xref: /libCEED/rust/libceed-sys/c-src/backends/ref/ceed-ref-restriction.c (revision 6e536b992ff6bc401c55631f1bc4464446496b52)
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 rstr, 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 *__restrict__ uu,
22                                                                       CeedScalar *__restrict__ vv) {
23   // No offsets provided, identity restriction
24   bool has_backend_strides;
25 
26   CeedCallBackend(CeedElemRestrictionHasBackendStrides(rstr, &has_backend_strides));
27   if (has_backend_strides) {
28     // CPU backend strides are {1, elem_size, elem_size*num_comp}
29     // This if branch is left separate to allow better inlining
30     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
31       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
32         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
33           CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
34             vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
35                 uu[n + k * elem_size + CeedIntMin(e + j, num_elem - 1) * elem_size * num_comp];
36           }
37         }
38       }
39     }
40   } else {
41     // User provided strides
42     CeedInt strides[3];
43 
44     CeedCallBackend(CeedElemRestrictionGetStrides(rstr, strides));
45     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
46       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
47         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
48           CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
49             vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
50                 uu[n * strides[0] + k * strides[1] + CeedIntMin(e + j, num_elem - 1) * strides[2]];
51           }
52         }
53       }
54     }
55   }
56   return CEED_ERROR_SUCCESS;
57 }
58 
59 static inline int CeedElemRestrictionApplyOffsetNoTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
60                                                                      const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
61                                                                      CeedInt elem_size, CeedInt v_offset, const CeedScalar *__restrict__ uu,
62                                                                      CeedScalar *__restrict__ vv) {
63   // Default restriction with offsets
64   CeedElemRestriction_Ref *impl;
65 
66   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
67   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
68     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
69       CeedPragmaSIMD for (CeedInt i = 0; i < elem_size * block_size; i++) {
70         vv[elem_size * (k * block_size + e * num_comp) + i - v_offset] = uu[impl->offsets[i + e * elem_size] + k * comp_stride];
71       }
72     }
73   }
74   return CEED_ERROR_SUCCESS;
75 }
76 
77 static inline int CeedElemRestrictionApplyOrientedNoTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
78                                                                        const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
79                                                                        CeedInt elem_size, CeedInt v_offset, const CeedScalar *__restrict__ uu,
80                                                                        CeedScalar *__restrict__ vv) {
81   // Restriction with orientations
82   CeedElemRestriction_Ref *impl;
83 
84   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
85   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
86     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
87       CeedPragmaSIMD for (CeedInt i = 0; i < elem_size * block_size; i++) {
88         vv[elem_size * (k * block_size + e * num_comp) + i - v_offset] =
89             uu[impl->offsets[i + e * elem_size] + k * comp_stride] * (impl->orients[i + e * elem_size] ? -1.0 : 1.0);
90       }
91     }
92   }
93   return CEED_ERROR_SUCCESS;
94 }
95 
96 static inline int CeedElemRestrictionApplyCurlOrientedNoTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
97                                                                            const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
98                                                                            CeedInt elem_size, CeedInt v_offset, const CeedScalar *__restrict__ uu,
99                                                                            CeedScalar *__restrict__ vv) {
100   // Restriction with tridiagonal transformation
101   CeedElemRestriction_Ref *impl;
102 
103   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
104   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
105     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
106       CeedInt n = 0;
107 
108       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
109         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
110             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
111                 impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
112             uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
113                 impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size];
114       }
115       CeedPragmaSIMD for (n = 1; n < elem_size - 1; n++) {
116         CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
117           vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
118               uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
119                   impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size] +
120               uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
121                   impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
122               uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
123                   impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size];
124         }
125       }
126       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
127         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
128             uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
129                 impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size] +
130             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
131                 impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size];
132       }
133     }
134   }
135   return CEED_ERROR_SUCCESS;
136 }
137 
138 static inline int CeedElemRestrictionApplyCurlOrientedUnsignedNoTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp,
139                                                                                    const CeedInt block_size, const CeedInt comp_stride, CeedInt start,
140                                                                                    CeedInt stop, CeedInt num_elem, CeedInt elem_size,
141                                                                                    CeedInt v_offset, const CeedScalar *__restrict__ uu,
142                                                                                    CeedScalar *__restrict__ vv) {
143   // Restriction with (unsigned) tridiagonal transformation
144   CeedElemRestriction_Ref *impl;
145 
146   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
147   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
148     CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
149       CeedInt n = 0;
150 
151       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
152         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
153             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
154                 abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
155             uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
156                 abs(impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size]);
157       }
158       CeedPragmaSIMD for (n = 1; n < elem_size - 1; n++) {
159         CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
160           vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
161               uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
162                   abs(impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size]) +
163               uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
164                   abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
165               uu[impl->offsets[j + (n + 1) * block_size + e * elem_size] + k * comp_stride] *
166                   abs(impl->curl_orients[j + (3 * n + 2) * block_size + e * 3 * elem_size]);
167         }
168       }
169       CeedPragmaSIMD for (CeedInt j = 0; j < block_size; j++) {
170         vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] =
171             uu[impl->offsets[j + (n - 1) * block_size + e * elem_size] + k * comp_stride] *
172                 abs(impl->curl_orients[j + (3 * n + 0) * block_size + e * 3 * elem_size]) +
173             uu[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] *
174                 abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]);
175       }
176     }
177   }
178   return CEED_ERROR_SUCCESS;
179 }
180 
181 static inline int CeedElemRestrictionApplyStridedTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
182                                                                     CeedInt start, CeedInt stop, CeedInt num_elem, CeedInt elem_size,
183                                                                     CeedInt v_offset, const CeedScalar *__restrict__ uu,
184                                                                     CeedScalar *__restrict__ vv) {
185   // No offsets provided, identity restriction
186   bool has_backend_strides;
187 
188   CeedCallBackend(CeedElemRestrictionHasBackendStrides(rstr, &has_backend_strides));
189   if (has_backend_strides) {
190     // CPU backend strides are {1, elem_size, elem_size*num_comp}
191     // This if brach is left separate to allow better inlining
192     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
193       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
194         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
195           CeedPragmaSIMD for (CeedInt j = 0; j < CeedIntMin(block_size, num_elem - e); j++) {
196             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];
197           }
198         }
199       }
200     }
201   } else {
202     // User provided strides
203     CeedInt strides[3];
204 
205     CeedCallBackend(CeedElemRestrictionGetStrides(rstr, strides));
206     for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
207       CeedPragmaSIMD for (CeedInt k = 0; k < num_comp; k++) {
208         CeedPragmaSIMD for (CeedInt n = 0; n < elem_size; n++) {
209           CeedPragmaSIMD for (CeedInt j = 0; j < CeedIntMin(block_size, num_elem - e); j++) {
210             vv[n * strides[0] + k * strides[1] + (e + j) * strides[2]] +=
211                 uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset];
212           }
213         }
214       }
215     }
216   }
217   return CEED_ERROR_SUCCESS;
218 }
219 
220 static inline int CeedElemRestrictionApplyOffsetTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
221                                                                    const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
222                                                                    CeedInt elem_size, CeedInt v_offset, const CeedScalar *__restrict__ uu,
223                                                                    CeedScalar *__restrict__ vv) {
224   // Default restriction with offsets
225   CeedElemRestriction_Ref *impl;
226 
227   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
228   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
229     for (CeedInt k = 0; k < num_comp; k++) {
230       for (CeedInt i = 0; i < elem_size * block_size; i += block_size) {
231         // Iteration bound set to discard padding elements
232         for (CeedInt j = i; j < i + CeedIntMin(block_size, num_elem - e); j++) {
233           CeedScalar vv_loc;
234 
235           vv_loc = uu[elem_size * (k * block_size + e * num_comp) + j - v_offset];
236           CeedPragmaAtomic vv[impl->offsets[j + e * elem_size] + k * comp_stride] += vv_loc;
237         }
238       }
239     }
240   }
241   return CEED_ERROR_SUCCESS;
242 }
243 
244 static inline int CeedElemRestrictionApplyOrientedTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
245                                                                      const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
246                                                                      CeedInt elem_size, CeedInt v_offset, const CeedScalar *__restrict__ uu,
247                                                                      CeedScalar *__restrict__ vv) {
248   // Restriction with orientations
249   CeedElemRestriction_Ref *impl;
250 
251   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
252   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
253     for (CeedInt k = 0; k < num_comp; k++) {
254       for (CeedInt i = 0; i < elem_size * block_size; i += block_size) {
255         // Iteration bound set to discard padding elements
256         for (CeedInt j = i; j < i + CeedIntMin(block_size, num_elem - e); j++) {
257           CeedScalar vv_loc;
258 
259           vv_loc = uu[elem_size * (k * block_size + e * num_comp) + j - v_offset] * (impl->orients[j + e * elem_size] ? -1.0 : 1.0);
260           CeedPragmaAtomic vv[impl->offsets[j + e * elem_size] + k * comp_stride] += vv_loc;
261         }
262       }
263     }
264   }
265   return CEED_ERROR_SUCCESS;
266 }
267 
268 static inline int CeedElemRestrictionApplyCurlOrientedTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
269                                                                          const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedInt num_elem,
270                                                                          CeedInt elem_size, CeedInt v_offset, const CeedScalar *__restrict__ uu,
271                                                                          CeedScalar *__restrict__ vv) {
272   // Restriction with tridiagonal transformation
273   CeedElemRestriction_Ref *impl;
274   CeedScalar               vv_loc[block_size];
275 
276   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
277   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
278     for (CeedInt k = 0; k < num_comp; k++) {
279       // Iteration bound set to discard padding elements
280       const CeedInt block_end = CeedIntMin(block_size, num_elem - e);
281       CeedInt       n         = 0;
282 
283       CeedPragmaSIMD for (CeedInt j = 0; j < block_end; j++) {
284         vv_loc[j] = uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
285                         impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
286                     uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
287                         impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size];
288       }
289       for (CeedInt j = 0; j < block_end; j++) {
290         CeedPragmaAtomic vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] += vv_loc[j];
291       }
292       for (n = 1; n < elem_size - 1; n++) {
293         CeedPragmaSIMD for (CeedInt j = 0; j < block_end; j++) {
294           vv_loc[j] = uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
295                           impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size] +
296                       uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
297                           impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size] +
298                       uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
299                           impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size];
300         }
301         for (CeedInt j = 0; j < block_end; j++) {
302           CeedPragmaAtomic vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] += vv_loc[j];
303         }
304       }
305       CeedPragmaSIMD for (CeedInt j = 0; j < block_end; j++) {
306         vv_loc[j] = uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
307                         impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size] +
308                     uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
309                         impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size];
310       }
311       for (CeedInt j = 0; j < block_end; j++) {
312         CeedPragmaAtomic vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] += vv_loc[j];
313       }
314     }
315   }
316   return CEED_ERROR_SUCCESS;
317 }
318 
319 static inline int CeedElemRestrictionApplyCurlOrientedUnsignedTranspose_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp,
320                                                                                  const CeedInt block_size, const CeedInt comp_stride, CeedInt start,
321                                                                                  CeedInt stop, CeedInt num_elem, CeedInt elem_size, CeedInt v_offset,
322                                                                                  const CeedScalar *__restrict__ uu, CeedScalar *__restrict__ vv) {
323   // Restriction with (unsigned) tridiagonal transformation
324   CeedElemRestriction_Ref *impl;
325   CeedScalar               vv_loc[block_size];
326 
327   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
328   for (CeedInt e = start * block_size; e < stop * block_size; e += block_size) {
329     for (CeedInt k = 0; k < num_comp; k++) {
330       // Iteration bound set to discard padding elements
331       const CeedInt block_end = CeedIntMin(block_size, num_elem - e);
332       CeedInt       n         = 0;
333 
334       CeedPragmaSIMD for (CeedInt j = 0; j < block_end; j++) {
335         vv_loc[j] = uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
336                         abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
337                     uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
338                         abs(impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size]);
339       }
340       for (CeedInt j = 0; j < block_end; j++) {
341         CeedPragmaAtomic vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] += vv_loc[j];
342       }
343       for (n = 1; n < elem_size - 1; n++) {
344         CeedPragmaSIMD for (CeedInt j = 0; j < block_end; j++) {
345           vv_loc[j] = uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
346                           abs(impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size]) +
347                       uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
348                           abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]) +
349                       uu[e * elem_size * num_comp + (k * elem_size + n + 1) * block_size + j - v_offset] *
350                           abs(impl->curl_orients[j + (3 * n + 3) * block_size + e * 3 * elem_size]);
351         }
352         for (CeedInt j = 0; j < block_end; j++) {
353           CeedPragmaAtomic vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] += vv_loc[j];
354         }
355       }
356       CeedPragmaSIMD for (CeedInt j = 0; j < block_end; j++) {
357         vv_loc[j] = uu[e * elem_size * num_comp + (k * elem_size + n - 1) * block_size + j - v_offset] *
358                         abs(impl->curl_orients[j + (3 * n - 1) * block_size + e * 3 * elem_size]) +
359                     uu[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] *
360                         abs(impl->curl_orients[j + (3 * n + 1) * block_size + e * 3 * elem_size]);
361       }
362       for (CeedInt j = 0; j < block_end; j++) {
363         CeedPragmaAtomic vv[impl->offsets[j + n * block_size + e * elem_size] + k * comp_stride] += vv_loc[j];
364       }
365     }
366   }
367   return CEED_ERROR_SUCCESS;
368 }
369 
370 static inline int CeedElemRestrictionApplyAtPointsInElement_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, CeedInt start, CeedInt stop,
371                                                                      CeedTransposeMode t_mode, const CeedScalar *__restrict__ uu,
372                                                                      CeedScalar *__restrict__ vv) {
373   CeedInt                  num_points, l_vec_offset, e_vec_offset = 0;
374   CeedElemRestriction_Ref *impl;
375 
376   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
377   for (CeedInt e = start; e < stop; e++) {
378     l_vec_offset = impl->offsets[e];
379     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr, e, &num_points));
380     if (t_mode == CEED_NOTRANSPOSE) {
381       for (CeedInt i = 0; i < num_points; i++) {
382         for (CeedInt j = 0; j < num_comp; j++) vv[j * num_points + i + e_vec_offset] = uu[impl->offsets[i + l_vec_offset] * num_comp + j];
383       }
384     } else {
385       for (CeedInt i = 0; i < num_points; i++) {
386         for (CeedInt j = 0; j < num_comp; j++) vv[impl->offsets[i + l_vec_offset] * num_comp + j] = uu[j * num_points + i + e_vec_offset];
387       }
388     }
389     e_vec_offset += num_points * num_comp;
390   }
391   return CEED_ERROR_SUCCESS;
392 }
393 
394 static inline int CeedElemRestrictionApply_Ref_Core(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size,
395                                                     const CeedInt comp_stride, CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs,
396                                                     bool use_orients, CeedVector u, CeedVector v, CeedRequest *request) {
397   CeedInt             num_elem, elem_size, v_offset;
398   CeedRestrictionType rstr_type;
399   const CeedScalar   *uu;
400   CeedScalar         *vv;
401 
402   CeedCallBackend(CeedElemRestrictionGetNumElements(rstr, &num_elem));
403   CeedCallBackend(CeedElemRestrictionGetElementSize(rstr, &elem_size));
404   v_offset = start * block_size * elem_size * num_comp;
405   CeedCallBackend(CeedElemRestrictionGetType(rstr, &rstr_type));
406   CeedCallBackend(CeedVectorGetArrayRead(u, CEED_MEM_HOST, &uu));
407 
408   if (t_mode == CEED_TRANSPOSE) {
409     // Sum into for transpose mode, E-vector to L-vector
410     CeedCallBackend(CeedVectorGetArray(v, CEED_MEM_HOST, &vv));
411   } else {
412     // Overwrite for notranspose mode, L-vector to E-vector
413     CeedCallBackend(CeedVectorGetArrayWrite(v, CEED_MEM_HOST, &vv));
414   }
415   if (t_mode == CEED_TRANSPOSE) {
416     // Restriction from E-vector to L-vector
417     // Performing v += r^T * u
418     // uu has shape [elem_size, num_comp, num_elem], row-major
419     // vv has shape [nnodes, num_comp]
420     // Sum into for transpose mode
421     switch (rstr_type) {
422       case CEED_RESTRICTION_STRIDED:
423         CeedCallBackend(
424             CeedElemRestrictionApplyStridedTranspose_Ref_Core(rstr, num_comp, block_size, start, stop, num_elem, elem_size, v_offset, uu, vv));
425         break;
426       case CEED_RESTRICTION_STANDARD:
427         CeedCallBackend(CeedElemRestrictionApplyOffsetTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size,
428                                                                          v_offset, uu, vv));
429         break;
430       case CEED_RESTRICTION_ORIENTED:
431         if (use_signs) {
432           CeedCallBackend(CeedElemRestrictionApplyOrientedTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem,
433                                                                              elem_size, v_offset, uu, vv));
434         } else {
435           CeedCallBackend(CeedElemRestrictionApplyOffsetTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size,
436                                                                            v_offset, uu, vv));
437         }
438         break;
439       case CEED_RESTRICTION_CURL_ORIENTED:
440         if (use_signs && use_orients) {
441           CeedCallBackend(CeedElemRestrictionApplyCurlOrientedTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem,
442                                                                                  elem_size, v_offset, uu, vv));
443         } else if (use_orients) {
444           CeedCallBackend(CeedElemRestrictionApplyCurlOrientedUnsignedTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop,
445                                                                                          num_elem, elem_size, v_offset, uu, vv));
446         } else {
447           CeedCallBackend(CeedElemRestrictionApplyOffsetTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size,
448                                                                            v_offset, uu, vv));
449         }
450         break;
451       case CEED_RESTRICTION_POINTS:
452         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement_Ref_Core(rstr, num_comp, start, stop, t_mode, uu, vv));
453         break;
454     }
455   } else {
456     // Restriction from L-vector to E-vector
457     // Perform: v = r * u
458     // vv has shape [elem_size, num_comp, num_elem], row-major
459     // uu has shape [nnodes, num_comp]
460     // Overwrite for notranspose mode
461     switch (rstr_type) {
462       case CEED_RESTRICTION_STRIDED:
463         CeedCallBackend(
464             CeedElemRestrictionApplyStridedNoTranspose_Ref_Core(rstr, num_comp, block_size, start, stop, num_elem, elem_size, v_offset, uu, vv));
465         break;
466       case CEED_RESTRICTION_STANDARD:
467         CeedCallBackend(CeedElemRestrictionApplyOffsetNoTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem, elem_size,
468                                                                            v_offset, uu, vv));
469         break;
470       case CEED_RESTRICTION_ORIENTED:
471         if (use_signs) {
472           CeedCallBackend(CeedElemRestrictionApplyOrientedNoTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem,
473                                                                                elem_size, v_offset, uu, vv));
474         } else {
475           CeedCallBackend(CeedElemRestrictionApplyOffsetNoTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem,
476                                                                              elem_size, v_offset, uu, vv));
477         }
478         break;
479       case CEED_RESTRICTION_CURL_ORIENTED:
480         if (use_signs && use_orients) {
481           CeedCallBackend(CeedElemRestrictionApplyCurlOrientedNoTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem,
482                                                                                    elem_size, v_offset, uu, vv));
483         } else if (use_orients) {
484           CeedCallBackend(CeedElemRestrictionApplyCurlOrientedUnsignedNoTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop,
485                                                                                            num_elem, elem_size, v_offset, uu, vv));
486         } else {
487           CeedCallBackend(CeedElemRestrictionApplyOffsetNoTranspose_Ref_Core(rstr, num_comp, block_size, comp_stride, start, stop, num_elem,
488                                                                              elem_size, v_offset, uu, vv));
489         }
490         break;
491       case CEED_RESTRICTION_POINTS:
492         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement_Ref_Core(rstr, num_comp, start, stop, t_mode, uu, vv));
493         break;
494     }
495   }
496   CeedCallBackend(CeedVectorRestoreArrayRead(u, &uu));
497   CeedCallBackend(CeedVectorRestoreArray(v, &vv));
498   if (request != CEED_REQUEST_IMMEDIATE && request != CEED_REQUEST_ORDERED) *request = NULL;
499   return CEED_ERROR_SUCCESS;
500 }
501 
502 //------------------------------------------------------------------------------
503 // ElemRestriction Apply - Common Sizes
504 //------------------------------------------------------------------------------
505 static int CeedElemRestrictionApply_Ref_110(CeedElemRestriction rstr, 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(rstr, 1, 1, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
509 }
510 
511 static int CeedElemRestrictionApply_Ref_111(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
512                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
513                                             CeedVector v, CeedRequest *request) {
514   return CeedElemRestrictionApply_Ref_Core(rstr, 1, 1, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
515 }
516 
517 static int CeedElemRestrictionApply_Ref_180(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
518                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
519                                             CeedVector v, CeedRequest *request) {
520   return CeedElemRestrictionApply_Ref_Core(rstr, 1, 8, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
521 }
522 
523 static int CeedElemRestrictionApply_Ref_181(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
524                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
525                                             CeedVector v, CeedRequest *request) {
526   return CeedElemRestrictionApply_Ref_Core(rstr, 1, 8, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
527 }
528 
529 static int CeedElemRestrictionApply_Ref_310(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
530                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
531                                             CeedVector v, CeedRequest *request) {
532   return CeedElemRestrictionApply_Ref_Core(rstr, 3, 1, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
533 }
534 
535 static int CeedElemRestrictionApply_Ref_311(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
536                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
537                                             CeedVector v, CeedRequest *request) {
538   return CeedElemRestrictionApply_Ref_Core(rstr, 3, 1, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
539 }
540 
541 static int CeedElemRestrictionApply_Ref_380(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
542                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
543                                             CeedVector v, CeedRequest *request) {
544   return CeedElemRestrictionApply_Ref_Core(rstr, 3, 8, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
545 }
546 
547 static int CeedElemRestrictionApply_Ref_381(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
548                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
549                                             CeedVector v, CeedRequest *request) {
550   return CeedElemRestrictionApply_Ref_Core(rstr, 3, 8, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
551 }
552 
553 // LCOV_EXCL_START
554 static int CeedElemRestrictionApply_Ref_510(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
555                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
556                                             CeedVector v, CeedRequest *request) {
557   return CeedElemRestrictionApply_Ref_Core(rstr, 5, 1, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
558 }
559 // LCOV_EXCL_STOP
560 
561 static int CeedElemRestrictionApply_Ref_511(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
562                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
563                                             CeedVector v, CeedRequest *request) {
564   return CeedElemRestrictionApply_Ref_Core(rstr, 5, 1, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
565 }
566 
567 // LCOV_EXCL_START
568 static int CeedElemRestrictionApply_Ref_580(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
569                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
570                                             CeedVector v, CeedRequest *request) {
571   return CeedElemRestrictionApply_Ref_Core(rstr, 5, 8, comp_stride, start, stop, t_mode, use_signs, use_orients, u, v, request);
572 }
573 // LCOV_EXCL_STOP
574 
575 static int CeedElemRestrictionApply_Ref_581(CeedElemRestriction rstr, const CeedInt num_comp, const CeedInt block_size, const CeedInt comp_stride,
576                                             CeedInt start, CeedInt stop, CeedTransposeMode t_mode, bool use_signs, bool use_orients, CeedVector u,
577                                             CeedVector v, CeedRequest *request) {
578   return CeedElemRestrictionApply_Ref_Core(rstr, 5, 8, 1, start, stop, t_mode, use_signs, use_orients, u, v, request);
579 }
580 
581 //------------------------------------------------------------------------------
582 // ElemRestriction Apply
583 //------------------------------------------------------------------------------
584 static int CeedElemRestrictionApply_Ref(CeedElemRestriction rstr, CeedTransposeMode t_mode, CeedVector u, CeedVector v, CeedRequest *request) {
585   CeedInt                  num_block, block_size, num_comp, comp_stride;
586   CeedElemRestriction_Ref *impl;
587 
588   CeedCallBackend(CeedElemRestrictionGetNumBlocks(rstr, &num_block));
589   CeedCallBackend(CeedElemRestrictionGetBlockSize(rstr, &block_size));
590   CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
591   CeedCallBackend(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
592   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
593   CeedCallBackend(impl->Apply(rstr, num_comp, block_size, comp_stride, 0, num_block, t_mode, true, true, u, v, request));
594   return CEED_ERROR_SUCCESS;
595 }
596 
597 //------------------------------------------------------------------------------
598 // ElemRestriction Apply Unsigned
599 //------------------------------------------------------------------------------
600 static int CeedElemRestrictionApplyUnsigned_Ref(CeedElemRestriction rstr, CeedTransposeMode t_mode, CeedVector u, CeedVector v,
601                                                 CeedRequest *request) {
602   CeedInt                  num_block, block_size, num_comp, comp_stride;
603   CeedElemRestriction_Ref *impl;
604 
605   CeedCallBackend(CeedElemRestrictionGetNumBlocks(rstr, &num_block));
606   CeedCallBackend(CeedElemRestrictionGetBlockSize(rstr, &block_size));
607   CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
608   CeedCallBackend(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
609   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
610   CeedCallBackend(impl->Apply(rstr, num_comp, block_size, comp_stride, 0, num_block, t_mode, false, true, u, v, request));
611   return CEED_ERROR_SUCCESS;
612 }
613 
614 //------------------------------------------------------------------------------
615 // ElemRestriction Apply Unoriented
616 //------------------------------------------------------------------------------
617 static int CeedElemRestrictionApplyUnoriented_Ref(CeedElemRestriction rstr, CeedTransposeMode t_mode, CeedVector u, CeedVector v,
618                                                   CeedRequest *request) {
619   CeedInt                  num_block, block_size, num_comp, comp_stride;
620   CeedElemRestriction_Ref *impl;
621 
622   CeedCallBackend(CeedElemRestrictionGetNumBlocks(rstr, &num_block));
623   CeedCallBackend(CeedElemRestrictionGetBlockSize(rstr, &block_size));
624   CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
625   CeedCallBackend(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
626   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
627   CeedCallBackend(impl->Apply(rstr, num_comp, block_size, comp_stride, 0, num_block, t_mode, false, false, u, v, request));
628   return CEED_ERROR_SUCCESS;
629 }
630 
631 //------------------------------------------------------------------------------
632 // ElemRestriction Apply Points
633 //------------------------------------------------------------------------------
634 static int CeedElemRestrictionApplyAtPointsInElement_Ref(CeedElemRestriction rstr, CeedInt elem, CeedTransposeMode t_mode, CeedVector u, CeedVector v,
635                                                          CeedRequest *request) {
636   CeedInt                  num_comp;
637   CeedElemRestriction_Ref *impl;
638 
639   CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
640   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
641   return impl->Apply(rstr, num_comp, 0, 1, elem, elem + 1, t_mode, false, false, u, v, request);
642 }
643 
644 //------------------------------------------------------------------------------
645 // ElemRestriction Apply Block
646 //------------------------------------------------------------------------------
647 static int CeedElemRestrictionApplyBlock_Ref(CeedElemRestriction rstr, CeedInt block, CeedTransposeMode t_mode, CeedVector u, CeedVector v,
648                                              CeedRequest *request) {
649   CeedInt                  block_size, num_comp, comp_stride;
650   CeedElemRestriction_Ref *impl;
651 
652   CeedCallBackend(CeedElemRestrictionGetBlockSize(rstr, &block_size));
653   CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
654   CeedCallBackend(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
655   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
656   CeedCallBackend(impl->Apply(rstr, num_comp, block_size, comp_stride, block, block + 1, t_mode, true, true, u, v, request));
657   return CEED_ERROR_SUCCESS;
658 }
659 
660 //------------------------------------------------------------------------------
661 // ElemRestriction Get Offsets
662 //------------------------------------------------------------------------------
663 static int CeedElemRestrictionGetOffsets_Ref(CeedElemRestriction rstr, CeedMemType mem_type, const CeedInt **offsets) {
664   CeedElemRestriction_Ref *impl;
665 
666   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
667 
668   CeedCheck(mem_type == CEED_MEM_HOST, CeedElemRestrictionReturnCeed(rstr), CEED_ERROR_BACKEND, "Can only provide to HOST memory");
669 
670   *offsets = impl->offsets;
671   return CEED_ERROR_SUCCESS;
672 }
673 
674 //------------------------------------------------------------------------------
675 // ElemRestriction Get Orientations
676 //------------------------------------------------------------------------------
677 static int CeedElemRestrictionGetOrientations_Ref(CeedElemRestriction rstr, CeedMemType mem_type, const bool **orients) {
678   CeedElemRestriction_Ref *impl;
679 
680   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
681 
682   CeedCheck(mem_type == CEED_MEM_HOST, CeedElemRestrictionReturnCeed(rstr), CEED_ERROR_BACKEND, "Can only provide to HOST memory");
683 
684   *orients = impl->orients;
685   return CEED_ERROR_SUCCESS;
686 }
687 
688 //------------------------------------------------------------------------------
689 // ElemRestriction Get Curl-Conforming Orientations
690 //------------------------------------------------------------------------------
691 static int CeedElemRestrictionGetCurlOrientations_Ref(CeedElemRestriction rstr, CeedMemType mem_type, const CeedInt8 **curl_orients) {
692   CeedElemRestriction_Ref *impl;
693 
694   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
695 
696   CeedCheck(mem_type == CEED_MEM_HOST, CeedElemRestrictionReturnCeed(rstr), CEED_ERROR_BACKEND, "Can only provide to HOST memory");
697 
698   *curl_orients = impl->curl_orients;
699   return CEED_ERROR_SUCCESS;
700 }
701 
702 //------------------------------------------------------------------------------
703 // ElemRestriction Destroy
704 //------------------------------------------------------------------------------
705 static int CeedElemRestrictionDestroy_Ref(CeedElemRestriction rstr) {
706   CeedElemRestriction_Ref *impl;
707 
708   CeedCallBackend(CeedElemRestrictionGetData(rstr, &impl));
709   CeedCallBackend(CeedFree(&impl->offsets_allocated));
710   CeedCallBackend(CeedFree(&impl->orients_allocated));
711   CeedCallBackend(CeedFree(&impl->curl_orients_allocated));
712   CeedCallBackend(CeedFree(&impl));
713   return CEED_ERROR_SUCCESS;
714 }
715 
716 //------------------------------------------------------------------------------
717 // ElemRestriction Create
718 //------------------------------------------------------------------------------
719 int CeedElemRestrictionCreate_Ref(CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets, const bool *orients,
720                                   const CeedInt8 *curl_orients, CeedElemRestriction rstr) {
721   Ceed                     ceed;
722   CeedInt                  num_elem, elem_size, num_block, block_size, num_comp, comp_stride, num_points = 0, num_offsets;
723   CeedRestrictionType      rstr_type;
724   CeedElemRestriction_Ref *impl;
725 
726   CeedCallBackend(CeedElemRestrictionGetCeed(rstr, &ceed));
727   CeedCallBackend(CeedElemRestrictionGetNumElements(rstr, &num_elem));
728   CeedCallBackend(CeedElemRestrictionGetElementSize(rstr, &elem_size));
729   CeedCallBackend(CeedElemRestrictionGetNumBlocks(rstr, &num_block));
730   CeedCallBackend(CeedElemRestrictionGetBlockSize(rstr, &block_size));
731   CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
732   CeedCallBackend(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
733   CeedCallBackend(CeedElemRestrictionGetType(rstr, &rstr_type));
734 
735   CeedCheck(mem_type == CEED_MEM_HOST, ceed, CEED_ERROR_BACKEND, "Only MemType = HOST supported");
736 
737   CeedCallBackend(CeedCalloc(1, &impl));
738   CeedCallBackend(CeedElemRestrictionSetData(rstr, impl));
739 
740   // Set layouts
741   {
742     bool    has_backend_strides;
743     CeedInt layout[3] = {1, elem_size, elem_size * num_comp};
744 
745     CeedCallBackend(CeedElemRestrictionSetELayout(rstr, layout));
746     if (rstr_type == CEED_RESTRICTION_STRIDED) {
747       CeedCallBackend(CeedElemRestrictionHasBackendStrides(rstr, &has_backend_strides));
748       if (has_backend_strides) {
749         CeedCallBackend(CeedElemRestrictionSetLLayout(rstr, layout));
750       }
751     }
752   }
753 
754   // Offsets data
755   if (rstr_type != CEED_RESTRICTION_STRIDED) {
756     const char *resource;
757 
758     // Check indices for ref or memcheck backends
759     {
760       Ceed current = ceed, parent = NULL;
761 
762       CeedCallBackend(CeedGetParent(current, &parent));
763       while (current != parent) {
764         current = parent;
765         CeedCallBackend(CeedGetParent(current, &parent));
766       }
767       CeedCallBackend(CeedGetResource(parent, &resource));
768     }
769     if (!strcmp(resource, "/cpu/self/ref/serial") || !strcmp(resource, "/cpu/self/ref/blocked") || !strcmp(resource, "/cpu/self/memcheck/serial") ||
770         !strcmp(resource, "/cpu/self/memcheck/blocked")) {
771       CeedSize l_size;
772 
773       CeedCallBackend(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
774       for (CeedInt i = 0; i < num_elem * elem_size; i++) {
775         CeedCheck(offsets[i] >= 0 && offsets[i] + (num_comp - 1) * comp_stride < l_size, ceed, CEED_ERROR_BACKEND,
776                   "Restriction offset %" CeedInt_FMT " (%" CeedInt_FMT ") out of range [0, %" CeedInt_FMT "]", i, offsets[i], l_size);
777       }
778     }
779 
780     // Copy data
781     if (rstr_type == CEED_RESTRICTION_POINTS) CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr, &num_points));
782     num_offsets = rstr_type == CEED_RESTRICTION_POINTS ? (num_elem + 1 + num_points) : (num_elem * elem_size);
783     switch (copy_mode) {
784       case CEED_COPY_VALUES:
785         CeedCallBackend(CeedMalloc(num_offsets, &impl->offsets_allocated));
786         memcpy(impl->offsets_allocated, offsets, num_offsets * sizeof(offsets[0]));
787         impl->offsets = impl->offsets_allocated;
788         break;
789       case CEED_OWN_POINTER:
790         impl->offsets_allocated = (CeedInt *)offsets;
791         impl->offsets           = impl->offsets_allocated;
792         break;
793       case CEED_USE_POINTER:
794         impl->offsets = offsets;
795     }
796 
797     // Orientation data
798     if (rstr_type == CEED_RESTRICTION_ORIENTED) {
799       CeedCheck(orients != NULL, ceed, CEED_ERROR_BACKEND, "No orients array provided for oriented restriction");
800       switch (copy_mode) {
801         case CEED_COPY_VALUES:
802           CeedCallBackend(CeedMalloc(num_offsets, &impl->orients_allocated));
803           memcpy(impl->orients_allocated, orients, num_offsets * sizeof(orients[0]));
804           impl->orients = impl->orients_allocated;
805           break;
806         case CEED_OWN_POINTER:
807           impl->orients_allocated = (bool *)orients;
808           impl->orients           = impl->orients_allocated;
809           break;
810         case CEED_USE_POINTER:
811           impl->orients = orients;
812       }
813     } else if (rstr_type == CEED_RESTRICTION_CURL_ORIENTED) {
814       CeedCheck(curl_orients != NULL, ceed, CEED_ERROR_BACKEND, "No curl_orients array provided for oriented restriction");
815       switch (copy_mode) {
816         case CEED_COPY_VALUES:
817           CeedCallBackend(CeedMalloc(3 * num_offsets, &impl->curl_orients_allocated));
818           memcpy(impl->curl_orients_allocated, curl_orients, 3 * num_offsets * sizeof(curl_orients[0]));
819           impl->curl_orients = impl->curl_orients_allocated;
820           break;
821         case CEED_OWN_POINTER:
822           impl->curl_orients_allocated = (CeedInt8 *)curl_orients;
823           impl->curl_orients           = impl->curl_orients_allocated;
824           break;
825         case CEED_USE_POINTER:
826           impl->curl_orients = curl_orients;
827       }
828     }
829   }
830 
831   // Set apply function based upon num_comp, block_size, and comp_stride
832   CeedInt index = -1;
833 
834   if (block_size < 10) index = 100 * num_comp + 10 * block_size + (comp_stride == 1);
835   switch (index) {
836     case 110:
837       impl->Apply = CeedElemRestrictionApply_Ref_110;
838       break;
839     case 111:
840       impl->Apply = CeedElemRestrictionApply_Ref_111;
841       break;
842     case 180:
843       impl->Apply = CeedElemRestrictionApply_Ref_180;
844       break;
845     case 181:
846       impl->Apply = CeedElemRestrictionApply_Ref_181;
847       break;
848     case 310:
849       impl->Apply = CeedElemRestrictionApply_Ref_310;
850       break;
851     case 311:
852       impl->Apply = CeedElemRestrictionApply_Ref_311;
853       break;
854     case 380:
855       impl->Apply = CeedElemRestrictionApply_Ref_380;
856       break;
857     case 381:
858       impl->Apply = CeedElemRestrictionApply_Ref_381;
859       break;
860     // LCOV_EXCL_START
861     case 510:
862       impl->Apply = CeedElemRestrictionApply_Ref_510;
863       break;
864     // LCOV_EXCL_STOP
865     case 511:
866       impl->Apply = CeedElemRestrictionApply_Ref_511;
867       break;
868     // LCOV_EXCL_START
869     case 580:
870       impl->Apply = CeedElemRestrictionApply_Ref_580;
871       break;
872     // LCOV_EXCL_STOP
873     case 581:
874       impl->Apply = CeedElemRestrictionApply_Ref_581;
875       break;
876     default:
877       impl->Apply = CeedElemRestrictionApply_Ref_Core;
878       break;
879   }
880 
881   // Register backend functions
882   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "Apply", CeedElemRestrictionApply_Ref));
883   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "ApplyUnsigned", CeedElemRestrictionApplyUnsigned_Ref));
884   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "ApplyUnoriented", CeedElemRestrictionApplyUnoriented_Ref));
885   if (rstr_type == CEED_RESTRICTION_POINTS) {
886     CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "ApplyAtPointsInElement", CeedElemRestrictionApplyAtPointsInElement_Ref));
887   }
888   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "ApplyBlock", CeedElemRestrictionApplyBlock_Ref));
889   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "GetOffsets", CeedElemRestrictionGetOffsets_Ref));
890   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "GetOrientations", CeedElemRestrictionGetOrientations_Ref));
891   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "GetCurlOrientations", CeedElemRestrictionGetCurlOrientations_Ref));
892   CeedCallBackend(CeedSetBackendFunction(ceed, "ElemRestriction", rstr, "Destroy", CeedElemRestrictionDestroy_Ref));
893   return CEED_ERROR_SUCCESS;
894 }
895 
896 //------------------------------------------------------------------------------
897