summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/tex/context/base/mkiv/math-noa.lua
blob: 3a45bb30d4751f4714a21b7d9c42ae9a8b35f45e (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
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
if not modules then modules = { } end modules ['math-noa'] = {
    version   = 1.001,
    comment   = "companion to math-ini.mkiv",
    author    = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
    copyright = "PRAGMA ADE / ConTeXt Development Team",
    license   = "see context related readme files"
}

-- beware: this is experimental code and there will be a more generic (attribute value
-- driven) interface too but for the moment this is ok (sometime in 2015-2016 i will
-- start cleaning up as by then the bigger picture is clear and code has been used for
-- years; the main handlers will get some extensions)
--
-- we will also make dedicated processors (faster)
--
-- beware: names will change as we wil make noads.xxx.handler i.e. xxx
-- subnamespaces

-- 20D6 -> 2190
-- 20D7 -> 2192

-- todo: most is math_char so we can have simple dedicated loops

-- nota bene: uunderdelimiter uoverdelimiter etc are radicals (we have 5 types)

local utfchar, utfbyte = utf.char, utf.byte
local formatters, gmatch = string.formatters, string.gmatch
local sortedhash = table.sortedhash
local insert, remove = table.insert, table.remove
local div = math.div
local setbit, hasbit = number.setbit, number.hasbit

local fonts                = fonts
local nodes                = nodes
local node                 = node
local mathematics          = mathematics
local context              = context

local otf                  = fonts.handlers.otf
local otffeatures          = fonts.constructors.features.otf
local registerotffeature   = otffeatures.register

local privateattribute     = attributes.private
local registertracker      = trackers.register
local registerdirective    = directives.register
local logreporter          = logs.reporter
local setmetatableindex    = table.setmetatableindex

local trace_remapping      = false  registertracker("math.remapping",   function(v) trace_remapping   = v end)
local trace_processing     = false  registertracker("math.processing",  function(v) trace_processing  = v end)
local trace_analyzing      = false  registertracker("math.analyzing",   function(v) trace_analyzing   = v end)
local trace_normalizing    = false  registertracker("math.normalizing", function(v) trace_normalizing = v end)
local trace_collapsing     = false  registertracker("math.collapsing",  function(v) trace_collapsing  = v end)
local trace_patching       = false  registertracker("math.patching",    function(v) trace_patching    = v end)
local trace_goodies        = false  registertracker("math.goodies",     function(v) trace_goodies     = v end)
local trace_variants       = false  registertracker("math.variants",    function(v) trace_variants    = v end)
local trace_alternates     = false  registertracker("math.alternates",  function(v) trace_alternates  = v end)
local trace_italics        = false  registertracker("math.italics",     function(v) trace_italics     = v end)
local trace_kernpairs      = false  registertracker("math.kernpairs",   function(v) trace_kernpairs   = v end)
local trace_domains        = false  registertracker("math.domains",     function(v) trace_domains     = v end)
local trace_families       = false  registertracker("math.families",    function(v) trace_families    = v end)
local trace_fences         = false  registertracker("math.fences",      function(v) trace_fences      = v end)

local check_coverage       = true   registerdirective("math.checkcoverage", function(v) check_coverage = v end)

local report_processing    = logreporter("mathematics","processing")
local report_remapping     = logreporter("mathematics","remapping")
local report_normalizing   = logreporter("mathematics","normalizing")
local report_collapsing    = logreporter("mathematics","collapsing")
local report_patching      = logreporter("mathematics","patching")
local report_goodies       = logreporter("mathematics","goodies")
local report_variants      = logreporter("mathematics","variants")
local report_alternates    = logreporter("mathematics","alternates")
local report_italics       = logreporter("mathematics","italics")
local report_kernpairs     = logreporter("mathematics","kernpairs")
local report_domains       = logreporter("mathematics","domains")
local report_families      = logreporter("mathematics","families")
local report_fences        = logreporter("mathematics","fences")

local a_mathrendering      = privateattribute("mathrendering")
local a_exportstatus       = privateattribute("exportstatus")

local nuts                 = nodes.nuts
local nodepool             = nuts.pool
local tonut                = nuts.tonut
local tonode               = nuts.tonode
local nutstring            = nuts.tostring

local setfield             = nuts.setfield
local setlink              = nuts.setlink
local setlist              = nuts.setlist
local setnext              = nuts.setnext
local setprev              = nuts.setprev
local setchar              = nuts.setchar
local setsubtype           = nuts.setsubtype
local setattr              = nuts.setattr

local getfield             = nuts.getfield
local getnext              = nuts.getnext
local getprev              = nuts.getprev
local getboth              = nuts.getboth
local getid                = nuts.getid
local getsubtype           = nuts.getsubtype
local getchar              = nuts.getchar
local getfont              = nuts.getfont
local getattr              = nuts.getattr
local getlist              = nuts.getlist

local getnucleus           = nuts.getnucleus
local getsub               = nuts.getsub
local getsup               = nuts.getsup

local setnucleus           = nuts.setnucleus
local setsub               = nuts.setsub
local setsup               = nuts.setsup

local flush_node           = nuts.flush
local new_node             = nuts.new -- todo: pool: math_noad math_sub
local copy_node            = nuts.copy
local slide_nodes          = nuts.slide
local set_visual           = nuts.setvisual

local mlist_to_hlist       = nodes.mlist_to_hlist

local font_of_family       = node.family_font

local new_kern             = nodepool.kern

local fonthashes           = fonts.hashes
local fontdata             = fonthashes.identifiers
local fontcharacters       = fonthashes.characters
local fontitalics          = fonthashes.italics

local variables            = interfaces.variables
local texsetattribute      = tex.setattribute
local texgetattribute      = tex.getattribute
local unsetvalue           = attributes.unsetvalue
local implement            = interfaces.implement

local v_reset              = variables.reset

local chardata             = characters.data

noads                      = noads or { }  -- todo: only here
local noads                = noads

noads.processors           = noads.processors or { }
local processors           = noads.processors

noads.handlers             = noads.handlers   or { }
local handlers             = noads.handlers

local tasks                = nodes.tasks
local enableaction         = tasks.enableaction
local setaction            = tasks.setaction

local nodecodes            = nodes.nodecodes
local noadcodes            = nodes.noadcodes
local fencecodes           = nodes.fencecodes

local noad_ord             = noadcodes.ord
local noad_rel             = noadcodes.rel
local noad_bin             = noadcodes.bin
local noad_open            = noadcodes.open
local noad_close           = noadcodes.close
local noad_punct           = noadcodes.punct
local noad_opdisplaylimits = noadcodes.opdisplaylimits
local noad_oplimits        = noadcodes.oplimits
local noad_opnolimits      = noadcodes.opnolimits
local noad_inner           = noadcodes.inner

local math_noad            = nodecodes.noad           -- attr nucleus sub sup
local math_accent          = nodecodes.accent         -- attr nucleus sub sup accent
local math_radical         = nodecodes.radical        -- attr nucleus sub sup left degree
local math_fraction        = nodecodes.fraction       -- attr nucleus sub sup left right
local math_box             = nodecodes.subbox         -- attr list
local math_sub             = nodecodes.submlist       -- attr list
local math_char            = nodecodes.mathchar       -- attr fam char
local math_textchar        = nodecodes.mathtextchar   -- attr fam char
local math_delim           = nodecodes.delim          -- attr small_fam small_char large_fam large_char
----- math_style           = nodecodes.style          -- attr style
local math_choice          = nodecodes.choice         -- attr display text script scriptscript
local math_fence           = nodecodes.fence          -- attr subtype

local left_fence_code      = fencecodes.left
local middle_fence_code    = fencecodes.middle
local right_fence_code     = fencecodes.right

-- local mathclasses          = mathematics.classes
-- local fenceclasses         = {
--     [left_fence_code]   = mathclasses.open,
--     [middle_fence_code] = mathclasses.middle,
--     [right_fence_code]  = mathclasses.close,
-- }

-- this initial stuff is tricky as we can have removed and new nodes with the same address
-- the only way out is a free-per-page list of nodes (not bad anyway)

-- local gf = getfield local gt = setmetatableindex("number") getfield = function(n,f)   gt[f] = gt[f] + 1 return gf(n,f)   end mathematics.GETFIELD = gt
-- local sf = setfield local st = setmetatableindex("number") setfield = function(n,f,v) st[f] = st[f] + 1        sf(n,f,v) end mathematics.SETFIELD = st

local function process(start,what,n,parent)
    if n then
        n = n + 1
    else
        n = 0
    end
    --
    local initial = start
    --
    slide_nodes(start) -- we still miss a prev in noads -- fences test code
    --
    while start do
        local id = getid(start)
        if trace_processing then
            if id == math_noad then
                report_processing("%w%S, class %a",n*2,nutstring(start),noadcodes[getsubtype(start)])
            elseif id == math_char then
                local char = getchar(start)
                local font = getfont(start)
                local fam  = getfield(start,"fam")
                report_processing("%w%S, family %a, font %a, char %a, shape %c",n*2,nutstring(start),fam,font,char,char)
            else
                report_processing("%w%S",n*2,nutstring(start))
            end
        end
        local proc = what[id]
        if proc then
         -- report_processing("start processing")
            local done, newstart, newinitial = proc(start,what,n,parent) -- prev is bugged:  or getprev(start)
            if newinitial then
                initial = newinitial -- temp hack .. we will make all return head
                if newstart then
                    start = newstart
                 -- report_processing("stop processing (new start)")
                else
                 -- report_processing("quit processing (done)")
                    break
                end
            else
                if newstart then
                    start = newstart
                 -- report_processing("stop processing (new start)")
                else
                 -- report_processing("stop processing")
                end
            end
        elseif id == math_noad then
            -- single characters are like this
            local noad = getnucleus(start)              if noad then process(noad,what,n,start) end -- list
                  noad = getsup    (start)              if noad then process(noad,what,n,start) end -- list
                  noad = getsub    (start)              if noad then process(noad,what,n,start) end -- list
        elseif id == math_char or id == math_textchar or id == math_delim then
            break
        elseif id == math_box or id == math_sub then
            local noad = getlist(start)                 if noad then process(noad,what,n,start) end -- list (not getlist !)
        elseif id == math_fraction then
            local noad = getfield(start,"num")          if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"denom")        if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"left")         if noad then process(noad,what,n,start) end -- delimiter
                  noad = getfield(start,"right")        if noad then process(noad,what,n,start) end -- delimiter
        elseif id == math_choice then
            local noad = getfield(start,"display")      if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"text")         if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"script")       if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"scriptscript") if noad then process(noad,what,n,start) end -- list
        elseif id == math_fence then
            local noad = getfield(start,"delim")        if noad then process(noad,what,n,start) end -- delimiter
        elseif id == math_radical then
            local noad = getnucleus(start)              if noad then process(noad,what,n,start) end -- list
                  noad = getsup    (start)              if noad then process(noad,what,n,start) end -- list
                  noad = getsub    (start)              if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"left")         if noad then process(noad,what,n,start) end -- delimiter
                  noad = getfield(start,"degree")       if noad then process(noad,what,n,start) end -- list
        elseif id == math_accent then
            local noad = getnucleus(start)              if noad then process(noad,what,n,start) end -- list
                  noad = getsup    (start)              if noad then process(noad,what,n,start) end -- list
                  noad = getsub    (start)              if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"accent")       if noad then process(noad,what,n,start) end -- list
                  noad = getfield(start,"bot_accent")   if noad then process(noad,what,n,start) end -- list
     -- elseif id == math_style then
     --     -- has a next
     -- else
     --     -- glue, penalty, etc
        end
        start = getnext(start)
    end
    if not parent then
        return initial, true -- only first level -- for now
    end
end

local function processnested(current,what,n)
    local noad = nil
    local id   = getid(current)
    if id == math_noad then
        noad = getnucleus(current)              if noad then process(noad,what,n,current) end -- list
        noad = getsup    (current)              if noad then process(noad,what,n,current) end -- list
        noad = getsub    (current)              if noad then process(noad,what,n,current) end -- list
    elseif id == math_box or id == math_sub then
        noad = getlist(current)                 if noad then process(noad,what,n,current) end -- list (not getlist !)
    elseif id == math_fraction then
        noad = getfield(current,"num")          if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"denom")        if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"left")         if noad then process(noad,what,n,current) end -- delimiter
        noad = getfield(current,"right")        if noad then process(noad,what,n,current) end -- delimiter
    elseif id == math_choice then
        noad = getfield(current,"display")      if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"text")         if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"script")       if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"scriptscript") if noad then process(noad,what,n,current) end -- list
    elseif id == math_fence then
        noad = getfield(current,"delim")        if noad then process(noad,what,n,current) end -- delimiter
    elseif id == math_radical then
        noad = getnucleus(current)              if noad then process(noad,what,n,current) end -- list
        noad = getsup    (current)              if noad then process(noad,what,n,current) end -- list
        noad = getsub    (current)              if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"left")         if noad then process(noad,what,n,current) end -- delimiter
        noad = getfield(current,"degree")       if noad then process(noad,what,n,current) end -- list
    elseif id == math_accent then
        noad = getnucleus(current)              if noad then process(noad,what,n,current) end -- list
        noad = getsup    (current)              if noad then process(noad,what,n,current) end -- list
        noad = getsub    (current)              if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"accent")       if noad then process(noad,what,n,current) end -- list
        noad = getfield(current,"bot_accent")   if noad then process(noad,what,n,current) end -- list
    end
end

local function processstep(current,process,n,id)
    local noad = nil
    local id   = id or getid(current)
    if id == math_noad then
        noad = getnucleus(current)              if noad then process(noad,n,current) end -- list
        noad = getsup    (current)              if noad then process(noad,n,current) end -- list
        noad = getsub    (current)              if noad then process(noad,n,current) end -- list
    elseif id == math_box or id == math_sub then
        noad = getlist(current)                 if noad then process(noad,n,current) end -- list (not getlist !)
    elseif id == math_fraction then
        noad = getfield(current,"num")          if noad then process(noad,n,current) end -- list
        noad = getfield(current,"denom")        if noad then process(noad,n,current) end -- list
        noad = getfield(current,"left")         if noad then process(noad,n,current) end -- delimiter
        noad = getfield(current,"right")        if noad then process(noad,n,current) end -- delimiter
    elseif id == math_choice then
        noad = getfield(current,"display")      if noad then process(noad,n,current) end -- list
        noad = getfield(current,"text")         if noad then process(noad,n,current) end -- list
        noad = getfield(current,"script")       if noad then process(noad,n,current) end -- list
        noad = getfield(current,"scriptscript") if noad then process(noad,n,current) end -- list
    elseif id == math_fence then
        noad = getfield(current,"delim")        if noad then process(noad,n,current) end -- delimiter
    elseif id == math_radical then
        noad = getnucleus(current)              if noad then process(noad,n,current) end -- list
        noad = getsup    (current)              if noad then process(noad,n,current) end -- list
        noad = getsub    (current)              if noad then process(noad,n,current) end -- list
        noad = getfield(current,"left")         if noad then process(noad,n,current) end -- delimiter
        noad = getfield(current,"degree")       if noad then process(noad,n,current) end -- list
    elseif id == math_accent then
        noad = getnucleus(current)              if noad then process(noad,n,current) end -- list
        noad = getsup    (current)              if noad then process(noad,n,current) end -- list
        noad = getsub    (current)              if noad then process(noad,n,current) end -- list
        noad = getfield(current,"accent")       if noad then process(noad,n,current) end -- list
        noad = getfield(current,"bot_accent")   if noad then process(noad,n,current) end -- list
    end
end

local function processnoads(head,actions,banner)
    local h, d
    if trace_processing then
        report_processing("start %a",banner)
        h, d = process(tonut(head),actions)
        report_processing("stop %a",banner)
    else
        h, d = process(tonut(head),actions)
    end
    return h and tonode(h) or head, d == nil and true or d
end

noads.process       = processnoads
noads.processnested = processnested
noads.processouter  = process


-- experiment (when not present fall back to fam 0) -- needs documentation

local unknowns = { }
local checked  = { } -- simple case
local tracked  = false  trackers.register("fonts.missing", function(v) tracked = v end)
local cached   = setmetatableindex("table") -- complex case

local function errorchar(font,char)
    local done = unknowns[char]
    if done then
        unknowns[char] = done  + 1
    else
        unknowns[char] = 1
    end
    if tracked then
        -- slower as we check each font too and we always replace as math has
        -- more demands than text
        local fake = cached[font][char]
        if fake then
            return fake
        else
            local kind, fake = fonts.checkers.placeholder(font,char)
            if not fake or kind ~= "char" then
                fake = 0x3F
            end
            cached[font][char] = fake
            return fake
        end
    else
        -- only simple checking, report at the end so one should take
        -- action anyway ... we can miss a few checks but that is ok
        -- as there is at least one reported
        if not checked[char] then
            if trace_normalizing then
                report_normalizing("character %C is not available",char)
            end
            checked[char] = true
        end
        return 0x3F
    end
end

-- 0-2 regular
-- 3-5 bold
-- 6-8 pseudobold

-- this could best be integrated in the remapper, and if we run into problems, we
-- might as well do this

do

    local families     = { }
    local a_mathfamily = privateattribute("mathfamily")
    local boldmap      = mathematics.boldmap

    local familymap = { [0] =
        "regular",
        "regular",
        "regular",
        "bold",
        "bold",
        "bold",
        "pseudobold",
        "pseudobold",
        "pseudobold",
    }

    families[math_char] = function(pointer)
        if getfield(pointer,"fam") == 0 then
            local a = getattr(pointer,a_mathfamily)
            if a and a > 0 then
                setattr(pointer,a_mathfamily,0)
                if a > 5 then
                    local char = getchar(pointer)
                    local bold = boldmap[char]
                    local newa = a - 3
                    if not bold then
                        if trace_families then
                            report_families("no bold replacement for %C, family %s with remap %s becomes %s with remap %s",char,a,familymap[a],newa,familymap[newa])
                        end
                        setfield(pointer,"fam",newa)
                    elseif not fontcharacters[font_of_family(newa)][bold] then
                        if trace_families then
                            report_families("no bold character for %C, family %s with remap %s becomes %s with remap %s",char,a,familymap[a],newa,familymap[newa])
                        end
                        if newa > 3 then
                            setfield(pointer,"fam",newa-3)
                        end
                    else
                        setattr(pointer,a_exportstatus,char)
                        setchar(pointer,bold)
                        if trace_families then
                            report_families("replacing %C by bold %C, family %s with remap %s becomes %s with remap %s",char,bold,a,familymap[a],newa,familymap[newa])
                        end
                        setfield(pointer,"fam",newa)
                    end
                else
                    local char = getchar(pointer)
                    if not fontcharacters[font_of_family(a)][char] then
                        if trace_families then
                            report_families("no bold replacement for %C",char)
                        end
                    else
                        if trace_families then
                            report_families("family of %C becomes %s with remap %s",char,a,familymap[a])
                        end
                        setfield(pointer,"fam",a)
                    end
                end
            end
        end
    end

    families[math_delim] = function(pointer)
        if getfield(pointer,"small_fam") == 0 then
            local a = getattr(pointer,a_mathfamily)
            if a and a > 0 then
                setattr(pointer,a_mathfamily,0)
                if a > 5 then
                    -- no bold delimiters in unicode
                    a = a - 3
                end
                local char = getfield(pointer,"small_char")
                local okay = fontcharacters[font_of_family(a)][char]
                if okay then
                    setfield(pointer,"small_fam",a)
                elseif a > 2 then
                    setfield(pointer,"small_fam",a-3)
                end
                local char = getfield(pointer,"large_char")
                local okay = fontcharacters[font_of_family(a)][char]
                if okay then
                    setfield(pointer,"large_fam",a)
                elseif a > 2 then
                    setfield(pointer,"large_fam",a-3)
                end
            else
                setfield(pointer,"small_fam",0)
                setfield(pointer,"large_fam",0)
            end
        end
    end

    families[math_textchar] = families[math_char]

    function handlers.families(head,style,penalties)
        processnoads(head,families,"families")
        return true
    end

end

-- character remapping

do

    local a_mathalphabet = privateattribute("mathalphabet")
    local a_mathgreek    = privateattribute("mathgreek")

    processors.relocate = { }

    local function report_remap(tag,id,old,new,extra)
        report_remapping("remapping %s in font %s from %C to %C%s",tag,id,old,new,extra)
    end

    local remapalphabets    = mathematics.remapalphabets
    local fallbackstyleattr = mathematics.fallbackstyleattr
    local setnodecolor      = nodes.tracers.colors.set

    local function checked(pointer)
        local char = getchar(pointer)
        local font = getfont(pointer)
        local data = fontcharacters[font]
        if not data[char] then
            local specials = characters.data[char].specials
            if specials and (specials[1] == "char" or specials[1] == "font") then
                local newchar = specials[#specials]
                if trace_remapping then
                    report_remap("fallback",font,char,newchar)
                end
                if trace_analyzing then
                    setnodecolor(pointer,"font:isol")
                end
                setattr(pointer,a_exportstatus,char) -- testcase: exponentiale
                setchar(pointer,newchar)
                return true
            end
        end
    end

    processors.relocate[math_char] = function(pointer)
        local g          = getattr(pointer,a_mathgreek) or 0
        local a          = getattr(pointer,a_mathalphabet) or 0
        local char       = getchar(pointer)
        local font       = getfont(pointer)
        local characters = fontcharacters[font]
        if a > 0 or g > 0 then
            if a > 0 then
                setattr(pointer,a_mathgreek,0)
            end
            if g > 0 then
                setattr(pointer,a_mathalphabet,0)
            end
            local newchar = remapalphabets(char,a,g)
            if newchar then
                if characters[newchar] then
                    if trace_remapping then
                        report_remap("char",font,char,newchar)
                    end
                    if trace_analyzing then
                        setnodecolor(pointer,"font:isol")
                    end
                    setchar(pointer,newchar)
                    return true
                else
                    local fallback = fallbackstyleattr(a)
                    if fallback then
                        local newchar = remapalphabets(char,fallback,g)
                        if newchar then
                            if characters[newchar] then
                                if trace_remapping then
                                    report_remap("char",font,char,newchar," (fallback remapping used)")
                                end
                                if trace_analyzing then
                                    setnodecolor(pointer,"font:isol")
                                end
                                setchar(pointer,newchar)
                                return true
                            elseif trace_remapping then
                                report_remap("char",font,char,newchar," fails (no fallback character)")
                            end
                        elseif trace_remapping then
                            report_remap("char",font,char,newchar," fails (no fallback remap character)")
                        end
                    elseif trace_remapping then
                        report_remap("char",font,char,newchar," fails (no fallback style)")
                    end
                end
            end
        end
        if not characters[char] then
            setchar(pointer,errorchar(font,char))
        end
        if trace_analyzing then
            setnodecolor(pointer,"font:medi")
        end
        if check_coverage then
            return checked(pointer)
        end
    end

    processors.relocate[math_textchar] = function(pointer)
        if trace_analyzing then
            setnodecolor(pointer,"font:init")
        end
    end

    processors.relocate[math_delim] = function(pointer)
        if trace_analyzing then
            setnodecolor(pointer,"font:fina")
        end
    end

    function handlers.relocate(head,style,penalties)
        processnoads(head,processors.relocate,"relocate")
        return true
    end

end

-- rendering (beware, not exported)

processors.render = { }

local rendersets = mathematics.renderings.numbers or { } -- store

processors.render[math_char] = function(pointer)
    local attr = getattr(pointer,a_mathrendering)
    if attr and attr > 0 then
        local char = getchar(pointer)
        local renderset = rendersets[attr]
        if renderset then
            local newchar = renderset[char]
            if newchar then
                local font       = getfont(pointer)
                local characters = fontcharacters[font]
                if characters and characters[newchar] then
                    setchar(pointer,newchar)
                    setattr(pointer,a_exportstatus,char)
                end
            end
        end
    end
end

function handlers.render(head,style,penalties)
    processnoads(head,processors.render,"render")
    return true
end

-- some resize options (this works ok because the content is
-- empty and no larger next will be forced)
--
-- beware: we don't use \delcode but \Udelcode and as such have
-- no large_fam; also, we need to check for subtype and/or
-- small_fam not being 0 because \. sits in 0,0 by default
--
-- todo: just replace the character by an ord noad
-- and remove the right delimiter as well

local a_mathsize  = privateattribute("mathsize") -- this might move into other fence code
local resize      = { }
processors.resize = resize

resize[math_fence] = function(pointer)
    local subtype = getsubtype(pointer)
    if subtype == left_fence_code or subtype == right_fence_code then
        local a = getattr(pointer,a_mathsize)
        if a and a > 0 then
            local method, size = div(a,100), a % 100
            setattr(pointer,a_mathsize,0)
            local delimiter = getfield(pointer,"delim")
            local chr = getfield(delimiter,"small_char")
            if chr > 0 then
                local fam = getfield(delimiter,"small_fam")
                local id = font_of_family(fam)
                if id > 0 then
                    setfield(delimiter,"small_char",mathematics.big(fontdata[id],chr,size,method))
                end
            end
        end
    end
end

function handlers.resize(head,style,penalties)
    processnoads(head,resize,"resize")
    return true
end

-- still not perfect:

local a_autofence     = privateattribute("mathautofence")
local autofences      = { }
processors.autofences = autofences
local dummyfencechar  = 0x2E

local function makefence(what,char)
    local d = new_node(math_delim)
    local f = new_node(math_fence)
    if char then
        local sym = getnucleus(char)
        local chr = getchar(sym)
        local fam = getfield(sym,"fam")
        if chr == dummyfencechar then
            chr = 0
        end
        setfield(d,"small_char",chr)
        setfield(d,"small_fam", fam)
        flush_node(sym)
    end
    setsubtype(f,what)
    setfield(f,"delim",d)
    setfield(f,"class",-1) -- tex itself does this, so not fenceclasses[what]
    return f
end

local function makelist(noad,f_o,o_next,c_prev,f_c,middle)
    local list = new_node(math_sub)
    setlist(list,f_o)
    setsubtype(noad,noad_inner)
    setnucleus(noad,list)
    setlink(f_o,o_next)
    setlink(c_prev,f_c)
    if middle and next(middle) then
        local prev    = f_o
        local current = o_next
        while current ~= f_c do
            local m = middle[current]
            if m then
                local next  = getnext(current)
                local fence = makefence(middle_fence_code,current)
                setnucleus(current)
                flush_node(current)
                middle[current] = nil
                -- replace_node
                setlink(prev,fence,next)
                prev    = fence
                current = next
            else
                prev = current
                current = getnext(current)
            end
        end
    end
end

local function convert_both(open,close,middle)
    local o_prev, o_next = getboth(open)
    local c_prev, c_next = getboth(close)
    if o_next == close then
        return close
    else
        local f_o = makefence(left_fence_code,open)
        local f_c = makefence(right_fence_code,close)
        makelist(open,f_o,o_next,c_prev,f_c,middle)
        setnucleus(close)
        flush_node(close)
        if c_next then
            setprev(c_next,open)
        end
        setnext(open,c_next)
        return open
    end
end

local function convert_open(open,last,middle)
    local f_o = makefence(left_fence_code,open)
    local f_c = makefence(right_fence_code)
    local o_prev, o_next = getboth(open)
    local l_prev, l_next = getboth(last)
    makelist(open,f_o,o_next,last,f_c,middle)
    if l_next then
        setprev(l_next,open)
    end
    setnext(open,l_next)
    return open
end

local function convert_close(close,first,middle)
    local f_o = makefence(left_fence_code)
    local f_c = makefence(right_fence_code,close)
    local c_prev = getprev(close)
    makelist(close,f_o,first,c_prev,f_c,middle)
    return close
end

local stacks = setmetatableindex("table")

local function processfences(pointer,n,parent)
    local current = pointer
    local last    = pointer
    local start   = pointer
    local done    = false
    local initial = pointer
    local stack   = nil
    local middle  = nil -- todo: use properties
    while current do
        local id = getid(current)
        if id == math_noad then
            local a = getattr(current,a_autofence)
            if a and a > 0 then
                local stack = stacks[n]
                setattr(current,a_autofence,0)
                if a == 1 or (a == 4 and (not stack or #stack == 0)) then
                    if trace_fences then
                        report_fences("%2i: pushing open on stack",n)
                    end
                    insert(stack,current)
                elseif a == 2 or a == 4 then
                    local open = remove(stack)
                    if open then
                        if trace_fences then
                            report_fences("%2i: handling %s, stack depth %i",n,"both",#stack+1)
                        end
                        current = convert_both(open,current,middle)
                    elseif current == start then
                        -- skip
                    else
                        if trace_fences then
                            report_fences("%2i: handling %s, stack depth %i",n,"close",#stack+1)
                        end
                        current = convert_close(current,initial,middle)
                        if not parent then
                            initial = current
                        end
                    end
                    if trace_fences then
                        report_fences("%2i: popping close from stack",n)
                    end
                elseif a == 3 then
                    if trace_fences then
                        report_fences("%2i: registering middle",n)
                    end
                    if middle then
                        middle[current] = last
                    else
                        middle = { [current] = last }
                    end
                end
                done = true
            else
                processstep(current,processfences,n+1,id)
            end
        else
            -- next at current level
            processstep(current,processfences,n,id)
        end
        last    = current
        current = getnext(current)
    end
    if done then
        local stack = stacks[n]
        local s = #stack
        if s > 0 then
            if trace_fences then
                report_fences("%2i: handling %s stack levels",n,s)
            end
            for i=1,s do
                local open = remove(stack)
                if trace_fences then
                    report_fences("%2i: handling %s, stack depth %i",n,"open",#stack)
                end
                last = convert_open(open,last,middle)
            end
        end
    end
end

-- we can have a first changed node .. an option is to have a leading dummy node in math
-- lists like the par node as it can save a  lot of mess

local enabled = false

implement {
    name     = "enableautofences",
    onlyonce = true,
    actions  = function()
        enableaction("math","noads.handlers.autofences")
        enabled = true
    end
}

function handlers.autofences(head,style,penalties)
    if enabled then -- tex.modes.c_math_fences_auto
     -- inspect(nodes.totree(head))
        processfences(tonut(head),1)
     -- inspect(nodes.totree(head))
    end
end

-- normalize scripts

local unscript     = { }  noads.processors.unscript = unscript
local superscripts = characters.superscripts
local subscripts   = characters.subscripts
local fractions    = characters.fractions
local replaced     = { }

local function replace(pointer,what,n,parent)
    pointer = parent -- we're following the parent list (chars trigger this)
    local next = getnext(pointer)
    local start_super, stop_super, start_sub, stop_sub
    local mode = "unset"
    while next and getid(next) == math_noad do
        local nextnucleus = getnucleus(next)
        if nextnucleus and getid(nextnucleus) == math_char and not getsub(next) and not getsup(next) then
            local char = getchar(nextnucleus)
            local s = superscripts[char]
            if s then
                if not start_super then
                    start_super = next
                    mode = "super"
                elseif mode == "sub" then
                    break
                end
                stop_super = next
                next = getnext(next)
                setchar(nextnucleus,s)
                replaced[char] = (replaced[char] or 0) + 1
                if trace_normalizing then
                    report_normalizing("superscript %C becomes %C",char,s)
                end
            else
                local s = subscripts[char]
                if s then
                    if not start_sub then
                        start_sub = next
                        mode = "sub"
                    elseif mode == "super" then
                        break
                    end
                    stop_sub = next
                    next = getnext(next)
                    setchar(nextnucleus,s)
                    replaced[char] = (replaced[char] or 0) + 1
                    if trace_normalizing then
                        report_normalizing("subscript %C becomes %C",char,s)
                    end
                else
                    break
                end
            end
        else
            break
        end
    end
    if start_super then
        if start_super == stop_super then
            setsup(pointer,getnucleus(start_super))
        else
            local list = new_node(math_sub) -- todo attr
            setlist(list,start_super)
            setsup(pointer,list)
        end
        if mode == "super" then
            setnext(pointer,getnext(stop_super))
        end
        setnext(stop_super)
    end
    if start_sub then
        if start_sub == stop_sub then
            setsub(pointer,getnucleus(start_sub))
        else
            local list = new_node(math_sub) -- todo attr
            setlist(list,start_sub)
            setsub(pointer,list)
        end
        if mode == "sub" then
            setnext(pointer,getnext(stop_sub))
        end
        setnext(stop_sub)
    end
    -- we could return stop
end

unscript[math_char] = replace -- not noads as we need to recurse

function handlers.unscript(head,style,penalties)
    processnoads(head,unscript,"unscript")
--  processnoads(head,checkers,"checkers")
    return true
end

local function collected(list)
    if list and next(list) then
        local n, t = 0, { }
        for k, v in sortedhash(list) do
            n = n + v
            t[#t+1] = formatters["%C"](k)
        end
        return formatters["% t (n=%s)"](t,n)
    end
end

statistics.register("math script replacements", function()
    return collected(replaced)
end)

statistics.register("unknown math characters", function()
    return collected(unknowns)
end)

-- math alternates: (in xits     lgf: $ABC$ $\cal ABC$ $\mathalternate{cal}\cal ABC$)
-- math alternates: (in lucidaot lgf: $ABC \mathalternate{italic} ABC$)

-- todo: set alternate for specific symbols
-- todo: no need to do this when already loaded
-- todo: use a fonts.hashes.mathalternates

do

    local last = 0

    local known = setmetatableindex(function(t,k)
        local v = setbit(0,2^last)
        t[k] = v
        last = last + 1
        return v
    end)

    local defaults = {
        dotless = { feature = 'dtls', value = 1, comment = "Mathematical Dotless Forms" },
     -- zero    = { feature = 'zero', value = 1, comment = "Slashed or Dotted Zero" }, -- in no math font (yet)
    }

    local function initializemathalternates(tfmdata)
        local goodies  = tfmdata.goodies
        local autolist = defaults -- table.copy(defaults)

        local function setthem(newalternates)
            local resources      = tfmdata.resources -- was tfmdata.shared
            local mathalternates = resources.mathalternates
            local alternates, attributes, registered, presets
            if mathalternates then
                alternates = mathalternates.alternates
                attributes = mathalternates.attributes
                registered = mathalternates.registered
            else
                alternates, attributes, registered = { }, { }, { }
                mathalternates = {
                    attributes = attributes,
                    alternates = alternates,
                    registered = registered,
                    presets    = { },
hashes = setmetatableindex("table")
                }
                resources.mathalternates = mathalternates
            end
            --
            for name, data in sortedhash(newalternates) do
                if alternates[name] then
                    -- ignore
                else
                    local attr = known[name]
                    attributes[attr] = data
                    alternates[name] = attr
                    registered[#registered+1] = attr
                end
            end
        end

        if goodies then
            local done = { }
            for i=1,#goodies do
                -- first one counts
                -- we can consider sharing the attributes ... todo (only once scan)
                local mathgoodies = goodies[i].mathematics
                local alternates  = mathgoodies and mathgoodies.alternates
                if alternates then
                    if trace_goodies then
                        report_goodies("loading alternates for font %a",tfmdata.properties.name)
                    end
                    for k, v in next, autolist do
                        if not alternates[k] then
                            alternates[k] = v
                        end
                    end
                    setthem(alternates)
                    return
                end
            end
        end

        if trace_goodies then
            report_goodies("loading default alternates for font %a",tfmdata.properties.name)
        end
        setthem(autolist)

    end

    registerotffeature {
        name        = "mathalternates",
        description = "additional math alternative shapes",
        initializers = {
            base = initializemathalternates,
            node = initializemathalternates,
        }
    }

    -- local getalternate = otf.getalternate (runtime new method so ...)

    -- todo: not shared but copies ... one never knows

    local a_mathalternate = privateattribute("mathalternate")
    local alternate       = { } -- processors.alternate = alternate
    local fontdata        = fonts.hashes.identifiers
    local fontresources   = fonts.hashes.resources

    local function getalternate(fam,tag)
        local resources = fontresources[font_of_family(fam)]
        local attribute = unsetvalue
        if resources then
            local mathalternates = resources.mathalternates
            if mathalternates then
                local presets = mathalternates.presets
                if presets then
                    attribute = presets[tag]
                    if not attribute then
                        attribute  = 0
                        local alternates = mathalternates.alternates
                        for s in gmatch(tag,"[^, ]+") do
                            local a = alternates[s] -- or known[s]
                            if a then
                                attribute = attribute + a
                            end
                        end
                        if attribute == 0 then
                            attribute = unsetvalue
                        end
                        presets[tag] = attribute
                    end
                end
            end
        end
        return attribute
    end

    local function presetalternate(fam,tag)
        texsetattribute(a_mathalternate,getalternate(fam,tag))
    end

    implement {
        name      = "presetmathalternate",
        actions   = presetalternate,
        arguments = { "integer", "string" }
    }

    local function setalternate(fam,tag)
        local a = texgetattribute(a_mathalternate)
        local v = getalternate(fam,tag)
        if a and a > 0 then
            v = a + v
        end
        texsetattribute(a_mathalternate,v)
    end

    implement {
        name      = "setmathalternate",
        actions   = setalternate,
        arguments = { "integer", "string" }
    }

    alternate[math_char] = function(pointer) -- slow
        local a = getattr(pointer,a_mathalternate)
        if a and a > 0 then
            setattr(pointer,a_mathalternate,0)
            local fontid    = getfont(pointer)
            local resources = fontresources[fontid]
            if resources then
                local mathalternates = resources.mathalternates
                if mathalternates then
                    local attributes = mathalternates.attributes
                    local registered = mathalternates.registered
                    local hashes     = mathalternates.hashes
                    for i=1,#registered do
                        local r = registered[i]
                        if hasbit(a,r) then
                            local char = getchar(pointer)
                            local alt  = hashes[i][char]
                            if alt == nil then
                                local what = attributes[r]
                                alt = otf.getalternate(fontdata[fontid],char,what.feature,what.value) or false
                                if alt == char then
                                    alt = false
                                elseif trace_alternates then
                                    report_alternates("alternate %a, value %a, replacing glyph %U by glyph %U",
                                        tostring(what.feature),tostring(what.value),getchar(pointer),alt)
                                end
                                hashes[i][char] = alt
                            end
                            if alt then
                                setchar(pointer,alt)
                                break
                            end
                        end
                    end
                end
            end
        end
    end

    function handlers.alternates(head,style,penalties)
        processnoads(head,alternate,"alternate")
        return true
    end

end

-- italics: we assume that only characters matter
--
-- = we check for correction first because accessing nodes is slower
-- = the actual glyph is not that important (we can control it with numbers)

-- Italic correction in luatex math is (was) a mess. There are all kind of assumptions based on
-- old fonts and new fonts. Eventually there should be a flag that can signal to ignore all
-- those heuristics. We want to deal with it ourselves also in the perspective of mixed math
-- and text. Also, for a while in context we had to deal with a mix of virtual math fonts and
-- real ones.

-- in opentype the italic correction of a limop is added to the width and luatex does
-- some juggling that we want to avoid but we need to do something here (in fact, we could
-- better fix the width of the character

local a_mathitalics = privateattribute("mathitalics")

local italics        = { }
local default_factor = 1/20

local setcolor     = nodes.tracers.colors.set
local resetcolor   = nodes.tracers.colors.reset
local italic_kern  = new_kern
local c_positive_d = "trace:dg"
local c_negative_d = "trace:dr"

local function insert_kern(current,kern)
    local sub  = new_node(math_sub)  -- todo: pool
    local noad = new_node(math_noad) -- todo: pool
    setlist(sub,kern)
    setnext(kern,noad)
    setnucleus(noad,current)
    return sub
end

registertracker("math.italics.visualize", function(v)
    if v then
        italic_kern = function(k)
            local n = new_kern(k)
            set_visual(n,"italic")
            return n
        end
    else
        italic_kern = new_kern
    end
end)

local function getcorrection(method,font,char) -- -- or character.italic -- (this one is for tex)

    local visual = chardata[char].visual

    if method == 1 then
        -- check on state
        local italics = fontitalics[font]
        if italics then
            local character = fontcharacters[font][char]
            if character then
                local correction = character.italic
                if correction and correction ~= 0 then
                    return correction, visual
                end
            end
        end
    elseif method == 2 then
        -- no check
        local character = fontcharacters[font][char]
        if character then
            local correction = character.italic
            if correction and correction ~= 0 then
                return correction, visual
            end
        end
    elseif method == 3 then
        -- check on visual
        if visual == "it" or visual == "bi" then
            local character = fontcharacters[font][char]
            if character then
                local correction = character.italic
                if correction and correction ~= 0 then
                    return correction, visual
                end
            end
        end
    elseif method == 4 then
        -- combination of 1 and 3
        local italics = fontitalics[font]
        if italics and (visual == "it" or visual == "bi") then
            local character = fontcharacters[font][char]
            if character then
                local correction = character.italic
                if correction and correction ~= 0 then
                    return correction, visual
                end
            end
        end
    end

end

italics[math_char] = function(pointer,what,n,parent)
    local method = getattr(pointer,a_mathitalics)
    if method and method > 0 and method < 100 then
        local char = getchar(pointer)
        local font = getfont(pointer)
        local correction, visual = getcorrection(method,font,char)
        if correction and correction ~= 0 then
            local next_noad = getnext(parent)
            if not next_noad then
                if n == 1 then
                    -- only at the outer level .. will become an option (always,endonly,none)
                    if trace_italics then
                        report_italics("method %a, flagging italic correction %p between %C and end math",method,correction,char)
                    end
                    if correction > 0 then
                        correction = correction + 100
                    else
                        correction = correction - 100
                    end
                    setattr(pointer,a_mathitalics,correction)
                    setattr(parent,a_mathitalics,correction)
                end
            end
        end
    end
end

function handlers.italics(head,style,penalties)
    processnoads(head,italics,"italics")
    return true
end

local enable

enable = function()
    enableaction("math", "noads.handlers.italics")
    if trace_italics then
        report_italics("enabling math italics")
    end
    -- we enable math (unless already enabled elsewhere)
    typesetters.italics.enablemath()
    enable = false
end

-- best do this only on math mode (less overhead)

function mathematics.setitalics(name)
    if enable then
        enable()
    end
    texsetattribute(a_mathitalics,name and name ~= v_reset and tonumber(name) or unsetvalue) -- maybe also v_none
end

function mathematics.getitalics(name)
    if enable then
        enable()
    end
    context(name and name ~= v_reset and tonumber(name) or unsetvalue)
end

function mathematics.resetitalics()
    texsetattribute(a_mathitalics,unsetvalue)
end

implement {
    name      = "initializemathitalics",
    actions   = enable,
    onlyonce  = true,
}

implement {
    name      = "setmathitalics",
    actions   = mathematics.setitalics,
    arguments = "string",
}

implement {
    name      = "getmathitalics",
    actions   = mathematics.getitalics,
    arguments = "string",
}

implement {
    name      = "resetmathitalics",
    actions   = mathematics.resetitalics
}

do

    -- math kerns (experiment) in goodies:
    --
    -- mathematics = {
    --     kernpairs = {
    --         [0x1D44E] = {
    --             [0x1D44F] = 400, -- 𝑎𝑏
    --         }
    --     },
    -- }

    local a_kernpairs = privateattribute("mathkernpairs")
    local kernpairs   = { }

    local function enable()
        enableaction("math", "noads.handlers.kernpairs")
        if trace_kernpairs then
            report_kernpairs("enabling math kern pairs")
        end
        enable = false
    end

    implement {
        name      = "initializemathkernpairs",
        actions   = enable,
        onlyonce  = true,
    }

    local hash = setmetatableindex(function(t,font)
        local g = fontdata[font].goodies
        local m = g and g[1].mathematics
        local k = m and m.kernpairs
        t[font] = k
        return k
    end)

    kernpairs[math_char] = function(pointer,what,n,parent)
        if getattr(pointer,a_kernpairs) == 1 then
            local font = getfont(pointer)
            local list = hash[font]
            if list then
                local first = getchar(pointer)
                local found = list[first]
                if found then
                    local next = getnext(parent)
                    if next and getid(next) == math_noad then
                        pointer = getnucleus(next)
                        if pointer then
                            if getfont(pointer) == font then
                                local second = getchar(pointer)
                                local kern   = found[second]
                                if kern then
                                    kern = kern * fonts.hashes.parameters[font].hfactor
                                    if trace_kernpairs then
                                        report_kernpairs("adding %p kerning between %C and %C",kern,first,second)
                                    end
                                    setlink(parent,new_kern(kern),getnext(parent))
                                end
                            end
                        end
                    end
                end
            end
        end
    end

    function handlers.kernpairs(head,style,penalties)
        processnoads(head,kernpairs,"kernpairs")
        return true
    end

end

-- primes and such

local collapse = { } processors.collapse = collapse

local mathpairs = characters.mathpairs -- next will move to char-def

mathpairs[0x2032] = { [0x2032] = 0x2033, [0x2033] = 0x2034, [0x2034] = 0x2057 } -- (prime,prime) (prime,doubleprime) (prime,tripleprime)
mathpairs[0x2033] = { [0x2032] = 0x2034, [0x2033] = 0x2057 }                    -- (doubleprime,prime) (doubleprime,doubleprime)
mathpairs[0x2034] = { [0x2032] = 0x2057 }                                       -- (tripleprime,prime)

mathpairs[0x2035] = { [0x2035] = 0x2036, [0x2036] = 0x2037 }                    -- (reversedprime,reversedprime) (reversedprime,doublereversedprime)
mathpairs[0x2036] = { [0x2035] = 0x2037 }                                       -- (doublereversedprime,reversedprime)

mathpairs[0x222B] = { [0x222B] = 0x222C, [0x222C] = 0x222D }
mathpairs[0x222C] = { [0x222B] = 0x222D }

mathpairs[0x007C] = { [0x007C] = 0x2016, [0x2016] = 0x2980 } -- bar+bar=double bar+double=triple
mathpairs[0x2016] = { [0x007C] = 0x2980 }                    -- double+bar=triple

local movesub = {
    -- primes
    [0x2032] = 0xFE932,
    [0x2033] = 0xFE933,
    [0x2034] = 0xFE934,
    [0x2057] = 0xFE957,
    -- reverse primes
    [0x2035] = 0xFE935,
    [0x2036] = 0xFE936,
    [0x2037] = 0xFE937,
}

local validpair = {
    [noad_rel]             = true,
    [noad_ord]             = true,
    [noad_bin]             = true, -- new
    [noad_punct]           = true, -- new
    [noad_opdisplaylimits] = true,
    [noad_oplimits]        = true,
    [noad_opnolimits]      = true,
}

local function movesubscript(parent,current_nucleus,current_char)
    local prev = getprev(parent)
    if prev and getid(prev) == math_noad then
        if not getsup(prev) and not getsub(prev) then
            -- {f} {'}_n => f_n^'
            setchar(current_nucleus,movesub[current_char or getchar(current_nucleus)])
            local nucleus = getnucleus(parent)
            local sub     = getsub(parent)
            local sup     = getsup(parent)
            setsup(prev,nucleus)
            setsub(prev,sub)
            local dummy = copy_node(nucleus)
            setchar(dummy,0)
            setnucleus(parent,dummy)
            setsub(parent)
            if trace_collapsing then
                report_collapsing("fixing subscript")
            end
        elseif not getsup(prev) then
            -- {f} {'}_n => f_n^'
            setchar(current_nucleus,movesub[current_char or getchar(current_nucleus)])
            local nucleus = getnucleus(parent)
            local sup     = getsup(parent)
            setsup(prev,nucleus)
            local dummy = copy_node(nucleus)
            setchar(dummy,0)
            setnucleus(parent,dummy)
            if trace_collapsing then
                report_collapsing("fixing subscript")
            end
        end
    end
end

local function collapsepair(pointer,what,n,parent,nested) -- todo: switch to turn in on and off
    if parent then
        if validpair[getsubtype(parent)] then
            local current_nucleus = getnucleus(parent)
            if getid(current_nucleus) == math_char then
                local current_char = getchar(current_nucleus)
                if not getsub(parent) and not getsup(parent) then
                    local mathpair = mathpairs[current_char]
                    if mathpair then
                        local next_noad = getnext(parent)
                        if next_noad and getid(next_noad) == math_noad then
                            if validpair[getsubtype(next_noad)] then
                                local next_nucleus = getnucleus(next_noad)
                                local next_char    = getchar(next_nucleus)
                                if getid(next_nucleus) == math_char then
                                    local newchar = mathpair[next_char]
                                    if newchar then
                                        local id         = getfont(current_nucleus)
                                        local characters = fontcharacters[id]
                                        if characters and characters[newchar] then
                                            if trace_collapsing then
                                                report_collapsing("%U + %U => %U",current_char,next_char,newchar)
                                            end
                                            setchar(current_nucleus,newchar)
                                            local next_next_noad = getnext(next_noad)
                                            if next_next_noad then
                                                setlink(parent,next_next_noad)
                                            else
                                                setnext(parent)
                                            end
                                            setsup(parent,getsup(next_noad))
                                            setsub(parent,getsub(next_noad))
                                            setsup(next_noad)
                                            setsub(next_noad)
                                            flush_node(next_noad)
                                            collapsepair(pointer,what,n,parent,true)
                                         -- if not nested and movesub[current_char] then
                                         --     movesubscript(parent,current_nucleus,current_char)
                                         -- end
                                        end
                                    elseif not nested and movesub[current_char] then
                                        movesubscript(parent,current_nucleus,current_char)
                                    end
                                end
                            end
                        elseif not nested and movesub[current_char] then
                            movesubscript(parent,current_nucleus,current_char)
                        end
                    elseif not nested and movesub[current_char] then
                        movesubscript(parent,current_nucleus,current_char)
                    end
                elseif not nested and movesub[current_char] then
                    movesubscript(parent,current_nucleus,current_char)
                end
            end
        end
    end
end

collapse[math_char] = collapsepair

function noads.handlers.collapse(head,style,penalties)
    processnoads(head,collapse,"collapse")
    return true
end

-- variants

local variants = { }

local validvariants = { -- fast check on valid
    [0x2229] = 0xFE00, [0x222A] = 0xFE00,
    [0x2268] = 0xFE00, [0x2269] = 0xFE00,
    [0x2272] = 0xFE00, [0x2273] = 0xFE00,
    [0x228A] = 0xFE00, [0x228B] = 0xFE00,
    [0x2293] = 0xFE00, [0x2294] = 0xFE00,
    [0x2295] = 0xFE00,
    [0x2297] = 0xFE00,
    [0x229C] = 0xFE00,
    [0x22DA] = 0xFE00, [0x22DB] = 0xFE00,
    [0x2A3C] = 0xFE00, [0x2A3D] = 0xFE00,
    [0x2A9D] = 0xFE00, [0x2A9E] = 0xFE00,
    [0x2AAC] = 0xFE00, [0x2AAD] = 0xFE00,
    [0x2ACB] = 0xFE00, [0x2ACC] = 0xFE00,
}

variants[math_char] = function(pointer,what,n,parent) -- also set export value
    local char = getchar(pointer)
    local selector = validvariants[char]
    if selector then
        local next = getnext(parent)
        if next and getid(next) == math_noad then
            local nucleus = getnucleus(next)
            if nucleus and getid(nucleus) == math_char and getchar(nucleus) == selector then
                local variant
                local tfmdata = fontdata[getfont(pointer)]
                local mathvariants = tfmdata.resources.variants -- and variantdata
                if mathvariants then
                    mathvariants = mathvariants[selector]
                    if mathvariants then
                        variant = mathvariants[char]
                    end
                end
                if variant then
                    setchar(pointer,variant)
                    setattr(pointer,a_exportstatus,char) -- we don't export the variant as it's visual markup
                    if trace_variants then
                        report_variants("variant (%U,%U) replaced by %U",char,selector,variant)
                    end
                else
                    if trace_variants then
                        report_variants("no variant (%U,%U)",char,selector)
                    end
                end
                setprev(next,pointer)
                setnext(parent,getnext(next))
                flush_node(next)
            end
        end
    end
end

function handlers.variants(head,style,penalties)
    processnoads(head,variants,"unicode variant")
    return true
end

-- for manuals

local classes = { }

local colors = {
    [noad_rel]             = "trace:dr",
    [noad_ord]             = "trace:db",
    [noad_bin]             = "trace:dg",
    [noad_open]            = "trace:dm",
    [noad_close]           = "trace:dm",
    [noad_punct]           = "trace:dc",
 -- [noad_opdisplaylimits] = "",
 -- [noad_oplimits]        = "",
 -- [noad_opnolimits]      = "",
 -- [noad_inner            = "",
 -- [noad_under            = "",
 -- [noad_over             = "",
 -- [noad_vcenter          = "",
}

classes[math_char] = function(pointer,what,n,parent)
    local color = colors[getsubtype(parent)]
    if color then
        setcolor(pointer,color)
    else
        resetcolor(pointer)
    end
end

function handlers.classes(head,style,penalties)
    processnoads(head,classes,"classes")
    return true
end

registertracker("math.classes",function(v)
    setaction("math","noads.handlers.classes",v)
end)

-- experimental

do

 -- mathematics.registerdomain {
 --     name       = "foo",
 --     parents    = { "bar" },
 --     characters = {
 --         [0x123] = { char = 0x234, class = binary },
 --     },
 -- }

    local domains       = { }
    local categories    = { }
    local numbers       = { }
    local a_mathdomain  = privateattribute("mathdomain")

    mathematics.domains = categories

    local permitted     = {
        ordinary    = noad_ord,
        binary      = noad_bin,
        relation    = noad_rel,
        punctuation = noad_punct,
        inner       = noad_inner,
    }

    function mathematics.registerdomain(data)
        local name = data.name
        if not name then
            return
        end
        local attr       = #numbers + 1
        categories[name] = data
        numbers[attr]    = data
        data.attribute   = attr
        -- we delay hashing
        return attr
    end

    local enable

    enable = function()
        enableaction("math", "noads.handlers.domains")
        if trace_domains then
            report_domains("enabling math domains")
        end
        enable = false
    end

    function mathematics.setdomain(name)
        if enable then
            enable()
        end
        local data = name and name ~= v_reset and categories[name]
        texsetattribute(a_mathdomain,data and data.attribute or unsetvalue)
    end

    function mathematics.getdomain(name)
        if enable then
            enable()
        end
        local data = name and name ~= v_reset and categories[name]
        context(data and data.attribute or unsetvalue)
    end

    implement {
        name      = "initializemathdomain",
        actions   = enable,
        onlyonce  = true,
    }

    implement {
        name      = "setmathdomain",
        arguments = "string",
        actions   = mathematics.setdomain,
    }

    implement {
        name      = "getmathdomain",
        arguments = "string",
        actions   = mathematics.getdomain,
    }

    local function makehash(data)
        local hash    = { }
        local parents = data.parents
        if parents then
            local function merge(name)
                if name then
                    local c = categories[name]
                    if c then
                        local hash = c.hash
                        if not hash then
                            hash = makehash(c)
                        end
                        for k, v in next, hash do
                            hash[k] = v
                        end
                    end
                end
            end
            if type(parents) == "string" then
                merge(parents)
            elseif type(parents) == "table" then
                for i=1,#parents do
                    merge(parents[i])
                end
            end
        end
        local characters = data.characters
        if characters then
            for k, v in next, characters do
             -- local chr = n.char
                local cls = v.class
                if cls then
                    v.code = permitted[cls]
                else
                    -- invalid class
                end
                hash[k] = v
            end
        end
        data.hash = hash
        return hash
    end

    domains[math_char] = function(pointer,what,n,parent)
        local attr = getattr(pointer,a_mathdomain)
        if attr then
            local domain = numbers[attr]
            if domain then
                local hash = domain.hash
                if not hash then
                    hash = makehash(domain)
                end
                local char = getchar(pointer)
                local okay = hash[char]
                if okay then
                    local chr = okay.char
                    local cls = okay.code
                    if chr and chr ~= char then
                        setchar(pointer,chr)
                    end
                    if cls and cls ~= getsubtype(parent) then
                        setsubtype(parent,cls)
                    end
                end
            end
        end
    end

    function handlers.domains(head,style,penalties)
        processnoads(head,domains,"domains")
        return true
    end

end

-- just for me

function handlers.showtree(head,style,penalties)
    inspect(nodes.totree(head))
end

registertracker("math.showtree",function(v)
    setaction("math","noads.handlers.showtree",v)
end)

-- also for me

local applyvisuals = nuts.applyvisuals
local visual       = false

function handlers.makeup(head)
    applyvisuals(tonut(head),visual)
end

registertracker("math.makeup",function(v)
    visual = v
    setaction("math","noads.handlers.makeup",v)
end)

-- the normal builder

function builders.kernel.mlist_to_hlist(head,style,penalties)
    return mlist_to_hlist(head,style,penalties), true
end

-- function builders.kernel.mlist_to_hlist(head,style,penalties)
--     print("!!!!!!! BEFORE",penalties)
--     for n in node.traverse(head) do print(n) end
--     print("!!!!!!!")
--     head = mlist_to_hlist(head,style,penalties)
--     print("!!!!!!! AFTER")
--     for n in node.traverse(head) do print(n) end
--     print("!!!!!!!")
--     return head, true
-- end

tasks.new {
    name      = "math",
    arguments = 2,
    processor = utilities.sequencers.nodeprocessor,
    sequence  = {
        "before",
        "normalizers",
        "builders",
        "after",
    },
}

tasks.freezegroup("math", "normalizers") -- experimental
tasks.freezegroup("math", "builders")    -- experimental

local actions = tasks.actions("math") -- head, style, penalties

local starttiming, stoptiming = statistics.starttiming, statistics.stoptiming

function processors.mlist_to_hlist(head,style,penalties)
    starttiming(noads)
    local head, done = actions(head,style,penalties)
    stoptiming(noads)
    return head, done
end

callbacks.register('mlist_to_hlist',processors.mlist_to_hlist,"preprocessing math list")

-- tracing

statistics.register("math processing time", function()
    return statistics.elapsedseconds(noads)
end)