xref: /libCEED/backends/ref/ceed-ref-restriction.c (revision 21f16bf6c2940c092555e126518ed0c98a2b88a9)
1 // Copyright (c) 2017-2022, 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 #include <ceed.h>
9 #include <ceed/backend.h>
10 #include <stdbool.h>
11 #include <stdlib.h>
12 #include <string.h>
13 
14 #include "ceed-ref.h"
15 
16 //------------------------------------------------------------------------------
17 // Core ElemRestriction Apply Code
18 //------------------------------------------------------------------------------
19 static inline int CeedElemRestrictionApplyStridedNoTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
20                                                                       CeedInt start, CeedInt stop, CeedInt num_elem, CeedInt elem_size,
21                                                                       CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
22   // No offsets provided, identity restriction
23   bool has_backend_strides;
24 
25   CeedCallBackend(CeedElemRestrictionHasBackendStrides(r, &has_backend_strides));
26   if (has_backend_strides) {
27     // CPU backend strides are {1, elem_size, elem_size*num_comp}
28     // This if branch is left separate to allow better inlining
29     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
30       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
31         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
32           CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
33             vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
34                 uu[n + k * elem_size + CeedIntMin(e + j, num_elem - 1) * elem_size * num_comp];
35           }
36         }
37       }
38     }
39   } else {
40     // User provided strides
41     CeedInt strides[3];
42 
43     CeedCallBackend(CeedElemRestrictionGetStrides(r, &strides));
44     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
45       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
46         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
47           CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
48             vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
49                 uu[n * strides[0] + k * strides[1] + CeedIntMin(e + j, num_elem - 1) * strides[2]];
50           }
51         }
52       }
53     }
54   }
55   return CEED_ERROR_SUCCESS;
56 }
57 
58 static inline int CeedElemRestrictionApplyStandardNoTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
59                                                                        const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
60                                                                        CeedInt elem_size, CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
61   // Default restriction with offsets
62   CeedElemRestriction_Ref *impl;
63 
64   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
65   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
66     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
67       CeedPragmaSIMD for (CeedInt i = 0; i < elem_size * block_size; i++) {
68         vv[elem_size * (k * block_size + e * num_comp) + i - v_offset] = uu[impl->offsets[i + e * elem_size] + k * comp_stride];
69       }
70     }
71   }
72   return CEED_ERROR_SUCCESS;
73 }
74 
75 static inline int CeedElemRestrictionApplyOrientedNoTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
76                                                                        const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
77                                                                        CeedInt elem_size, CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
78   // Restriction with orientations
79   CeedElemRestriction_Ref *impl;
80 
81   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
82   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
83     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
84       CeedPragmaSIMD for (CeedInt i = 0; i < elem_size * block_size; i++) {
85         vv[elem_size * (k * block_size + e * num_comp) + i - v_offset] =
86             uu[impl->offsets[i + e * elem_size] + k * comp_stride] * (impl->orients[i + e * elem_size] ? -1.0 : 1.0);
87       }
88     }
89   }
90   return CEED_ERROR_SUCCESS;
91 }
92 
93 static inline int CeedElemRestrictionApplyCurlOrientedNoTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
94                                                                            const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
95                                                                            CeedInt elem_size, CeedInt v_offset, const CeedScalar *uu,
96                                                                            CeedScalar *vv) {
97   // Restriction with tridiagonal transformation
98   CeedElemRestriction_Ref *impl;
99 
100   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
101   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
102     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
103       CeedInt n = 0;
104       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
105         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
106             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
107                 impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
108             uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
109                 impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size];
110       }
111       for (n = 1; n < elem_size - 1; n++) {
112         CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
113           vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
114               uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
115                   impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size] +
116               uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
117                   impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
118               uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
119                   impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size];
120         }
121       }
122       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
123         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
124             uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
125                 impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size] +
126             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
127                 impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size];
128       }
129     }
130   }
131   return CEED_ERROR_SUCCESS;
132 }
133 
134 static inline int CeedElemRestrictionApplyCurlOrientedUnsignedNoTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp,
135                                                                                    const CeedInt block_size, const CeedInt comp_stride, CeedInt start,
136                                                                                    CeedInt stop, CeedInt num_elem, CeedInt elem_size,
137                                                                                    CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
138   // Restriction with (unsigned) tridiagonal transformation
139   CeedElemRestriction_Ref *impl;
140 
141   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
142   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
143     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
144       CeedInt n = 0;
145 
146       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
147         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
148             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
149                 abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
150             uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
151                 abs(impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size]);
152       }
153       for (n = 1; n < elem_size - 1; n++) {
154         CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
155           vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
156               uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
157                   abs(impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size]) +
158               uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
159                   abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
160               uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
161                   abs(impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size]);
162         }
163       }
164       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
165         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
166             uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
167                 abs(impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size]) +
168             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
169                 abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]);
170       }
171     }
172   }
173   return CEED_ERROR_SUCCESS;
174 }
175 
176 static inline int CeedElemRestrictionApplyStridedTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
177                                                                     CeedInt start, CeedInt stop, CeedInt num_elem, CeedInt elem_size,
178                                                                     CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
179   // No offsets provided, identity restriction
180   bool has_backend_strides;
181 
182   CeedCallBackend(CeedElemRestrictionHasBackendStrides(r, &has_backend_strides));
183   if (has_backend_strides) {
184     // CPU backend strides are {1, elem_size, elem_size*num_comp}
185     // This if brach is left separate to allow better inlining
186     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
187       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
188         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
189           CeedPragmaSIMD for (CeedInt j = 0; j < CeedIntMin(block_size, num_elem - e); j++) {
190             vv[n + k * elem_size + (e + j) * elem_size * num_comp] += uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset];
191           }
192         }
193       }
194     }
195   } else {
196     // User provided strides
197     CeedInt strides[3];
198 
199     CeedCallBackend(CeedElemRestrictionGetStrides(r, &strides));
200     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
201       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
202         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
203           CeedPragmaSIMD for (CeedInt j = 0; j < CeedIntMin(block_size, num_elem - e); j++) {
204             vv[n * strides[0] + k * strides[1] + (e + j) * strides[2]] +=
205                 uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset];
206           }
207         }
208       }
209     }
210   }
211   return CEED_ERROR_SUCCESS;
212 }
213 
214 static inline int CeedElemRestrictionApplyStandardTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
215                                                                      const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
216                                                                      CeedInt elem_size, CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
217   // Default restriction with offsets
218   CeedElemRestriction_Ref *impl;
219 
220   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
221   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
222     for (CeedInt k = 0; k < num_comp; k++) {
223       for (CeedInt i = 0; i < elem_size * block_size; i += block_size) {
224         // Iteration bound set to discard padding elements
225         for (CeedInt j = i; j < i + CeedIntMin(block_size, num_elem - e); j++) {
226           vv[impl->offsets[j + e * elem_size] + k * comp_stride] += uu[elem_size * (k * block_size + e * num_comp) + j - v_offset];
227         }
228       }
229     }
230   }
231   return CEED_ERROR_SUCCESS;
232 }
233 
234 static inline int CeedElemRestrictionApplyOrientedTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
235                                                                      const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
236                                                                      CeedInt elem_size, CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
237   // Restriction with orientations
238   CeedElemRestriction_Ref *impl;
239 
240   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
241   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
242     for (CeedInt k = 0; k < num_comp; k++) {
243       for (CeedInt i = 0; i < elem_size * block_size; i += block_size) {
244         // Iteration bound set to discard padding elements
245         for (CeedInt j = i; j < i + CeedIntMin(block_size, num_elem - e); j++) {
246           vv[impl->offsets[j + e * elem_size] + k * comp_stride] +=
247               uu[elem_size * (k * block_size + e * num_comp) + j - v_offset] * (impl->orients[j + e * elem_size] ? -1.0 : 1.0);
248         }
249       }
250     }
251   }
252   return CEED_ERROR_SUCCESS;
253 }
254 
255 static inline int CeedElemRestrictionApplyCurlOrientedTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
256                                                                          const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
257                                                                          CeedInt elem_size, CeedInt v_offset, const CeedScalar *uu, CeedScalar *vv) {
258   // Restriction with tridiagonal transformation
259   CeedElemRestriction_Ref *impl;
260 
261   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
262   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
263     for (CeedInt k = 0; k < num_comp; k++) {
264       // Iteration bound set to discard padding elements
265       CeedInt block_end = CeedIntMin(block_size, num_elem - e), n = 0;
266       for (CeedInt j = 0; j < block_end; j++) {
267         vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] +=
268             uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
269                 impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
270             uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
271                 impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size];
272       }
273       for (n = 1; n < elem_size - 1; n++) {
274         for (CeedInt j = 0; j < block_end; j++) {
275           vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] +=
276               uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
277                   impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size] +
278               uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
279                   impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
280               uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
281                   impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size];
282         }
283       }
284       for (CeedInt j = 0; j < block_end; j++) {
285         vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] +=
286             uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
287                 impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size] +
288             uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
289                 impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size];
290       }
291     }
292   }
293   return CEED_ERROR_SUCCESS;
294 }
295 
296 static inline int CeedElemRestrictionApplyCurlOrientedUnsignedTranspose_Ref_Core(CeedElemRestriction r, const CeedInt num_comp,
297                                                                                  const CeedInt block_size, const CeedInt comp_stride, CeedInt start,
298                                                                                  CeedInt stop, CeedInt num_elem, CeedInt elem_size, CeedInt v_offset,
299                                                                                  const CeedScalar *uu, CeedScalar *vv) {
300   // Restriction with (unsigned) tridiagonal transformation
301   CeedElemRestriction_Ref *impl;
302 
303   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
304   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
305     for (CeedInt k = 0; k < num_comp; k++) {
306       // Iteration bound set to discard padding elements
307       CeedInt       n         = 0;
308       const CeedInt block_end = CeedIntMin(block_size, num_elem - e);
309 
310       for (CeedInt j = 0; j < block_end; j++) {
311         vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] +=
312             uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
313                 abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
314             uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
315                 abs(impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size]);
316       }
317       for (n = 1; n < elem_size - 1; n++) {
318         for (CeedInt j = 0; j < block_end; j++) {
319           vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] +=
320               uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
321                   abs(impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size]) +
322               uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
323                   abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
324               uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
325                   abs(impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size]);
326         }
327       }
328       for (CeedInt j = 0; j < block_end; j++) {
329         vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] +=
330             uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
331                 abs(impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size]) +
332             uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
333                 abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]);
334       }
335     }
336   }
337   return CEED_ERROR_SUCCESS;
338 }
339 
340 static inline int CeedElemRestrictionApply_Ref_Core(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size,
341                                                     const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs,
342                                                     bool use_orients, CeedVector u, CeedVector v, CeedRequest *request) {
343   CeedInt             num_elem, elem_size, v_offset;
344   CeedRestrictionType rstr_type;
345   const CeedScalar   *uu;
346   CeedScalar         *vv;
347 
348   CeedCallBackend(CeedElemRestrictionGetNumElements(r, &num_elem));
349   CeedCallBackend(CeedElemRestrictionGetElementSize(r, &elem_size));
350   v_offset = start * block_size * elem_size * num_comp;
351   CeedCallBackend(CeedElemRestrictionGetType(r, &rstr_type));
352   CeedCallBackend(CeedVectorGetArrayRead(u, CEED_MEM_HOST, &uu));
353 
354   if (t_mode == CEED_TRANSPOSE) {
355     // Sum into for transpose mode, E-vector to L-vector
356     CeedCallBackend(CeedVectorGetArray(v, CEED_MEM_HOST, &vv));
357   } else {
358     // Overwrite for notranspose mode, L-vector to E-vector
359     CeedCallBackend(CeedVectorGetArrayWrite(v, CEED_MEM_HOST, &vv));
360   }
361   if (t_mode == CEED_TRANSPOSE) {
362     // Restriction from E-vector to L-vector
363     // Performing v += r^T * u
364     // uu has shape [elem_size, num_comp, num_elem], row-major
365     // vv has shape [nnodes, num_comp]
366     // Sum into for transpose mode
367     switch (rstr_type) {
368       case CEED_RESTRICTION_STRIDED:
369         CeedElemRestrictionApplyStridedTranspose_Ref_Core(r, num_comp, block_size, start, stop, num_elem, elem_size, v_offset, uu, vv);
370         break;
371       case CEED_RESTRICTION_STANDARD:
372         CeedElemRestrictionApplyStandardTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu, vv);
373         break;
374       case CEED_RESTRICTION_ORIENTED:
375         if (use_signs) {
376           CeedElemRestrictionApplyOrientedTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
377                                                              vv);
378         } else {
379           CeedElemRestrictionApplyStandardTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
380                                                              vv);
381         }
382         break;
383       case CEED_RESTRICTION_CURL_ORIENTED:
384         if (use_signs && use_orients) {
385           CeedElemRestrictionApplyCurlOrientedTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
386                                                                  vv);
387         } else if (use_orients) {
388           CeedElemRestrictionApplyCurlOrientedUnsignedTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size,
389                                                                          v_offset, uu, vv);
390         } else {
391           CeedElemRestrictionApplyStandardTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
392                                                              vv);
393         }
394         break;
395     }
396   } else {
397     // Restriction from L-vector to E-vector
398     // Perform: v = r * u
399     // vv has shape [elem_size, num_comp, num_elem], row-major
400     // uu has shape [nnodes, num_comp]
401     // Overwrite for notranspose mode
402     switch (rstr_type) {
403       case CEED_RESTRICTION_STRIDED:
404         CeedElemRestrictionApplyStridedNoTranspose_Ref_Core(r, num_comp, block_size, start, stop, num_elem, elem_size, v_offset, uu, vv);
405         break;
406       case CEED_RESTRICTION_STANDARD:
407         CeedElemRestrictionApplyStandardNoTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
408                                                              vv);
409         break;
410       case CEED_RESTRICTION_ORIENTED:
411         if (use_signs) {
412           CeedElemRestrictionApplyOrientedNoTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
413                                                                vv);
414         } else {
415           CeedElemRestrictionApplyStandardNoTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
416                                                                vv);
417         }
418         break;
419       case CEED_RESTRICTION_CURL_ORIENTED:
420         if (use_signs && use_orients) {
421           CeedElemRestrictionApplyCurlOrientedNoTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset,
422                                                                    uu, vv);
423         } else if (use_orients) {
424           CeedElemRestrictionApplyCurlOrientedUnsignedNoTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size,
425                                                                            v_offset, uu, vv);
426         } else {
427           CeedElemRestrictionApplyStandardNoTranspose_Ref_Core(r, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size, v_offset, uu,
428                                                                vv);
429         }
430         break;
431     }
432   }
433   CeedCallBackend(CeedVectorRestoreArrayRead(u, &uu));
434   CeedCallBackend(CeedVectorRestoreArray(v, &vv));
435   if (request != CEED_REQUEST_IMMEDIATE && request != CEED_REQUEST_ORDERED) *request = NULL;
436   return CEED_ERROR_SUCCESS;
437 }
438 
439 //------------------------------------------------------------------------------
440 // ElemRestriction Apply - Common Sizes
441 //------------------------------------------------------------------------------
442 static int CeedElemRestrictionApply_Ref_110(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
443                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
444                                             CeedVector v, CeedRequest *request) {
445   return CeedElemRestrictionApply_Ref_Core(r, 1, 1, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
446 }
447 
448 static int CeedElemRestrictionApply_Ref_111(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
449                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
450                                             CeedVector v, CeedRequest *request) {
451   return CeedElemRestrictionApply_Ref_Core(r, 1, 1, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
452 }
453 
454 static int CeedElemRestrictionApply_Ref_180(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
455                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
456                                             CeedVector v, CeedRequest *request) {
457   return CeedElemRestrictionApply_Ref_Core(r, 1, 8, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
458 }
459 
460 static int CeedElemRestrictionApply_Ref_181(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
461                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
462                                             CeedVector v, CeedRequest *request) {
463   return CeedElemRestrictionApply_Ref_Core(r, 1, 8, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
464 }
465 
466 static int CeedElemRestrictionApply_Ref_310(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
467                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
468                                             CeedVector v, CeedRequest *request) {
469   return CeedElemRestrictionApply_Ref_Core(r, 3, 1, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
470 }
471 
472 static int CeedElemRestrictionApply_Ref_311(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
473                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
474                                             CeedVector v, CeedRequest *request) {
475   return CeedElemRestrictionApply_Ref_Core(r, 3, 1, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
476 }
477 
478 static int CeedElemRestrictionApply_Ref_380(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
479                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
480                                             CeedVector v, CeedRequest *request) {
481   return CeedElemRestrictionApply_Ref_Core(r, 3, 8, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
482 }
483 
484 static int CeedElemRestrictionApply_Ref_381(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
485                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
486                                             CeedVector v, CeedRequest *request) {
487   return CeedElemRestrictionApply_Ref_Core(r, 3, 8, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
488 }
489 
490 // LCOV_EXCL_START
491 static int CeedElemRestrictionApply_Ref_510(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
492                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
493                                             CeedVector v, CeedRequest *request) {
494   return CeedElemRestrictionApply_Ref_Core(r, 5, 1, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
495 }
496 // LCOV_EXCL_STOP
497 
498 static int CeedElemRestrictionApply_Ref_511(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
499                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
500                                             CeedVector v, CeedRequest *request) {
501   return CeedElemRestrictionApply_Ref_Core(r, 5, 1, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
502 }
503 
504 // LCOV_EXCL_START
505 static int CeedElemRestrictionApply_Ref_580(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
506                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
507                                             CeedVector v, CeedRequest *request) {
508   return CeedElemRestrictionApply_Ref_Core(r, 5, 8, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
509 }
510 // LCOV_EXCL_STOP
511 
512 static int CeedElemRestrictionApply_Ref_581(CeedElemRestriction r, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
513                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
514                                             CeedVector v, CeedRequest *request) {
515   return CeedElemRestrictionApply_Ref_Core(r, 5, 8, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
516 }
517 
518 //------------------------------------------------------------------------------
519 // ElemRestriction Apply
520 //------------------------------------------------------------------------------
521 static int CeedElemRestrictionApply_Ref(CeedElemRestriction r, CeedTransposeMode t_mode, CeedVector u, CeedVector v, CeedRequest *request) {
522   CeedInt                  num_block, block_size, num_comp, comp_stride;
523   CeedElemRestriction_Ref *impl;
524 
525   CeedCallBackend(CeedElemRestrictionGetNumBlocks(r, &num_block));
526   CeedCallBackend(CeedElemRestrictionGetBlockSize(r, &block_size));
527   CeedCallBackend(CeedElemRestrictionGetNumComponents(r, &num_comp));
528   CeedCallBackend(CeedElemRestrictionGetCompStride(r, &comp_stride));
529   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
530   return impl->Apply(r, num_comp, block_size, comp_stride, 0, num_block, t_mode, true, true, u, v, request);
531 }
532 
533 //------------------------------------------------------------------------------
534 // ElemRestriction Apply Unsigned
535 //------------------------------------------------------------------------------
536 static int CeedElemRestrictionApplyUnsigned_Ref(CeedElemRestriction r, CeedTransposeMode t_mode, CeedVector u, CeedVector v, CeedRequest *request) {
537   CeedInt                  num_block, block_size, num_comp, comp_stride;
538   CeedElemRestriction_Ref *impl;
539 
540   CeedCallBackend(CeedElemRestrictionGetNumBlocks(r, &num_block));
541   CeedCallBackend(CeedElemRestrictionGetBlockSize(r, &block_size));
542   CeedCallBackend(CeedElemRestrictionGetNumComponents(r, &num_comp));
543   CeedCallBackend(CeedElemRestrictionGetCompStride(r, &comp_stride));
544   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
545   return impl->Apply(r, num_comp, block_size, comp_stride, 0, num_block, t_mode, false, true, u, v, request);
546 }
547 
548 //------------------------------------------------------------------------------
549 // ElemRestriction Apply Unoriented
550 //------------------------------------------------------------------------------
551 static int CeedElemRestrictionApplyUnoriented_Ref(CeedElemRestriction r, CeedTransposeMode t_mode, CeedVector u, CeedVector v, CeedRequest *request) {
552   CeedInt                  num_block, block_size, num_comp, comp_stride;
553   CeedElemRestriction_Ref *impl;
554 
555   CeedCallBackend(CeedElemRestrictionGetNumBlocks(r, &num_block));
556   CeedCallBackend(CeedElemRestrictionGetBlockSize(r, &block_size));
557   CeedCallBackend(CeedElemRestrictionGetNumComponents(r, &num_comp));
558   CeedCallBackend(CeedElemRestrictionGetCompStride(r, &comp_stride));
559   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
560   return impl->Apply(r, num_comp, block_size, comp_stride, 0, num_block, t_mode, false, false, u, v, request);
561 }
562 
563 //------------------------------------------------------------------------------
564 // ElemRestriction Apply Block
565 //------------------------------------------------------------------------------
566 static int CeedElemRestrictionApplyBlock_Ref(CeedElemRestriction r, CeedInt block, CeedTransposeMode t_mode, CeedVector u, CeedVector v,
567                                              CeedRequest *request) {
568   CeedInt                  block_size, num_comp, comp_stride;
569   CeedElemRestriction_Ref *impl;
570 
571   CeedCallBackend(CeedElemRestrictionGetBlockSize(r, &block_size));
572   CeedCallBackend(CeedElemRestrictionGetNumComponents(r, &num_comp));
573   CeedCallBackend(CeedElemRestrictionGetCompStride(r, &comp_stride));
574   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
575   return impl->Apply(r, num_comp, block_size, comp_stride, block, block + 1, t_mode, true, true, u, v, request);
576 }
577 
578 //------------------------------------------------------------------------------
579 // ElemRestriction Get Offsets
580 //------------------------------------------------------------------------------
581 static int CeedElemRestrictionGetOffsets_Ref(CeedElemRestriction rstr, CeedMemType mem_type, const CeedInt **offsets) {
582   Ceed                     ceed;
583   CeedElemRestriction_Ref *impl;
584 
585   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
586   CeedCallBackend(CeedElemRestrictionGetCeed(rstr, &ceed));
587 
588   CeedCheck(mem_type == CEED_MEM_HOST, ceed, CEED_ERROR_BACKEND, "Can only provide to HOST memory");
589 
590   *offsets = impl->offsets;
591   return CEED_ERROR_SUCCESS;
592 }
593 
594 //------------------------------------------------------------------------------
595 // ElemRestriction Get Orientations
596 //------------------------------------------------------------------------------
597 static int CeedElemRestrictionGetOrientations_Ref(CeedElemRestriction rstr, CeedMemType mem_type, const bool **orients) {
598   Ceed                     ceed;
599   CeedElemRestriction_Ref *impl;
600 
601   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
602   CeedCallBackend(CeedElemRestrictionGetCeed(rstr, &ceed));
603 
604   CeedCheck(mem_type == CEED_MEM_HOST, ceed, CEED_ERROR_BACKEND, "Can only provide to HOST memory");
605 
606   *orients = impl->orients;
607   return CEED_ERROR_SUCCESS;
608 }
609 
610 //------------------------------------------------------------------------------
611 // ElemRestriction Get Curl-Conforming Orientations
612 //------------------------------------------------------------------------------
613 static int CeedElemRestrictionGetCurlOrientations_Ref(CeedElemRestriction rstr, CeedMemType mem_type, const CeedInt8 **curl_orients) {
614   Ceed                     ceed;
615   CeedElemRestriction_Ref *impl;
616 
617   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
618   CeedCallBackend(CeedElemRestrictionGetCeed(rstr, &ceed));
619 
620   CeedCheck(mem_type == CEED_MEM_HOST, ceed, CEED_ERROR_BACKEND, "Can only provide to HOST memory");
621 
622   *curl_orients = impl->curl_orients;
623   return CEED_ERROR_SUCCESS;
624 }
625 
626 //------------------------------------------------------------------------------
627 // ElemRestriction Destroy
628 //------------------------------------------------------------------------------
629 static int CeedElemRestrictionDestroy_Ref(CeedElemRestriction r) {
630   CeedElemRestriction_Ref *impl;
631 
632   CeedCallBackend(CeedElemRestrictionGetData(r, &impl));
633   CeedCallBackend(CeedFree(&impl->offsets_allocated));
634   CeedCallBackend(CeedFree(&impl->orients_allocated));
635   CeedCallBackend(CeedFree(&impl->curl_orients_allocated));
636   CeedCallBackend(CeedFree(&impl));
637   return CEED_ERROR_SUCCESS;
638 }
639 
640 //------------------------------------------------------------------------------
641 // ElemRestriction Create
642 //------------------------------------------------------------------------------
643 int CeedElemRestrictionCreate_Ref(CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets, const bool *orients,
644                                   const CeedInt8 *curl_orients, CeedElemRestriction r) {
645   Ceed                     ceed;
646   CeedInt                  num_elem, elem_size, num_block, block_size, num_comp, comp_stride;
647   CeedRestrictionType      rstr_type;
648   CeedElemRestriction_Ref *impl;
649 
650   CeedCallBackend(CeedElemRestrictionGetCeed(r, &ceed));
651   CeedCallBackend(CeedElemRestrictionGetNumElements(r, &num_elem));
652   CeedCallBackend(CeedElemRestrictionGetElementSize(r, &elem_size));
653   CeedCallBackend(CeedElemRestrictionGetNumBlocks(r, &num_block));
654   CeedCallBackend(CeedElemRestrictionGetBlockSize(r, &block_size));
655   CeedCallBackend(CeedElemRestrictionGetNumComponents(r, &num_comp));
656   CeedCallBackend(CeedElemRestrictionGetCompStride(r, &comp_stride));
657   CeedInt layout[3] = {1, elem_size, elem_size * num_comp};
658 
659   CeedCheck(mem_type == CEED_MEM_HOST, ceed, CEED_ERROR_BACKEND, "Only MemType = HOST supported");
660   CeedCallBackend(CeedCalloc(1, &impl));
661 
662   // Offsets data
663   CeedCallBackend(CeedElemRestrictionGetType(r, &rstr_type));
664   if (rstr_type != CEED_RESTRICTION_STRIDED) {
665     const char *resource;
666 
667     // Check indices for ref or memcheck backends
668     CeedCallBackend(CeedGetResource(ceed, &resource));
669     if (!strcmp(resource, "/cpu/self/ref/serial") || !strcmp(resource, "/cpu/self/ref/blocked") || !strcmp(resource, "/cpu/self/memcheck/serial") ||
670         !strcmp(resource, "/cpu/self/memcheck/blocked")) {
671       CeedSize l_size;
672 
673       CeedCallBackend(CeedElemRestrictionGetLVectorSize(r, &l_size));
674       for (CeedInt i = 0; i < num_elem * elem_size; i++) {
675         CeedCheck(offsets[i] >= 0 && offsets[i] + (num_comp - 1) * comp_stride < l_size, ceed, CEED_ERROR_BACKEND,
676                   "Restriction offset %" CeedInt_FMT " (%" CeedInt_FMT ") out of range [0, %" CeedInt_FMT "]", i, offsets[i], l_size);
677       }
678     }
679 
680     // Copy data
681     switch (copy_mode) {
682       case CEED_COPY_VALUES:
683         CeedCallBackend(CeedMalloc(num_elem * elem_size, &impl->offsets_allocated));
684         memcpy(impl->offsets_allocated, offsets, num_elem * elem_size * sizeof(offsets[0]));
685         impl->offsets = impl->offsets_allocated;
686         break;
687       case CEED_OWN_POINTER:
688         impl->offsets_allocated = (CeedInt *)offsets;
689         impl->offsets           = impl->offsets_allocated;
690         break;
691       case CEED_USE_POINTER:
692         impl->offsets = offsets;
693     }
694 
695     // Orientation data
696     if (rstr_type == CEED_RESTRICTION_ORIENTED) {
697       CeedCheck(orients != NULL, ceed, CEED_ERROR_BACKEND, "No orients array provided for oriented restriction");
698       switch (copy_mode) {
699         case CEED_COPY_VALUES:
700           CeedCallBackend(CeedMalloc(num_elem * elem_size, &impl->orients_allocated));
701           memcpy(impl->orients_allocated, orients, num_elem * elem_size * sizeof(orients[0]));
702           impl->orients = impl->orients_allocated;
703           break;
704         case CEED_OWN_POINTER:
705           impl->orients_allocated = (bool *)orients;
706           impl->orients           = impl->orients_allocated;
707           break;
708         case CEED_USE_POINTER:
709           impl->orients = orients;
710       }
711     } else if (rstr_type == CEED_RESTRICTION_CURL_ORIENTED) {
712       CeedCheck(curl_orients != NULL, ceed, CEED_ERROR_BACKEND, "No curl_orients array provided for oriented restriction");
713       switch (copy_mode) {
714         case CEED_COPY_VALUES:
715           CeedCallBackend(CeedMalloc(num_elem * 3 * elem_size, &impl->curl_orients_allocated));
716           memcpy(impl->curl_orients_allocated, curl_orients, num_elem * 3 * elem_size * sizeof(curl_orients[0]));
717           impl->curl_orients = impl->curl_orients_allocated;
718           break;
719         case CEED_OWN_POINTER:
720           impl->curl_orients_allocated = (CeedInt8 *)curl_orients;
721           impl->curl_orients           = impl->curl_orients_allocated;
722           break;
723         case CEED_USE_POINTER:
724           impl->curl_orients = curl_orients;
725       }
726     }
727   }
728 
729   CeedCallBackend(CeedElemRestrictionSetData(r, impl));
730   CeedCallBackend(CeedElemRestrictionSetELayout(r, layout));
731   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "Apply", CeedElemRestrictionApply_Ref));
732   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "ApplyUnsigned", CeedElemRestrictionApplyUnsigned_Ref));
733   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "ApplyUnoriented", CeedElemRestrictionApplyUnoriented_Ref));
734   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "ApplyBlock", CeedElemRestrictionApplyBlock_Ref));
735   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "GetOffsets", CeedElemRestrictionGetOffsets_Ref));
736   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "GetOrientations", CeedElemRestrictionGetOrientations_Ref));
737   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "GetCurlOrientations", CeedElemRestrictionGetCurlOrientations_Ref));
738   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", r, "Destroy", CeedElemRestrictionDestroy_Ref));
739 
740   // Set apply function based upon num_comp, block_size, and comp_stride
741   CeedInt index = -1;
742 
743   if (block_size < 10) index = 100 * num_comp + 10 * block_size + (comp_stride == 1);
744   switch (index) {
745     case 110:
746       impl->Apply = CeedElemRestrictionApply_Ref_110;
747       break;
748     case 111:
749       impl->Apply = CeedElemRestrictionApply_Ref_111;
750       break;
751     case 180:
752       impl->Apply = CeedElemRestrictionApply_Ref_180;
753       break;
754     case 181:
755       impl->Apply = CeedElemRestrictionApply_Ref_181;
756       break;
757     case 310:
758       impl->Apply = CeedElemRestrictionApply_Ref_310;
759       break;
760     case 311:
761       impl->Apply = CeedElemRestrictionApply_Ref_311;
762       break;
763     case 380:
764       impl->Apply = CeedElemRestrictionApply_Ref_380;
765       break;
766     case 381:
767       impl->Apply = CeedElemRestrictionApply_Ref_381;
768       break;
769     // LCOV_EXCL_START
770     case 510:
771       impl->Apply = CeedElemRestrictionApply_Ref_510;
772       break;
773     // LCOV_EXCL_STOP
774     case 511:
775       impl->Apply = CeedElemRestrictionApply_Ref_511;
776       break;
777     // LCOV_EXCL_START
778     case 580:
779       impl->Apply = CeedElemRestrictionApply_Ref_580;
780       break;
781     // LCOV_EXCL_STOP
782     case 581:
783       impl->Apply = CeedElemRestrictionApply_Ref_581;
784       break;
785     default:
786       impl->Apply = CeedElemRestrictionApply_Ref_Core;
787       break;
788   }
789   return CEED_ERROR_SUCCESS;
790 }
791 
792 //------------------------------------------------------------------------------
793