File: layer_example_bf16.c

package info (click to toggle)
libxsmm 1.17-4
  • links: PTS, VCS
  • area: main
  • in suites: sid, trixie
  • size: 14,976 kB
  • sloc: ansic: 119,587; cpp: 27,680; fortran: 9,179; sh: 5,765; makefile: 5,040; pascal: 2,312; python: 1,812; f90: 1,773
file content (760 lines) | stat: -rw-r--r-- 44,054 bytes parent folder | download | duplicates (2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
/******************************************************************************
* Copyright (c) Intel Corporation - All rights reserved.                      *
* This file is part of the LIBXSMM library.                                   *
*                                                                             *
* For information on the license, see the LICENSE file.                       *
* Further information: https://github.com/hfp/libxsmm/                        *
* SPDX-License-Identifier: BSD-3-Clause                                       *
******************************************************************************/
/* Alexander Heinecke (Intel Corp.)
******************************************************************************/
#include <libxsmm.h>

#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <math.h>
#if defined(_OPENMP)
# include <omp.h>
#endif

/* include c-based dnn library */
#include "../common/dnn_common.h"

#define CHKERR_LIBXSMM_DNN(A) { const int chkerr_libxsmm_dnn_ = A; if (LIBXSMM_DNN_SUCCESS != chkerr_libxsmm_dnn_) { \
  fprintf(stderr, "%s\n", libxsmm_dnn_get_error(chkerr_libxsmm_dnn_)); global_status = chkerr_libxsmm_dnn_; } \
}

int main(int argc, char* argv[])
{
  float *naive_input, *naive_output, *naive_input_add, *naive_delinput_add, *naive_delinput, *naive_deloutput;
  float *naive_input_pad, *naive_output_pad, *naive_input_add_pad, *naive_delinput_add_pad, *naive_delinput_pad, *naive_deloutput_pad;
  libxsmm_bfloat16 *naive_input_pad_bf16, *naive_output_pad_bf16, *naive_input_add_pad_bf16, *naive_delinput_add_pad_bf16, *naive_delinput_pad_bf16, *naive_deloutput_pad_bf16;
  libxsmm_bfloat16 *naive_libxsmm_output, *naive_libxsmm_delinput, *naive_libxsmm_delinput_add;
  float *naive_libxsmm_output_f32, *naive_libxsmm_delinput_f32, *naive_libxsmm_delinput_add_f32;
  float *naive_beta, *naive_gamma, *naive_delbeta, *naive_delgamma, *naive_expectval, *naive_rcpstddev, *naive_variance;
  libxsmm_bfloat16 *input_libxsmm, *output_libxsmm, *input_add_libxsmm, *delinput_libxsmm, *deloutput_libxsmm, *delinput_add_libxsmm;
  float *beta_libxsmm, *gamma_libxsmm, *delbeta_libxsmm, *delgamma_libxsmm, *expectval_libxsmm, *rcpstddev_libxsmm, *variance_libxsmm;
  unsigned char* relumask_libxsmm;

  int ifhp, ifwp, ofhp, ofwp, ofh, ofw;
  int stride_h, stride_w;
  naive_fusedbatchnorm_t naive_param;
  void* scratch;
  size_t scratch_size = 0;

  /* some parameters we can overwrite via cli,
     default is some inner layer of overfeat */
  int iters = 10;         /* repetitions of benchmark */
  int ifw = 14;           /* input width, "W" */
  int ifh = 20;           /* input height, "H" */
  int nImg = 32;          /* mini-batch size, "N" */
  int nFm = 256;          /* number of input feature maps, "C" */
  int stride = 1;         /* stride when accessing inputs */
  int pad_h_in = 0;       /* padding mode */
  int pad_w_in = 0;       /* padding mode */
  int pad_h_out = 0;      /* padding mode */
  int pad_w_out = 0;      /* padding mode */
  int norm_type = 0;      /* 0: full batchnorm, 1: batch scaling only */
  int fuse_type = 0;      /* 0: nothing fused, 1: relu fused, 2: elementwise fused, 3: relu and elementwise fused */
  char type = 'A';        /* 'A': ALL, 'F': FP, 'B': BP, 'U', WU */
  char format = 'L';

  const char *const env_check = getenv("CHECK");
  const double check = LIBXSMM_ABS(0 == env_check ? 1 : atof(env_check));

#if defined(_OPENMP)
  int nThreads = omp_get_max_threads(); /* number of threads */
#else
  int nThreads = 1; /* number of threads */
#endif

  unsigned long long l_start, l_end;
  double l_total = 0.0;
  double gb = 0.0;
  double gib = 0.0;
  int i;
  int relu_no_match;

  libxsmm_dnn_fusedbatchnorm_desc fusedbatchnorm_desc;
  libxsmm_dnn_fusedbatchnorm* libxsmm_handle;
  libxsmm_dnn_tensor*  libxsmm_input;
  libxsmm_dnn_tensor*  libxsmm_delinput;
  libxsmm_dnn_tensor*  libxsmm_output;
  libxsmm_dnn_tensor*  libxsmm_deloutput;
  libxsmm_dnn_tensor*  libxsmm_input_add;
  libxsmm_dnn_tensor*  libxsmm_delinput_add;
  libxsmm_dnn_tensor*  libxsmm_beta;
  libxsmm_dnn_tensor*  libxsmm_gamma;
  libxsmm_dnn_tensor*  libxsmm_delbeta;
  libxsmm_dnn_tensor*  libxsmm_delgamma;
  libxsmm_dnn_tensor*  libxsmm_expectval;
  libxsmm_dnn_tensor*  libxsmm_rcpstddev;
  libxsmm_dnn_tensor*  libxsmm_variance;
  libxsmm_dnn_tensor*  libxsmm_relumask;
  libxsmm_dnn_tensor_datalayout* libxsmm_layout;
  libxsmm_dnn_err_t status;
  libxsmm_dnn_err_t global_status = LIBXSMM_DNN_SUCCESS;

  libxsmm_matdiff_info norms_fwd, norms_bwd, diff;
  libxsmm_matdiff_clear(&norms_fwd);
  libxsmm_matdiff_clear(&norms_bwd);
  libxsmm_matdiff_clear(&diff);

  if (argc > 1 && !strncmp(argv[1], "-h", 3)) {
    printf("Usage: %s iters inpWidth inpHeight nImg nFm pad_w_in pad_h_in pad_w_out pad_h_out stride type format\n", argv[0]);
    return 0;
  }
  libxsmm_rng_set_seed(1);

  /* reading new values from cli */
  i = 1;
  if (argc > i) iters      = atoi(argv[i++]);
  if (argc > i) ifw        = atoi(argv[i++]);
  if (argc > i) ifh        = atoi(argv[i++]);
  if (argc > i) nImg       = atoi(argv[i++]);
  if (argc > i) nFm        = atoi(argv[i++]);
  if (argc > i) pad_w_in   = atoi(argv[i++]);
  if (argc > i) pad_h_in   = atoi(argv[i++]);
  if (argc > i) pad_w_out  = atoi(argv[i++]);
  if (argc > i) pad_h_out  = atoi(argv[i++]);
  if (argc > i) stride     = atoi(argv[i++]);
  if (argc > i) norm_type  = atoi(argv[i++]);
  if (argc > i) fuse_type  = atoi(argv[i++]);
  if (argc > i) type       = *(argv[i++]);

  if (type != 'A' && type != 'F' && type != 'B') {
    printf("type needs to be 'A' (All), 'F' (FP only), 'B' (BP only)\n");
    return -1;
  }
  if ((norm_type != 0) && (norm_type != 1)) {
    printf("norm type needs to be 0 or 1\n");
    return -1;
  }
  if ((fuse_type < 0) || (fuse_type > 5)) {
    printf("fuse type needs to be 0, 1, 2, 3, 4 or 5\n");
    return -1;
  }

  stride_w = stride;
  stride_h = stride;

  /* deriving some values for naive code */
  ofh  = ifh/stride_h;
  ofw  = ifw/stride_w;
  ifhp = ifh + 2 * pad_h_in;
  ifwp = ifw + 2 * pad_w_in;
  ofhp = ofh + 2 * pad_h_out;
  ofwp = ofw + 2 * pad_w_out;

  /* set struct for naive convolution */
  naive_param.N = nImg;
  naive_param.C = nFm;
  naive_param.H = ifh;
  naive_param.W = ifw;
  naive_param.stride_h = stride_h;
  naive_param.stride_w = stride_w;
  naive_param.norm_type = norm_type;
  naive_param.fuse_type = fuse_type;

#if defined(__SSE3__)
  _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);
  _MM_SET_DENORMALS_ZERO_MODE(_MM_DENORMALS_ZERO_ON);
  _MM_SET_ROUNDING_MODE(_MM_ROUND_NEAREST);
#endif

  /* print some summary */
  printf("##########################################\n");
  printf("#          Setting Up (Common)           #\n");
  printf("##########################################\n");
  printf("PARAMS: W:%d  H:%d  N:%d  C:%d  P:%d  Q:%d  STRIDE:%d\n", ifw, ifh, nImg, nFm, ofh, ofw, stride);
  printf("PARAMS: ITERS:%d", iters); if (LIBXSMM_FEQ(0, check)) printf("  Threads:%d\n", nThreads); else printf("\n");
  printf(" InImg %dx%d Padded (%dx%d)\n", ifh, ifw, ifhp, ifwp);
  printf("OutImg %dx%d Padded (%dx%d)\n", ofh, ofw, ofhp, ofwp);
  printf("SIZE Input  (MB): %10.2f MiB\n", (double)(nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16))/(1024.0*1024.0) );
  printf("SIZE Output (MB): %10.2f MiB\n", (double)(nImg*nFm*ofhp*ofwp*sizeof(libxsmm_bfloat16))/(1024.0*1024.0) );
  printf("SIZE Input   (1): %10.2f MiB\n", (double)(1*nFm*ifhp*ifwp*  sizeof(libxsmm_bfloat16))/(1024.0*1024.0) );
  printf("SIZE Output  (1): %10.2f MiB\n", (double)(1*nFm*ofhp*ofwp*  sizeof(libxsmm_bfloat16))/(1024.0*1024.0) );
#if defined(USE_OVERWRITE)
  printf("Using Overwrite Option\n");
#endif

  /* allocate data */
  naive_input                    = (float*)libxsmm_aligned_malloc( nImg*nFm*ifh *ifw *sizeof(float), 2097152);
  naive_input_add                = (float*)libxsmm_aligned_malloc( nImg*nFm*ifh *ifw *sizeof(float), 2097152);
  naive_delinput                 = (float*)libxsmm_aligned_malloc( nImg*nFm*ifh *ifw *sizeof(float), 2097152);
  naive_delinput_add             = (float*)libxsmm_aligned_malloc( nImg*nFm*ifh *ifw *sizeof(float), 2097152);
  naive_output                   = (float*)libxsmm_aligned_malloc( nImg*nFm*ofh *ofw *sizeof(float), 2097152);
  naive_deloutput                = (float*)libxsmm_aligned_malloc( nImg*nFm*ofh *ofw *sizeof(float), 2097152);

  naive_input_pad                = (float*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(float), 2097152);
  naive_input_add_pad            = (float*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(float), 2097152);
  naive_delinput_pad             = (float*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(float), 2097152);
  naive_delinput_add_pad         = (float*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(float), 2097152);
  naive_output_pad               = (float*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(float), 2097152);
  naive_deloutput_pad            = (float*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(float), 2097152);

  naive_input_pad_bf16           = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_input_add_pad_bf16       = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_delinput_pad_bf16        = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_delinput_add_pad_bf16    = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_output_pad_bf16          = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_deloutput_pad_bf16       = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(libxsmm_bfloat16), 2097152);

  naive_libxsmm_output           = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_libxsmm_delinput         = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_libxsmm_delinput_add     = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  naive_libxsmm_output_f32       = (float*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(float), 2097152);
  naive_libxsmm_delinput_f32     = (float*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(float), 2097152);
  naive_libxsmm_delinput_add_f32 = (float*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(float), 2097152);

  input_libxsmm                  = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  delinput_libxsmm               = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  input_add_libxsmm              = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  delinput_add_libxsmm           = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ifhp*ifwp*sizeof(libxsmm_bfloat16), 2097152);
  output_libxsmm                 = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(libxsmm_bfloat16), 2097152);
  deloutput_libxsmm              = (libxsmm_bfloat16*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(libxsmm_bfloat16), 2097152);

  naive_beta                     = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  naive_gamma                    = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  naive_delbeta                  = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  naive_delgamma                 = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  naive_expectval                = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  naive_rcpstddev                = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  naive_variance                 = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);

  beta_libxsmm                   = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  gamma_libxsmm                  = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  delbeta_libxsmm                = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  delgamma_libxsmm               = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  expectval_libxsmm              = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  rcpstddev_libxsmm              = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);
  variance_libxsmm               = (float*)libxsmm_aligned_malloc( nFm*               sizeof(float), 2097152);

  relumask_libxsmm               = (unsigned char*)libxsmm_aligned_malloc( nImg*nFm*ofhp*ofwp*sizeof(unsigned char), 2097152);

 /* initialize data */
  init_buf( naive_input, nImg*nFm*ifh*ifw, 0, 0 );
  copy_internal_nchw( naive_input_pad , naive_input, nImg, nFm, ifh, ifw, pad_h_in, pad_w_in );
  init_buf( naive_delinput, nImg*nFm*ifh*ifw, 0, 0 );
  copy_internal_nchw( naive_delinput_pad, naive_delinput, nImg, nFm, ifh, ifw, pad_h_in, pad_w_in );
  init_buf( naive_input_add, nImg*nFm*ifh*ifw, 0, 0 );
  copy_internal_nchw( naive_input_add_pad, naive_input_add, nImg, nFm, ifh, ifw, pad_h_in, pad_w_in );
  init_buf( naive_delinput_add, nImg*nFm*ifh*ifw, 0, 0 );
  copy_internal_nchw( naive_delinput_add_pad, naive_delinput_add, nImg, nFm, ifh, ifw, pad_h_in, pad_w_in );
  init_buf( naive_output, nImg*nFm*ofh*ofw, 0, 0  );
  copy_internal_nchw( naive_output_pad, naive_output, nImg, nFm, ofh, ofw, pad_h_out, pad_w_out );
  init_buf( naive_deloutput, nImg*nFm*ofh*ofw, 0, 0 );
  copy_internal_nchw( naive_deloutput_pad, naive_deloutput, nImg, nFm, ofh, ofw, pad_h_out, pad_w_out );

  set_zeropad_nchw(naive_input_pad,        nImg, nFm, ifhp, ifwp, pad_h_in,  pad_w_in);
  set_zeropad_nchw(naive_delinput_pad,     nImg, nFm, ifhp, ifwp, pad_h_in,  pad_w_in);
  set_zeropad_nchw(naive_input_add_pad,    nImg, nFm, ifhp, ifwp, pad_h_in,  pad_w_in);
  set_zeropad_nchw(naive_delinput_add_pad, nImg, nFm, ifhp, ifwp, pad_h_in,  pad_w_in);
  set_zeropad_nchw(naive_output_pad,       nImg, nFm, ofhp, ofwp, pad_h_out, pad_w_out);
  set_zeropad_nchw(naive_deloutput_pad,    nImg, nFm, ofhp, ofwp, pad_h_out, pad_w_out);

  libxsmm_rne_convert_fp32_bf16( naive_input_pad,        naive_input_pad_bf16,        nImg*nFm*ifhp*ifwp );
  libxsmm_rne_convert_fp32_bf16( naive_delinput_pad,     naive_delinput_pad_bf16,     nImg*nFm*ifhp*ifwp );
  libxsmm_rne_convert_fp32_bf16( naive_input_add_pad,    naive_input_add_pad_bf16,    nImg*nFm*ifhp*ifwp );
  libxsmm_rne_convert_fp32_bf16( naive_delinput_add_pad, naive_delinput_add_pad_bf16, nImg*nFm*ifhp*ifwp );
  libxsmm_rne_convert_fp32_bf16( naive_output_pad,       naive_output_pad_bf16,       nImg*nFm*ofhp*ofwp );
  libxsmm_rne_convert_fp32_bf16( naive_deloutput_pad,    naive_deloutput_pad_bf16,    nImg*nFm*ofhp*ofwp );

  init_buf(naive_beta,      nFm, 0, 0);
  init_buf(naive_gamma,     nFm, 0, 0);
  init_buf(naive_delbeta,   nFm, 0, 0);
  init_buf(naive_delgamma,  nFm, 0, 0);
  init_buf(naive_expectval, nFm, 0, 0);
  init_buf(naive_rcpstddev, nFm, 0, 0);
  init_buf(naive_variance,  nFm, 0, 0);
  copy_buf(naive_beta,      beta_libxsmm,      nFm);
  copy_buf(naive_gamma,     gamma_libxsmm,     nFm);
  copy_buf(naive_delbeta,   delbeta_libxsmm,   nFm);
  copy_buf(naive_delgamma,  delgamma_libxsmm,  nFm);
  copy_buf(naive_expectval, expectval_libxsmm, nFm);
  copy_buf(naive_rcpstddev, rcpstddev_libxsmm, nFm);
  copy_buf(naive_variance,  variance_libxsmm,  nFm);

  if (LIBXSMM_NEQ(0, check)) {
    printf("##########################################\n");
    printf("#         Computing Reference ...        #\n");
    printf("##########################################\n");
    if (type == 'A' || type == 'F') {
      naive_fusedbatchnorm_fp(&naive_param, naive_input, naive_output, naive_input_add, naive_beta, naive_gamma, naive_expectval, naive_rcpstddev, naive_variance);
    }
    if (type == 'A' || type == 'B') {
      naive_fusedbatchnorm_bp(&naive_param, naive_input, naive_delinput, naive_output, naive_deloutput, naive_delinput_add,
                       naive_beta, naive_delbeta, naive_gamma, naive_delgamma, naive_expectval, naive_rcpstddev);
    }
    printf("##########################################\n");
    printf("#      Computing Reference ... done      #\n");
    printf("##########################################\n");
  }

  if (format == 'A' || format == 'L') {
    printf("\n");
    printf("##########################################\n");
    printf("#      Setting Up  (custom-Storage)      #\n");
    printf("##########################################\n");

    /* setup LIBXSMM handle */
    fusedbatchnorm_desc.partN = nImg;
    fusedbatchnorm_desc.fullN = nImg;
    fusedbatchnorm_desc.C = nFm;
    fusedbatchnorm_desc.H = ifh;
    fusedbatchnorm_desc.W = ifw;
    fusedbatchnorm_desc.u = stride_h;
    fusedbatchnorm_desc.v = stride_w;
    fusedbatchnorm_desc.pad_h_in = pad_h_in;
    fusedbatchnorm_desc.pad_w_in = pad_w_in;
    fusedbatchnorm_desc.pad_h_out = pad_h_out;
    fusedbatchnorm_desc.pad_w_out = pad_w_out;
    fusedbatchnorm_desc.threads = nThreads;
    fusedbatchnorm_desc.datatype_in = LIBXSMM_DNN_DATATYPE_BF16;
    fusedbatchnorm_desc.datatype_out = LIBXSMM_DNN_DATATYPE_BF16;
    fusedbatchnorm_desc.datatype_stats = LIBXSMM_DNN_DATATYPE_F32;
    fusedbatchnorm_desc.buffer_format = LIBXSMM_DNN_TENSOR_FORMAT_LIBXSMM;
    fusedbatchnorm_desc.fuse_order = LIBXSMM_DNN_FUSEDBN_ORDER_BN_ELTWISE_RELU;
    if ( norm_type == 0 ) {
      if ( fuse_type == 0 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BN;
      } else if ( fuse_type == 1 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BN_RELU;
      } else if ( fuse_type == 2 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BN_ELTWISE;
      } else if ( fuse_type == 3 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BN_ELTWISE_RELU;
      } else if ( fuse_type == 4 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BN_RELU_WITH_MASK;
      } else if ( fuse_type == 5 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BN_ELTWISE_RELU_WITH_MASK;
      } else {
        /* shouldn't happen */
        return -1;
      }
    } else {
      if ( fuse_type == 0 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BNSCALE;
      } else if ( fuse_type == 1 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BNSCALE_RELU;
      } else if ( fuse_type == 2 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BNSCALE_ELTWISE;
      } else if ( fuse_type == 3 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BNSCALE_ELTWISE_RELU;
      } else if ( fuse_type == 4 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BNSCALE_RELU_WITH_MASK;
      } else if ( fuse_type == 5 ) {
        fusedbatchnorm_desc.fuse_ops = LIBXSMM_DNN_FUSEDBN_OPS_BNSCALE_ELTWISE_RELU_WITH_MASK;
      } else {
        /* shouldn't happen */
        return -1;
      }
    }

    libxsmm_handle = libxsmm_dnn_create_fusedbatchnorm( fusedbatchnorm_desc, &status );
    CHKERR_LIBXSMM_DNN( status );

    /* setup LIBXSMM buffers */
    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_REGULAR_INPUT, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_input  = libxsmm_dnn_link_tensor( libxsmm_layout, input_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_GRADIENT_INPUT, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_delinput  = libxsmm_dnn_link_tensor( libxsmm_layout, delinput_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_REGULAR_INPUT_ADD, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_input_add  = libxsmm_dnn_link_tensor( libxsmm_layout, input_add_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_GRADIENT_INPUT_ADD, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_delinput_add  = libxsmm_dnn_link_tensor( libxsmm_layout, delinput_add_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_REGULAR_OUTPUT, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_output  = libxsmm_dnn_link_tensor( libxsmm_layout, output_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_GRADIENT_OUTPUT, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_deloutput  = libxsmm_dnn_link_tensor( libxsmm_layout, deloutput_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_REGULAR_CHANNEL_BETA, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_beta  = libxsmm_dnn_link_tensor( libxsmm_layout, beta_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_GRADIENT_CHANNEL_BETA, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_delbeta  = libxsmm_dnn_link_tensor( libxsmm_layout, delbeta_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_REGULAR_CHANNEL_GAMMA, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_gamma  = libxsmm_dnn_link_tensor( libxsmm_layout, gamma_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_GRADIENT_CHANNEL_GAMMA, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_delgamma  = libxsmm_dnn_link_tensor( libxsmm_layout, delgamma_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_CHANNEL_EXPECTVAL, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_expectval  = libxsmm_dnn_link_tensor( libxsmm_layout, expectval_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_CHANNEL_RCPSTDDEV, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_rcpstddev  = libxsmm_dnn_link_tensor( libxsmm_layout, rcpstddev_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_CHANNEL_VARIANCE, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_variance  = libxsmm_dnn_link_tensor( libxsmm_layout, variance_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    libxsmm_layout = libxsmm_dnn_fusedbatchnorm_create_tensor_datalayout( libxsmm_handle, LIBXSMM_DNN_RELU_MASK, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_relumask  = libxsmm_dnn_link_tensor( libxsmm_layout, relumask_libxsmm, &status ); CHKERR_LIBXSMM_DNN( status );
    libxsmm_dnn_destroy_tensor_datalayout( libxsmm_layout );

    /* copy in data to LIBXSMM format */
    /* we can also use the layout functions and set the data on our
       own external to the library */
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyin_tensor( libxsmm_input,        (void*)naive_input_pad_bf16,        LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyin_tensor( libxsmm_output,       (void*)naive_output_pad_bf16,       LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyin_tensor( libxsmm_input_add,    (void*)naive_input_add_pad_bf16,    LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyin_tensor( libxsmm_delinput,     (void*)naive_delinput_pad_bf16,     LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyin_tensor( libxsmm_deloutput,    (void*)naive_deloutput_pad_bf16,    LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyin_tensor( libxsmm_delinput_add, (void*)naive_delinput_add_pad_bf16, LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );

    /* bind buffers and filter to handle */
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_input,        LIBXSMM_DNN_REGULAR_INPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_delinput,     LIBXSMM_DNN_GRADIENT_INPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_output,       LIBXSMM_DNN_REGULAR_OUTPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_deloutput,    LIBXSMM_DNN_GRADIENT_OUTPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_input_add,    LIBXSMM_DNN_REGULAR_INPUT_ADD ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_delinput_add, LIBXSMM_DNN_GRADIENT_INPUT_ADD ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_beta,         LIBXSMM_DNN_REGULAR_CHANNEL_BETA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_gamma,        LIBXSMM_DNN_REGULAR_CHANNEL_GAMMA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_delbeta,      LIBXSMM_DNN_GRADIENT_CHANNEL_BETA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_delgamma,     LIBXSMM_DNN_GRADIENT_CHANNEL_GAMMA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_expectval,    LIBXSMM_DNN_CHANNEL_EXPECTVAL ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_rcpstddev,    LIBXSMM_DNN_CHANNEL_RCPSTDDEV ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_variance,     LIBXSMM_DNN_CHANNEL_VARIANCE ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_tensor( libxsmm_handle, libxsmm_relumask,     LIBXSMM_DNN_RELU_MASK ) );

    /* let's allocate and bind scratch */
    scratch_size = libxsmm_dnn_fusedbatchnorm_get_scratch_size( libxsmm_handle, &status );
    CHKERR_LIBXSMM_DNN( status );
    scratch = libxsmm_aligned_scratch( scratch_size, 2097152 );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_bind_scratch( libxsmm_handle, scratch ) );
    /* set scratch to bogus to make sure that libxsmm takes care of zeroing internally */
    init_buf( (float*)scratch, scratch_size/4, 0, 0 );

    if ((type == 'A' || type == 'F') && LIBXSMM_NEQ(0, check)) {
      printf("##########################################\n");
      printf("#   Correctness - FWD (custom-Storage)   #\n");
      printf("##########################################\n");
      /* run LIBXSMM convolutions */
#if defined(_OPENMP)
#     pragma omp parallel
#endif
      {
#if defined(_OPENMP)
        const int tid = omp_get_thread_num();
#else
        const int tid = 0;
#endif
        CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_execute_st( libxsmm_handle, LIBXSMM_DNN_COMPUTE_KIND_FWD, 0, tid ) );
      }
      /* copy out data */
      CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyout_tensor( libxsmm_output, (void*)naive_libxsmm_output, LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
      libxsmm_convert_bf16_f32( naive_libxsmm_output, naive_libxsmm_output_f32, nImg*nFm*ofhp*ofwp );
      copy_internal_nchw( naive_output_pad, naive_output, nImg, nFm, ofh, ofw, pad_h_out, pad_w_out);

      /* compare */
      printf("rcpstddev:\n");
      libxsmm_matdiff(&norms_fwd, LIBXSMM_DATATYPE_F32, nFm, 1, naive_rcpstddev, rcpstddev_libxsmm, 0, 0);
      printf("L1 reference  : %.25g\n", norms_fwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_fwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_fwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_fwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_fwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_fwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_fwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_fwd);
      printf("variance:\n");
      libxsmm_matdiff(&norms_fwd, LIBXSMM_DATATYPE_F32, nFm, 1, naive_variance, variance_libxsmm, 0, 0);
      printf("L1 reference  : %.25g\n", norms_fwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_fwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_fwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_fwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_fwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_fwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_fwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_fwd);
      printf("expected value:\n");
      libxsmm_matdiff(&norms_fwd, LIBXSMM_DATATYPE_F32, nFm, 1, naive_expectval, expectval_libxsmm, 0, 0);
      printf("L1 reference  : %.25g\n", norms_fwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_fwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_fwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_fwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_fwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_fwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_fwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_fwd);
      printf("output:\n");
      libxsmm_matdiff(&norms_fwd, LIBXSMM_DATATYPE_F32, nImg*nFm*ofhp*ofwp, 1, naive_output_pad, naive_libxsmm_output_f32, 0, 0);
      printf("L1 reference  : %.25g\n", norms_fwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_fwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_fwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_fwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_fwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_fwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_fwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_fwd);

      /* let's check ReLU positions */
      relu_no_match = 0;
      for ( i = 0; i < nImg*nFm*ofhp*ofwp; ++i ) {
        if ( (naive_output_pad[i] == 0.0f && naive_libxsmm_output_f32[i] != 0.0f) ||
             (naive_output_pad[i] != 0.0f && naive_libxsmm_output_f32[i] == 0.0f)    ) {
          relu_no_match++;
        }
      }
      printf("ReLU mismatch count: %i\n", relu_no_match );
    }

    if ( (type == 'A' || type == 'B') && LIBXSMM_NEQ(0, check) ) {
      printf("##########################################\n");
      printf("#   Correctness - BWD (custom-Storage)   #\n");
      printf("##########################################\n");

      /* run LIBXSMM convolutions */
#if defined(_OPENMP)
#     pragma omp parallel
#endif
      {
#if defined(_OPENMP)
        const int tid = omp_get_thread_num();
#else
        const int tid = 0;
#endif
        CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_execute_st( libxsmm_handle, LIBXSMM_DNN_COMPUTE_KIND_BWD, 0, tid ) );
      }

      /* copy out data */
      CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyout_tensor( libxsmm_delinput,     (void*)naive_libxsmm_delinput,     LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
      CHKERR_LIBXSMM_DNN( libxsmm_dnn_copyout_tensor( libxsmm_delinput_add, (void*)naive_libxsmm_delinput_add, LIBXSMM_DNN_TENSOR_FORMAT_NCHW ) );
      libxsmm_convert_bf16_f32( naive_libxsmm_delinput,     naive_libxsmm_delinput_f32,     nImg*nFm*ifhp*ifwp );
      libxsmm_convert_bf16_f32( naive_libxsmm_delinput_add, naive_libxsmm_delinput_add_f32, nImg*nFm*ifhp*ifwp );
      copy_internal_nchw( naive_delinput_pad, naive_delinput, nImg, nFm, ifh, ifw, pad_h_in, pad_w_in);
      copy_internal_nchw( naive_delinput_add_pad, naive_delinput_add, nImg, nFm, ifh, ifw, pad_h_in, pad_w_in);

      /* compare */
      printf("delinput_add:\n");
      libxsmm_matdiff(&norms_bwd, LIBXSMM_DATATYPE_F32, nImg*nFm*ifhp*ifwp, 1, naive_delinput_add_pad, naive_libxsmm_delinput_add_f32, 0, 0);
      printf("L1 reference  : %.25g\n", norms_bwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_bwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_bwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_bwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_bwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_bwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_bwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_bwd);
      printf("delbeta:\n");
      libxsmm_matdiff(&norms_bwd, LIBXSMM_DATATYPE_F32, nFm, 1, naive_delbeta, delbeta_libxsmm, 0, 0);
      printf("L1 reference  : %.25g\n", norms_bwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_bwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_bwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_bwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_bwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_bwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_bwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_bwd);
      printf("delgamma:\n");
      libxsmm_matdiff(&norms_bwd, LIBXSMM_DATATYPE_F32, nFm, 1, naive_delgamma, delgamma_libxsmm, 0, 0);
      printf("L1 reference  : %.25g\n", norms_bwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_bwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_bwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_bwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_bwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_bwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_bwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_bwd);
      printf("delinput:\n");
      libxsmm_matdiff(&norms_bwd, LIBXSMM_DATATYPE_F32, nImg*nFm*ifhp*ifwp, 1, naive_delinput_pad, naive_libxsmm_delinput_f32, 0, 0);
      printf("L1 reference  : %.25g\n", norms_bwd.l1_ref);
      printf("L1 test       : %.25g\n", norms_bwd.l1_tst);
      printf("L2 abs.error  : %.24f\n", norms_bwd.l2_abs);
      printf("L2 rel.error  : %.24f\n", norms_bwd.l2_rel);
      printf("Linf abs.error: %.24f\n", norms_bwd.linf_abs);
      printf("Linf rel.error: %.24f\n", norms_bwd.linf_rel);
      printf("Check-norm    : %.24f\n", norms_bwd.normf_rel);
      libxsmm_matdiff_reduce(&diff, &norms_bwd);
    }

    if (type == 'A' || type == 'F') {
      printf("##########################################\n");
      printf("#   Performance - FWD (custom-Storage)   #\n");
      printf("##########################################\n");
      /* run LIBXSMM convolution for performance */
      l_start = libxsmm_timer_tick();
#if defined(_OPENMP)
#     pragma omp parallel private(i)
#endif
      {
#if defined(_OPENMP)
        const int tid = omp_get_thread_num();
#else
        const int tid = 0;
#endif
        for (i = 0; i < iters; ++i) {
          libxsmm_dnn_fusedbatchnorm_execute_st( libxsmm_handle, LIBXSMM_DNN_COMPUTE_KIND_FWD, 0, tid );
        }
      }
      l_end = libxsmm_timer_tick();
      l_total = libxsmm_timer_duration(l_start, l_end);

      gb = ((double)nImg*(double)nFm*(((double)ifh*(double)ifw) + ((double)ofh*(double)ofw))*(double)sizeof(float)*(double)iters) / (1000*1000*1000);
      gib = ((double)nImg*(double)nFm*(((double)ifh*(double)ifw) + ((double)ofh*(double)ofw))*(double)sizeof(float)*(double)iters) / (1024*1024*1024);

      printf("GB  = %.5g\n", gb/(double)iters);
      printf("GiB  = %.5g\n", gib/(double)iters);
      printf("fp time = %.5g\n", ((double)(l_total/iters)));
      printf("GB/s  = %.5g\n", gb/l_total);
      printf("GiB/s  = %.5g\n", gib/l_total);

      printf("PERFDUMP,FP,%s,%i,%i,%i,%i,%i,%i,%i,%i,%i,%i,%.5g,%.5g,%.5g,%f,%f,%f,%f,%f,%f,%f\n", LIBXSMM_VERSION, nThreads, nImg, nFm,
        ifw, ifh, stride, pad_w_in, pad_h_in, pad_w_out, pad_h_out, ((double)(l_total/iters)), gb/l_total, gib/l_total, norms_fwd.l1_ref, norms_fwd.l1_tst,
        norms_fwd.l2_abs, norms_fwd.l2_rel, norms_fwd.linf_abs, norms_fwd.linf_rel, norms_fwd.normf_rel);
    }

    if ( (type == 'A' || type == 'B') ) {
      printf("##########################################\n");
      printf("#   Performance - BWD (custom-Storage)   #\n");
      printf("##########################################\n");
      /* run LIBXSMM convolution for performance */
      l_start = libxsmm_timer_tick();

#if defined(_OPENMP)
#     pragma omp parallel  private(i)
#endif
      {
#if defined(_OPENMP)
        const int tid = omp_get_thread_num();
#else
        const int tid = 0;
#endif
        for (i = 0; i < iters; ++i) {
          libxsmm_dnn_fusedbatchnorm_execute_st( libxsmm_handle, LIBXSMM_DNN_COMPUTE_KIND_BWD, 0, tid );
        }
      }
      l_end = libxsmm_timer_tick();
      l_total = libxsmm_timer_duration(l_start, l_end);

      gb = (2.0*(double)nImg*(double)nFm*(((double)ifh*(double)ifw) + (2.0*(double)ofh*(double)ofw))*(double)sizeof(float)*(double)iters) / (1000*1000*1000);
      gib = (2.0*(double)nImg*(double)nFm*(((double)ifh*(double)ifw) + (2.0*(double)ofh*(double)ofw))*(double)sizeof(float)*(double)iters) / (1024*1024*1024);

      printf("GB  = %.5g\n", gb/(double)iters);
      printf("GiB  = %.5g\n", gib/(double)iters);
      printf("fp time = %.5g\n", ((double)(l_total/iters)));
      printf("GB/s  = %.5g\n", gb/l_total);
      printf("GiB/s  = %.5g\n", gib/l_total);

      printf("PERFDUMP,BP,%s,%i,%i,%i,%i,%i,%i,%i,%i,%i,%i,%.5g,%.5g,%.5g,%f,%f,%f,%f,%f,%f,%f\n", LIBXSMM_VERSION, nThreads, nImg, nFm,
        ifw, ifh, stride, pad_w_in, pad_h_in, pad_w_out, pad_h_out, ((double)(l_total/iters)), gb/l_total, gib/l_total, norms_bwd.l1_ref, norms_bwd.l1_tst,
        norms_bwd.l2_abs, norms_bwd.l2_rel, norms_bwd.linf_abs, norms_bwd.linf_rel, norms_bwd.normf_rel);
    }

    /* clean-up */
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_scratch( libxsmm_handle ) );
    libxsmm_free(scratch);
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_REGULAR_INPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_GRADIENT_INPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_REGULAR_OUTPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_GRADIENT_OUTPUT ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_REGULAR_INPUT_ADD ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_GRADIENT_INPUT_ADD ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_REGULAR_CHANNEL_BETA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_GRADIENT_CHANNEL_BETA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_REGULAR_CHANNEL_GAMMA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_GRADIENT_CHANNEL_GAMMA ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_CHANNEL_EXPECTVAL ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_CHANNEL_RCPSTDDEV ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_CHANNEL_VARIANCE ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_fusedbatchnorm_release_tensor( libxsmm_handle, LIBXSMM_DNN_RELU_MASK) );

    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_input ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_delinput ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_output ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_deloutput ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_input_add ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_delinput_add ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_beta ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_delbeta ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_gamma ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_delgamma ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_expectval ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_rcpstddev ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_variance ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_tensor( libxsmm_relumask ) );
    CHKERR_LIBXSMM_DNN( libxsmm_dnn_destroy_fusedbatchnorm( libxsmm_handle ) );
  }

  /* deallocate data */
  libxsmm_free(naive_input);
  libxsmm_free(naive_input_add);
  libxsmm_free(naive_output);
  libxsmm_free(naive_delinput);
  libxsmm_free(naive_delinput_add);
  libxsmm_free(naive_deloutput);
  libxsmm_free(naive_input_pad);
  libxsmm_free(naive_input_add_pad);
  libxsmm_free(naive_output_pad);
  libxsmm_free(naive_delinput_pad);
  libxsmm_free(naive_delinput_add_pad);
  libxsmm_free(naive_deloutput_pad);
  libxsmm_free(naive_input_pad_bf16);
  libxsmm_free(naive_input_add_pad_bf16);
  libxsmm_free(naive_output_pad_bf16);
  libxsmm_free(naive_delinput_pad_bf16);
  libxsmm_free(naive_delinput_add_pad_bf16);
  libxsmm_free(naive_deloutput_pad_bf16);
  libxsmm_free(naive_beta);
  libxsmm_free(naive_gamma);
  libxsmm_free(naive_delbeta);
  libxsmm_free(naive_delgamma);
  libxsmm_free(naive_expectval);
  libxsmm_free(naive_rcpstddev);
  libxsmm_free(naive_variance);
  libxsmm_free(naive_libxsmm_output);
  libxsmm_free(naive_libxsmm_delinput);
  libxsmm_free(naive_libxsmm_delinput_add);
  libxsmm_free(naive_libxsmm_output_f32);
  libxsmm_free(naive_libxsmm_delinput_f32);
  libxsmm_free(naive_libxsmm_delinput_add_f32);
  libxsmm_free(input_libxsmm);
  libxsmm_free(input_add_libxsmm);
  libxsmm_free(output_libxsmm);
  libxsmm_free(delinput_libxsmm);
  libxsmm_free(delinput_add_libxsmm);
  libxsmm_free(deloutput_libxsmm);
  libxsmm_free(beta_libxsmm);
  libxsmm_free(gamma_libxsmm);
  libxsmm_free(delbeta_libxsmm);
  libxsmm_free(delgamma_libxsmm);
  libxsmm_free(expectval_libxsmm);
  libxsmm_free(rcpstddev_libxsmm);
  libxsmm_free(variance_libxsmm);
  libxsmm_free(relumask_libxsmm);

  { const char *const env_check_scale = getenv("CHECK_SCALE");
    const double check_scale = LIBXSMM_ABS(0 == env_check_scale ? 1.0 : atof(env_check_scale));
    if (LIBXSMM_NEQ(0, check) && (check < 100.0 * check_scale * diff.normf_rel) && (global_status == LIBXSMM_DNN_SUCCESS)) {
      fprintf(stderr, "FAILED with an error of %f%%!\n", 100.0 * diff.normf_rel);
      exit(EXIT_FAILURE);
    }
  }

  /* some empty lines at the end */
  printf("\n\n\n");

  return global_status;
}