xlu_kernels.c 14 KB

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  1. /* StarPU --- Runtime system for heterogeneous multicore architectures.
  2. *
  3. * Copyright (C) 2009, 2010-2012, 2014 Université de Bordeaux 1
  4. * Copyright (C) 2010, 2011, 2012 Centre National de la Recherche Scientifique
  5. *
  6. * StarPU is free software; you can redistribute it and/or modify
  7. * it under the terms of the GNU Lesser General Public License as published by
  8. * the Free Software Foundation; either version 2.1 of the License, or (at
  9. * your option) any later version.
  10. *
  11. * StarPU is distributed in the hope that it will be useful, but
  12. * WITHOUT ANY WARRANTY; without even the implied warranty of
  13. * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
  14. *
  15. * See the GNU Lesser General Public License in COPYING.LGPL for more details.
  16. */
  17. #include "xlu.h"
  18. #include <math.h>
  19. #define str(s) #s
  20. #define xstr(s) str(s)
  21. #define STARPU_LU_STR(name) xstr(STARPU_LU(name))
  22. #ifdef STARPU_USE_CUDA
  23. static const TYPE p1 = 1.0f;
  24. static const TYPE m1 = -1.0f;
  25. #endif
  26. /*
  27. * U22
  28. */
  29. static inline void STARPU_LU(common_u22)(void *descr[],
  30. int s, STARPU_ATTRIBUTE_UNUSED void *_args)
  31. {
  32. TYPE *right = (TYPE *)STARPU_MATRIX_GET_PTR(descr[0]);
  33. TYPE *left = (TYPE *)STARPU_MATRIX_GET_PTR(descr[1]);
  34. TYPE *center = (TYPE *)STARPU_MATRIX_GET_PTR(descr[2]);
  35. unsigned dx = STARPU_MATRIX_GET_NX(descr[2]);
  36. unsigned dy = STARPU_MATRIX_GET_NY(descr[2]);
  37. unsigned dz = STARPU_MATRIX_GET_NY(descr[0]);
  38. unsigned ld12 = STARPU_MATRIX_GET_LD(descr[0]);
  39. unsigned ld21 = STARPU_MATRIX_GET_LD(descr[1]);
  40. unsigned ld22 = STARPU_MATRIX_GET_LD(descr[2]);
  41. #ifdef STARPU_USE_CUDA
  42. cublasStatus status;
  43. cudaError_t cures;
  44. #endif
  45. switch (s)
  46. {
  47. case 0:
  48. CPU_GEMM("N", "N", dy, dx, dz,
  49. (TYPE)-1.0, right, ld21, left, ld12,
  50. (TYPE)1.0, center, ld22);
  51. break;
  52. #ifdef STARPU_USE_CUDA
  53. case 1:
  54. {
  55. CUBLAS_GEMM('n', 'n', dx, dy, dz,
  56. *(CUBLAS_TYPE*)&m1, (CUBLAS_TYPE *)right, ld21, (CUBLAS_TYPE *)left, ld12,
  57. *(CUBLAS_TYPE*)&p1, (CUBLAS_TYPE *)center, ld22);
  58. status = cublasGetError();
  59. if (STARPU_UNLIKELY(status != CUBLAS_STATUS_SUCCESS))
  60. STARPU_CUBLAS_REPORT_ERROR(status);
  61. break;
  62. }
  63. #endif
  64. default:
  65. STARPU_ABORT();
  66. break;
  67. }
  68. }
  69. void STARPU_LU(cpu_u22)(void *descr[], void *_args)
  70. {
  71. STARPU_LU(common_u22)(descr, 0, _args);
  72. }
  73. #ifdef STARPU_USE_CUDA
  74. void STARPU_LU(cublas_u22)(void *descr[], void *_args)
  75. {
  76. STARPU_LU(common_u22)(descr, 1, _args);
  77. }
  78. #endif /* STARPU_USE_CUDA */
  79. static struct starpu_perfmodel STARPU_LU(model_22) =
  80. {
  81. .type = STARPU_HISTORY_BASED,
  82. #ifdef STARPU_ATLAS
  83. .symbol = STARPU_LU_STR(lu_model_22_atlas)
  84. #elif defined(STARPU_GOTO)
  85. .symbol = STARPU_LU_STR(lu_model_22_goto)
  86. #else
  87. .symbol = STARPU_LU_STR(lu_model_22)
  88. #endif
  89. };
  90. #ifdef STARPU_USE_CUDA
  91. static int can_execute(unsigned workerid, struct starpu_task *task, unsigned nimpl) {
  92. if (starpu_worker_get_type(workerid) == STARPU_CPU_WORKER)
  93. return 1;
  94. /* Cuda device */
  95. const struct cudaDeviceProp *props;
  96. props = starpu_cuda_get_device_properties(workerid);
  97. if (props->major >= 2 || props->minor >= 3)
  98. {
  99. /* At least compute capability 1.3, supports doubles */
  100. return 1;
  101. }
  102. else
  103. {
  104. /* Old card does not support doubles */
  105. return 0;
  106. }
  107. }
  108. #endif
  109. struct starpu_codelet cl22 =
  110. {
  111. .where = STARPU_CPU|STARPU_CUDA,
  112. .cpu_funcs = {STARPU_LU(cpu_u22), NULL},
  113. #ifdef STARPU_USE_CUDA
  114. .cuda_funcs = {STARPU_LU(cublas_u22), NULL},
  115. .cuda_flags = {STARPU_CUDA_ASYNC},
  116. CAN_EXECUTE
  117. #endif
  118. .nbuffers = 3,
  119. .modes = {STARPU_R, STARPU_R, STARPU_RW},
  120. .model = &STARPU_LU(model_22)
  121. };
  122. /*
  123. * U12
  124. */
  125. static inline void STARPU_LU(common_u12)(void *descr[],
  126. int s, STARPU_ATTRIBUTE_UNUSED void *_args)
  127. {
  128. TYPE *sub11;
  129. TYPE *sub12;
  130. sub11 = (TYPE *)STARPU_MATRIX_GET_PTR(descr[0]);
  131. sub12 = (TYPE *)STARPU_MATRIX_GET_PTR(descr[1]);
  132. unsigned ld11 = STARPU_MATRIX_GET_LD(descr[0]);
  133. unsigned ld12 = STARPU_MATRIX_GET_LD(descr[1]);
  134. unsigned nx12 = STARPU_MATRIX_GET_NX(descr[1]);
  135. unsigned ny12 = STARPU_MATRIX_GET_NY(descr[1]);
  136. #ifdef STARPU_USE_CUDA
  137. cublasStatus status;
  138. cudaError_t cures;
  139. #endif
  140. /* solve L11 U12 = A12 (find U12) */
  141. switch (s)
  142. {
  143. case 0:
  144. CPU_TRSM("L", "L", "N", "N", nx12, ny12,
  145. (TYPE)1.0, sub11, ld11, sub12, ld12);
  146. break;
  147. #ifdef STARPU_USE_CUDA
  148. case 1:
  149. CUBLAS_TRSM('L', 'L', 'N', 'N', ny12, nx12,
  150. *(CUBLAS_TYPE*)&p1, (CUBLAS_TYPE*)sub11, ld11, (CUBLAS_TYPE*)sub12, ld12);
  151. status = cublasGetError();
  152. if (STARPU_UNLIKELY(status != CUBLAS_STATUS_SUCCESS))
  153. STARPU_CUBLAS_REPORT_ERROR(status);
  154. break;
  155. #endif
  156. default:
  157. STARPU_ABORT();
  158. break;
  159. }
  160. }
  161. void STARPU_LU(cpu_u12)(void *descr[], void *_args)
  162. {
  163. STARPU_LU(common_u12)(descr, 0, _args);
  164. }
  165. #ifdef STARPU_USE_CUDA
  166. void STARPU_LU(cublas_u12)(void *descr[], void *_args)
  167. {
  168. STARPU_LU(common_u12)(descr, 1, _args);
  169. }
  170. #endif /* STARPU_USE_CUDA */
  171. static struct starpu_perfmodel STARPU_LU(model_12) =
  172. {
  173. .type = STARPU_HISTORY_BASED,
  174. #ifdef STARPU_ATLAS
  175. .symbol = STARPU_LU_STR(lu_model_12_atlas)
  176. #elif defined(STARPU_GOTO)
  177. .symbol = STARPU_LU_STR(lu_model_12_goto)
  178. #else
  179. .symbol = STARPU_LU_STR(lu_model_12)
  180. #endif
  181. };
  182. struct starpu_codelet cl12 =
  183. {
  184. .where = STARPU_CPU|STARPU_CUDA,
  185. .cpu_funcs = {STARPU_LU(cpu_u12), NULL},
  186. #ifdef STARPU_USE_CUDA
  187. .cuda_funcs = {STARPU_LU(cublas_u12), NULL},
  188. .cuda_flags = {STARPU_CUDA_ASYNC},
  189. CAN_EXECUTE
  190. #endif
  191. .nbuffers = 2,
  192. .modes = {STARPU_R, STARPU_RW},
  193. .model = &STARPU_LU(model_12)
  194. };
  195. /*
  196. * U21
  197. */
  198. static inline void STARPU_LU(common_u21)(void *descr[],
  199. int s, STARPU_ATTRIBUTE_UNUSED void *_args)
  200. {
  201. TYPE *sub11;
  202. TYPE *sub21;
  203. sub11 = (TYPE *)STARPU_MATRIX_GET_PTR(descr[0]);
  204. sub21 = (TYPE *)STARPU_MATRIX_GET_PTR(descr[1]);
  205. unsigned ld11 = STARPU_MATRIX_GET_LD(descr[0]);
  206. unsigned ld21 = STARPU_MATRIX_GET_LD(descr[1]);
  207. unsigned nx21 = STARPU_MATRIX_GET_NX(descr[1]);
  208. unsigned ny21 = STARPU_MATRIX_GET_NY(descr[1]);
  209. #ifdef STARPU_USE_CUDA
  210. cublasStatus status;
  211. #endif
  212. switch (s)
  213. {
  214. case 0:
  215. CPU_TRSM("R", "U", "N", "U", nx21, ny21,
  216. (TYPE)1.0, sub11, ld11, sub21, ld21);
  217. break;
  218. #ifdef STARPU_USE_CUDA
  219. case 1:
  220. CUBLAS_TRSM('R', 'U', 'N', 'U', ny21, nx21,
  221. *(CUBLAS_TYPE*)&p1, (CUBLAS_TYPE*)sub11, ld11, (CUBLAS_TYPE*)sub21, ld21);
  222. status = cublasGetError();
  223. if (status != CUBLAS_STATUS_SUCCESS)
  224. STARPU_CUBLAS_REPORT_ERROR(status);
  225. break;
  226. #endif
  227. default:
  228. STARPU_ABORT();
  229. break;
  230. }
  231. }
  232. void STARPU_LU(cpu_u21)(void *descr[], void *_args)
  233. {
  234. STARPU_LU(common_u21)(descr, 0, _args);
  235. }
  236. #ifdef STARPU_USE_CUDA
  237. void STARPU_LU(cublas_u21)(void *descr[], void *_args)
  238. {
  239. STARPU_LU(common_u21)(descr, 1, _args);
  240. }
  241. #endif
  242. static struct starpu_perfmodel STARPU_LU(model_21) =
  243. {
  244. .type = STARPU_HISTORY_BASED,
  245. #ifdef STARPU_ATLAS
  246. .symbol = STARPU_LU_STR(lu_model_21_atlas)
  247. #elif defined(STARPU_GOTO)
  248. .symbol = STARPU_LU_STR(lu_model_21_goto)
  249. #else
  250. .symbol = STARPU_LU_STR(lu_model_21)
  251. #endif
  252. };
  253. struct starpu_codelet cl21 =
  254. {
  255. .where = STARPU_CPU|STARPU_CUDA,
  256. .cpu_funcs = {STARPU_LU(cpu_u21), NULL},
  257. #ifdef STARPU_USE_CUDA
  258. .cuda_funcs = {STARPU_LU(cublas_u21), NULL},
  259. .cuda_flags = {STARPU_CUDA_ASYNC},
  260. CAN_EXECUTE
  261. #endif
  262. .nbuffers = 2,
  263. .modes = {STARPU_R, STARPU_RW},
  264. .model = &STARPU_LU(model_21)
  265. };
  266. /*
  267. * U11
  268. */
  269. static inline void STARPU_LU(common_u11)(void *descr[],
  270. int s, STARPU_ATTRIBUTE_UNUSED void *_args)
  271. {
  272. TYPE *sub11;
  273. sub11 = (TYPE *)STARPU_MATRIX_GET_PTR(descr[0]);
  274. unsigned long nx = STARPU_MATRIX_GET_NX(descr[0]);
  275. unsigned long ld = STARPU_MATRIX_GET_LD(descr[0]);
  276. unsigned long z;
  277. switch (s)
  278. {
  279. case 0:
  280. for (z = 0; z < nx; z++)
  281. {
  282. TYPE pivot;
  283. pivot = sub11[z+z*ld];
  284. STARPU_ASSERT(fpclassify(pivot) != FP_ZERO);
  285. CPU_SCAL(nx - z - 1, (1.0/pivot), &sub11[z+(z+1)*ld], ld);
  286. CPU_GER(nx - z - 1, nx - z - 1, -1.0,
  287. &sub11[(z+1)+z*ld], 1,
  288. &sub11[z+(z+1)*ld], ld,
  289. &sub11[(z+1) + (z+1)*ld],ld);
  290. }
  291. break;
  292. #ifdef STARPU_USE_CUDA
  293. case 1:
  294. for (z = 0; z < nx; z++)
  295. {
  296. TYPE pivot;
  297. TYPE inv_pivot;
  298. cudaMemcpyAsync(&pivot, &sub11[z+z*ld], sizeof(TYPE), cudaMemcpyDeviceToHost, starpu_cuda_get_local_stream());
  299. cudaStreamSynchronize(starpu_cuda_get_local_stream());
  300. STARPU_ASSERT(fpclassify(pivot) != FP_ZERO);
  301. inv_pivot = 1.0/pivot;
  302. CUBLAS_SCAL(nx - z - 1, *(CUBLAS_TYPE*)&inv_pivot, (CUBLAS_TYPE*)&sub11[z+(z+1)*ld], ld);
  303. CUBLAS_GER(nx - z - 1, nx - z - 1, *(CUBLAS_TYPE*)&m1,
  304. (CUBLAS_TYPE*)&sub11[(z+1)+z*ld], 1,
  305. (CUBLAS_TYPE*)&sub11[z+(z+1)*ld], ld,
  306. (CUBLAS_TYPE*)&sub11[(z+1) + (z+1)*ld],ld);
  307. }
  308. cudaStreamSynchronize(starpu_cuda_get_local_stream());
  309. break;
  310. #endif
  311. default:
  312. STARPU_ABORT();
  313. break;
  314. }
  315. }
  316. void STARPU_LU(cpu_u11)(void *descr[], void *_args)
  317. {
  318. STARPU_LU(common_u11)(descr, 0, _args);
  319. }
  320. #ifdef STARPU_USE_CUDA
  321. void STARPU_LU(cublas_u11)(void *descr[], void *_args)
  322. {
  323. STARPU_LU(common_u11)(descr, 1, _args);
  324. }
  325. #endif /* STARPU_USE_CUDA */
  326. static struct starpu_perfmodel STARPU_LU(model_11) =
  327. {
  328. .type = STARPU_HISTORY_BASED,
  329. #ifdef STARPU_ATLAS
  330. .symbol = STARPU_LU_STR(lu_model_11_atlas)
  331. #elif defined(STARPU_GOTO)
  332. .symbol = STARPU_LU_STR(lu_model_11_goto)
  333. #else
  334. .symbol = STARPU_LU_STR(lu_model_11)
  335. #endif
  336. };
  337. struct starpu_codelet cl11 =
  338. {
  339. .where = STARPU_CPU|STARPU_CUDA,
  340. .cpu_funcs = {STARPU_LU(cpu_u11), NULL},
  341. #ifdef STARPU_USE_CUDA
  342. .cuda_funcs = {STARPU_LU(cublas_u11), NULL},
  343. CAN_EXECUTE
  344. #endif
  345. .nbuffers = 1,
  346. .modes = {STARPU_RW},
  347. .model = &STARPU_LU(model_11)
  348. };
  349. /*
  350. * U11 with pivoting
  351. */
  352. static inline void STARPU_LU(common_u11_pivot)(void *descr[],
  353. int s, void *_args)
  354. {
  355. TYPE *sub11;
  356. sub11 = (TYPE *)STARPU_MATRIX_GET_PTR(descr[0]);
  357. unsigned long nx = STARPU_MATRIX_GET_NX(descr[0]);
  358. unsigned long ld = STARPU_MATRIX_GET_LD(descr[0]);
  359. unsigned long z;
  360. struct piv_s *piv = _args;
  361. unsigned *ipiv = piv->piv;
  362. unsigned first = piv->first;
  363. switch (s)
  364. {
  365. case 0:
  366. for (z = 0; z < nx; z++)
  367. {
  368. TYPE pivot;
  369. pivot = sub11[z+z*ld];
  370. if (fabs((double)(pivot)) < PIVOT_THRESHHOLD)
  371. {
  372. /* find the pivot */
  373. int piv_ind = CPU_IAMAX(nx - z, &sub11[z*(ld+1)], ld);
  374. ipiv[z + first] = piv_ind + z + first;
  375. /* swap if needed */
  376. if (piv_ind != 0)
  377. {
  378. CPU_SWAP(nx, &sub11[z*ld], 1, &sub11[(z+piv_ind)*ld], 1);
  379. }
  380. pivot = sub11[z+z*ld];
  381. }
  382. STARPU_ASSERT(pivot != 0.0);
  383. CPU_SCAL(nx - z - 1, (1.0/pivot), &sub11[z+(z+1)*ld], ld);
  384. CPU_GER(nx - z - 1, nx - z - 1, -1.0,
  385. &sub11[(z+1)+z*ld], 1,
  386. &sub11[z+(z+1)*ld], ld,
  387. &sub11[(z+1) + (z+1)*ld],ld);
  388. }
  389. break;
  390. #ifdef STARPU_USE_CUDA
  391. case 1:
  392. for (z = 0; z < nx; z++)
  393. {
  394. TYPE pivot;
  395. TYPE inv_pivot;
  396. cudaMemcpyAsync(&pivot, &sub11[z+z*ld], sizeof(TYPE), cudaMemcpyDeviceToHost, starpu_cuda_get_local_stream());
  397. cudaStreamSynchronize(starpu_cuda_get_local_stream());
  398. if (fabs((double)(pivot)) < PIVOT_THRESHHOLD)
  399. {
  400. /* find the pivot */
  401. int piv_ind = CUBLAS_IAMAX(nx - z, (CUBLAS_TYPE*)&sub11[z*(ld+1)], ld) - 1;
  402. ipiv[z + first] = piv_ind + z + first;
  403. /* swap if needed */
  404. if (piv_ind != 0)
  405. {
  406. CUBLAS_SWAP(nx, (CUBLAS_TYPE*)&sub11[z*ld], 1, (CUBLAS_TYPE*)&sub11[(z+piv_ind)*ld], 1);
  407. }
  408. cudaMemcpyAsync(&pivot, &sub11[z+z*ld], sizeof(TYPE), cudaMemcpyDeviceToHost, starpu_cuda_get_local_stream());
  409. cudaStreamSynchronize(starpu_cuda_get_local_stream());
  410. }
  411. STARPU_ASSERT(pivot != 0.0);
  412. inv_pivot = 1.0/pivot;
  413. CUBLAS_SCAL(nx - z - 1, *(CUBLAS_TYPE*)&inv_pivot, (CUBLAS_TYPE*)&sub11[z+(z+1)*ld], ld);
  414. CUBLAS_GER(nx - z - 1, nx - z - 1, *(CUBLAS_TYPE*)&m1,
  415. (CUBLAS_TYPE*)&sub11[(z+1)+z*ld], 1,
  416. (CUBLAS_TYPE*)&sub11[z+(z+1)*ld], ld,
  417. (CUBLAS_TYPE*)&sub11[(z+1) + (z+1)*ld],ld);
  418. }
  419. cudaStreamSynchronize(starpu_cuda_get_local_stream());
  420. break;
  421. #endif
  422. default:
  423. STARPU_ABORT();
  424. break;
  425. }
  426. }
  427. void STARPU_LU(cpu_u11_pivot)(void *descr[], void *_args)
  428. {
  429. STARPU_LU(common_u11_pivot)(descr, 0, _args);
  430. }
  431. #ifdef STARPU_USE_CUDA
  432. void STARPU_LU(cublas_u11_pivot)(void *descr[], void *_args)
  433. {
  434. STARPU_LU(common_u11_pivot)(descr, 1, _args);
  435. }
  436. #endif /* STARPU_USE_CUDA */
  437. static struct starpu_perfmodel STARPU_LU(model_11_pivot) =
  438. {
  439. .type = STARPU_HISTORY_BASED,
  440. #ifdef STARPU_ATLAS
  441. .symbol = STARPU_LU_STR(lu_model_11_pivot_atlas)
  442. #elif defined(STARPU_GOTO)
  443. .symbol = STARPU_LU_STR(lu_model_11_pivot_goto)
  444. #else
  445. .symbol = STARPU_LU_STR(lu_model_11_pivot)
  446. #endif
  447. };
  448. struct starpu_codelet cl11_pivot =
  449. {
  450. .where = STARPU_CPU|STARPU_CUDA,
  451. .cpu_funcs = {STARPU_LU(cpu_u11_pivot), NULL},
  452. #ifdef STARPU_USE_CUDA
  453. .cuda_funcs = {STARPU_LU(cublas_u11_pivot), NULL},
  454. CAN_EXECUTE
  455. #endif
  456. .nbuffers = 1,
  457. .modes = {STARPU_RW},
  458. .model = &STARPU_LU(model_11_pivot)
  459. };
  460. /*
  461. * Pivoting
  462. */
  463. static inline void STARPU_LU(common_pivot)(void *descr[],
  464. int s, void *_args)
  465. {
  466. TYPE *matrix;
  467. matrix = (TYPE *)STARPU_MATRIX_GET_PTR(descr[0]);
  468. unsigned long nx = STARPU_MATRIX_GET_NX(descr[0]);
  469. unsigned long ld = STARPU_MATRIX_GET_LD(descr[0]);
  470. unsigned row;
  471. struct piv_s *piv = _args;
  472. unsigned *ipiv = piv->piv;
  473. unsigned first = piv->first;
  474. switch (s)
  475. {
  476. case 0:
  477. for (row = 0; row < nx; row++)
  478. {
  479. unsigned rowpiv = ipiv[row+first] - first;
  480. if (rowpiv != row)
  481. {
  482. CPU_SWAP(nx, &matrix[row*ld], 1, &matrix[rowpiv*ld], 1);
  483. }
  484. }
  485. break;
  486. #ifdef STARPU_USE_CUDA
  487. case 1:
  488. for (row = 0; row < nx; row++)
  489. {
  490. unsigned rowpiv = ipiv[row+first] - first;
  491. if (rowpiv != row)
  492. {
  493. CUBLAS_SWAP(nx, (CUBLAS_TYPE*)&matrix[row*ld], 1, (CUBLAS_TYPE*)&matrix[rowpiv*ld], 1);
  494. }
  495. }
  496. break;
  497. #endif
  498. default:
  499. STARPU_ABORT();
  500. break;
  501. }
  502. }
  503. void STARPU_LU(cpu_pivot)(void *descr[], void *_args)
  504. {
  505. STARPU_LU(common_pivot)(descr, 0, _args);
  506. }
  507. #ifdef STARPU_USE_CUDA
  508. void STARPU_LU(cublas_pivot)(void *descr[], void *_args)
  509. {
  510. STARPU_LU(common_pivot)(descr, 1, _args);
  511. }
  512. #endif /* STARPU_USE_CUDA */
  513. static struct starpu_perfmodel STARPU_LU(model_pivot) =
  514. {
  515. .type = STARPU_HISTORY_BASED,
  516. #ifdef STARPU_ATLAS
  517. .symbol = STARPU_LU_STR(lu_model_pivot_atlas)
  518. #elif defined(STARPU_GOTO)
  519. .symbol = STARPU_LU_STR(lu_model_pivot_goto)
  520. #else
  521. .symbol = STARPU_LU_STR(lu_model_pivot)
  522. #endif
  523. };
  524. struct starpu_codelet cl_pivot =
  525. {
  526. .where = STARPU_CPU|STARPU_CUDA,
  527. .cpu_funcs = {STARPU_LU(cpu_pivot), NULL},
  528. #ifdef STARPU_USE_CUDA
  529. .cuda_funcs = {STARPU_LU(cublas_pivot), NULL},
  530. .cuda_flags = {STARPU_CUDA_ASYNC},
  531. CAN_EXECUTE
  532. #endif
  533. .nbuffers = 1,
  534. .modes = {STARPU_RW},
  535. .model = &STARPU_LU(model_pivot)
  536. };