master
/ miniconda3 / envs / poem / lib / python3.10 / site-packages / fontTools / varLib / merger.py

merger.py @62ac136 raw · history · blame

   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
"""
Merge OpenType Layout tables (GDEF / GPOS / GSUB).
"""
import os
import copy
import enum
from operator import ior
import logging
from fontTools.colorLib.builder import MAX_PAINT_COLR_LAYER_COUNT, LayerReuseCache
from fontTools.misc import classifyTools
from fontTools.misc.roundTools import otRound
from fontTools.misc.treeTools import build_n_ary_tree
from fontTools.ttLib.tables import otTables as ot
from fontTools.ttLib.tables import otBase as otBase
from fontTools.ttLib.tables.otConverters import BaseFixedValue
from fontTools.ttLib.tables.otTraverse import dfs_base_table
from fontTools.ttLib.tables.DefaultTable import DefaultTable
from fontTools.varLib import builder, models, varStore
from fontTools.varLib.models import nonNone, allNone, allEqual, allEqualTo, subList
from fontTools.varLib.varStore import VarStoreInstancer
from functools import reduce
from fontTools.otlLib.builder import buildSinglePos
from fontTools.otlLib.optimize.gpos import (
    _compression_level_from_env,
    compact_pair_pos,
)

log = logging.getLogger("fontTools.varLib.merger")

from .errors import (
    ShouldBeConstant,
    FoundANone,
    MismatchedTypes,
    NotANone,
    LengthsDiffer,
    KeysDiffer,
    InconsistentGlyphOrder,
    InconsistentExtensions,
    InconsistentFormats,
    UnsupportedFormat,
    VarLibMergeError,
)


class Merger(object):
    def __init__(self, font=None):
        self.font = font
        # mergeTables populates this from the parent's master ttfs
        self.ttfs = None

    @classmethod
    def merger(celf, clazzes, attrs=(None,)):
        assert celf != Merger, "Subclass Merger instead."
        if "mergers" not in celf.__dict__:
            celf.mergers = {}
        if type(clazzes) in (type, enum.EnumMeta):
            clazzes = (clazzes,)
        if type(attrs) == str:
            attrs = (attrs,)

        def wrapper(method):
            assert method.__name__ == "merge"
            done = []
            for clazz in clazzes:
                if clazz in done:
                    continue  # Support multiple names of a clazz
                done.append(clazz)
                mergers = celf.mergers.setdefault(clazz, {})
                for attr in attrs:
                    assert attr not in mergers, (
                        "Oops, class '%s' has merge function for '%s' defined already."
                        % (clazz.__name__, attr)
                    )
                    mergers[attr] = method
            return None

        return wrapper

    @classmethod
    def mergersFor(celf, thing, _default={}):
        typ = type(thing)

        for celf in celf.mro():
            mergers = getattr(celf, "mergers", None)
            if mergers is None:
                break

            m = celf.mergers.get(typ, None)
            if m is not None:
                return m

        return _default

    def mergeObjects(self, out, lst, exclude=()):
        if hasattr(out, "ensureDecompiled"):
            out.ensureDecompiled(recurse=False)
        for item in lst:
            if hasattr(item, "ensureDecompiled"):
                item.ensureDecompiled(recurse=False)
        keys = sorted(vars(out).keys())
        if not all(keys == sorted(vars(v).keys()) for v in lst):
            raise KeysDiffer(
                self, expected=keys, got=[sorted(vars(v).keys()) for v in lst]
            )
        mergers = self.mergersFor(out)
        defaultMerger = mergers.get("*", self.__class__.mergeThings)
        try:
            for key in keys:
                if key in exclude:
                    continue
                value = getattr(out, key)
                values = [getattr(table, key) for table in lst]
                mergerFunc = mergers.get(key, defaultMerger)
                mergerFunc(self, value, values)
        except VarLibMergeError as e:
            e.stack.append("." + key)
            raise

    def mergeLists(self, out, lst):
        if not allEqualTo(out, lst, len):
            raise LengthsDiffer(self, expected=len(out), got=[len(x) for x in lst])
        for i, (value, values) in enumerate(zip(out, zip(*lst))):
            try:
                self.mergeThings(value, values)
            except VarLibMergeError as e:
                e.stack.append("[%d]" % i)
                raise

    def mergeThings(self, out, lst):
        if not allEqualTo(out, lst, type):
            raise MismatchedTypes(
                self, expected=type(out).__name__, got=[type(x).__name__ for x in lst]
            )
        mergerFunc = self.mergersFor(out).get(None, None)
        if mergerFunc is not None:
            mergerFunc(self, out, lst)
        elif isinstance(out, enum.Enum):
            # need to special-case Enums as have __dict__ but are not regular 'objects',
            # otherwise mergeObjects/mergeThings get trapped in a RecursionError
            if not allEqualTo(out, lst):
                raise ShouldBeConstant(self, expected=out, got=lst)
        elif hasattr(out, "__dict__"):
            self.mergeObjects(out, lst)
        elif isinstance(out, list):
            self.mergeLists(out, lst)
        else:
            if not allEqualTo(out, lst):
                raise ShouldBeConstant(self, expected=out, got=lst)

    def mergeTables(self, font, master_ttfs, tableTags):
        for tag in tableTags:
            if tag not in font:
                continue
            try:
                self.ttfs = master_ttfs
                self.mergeThings(font[tag], [m.get(tag) for m in master_ttfs])
            except VarLibMergeError as e:
                e.stack.append(tag)
                raise


#
# Aligning merger
#
class AligningMerger(Merger):
    pass


@AligningMerger.merger(ot.GDEF, "GlyphClassDef")
def merge(merger, self, lst):
    if self is None:
        if not allNone(lst):
            raise NotANone(merger, expected=None, got=lst)
        return

    lst = [l.classDefs for l in lst]
    self.classDefs = {}
    # We only care about the .classDefs
    self = self.classDefs

    allKeys = set()
    allKeys.update(*[l.keys() for l in lst])
    for k in allKeys:
        allValues = nonNone(l.get(k) for l in lst)
        if not allEqual(allValues):
            raise ShouldBeConstant(
                merger, expected=allValues[0], got=lst, stack=["." + k]
            )
        if not allValues:
            self[k] = None
        else:
            self[k] = allValues[0]


def _SinglePosUpgradeToFormat2(self):
    if self.Format == 2:
        return self

    ret = ot.SinglePos()
    ret.Format = 2
    ret.Coverage = self.Coverage
    ret.ValueFormat = self.ValueFormat
    ret.Value = [self.Value for _ in ret.Coverage.glyphs]
    ret.ValueCount = len(ret.Value)

    return ret


def _merge_GlyphOrders(font, lst, values_lst=None, default=None):
    """Takes font and list of glyph lists (must be sorted by glyph id), and returns
    two things:
    - Combined glyph list,
    - If values_lst is None, return input glyph lists, but padded with None when a glyph
      was missing in a list.  Otherwise, return values_lst list-of-list, padded with None
      to match combined glyph lists.
    """
    if values_lst is None:
        dict_sets = [set(l) for l in lst]
    else:
        dict_sets = [{g: v for g, v in zip(l, vs)} for l, vs in zip(lst, values_lst)]
    combined = set()
    combined.update(*dict_sets)

    sortKey = font.getReverseGlyphMap().__getitem__
    order = sorted(combined, key=sortKey)
    # Make sure all input glyphsets were in proper order
    if not all(sorted(vs, key=sortKey) == vs for vs in lst):
        raise InconsistentGlyphOrder()
    del combined

    paddedValues = None
    if values_lst is None:
        padded = [
            [glyph if glyph in dict_set else default for glyph in order]
            for dict_set in dict_sets
        ]
    else:
        assert len(lst) == len(values_lst)
        padded = [
            [dict_set[glyph] if glyph in dict_set else default for glyph in order]
            for dict_set in dict_sets
        ]
    return order, padded


@AligningMerger.merger(otBase.ValueRecord)
def merge(merger, self, lst):
    # Code below sometimes calls us with self being
    # a new object. Copy it from lst and recurse.
    self.__dict__ = lst[0].__dict__.copy()
    merger.mergeObjects(self, lst)


@AligningMerger.merger(ot.Anchor)
def merge(merger, self, lst):
    # Code below sometimes calls us with self being
    # a new object. Copy it from lst and recurse.
    self.__dict__ = lst[0].__dict__.copy()
    merger.mergeObjects(self, lst)


def _Lookup_SinglePos_get_effective_value(merger, subtables, glyph):
    for self in subtables:
        if (
            self is None
            or type(self) != ot.SinglePos
            or self.Coverage is None
            or glyph not in self.Coverage.glyphs
        ):
            continue
        if self.Format == 1:
            return self.Value
        elif self.Format == 2:
            return self.Value[self.Coverage.glyphs.index(glyph)]
        else:
            raise UnsupportedFormat(merger, subtable="single positioning lookup")
    return None


def _Lookup_PairPos_get_effective_value_pair(
    merger, subtables, firstGlyph, secondGlyph
):
    for self in subtables:
        if (
            self is None
            or type(self) != ot.PairPos
            or self.Coverage is None
            or firstGlyph not in self.Coverage.glyphs
        ):
            continue
        if self.Format == 1:
            ps = self.PairSet[self.Coverage.glyphs.index(firstGlyph)]
            pvr = ps.PairValueRecord
            for rec in pvr:  # TODO Speed up
                if rec.SecondGlyph == secondGlyph:
                    return rec
            continue
        elif self.Format == 2:
            klass1 = self.ClassDef1.classDefs.get(firstGlyph, 0)
            klass2 = self.ClassDef2.classDefs.get(secondGlyph, 0)
            return self.Class1Record[klass1].Class2Record[klass2]
        else:
            raise UnsupportedFormat(merger, subtable="pair positioning lookup")
    return None


@AligningMerger.merger(ot.SinglePos)
def merge(merger, self, lst):
    self.ValueFormat = valueFormat = reduce(int.__or__, [l.ValueFormat for l in lst], 0)
    if not (len(lst) == 1 or (valueFormat & ~0xF == 0)):
        raise UnsupportedFormat(merger, subtable="single positioning lookup")

    # If all have same coverage table and all are format 1,
    coverageGlyphs = self.Coverage.glyphs
    if all(v.Format == 1 for v in lst) and all(
        coverageGlyphs == v.Coverage.glyphs for v in lst
    ):
        self.Value = otBase.ValueRecord(valueFormat, self.Value)
        if valueFormat != 0:
            # If v.Value is None, it means a kerning of 0; we want
            # it to participate in the model still.
            # https://github.com/fonttools/fonttools/issues/3111
            merger.mergeThings(
                self.Value,
                [v.Value if v.Value is not None else otBase.ValueRecord() for v in lst],
            )
        self.ValueFormat = self.Value.getFormat()
        return

    # Upgrade everything to Format=2
    self.Format = 2
    lst = [_SinglePosUpgradeToFormat2(v) for v in lst]

    # Align them
    glyphs, padded = _merge_GlyphOrders(
        merger.font, [v.Coverage.glyphs for v in lst], [v.Value for v in lst]
    )

    self.Coverage.glyphs = glyphs
    self.Value = [otBase.ValueRecord(valueFormat) for _ in glyphs]
    self.ValueCount = len(self.Value)

    for i, values in enumerate(padded):
        for j, glyph in enumerate(glyphs):
            if values[j] is not None:
                continue
            # Fill in value from other subtables
            # Note!!! This *might* result in behavior change if ValueFormat2-zeroedness
            # is different between used subtable and current subtable!
            # TODO(behdad) Check and warn if that happens?
            v = _Lookup_SinglePos_get_effective_value(
                merger, merger.lookup_subtables[i], glyph
            )
            if v is None:
                v = otBase.ValueRecord(valueFormat)
            values[j] = v

    merger.mergeLists(self.Value, padded)

    # Merge everything else; though, there shouldn't be anything else. :)
    merger.mergeObjects(
        self, lst, exclude=("Format", "Coverage", "Value", "ValueCount", "ValueFormat")
    )
    self.ValueFormat = reduce(
        int.__or__, [v.getEffectiveFormat() for v in self.Value], 0
    )


@AligningMerger.merger(ot.PairSet)
def merge(merger, self, lst):
    # Align them
    glyphs, padded = _merge_GlyphOrders(
        merger.font,
        [[v.SecondGlyph for v in vs.PairValueRecord] for vs in lst],
        [vs.PairValueRecord for vs in lst],
    )

    self.PairValueRecord = pvrs = []
    for glyph in glyphs:
        pvr = ot.PairValueRecord()
        pvr.SecondGlyph = glyph
        pvr.Value1 = (
            otBase.ValueRecord(merger.valueFormat1) if merger.valueFormat1 else None
        )
        pvr.Value2 = (
            otBase.ValueRecord(merger.valueFormat2) if merger.valueFormat2 else None
        )
        pvrs.append(pvr)
    self.PairValueCount = len(self.PairValueRecord)

    for i, values in enumerate(padded):
        for j, glyph in enumerate(glyphs):
            # Fill in value from other subtables
            v = ot.PairValueRecord()
            v.SecondGlyph = glyph
            if values[j] is not None:
                vpair = values[j]
            else:
                vpair = _Lookup_PairPos_get_effective_value_pair(
                    merger, merger.lookup_subtables[i], self._firstGlyph, glyph
                )
            if vpair is None:
                v1, v2 = None, None
            else:
                v1 = getattr(vpair, "Value1", None)
                v2 = getattr(vpair, "Value2", None)
            v.Value1 = (
                otBase.ValueRecord(merger.valueFormat1, src=v1)
                if merger.valueFormat1
                else None
            )
            v.Value2 = (
                otBase.ValueRecord(merger.valueFormat2, src=v2)
                if merger.valueFormat2
                else None
            )
            values[j] = v
    del self._firstGlyph

    merger.mergeLists(self.PairValueRecord, padded)


def _PairPosFormat1_merge(self, lst, merger):
    assert allEqual(
        [l.ValueFormat2 == 0 for l in lst if l.PairSet]
    ), "Report bug against fonttools."

    # Merge everything else; makes sure Format is the same.
    merger.mergeObjects(
        self,
        lst,
        exclude=("Coverage", "PairSet", "PairSetCount", "ValueFormat1", "ValueFormat2"),
    )

    empty = ot.PairSet()
    empty.PairValueRecord = []
    empty.PairValueCount = 0

    # Align them
    glyphs, padded = _merge_GlyphOrders(
        merger.font,
        [v.Coverage.glyphs for v in lst],
        [v.PairSet for v in lst],
        default=empty,
    )

    self.Coverage.glyphs = glyphs
    self.PairSet = [ot.PairSet() for _ in glyphs]
    self.PairSetCount = len(self.PairSet)
    for glyph, ps in zip(glyphs, self.PairSet):
        ps._firstGlyph = glyph

    merger.mergeLists(self.PairSet, padded)


def _ClassDef_invert(self, allGlyphs=None):
    if isinstance(self, dict):
        classDefs = self
    else:
        classDefs = self.classDefs if self and self.classDefs else {}
    m = max(classDefs.values()) if classDefs else 0

    ret = []
    for _ in range(m + 1):
        ret.append(set())

    for k, v in classDefs.items():
        ret[v].add(k)

    # Class-0 is special.  It's "everything else".
    if allGlyphs is None:
        ret[0] = None
    else:
        # Limit all classes to glyphs in allGlyphs.
        # Collect anything without a non-zero class into class=zero.
        ret[0] = class0 = set(allGlyphs)
        for s in ret[1:]:
            s.intersection_update(class0)
            class0.difference_update(s)

    return ret


def _ClassDef_merge_classify(lst, allGlyphses=None):
    self = ot.ClassDef()
    self.classDefs = classDefs = {}
    allGlyphsesWasNone = allGlyphses is None
    if allGlyphsesWasNone:
        allGlyphses = [None] * len(lst)

    classifier = classifyTools.Classifier()
    for classDef, allGlyphs in zip(lst, allGlyphses):
        sets = _ClassDef_invert(classDef, allGlyphs)
        if allGlyphs is None:
            sets = sets[1:]
        classifier.update(sets)
    classes = classifier.getClasses()

    if allGlyphsesWasNone:
        classes.insert(0, set())

    for i, classSet in enumerate(classes):
        if i == 0:
            continue
        for g in classSet:
            classDefs[g] = i

    return self, classes


def _PairPosFormat2_align_matrices(self, lst, font, transparent=False):
    matrices = [l.Class1Record for l in lst]

    # Align first classes
    self.ClassDef1, classes = _ClassDef_merge_classify(
        [l.ClassDef1 for l in lst], [l.Coverage.glyphs for l in lst]
    )
    self.Class1Count = len(classes)
    new_matrices = []
    for l, matrix in zip(lst, matrices):
        nullRow = None
        coverage = set(l.Coverage.glyphs)
        classDef1 = l.ClassDef1.classDefs
        class1Records = []
        for classSet in classes:
            exemplarGlyph = next(iter(classSet))
            if exemplarGlyph not in coverage:
                # Follow-up to e6125b353e1f54a0280ded5434b8e40d042de69f,
                # Fixes https://github.com/googlei18n/fontmake/issues/470
                # Again, revert 8d441779e5afc664960d848f62c7acdbfc71d7b9
                # when merger becomes selfless.
                nullRow = None
                if nullRow is None:
                    nullRow = ot.Class1Record()
                    class2records = nullRow.Class2Record = []
                    # TODO: When merger becomes selfless, revert e6125b353e1f54a0280ded5434b8e40d042de69f
                    for _ in range(l.Class2Count):
                        if transparent:
                            rec2 = None
                        else:
                            rec2 = ot.Class2Record()
                            rec2.Value1 = (
                                otBase.ValueRecord(self.ValueFormat1)
                                if self.ValueFormat1
                                else None
                            )
                            rec2.Value2 = (
                                otBase.ValueRecord(self.ValueFormat2)
                                if self.ValueFormat2
                                else None
                            )
                        class2records.append(rec2)
                rec1 = nullRow
            else:
                klass = classDef1.get(exemplarGlyph, 0)
                rec1 = matrix[klass]  # TODO handle out-of-range?
            class1Records.append(rec1)
        new_matrices.append(class1Records)
    matrices = new_matrices
    del new_matrices

    # Align second classes
    self.ClassDef2, classes = _ClassDef_merge_classify([l.ClassDef2 for l in lst])
    self.Class2Count = len(classes)
    new_matrices = []
    for l, matrix in zip(lst, matrices):
        classDef2 = l.ClassDef2.classDefs
        class1Records = []
        for rec1old in matrix:
            oldClass2Records = rec1old.Class2Record
            rec1new = ot.Class1Record()
            class2Records = rec1new.Class2Record = []
            for classSet in classes:
                if not classSet:  # class=0
                    rec2 = oldClass2Records[0]
                else:
                    exemplarGlyph = next(iter(classSet))
                    klass = classDef2.get(exemplarGlyph, 0)
                    rec2 = oldClass2Records[klass]
                class2Records.append(copy.deepcopy(rec2))
            class1Records.append(rec1new)
        new_matrices.append(class1Records)
    matrices = new_matrices
    del new_matrices

    return matrices


def _PairPosFormat2_merge(self, lst, merger):
    assert allEqual(
        [l.ValueFormat2 == 0 for l in lst if l.Class1Record]
    ), "Report bug against fonttools."

    merger.mergeObjects(
        self,
        lst,
        exclude=(
            "Coverage",
            "ClassDef1",
            "Class1Count",
            "ClassDef2",
            "Class2Count",
            "Class1Record",
            "ValueFormat1",
            "ValueFormat2",
        ),
    )

    # Align coverages
    glyphs, _ = _merge_GlyphOrders(merger.font, [v.Coverage.glyphs for v in lst])
    self.Coverage.glyphs = glyphs

    # Currently, if the coverage of PairPosFormat2 subtables are different,
    # we do NOT bother walking down the subtable list when filling in new
    # rows for alignment.  As such, this is only correct if current subtable
    # is the last subtable in the lookup.  Ensure that.
    #
    # Note that our canonicalization process merges trailing PairPosFormat2's,
    # so in reality this is rare.
    for l, subtables in zip(lst, merger.lookup_subtables):
        if l.Coverage.glyphs != glyphs:
            assert l == subtables[-1]

    matrices = _PairPosFormat2_align_matrices(self, lst, merger.font)

    self.Class1Record = list(matrices[0])  # TODO move merger to be selfless
    merger.mergeLists(self.Class1Record, matrices)


@AligningMerger.merger(ot.PairPos)
def merge(merger, self, lst):
    merger.valueFormat1 = self.ValueFormat1 = reduce(
        int.__or__, [l.ValueFormat1 for l in lst], 0
    )
    merger.valueFormat2 = self.ValueFormat2 = reduce(
        int.__or__, [l.ValueFormat2 for l in lst], 0
    )

    if self.Format == 1:
        _PairPosFormat1_merge(self, lst, merger)
    elif self.Format == 2:
        _PairPosFormat2_merge(self, lst, merger)
    else:
        raise UnsupportedFormat(merger, subtable="pair positioning lookup")

    del merger.valueFormat1, merger.valueFormat2

    # Now examine the list of value records, and update to the union of format values,
    # as merge might have created new values.
    vf1 = 0
    vf2 = 0
    if self.Format == 1:
        for pairSet in self.PairSet:
            for pairValueRecord in pairSet.PairValueRecord:
                pv1 = getattr(pairValueRecord, "Value1", None)
                if pv1 is not None:
                    vf1 |= pv1.getFormat()
                pv2 = getattr(pairValueRecord, "Value2", None)
                if pv2 is not None:
                    vf2 |= pv2.getFormat()
    elif self.Format == 2:
        for class1Record in self.Class1Record:
            for class2Record in class1Record.Class2Record:
                pv1 = getattr(class2Record, "Value1", None)
                if pv1 is not None:
                    vf1 |= pv1.getFormat()
                pv2 = getattr(class2Record, "Value2", None)
                if pv2 is not None:
                    vf2 |= pv2.getFormat()
    self.ValueFormat1 = vf1
    self.ValueFormat2 = vf2


def _MarkBasePosFormat1_merge(self, lst, merger, Mark="Mark", Base="Base"):
    self.ClassCount = max(l.ClassCount for l in lst)

    MarkCoverageGlyphs, MarkRecords = _merge_GlyphOrders(
        merger.font,
        [getattr(l, Mark + "Coverage").glyphs for l in lst],
        [getattr(l, Mark + "Array").MarkRecord for l in lst],
    )
    getattr(self, Mark + "Coverage").glyphs = MarkCoverageGlyphs

    BaseCoverageGlyphs, BaseRecords = _merge_GlyphOrders(
        merger.font,
        [getattr(l, Base + "Coverage").glyphs for l in lst],
        [getattr(getattr(l, Base + "Array"), Base + "Record") for l in lst],
    )
    getattr(self, Base + "Coverage").glyphs = BaseCoverageGlyphs

    # MarkArray
    records = []
    for g, glyphRecords in zip(MarkCoverageGlyphs, zip(*MarkRecords)):
        allClasses = [r.Class for r in glyphRecords if r is not None]

        # TODO Right now we require that all marks have same class in
        # all masters that cover them.  This is not required.
        #
        # We can relax that by just requiring that all marks that have
        # the same class in a master, have the same class in every other
        # master.  Indeed, if, say, a sparse master only covers one mark,
        # that mark probably will get class 0, which would possibly be
        # different from its class in other masters.
        #
        # We can even go further and reclassify marks to support any
        # input.  But, since, it's unlikely that two marks being both,
        # say, "top" in one master, and one being "top" and other being
        # "top-right" in another master, we shouldn't do that, as any
        # failures in that case will probably signify mistakes in the
        # input masters.

        if not allEqual(allClasses):
            raise ShouldBeConstant(merger, expected=allClasses[0], got=allClasses)
        else:
            rec = ot.MarkRecord()
            rec.Class = allClasses[0]
            allAnchors = [None if r is None else r.MarkAnchor for r in glyphRecords]
            if allNone(allAnchors):
                anchor = None
            else:
                anchor = ot.Anchor()
                anchor.Format = 1
                merger.mergeThings(anchor, allAnchors)
            rec.MarkAnchor = anchor
        records.append(rec)
    array = ot.MarkArray()
    array.MarkRecord = records
    array.MarkCount = len(records)
    setattr(self, Mark + "Array", array)

    # BaseArray
    records = []
    for g, glyphRecords in zip(BaseCoverageGlyphs, zip(*BaseRecords)):
        if allNone(glyphRecords):
            rec = None
        else:
            rec = getattr(ot, Base + "Record")()
            anchors = []
            setattr(rec, Base + "Anchor", anchors)
            glyphAnchors = [
                [] if r is None else getattr(r, Base + "Anchor") for r in glyphRecords
            ]
            for l in glyphAnchors:
                l.extend([None] * (self.ClassCount - len(l)))
            for allAnchors in zip(*glyphAnchors):
                if allNone(allAnchors):
                    anchor = None
                else:
                    anchor = ot.Anchor()
                    anchor.Format = 1
                    merger.mergeThings(anchor, allAnchors)
                anchors.append(anchor)
        records.append(rec)
    array = getattr(ot, Base + "Array")()
    setattr(array, Base + "Record", records)
    setattr(array, Base + "Count", len(records))
    setattr(self, Base + "Array", array)


@AligningMerger.merger(ot.MarkBasePos)
def merge(merger, self, lst):
    if not allEqualTo(self.Format, (l.Format for l in lst)):
        raise InconsistentFormats(
            merger,
            subtable="mark-to-base positioning lookup",
            expected=self.Format,
            got=[l.Format for l in lst],
        )
    if self.Format == 1:
        _MarkBasePosFormat1_merge(self, lst, merger)
    else:
        raise UnsupportedFormat(merger, subtable="mark-to-base positioning lookup")


@AligningMerger.merger(ot.MarkMarkPos)
def merge(merger, self, lst):
    if not allEqualTo(self.Format, (l.Format for l in lst)):
        raise InconsistentFormats(
            merger,
            subtable="mark-to-mark positioning lookup",
            expected=self.Format,
            got=[l.Format for l in lst],
        )
    if self.Format == 1:
        _MarkBasePosFormat1_merge(self, lst, merger, "Mark1", "Mark2")
    else:
        raise UnsupportedFormat(merger, subtable="mark-to-mark positioning lookup")


def _PairSet_flatten(lst, font):
    self = ot.PairSet()
    self.Coverage = ot.Coverage()

    # Align them
    glyphs, padded = _merge_GlyphOrders(
        font,
        [[v.SecondGlyph for v in vs.PairValueRecord] for vs in lst],
        [vs.PairValueRecord for vs in lst],
    )

    self.Coverage.glyphs = glyphs
    self.PairValueRecord = pvrs = []
    for values in zip(*padded):
        for v in values:
            if v is not None:
                pvrs.append(v)
                break
        else:
            assert False
    self.PairValueCount = len(self.PairValueRecord)

    return self


def _Lookup_PairPosFormat1_subtables_flatten(lst, font):
    assert allEqual(
        [l.ValueFormat2 == 0 for l in lst if l.PairSet]
    ), "Report bug against fonttools."

    self = ot.PairPos()
    self.Format = 1
    self.Coverage = ot.Coverage()
    self.ValueFormat1 = reduce(int.__or__, [l.ValueFormat1 for l in lst], 0)
    self.ValueFormat2 = reduce(int.__or__, [l.ValueFormat2 for l in lst], 0)

    # Align them
    glyphs, padded = _merge_GlyphOrders(
        font, [v.Coverage.glyphs for v in lst], [v.PairSet for v in lst]
    )

    self.Coverage.glyphs = glyphs
    self.PairSet = [
        _PairSet_flatten([v for v in values if v is not None], font)
        for values in zip(*padded)
    ]
    self.PairSetCount = len(self.PairSet)
    return self


def _Lookup_PairPosFormat2_subtables_flatten(lst, font):
    assert allEqual(
        [l.ValueFormat2 == 0 for l in lst if l.Class1Record]
    ), "Report bug against fonttools."

    self = ot.PairPos()
    self.Format = 2
    self.Coverage = ot.Coverage()
    self.ValueFormat1 = reduce(int.__or__, [l.ValueFormat1 for l in lst], 0)
    self.ValueFormat2 = reduce(int.__or__, [l.ValueFormat2 for l in lst], 0)

    # Align them
    glyphs, _ = _merge_GlyphOrders(font, [v.Coverage.glyphs for v in lst])
    self.Coverage.glyphs = glyphs

    matrices = _PairPosFormat2_align_matrices(self, lst, font, transparent=True)

    matrix = self.Class1Record = []
    for rows in zip(*matrices):
        row = ot.Class1Record()
        matrix.append(row)
        row.Class2Record = []
        row = row.Class2Record
        for cols in zip(*list(r.Class2Record for r in rows)):
            col = next(iter(c for c in cols if c is not None))
            row.append(col)

    return self


def _Lookup_PairPos_subtables_canonicalize(lst, font):
    """Merge multiple Format1 subtables at the beginning of lst,
    and merge multiple consecutive Format2 subtables that have the same
    Class2 (ie. were split because of offset overflows).  Returns new list."""
    lst = list(lst)

    l = len(lst)
    i = 0
    while i < l and lst[i].Format == 1:
        i += 1
    lst[:i] = [_Lookup_PairPosFormat1_subtables_flatten(lst[:i], font)]

    l = len(lst)
    i = l
    while i > 0 and lst[i - 1].Format == 2:
        i -= 1
    lst[i:] = [_Lookup_PairPosFormat2_subtables_flatten(lst[i:], font)]

    return lst


def _Lookup_SinglePos_subtables_flatten(lst, font, min_inclusive_rec_format):
    glyphs, _ = _merge_GlyphOrders(font, [v.Coverage.glyphs for v in lst], None)
    num_glyphs = len(glyphs)
    new = ot.SinglePos()
    new.Format = 2
    new.ValueFormat = min_inclusive_rec_format
    new.Coverage = ot.Coverage()
    new.Coverage.glyphs = glyphs
    new.ValueCount = num_glyphs
    new.Value = [None] * num_glyphs
    for singlePos in lst:
        if singlePos.Format == 1:
            val_rec = singlePos.Value
            for gname in singlePos.Coverage.glyphs:
                i = glyphs.index(gname)
                new.Value[i] = copy.deepcopy(val_rec)
        elif singlePos.Format == 2:
            for j, gname in enumerate(singlePos.Coverage.glyphs):
                val_rec = singlePos.Value[j]
                i = glyphs.index(gname)
                new.Value[i] = copy.deepcopy(val_rec)
    return [new]


@AligningMerger.merger(ot.Lookup)
def merge(merger, self, lst):
    subtables = merger.lookup_subtables = [l.SubTable for l in lst]

    # Remove Extension subtables
    for l, sts in list(zip(lst, subtables)) + [(self, self.SubTable)]:
        if not sts:
            continue
        if sts[0].__class__.__name__.startswith("Extension"):
            if not allEqual([st.__class__ for st in sts]):
                raise InconsistentExtensions(
                    merger,
                    expected="Extension",
                    got=[st.__class__.__name__ for st in sts],
                )
            if not allEqual([st.ExtensionLookupType for st in sts]):
                raise InconsistentExtensions(merger)
            l.LookupType = sts[0].ExtensionLookupType
            new_sts = [st.ExtSubTable for st in sts]
            del sts[:]
            sts.extend(new_sts)

    isPairPos = self.SubTable and isinstance(self.SubTable[0], ot.PairPos)

    if isPairPos:
        # AFDKO and feaLib sometimes generate two Format1 subtables instead of one.
        # Merge those before continuing.
        # https://github.com/fonttools/fonttools/issues/719
        self.SubTable = _Lookup_PairPos_subtables_canonicalize(
            self.SubTable, merger.font
        )
        subtables = merger.lookup_subtables = [
            _Lookup_PairPos_subtables_canonicalize(st, merger.font) for st in subtables
        ]
    else:
        isSinglePos = self.SubTable and isinstance(self.SubTable[0], ot.SinglePos)
        if isSinglePos:
            numSubtables = [len(st) for st in subtables]
            if not all([nums == numSubtables[0] for nums in numSubtables]):
                # Flatten list of SinglePos subtables to single Format 2 subtable,
                # with all value records set to the rec format type.
                # We use buildSinglePos() to optimize the lookup after merging.
                valueFormatList = [t.ValueFormat for st in subtables for t in st]
                # Find the minimum value record that can accomodate all the singlePos subtables.
                mirf = reduce(ior, valueFormatList)
                self.SubTable = _Lookup_SinglePos_subtables_flatten(
                    self.SubTable, merger.font, mirf
                )
                subtables = merger.lookup_subtables = [
                    _Lookup_SinglePos_subtables_flatten(st, merger.font, mirf)
                    for st in subtables
                ]
                flattened = True
            else:
                flattened = False

    merger.mergeLists(self.SubTable, subtables)
    self.SubTableCount = len(self.SubTable)

    if isPairPos:
        # If format-1 subtable created during canonicalization is empty, remove it.
        assert len(self.SubTable) >= 1 and self.SubTable[0].Format == 1
        if not self.SubTable[0].Coverage.glyphs:
            self.SubTable.pop(0)
            self.SubTableCount -= 1

        # If format-2 subtable created during canonicalization is empty, remove it.
        assert len(self.SubTable) >= 1 and self.SubTable[-1].Format == 2
        if not self.SubTable[-1].Coverage.glyphs:
            self.SubTable.pop(-1)
            self.SubTableCount -= 1

        # Compact the merged subtables
        # This is a good moment to do it because the compaction should create
        # smaller subtables, which may prevent overflows from happening.
        # Keep reading the value from the ENV until ufo2ft switches to the config system
        level = merger.font.cfg.get(
            "fontTools.otlLib.optimize.gpos:COMPRESSION_LEVEL",
            default=_compression_level_from_env(),
        )
        if level != 0:
            log.info("Compacting GPOS...")
            self.SubTable = compact_pair_pos(merger.font, level, self.SubTable)
            self.SubTableCount = len(self.SubTable)

    elif isSinglePos and flattened:
        singlePosTable = self.SubTable[0]
        glyphs = singlePosTable.Coverage.glyphs
        # We know that singlePosTable is Format 2, as this is set
        # in _Lookup_SinglePos_subtables_flatten.
        singlePosMapping = {
            gname: valRecord for gname, valRecord in zip(glyphs, singlePosTable.Value)
        }
        self.SubTable = buildSinglePos(
            singlePosMapping, merger.font.getReverseGlyphMap()
        )
    merger.mergeObjects(self, lst, exclude=["SubTable", "SubTableCount"])

    del merger.lookup_subtables


#
# InstancerMerger
#


class InstancerMerger(AligningMerger):
    """A merger that takes multiple master fonts, and instantiates
    an instance."""

    def __init__(self, font, model, location):
        Merger.__init__(self, font)
        self.model = model
        self.location = location
        self.scalars = model.getScalars(location)


@InstancerMerger.merger(ot.CaretValue)
def merge(merger, self, lst):
    assert self.Format == 1
    Coords = [a.Coordinate for a in lst]
    model = merger.model
    scalars = merger.scalars
    self.Coordinate = otRound(model.interpolateFromMastersAndScalars(Coords, scalars))


@InstancerMerger.merger(ot.Anchor)
def merge(merger, self, lst):
    assert self.Format == 1
    XCoords = [a.XCoordinate for a in lst]
    YCoords = [a.YCoordinate for a in lst]
    model = merger.model
    scalars = merger.scalars
    self.XCoordinate = otRound(model.interpolateFromMastersAndScalars(XCoords, scalars))
    self.YCoordinate = otRound(model.interpolateFromMastersAndScalars(YCoords, scalars))


@InstancerMerger.merger(otBase.ValueRecord)
def merge(merger, self, lst):
    model = merger.model
    scalars = merger.scalars
    # TODO Handle differing valueformats
    for name, tableName in [
        ("XAdvance", "XAdvDevice"),
        ("YAdvance", "YAdvDevice"),
        ("XPlacement", "XPlaDevice"),
        ("YPlacement", "YPlaDevice"),
    ]:
        assert not hasattr(self, tableName)

        if hasattr(self, name):
            values = [getattr(a, name, 0) for a in lst]
            value = otRound(model.interpolateFromMastersAndScalars(values, scalars))
            setattr(self, name, value)


#
# MutatorMerger
#


class MutatorMerger(AligningMerger):
    """A merger that takes a variable font, and instantiates
    an instance.  While there's no "merging" to be done per se,
    the operation can benefit from many operations that the
    aligning merger does."""

    def __init__(self, font, instancer, deleteVariations=True):
        Merger.__init__(self, font)
        self.instancer = instancer
        self.deleteVariations = deleteVariations


@MutatorMerger.merger(ot.CaretValue)
def merge(merger, self, lst):
    # Hack till we become selfless.
    self.__dict__ = lst[0].__dict__.copy()

    if self.Format != 3:
        return

    instancer = merger.instancer
    dev = self.DeviceTable
    if merger.deleteVariations:
        del self.DeviceTable
    if dev:
        assert dev.DeltaFormat == 0x8000
        varidx = (dev.StartSize << 16) + dev.EndSize
        delta = otRound(instancer[varidx])
        self.Coordinate += delta

    if merger.deleteVariations:
        self.Format = 1


@MutatorMerger.merger(ot.Anchor)
def merge(merger, self, lst):
    # Hack till we become selfless.
    self.__dict__ = lst[0].__dict__.copy()

    if self.Format != 3:
        return

    instancer = merger.instancer
    for v in "XY":
        tableName = v + "DeviceTable"
        if not hasattr(self, tableName):
            continue
        dev = getattr(self, tableName)
        if merger.deleteVariations:
            delattr(self, tableName)
        if dev is None:
            continue

        assert dev.DeltaFormat == 0x8000
        varidx = (dev.StartSize << 16) + dev.EndSize
        delta = otRound(instancer[varidx])

        attr = v + "Coordinate"
        setattr(self, attr, getattr(self, attr) + delta)

    if merger.deleteVariations:
        self.Format = 1


@MutatorMerger.merger(otBase.ValueRecord)
def merge(merger, self, lst):
    # Hack till we become selfless.
    self.__dict__ = lst[0].__dict__.copy()

    instancer = merger.instancer
    for name, tableName in [
        ("XAdvance", "XAdvDevice"),
        ("YAdvance", "YAdvDevice"),
        ("XPlacement", "XPlaDevice"),
        ("YPlacement", "YPlaDevice"),
    ]:
        if not hasattr(self, tableName):
            continue
        dev = getattr(self, tableName)
        if merger.deleteVariations:
            delattr(self, tableName)
        if dev is None:
            continue

        assert dev.DeltaFormat == 0x8000
        varidx = (dev.StartSize << 16) + dev.EndSize
        delta = otRound(instancer[varidx])

        setattr(self, name, getattr(self, name, 0) + delta)


#
# VariationMerger
#


class VariationMerger(AligningMerger):
    """A merger that takes multiple master fonts, and builds a
    variable font."""

    def __init__(self, model, axisTags, font):
        Merger.__init__(self, font)
        self.store_builder = varStore.OnlineVarStoreBuilder(axisTags)
        self.setModel(model)

    def setModel(self, model):
        self.model = model
        self.store_builder.setModel(model)

    def mergeThings(self, out, lst):
        masterModel = None
        origTTFs = None
        if None in lst:
            if allNone(lst):
                if out is not None:
                    raise FoundANone(self, got=lst)
                return

            # temporarily subset the list of master ttfs to the ones for which
            # master values are not None
            origTTFs = self.ttfs
            if self.ttfs:
                self.ttfs = subList([v is not None for v in lst], self.ttfs)

            masterModel = self.model
            model, lst = masterModel.getSubModel(lst)
            self.setModel(model)

        super(VariationMerger, self).mergeThings(out, lst)

        if masterModel:
            self.setModel(masterModel)
        if origTTFs:
            self.ttfs = origTTFs


def buildVarDevTable(store_builder, master_values):
    if allEqual(master_values):
        return master_values[0], None
    base, varIdx = store_builder.storeMasters(master_values)
    return base, builder.buildVarDevTable(varIdx)


@VariationMerger.merger(ot.BaseCoord)
def merge(merger, self, lst):
    if self.Format != 1:
        raise UnsupportedFormat(merger, subtable="a baseline coordinate")
    self.Coordinate, DeviceTable = buildVarDevTable(
        merger.store_builder, [a.Coordinate for a in lst]
    )
    if DeviceTable:
        self.Format = 3
        self.DeviceTable = DeviceTable


@VariationMerger.merger(ot.CaretValue)
def merge(merger, self, lst):
    if self.Format != 1:
        raise UnsupportedFormat(merger, subtable="a caret")
    self.Coordinate, DeviceTable = buildVarDevTable(
        merger.store_builder, [a.Coordinate for a in lst]
    )
    if DeviceTable:
        self.Format = 3
        self.DeviceTable = DeviceTable


@VariationMerger.merger(ot.Anchor)
def merge(merger, self, lst):
    if self.Format != 1:
        raise UnsupportedFormat(merger, subtable="an anchor")
    self.XCoordinate, XDeviceTable = buildVarDevTable(
        merger.store_builder, [a.XCoordinate for a in lst]
    )
    self.YCoordinate, YDeviceTable = buildVarDevTable(
        merger.store_builder, [a.YCoordinate for a in lst]
    )
    if XDeviceTable or YDeviceTable:
        self.Format = 3
        self.XDeviceTable = XDeviceTable
        self.YDeviceTable = YDeviceTable


@VariationMerger.merger(otBase.ValueRecord)
def merge(merger, self, lst):
    for name, tableName in [
        ("XAdvance", "XAdvDevice"),
        ("YAdvance", "YAdvDevice"),
        ("XPlacement", "XPlaDevice"),
        ("YPlacement", "YPlaDevice"),
    ]:
        if hasattr(self, name):
            value, deviceTable = buildVarDevTable(
                merger.store_builder, [getattr(a, name, 0) for a in lst]
            )
            setattr(self, name, value)
            if deviceTable:
                setattr(self, tableName, deviceTable)


class COLRVariationMerger(VariationMerger):
    """A specialized VariationMerger that takes multiple master fonts containing
    COLRv1 tables, and builds a variable COLR font.

    COLR tables are special in that variable subtables can be associated with
    multiple delta-set indices (via VarIndexBase).
    They also contain tables that must change their type (not simply the Format)
    as they become variable (e.g. Affine2x3 -> VarAffine2x3) so this merger takes
    care of that too.
    """

    def __init__(self, model, axisTags, font, allowLayerReuse=True):
        VariationMerger.__init__(self, model, axisTags, font)
        # maps {tuple(varIdxes): VarIndexBase} to facilitate reuse of VarIndexBase
        # between variable tables with same varIdxes.
        self.varIndexCache = {}
        # flat list of all the varIdxes generated while merging
        self.varIdxes = []
        # set of id()s of the subtables that contain variations after merging
        # and need to be upgraded to the associated VarType.
        self.varTableIds = set()
        # we keep these around for rebuilding a LayerList while merging PaintColrLayers
        self.layers = []
        self.layerReuseCache = None
        if allowLayerReuse:
            self.layerReuseCache = LayerReuseCache()
        # flag to ensure BaseGlyphList is fully merged before LayerList gets processed
        self._doneBaseGlyphs = False

    def mergeTables(self, font, master_ttfs, tableTags=("COLR",)):
        if "COLR" in tableTags and "COLR" in font:
            # The merger modifies the destination COLR table in-place. If this contains
            # multiple PaintColrLayers referencing the same layers from LayerList, it's
            # a problem because we may risk modifying the same paint more than once, or
            # worse, fail while attempting to do that.
            # We don't know whether the master COLR table was built with layer reuse
            # disabled, thus to be safe we rebuild its LayerList so that it contains only
            # unique layers referenced from non-overlapping PaintColrLayers throughout
            # the base paint graphs.
            self.expandPaintColrLayers(font["COLR"].table)
        VariationMerger.mergeTables(self, font, master_ttfs, tableTags)

    def checkFormatEnum(self, out, lst, validate=lambda _: True):
        fmt = out.Format
        formatEnum = out.formatEnum
        ok = False
        try:
            fmt = formatEnum(fmt)
        except ValueError:
            pass
        else:
            ok = validate(fmt)
        if not ok:
            raise UnsupportedFormat(self, subtable=type(out).__name__, value=fmt)
        expected = fmt
        got = []
        for v in lst:
            fmt = getattr(v, "Format", None)
            try:
                fmt = formatEnum(fmt)
            except ValueError:
                pass
            got.append(fmt)
        if not allEqualTo(expected, got):
            raise InconsistentFormats(
                self,
                subtable=type(out).__name__,
                expected=expected,
                got=got,
            )
        return expected

    def mergeSparseDict(self, out, lst):
        for k in out.keys():
            try:
                self.mergeThings(out[k], [v.get(k) for v in lst])
            except VarLibMergeError as e:
                e.stack.append(f"[{k!r}]")
                raise

    def mergeAttrs(self, out, lst, attrs):
        for attr in attrs:
            value = getattr(out, attr)
            values = [getattr(item, attr) for item in lst]
            try:
                self.mergeThings(value, values)
            except VarLibMergeError as e:
                e.stack.append(f".{attr}")
                raise

    def storeMastersForAttr(self, out, lst, attr):
        master_values = [getattr(item, attr) for item in lst]

        # VarStore treats deltas for fixed-size floats as integers, so we
        # must convert master values to int before storing them in the builder
        # then back to float.
        is_fixed_size_float = False
        conv = out.getConverterByName(attr)
        if isinstance(conv, BaseFixedValue):
            is_fixed_size_float = True
            master_values = [conv.toInt(v) for v in master_values]

        baseValue = master_values[0]
        varIdx = ot.NO_VARIATION_INDEX
        if not allEqual(master_values):
            baseValue, varIdx = self.store_builder.storeMasters(master_values)

        if is_fixed_size_float:
            baseValue = conv.fromInt(baseValue)

        return baseValue, varIdx

    def storeVariationIndices(self, varIdxes) -> int:
        # try to reuse an existing VarIndexBase for the same varIdxes, or else
        # create a new one
        key = tuple(varIdxes)
        varIndexBase = self.varIndexCache.get(key)

        if varIndexBase is None:
            # scan for a full match anywhere in the self.varIdxes
            for i in range(len(self.varIdxes) - len(varIdxes) + 1):
                if self.varIdxes[i : i + len(varIdxes)] == varIdxes:
                    self.varIndexCache[key] = varIndexBase = i
                    break

        if varIndexBase is None:
            # try find a partial match at the end of the self.varIdxes
            for n in range(len(varIdxes) - 1, 0, -1):
                if self.varIdxes[-n:] == varIdxes[:n]:
                    varIndexBase = len(self.varIdxes) - n
                    self.varIndexCache[key] = varIndexBase
                    self.varIdxes.extend(varIdxes[n:])
                    break

        if varIndexBase is None:
            # no match found, append at the end
            self.varIndexCache[key] = varIndexBase = len(self.varIdxes)
            self.varIdxes.extend(varIdxes)

        return varIndexBase

    def mergeVariableAttrs(self, out, lst, attrs) -> int:
        varIndexBase = ot.NO_VARIATION_INDEX
        varIdxes = []
        for attr in attrs:
            baseValue, varIdx = self.storeMastersForAttr(out, lst, attr)
            setattr(out, attr, baseValue)
            varIdxes.append(varIdx)

        if any(v != ot.NO_VARIATION_INDEX for v in varIdxes):
            varIndexBase = self.storeVariationIndices(varIdxes)

        return varIndexBase

    @classmethod
    def convertSubTablesToVarType(cls, table):
        for path in dfs_base_table(
            table,
            skip_root=True,
            predicate=lambda path: (
                getattr(type(path[-1].value), "VarType", None) is not None
            ),
        ):
            st = path[-1]
            subTable = st.value
            varType = type(subTable).VarType
            newSubTable = varType()
            newSubTable.__dict__.update(subTable.__dict__)
            newSubTable.populateDefaults()
            parent = path[-2].value
            if st.index is not None:
                getattr(parent, st.name)[st.index] = newSubTable
            else:
                setattr(parent, st.name, newSubTable)

    @staticmethod
    def expandPaintColrLayers(colr):
        """Rebuild LayerList without PaintColrLayers reuse.

        Each base paint graph is fully DFS-traversed (with exception of PaintColrGlyph
        which are irrelevant for this); any layers referenced via PaintColrLayers are
        collected into a new LayerList and duplicated when reuse is detected, to ensure
        that all paints are distinct objects at the end of the process.
        PaintColrLayers's FirstLayerIndex/NumLayers are updated so that no overlap
        is left. Also, any consecutively nested PaintColrLayers are flattened.
        The COLR table's LayerList is replaced with the new unique layers.
        A side effect is also that any layer from the old LayerList which is not
        referenced by any PaintColrLayers is dropped.
        """
        if not colr.LayerList:
            # if no LayerList, there's nothing to expand
            return
        uniqueLayerIDs = set()
        newLayerList = []
        for rec in colr.BaseGlyphList.BaseGlyphPaintRecord:
            frontier = [rec.Paint]
            while frontier:
                paint = frontier.pop()
                if paint.Format == ot.PaintFormat.PaintColrGlyph:
                    # don't traverse these, we treat them as constant for merging
                    continue
                elif paint.Format == ot.PaintFormat.PaintColrLayers:
                    # de-treeify any nested PaintColrLayers, append unique copies to
                    # the new layer list and update PaintColrLayers index/count
                    children = list(_flatten_layers(paint, colr))
                    first_layer_index = len(newLayerList)
                    for layer in children:
                        if id(layer) in uniqueLayerIDs:
                            layer = copy.deepcopy(layer)
                            assert id(layer) not in uniqueLayerIDs
                        newLayerList.append(layer)
                        uniqueLayerIDs.add(id(layer))
                    paint.FirstLayerIndex = first_layer_index
                    paint.NumLayers = len(children)
                else:
                    children = paint.getChildren(colr)
                frontier.extend(reversed(children))
        # sanity check all the new layers are distinct objects
        assert len(newLayerList) == len(uniqueLayerIDs)
        colr.LayerList.Paint = newLayerList
        colr.LayerList.LayerCount = len(newLayerList)


@COLRVariationMerger.merger(ot.BaseGlyphList)
def merge(merger, self, lst):
    # ignore BaseGlyphCount, allow sparse glyph sets across masters
    out = {rec.BaseGlyph: rec for rec in self.BaseGlyphPaintRecord}
    masters = [{rec.BaseGlyph: rec for rec in m.BaseGlyphPaintRecord} for m in lst]

    for i, g in enumerate(out.keys()):
        try:
            # missing base glyphs don't participate in the merge
            merger.mergeThings(out[g], [v.get(g) for v in masters])
        except VarLibMergeError as e:
            e.stack.append(f".BaseGlyphPaintRecord[{i}]")
            e.cause["location"] = f"base glyph {g!r}"
            raise

    merger._doneBaseGlyphs = True


@COLRVariationMerger.merger(ot.LayerList)
def merge(merger, self, lst):
    # nothing to merge for LayerList, assuming we have already merged all PaintColrLayers
    # found while traversing the paint graphs rooted at BaseGlyphPaintRecords.
    assert merger._doneBaseGlyphs, "BaseGlyphList must be merged before LayerList"
    # Simply flush the final list of layers and go home.
    self.LayerCount = len(merger.layers)
    self.Paint = merger.layers


def _flatten_layers(root, colr):
    assert root.Format == ot.PaintFormat.PaintColrLayers
    for paint in root.getChildren(colr):
        if paint.Format == ot.PaintFormat.PaintColrLayers:
            yield from _flatten_layers(paint, colr)
        else:
            yield paint


def _merge_PaintColrLayers(self, out, lst):
    # we only enforce that the (flat) number of layers is the same across all masters
    # but we allow FirstLayerIndex to differ to acommodate for sparse glyph sets.

    out_layers = list(_flatten_layers(out, self.font["COLR"].table))

    # sanity check ttfs are subset to current values (see VariationMerger.mergeThings)
    # before matching each master PaintColrLayers to its respective COLR by position
    assert len(self.ttfs) == len(lst)
    master_layerses = [
        list(_flatten_layers(lst[i], self.ttfs[i]["COLR"].table))
        for i in range(len(lst))
    ]

    try:
        self.mergeLists(out_layers, master_layerses)
    except VarLibMergeError as e:
        # NOTE: This attribute doesn't actually exist in PaintColrLayers but it's
        # handy to have it in the stack trace for debugging.
        e.stack.append(".Layers")
        raise

    # following block is very similar to LayerListBuilder._beforeBuildPaintColrLayers
    # but I couldn't find a nice way to share the code between the two...

    if self.layerReuseCache is not None:
        # successful reuse can make the list smaller
        out_layers = self.layerReuseCache.try_reuse(out_layers)

    # if the list is still too big we need to tree-fy it
    is_tree = len(out_layers) > MAX_PAINT_COLR_LAYER_COUNT
    out_layers = build_n_ary_tree(out_layers, n=MAX_PAINT_COLR_LAYER_COUNT)

    # We now have a tree of sequences with Paint leaves.
    # Convert the sequences into PaintColrLayers.
    def listToColrLayers(paint):
        if isinstance(paint, list):
            layers = [listToColrLayers(l) for l in paint]
            paint = ot.Paint()
            paint.Format = int(ot.PaintFormat.PaintColrLayers)
            paint.NumLayers = len(layers)
            paint.FirstLayerIndex = len(self.layers)
            self.layers.extend(layers)
            if self.layerReuseCache is not None:
                self.layerReuseCache.add(layers, paint.FirstLayerIndex)
        return paint

    out_layers = [listToColrLayers(l) for l in out_layers]

    if len(out_layers) == 1 and out_layers[0].Format == ot.PaintFormat.PaintColrLayers:
        # special case when the reuse cache finds a single perfect PaintColrLayers match
        # (it can only come from a successful reuse, _flatten_layers has gotten rid of
        # all nested PaintColrLayers already); we assign it directly and avoid creating
        # an extra table
        out.NumLayers = out_layers[0].NumLayers
        out.FirstLayerIndex = out_layers[0].FirstLayerIndex
    else:
        out.NumLayers = len(out_layers)
        out.FirstLayerIndex = len(self.layers)

        self.layers.extend(out_layers)

        # Register our parts for reuse provided we aren't a tree
        # If we are a tree the leaves registered for reuse and that will suffice
        if self.layerReuseCache is not None and not is_tree:
            self.layerReuseCache.add(out_layers, out.FirstLayerIndex)


@COLRVariationMerger.merger((ot.Paint, ot.ClipBox))
def merge(merger, self, lst):
    fmt = merger.checkFormatEnum(self, lst, lambda fmt: not fmt.is_variable())

    if fmt is ot.PaintFormat.PaintColrLayers:
        _merge_PaintColrLayers(merger, self, lst)
        return

    varFormat = fmt.as_variable()

    varAttrs = ()
    if varFormat is not None:
        varAttrs = otBase.getVariableAttrs(type(self), varFormat)
    staticAttrs = (c.name for c in self.getConverters() if c.name not in varAttrs)

    merger.mergeAttrs(self, lst, staticAttrs)

    varIndexBase = merger.mergeVariableAttrs(self, lst, varAttrs)

    subTables = [st.value for st in self.iterSubTables()]

    # Convert table to variable if itself has variations or any subtables have
    isVariable = varIndexBase != ot.NO_VARIATION_INDEX or any(
        id(table) in merger.varTableIds for table in subTables
    )

    if isVariable:
        if varAttrs:
            # Some PaintVar* don't have any scalar attributes that can vary,
            # only indirect offsets to other variable subtables, thus have
            # no VarIndexBase of their own (e.g. PaintVarTransform)
            self.VarIndexBase = varIndexBase

        if subTables:
            # Convert Affine2x3 -> VarAffine2x3, ColorLine -> VarColorLine, etc.
            merger.convertSubTablesToVarType(self)

        assert varFormat is not None
        self.Format = int(varFormat)


@COLRVariationMerger.merger((ot.Affine2x3, ot.ColorStop))
def merge(merger, self, lst):
    varType = type(self).VarType

    varAttrs = otBase.getVariableAttrs(varType)
    staticAttrs = (c.name for c in self.getConverters() if c.name not in varAttrs)

    merger.mergeAttrs(self, lst, staticAttrs)

    varIndexBase = merger.mergeVariableAttrs(self, lst, varAttrs)

    if varIndexBase != ot.NO_VARIATION_INDEX:
        self.VarIndexBase = varIndexBase
        # mark as having variations so the parent table will convert to Var{Type}
        merger.varTableIds.add(id(self))


@COLRVariationMerger.merger(ot.ColorLine)
def merge(merger, self, lst):
    merger.mergeAttrs(self, lst, (c.name for c in self.getConverters()))

    if any(id(stop) in merger.varTableIds for stop in self.ColorStop):
        merger.convertSubTablesToVarType(self)
        merger.varTableIds.add(id(self))


@COLRVariationMerger.merger(ot.ClipList, "clips")
def merge(merger, self, lst):
    # 'sparse' in that we allow non-default masters to omit ClipBox entries
    # for some/all glyphs (i.e. they don't participate)
    merger.mergeSparseDict(self, lst)