_LEN * BASIS_Q_1D]; 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 __syncthreads(); 237 for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) { 238 for (CeedInt dim_1 = 0; dim_1 < BASIS_DIM; dim_1++) { 239 const CeedScalar *cur_u = &u[elem * u_stride + dim_1 * u_dim_stride + comp * u_comp_stride]; 240 241 pre = 1; 242 post = 1; 243 for (CeedInt dim_2 = 0; dim_2 < BASIS_DIM; dim_2++) { 244 // Update buffers used 245 pre /= 1; 246 const CeedScalar *in = dim_2 == 0 ? (&cur_u[p]) : (dim_2 % 2 ? buffer_2 : buffer_1); 247 CeedScalar *out = dim_2 == BASIS_DIM - 1 ? s_chebyshev_coeffs : (dim_2 % 2 ? buffer_1 : buffer_2); 248 249 // Build Chebyshev polynomial values 250 if (dim_1 == dim_2) ChebyshevDerivativeAtPoint<BASIS_Q_1D>(coords[elem * u_stride + dim_2 * u_comp_stride + p], chebyshev_x); 251 else ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * u_stride + dim_2 * u_comp_stride + p], chebyshev_x); 252 253 // Contract along middle index 254 for (CeedInt a = 0; a < pre; a++) { 255 for (CeedInt c = 0; c < post; c++) { 256 if (dim_2 == BASIS_DIM - 1) { 257 for (CeedInt j = 0; j < Q; j++) atomicAdd(&out[(a * Q + (j + p) % Q) * post + c], chebyshev_x[(j + p) % Q] * in[a * post + c]); 258 } else { 259 for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] = chebyshev_x[j] * in[a * post + c]; 260 } 261 } 262 } 263 post *= Q; 264 } 265 } 266 } 267 268 // Map from coefficients 269 pre = BASIS_NUM_QPTS; 270 post = 1; 271 for (CeedInt d = 0; d < BASIS_DIM; d++) { 272 __syncthreads(); 273 // Update buffers used 274 pre /= Q; 275 const CeedScalar *in = d == 0 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_2 : s_buffer_1); 276 CeedScalar *out = d == BASIS_DIM - 1 ? cur_v : (d % 2 ? s_buffer_1 : s_buffer_2); 277 const CeedInt writeLen = pre * post * P; 278 279 // Contract along middle index 280 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 281 const CeedInt c = k % post; 282 const CeedInt j = (k / post) % P; 283 const CeedInt a = k / (post * P); 284 CeedScalar v_k = 0; 285 286 for (CeedInt b = 0; b < Q; b++) v_k += s_chebyshev_interp_1d[j + b * BASIS_P_1D] * in[(a * Q + b) * post + c]; 287 if (d == BASIS_DIM - 1) out[k] += v_k; 288 else out[k] = v_k; 289 } 290 post *= P; 291 } 292 } 293 } 294 } else { 295 for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) { 296 for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) { 297 const CeedScalar *cur_u = &u[elem * u_stride + comp * u_comp_stride]; 298 CeedInt pre = u_size; 299 CeedInt post = 1; 300 301 // Map to coefficients 302 for (CeedInt d = 0; d < BASIS_DIM; d++) { 303 __syncthreads(); 304 // Update buffers used 305 pre /= P; 306 const CeedScalar *in = d == 0 ? cur_u : (d % 2 ? s_buffer_2 : s_buffer_1); 307 CeedScalar *out = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_1 : s_buffer_2); 308 const CeedInt writeLen = pre * post * Q; 309 310 // Contract along middle index 311 for (CeedInt k = i; k < writeLen; k += blockDim.x) { 312 const CeedInt c = k % post; 313 const CeedInt j = (k / post) % Q; 314 const CeedInt a = k / (post * Q); 315 CeedScalar v_k = 0; 316 317 for (CeedInt b = 0; b < P; b++) v_k += s_chebyshev_interp_1d[j * BASIS_P_1D + b] * in[(a * P + b) * post + c]; 318 out[k] = v_k; 319 } 320 post *= Q; 321 } 322 323 // Map to point 324 __syncthreads(); 325 for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) { 326 for (CeedInt dim_1 = 0; dim_1 < BASIS_DIM; dim_1++) { 327 CeedScalar *cur_v = &v[elem * v_stride + dim_1 * v_dim_stride + comp * v_comp_stride]; 328 329 pre = BASIS_NUM_QPTS; 330 post = 1; 331 for (CeedInt dim_2 = 0; dim_2 < BASIS_DIM; dim_2++) { 332 // Update buffers used 333 pre /= Q; 334 const CeedScalar *in = dim_2 == 0 ? s_chebyshev_coeffs : (dim_2 % 2 ? buffer_2 : buffer_1); 335 CeedScalar *out = dim_2 == BASIS_DIM - 1 ? (&cur_v[p]) : (dim_2 % 2 ? buffer_1 : buffer_2); 336 337 // Build Chebyshev polynomial values 338 if (dim_1 == dim_2) ChebyshevDerivativeAtPoint<BASIS_Q_1D>(coords[elem * v_stride + dim_2 * v_comp_stride + p], chebyshev_x); 339 else ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * v_stride + dim_2 * v_comp_stride + p], chebyshev_x); 340 341 // Contract along middle index 342 for (CeedInt a = 0; a < pre; a++) { 343 for (CeedInt c = 0; c < post; c++) { 344 CeedScalar v_k = 0; 345 346 for (CeedInt b = 0; b < Q; b++) v_k += chebyshev_x[b] * in[(a * Q + b) * post + c]; 347 out[a * post + c] = v_k; 348 } 349 } 350 post *= 1; 351 } 352 } 353 } 354 } 355 } 356 } 357 } 358