aboutsummaryrefslogtreecommitdiff
path: root/mlir/test/Dialect/SparseTensor/sparse_2d.mlir
blob: 4afa0a8ceccd4b5f05890b99afb3175a0f6f6ca6 (plain)
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
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
// NOTE: Assertions have been autogenerated by utils/generate-test-checks.py
// RUN: mlir-opt %s --sparse-reinterpret-map -sparsification | FileCheck %s

#Tdd = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : dense, d1 : dense) }>
#Tds = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : dense, d1 : compressed) }>
#Tsd = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed, d1 : dense) }>
#Tss = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed, d1 : compressed) }>

#trait2 = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (i,j)>,  // B
    affine_map<(i,j) -> (i,j)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel"],
  doc = "X(i,j) = A(i,j) OP B(i,j)"
}

// CHECK-LABEL:   func @add_dd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_10]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
// CHECK:             %[[VAL_13:.*]] = arith.muli %[[VAL_11]], %[[VAL_4]] : index
// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:               %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_13]] : index
// CHECK:               %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:               %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:               %[[VAL_17:.*]] = arith.addf %[[VAL_15]], %[[VAL_16]] : f32
// CHECK:               memref.store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_18:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<32x16xf32>
// CHECK:           return %[[VAL_18]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_dd(%arga: tensor<32x16xf32, #Tdd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tdd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_dd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_10]] : memref<32x16xi1>)
// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_13:.*]] = arith.muli %[[VAL_11]], %[[VAL_4]] : index
// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_13]] : index
// CHECK:               %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:               %[[VAL_16:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:               %[[VAL_17:.*]] = arith.cmpf ult, %[[VAL_15]], %[[VAL_16]] : f32
// CHECK:               memref.store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_18:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<32x16xi1>
// CHECK:           return %[[VAL_18]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_dd(%arga: tensor<32x16xf32, #Tdd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tdd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_dd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_10]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
// CHECK:             %[[VAL_13:.*]] = arith.muli %[[VAL_11]], %[[VAL_4]] : index
// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:               %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_13]] : index
// CHECK:               %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:               %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:               %[[VAL_17:.*]] = arith.mulf %[[VAL_15]], %[[VAL_16]] : f32
// CHECK:               memref.store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_18:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<32x16xf32>
// CHECK:           return %[[VAL_18]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_dd(%arga: tensor<32x16xf32, #Tdd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tdd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_13]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             %[[VAL_16:.*]] = arith.addi %[[VAL_14]], %[[VAL_7]] : index
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:             %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_15]], %[[VAL_20:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
// CHECK:               %[[VAL_21:.*]] = arith.cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
// CHECK:               scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
// CHECK:               %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               %[[VAL_25:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:               scf.if %[[VAL_25]] {
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xf32>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_28:.*]] = arith.addf %[[VAL_26]], %[[VAL_27]] : f32
// CHECK:                 memref.store %[[VAL_28]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:               } else {
// CHECK:                 scf.if %[[VAL_6]] {
// CHECK:                   %[[VAL_29:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:                   memref.store %[[VAL_29]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:               %[[VAL_30:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:               %[[VAL_31:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:               %[[VAL_32:.*]] = arith.select %[[VAL_30]], %[[VAL_31]], %[[VAL_22]] : index
// CHECK:               %[[VAL_33:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               scf.yield %[[VAL_32]], %[[VAL_33]] : index, index
// CHECK:             }
// CHECK:             scf.for %[[VAL_34:.*]] = %[[VAL_35:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:               memref.store %[[VAL_36]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_37:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16xf32>
// CHECK:           return %[[VAL_37]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_ds(%arga: tensor<32x16xf32, #Tds>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tds>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_14]] : memref<32x16xi1>)
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.addi %[[VAL_15]], %[[VAL_7]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:               %[[VAL_22:.*]] = arith.cmpi ult, %[[VAL_20]], %[[VAL_18]] : index
// CHECK:               scf.condition(%[[VAL_22]]) %[[VAL_20]], %[[VAL_21]] : index, index
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
// CHECK:               %[[VAL_25:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_26:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:               scf.if %[[VAL_26]] {
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_23]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.cmpf ult, %[[VAL_27]], %[[VAL_28]] : f32
// CHECK:                 memref.store %[[VAL_29]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xi1>
// CHECK:               } else {
// CHECK:                 scf.if %[[VAL_8]] {
// CHECK:                   %[[VAL_30:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_31:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_30]] : f32
// CHECK:                   memref.store %[[VAL_31]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xi1>
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:               %[[VAL_32:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:               %[[VAL_33:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               %[[VAL_34:.*]] = arith.select %[[VAL_32]], %[[VAL_33]], %[[VAL_23]] : index
// CHECK:               %[[VAL_35:.*]] = arith.addi %[[VAL_24]], %[[VAL_7]] : index
// CHECK:               scf.yield %[[VAL_34]], %[[VAL_35]] : index, index
// CHECK:             } attributes
// CHECK:             scf.for %[[VAL_36:.*]] = %[[VAL_37:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_36]]] : memref<32x16xf32>
// CHECK:               %[[VAL_39:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_38]] : f32
// CHECK:               memref.store %[[VAL_39]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_36]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_40:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16xi1>
// CHECK:           return %[[VAL_40]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_ds(%arga: tensor<32x16xf32, #Tds>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tds>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_11]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK:             %[[VAL_13:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
// CHECK:             %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_5]] : index
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] {
// CHECK:               %[[VAL_17:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:               %[[VAL_18:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xf32>
// CHECK:               %[[VAL_19:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
// CHECK:               %[[VAL_20:.*]] = arith.mulf %[[VAL_18]], %[[VAL_19]] : f32
// CHECK:               memref.store %[[VAL_20]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_21:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<32x16xf32>
// CHECK:           return %[[VAL_21]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_ds(%arga: tensor<32x16xf32, #Tds>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tds>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_sd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_13]] : memref<32x16xf32>)
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]]:2 = scf.while (%[[VAL_17:.*]] = %[[VAL_14]], %[[VAL_18:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_19:.*]] = arith.cmpi ult, %[[VAL_17]], %[[VAL_15]] : index
// CHECK:             scf.condition(%[[VAL_19]]) %[[VAL_17]], %[[VAL_18]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_20:.*]]: index, %[[VAL_21:.*]]: index):
// CHECK:             %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xindex>
// CHECK:             %[[VAL_23:.*]] = arith.cmpi eq, %[[VAL_22]], %[[VAL_21]] : index
// CHECK:             scf.if %[[VAL_23]] {
// CHECK:               %[[VAL_25:.*]] = arith.muli %[[VAL_20]], %[[VAL_4]] : index
// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_26:.*]] = arith.addi %[[VAL_24]], %[[VAL_25]] : index
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.addf %[[VAL_27]], %[[VAL_28]] : f32
// CHECK:                 memref.store %[[VAL_29]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_5]] {
// CHECK:                 scf.for %[[VAL_30:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_31:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
// CHECK:                   memref.store %[[VAL_31]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_32:.*]] = arith.cmpi eq, %[[VAL_22]], %[[VAL_21]] : index
// CHECK:             %[[VAL_33:.*]] = arith.addi %[[VAL_20]], %[[VAL_7]] : index
// CHECK:             %[[VAL_34:.*]] = arith.select %[[VAL_32]], %[[VAL_33]], %[[VAL_20]] : index
// CHECK:             %[[VAL_35:.*]] = arith.addi %[[VAL_21]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_34]], %[[VAL_35]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_36:.*]] = %[[VAL_37:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_38:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
// CHECK:               memref.store %[[VAL_39]], %[[VAL_13]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_40:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16xf32>
// CHECK:           return %[[VAL_40]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_sd(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_sd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK:           %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_14]] : memref<32x16xi1>)
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_15]], %[[VAL_19:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_20:.*]] = arith.cmpi ult, %[[VAL_18]], %[[VAL_16]] : index
// CHECK:             scf.condition(%[[VAL_20]]) %[[VAL_18]], %[[VAL_19]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_21:.*]]: index, %[[VAL_22:.*]]: index):
// CHECK:             %[[VAL_23:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:             %[[VAL_24:.*]] = arith.cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
// CHECK:             scf.if %[[VAL_24]] {
// CHECK:               %[[VAL_26:.*]] = arith.muli %[[VAL_21]], %[[VAL_3]] : index
// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_27:.*]] = arith.addi %[[VAL_25]], %[[VAL_26]] : index
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xf32>
// CHECK:                 %[[VAL_29:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_25]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_30:.*]] = arith.cmpf ult, %[[VAL_28]], %[[VAL_29]] : f32
// CHECK:                 memref.store %[[VAL_30]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_25]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_8]] {
// CHECK:                 scf.for %[[VAL_31:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_32:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_31]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_33:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_32]] : f32
// CHECK:                   memref.store %[[VAL_33]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_31]]] : memref<32x16xi1>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
// CHECK:             %[[VAL_35:.*]] = arith.addi %[[VAL_21]], %[[VAL_7]] : index
// CHECK:             %[[VAL_36:.*]] = arith.select %[[VAL_34]], %[[VAL_35]], %[[VAL_21]] : index
// CHECK:             %[[VAL_37:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_36]], %[[VAL_37]] : index, index
// CHECK:           } attributes
// CHECK:           scf.for %[[VAL_38:.*]] = %[[VAL_39:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_40:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_38]], %[[VAL_40]]] : memref<32x16xf32>
// CHECK:               %[[VAL_42:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_41]] : f32
// CHECK:               memref.store %[[VAL_42]], %[[VAL_14]]{{\[}}%[[VAL_38]], %[[VAL_40]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_43:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16xi1>
// CHECK:           return %[[VAL_43]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_sd(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_sd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_11]] : memref<32x16xf32>)
// CHECK:           %[[VAL_12:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_5]] {
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.muli %[[VAL_14]], %[[VAL_3]] : index
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK:               %[[VAL_18:.*]] = arith.addi %[[VAL_16]], %[[VAL_17]] : index
// CHECK:               %[[VAL_19:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf32>
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
// CHECK:               %[[VAL_21:.*]] = arith.mulf %[[VAL_19]], %[[VAL_20]] : f32
// CHECK:               memref.store %[[VAL_21]], %[[VAL_11]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_22:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<32x16xf32>
// CHECK:           return %[[VAL_22]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_sd(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_ss(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_15]] : memref<32x16xf32>)
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_16]], %[[VAL_20:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_21:.*]] = arith.cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
// CHECK:             scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
// CHECK:             %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:             %[[VAL_25:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             scf.if %[[VAL_25]] {
// CHECK:               %[[VAL_26:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               %[[VAL_27:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:               %[[VAL_28:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_26]], %[[VAL_31:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_32:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_28]] : index
// CHECK:                 scf.condition(%[[VAL_32]]) %[[VAL_30]], %[[VAL_31]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_33:.*]]: index, %[[VAL_34:.*]]: index):
// CHECK:                 %[[VAL_35:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:                 %[[VAL_36:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 scf.if %[[VAL_36]] {
// CHECK:                   %[[VAL_37:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:                   %[[VAL_38:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_39:.*]] = arith.addf %[[VAL_37]], %[[VAL_38]] : f32
// CHECK:                   memref.store %[[VAL_39]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_5]] {
// CHECK:                     %[[VAL_40:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                     memref.store %[[VAL_40]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_41:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_42:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_43:.*]] = arith.select %[[VAL_41]], %[[VAL_42]], %[[VAL_33]] : index
// CHECK:                 %[[VAL_44:.*]] = arith.addi %[[VAL_34]], %[[VAL_7]] : index
// CHECK:                 scf.yield %[[VAL_43]], %[[VAL_44]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_45:.*]] = %[[VAL_46:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_47:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
// CHECK:                 memref.store %[[VAL_47]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_5]] {
// CHECK:                 scf.for %[[VAL_48:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_49:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
// CHECK:                   memref.store %[[VAL_49]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_50:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             %[[VAL_51:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:             %[[VAL_52:.*]] = arith.select %[[VAL_50]], %[[VAL_51]], %[[VAL_22]] : index
// CHECK:             %[[VAL_53:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_52]], %[[VAL_53]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_56:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_57:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
// CHECK:               memref.store %[[VAL_57]], %[[VAL_15]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_58:.*]] = bufferization.to_tensor %[[VAL_15]] : memref<32x16xf32>
// CHECK:           return %[[VAL_58]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_ss(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK:           %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK:           %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_16]] : memref<32x16xi1>)
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_17]], %[[VAL_21:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_22:.*]] = arith.cmpi ult, %[[VAL_20]], %[[VAL_18]] : index
// CHECK:             scf.condition(%[[VAL_22]]) %[[VAL_20]], %[[VAL_21]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
// CHECK:             %[[VAL_25:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:             %[[VAL_26:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:             scf.if %[[VAL_26]] {
// CHECK:               %[[VAL_27:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_28:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               %[[VAL_29:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_30:.*]]:2 = scf.while (%[[VAL_31:.*]] = %[[VAL_27]], %[[VAL_32:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_33:.*]] = arith.cmpi ult, %[[VAL_31]], %[[VAL_29]] : index
// CHECK:                 scf.condition(%[[VAL_33]]) %[[VAL_31]], %[[VAL_32]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_34:.*]]: index, %[[VAL_35:.*]]: index):
// CHECK:                 %[[VAL_36:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_34]]] : memref<?xindex>
// CHECK:                 %[[VAL_37:.*]] = arith.cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
// CHECK:                 scf.if %[[VAL_37]] {
// CHECK:                   %[[VAL_38:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_34]]] : memref<?xf32>
// CHECK:                   %[[VAL_39:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_40:.*]] = arith.cmpf ult, %[[VAL_38]], %[[VAL_39]] : f32
// CHECK:                   memref.store %[[VAL_40]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xi1>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_8]] {
// CHECK:                     %[[VAL_41:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xf32>
// CHECK:                     %[[VAL_42:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_41]] : f32
// CHECK:                     memref.store %[[VAL_42]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xi1>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_43:.*]] = arith.cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
// CHECK:                 %[[VAL_44:.*]] = arith.addi %[[VAL_34]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_45:.*]] = arith.select %[[VAL_43]], %[[VAL_44]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.addi %[[VAL_35]], %[[VAL_7]] : index
// CHECK:                 scf.yield %[[VAL_45]], %[[VAL_46]] : index, index
// CHECK:               } attributes
// CHECK:               scf.for %[[VAL_47:.*]] = %[[VAL_48:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_49:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_47]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_50:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_49]] : f32
// CHECK:                 memref.store %[[VAL_50]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_47]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_8]] {
// CHECK:                 scf.for %[[VAL_51:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_52:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_51]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_53:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_52]] : f32
// CHECK:                   memref.store %[[VAL_53]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_51]]] : memref<32x16xi1>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:             %[[VAL_55:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:             %[[VAL_56:.*]] = arith.select %[[VAL_54]], %[[VAL_55]], %[[VAL_23]] : index
// CHECK:             %[[VAL_57:.*]] = arith.addi %[[VAL_24]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_56]], %[[VAL_57]] : index, index
// CHECK:           } attributes
// CHECK:           scf.for %[[VAL_58:.*]] = %[[VAL_59:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_60:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_61:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_58]], %[[VAL_60]]] : memref<32x16xf32>
// CHECK:               %[[VAL_62:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_61]] : f32
// CHECK:               memref.store %[[VAL_62]], %[[VAL_16]]{{\[}}%[[VAL_58]], %[[VAL_60]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_63:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16xi1>
// CHECK:           return %[[VAL_63]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_ss(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_12]] : memref<32x16xf32>)
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_4]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_18:.*]] = arith.addi %[[VAL_15]], %[[VAL_4]] : index
// CHECK:             %[[VAL_19:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_20:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_4]] {
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<?xindex>
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xf32>
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
// CHECK:               %[[VAL_24:.*]] = arith.mulf %[[VAL_22]], %[[VAL_23]] : f32
// CHECK:               memref.store %[[VAL_24]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_25:.*]] = bufferization.to_tensor %[[VAL_12]] : memref<32x16xf32>
// CHECK:           return %[[VAL_25]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_ss_ss(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<32x16xf32, #sparse{{[0-9]*}}>, %[[VAL_1:.*1]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_16]] : memref<32x16xf32>)
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_24:.*]] = arith.cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
// CHECK:             %[[VAL_26:.*]] = arith.andi %[[VAL_24]], %[[VAL_25]] : i1
// CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
// CHECK:             %[[VAL_29:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:             %[[VAL_30:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:             %[[VAL_31:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_32:.*]] = arith.select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_33:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_35:.*]] = arith.andi %[[VAL_33]], %[[VAL_34]] : i1
// CHECK:             scf.if %[[VAL_35]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_37:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_40:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
// CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_45:.*]] = arith.cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.andi %[[VAL_45]], %[[VAL_46]] : i1
// CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
// CHECK:                 %[[VAL_50:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
// CHECK:                 %[[VAL_52:.*]] = arith.cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_53:.*]] = arith.select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.andi %[[VAL_54]], %[[VAL_55]] : i1
// CHECK:                 scf.if %[[VAL_56]] {
// CHECK:                   %[[VAL_57:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                   %[[VAL_58:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                   %[[VAL_59:.*]] = arith.addf %[[VAL_57]], %[[VAL_58]] : f32
// CHECK:                   memref.store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                   %[[VAL_60:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                   scf.if %[[VAL_60]] {
// CHECK:                     %[[VAL_61:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                     memref.store %[[VAL_61]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                   } else {
// CHECK:                     %[[VAL_62:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                     scf.if %[[VAL_62]] {
// CHECK:                       %[[VAL_63:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                       memref.store %[[VAL_63]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                     } else {
// CHECK:                     }
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_64:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_65:.*]] = arith.addi %[[VAL_48]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_66:.*]] = arith.select %[[VAL_64]], %[[VAL_65]], %[[VAL_48]] : index
// CHECK:                 %[[VAL_67:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.addi %[[VAL_49]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_69:.*]] = arith.select %[[VAL_67]], %[[VAL_68]], %[[VAL_49]] : index
// CHECK:                 scf.yield %[[VAL_66]], %[[VAL_69]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_70:.*]] = %[[VAL_71:.*]]#0 to %[[VAL_38]] step %[[VAL_4]] {
// CHECK:                 %[[VAL_72:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_70]]] : memref<?xindex>
// CHECK:                 %[[VAL_73:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_70]]] : memref<?xf32>
// CHECK:                 memref.store %[[VAL_73]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_72]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:               scf.for %[[VAL_74:.*]] = %[[VAL_75:.*]]#1 to %[[VAL_41]] step %[[VAL_4]] {
// CHECK:                 %[[VAL_76:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_74]]] : memref<?xindex>
// CHECK:                 %[[VAL_77:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_74]]] : memref<?xf32>
// CHECK:                 memref.store %[[VAL_77]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_76]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               %[[VAL_78:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:               scf.if %[[VAL_78]] {
// CHECK:                 %[[VAL_79:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:                 %[[VAL_80:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_81:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_80]]] : memref<?xindex>
// CHECK:                 scf.for %[[VAL_82:.*]] = %[[VAL_79]] to %[[VAL_81]] step %[[VAL_4]] {
// CHECK:                   %[[VAL_83:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_82]]] : memref<?xindex>
// CHECK:                   %[[VAL_84:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_82]]] : memref<?xf32>
// CHECK:                   memref.store %[[VAL_84]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_83]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:                 %[[VAL_85:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:                 scf.if %[[VAL_85]] {
// CHECK:                   %[[VAL_86:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:                   %[[VAL_87:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:                   %[[VAL_88:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_87]]] : memref<?xindex>
// CHECK:                   scf.for %[[VAL_89:.*]] = %[[VAL_86]] to %[[VAL_88]] step %[[VAL_4]] {
// CHECK:                     %[[VAL_90:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_89]]] : memref<?xindex>
// CHECK:                     %[[VAL_91:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_89]]] : memref<?xf32>
// CHECK:                     memref.store %[[VAL_91]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_90]]] : memref<32x16xf32>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_92:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_93:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:             %[[VAL_94:.*]] = arith.select %[[VAL_92]], %[[VAL_93]], %[[VAL_27]] : index
// CHECK:             %[[VAL_95:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_96:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:             %[[VAL_97:.*]] = arith.select %[[VAL_95]], %[[VAL_96]], %[[VAL_28]] : index
// CHECK:             scf.yield %[[VAL_94]], %[[VAL_97]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_98:.*]] = %[[VAL_99:.*]]#0 to %[[VAL_18]] step %[[VAL_4]] {
// CHECK:             %[[VAL_100:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_98]]] : memref<?xindex>
// CHECK:             %[[VAL_101:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_98]]] : memref<?xindex>
// CHECK:             %[[VAL_102:.*]] = arith.addi %[[VAL_98]], %[[VAL_4]] : index
// CHECK:             %[[VAL_103:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_102]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_104:.*]] = %[[VAL_101]] to %[[VAL_103]] step %[[VAL_4]] {
// CHECK:               %[[VAL_105:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_104]]] : memref<?xindex>
// CHECK:               %[[VAL_106:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_104]]] : memref<?xf32>
// CHECK:               memref.store %[[VAL_106]], %[[VAL_16]]{{\[}}%[[VAL_100]], %[[VAL_105]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           scf.for %[[VAL_107:.*]] = %[[VAL_108:.*]]#1 to %[[VAL_20]] step %[[VAL_4]] {
// CHECK:             %[[VAL_109:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_107]]] : memref<?xindex>
// CHECK:             %[[VAL_110:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_107]]] : memref<?xindex>
// CHECK:             %[[VAL_111:.*]] = arith.addi %[[VAL_107]], %[[VAL_4]] : index
// CHECK:             %[[VAL_112:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_111]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_113:.*]] = %[[VAL_110]] to %[[VAL_112]] step %[[VAL_4]] {
// CHECK:               %[[VAL_114:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_113]]] : memref<?xindex>
// CHECK:               %[[VAL_115:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_113]]] : memref<?xf32>
// CHECK:               memref.store %[[VAL_115]], %[[VAL_16]]{{\[}}%[[VAL_109]], %[[VAL_114]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_116:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16xf32>
// CHECK:           return %[[VAL_116]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #Tss>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32, #Tss>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_ss_ss(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<32x16xf32, #sparse{{[0-9]*}}>, %[[VAL_1:.*1]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_15:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_16:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:           %[[VAL_17:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_3]] : i1) outs(%[[VAL_17]] : memref<32x16xi1>)
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_22:.*]]:2 = scf.while (%[[VAL_23:.*]] = %[[VAL_18]], %[[VAL_24:.*]] = %[[VAL_20]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_19]] : index
// CHECK:             %[[VAL_26:.*]] = arith.cmpi ult, %[[VAL_24]], %[[VAL_21]] : index
// CHECK:             %[[VAL_27:.*]] = arith.andi %[[VAL_25]], %[[VAL_26]] : i1
// CHECK:             scf.condition(%[[VAL_27]]) %[[VAL_23]], %[[VAL_24]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_28:.*]]: index, %[[VAL_29:.*]]: index):
// CHECK:             %[[VAL_30:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:             %[[VAL_31:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_29]]] : memref<?xindex>
// CHECK:             %[[VAL_32:.*]] = arith.cmpi ult, %[[VAL_31]], %[[VAL_30]] : index
// CHECK:             %[[VAL_33:.*]] = arith.select %[[VAL_32]], %[[VAL_31]], %[[VAL_30]] : index
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_33]] : index
// CHECK:             %[[VAL_35:.*]] = arith.cmpi eq, %[[VAL_31]], %[[VAL_33]] : index
// CHECK:             %[[VAL_36:.*]] = arith.andi %[[VAL_34]], %[[VAL_35]] : i1
// CHECK:             scf.if %[[VAL_36]] {
// CHECK:               %[[VAL_37:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_38:.*]] = arith.addi %[[VAL_28]], %[[VAL_5]] : index
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_38]]] : memref<?xindex>
// CHECK:               %[[VAL_40:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_29]]] : memref<?xindex>
// CHECK:               %[[VAL_41:.*]] = arith.addi %[[VAL_29]], %[[VAL_5]] : index
// CHECK:               %[[VAL_42:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_41]]] : memref<?xindex>
// CHECK:               %[[VAL_43:.*]]:2 = scf.while (%[[VAL_44:.*]] = %[[VAL_37]], %[[VAL_45:.*]] = %[[VAL_40]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi ult, %[[VAL_44]], %[[VAL_39]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.cmpi ult, %[[VAL_45]], %[[VAL_42]] : index
// CHECK:                 %[[VAL_48:.*]] = arith.andi %[[VAL_46]], %[[VAL_47]] : i1
// CHECK:                 scf.condition(%[[VAL_48]]) %[[VAL_44]], %[[VAL_45]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_49:.*]]: index, %[[VAL_50:.*]]: index):
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_49]]] : memref<?xindex>
// CHECK:                 %[[VAL_52:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_50]]] : memref<?xindex>
// CHECK:                 %[[VAL_53:.*]] = arith.cmpi ult, %[[VAL_52]], %[[VAL_51]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.select %[[VAL_53]], %[[VAL_52]], %[[VAL_51]] : index
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.cmpi eq, %[[VAL_52]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_57:.*]] = arith.andi %[[VAL_55]], %[[VAL_56]] : i1
// CHECK:                 scf.if %[[VAL_57]] {
// CHECK:                   %[[VAL_58:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                   %[[VAL_59:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_50]]] : memref<?xf32>
// CHECK:                   %[[VAL_60:.*]] = arith.cmpf ult, %[[VAL_58]], %[[VAL_59]] : f32
// CHECK:                   memref.store %[[VAL_60]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_54]]] : memref<32x16xi1>
// CHECK:                 } else {
// CHECK:                   %[[VAL_61:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_54]] : index
// CHECK:                   scf.if %[[VAL_61]] {
// CHECK:                     %[[VAL_62:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                     %[[VAL_63:.*]] = arith.cmpf ult, %[[VAL_62]], %[[VAL_6]] : f32
// CHECK:                     memref.store %[[VAL_63]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_54]]] : memref<32x16xi1>
// CHECK:                   } else {
// CHECK:                     %[[VAL_64:.*]] = arith.cmpi eq, %[[VAL_52]], %[[VAL_54]] : index
// CHECK:                     scf.if %[[VAL_64]] {
// CHECK:                       %[[VAL_65:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_50]]] : memref<?xf32>
// CHECK:                       %[[VAL_66:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_65]] : f32
// CHECK:                       memref.store %[[VAL_66]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_54]]] : memref<32x16xi1>
// CHECK:                     } else {
// CHECK:                     }
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_67:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.addi %[[VAL_49]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_69:.*]] = arith.select %[[VAL_67]], %[[VAL_68]], %[[VAL_49]] : index
// CHECK:                 %[[VAL_70:.*]] = arith.cmpi eq, %[[VAL_52]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_71:.*]] = arith.addi %[[VAL_50]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_72:.*]] = arith.select %[[VAL_70]], %[[VAL_71]], %[[VAL_50]] : index
// CHECK:                 scf.yield %[[VAL_69]], %[[VAL_72]] : index, index
// CHECK:               } attributes
// CHECK:               scf.for %[[VAL_73:.*]] = %[[VAL_74:.*]]#0 to %[[VAL_39]] step %[[VAL_5]] {
// CHECK:                 %[[VAL_75:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_73]]] : memref<?xindex>
// CHECK:                 %[[VAL_76:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_73]]] : memref<?xf32>
// CHECK:                 %[[VAL_77:.*]] = arith.cmpf ult, %[[VAL_76]], %[[VAL_6]] : f32
// CHECK:                 memref.store %[[VAL_77]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_75]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:               scf.for %[[VAL_78:.*]] = %[[VAL_79:.*]]#1 to %[[VAL_42]] step %[[VAL_5]] {
// CHECK:                 %[[VAL_80:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_78]]] : memref<?xindex>
// CHECK:                 %[[VAL_81:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_78]]] : memref<?xf32>
// CHECK:                 %[[VAL_82:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_81]] : f32
// CHECK:                 memref.store %[[VAL_82]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_80]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:             } else {
// CHECK:               %[[VAL_83:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_33]] : index
// CHECK:               scf.if %[[VAL_83]] {
// CHECK:                 %[[VAL_84:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:                 %[[VAL_85:.*]] = arith.addi %[[VAL_28]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_86:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_85]]] : memref<?xindex>
// CHECK:                 scf.for %[[VAL_87:.*]] = %[[VAL_84]] to %[[VAL_86]] step %[[VAL_5]] {
// CHECK:                   %[[VAL_88:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_87]]] : memref<?xindex>
// CHECK:                   %[[VAL_89:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_87]]] : memref<?xf32>
// CHECK:                   %[[VAL_90:.*]] = arith.cmpf ult, %[[VAL_89]], %[[VAL_6]] : f32
// CHECK:                   memref.store %[[VAL_90]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_88]]] : memref<32x16xi1>
// CHECK:                 }
// CHECK:               } else {
// CHECK:                 %[[VAL_91:.*]] = arith.cmpi eq, %[[VAL_31]], %[[VAL_33]] : index
// CHECK:                 scf.if %[[VAL_91]] {
// CHECK:                   %[[VAL_92:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_29]]] : memref<?xindex>
// CHECK:                   %[[VAL_93:.*]] = arith.addi %[[VAL_29]], %[[VAL_5]] : index
// CHECK:                   %[[VAL_94:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_93]]] : memref<?xindex>
// CHECK:                   scf.for %[[VAL_95:.*]] = %[[VAL_92]] to %[[VAL_94]] step %[[VAL_5]] {
// CHECK:                     %[[VAL_96:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_95]]] : memref<?xindex>
// CHECK:                     %[[VAL_97:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_95]]] : memref<?xf32>
// CHECK:                     %[[VAL_98:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_97]] : f32
// CHECK:                     memref.store %[[VAL_98]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_96]]] : memref<32x16xi1>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_99:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_33]] : index
// CHECK:             %[[VAL_100:.*]] = arith.addi %[[VAL_28]], %[[VAL_5]] : index
// CHECK:             %[[VAL_101:.*]] = arith.select %[[VAL_99]], %[[VAL_100]], %[[VAL_28]] : index
// CHECK:             %[[VAL_102:.*]] = arith.cmpi eq, %[[VAL_31]], %[[VAL_33]] : index
// CHECK:             %[[VAL_103:.*]] = arith.addi %[[VAL_29]], %[[VAL_5]] : index
// CHECK:             %[[VAL_104:.*]] = arith.select %[[VAL_102]], %[[VAL_103]], %[[VAL_29]] : index
// CHECK:             scf.yield %[[VAL_101]], %[[VAL_104]] : index, index
// CHECK:           } attributes
// CHECK:           scf.for %[[VAL_105:.*]] = %[[VAL_106:.*]]#0 to %[[VAL_19]] step %[[VAL_5]] {
// CHECK:             %[[VAL_107:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_105]]] : memref<?xindex>
// CHECK:             %[[VAL_108:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_105]]] : memref<?xindex>
// CHECK:             %[[VAL_109:.*]] = arith.addi %[[VAL_105]], %[[VAL_5]] : index
// CHECK:             %[[VAL_110:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_109]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_111:.*]] = %[[VAL_108]] to %[[VAL_110]] step %[[VAL_5]] {
// CHECK:               %[[VAL_112:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_111]]] : memref<?xindex>
// CHECK:               %[[VAL_113:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_111]]] : memref<?xf32>
// CHECK:               %[[VAL_114:.*]] = arith.cmpf ult, %[[VAL_113]], %[[VAL_6]] : f32
// CHECK:               memref.store %[[VAL_114]], %[[VAL_17]]{{\[}}%[[VAL_107]], %[[VAL_112]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           scf.for %[[VAL_115:.*]] = %[[VAL_116:.*]]#1 to %[[VAL_21]] step %[[VAL_5]] {
// CHECK:             %[[VAL_117:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_115]]] : memref<?xindex>
// CHECK:             %[[VAL_118:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_115]]] : memref<?xindex>
// CHECK:             %[[VAL_119:.*]] = arith.addi %[[VAL_115]], %[[VAL_5]] : index
// CHECK:             %[[VAL_120:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_119]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_121:.*]] = %[[VAL_118]] to %[[VAL_120]] step %[[VAL_5]] {
// CHECK:               %[[VAL_122:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_121]]] : memref<?xindex>
// CHECK:               %[[VAL_123:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_121]]] : memref<?xf32>
// CHECK:               %[[VAL_124:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_123]] : f32
// CHECK:               memref.store %[[VAL_124]], %[[VAL_17]]{{\[}}%[[VAL_117]], %[[VAL_122]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_125:.*]] = bufferization.to_tensor %[[VAL_17]] : memref<32x16xi1>
// CHECK:           return %[[VAL_125]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #Tss>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32, #Tss>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

#BatchedVector = #sparse_tensor.encoding<{
  map = (d0, d1) -> (d0 : dense, d1 : loose_compressed)
}>
// CHECK-LABEL:   func.func @sub_ss_batched(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<2x3xf64, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<2x3xf64, #sparse{{[0-9]*}}>) -> tensor<2x3xf64, #sparse{{[0-9]*}}> {
// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 2 : index
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = tensor.empty() : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<2x3xf64, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<2x3xf64, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<2x3xf64, #sparse{{[0-9]*}}> to memref<?xf64>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<2x3xf64, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<2x3xf64, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<2x3xf64, #sparse{{[0-9]*}}> to memref<?xf64>
// CHECK:           %[[VAL_12:.*]] = scf.for %[[VAL_13:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] iter_args(%[[VAL_14:.*]] = %[[VAL_5]]) -> (tensor<2x3xf64, #sparse{{[0-9]*}}>) {
// CHECK:             %[[VAL_15:.*]] = arith.muli %[[VAL_13]], %[[VAL_2]] : index
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.addi %[[VAL_15]], %[[VAL_4]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]] = arith.muli %[[VAL_13]], %[[VAL_2]] : index
// CHECK:             %[[VAL_20:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:             %[[VAL_21:.*]] = arith.addi %[[VAL_19]], %[[VAL_4]] : index
// CHECK:             %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:             %[[VAL_23:.*]]:3 = scf.while (%[[VAL_24:.*]] = %[[VAL_16]], %[[VAL_25:.*]] = %[[VAL_20]], %[[VAL_26:.*]] = %[[VAL_14]])
// CHECK:               %[[VAL_27:.*]] = arith.cmpi ult, %[[VAL_24]], %[[VAL_18]] : index
// CHECK:               %[[VAL_28:.*]] = arith.cmpi ult, %[[VAL_25]], %[[VAL_22]] : index
// CHECK:               %[[VAL_29:.*]] = arith.andi %[[VAL_27]], %[[VAL_28]] : i1
// CHECK:               scf.condition(%[[VAL_29]]) %[[VAL_24]], %[[VAL_25]], %[[VAL_26]] : index, index, tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_30:.*]]: index, %[[VAL_31:.*]]: index, %[[VAL_32:.*]]: tensor<2x3xf64, #sparse{{[0-9]*}}>):
// CHECK:               %[[VAL_33:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_30]]] : memref<?xindex>
// CHECK:               %[[VAL_34:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_31]]] : memref<?xindex>
// CHECK:               %[[VAL_35:.*]] = arith.cmpi ult, %[[VAL_34]], %[[VAL_33]] : index
// CHECK:               %[[VAL_36:.*]] = arith.select %[[VAL_35]], %[[VAL_34]], %[[VAL_33]] : index
// CHECK:               %[[VAL_37:.*]] = arith.cmpi eq, %[[VAL_33]], %[[VAL_36]] : index
// CHECK:               %[[VAL_38:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_36]] : index
// CHECK:               %[[VAL_39:.*]] = arith.andi %[[VAL_37]], %[[VAL_38]] : i1
// CHECK:               %[[VAL_40:.*]] = scf.if %[[VAL_39]] -> (tensor<2x3xf64, #sparse{{[0-9]*}}>) {
// CHECK:                 %[[VAL_41:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_30]]] : memref<?xf64>
// CHECK:                 %[[VAL_42:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_31]]] : memref<?xf64>
// CHECK:                 %[[VAL_43:.*]] = arith.subf %[[VAL_41]], %[[VAL_42]] : f64
// CHECK:                 %[[VAL_44:.*]] = tensor.insert %[[VAL_43]] into %[[VAL_32]]{{\[}}%[[VAL_13]], %[[VAL_36]]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                 scf.yield %[[VAL_44]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:               } else {
// CHECK:                 %[[VAL_45:.*]] = arith.cmpi eq, %[[VAL_33]], %[[VAL_36]] : index
// CHECK:                 %[[VAL_46:.*]] = scf.if %[[VAL_45]] -> (tensor<2x3xf64, #sparse{{[0-9]*}}>) {
// CHECK:                   %[[VAL_47:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_30]]] : memref<?xf64>
// CHECK:                   %[[VAL_48:.*]] = tensor.insert %[[VAL_47]] into %[[VAL_32]]{{\[}}%[[VAL_13]], %[[VAL_36]]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                   scf.yield %[[VAL_48]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                 } else {
// CHECK:                   %[[VAL_49:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_36]] : index
// CHECK:                   %[[VAL_50:.*]] = scf.if %[[VAL_49]] -> (tensor<2x3xf64, #sparse{{[0-9]*}}>) {
// CHECK:                     %[[VAL_51:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_31]]] : memref<?xf64>
// CHECK:                     %[[VAL_52:.*]] = arith.negf %[[VAL_51]] : f64
// CHECK:                     %[[VAL_53:.*]] = tensor.insert %[[VAL_52]] into %[[VAL_32]]{{\[}}%[[VAL_13]], %[[VAL_36]]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                     scf.yield %[[VAL_53]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                   } else {
// CHECK:                     scf.yield %[[VAL_32]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                   }
// CHECK:                   scf.yield %[[VAL_54:.*]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:                 }
// CHECK:                 scf.yield %[[VAL_55:.*]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:               }
// CHECK:               %[[VAL_56:.*]] = arith.cmpi eq, %[[VAL_33]], %[[VAL_36]] : index
// CHECK:               %[[VAL_57:.*]] = arith.addi %[[VAL_30]], %[[VAL_4]] : index
// CHECK:               %[[VAL_58:.*]] = arith.select %[[VAL_56]], %[[VAL_57]], %[[VAL_30]] : index
// CHECK:               %[[VAL_59:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_36]] : index
// CHECK:               %[[VAL_60:.*]] = arith.addi %[[VAL_31]], %[[VAL_4]] : index
// CHECK:               %[[VAL_61:.*]] = arith.select %[[VAL_59]], %[[VAL_60]], %[[VAL_31]] : index
// CHECK:               scf.yield %[[VAL_58]], %[[VAL_61]], %[[VAL_62:.*]] : index, index, tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:             } attributes
// CHECK:             %[[VAL_63:.*]] = scf.for %[[VAL_64:.*]] = %[[VAL_65:.*]]#0 to %[[VAL_18]] step %[[VAL_4]] iter_args(%[[VAL_66:.*]] = %[[VAL_65]]#2)
// CHECK:               %[[VAL_67:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_64]]] : memref<?xindex>
// CHECK:               %[[VAL_68:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_64]]] : memref<?xf64>
// CHECK:               %[[VAL_69:.*]] = tensor.insert %[[VAL_68]] into %[[VAL_66]]{{\[}}%[[VAL_13]], %[[VAL_67]]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:               scf.yield %[[VAL_69]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:             }
// CHECK:             %[[VAL_70:.*]] = scf.for %[[VAL_71:.*]] = %[[VAL_72:.*]]#1 to %[[VAL_22]] step %[[VAL_4]] iter_args(%[[VAL_73:.*]] = %[[VAL_74:.*]])
// CHECK:               %[[VAL_75:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_71]]] : memref<?xindex>
// CHECK:               %[[VAL_76:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_71]]] : memref<?xf64>
// CHECK:               %[[VAL_77:.*]] = arith.negf %[[VAL_76]] : f64
// CHECK:               %[[VAL_78:.*]] = tensor.insert %[[VAL_77]] into %[[VAL_73]]{{\[}}%[[VAL_13]], %[[VAL_75]]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:               scf.yield %[[VAL_78]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:             }
// CHECK:             scf.yield %[[VAL_79:.*]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:           }
// CHECK:           %[[VAL_80:.*]] = sparse_tensor.load %[[VAL_81:.*]] hasInserts : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:           return %[[VAL_80]] : tensor<2x3xf64, #sparse{{[0-9]*}}>
// CHECK:         }
func.func @sub_ss_batched(%0: tensor<2x3xf64, #BatchedVector>, %1: tensor<2x3xf64, #BatchedVector>)
                           -> tensor<2x3xf64, #BatchedVector> {
  %2 = tensor.empty() : tensor<2x3xf64, #BatchedVector>
  %3 = linalg.generic #trait2
       ins(%0, %1 : tensor<2x3xf64, #BatchedVector>, tensor<2x3xf64, #BatchedVector>)
       outs(%2 : tensor<2x3xf64, #BatchedVector>) {
    ^bb0(%in: f64, %in_0: f64, %out: f64):
      %7 = arith.subf %in, %in_0 : f64
      linalg.yield %7 : f64
    } -> tensor<2x3xf64, #BatchedVector>
  return %3 : tensor<2x3xf64, #BatchedVector>
}

// CHECK-LABEL:   func @mul_ss_ss(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<32x16xf32, #sparse{{[0-9]*}}>, %[[VAL_1:.*1]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_16]] : memref<32x16xf32>)
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_24:.*]] = arith.cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
// CHECK:             %[[VAL_26:.*]] = arith.andi %[[VAL_24]], %[[VAL_25]] : i1
// CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
// CHECK:             %[[VAL_29:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:             %[[VAL_30:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:             %[[VAL_31:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_32:.*]] = arith.select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_33:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_35:.*]] = arith.andi %[[VAL_33]], %[[VAL_34]] : i1
// CHECK:             scf.if %[[VAL_35]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_37:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_40:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
// CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_45:.*]] = arith.cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.andi %[[VAL_45]], %[[VAL_46]] : i1
// CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
// CHECK:                 %[[VAL_50:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
// CHECK:                 %[[VAL_52:.*]] = arith.cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_53:.*]] = arith.select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.andi %[[VAL_54]], %[[VAL_55]] : i1
// CHECK:                 scf.if %[[VAL_56]] {
// CHECK:                   %[[VAL_57:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                   %[[VAL_58:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                   %[[VAL_59:.*]] = arith.mulf %[[VAL_57]], %[[VAL_58]] : f32
// CHECK:                   memref.store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                 }
// CHECK:                 %[[VAL_60:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_61:.*]] = arith.addi %[[VAL_48]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_62:.*]] = arith.select %[[VAL_60]], %[[VAL_61]], %[[VAL_48]] : index
// CHECK:                 %[[VAL_63:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_64:.*]] = arith.addi %[[VAL_49]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_65:.*]] = arith.select %[[VAL_63]], %[[VAL_64]], %[[VAL_49]] : index
// CHECK:                 scf.yield %[[VAL_62]], %[[VAL_65]] : index, index
// CHECK:               }
// CHECK:             } else {
// CHECK:             }
// CHECK:             %[[VAL_66:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_67:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:             %[[VAL_68:.*]] = arith.select %[[VAL_66]], %[[VAL_67]], %[[VAL_27]] : index
// CHECK:             %[[VAL_69:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_70:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:             %[[VAL_71:.*]] = arith.select %[[VAL_69]], %[[VAL_70]], %[[VAL_28]] : index
// CHECK:             scf.yield %[[VAL_68]], %[[VAL_71]] : index, index
// CHECK:           }
// CHECK:           %[[VAL_72:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16xf32>
// CHECK:           return %[[VAL_72]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #Tss>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32, #Tss>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_sd_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>, %[[VAL_1:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_15]] : memref<32x16xf32>)
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_16]], %[[VAL_20:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_21:.*]] = arith.cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
// CHECK:             scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
// CHECK:             %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:             %[[VAL_25:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             scf.if %[[VAL_25]] {
// CHECK:               %[[VAL_36:.*]] = arith.muli %[[VAL_22]], %[[VAL_4]] : index
// CHECK:               %[[VAL_26:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_27:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_26]], %[[VAL_31:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_32:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_28]] : index
// CHECK:                 scf.condition(%[[VAL_32]]) %[[VAL_30]], %[[VAL_31]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_33:.*]]: index, %[[VAL_34:.*]]: index):
// CHECK:                 %[[VAL_35:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:                 %[[VAL_37:.*]] = arith.addi %[[VAL_34]], %[[VAL_36]] : index
// CHECK:                 %[[VAL_38:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 scf.if %[[VAL_38]] {
// CHECK:                   %[[VAL_39:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_37]]] : memref<?xf32>
// CHECK:                   %[[VAL_40:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:                   %[[VAL_41:.*]] = arith.addf %[[VAL_39]], %[[VAL_40]] : f32
// CHECK:                   memref.store %[[VAL_41]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_6]] {
// CHECK:                     %[[VAL_42:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_37]]] : memref<?xf32>
// CHECK:                     memref.store %[[VAL_42]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_43:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_44:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_45:.*]] = arith.select %[[VAL_43]], %[[VAL_44]], %[[VAL_33]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.addi %[[VAL_34]], %[[VAL_7]] : index
// CHECK:                 scf.yield %[[VAL_45]], %[[VAL_46]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_47:.*]] = %[[VAL_48:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_50:.*]] = arith.addi %[[VAL_47]], %[[VAL_36]] : index
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_50]]] : memref<?xf32>
// CHECK:                 memref.store %[[VAL_51]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_47]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_6]] {
// CHECK:                 %[[VAL_52:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:                 %[[VAL_53:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_54:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_53]]] : memref<?xindex>
// CHECK:                 scf.for %[[VAL_55:.*]] = %[[VAL_52]] to %[[VAL_54]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_56:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_55]]] : memref<?xindex>
// CHECK:                   %[[VAL_57:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_55]]] : memref<?xf32>
// CHECK:                   memref.store %[[VAL_57]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_56]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_58:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             %[[VAL_59:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:             %[[VAL_60:.*]] = arith.select %[[VAL_58]], %[[VAL_59]], %[[VAL_22]] : index
// CHECK:             %[[VAL_61:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_60]], %[[VAL_61]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_62:.*]] = %[[VAL_63:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_64:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_62]]] : memref<?xindex>
// CHECK:             %[[VAL_65:.*]] = arith.addi %[[VAL_62]], %[[VAL_7]] : index
// CHECK:             %[[VAL_66:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_65]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_67:.*]] = %[[VAL_64]] to %[[VAL_66]] step %[[VAL_7]] {
// CHECK:               %[[VAL_68:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_67]]] : memref<?xindex>
// CHECK:               %[[VAL_69:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_67]]] : memref<?xf32>
// CHECK:               memref.store %[[VAL_69]], %[[VAL_15]]{{\[}}%[[VAL_62]], %[[VAL_68]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_70:.*]] = bufferization.to_tensor %[[VAL_15]] : memref<32x16xf32>
// CHECK:           return %[[VAL_70]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_sd_ds(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32, #Tds>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32, #Tds>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @mul_sd_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>, %[[VAL_1:.*]]: tensor<32x16xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_13]] : memref<32x16xf32>)
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_16:.*]] = %[[VAL_14]] to %[[VAL_15]] step %[[VAL_5]] {
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:             %[[VAL_23:.*]] = arith.muli %[[VAL_16]], %[[VAL_3]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]] = arith.addi %[[VAL_17]], %[[VAL_5]] : index
// CHECK:             %[[VAL_20:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_5]] {
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:               %[[VAL_24:.*]] = arith.addi %[[VAL_22]], %[[VAL_23]] : index
// CHECK:               %[[VAL_25:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_24]]] : memref<?xf32>
// CHECK:               %[[VAL_26:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]]] : memref<?xf32>
// CHECK:               %[[VAL_27:.*]] = arith.mulf %[[VAL_25]], %[[VAL_26]] : f32
// CHECK:               memref.store %[[VAL_27]], %[[VAL_13]]{{\[}}%[[VAL_17]], %[[VAL_22]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_28:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16xf32>
// CHECK:           return %[[VAL_28]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_sd_ds(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32, #Tds>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32, #Tds>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

#trait_matvec = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (j)>,    // b
    affine_map<(i,j) -> (i)>     // x (out)
  ],
  iterator_types = ["parallel", "reduction"],
  doc = "x(i) += SUM_j A(i,j) * b(j)"
}

// CHECK-LABEL:   func @matvec(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<16x32xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<16xf32>) -> tensor<16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<16x32xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<16x32xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<16x32xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<16xf32>
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK-DAG:         %[[VAL_13:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
// CHECK-DAG:         %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_5]] : index
// CHECK-DAG:         %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK-DAG:         %[[VAL_16:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
// CHECK:             %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f32) {
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf32>
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<32xf32>
// CHECK:               %[[VAL_23:.*]] = arith.mulf %[[VAL_21]], %[[VAL_22]] : f32
// CHECK:               %[[VAL_24:.*]] = arith.addf %[[VAL_23]], %[[VAL_19]] : f32
// CHECK:               scf.yield %[[VAL_24]] : f32
// CHECK:             }
// CHECK:             memref.store %[[VAL_17]], %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
// CHECK:           }
// CHECK:           %[[VAL_26:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<16xf32>
// CHECK:           return %[[VAL_26]] : tensor<16xf32>
// CHECK:         }
func.func @matvec(%argA: tensor<16x32xf32, #Tds>, %argb: tensor<32xf32>, %argx: tensor<16xf32>) -> tensor<16xf32> {
  %0 = linalg.generic #trait_matvec
       ins(%argA, %argb: tensor<16x32xf32, #Tds>, tensor<32xf32>)
      outs(%argx: tensor<16xf32>) {
    ^bb(%A: f32, %b: f32, %x: f32):
      %0 = arith.mulf %A, %b : f32
      %1 = arith.addf %0, %x : f32
      linalg.yield %1 : f32
  } -> tensor<16xf32>
  return %0 : tensor<16xf32>
}

#trait_sum_reduction = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>, // A
    affine_map<(i,j) -> ()>     // x (scalar out)
  ],
  iterator_types = ["reduction", "reduction"],
  doc = "x += SUM_ij A(i,j)"
}

// CHECK-LABEL:   func @sum_reduction(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<10x20xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<f32>) -> tensor<f32> {
// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 10 : index
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<10x20xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<10x20xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_1]] : memref<f32>
// CHECK:           %[[VAL_9:.*]] = memref.load %[[VAL_8]][] : memref<f32>
// CHECK:           %[[VAL_10:.*]] = scf.for %[[VAL_11:.*]] = %[[VAL_4]] to %[[VAL_2]] step %[[VAL_3]] iter_args(%[[VAL_12:.*]] = %[[VAL_9]]) -> (f32) {
// CHECK:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xindex>
// CHECK:             %[[VAL_14:.*]] = arith.addi %[[VAL_11]], %[[VAL_3]] : index
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             %[[VAL_16:.*]] = scf.for %[[VAL_17:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_3]] iter_args(%[[VAL_18:.*]] = %[[VAL_12]]) -> (f32) {
// CHECK:               %[[VAL_19:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_17]]] : memref<?xf32>
// CHECK:               %[[VAL_20:.*]] = arith.addf %[[VAL_18]], %[[VAL_19]] : f32
// CHECK:               scf.yield %[[VAL_20]] : f32
// CHECK:             }
// CHECK:             scf.yield %[[VAL_16]] : f32
// CHECK:           }
// CHECK:           memref.store %[[VAL_10]], %[[VAL_8]][] : memref<f32>
// CHECK:           %[[VAL_23:.*]] = bufferization.to_tensor %[[VAL_8]] : memref<f32>
// CHECK:           return %[[VAL_23]] : tensor<f32>
// CHECK:         }
func.func @sum_reduction(%arga: tensor<10x20xf32, #Tds>, %argx: tensor<f32>) -> tensor<f32> {
  %0 = linalg.generic #trait_sum_reduction
     ins(%arga: tensor<10x20xf32, #Tds>)
    outs(%argx: tensor<f32>) {
      ^bb(%a: f32, %x: f32):
        %0 = arith.addf %x, %a : f32
        linalg.yield %0 : f32
  } -> tensor<f32>
  return %0 : tensor<f32>
}

#trait_scale = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (i,j)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel"],
  doc = "X(i,j) = A(i,j) * SCALE"
}

// CHECK-LABEL:   func @scale(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<?x?xf64, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<?x?xf64>) -> tensor<?x?xf64> {
// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 2.000000e+00 : f64
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<?x?xf64, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<?x?xf64, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<?x?xf64, #sparse{{[0-9]*}}> to memref<?xf64>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.lvl %[[VAL_0]], %[[VAL_3]] : tensor<?x?xf64, #sparse{{[0-9]*}}>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<?x?xf64>
// CHECK:           linalg.fill ins(%{{.*}} : f64) outs(%[[VAL_11]] : memref<?x?xf64>)
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_3]] to %[[VAL_8]] step %[[VAL_4]] {
// CHECK:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_12]]] : memref<?xindex>
// CHECK:             %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_4]] : index
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_4]] {
// CHECK:               %[[VAL_17:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:               %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xf64>
// CHECK:               %[[VAL_19:.*]] = arith.mulf %[[VAL_18]], %[[VAL_2]] : f64
// CHECK:               memref.store %[[VAL_19]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<?x?xf64>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_20:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<?x?xf64>
// CHECK:           return %[[VAL_20]] : tensor<?x?xf64>
// CHECK:         }
func.func @scale(%arga: tensor<?x?xf64, #Tds>, %argx: tensor<?x?xf64>) -> tensor<?x?xf64> {
  %0 = arith.constant 2.0 : f64
  %1 = linalg.generic #trait_scale
     ins(%arga: tensor<?x?xf64, #Tds>)
    outs(%argx: tensor<?x?xf64>) {
      ^bb(%a: f64, %x: f64):
        %2 = arith.mulf %a, %0 : f64
        linalg.yield %2 : f64
  } -> tensor<?x?xf64>
  return %1 : tensor<?x?xf64>
}

#trait_sampled_dense_dense = {
  indexing_maps = [
    affine_map<(i,j,k) -> (i,j)>,  // S
    affine_map<(i,j,k) -> (i,k)>,  // A
    affine_map<(i,j,k) -> (k,j)>,  // B
    affine_map<(i,j,k) -> (i,j)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel", "reduction"],
  doc = "X(i,j) += S(i,j) SUM_k A(i,k) B(k,j)"
}

// CHECK-LABEL:   func.func @sampled_dense_dense(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<?x?xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<?x?xf32>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<?x?xf32>,
// CHECK-SAME:      %[[VAL_3:.*3]]: tensor<?x?xf32>) -> tensor<?x?xf32> {
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = tensor.dim %[[VAL_1]], %[[VAL_4]] : tensor<?x?xf32>
// CHECK-DAG:       %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_1]] : memref<?x?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<?x?xf32>
// CHECK-DAG:       %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_3]] : memref<?x?xf32>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_15]] to %[[VAL_16]] step %[[VAL_4]] {
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_11]] step %[[VAL_4]] {
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_18]], %[[VAL_19]]] : memref<?x?xf32>
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:               %[[VAL_22:.*]] = arith.addi %[[VAL_17]], %[[VAL_4]] : index
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_4]] {
// CHECK:                 %[[VAL_25:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xindex>
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_25]]] : memref<?x?xf32>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_19]], %[[VAL_25]]] : memref<?x?xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.mulf %[[VAL_20]], %[[VAL_28]] : f32
// CHECK:                 %[[VAL_30:.*]] = arith.mulf %[[VAL_27]], %[[VAL_29]] : f32
// CHECK:                 %[[VAL_31:.*]] = arith.addf %[[VAL_26]], %[[VAL_30]] : f32
// CHECK:                 memref.store %[[VAL_31]], %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_25]]] : memref<?x?xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_32:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<?x?xf32>
// CHECK:           return %[[VAL_32]] : tensor<?x?xf32>
// CHECK:         }
func.func @sampled_dense_dense(%args: tensor<?x?xf32, #Tss>,
                          %arga: tensor<?x?xf32>,
                          %argb: tensor<?x?xf32>,
                          %argx: tensor<?x?xf32>) -> tensor<?x?xf32> {
  %0 = linalg.generic #trait_sampled_dense_dense
     ins(%args, %arga, %argb: tensor<?x?xf32, #Tss>, tensor<?x?xf32>, tensor<?x?xf32>)
    outs(%argx: tensor<?x?xf32>) {
      ^bb(%s: f32, %a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        %1 = arith.mulf %s, %0 : f32
        %2 = arith.addf %x, %1 : f32
        linalg.yield %2 : f32
  } -> tensor<?x?xf32>
  return %0 : tensor<?x?xf32>
}

#trait_sum_kernel_with_inv = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (i,j)>,  // B
    affine_map<(i,j) -> (i,j)>,  // C
    affine_map<(i,j) -> (i)>,    // d
    affine_map<(i,j) -> ()>,     // e
    affine_map<(i,j) -> (i)>     // x (out)
  ],
  iterator_types = ["parallel", "reduction"],
  doc = "x(i) = SUM_j A(i,j) * B(i,j) * d(i) * e + C(i,j)"
}

// CHECK-LABEL:   func @sum_kernel_with_inv(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<?x?xf32, #sparse{{[0-9]*}}>, %[[VAL_1:.*1]]: tensor<?x?xf32, #sparse{{[0-9]*}}>, %[[VAL_2:.*2]]: tensor<?x?xf32, #sparse{{[0-9]*}}>,
// CHECK-SAME:      %[[VAL_3:.*3]]: tensor<?xf32>,
// CHECK-SAME:      %[[VAL_4:.*4]]: tensor<f32>,
// CHECK-SAME:      %[[VAL_5:.*5]]: tensor<?xf32>) -> tensor<?xf32> {
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_15:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_17:.*]] = sparse_tensor.positions %[[VAL_2]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_18:.*]] = sparse_tensor.coordinates %[[VAL_2]] {level = 1 : index} : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xindex>
// CHECK-DAG:       %[[VAL_19:.*]] = sparse_tensor.values %[[VAL_2]] : tensor<?x?xf32, #sparse{{[0-9]*}}> to memref<?xf32>
// CHECK-DAG:       %[[VAL_20:.*]] = bufferization.to_memref %[[VAL_3]] : memref<?xf32>
// CHECK-DAG:       %[[VAL_21:.*]] = bufferization.to_memref %[[VAL_4]] : memref<f32>
// CHECK-DAG:       %[[VAL_22:.*]] = sparse_tensor.lvl %[[VAL_2]], %[[VAL_6]] : tensor<?x?xf32,
// CHECK-DAG:       %[[VAL_24:.*]] = bufferization.to_memref %[[VAL_5]] : memref<?xf32>
// CHECK:           %[[VAL_25:.*]] = memref.load %[[VAL_21]][] : memref<f32>
// CHECK:           %[[VAL_26:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_27:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_28:.*]]:2 = scf.while (%[[VAL_29:.*]] = %[[VAL_26]], %[[VAL_30:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_31:.*]] = arith.cmpi ult, %[[VAL_29]], %[[VAL_27]] : index
// CHECK:             scf.condition(%[[VAL_31]]) %[[VAL_29]], %[[VAL_30]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_32:.*]]: index, %[[VAL_33:.*]]: index):
// CHECK:             %[[VAL_34:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_32]]] : memref<?xindex>
// CHECK:             %[[VAL_35:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_33]] : index
// CHECK:             scf.if %[[VAL_35]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:               %[[VAL_37:.*]] = memref.load %[[VAL_20]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_32]]] : memref<?xindex>
// CHECK:               %[[VAL_39:.*]] = arith.addi %[[VAL_32]], %[[VAL_7]] : index
// CHECK:               %[[VAL_40:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_39]]] : memref<?xindex>
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:               %[[VAL_42:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:               %[[VAL_43:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_42]]] : memref<?xindex>
// CHECK:               %[[VAL_44:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:               %[[VAL_45:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:               %[[VAL_46:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_45]]] : memref<?xindex>
// CHECK:               %[[VAL_47:.*]]:4 = scf.while (%[[VAL_48:.*]] = %[[VAL_38]], %[[VAL_49:.*]] = %[[VAL_41]], %[[VAL_50:.*]] = %[[VAL_44]], %[[VAL_51:.*]] = %[[VAL_36]]) : (index, index, index, f32) -> (index, index, index, f32) {
// CHECK:                 %[[VAL_52:.*]] = arith.cmpi ult, %[[VAL_48]], %[[VAL_40]] : index
// CHECK:                 %[[VAL_53:.*]] = arith.cmpi ult, %[[VAL_49]], %[[VAL_43]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.andi %[[VAL_52]], %[[VAL_53]] : i1
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi ult, %[[VAL_50]], %[[VAL_46]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.andi %[[VAL_54]], %[[VAL_55]] : i1
// CHECK:                 scf.condition(%[[VAL_56]]) %[[VAL_48]], %[[VAL_49]], %[[VAL_50]], %[[VAL_51]] : index, index, index, f32
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_57:.*]]: index, %[[VAL_58:.*]]: index, %[[VAL_59:.*]]: index, %[[VAL_60:.*]]: f32):
// CHECK-DAG:             %[[VAL_61:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_57]]] : memref<?xindex>
// CHECK-DAG:             %[[VAL_62:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_58]]] : memref<?xindex>
// CHECK-DAG:             %[[VAL_65:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_59]]] : memref<?xindex>
// CHECK:                 %[[VAL_63:.*]] = arith.cmpi ult, %[[VAL_62]], %[[VAL_61]] : index
// CHECK:                 %[[VAL_64:.*]] = arith.select %[[VAL_63]], %[[VAL_62]], %[[VAL_61]] : index
// CHECK:                 %[[VAL_66:.*]] = arith.cmpi ult, %[[VAL_65]], %[[VAL_64]] : index
// CHECK:                 %[[VAL_67:.*]] = arith.select %[[VAL_66]], %[[VAL_65]], %[[VAL_64]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.cmpi eq, %[[VAL_61]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_69:.*]] = arith.cmpi eq, %[[VAL_62]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_70:.*]] = arith.andi %[[VAL_68]], %[[VAL_69]] : i1
// CHECK:                 %[[VAL_71:.*]] = arith.cmpi eq, %[[VAL_65]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_72:.*]] = arith.andi %[[VAL_70]], %[[VAL_71]] : i1
// CHECK:                 %[[VAL_73:.*]] = scf.if %[[VAL_72]] -> (f32) {
// CHECK:                   %[[VAL_74:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_57]]] : memref<?xf32>
// CHECK:                   %[[VAL_75:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_58]]] : memref<?xf32>
// CHECK:                   %[[VAL_76:.*]] = arith.mulf %[[VAL_74]], %[[VAL_75]] : f32
// CHECK:                   %[[VAL_77:.*]] = arith.mulf %[[VAL_76]], %[[VAL_37]] : f32
// CHECK:                   %[[VAL_78:.*]] = arith.mulf %[[VAL_77]], %[[VAL_25]] : f32
// CHECK:                   %[[VAL_79:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_59]]] : memref<?xf32>
// CHECK:                   %[[VAL_80:.*]] = arith.addf %[[VAL_78]], %[[VAL_79]] : f32
// CHECK:                   %[[VAL_81:.*]] = arith.addf %[[VAL_60]], %[[VAL_80]] : f32
// CHECK:                   scf.yield %[[VAL_81]] : f32
// CHECK:                 } else {
// CHECK:                   %[[VAL_82:.*]] = arith.cmpi eq, %[[VAL_61]], %[[VAL_67]] : index
// CHECK:                   %[[VAL_83:.*]] = arith.cmpi eq, %[[VAL_62]], %[[VAL_67]] : index
// CHECK:                   %[[VAL_84:.*]] = arith.andi %[[VAL_82]], %[[VAL_83]] : i1
// CHECK:                   %[[VAL_85:.*]] = scf.if %[[VAL_84]] -> (f32) {
// CHECK:                     %[[VAL_86:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_57]]] : memref<?xf32>
// CHECK:                     %[[VAL_87:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_58]]] : memref<?xf32>
// CHECK:                     %[[VAL_88:.*]] = arith.mulf %[[VAL_86]], %[[VAL_87]] : f32
// CHECK:                     %[[VAL_89:.*]] = arith.mulf %[[VAL_88]], %[[VAL_37]] : f32
// CHECK:                     %[[VAL_90:.*]] = arith.mulf %[[VAL_89]], %[[VAL_25]] : f32
// CHECK:                     %[[VAL_91:.*]] = arith.addf %[[VAL_60]], %[[VAL_90]] : f32
// CHECK:                     scf.yield %[[VAL_91]] : f32
// CHECK:                   } else {
// CHECK:                     %[[VAL_92:.*]] = arith.cmpi eq, %[[VAL_65]], %[[VAL_67]] : index
// CHECK:                     %[[VAL_93:.*]] = scf.if %[[VAL_92]] -> (f32) {
// CHECK:                       %[[VAL_94:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_59]]] : memref<?xf32>
// CHECK:                       %[[VAL_95:.*]] = arith.addf %[[VAL_60]], %[[VAL_94]] : f32
// CHECK:                       scf.yield %[[VAL_95]] : f32
// CHECK:                     } else {
// CHECK:                       scf.yield %[[VAL_60]] : f32
// CHECK:                     }
// CHECK:                     scf.yield %[[VAL_96:.*]] : f32
// CHECK:                   }
// CHECK:                   scf.yield %[[VAL_97:.*]] : f32
// CHECK:                 }
// CHECK:                 %[[VAL_98:.*]] = arith.cmpi eq, %[[VAL_61]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_99:.*]] = arith.addi %[[VAL_57]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_100:.*]] = arith.select %[[VAL_98]], %[[VAL_99]], %[[VAL_57]] : index
// CHECK:                 %[[VAL_101:.*]] = arith.cmpi eq, %[[VAL_62]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_102:.*]] = arith.addi %[[VAL_58]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_103:.*]] = arith.select %[[VAL_101]], %[[VAL_102]], %[[VAL_58]] : index
// CHECK:                 %[[VAL_104:.*]] = arith.cmpi eq, %[[VAL_65]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_105:.*]] = arith.addi %[[VAL_59]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_106:.*]] = arith.select %[[VAL_104]], %[[VAL_105]], %[[VAL_59]] : index
// CHECK:                 scf.yield %[[VAL_100]], %[[VAL_103]], %[[VAL_106]], %[[VAL_107:.*]] : index, index, index, f32
// CHECK:               }
// CHECK:               %[[VAL_108:.*]]:3 = scf.while (%[[VAL_109:.*]] = %[[VAL_110:.*]]#0, %[[VAL_111:.*]] = %[[VAL_110]]#1, %[[VAL_112:.*]] = %[[VAL_110]]#3) : (index, index, f32) -> (index, index, f32) {
// CHECK:                 %[[VAL_113:.*]] = arith.cmpi ult, %[[VAL_109]], %[[VAL_40]] : index
// CHECK:                 %[[VAL_114:.*]] = arith.cmpi ult, %[[VAL_111]], %[[VAL_43]] : index
// CHECK:                 %[[VAL_115:.*]] = arith.andi %[[VAL_113]], %[[VAL_114]] : i1
// CHECK:                 scf.condition(%[[VAL_115]]) %[[VAL_109]], %[[VAL_111]], %[[VAL_112]] : index, index, f32
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_116:.*]]: index, %[[VAL_117:.*]]: index, %[[VAL_118:.*]]: f32):
// CHECK:                 %[[VAL_119:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_116]]] : memref<?xindex>
// CHECK:                 %[[VAL_120:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_117]]] : memref<?xindex>
// CHECK:                 %[[VAL_121:.*]] = arith.cmpi ult, %[[VAL_120]], %[[VAL_119]] : index
// CHECK:                 %[[VAL_122:.*]] = arith.select %[[VAL_121]], %[[VAL_120]], %[[VAL_119]] : index
// CHECK:                 %[[VAL_123:.*]] = arith.cmpi eq, %[[VAL_119]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_124:.*]] = arith.cmpi eq, %[[VAL_120]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_125:.*]] = arith.andi %[[VAL_123]], %[[VAL_124]] : i1
// CHECK:                 %[[VAL_126:.*]] = scf.if %[[VAL_125]] -> (f32) {
// CHECK:                   %[[VAL_127:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_116]]] : memref<?xf32>
// CHECK:                   %[[VAL_128:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_117]]] : memref<?xf32>
// CHECK:                   %[[VAL_129:.*]] = arith.mulf %[[VAL_127]], %[[VAL_128]] : f32
// CHECK:                   %[[VAL_130:.*]] = arith.mulf %[[VAL_129]], %[[VAL_37]] : f32
// CHECK:                   %[[VAL_131:.*]] = arith.mulf %[[VAL_130]], %[[VAL_25]] : f32
// CHECK:                   %[[VAL_132:.*]] = arith.addf %[[VAL_118]], %[[VAL_131]] : f32
// CHECK:                   scf.yield %[[VAL_132]] : f32
// CHECK:                 } else {
// CHECK:                   scf.yield %[[VAL_118]] : f32
// CHECK:                 }
// CHECK:                 %[[VAL_133:.*]] = arith.cmpi eq, %[[VAL_119]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_134:.*]] = arith.addi %[[VAL_116]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_135:.*]] = arith.select %[[VAL_133]], %[[VAL_134]], %[[VAL_116]] : index
// CHECK:                 %[[VAL_136:.*]] = arith.cmpi eq, %[[VAL_120]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_137:.*]] = arith.addi %[[VAL_117]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_138:.*]] = arith.select %[[VAL_136]], %[[VAL_137]], %[[VAL_117]] : index
// CHECK:                 scf.yield %[[VAL_135]], %[[VAL_138]], %[[VAL_139:.*]] : index, index, f32
// CHECK:               }
// CHECK:               %[[VAL_140:.*]] = scf.for %[[VAL_141:.*]] = %[[VAL_142:.*]]#2 to %[[VAL_46]] step %[[VAL_7]] iter_args(%[[VAL_143:.*]] = %[[VAL_144:.*]]#2) -> (f32) {
// CHECK:                 %[[VAL_145:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_141]]] : memref<?xf32>
// CHECK:                 %[[VAL_146:.*]] = arith.addf %[[VAL_143]], %[[VAL_145]] : f32
// CHECK:                 scf.yield %[[VAL_146]] : f32
// CHECK:               }
// CHECK:               memref.store %[[VAL_147:.*]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_8]] {
// CHECK:                 %[[VAL_148:.*]] = memref.load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:                 %[[VAL_149:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:                 %[[VAL_150:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_151:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_150]]] : memref<?xindex>
// CHECK:                 %[[VAL_152:.*]] = scf.for %[[VAL_153:.*]] = %[[VAL_149]] to %[[VAL_151]] step %[[VAL_7]] iter_args(%[[VAL_154:.*]] = %[[VAL_148]]) -> (f32) {
// CHECK:                   %[[VAL_155:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_153]]] : memref<?xf32>
// CHECK:                   %[[VAL_156:.*]] = arith.addf %[[VAL_154]], %[[VAL_155]] : f32
// CHECK:                   scf.yield %[[VAL_156]] : f32
// CHECK:                 }
// CHECK:                 memref.store %[[VAL_157:.*]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_158:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_33]] : index
// CHECK:             %[[VAL_159:.*]] = arith.addi %[[VAL_32]], %[[VAL_7]] : index
// CHECK:             %[[VAL_160:.*]] = arith.select %[[VAL_158]], %[[VAL_159]], %[[VAL_32]] : index
// CHECK:             %[[VAL_161:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_160]], %[[VAL_161]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_162:.*]] = %[[VAL_163:.*]]#1 to %[[VAL_22]] step %[[VAL_7]] {
// CHECK:             %[[VAL_164:.*]] = memref.load %[[VAL_24]]{{\[}}%[[VAL_162]]] : memref<?xf32>
// CHECK:             %[[VAL_165:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_162]]] : memref<?xindex>
// CHECK:             %[[VAL_166:.*]] = arith.addi %[[VAL_162]], %[[VAL_7]] : index
// CHECK:             %[[VAL_167:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_166]]] : memref<?xindex>
// CHECK:             %[[VAL_168:.*]] = scf.for %[[VAL_169:.*]] = %[[VAL_165]] to %[[VAL_167]] step %[[VAL_7]] iter_args(%[[VAL_170:.*]] = %[[VAL_164]]) -> (f32) {
// CHECK:               %[[VAL_171:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_169]]] : memref<?xf32>
// CHECK:               %[[VAL_172:.*]] = arith.addf %[[VAL_170]], %[[VAL_171]] : f32
// CHECK:               scf.yield %[[VAL_172]] : f32
// CHECK:             }
// CHECK:             memref.store %[[VAL_173:.*]], %[[VAL_24]]{{\[}}%[[VAL_162]]] : memref<?xf32>
// CHECK:           }
// CHECK:           %[[VAL_174:.*]] = bufferization.to_tensor %[[VAL_24]] : memref<?xf32>
// CHECK:           return %[[VAL_174]] : tensor<?xf32>
// CHECK:         }
func.func @sum_kernel_with_inv(%arga: tensor<?x?xf32, #Tss>,
                          %argb: tensor<?x?xf32, #Tds>,
                          %argc: tensor<?x?xf32, #Tds>,
                          %argd: tensor<?xf32>,
                          %arge: tensor<f32>,
                          %argx: tensor<?xf32>) -> tensor<?xf32> {
  %0 = linalg.generic #trait_sum_kernel_with_inv
    ins(%arga, %argb, %argc, %argd, %arge : tensor<?x?xf32, #Tss>,
                                            tensor<?x?xf32, #Tds>,
                                            tensor<?x?xf32, #Tds>,
                                            tensor<?xf32>,
                                            tensor<f32>)
    outs(%argx: tensor<?xf32>) {
      ^bb(%a: f32, %b: f32, %c: f32, %d: f32, %e: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        %1 = arith.mulf %0, %d : f32
        %2 = arith.mulf %1, %e : f32
        %3 = arith.addf %2, %c : f32
        %4 = arith.addf %x, %3 : f32
        linalg.yield %4 : f32
  } -> tensor<?xf32>
  return %0 : tensor<?xf32>
}