xref: /libCEED/include/ceed/jit-source/cuda/cuda-shared-basis-tensor-at-points.h (revision 5a526491291e2ef13670ec99232a2cb0069702e5)
1 // Copyright (c) 2017-2025, 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 #include <ceed/types.h>
11 
12 #include "cuda-shared-basis-read-write-templates.h"
13 #include "cuda-shared-basis-tensor-at-points-templates.h"
14 #include "cuda-shared-basis-tensor-templates.h"
15 
16 //------------------------------------------------------------------------------
17 // Tensor Basis Kernels AtPoints
18 //------------------------------------------------------------------------------
19 
20 //------------------------------------------------------------------------------
21 // Interp
22 //------------------------------------------------------------------------------
23 extern "C" __global__ void InterpAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ c_B, const CeedInt *__restrict__ points_per_elem,
24                                           const CeedScalar *__restrict__ d_X, const CeedScalar *__restrict__ d_U, CeedScalar *__restrict__ d_V) {
25   extern __shared__ CeedScalar slice[];
26 
27   SharedData_Cuda data;
28   data.t_id_x = threadIdx.x;
29   data.t_id_y = threadIdx.y;
30   data.t_id_z = threadIdx.z;
31   data.t_id   = threadIdx.x + threadIdx.y * blockDim.x + threadIdx.z * blockDim.y * blockDim.x;
32   data.slice  = slice + data.t_id_z * BASIS_T_1D * (BASIS_DIM > 1 ? BASIS_T_1D : 1);
33 
34   CeedScalar r_X[BASIS_DIM];
35   CeedScalar r_U[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_P_1D : 1)];
36   CeedScalar r_C[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
37   CeedScalar r_V[BASIS_NUM_COMP];
38 
39   // load interp_1d into shared memory
40   __shared__ CeedScalar s_B[BASIS_P_1D * BASIS_Q_1D];
41   LoadMatrix<BASIS_P_1D, BASIS_Q_1D>(data, c_B, s_B);
42   __syncthreads();
43 
44   // Apply basis element by element
45   for (CeedInt elem = blockIdx.x * blockDim.z + threadIdx.z; elem < num_elem; elem += gridDim.x * blockDim.z) {
46     // Map to coefficients
47     if (BASIS_DIM == 1) {
48       ReadElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, d_U, r_U);
49       Interp1d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_U, s_B, r_C);
50     } else if (BASIS_DIM == 2) {
51       ReadElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, d_U, r_U);
52       InterpTensor2d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_U, s_B, r_C);
53     } else if (BASIS_DIM == 3) {
54       ReadElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
55                                                        BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, d_U, r_U);
56       InterpTensor3d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_U, s_B, r_C);
57     }
58 
59     // Map to points
60     const CeedInt point_loop_bound = (blockDim.x * blockDim.y) * ceil(1.0 * BASIS_NUM_PTS / (blockDim.x * blockDim.y));
61 
62     for (CeedInt i = threadIdx.x + threadIdx.y * blockDim.x; i < point_loop_bound; i += blockDim.x * blockDim.y) {
63       const CeedInt p = i % BASIS_NUM_PTS;
64 
65       ReadPoint<BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_X, r_X);
66       if (BASIS_DIM == 1) {
67         InterpAtPoints1d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_C, r_X, r_V);
68       } else if (BASIS_DIM == 2) {
69         InterpAtPoints2d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_C, r_X, r_V);
70       } else if (BASIS_DIM == 3) {
71         InterpAtPoints3d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_C, r_X, r_V);
72       }
73       WritePoint<BASIS_NUM_COMP, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, r_V, d_V);
74     }
75   }
76 }
77 
78 extern "C" __global__ void InterpTransposeAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ c_B,
79                                                    const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ d_X,
80                                                    const CeedScalar *__restrict__ d_U, CeedScalar *__restrict__ d_V) {
81   extern __shared__ CeedScalar slice[];
82 
83   SharedData_Cuda data;
84   data.t_id_x = threadIdx.x;
85   data.t_id_y = threadIdx.y;
86   data.t_id_z = threadIdx.z;
87   data.t_id   = threadIdx.x + threadIdx.y * blockDim.x + threadIdx.z * blockDim.y * blockDim.x;
88   data.slice  = slice + data.t_id_z * BASIS_T_1D * (BASIS_DIM > 1 ? BASIS_T_1D : 1);
89 
90   CeedScalar r_X[BASIS_DIM];
91   CeedScalar r_U[BASIS_NUM_COMP];
92   CeedScalar r_C[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
93   CeedScalar r_V[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
94 
95   // load interp_1d into shared memory
96   __shared__ CeedScalar s_B[BASIS_P_1D * BASIS_Q_1D];
97   LoadMatrix<BASIS_P_1D, BASIS_Q_1D>(data, c_B, s_B);
98   __syncthreads();
99 
100   // Apply basis element by element
101   for (CeedInt elem = blockIdx.x * blockDim.z + threadIdx.z; elem < num_elem; elem += gridDim.x * blockDim.z) {
102     // Clear register
103     for (CeedInt i = 0; i < BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1); i++) r_C[i] = 0.0;
104 
105     // Clear output vector
106     for (CeedInt i = 0; i < BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1); i++) r_V[i] = 0.0;
107     if (BASIS_DIM == 1) {
108       WriteElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, r_V, d_V);
109     } else if (BASIS_DIM == 2) {
110       WriteElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, r_V, d_V);
111     } else if (BASIS_DIM == 3) {
112       WriteElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
113                                                         BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, r_V, d_V);
114     }
115 
116     // Map from points
117     const CeedInt point_loop_bound = (blockDim.x * blockDim.y) * ceil(1.0 * BASIS_NUM_PTS / (blockDim.x * blockDim.y));
118 
119     for (CeedInt i = threadIdx.x + threadIdx.y * blockDim.x; i < point_loop_bound; i += blockDim.x * blockDim.y) {
120       const CeedInt p = i % BASIS_NUM_PTS;
121 
122       ReadPoint<BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_X, r_X);
123       ReadPoint<BASIS_NUM_COMP, BASIS_NUM_PTS>(data, elem, i, points_per_elem[elem], 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_U, r_U);
124       if (BASIS_DIM == 1) {
125         InterpTransposeAtPoints1d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
126       } else if (BASIS_DIM == 2) {
127         InterpTransposeAtPoints2d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
128       } else if (BASIS_DIM == 3) {
129         InterpTransposeAtPoints3d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
130       }
131     }
132 
133     // Map from coefficients
134     if (BASIS_DIM == 1) {
135       InterpTranspose1d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
136       SumElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, r_V, d_V);
137     } else if (BASIS_DIM == 2) {
138       InterpTransposeTensor2d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
139       SumElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, r_V, d_V);
140     } else if (BASIS_DIM == 3) {
141       InterpTransposeTensor3d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
142       SumElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
143                                                       BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, r_V, d_V);
144     }
145   }
146 }
147 
148 extern "C" __global__ void InterpTransposeAddAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ c_B,
149                                                       const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ d_X,
150                                                       const CeedScalar *__restrict__ d_U, CeedScalar *__restrict__ d_V) {
151   extern __shared__ CeedScalar slice[];
152 
153   SharedData_Cuda data;
154   data.t_id_x = threadIdx.x;
155   data.t_id_y = threadIdx.y;
156   data.t_id_z = threadIdx.z;
157   data.t_id   = threadIdx.x + threadIdx.y * blockDim.x + threadIdx.z * blockDim.y * blockDim.x;
158   data.slice  = slice + data.t_id_z * BASIS_T_1D * (BASIS_DIM > 1 ? BASIS_T_1D : 1);
159 
160   CeedScalar r_X[BASIS_DIM];
161   CeedScalar r_U[BASIS_NUM_COMP];
162   CeedScalar r_C[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
163   CeedScalar r_V[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
164 
165   // load interp_1d into shared memory
166   __shared__ CeedScalar s_B[BASIS_P_1D * BASIS_Q_1D];
167   LoadMatrix<BASIS_P_1D, BASIS_Q_1D>(data, c_B, s_B);
168   __syncthreads();
169 
170   // Apply basis element by element
171   for (CeedInt elem = blockIdx.x * blockDim.z + threadIdx.z; elem < num_elem; elem += gridDim.x * blockDim.z) {
172     // Clear register
173     for (CeedInt i = 0; i < BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1); i++) r_C[i] = 0.0;
174 
175     // Map from points
176     const CeedInt point_loop_bound = (blockDim.x * blockDim.y) * ceil(1.0 * BASIS_NUM_PTS / (blockDim.x * blockDim.y));
177 
178     for (CeedInt i = threadIdx.x + threadIdx.y * blockDim.x; i < point_loop_bound; i += blockDim.x * blockDim.y) {
179       const CeedInt p = i % BASIS_NUM_PTS;
180 
181       ReadPoint<BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_X, r_X);
182       ReadPoint<BASIS_NUM_COMP, BASIS_NUM_PTS>(data, elem, i, points_per_elem[elem], 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_U, r_U);
183       if (BASIS_DIM == 1) {
184         InterpTransposeAtPoints1d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
185       } else if (BASIS_DIM == 2) {
186         InterpTransposeAtPoints2d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
187       } else if (BASIS_DIM == 3) {
188         InterpTransposeAtPoints3d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
189       }
190     }
191 
192     // Map from coefficients
193     if (BASIS_DIM == 1) {
194       InterpTranspose1d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
195       SumElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, r_V, d_V);
196     } else if (BASIS_DIM == 2) {
197       InterpTransposeTensor2d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
198       SumElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, r_V, d_V);
199     } else if (BASIS_DIM == 3) {
200       InterpTransposeTensor3d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
201       SumElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
202                                                       BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, r_V, d_V);
203     }
204   }
205 }
206 
207 //------------------------------------------------------------------------------
208 // Grad
209 //------------------------------------------------------------------------------
210 extern "C" __global__ void GradAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ c_B, const CeedInt *__restrict__ points_per_elem,
211                                         const CeedScalar *__restrict__ d_X, const CeedScalar *__restrict__ d_U, CeedScalar *__restrict__ d_V) {
212   extern __shared__ CeedScalar slice[];
213 
214   SharedData_Cuda data;
215   data.t_id_x = threadIdx.x;
216   data.t_id_y = threadIdx.y;
217   data.t_id_z = threadIdx.z;
218   data.t_id   = threadIdx.x + threadIdx.y * blockDim.x + threadIdx.z * blockDim.y * blockDim.x;
219   data.slice  = slice + data.t_id_z * BASIS_T_1D * (BASIS_DIM > 1 ? BASIS_T_1D : 1);
220 
221   CeedScalar r_X[BASIS_DIM];
222   CeedScalar r_U[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_P_1D : 1)];
223   CeedScalar r_C[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
224   CeedScalar r_V[BASIS_NUM_COMP * BASIS_DIM];
225 
226   // load interp_1d into shared memory
227   __shared__ CeedScalar s_B[BASIS_P_1D * BASIS_Q_1D];
228   LoadMatrix<BASIS_P_1D, BASIS_Q_1D>(data, c_B, s_B);
229   __syncthreads();
230 
231   // Apply basis element by element
232   for (CeedInt elem = blockIdx.x * blockDim.z + threadIdx.z; elem < num_elem; elem += gridDim.x * blockDim.z) {
233     // Map to coefficients
234     if (BASIS_DIM == 1) {
235       ReadElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, d_U, r_U);
236       Interp1d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_U, s_B, r_C);
237     } else if (BASIS_DIM == 2) {
238       ReadElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, d_U, r_U);
239       InterpTensor2d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_U, s_B, r_C);
240     } else if (BASIS_DIM == 3) {
241       ReadElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
242                                                        BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, d_U, r_U);
243       InterpTensor3d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_U, s_B, r_C);
244     }
245 
246     // Map to points
247     const CeedInt point_loop_bound = (blockDim.x * blockDim.y) * ceil(1.0 * BASIS_NUM_PTS / (blockDim.x * blockDim.y));
248 
249     for (CeedInt i = threadIdx.x + threadIdx.y * blockDim.x; i < point_loop_bound; i += blockDim.x * blockDim.y) {
250       const CeedInt p = i % BASIS_NUM_PTS;
251 
252       ReadPoint<BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_X, r_X);
253       if (BASIS_DIM == 1) {
254         GradAtPoints1d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_C, r_X, r_V);
255       } else if (BASIS_DIM == 2) {
256         GradAtPoints2d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_C, r_X, r_V);
257       } else if (BASIS_DIM == 3) {
258         GradAtPoints3d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_C, r_X, r_V);
259       }
260       WritePoint<BASIS_NUM_COMP * BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, r_V, d_V);
261     }
262   }
263 }
264 
265 extern "C" __global__ void GradTransposeAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ c_B,
266                                                  const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ d_X,
267                                                  const CeedScalar *__restrict__ d_U, CeedScalar *__restrict__ d_V) {
268   extern __shared__ CeedScalar slice[];
269 
270   SharedData_Cuda data;
271   data.t_id_x = threadIdx.x;
272   data.t_id_y = threadIdx.y;
273   data.t_id_z = threadIdx.z;
274   data.t_id   = threadIdx.x + threadIdx.y * blockDim.x + threadIdx.z * blockDim.y * blockDim.x;
275   data.slice  = slice + data.t_id_z * BASIS_T_1D * (BASIS_DIM > 1 ? BASIS_T_1D : 1);
276 
277   CeedScalar r_X[BASIS_DIM];
278   CeedScalar r_U[BASIS_NUM_COMP * BASIS_DIM];
279   CeedScalar r_C[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
280   CeedScalar r_V[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
281 
282   // load interp_1d into shared memory
283   __shared__ CeedScalar s_B[BASIS_P_1D * BASIS_Q_1D];
284   LoadMatrix<BASIS_P_1D, BASIS_Q_1D>(data, c_B, s_B);
285   __syncthreads();
286 
287   // Apply basis element by element
288   for (CeedInt elem = blockIdx.x * blockDim.z + threadIdx.z; elem < num_elem; elem += gridDim.x * blockDim.z) {
289     // Clear register
290     for (CeedInt i = 0; i < BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1); i++) r_C[i] = 0.0;
291 
292     // Clear output vector
293     for (CeedInt i = 0; i < BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1); i++) r_V[i] = 0.0;
294     if (BASIS_DIM == 1) {
295       WriteElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, r_V, d_V);
296     } else if (BASIS_DIM == 2) {
297       WriteElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, r_V, d_V);
298     } else if (BASIS_DIM == 3) {
299       WriteElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
300                                                         BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, r_V, d_V);
301     }
302 
303     // Map from points
304     const CeedInt point_loop_bound = (blockDim.x * blockDim.y) * ceil(1.0 * BASIS_NUM_PTS / (blockDim.x * blockDim.y));
305 
306     for (CeedInt i = threadIdx.x + threadIdx.y * blockDim.x; i < point_loop_bound; i += blockDim.x * blockDim.y) {
307       const CeedInt p = i % BASIS_NUM_PTS;
308 
309       ReadPoint<BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_X, r_X);
310       ReadPoint<BASIS_NUM_COMP * BASIS_DIM, BASIS_NUM_PTS>(data, elem, i, points_per_elem[elem], 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_U,
311                                                            r_U);
312       if (BASIS_DIM == 1) {
313         GradTransposeAtPoints1d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
314       } else if (BASIS_DIM == 2) {
315         GradTransposeAtPoints2d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
316       } else if (BASIS_DIM == 3) {
317         GradTransposeAtPoints3d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
318       }
319     }
320 
321     // Map from coefficients
322     if (BASIS_DIM == 1) {
323       InterpTranspose1d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
324       SumElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, r_V, d_V);
325     } else if (BASIS_DIM == 2) {
326       InterpTransposeTensor2d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
327       SumElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, r_V, d_V);
328     } else if (BASIS_DIM == 3) {
329       InterpTransposeTensor3d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
330       SumElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
331                                                       BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, r_V, d_V);
332     }
333   }
334 }
335 
336 extern "C" __global__ void GradTransposeAddAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ c_B,
337                                                     const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ d_X,
338                                                     const CeedScalar *__restrict__ d_U, CeedScalar *__restrict__ d_V) {
339   extern __shared__ CeedScalar slice[];
340 
341   SharedData_Cuda data;
342   data.t_id_x = threadIdx.x;
343   data.t_id_y = threadIdx.y;
344   data.t_id_z = threadIdx.z;
345   data.t_id   = threadIdx.x + threadIdx.y * blockDim.x + threadIdx.z * blockDim.y * blockDim.x;
346   data.slice  = slice + data.t_id_z * BASIS_T_1D * (BASIS_DIM > 1 ? BASIS_T_1D : 1);
347 
348   CeedScalar r_X[BASIS_DIM];
349   CeedScalar r_U[BASIS_NUM_COMP * BASIS_DIM];
350   CeedScalar r_C[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
351   CeedScalar r_V[BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1)];
352 
353   // load interp_1d into shared memory
354   __shared__ CeedScalar s_B[BASIS_P_1D * BASIS_Q_1D];
355   LoadMatrix<BASIS_P_1D, BASIS_Q_1D>(data, c_B, s_B);
356   __syncthreads();
357 
358   // Apply basis element by element
359   for (CeedInt elem = blockIdx.x * blockDim.z + threadIdx.z; elem < num_elem; elem += gridDim.x * blockDim.z) {
360     // Clear register
361     for (CeedInt i = 0; i < BASIS_NUM_COMP * (BASIS_DIM > 2 ? BASIS_Q_1D : 1); i++) r_C[i] = 0.0;
362 
363     // Map from points
364     const CeedInt point_loop_bound = (blockDim.x * blockDim.y) * ceil(1.0 * BASIS_NUM_PTS / (blockDim.x * blockDim.y));
365 
366     for (CeedInt i = threadIdx.x + threadIdx.y * blockDim.x; i < point_loop_bound; i += blockDim.x * blockDim.y) {
367       const CeedInt p = i % BASIS_NUM_PTS;
368 
369       ReadPoint<BASIS_DIM, BASIS_NUM_PTS>(data, elem, p, BASIS_NUM_PTS, 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_X, r_X);
370       ReadPoint<BASIS_NUM_COMP * BASIS_DIM, BASIS_NUM_PTS>(data, elem, i, points_per_elem[elem], 1, num_elem * BASIS_NUM_PTS, BASIS_NUM_PTS, d_U,
371                                                            r_U);
372       if (BASIS_DIM == 1) {
373         GradTransposeAtPoints1d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
374       } else if (BASIS_DIM == 2) {
375         GradTransposeAtPoints2d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
376       } else if (BASIS_DIM == 3) {
377         GradTransposeAtPoints3d<BASIS_NUM_COMP, BASIS_NUM_PTS, BASIS_P_1D, BASIS_Q_1D>(data, i, r_U, r_X, r_C);
378       }
379     }
380 
381     // Map from coefficients
382     if (BASIS_DIM == 1) {
383       InterpTranspose1d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
384       SumElementStrided1d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * num_elem, BASIS_P_1D, r_V, d_V);
385     } else if (BASIS_DIM == 2) {
386       InterpTransposeTensor2d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
387       SumElementStrided2d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * num_elem, BASIS_P_1D * BASIS_P_1D, r_V, d_V);
388     } else if (BASIS_DIM == 3) {
389       InterpTransposeTensor3d<BASIS_NUM_COMP, BASIS_P_1D, BASIS_Q_1D, BASIS_T_1D>(data, r_C, s_B, r_V);
390       SumElementStrided3d<BASIS_NUM_COMP, BASIS_P_1D>(data, elem, 1, BASIS_P_1D * BASIS_P_1D * BASIS_P_1D * num_elem,
391                                                       BASIS_P_1D * BASIS_P_1D * BASIS_P_1D, r_V, d_V);
392     }
393   }
394 }
395