summaryrefslogtreecommitdiff
path: root/tex/context/base/mkxl/math-act.lmt
blob: f6fd5dab5f50be06129189518ed5fcb444b299de (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
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
if not modules then modules = { } end modules ['math-act'] = {
    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"
}

-- Here we tweak some font properties (if needed). The commented sections
-- have been removed (no longer viable) but can be found in the .lua variant.

-- The tweaks here evolved from experiments with, discussions about and upgrades of
-- the math subsystem, a project that Mikael Sundvist and I started end 2021 and
-- that is still ongoing in 2023 (and probably beyond as we find new challenges as
-- we go).

local type, next, tonumber = type, next, tonumber
local fastcopy, copytable, insert, remove, concat = table.fastcopy, table.copy, table.insert, table.remove, table.concat
local formatters = string.formatters
local byte = string.byte
local max = math.max
local setmetatableindex, sortedkeys, sortedhash  = table.setmetatableindex, table.sortedkeys, table.sortedhash
local lpegmatch = lpeg.match

local trace_defining   = false  trackers.register("math.defining",   function(v) trace_defining   = v end)
local trace_collecting = false  trackers.register("math.collecting", function(v) trace_collecting = v end)
local trace_tweaking   = false  trackers.register("math.tweaks",     function(v) trace_tweaking   = v end)

local report_math      = logs.reporter("mathematics","initializing")
local report_mathtweak = logs.reporter("mathematics","tweak")

local getfontoffamily  = tex.getfontoffamily
local texget           = tex.get
local fontcharacters   = fonts.hashes.characters
local chardata         = characters.data
local extensibles      = mathematics.extensibles

local context          = context
local commands         = commands
local mathematics      = mathematics
local texsetdimen      = tex.setdimen
local texisdimen       = tex.isdimen
local abs              = math.abs

local blocks           = characters.blocks
local stepper          = utilities.parsers.stepper

local helpers          = fonts.helpers
local prependcommands  = helpers.prependcommands

local vfcommands       = helpers.commands
local upcommand        = vfcommands.up
local downcommand      = vfcommands.down
local rightcommand     = vfcommands.right
local leftcommand      = vfcommands.left
local slotcommand      = vfcommands.slot
local charcommand      = vfcommands.char
local push             = vfcommands.push
local pop              = vfcommands.pop

local sequencers       = utilities.sequencers
local appendgroup      = sequencers.appendgroup
local appendaction     = sequencers.appendaction

local fontchars        = fonts.hashes.characters
local fontproperties   = fonts.hashes.properties

local mathgaps         = mathematics.gaps

local d_scratchleftoffset  = texisdimen("scratchleftoffset")
local d_scratchrightoffset = texisdimen("scratchrightoffset")

local use_math_goodies = true   directives.register("math.nogoodies",    function(v) use_math_goodies = not v end)
local checkitalics     = false  trackers  .register("math.checkitalics", function(v) checkitalics     =     v end)

local mathfontparameteractions = sequencers.new {
    name      = "mathparameters",
    arguments = "target,original",
}

appendgroup("mathparameters","before") -- user
appendgroup("mathparameters","system") -- private
appendgroup("mathparameters","after" ) -- user

function fonts.constructors.assignmathparameters(original,target) -- wrong way around
    local runner = mathfontparameteractions.runner
    if runner then
        runner(original,target)
    end
end

-- we need a better reset because the following will scale

local undefined <const> = 0x3FFFFFFF -- maxdimen or undefined_math_parameter

function mathematics.initializeparameters(target,original,nodimensions)
    local mathparameters = original.mathparameters
    if mathparameters and next(mathparameters) then
        if nodimensions ~= "noscale" then
            mathparameters = mathematics.dimensions(mathparameters)
        end
        --
     -- if not mathparameters.MinConnectorOverlap               then mathparameters.MinConnectorOverlap               = undefined end
        if not mathparameters.SubscriptShiftDownWithSuperscript then mathparameters.SubscriptShiftDownWithSuperscript = mathparameters.SubscriptShiftDown * 1.5 end
     -- if not mathparameters.FractionDelimiterSize             then mathparameters.FractionDelimiterSize             = undefined end
     -- if not mathparameters.FractionDelimiterDisplayStyleSize then mathparameters.FractionDelimiterDisplayStyleSize = undefined end
     -- if not mathparameters.SkewedDelimiterTolerance          then mathparameters.SkewedDelimiterTolerance          = undefined end
        -- some more can be undefined:
        if not mathparameters.PrimeRaisePercent                 then mathparameters.PrimeRaisePercent                 = 0 end
        if not mathparameters.PrimeRaiseComposedPercent         then mathparameters.PrimeRaiseComposedPercent         = 0 end
        if not mathparameters.PrimeShiftUp                      then mathparameters.PrimeShiftUp                      = mathparameters.SuperscriptShiftUp end
        if not mathparameters.PrimeBaselineDropMax              then mathparameters.PrimeBaselineDropMax              = mathparameters.SuperscriptBaselineDropMax end
        if not mathparameters.PrimeShiftUpCramped               then mathparameters.PrimeShiftUpCramped               = mathparameters.SuperscriptShiftUpCramped end
        if not mathparameters.PrimeSpaceAfter                   then mathparameters.PrimeSpaceAfter                   = 0 end
        if not mathparameters.PrimeWidthPercent                 then mathparameters.PrimeWidthPercent                 = 50 end
        if not mathparameters.SpaceBeforeScript                 then mathparameters.SpaceBeforeScript                 = mathparameters.SpaceAfterScript end
        if not mathparameters.NoLimitSupFactor                  then mathparameters.NoLimitSupFactor                  = 0 end
        if not mathparameters.NoLimitSubFactor                  then mathparameters.NoLimitSubFactor                  = 0 end
        if not mathparameters.AccentTopShiftUp                  then mathparameters.AccentTopShiftUp                  = 0 end
        if not mathparameters.AccentBottomShiftDown             then mathparameters.AccentBottomShiftDown             = 0 end
        if not mathparameters.FlattenedAccentTopShiftUp         then mathparameters.AccentTopShiftUp                  = 0 end
        if not mathparameters.FlattenedAccentBottomShiftDown    then mathparameters.AccentBottomShiftDown             = 0 end
        if not mathparameters.AccentBaseDepth                   then mathparameters.AccentBaseDepth                   = 0 end
        if not mathparameters.AccentFlattenedBaseDepth          then mathparameters.AccentFlattenedBaseDepth          = 0 end
        if not mathparameters.AccentTopOvershoot                then mathparameters.AccentTopOvershoot                = 0 end
        if not mathparameters.AccentBottomOvershoot             then mathparameters.AccentBottomOvershoot             = 0 end
        if not mathparameters.AccentSuperscriptDrop             then mathparameters.AccentSuperscriptDrop             = 0 end
        if not mathparameters.AccentSuperscriptPercent          then mathparameters.AccentSuperscriptPercent          = 0 end
        if not mathparameters.AccentExtendMargin                then mathparameters.AccentExtendMargin                = 50 end
        if not mathparameters.DelimiterPercent                  then mathparameters.DelimiterPercent                  = 100 end
        if not mathparameters.DelimiterShortfall                then mathparameters.DelimiterShortfall                = 0 end
        if not mathparameters.RadicalKernAfterExtensible        then mathparameters.RadicalKernAfterExtensible        = 0 end
        if not mathparameters.RadicalKernBeforeExtensible       then mathparameters.RadicalKernBeforeExtensible       = 0 end
        --
        target.mathparameters = mathparameters
    end
end

sequencers.appendaction("mathparameters","system","mathematics.initializeparameters")

local how = {
 -- RadicalKernBeforeDegree         = "horizontal",
 -- RadicalKernAfterDegree          = "horizontal",
    ScriptPercentScaleDown          = "unscaled",
    ScriptScriptPercentScaleDown    = "unscaled",
    RadicalDegreeBottomRaisePercent = "unscaled",
    NoLimitSupFactor                = "unscaled",
    NoLimitSubFactor                = "unscaled",
    PrimeRaisePercent               = "unscaled",
    PrimeRaiseComposedPercent       = "unscaled",
    PrimeWidthPercent               = "unscaled",
    AccentTopOvershoot              = "unscaled",
    AccentBottomOvershoot           = "unscaled",
    AccentSuperscriptPercent        = "unscaled",
    DelimiterPercent                = "unscaled",
    --
    RadicalRuleThickness            = "vertical",
    OverbarRuleThickness            = "vertical",
    FractionRuleThickness           = "vertical",
    UnderbarRuleThickness           = "vertical",
}

local function scaleparameters(mathparameters,parameters)
    if mathparameters and next(mathparameters) and parameters then
        local factor  = parameters.factor
        local hfactor = parameters.hfactor
        local vfactor = parameters.vfactor
        for name, value in next, mathparameters do
            local h = how[name]
            if h == "unscaled" then
                -- kept
            elseif h == "horizontal" then
                value = value * hfactor
            elseif h == "vertical" then
                value = value * vfactor
            else
                value = value * factor
            end
            mathparameters[name] = value
        end
    end
end

function mathematics.scaleparameters(target,original)
    if not target.properties.math_is_scaled then
        scaleparameters(target.mathparameters,target.parameters)
        target.properties.math_is_scaled = true
    end
end

-- AccentBaseHeight vs FlattenedAccentBaseHeight

-- function mathematics.checkaccentbaseheight(target,original)
--     local mathparameters = target.mathparameters
--     if mathparameters and mathparameters.AccentBaseHeight == 0 then
--         if trace_defining then
--             report_math("zero AccentBaseHeight corrected %a @ %p",target.properties.fullname,target.parameters.size)
--         end
--         mathparameters.AccentBaseHeight = target.parameters.xheight -- needs checking
--     end
-- end

function mathematics.overloadparameters(target,original)
    if use_math_goodies then
        local mathparameters = target.mathparameters
        if mathparameters and next(mathparameters) then
            local goodies = target.goodies
            if goodies then
                for i=1,#goodies do
                    local goodie = goodies[i]
                    local mathematics = goodie.mathematics
                    if mathematics then
                        local parameters = mathematics.parameters
                        local bigslots   = mathematics.bigslots or mathematics.bigs
                        if parameters then
                            if trace_defining then
                                report_math("overloading math parameters in %a @ %p",target.properties.fullname,target.parameters.size)
                            end
                            for name, value in next, parameters do
                                local tvalue   = type(value)
                                local oldvalue = mathparameters[name]
                                local newvalue = oldvalue
                                if tvalue == "number" then
                                    newvalue = value
                                elseif tvalue == "string" then
                                    -- delay till all set
                                elseif tvalue == "function" then
                                    newvalue = value(oldvalue,target,original)
                                elseif not tvalue then
                                    newvalue = nil
                                end
                                if trace_defining and oldvalue ~= newvalue then
                                    report_math("overloading math parameter %a: %S => %S",name,oldvalue or 0,newvalue)
                                end
                                mathparameters[name] = newvalue
                            end
                            for name, value in next, parameters do
                                local tvalue = type(value)
                                if tvalue == "string" then
                                    local newvalue = mathparameters[value]
                                    if not newvalue then
                                        local code = loadstring("return " .. value,"","t",mathparameters)
                                        if type(code) == "function" then
                                            local okay, v = pcall(code)
                                            if okay then
                                                newvalue = v
                                            end
                                        end
                                    end
                                    if newvalue then
                                        -- split in number and string
                                        mathparameters[name] = newvalue
                                    elseif trace_defining then
                                        report_math("ignoring math parameter %a: %S",name,value)
                                    end
                                end
                            end
                        end
                        if bigslots then
                            target.bigslots = bigslots
                        end
                    end
                end
            end
        end
    end
end

-- a couple of predefined tweaks:

local datasets       = { }
local mathtweaks     = { datasets = datasets }
mathematics.tweaks   = mathtweaks

-- can be a common helper:

local f_u = formatters["%U"]

local function unicodecharlist(t)
    local r = { }
    local n = 0
    for u in sortedhash(t) do
        n = n + 1 ; r[n] = f_u(u)
    end
    return concat(r," ")
end

local function report_tweak(fmt,target,original,...)
    if fmt then
        local metadata   = (original and original.shared.rawdata.metadata) or
                           (target   and target  .shared.rawdata.metadata)
        local parameters = target.parameters
        if parameters then
            report_mathtweak(
                "%a, size %P, math size %i, %s",
                metadata and metadata.fontname or "unknown",
                parameters.size or 655360,
                parameters.mathsize or 1,
                formatters[fmt](...)
            )
        else
            print("something is wrong")
        end
    else
        report_mathtweak("")
    end
end

local function feedback_tweak(tweak,target,original,done)
    if not done or (type(done) == "table" and not next(done)) then
if trace_tweaking then -- for now
        report_tweak("no need for %a",target,original,tweak)
end
    elseif trace_tweaking then
        report_tweak("tweak %a applied to: %s",target,original,tweak,unicodecharlist(done))
    end
end

mathtweaks.subsets = {
    acenorsuvxz      = { 0x1D44E, 0x1D450, 0x1D452, 0x1D45B, 0x1D45C, 0x1D45F, 0x1D460, 0x1D462, 0x1D463, 0x1D465, 0x1D467 },
    bhklt            = { 0x1D44F, 0x1D455, 0x1D458, 0x1D459, 0x1D461 },
    d                = { 0x1D451 },
    f                = { 0x1D453 },
    gjqy             = { 0x1D454, 0x1D457, 0x1D45E, 0x1D466 },
    i                = { 0x1D456 },
    mw               = { 0x1D45A, 0x1D464 },
    p                = { 0x1D45D },
    dotless          = { 0x00049, 0x0004A, 0x00131, 0x00237, 0x1D6A4, 0x1D6A5 },
    integrals        = { 0x0222B, 0x0222C, 0x0222D, 0x0222E, 0x0222F, 0x02230, 0x02231, 0x02232, 0x02233, 0x02A0B, 0x02A0C, 0x02A0D, 0x02A0E, 0x02A0F, 0x02A10, 0x02A11, 0x02A12, 0x02A13, 0x02A14, 0x02A15, 0x02A16, 0x02A17, 0x02A18, 0x02A19, 0x02A1A, 0x02A1B, 0x02A1C, 0x02320, 0x02321 },
    horizontalfences = { 0x0203E, 0x023B4, 0x023B5, 0x023DC, 0x023DD, 0x023DE, 0x023DF, 0x023E0, 0x023E1 }, -- not really used
}

local function getalso(target,original)
    local also = target.tweakalso -- maybe
    if not also then
        also = { }
     -- for k, v in sortedhash(target.characters) do
        for k, v in next, target.characters do
            local u = v.unicode
            if u and k ~= u then
                local a = also[u]
                if a then
                    a[#a+1] = k
                else
                    also[u] = { k }
                end
            end
        end
        target.tweakalso = also
    end
    return also
end

-- {
--     tweak = "dimensions",
--     list  = {
--         ["lowercasegreeksansserifbolditalic"] = {
--          -- delta    = 0x003B1 - 0x1D7AA,
--             slant    = -0.2,
--             line     = 0.1,
--             mode     = 1,
--             width    = 0.675,
--          -- scale    = 0.975,
--             squeeze  = 0.975,
--             extend   = .7,
--         },
--     },
-- },

 -- ["0x7C.variants.*"] = { squeeze = 0.10, height = 0.10, depth = 0.10 },

local detail  do

    local splitter = lpeg.tsplitat(".")

    detail = function(characters,k)
        if type(k) == "string" then
            local t = lpegmatch(splitter,k)
            local n = #t
            if n > 0 then
                local base = tonumber(t[1]) or tonumber(t[1],16)
                if base then
                    local c = characters[base]
                    if c and n > 1 then
                        local list = t[2]
                        if list == "parts" then
                            local nxt = c.next
                            while nxt do
                                c = characters[nxt]
                                nxt = c.next
                            end
                            c = c.parts
                            if c then
                                local index = t[3]
                                if index == "*" then
                                    return t
                                else
                                    if index == "top" then
                                        index = #c
                                    elseif index == "bottom" then
                                        index = 1
                                    else
                                        index = tonumber(index)
                                    end
                                    if index then
                                        c = c[index]
                                        if c then
                                            return c.glyph
                                        end
                                    end
                                end
                            end
                        elseif list == "variants" then
                            local index = t[3]
                            if index == "*" then
                                local t = { }
                                local nxt = c.next
                                while nxt do
                                    t[#t+1] = nxt
                                    c = characters[nxt]
                                    nxt = c.next
                                end
                                return t
                            else
                                index = tonumber(index)
                                if index then
                                    local nxt = c.next
                                    while nxt and index > 1 do
                                        c = characters[nxt]
                                        nxt = c.next
                                        index = index - 1
                                    end
                                    return nxt
                                end
                            end
                        end
                    end
                end
            end
        else
            return k
        end
    end

end

-- This temporary tweak was used when we (MS & HH) were fixing the Latin Modern
-- parameters that relate to script placement. We started from the original cmr
-- ratios combined with the formal specification and ended up with the following
-- values. In the end we rejected this tweak and setteled for checking and fixing:
--
-- SubscriptShiftDown
-- SubscriptShiftDownWithSuperscript
-- SuperscriptShiftUp
-- SuperscriptShiftUpCramped
--
-- because it looks a bit arbitrary what values are set. We keep the code below
-- as documentation.

-- do
--     -- modern
--     --
--     -- local factors = {
--     --     scripts = {
--     --         SubscriptBaselineDropMin          = 0.116,
--     --         SubscriptShiftDown                = 0.348,
--     --         SubscriptShiftDownWithSuperscript = 0.573,
--     --         SubscriptTopMax                   = 0.800,
--     --         SuperscriptBaselineDropMax        = 0.896,
--     --         SuperscriptBottomMaxWithSubscript = 0.800,
--     --         SuperscriptBottomMin              = 0.250,
--     --         SuperscriptShiftUp                = 0.958,
--     --         SuperscriptShiftUpCramped         = 0.958,
--     --     }
--     -- }
--
--     -- -- cambria
--     --
--     -- local factors = {
--     --     scripts = {
--     --         SubscriptBaselineDropMin          = 0.279,
--     --         SubscriptShiftDown                = 0.364,
--     --         SubscriptShiftDownWithSuperscript = 0.547,
--     --         SubscriptTopMax                   = 0.662,
--     --         SuperscriptBaselineDropMax        = 0.401,
--     --         SuperscriptBottomMaxWithSubscript = 0.667,
--     --         SuperscriptBottomMin              = 0.208,
--     --         SuperscriptShiftUp                = 0.654,
--     --         SuperscriptShiftUpCramped         = 0.654,
--     --     }
--     -- }
--
--     -- after some tests and inspection
--     --
--
--     local factors = {
--         scripts = {
--             SubscriptBaselineDropMin          = 0.100, -- harmless but small (seldom triggered)
--             SubscriptShiftDown                = 0.400, -- by inspection in several files
--             SubscriptShiftDownWithSuperscript = 0.400, -- as above
--             SubscriptTopMax                   = 0.800, -- Microsoft recommendation
--             SuperscriptBaselineDropMax        = 0.100, -- see SubscriptBaselineDropMin
--             SuperscriptBottomMaxWithSubscript = 0.800, -- Microsoft recommendation
--             SuperscriptBottomMin              = 0.250, -- Microsoft recommendation
--             SuperscriptShiftUp                = 0.650, -- by inspection, but also a bit gamble
--             SuperscriptShiftUpCramped         = 0.650, -- see above, non-TeX
--         }
--     }
--
--     datasets.fixparameters = factors
--
--     function mathtweaks.fixparameters(target,original,parameters)
--         local mathparameters = target.mathparameters
--         if mathparameters and next(mathparameters) then
--             local xheight = target.parameters.xheight
--             -- todo : options
--             for k, v in next, factors.scripts do
--                 mathparameters[k] = v * xheight
--             end
--         end
--     end
--
-- end

do

    local stepper     = utilities.parsers.stepper
    local count       = 0
    local toeffect    = fonts.toeffect
    local privateslot = fonts.helpers.privateslot

    local function adapt(list,target,original,targetcharacters,originalcharacters,k,v,compact,n)
        k = mathgaps[k] or k
        local character = targetcharacters[k]
        if character then
         -- if not character.tweaked then -- todo: add a force
                local t = type(v)
                if t == "number" then
                    v = list[v]
                    t = type(v)
                end
                if t == "table" and next(v) then

                    local axis = tonumber(v.axis)
                    if axis then
                        axis = target.mathparameters.AxisHeight * axis
                    end

                    local factor    = v.factor
                    if factor then
                        local m = v
                        v = setmetatableindex({
                            width   = factor,
                            height  = factor,
                            depth   = factor,
                            squeeze = factor,
                            extend  = factor,
                        }, v)
                    end
                    local originalslot = v.original
                    if not originalslot then
                        local delta = v.delta
                        if delta then
                            originalslot = k + delta
                        end
                    end
                    if originalslot then
                        originalslot = mathgaps[originalslot] or originalslot
                        local data = targetcharacters[originalslot]
                        if data then
                            data = copytable(data)
                            data.unicode = originalslot
                            targetcharacters[k] = data
                            character = data
                        else
                            report_mathtweak("no slot %U",originalslot)
                            return
                        end
                    end
                    --
                    local width        = character.width
                    local height       = character.height
                    local depth        = character.depth
                    local italic       = character.italic
                    local topanchor    = character.topanchor
                    local bottomanchor = character.bottomanchor
                    --
                    local widthfactor   = v.width
                    local heightfactor  = v.height
                    local depthfactor   = v.depth
                    local italicfactor  = v.italic
                    local anchorfactor  = v.anchor
                    local advancefactor = v.advance
                    local xoffsetfactor = v.xoffset
                    local yoffsetfactor = v.yoffset
                    local scalefactor   = v.scale
                    local total = (height or 0) + (depth or 0)
                    if scalefactor ~= 1 then
                        character.scale = scalefactor
                    end
                    if width and width ~= 0 then
                        if advancefactor then
                            character.advance = advancefactor * width
                        else
                            character.advance = character.advance or width -- so advance is oldwidth
                        end
                        if widthfactor then
                            character.width = widthfactor * width
                        end
                        if xoffsetfactor then
                            character.xoffset = xoffsetfactor * width
                        end
                    end
                    if height and height ~= 0 then
                        if heightfactor then
                            character.height  = heightfactor * height
                        end
                    end
                    if depth and depthfactor then
                        character.depth = depthfactor * depth
                    end
                    if yoffsetfactor then
                        character.yoffset = yoffsetfactor * total
                    end

                    if axis then
                        character.height  = (character.height  or 0) - axis
                        character.depth   = (character.depth   or 0) + axis
                        character.yoffset = (character.yoffset or 0) + axis
                    end

                    if italicfactor then
                        if italic then
                            character.italic = italicfactor * italic
                        elseif width and italicfactor ~= 1 then
                            character.italic = italicfactor * width
                        end
                    end
                    if anchorfactor then
                        character.topanchor = anchorfactor * (topanchor or width)
                    end
--                     if anchorfactor then
--                         character.bottomaccent = anchorfactor * (bottomanchor or width)
--                     end
                 -- begin experiment
                    local line = v.wline
                    if line then
                        local parameters = target.parameters
                        v.line = parameters.hfactor * line / parameters.units
                    end
                 -- end experiment
                    character.effect = toeffect(v) -- todo: move wline test inside here
                 -- begin experiment
                    v.line = line
                 -- end experiment
                    if trace_tweaking then
                        report_tweak("adapting dimensions of %U ",target,original,k)
                    end
                     -- missing when private
                    local originaldata = originalcharacters[k] -- or targetcharacters[k]
                    local smaller = originaldata and originaldata.smaller
                    if compact and smaller and smaller ~= k then
                        adapt(list,target,original,targetcharacters,originalcharacters,smaller,v,compact,n+1)
                    end
                    count = count + 1
                else
                    report_mathtweak("invalid dimension entry %U",k)
                end
             -- character.tweaked = true
                if v.all then
                    local nxt = character.next
                    if nxt then
                        adapt(list,target,original,targetcharacters,originalcharacters,nxt,v,compact,n)
                    else
                        local parts = character.parts
                        if parts then
                            for i=1,#parts do
                                adapt(list,target,original,targetcharacters,originalcharacters,parts[i],v,compact,n)
                            end
                        end
                    end
                end
         -- end
        else
            report_tweak("no character %U",target,original,k)
        end
    end

    function mathtweaks.dimensions(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local compact = target.parameters.textscale and true or false
            count = 0
            for k, v in sortedhash(list) do
                local t = type(k)
                if t == "number" then
                    adapt(list,target,original,targetcharacters,originalcharacters,k,v,compact,1)
                elseif t == "string" then
                    local d = privateslot(k) or detail(targetcharacters,k) -- watch the private here
                    local t = type(d)
                    if t == "table" then
                        for i=1,#d do
                            adapt(list,target,original,targetcharacters,originalcharacters,d[i],v,compact,1)
                        end
                    elseif t == "number" then
                        adapt(list,target,original,targetcharacters,originalcharacters,d,v,compact,1)
                    elseif d then
                        -- some kind of error
                    else
                        local r = blocks[k]
                        if r then
                            local done = false
                            for i=r.first,r.last do
                                adapt(list,target,original,targetcharacters,originalcharacters,i,v,compact,1)
                            end
                        else
                            stepper(k,function(n)
                                adapt(list,target,original,targetcharacters,originalcharacters,n,v,compact,1)
                            end)
                        end
                    end
             -- elseif t == "table" then
             --     for i=1,#t do
             --         adapt(list,target,original,targetcharacters,originalcharacters,t[i],v,compact,1)
             --     end
                end
            end
            if trace_tweaking and count > 0 then
                report_mathtweak("%i dimensions adapted",count)
            end
        end
    end

end

do

    function mathtweaks.message(target,original,parameters)
        report_mathtweak(parameters.text or "no message")
    end

    function mathtweaks.showinfo(target,original,parameters)
        local mathparameters = target.mathparameters
        for k, v in sortedhash(mathparameters) do
            report_mathtweak("%s : %s",k,v)
        end
    end

end


do

    function mathtweaks.wipevariants(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
         -- local originalcharacters = original.characters
            local count = 0
         -- local also  = getalso(target,original)
            local done  = false
            for k, v in sortedhash(list) do
                local ori = targetcharacters[k]
                local nxt = ori.next
                local cnt = v
                if nxt then
                    local prt = nil
                    local lst = { }
                    while nxt do
                        local chr = targetcharacters[nxt]
                        lst[#lst+1] = chr
                        nxt = chr.next
                        if not nxt then
                            prt = chr.parts
                            break
                        end
                    end
                    if prt then
                        count = count + 1
                        if cnt ~= "*" then
                            if #lst < cnt then
                                cnt = #lst
                            end
                            ori = lst[cnt]
                        end
                        ori.parts = prt
                    end
                    if not trace_tweaking then
                        done = true
                    elseif done then
                        done[k] = true
                    else
                        done = { [k] = true }
                    end
                end
            end
            feedback_tweak("wipevariants",target,original,done)
        end
    end

end

do

    function mathtweaks.replace(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local unicodes = original.resources.unicodes
            if unicodes then
                local count = 0
                for k, v in sortedhash(list) do
                    if type(v) == "string" then
                        v = unicodes[v]
                    end
                    if type(v) == "number" then
                        targetcharacters[mathgaps[k] or k] = targetcharacters[mathgaps[v] or v]
                        count = count + 1
                    end
                end
                if trace_tweaking and count > 0 then
                    report_tweak("%i permanent replacements",target,original,count)
                end
            end
        end
    end

    function mathtweaks.substitute(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local getsubstitution    = fonts.handlers.otf.getsubstitution
            local count              = 0
            for k, v in next, list do -- no need for sortedhash(list) unless we report
                local sub = getsubstitution(original,k,v,true)
                if sub then
                    targetcharacters[mathgaps[k] or k] = targetcharacters[mathgaps[sub] or sub]
                    count = count + 1
                end
            end
            if trace_tweaking and count > 0 then
                report_tweak("%i permanent substitutions",target,original,count)
            end
        end
    end

end

do

    -- maybe we'll have a different name

    function mathtweaks.kernpairs(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local done               = false

            local function add(v,n)
                local chardata = targetcharacters[mathgaps[n] or n]
                if chardata then
                    local width = chardata.width
                    if width then
                        local kerns = chardata.kerns or { }
                        for kk, vv in next, v do
--                         for kk, vv in sortedhash(v) do
                            stepper(kk,function(nn) -- todo: also make stepper accept a table
                                local t = mathgaps[nn] or nn
                                if t then
                                    kerns[t] = vv * width
                                    if not trace_tweaking then
                                        done = true
                                    elseif done then
                                        done[t] = true
                                    else
                                        done = { [t] = true }
                                    end
                                end
                            end)
                        end
                        chardata.kerns = kerns
                    end
                end
            end

            for k, v in next, list do -- no need for sortedhash(list) unless we report
                stepper(k,function(n) -- todo: also make stepper accept a table
                    add(v,n)
                end)
            end

--             for k, v in next, list do -- no need for sortedhash(list) unless we report
--                 local chardata = targetcharacters[mathgaps[k] or k]
--                 if chardata then
--                     local width = chardata.width
--                     if width then
--                         local kerns = chardata.kerns or { }
--                         for kk, vv in next, v do
--                             local t = mathgaps[kk] or kk
--                             if t then
--                                 kerns[t] = vv * width
--                                 count = count + 1
--                             end
--                         end
--                         chardata.kerns = kerns
--                     end
--                 end
--             end

            feedback_tweak("kernpairs",target,original,done)
        end
    end

end

do

    local nps = fonts.helpers.newprivateslot

    local list = {
        { 0x2032, nps("delimited ghost 0x2032"), 1 },
        { 0x2033, nps("delimited ghost 0x2033"), 2, 0x2032 },
        { 0x2034, nps("delimited ghost 0x2034"), 3, 0x2032 },
        { 0x2057, nps("delimited ghost 0x2057"), 4, 0x2032 },
        { 0x2035, nps("delimited ghost 0x2035"), 1 },
        { 0x2036, nps("delimited ghost 0x2036"), 2, 0x2035 },
        { 0x2037, nps("delimited ghost 0x2037"), 3, 0x2035 },
    }

    datasets.fixprimes = list

    function mathtweaks.fixprimes(target,original,parameters)
        local targetcharacters = target.characters
        local factor = parameters.factor or 1
        local fake   = tonumber(parameters.fake)
        for i=1,#list do
            local entry   = list[i]
            local unicode = entry[1]
            local count   = entry[3]
            local used    = fonts.handlers.otf.getsubstitution(target,unicode,"ssty",true,"math","dflt") or unicode
            local data    = targetcharacters[used]
            if data then
                targetcharacters[unicode] = data
                local oldheight = data.height or 0
                local newheight = factor * oldheight
                data.yoffset = newheight - (oldheight or 0)
                data.height  = newheight
                data.smaller = nil
            elseif not fake then
                report_tweak("missing %i prime %U",target,original,count,unicode)
            end
        end
        if fake then
            for i=1,#list do
                local entry = list[i]
                local count = entry[3]
                if count > 1 then
                    local unicode  = entry[1]
                    local original = entry[4]
                    local data     = targetcharacters[original]
                    if data then
                        local oldwidth = data.width
                        local xoffset  = fake * oldwidth
                        local newwidth = oldwidth + (count - 1) * xoffset
                        targetcharacters[unicode] = {
                            width    = newwidth,
                            height   = data.height,
                            unicode  = unicode,
                            commands = {
                                              { "offset",           0, 0, original },
                                              { "offset",     xoffset, 0, original },
                                count > 2 and { "offset", 2 * xoffset, 0, original } or nil,
                                count > 3 and { "offset", 3 * xoffset, 0, original } or nil,
                            },
                        }
                    end
                end
            end
        end
    end

    function mathtweaks.addprimed(target,original,parameters)
        local characters = target.characters
        for i=1,#list do
            local entry    = list[i]
            local basecode = entry[1]
            local movecode = entry[2]
            local basedata = characters[basecode]
            if basedata then
                local baseheight = basedata.height or 0
                local basewidth  = basedata.width  or 0
                local used       = baseheight
                local total      = baseheight
                characters[movecode] = { -- todo:share
                    width    = basewidth,
                    height   = used,
                    unicode  = basecode, -- 0xFFFD or space or so
        --             callback = "devirtualize",
                    commands = {
                        downcommand[used],
                        { "rule", used, 0 },
                    },
                }
                basedata.partsorientation = "vertical"
                basedata.parts = {
                    {
                        advance  = used,
                        ["end"]  = used,
                        extender = 1,
                        glyph    = movecode,
                        start    = used,
                    },
                    {
                        advance  = total,
                        ["end"]  = 0,
                        glyph    = basecode,
                        start    = total,
                    },
                }
                if trace_tweaking then
                    report_tweak("primed %U added",target,original,basecode)
                end
            end
        end
    end

end

do

    local nps = fonts.helpers.newprivateslot

    local privates = {
        [0x2212] = nps("unary minus"),
        [0x002B] = nps("unary plus"),
        [0x00B1] = nps("unary plus minus"),
        [0x2213] = nps("unary minus plus"),
    }

    -- these are the values tested with texgyre-bonum

    local predefined  = {
        ["unary minus"] = {
            original = 0x2212,
            extend   = .5,
            width    = .5,
            unicode  = 0x002D, -- hyphen minus
        },
        ["unary plus"] = {
            original = 0x002B,
            extend   = .5,
            squeeze  = .5,
            width    = .5,
            height   = .5,
            yoffset  = .2,
            mode     = 2,
            wline    = .5,
            unicode  = 0x002B,
        },
        ["unary plus minus"] = {
            original = 0x00B1,
            extend   = .5,
            squeeze  = .5,
            width    = .5,
            height   = .5,
            yoffset  = .2,
            mode     = 2,
            wline    = .5,
        },
        ["unary minus plus"] = {
            original = 0x2213,
            extend   = .5,
            squeeze  = .5,
            width    = .5,
            height   = .5,
            yoffset  = .2,
            mode     = 2,
            wline    = .5,
        },
    }

 -- {
 --     tweak = "addprivates",
 --     list  = {
 --         -- for specific parameters see act file
 --         ["unary minus"]      = { preset = "unary minus"      },
 --         ["unary plus"]       = { preset = "unary plus"       },
 --         ["unary plus minus"] = { preset = "unary plus minus" },
 --         ["unary minus plus"] = { preset = "unary minus plus" },
 --     },
 -- },

    function mathtweaks.addprivates(target,original,parameters)
        local list = parameters.list or predefined
        if list then
            local targetcharacters   = target.characters
            local targetparameters   = target.parameters
            local originalcharacters = original.characters
            local processedprivates  = { }
            for name, v in sortedhash(list) do
                if type(v) == "table" then
                    local preset = v.preset
                    if preset then
                        local p = predefined[preset]
                        if p then
                            v = table.combine(p,v)
                            p.preset = nil
                        else
                            goto next
                        end
                    end
                    local charslot = v.original
                    if charslot then
                        local chardata = targetcharacters[charslot]
                        if chardata then
                            local clonedata = copytable(chardata)
                            local cloneslot = nps(name)
                            local unicode   = v.unicode or clonedata.unicode
                            clonedata.uncode = unicode
                            targetcharacters[cloneslot] = clonedata
                            if trace_tweaking then
                                report_tweak("cloning %a from %C into %U with tounicode %U",target,original,name,charslot,cloneslot,unicode)
                            end
                        end
                        processedprivates[name] = v
                    end
                  ::next::
                end
            end
            mathtweaks.dimensions(target,original,{
                tweak = parameters.tweak,
                list  = processedprivates,
            })
        end
    end

end

-- do
--
--     function mathtweaks.fixanchors(target,original,parameters)
--         local targetcharacters= target.characters
--         local factor = tonumber(parameters.factor) or 0
--         if factor ~= 0 then
--             local done = false
--             for k, v in next, targetcharacters do
--                 local a = v.topanchor
--                 if a and a > 0 then
--                     v.topanchor = a * factor
--                     count = count + 1
--                     if not trace_tweaking then
--                         done = true
--                     elseif done then
--                         done[u] = true
--                     else
--                         done = { [u] = true }
--                     end
--                 end
--             end
--         end
--         feedback_tweak("fixanchors",target,original,done)
--     end
--
-- end

-- do
--
--     -- actually this should be a an engine feature driven by category because we don't
--     -- want this in display mode .. only a test for MS and HH
--
--     local issymbol = characters.is_symbol
--
--     function mathtweaks.oldstylemath(target,original,parameters)
--         local chardata = characters.data
--         local characters = target.characters
--         local axis       = target.mathparameters.AxisHeight
--         local delta      = (parameters.factor or .1) * axis
--         target.mathparameters.AxisHeight = (axis - delta)
--         for k, v in sortedhash(characters) do
--             if issymbol[k] then -- quick hack, engine knows
--                 v.yoffset = -delta
--                 v.height  = (v.height or 0) - delta
--                 v.depth   = (v.depth  or 0) - delta
--             end
--         end
--     end
--
--     function mathtweaks.oldstylemath(target,original,parameters)
--         -- not relevant
--     end
--
-- end

do

    function mathtweaks.simplifykerns(target,original,parameters)
        local characters = target.characters
        local done       = false
     -- for u, v in sortedhash(characters) do
        for u, v in next, characters do
            local mathkerns = v.mathkerns
            if mathkerns then
                local k = mathkerns.topleft
                if k then
                    k = k[#k].kern
                    if k then
                        v.topleft = k
                    end
                end
                local k = mathkerns.topright
                if k then
                    k = k[#k].kern
                    if k then
                        v.topright = k
                    end
                end
                local k = mathkerns.bottomleft
                if k then
                    k = k[1].kern -- todo get value at baseline
                    if k then
                        v.bottomleft = k
                    end
                end
                local k = mathkerns.bottomright
                if k then
                    k = k[1].kern -- todo get value at baseline
                    if k then
                        v.bottomright = k
                    end
                end
                v.mathkerns = nil
                if not trace_tweaking then
                    done = true
                elseif done then
                    done[u] = true
                else
                    done = { [u] = true }
                end
            end
        end
        feedback_tweak("simplifykerns",target,original,done)
    end

end

do

     local function wipe(whatever,target,original,parameters,field,move,integrals)
        local targetcharacters   = target.characters
        local targetdescriptions = target.descriptions
        local factor             = target.parameters.factor
        local correct            = parameters.correct
        local done               = false
        local function getllx(u)
            local d = targetdescriptions[u]
            if d then
                local b = d.boundingbox
                if b then
                    local llx = b[1]
                    if llx < 0 then
                        return - llx
                    end
                end
            end
            return false
        end
        local function step(s)
            while s do
                local u = mathgaps[s] or s
                local c = targetcharacters[u]
                if c then
                    if field == "topanchor" then
                        if c.topanchor then
                            c.topanchor = nil
                        else
                            goto smaller
                        end
                    else
                        local okay   = false
                        local italic = c.italic
                        if move and not c.advance then -- advance check prevents double move
                            local width  = c.width or 0
                            c.advance = width
                            if correct then
                                local llx = getllx(u)
                                if llx then
                                    local topanchor = c.topanchor
                                    llx   = llx * factor
                                    width = width + llx
                                    c.xoffset = llx
                                    if topanchor then
                                        c.topanchor = topanchor + llx
                                    end
                                    -- too bad (schola e^x):
                                 -- c.bottomleft = (c.bottomleft or 0) - llx
                                 -- c.topleft    = (c.topleft    or 0) - llx
                                    okay = true
                                end
                            end
                            if italic and italic ~= 0 then
                                c.width       = width + italic
                                c.bottomright = - italic
                                okay = true
                            else
                                c.width = width
                            end
c.bottomanchor = width/2 -- maybe optional
                        end
                        if italic then
                            c.italic = nil
                            okay = true
                        end
                        if okay then
                            if not trace_tweaking then
                                done = true
                            elseif done then
                                done[u] = true
                            else
                                done = { [u] = true }
                            end
                        else
                            goto smaller
                        end
                    end
                    goto smaller
                  ::smaller::
                    s = c.smaller
                  ::variants::
                    -- no italics here anyway but we could check them some day
                else
                    break
                end
            end
        end
        local list = parameters.list -- todo: ranges
        if list == "letters" or parameters.letters then
            local chardata = characters.data
         -- for k, v in sortedhash(targetcharacters) do
            for k, v in next, targetcharacters do
                if v.italic then
                    local d = chardata[v.unicode]
                    local c = d and d.category
                    if c == "ll" or c == "lu" then
                        step(k)
                    end
                end
            end
            goto done
        end
        if not list or list == "all" or list == true or parameters.all then
            list = sortedkeys(targetcharacters)
        elseif type(list) == "string" then
            list = { list }
        end
        for i=1,#list do
            local l = list[i]
            local t = type(l)
            if not l then
                -- can be false
            elseif t == "table" then
                for i=1,#l do
                    step(l[i])
                end
            elseif t == "number" then
                step(l)
            else
                local r = blocks[l]
                if r then
                    for i=r.first,r.last do
                        step(i)
                    end
                else
                    stepper(l,step)
                end
            end
        end
       ::done::
        feedback_tweak(whatever,target,original,done)
    end

    function mathtweaks.wipeanchors(target,original,parameters)
        wipe("wipeanchors",target,original,parameters,"topanchor")
    end

    function mathtweaks.wipeitalics(target,original,parameters)
        if not checkitalics then
            wipe("wipeitalics",target,original,parameters,"italic")
        end
    end

    function mathtweaks.moveitalics(target,original,parameters)
        wipe("moveitalics",target,original,parameters,"italic",true)
    end

 -- function mathtweaks.fixdigits(target,original,parameters)
 --     mathtweaks.fixanchors(target,original,{ list = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } })
 -- end

end

do

    function mathtweaks.topanchors(target,original,parameters)
        local characters = target.characters
        local list       = parameters.list
        if list then
            local done = false
            for u, v in sortedhash(list) do
                local c = characters[k]
                if c then
                    local w = c.width
                    if w and w ~= 0 then
                        c.topanchor = v * w
                        if trace_tweaking then
                            -- todo
                        end
                        if not trace_tweaking then
                            done = true
                        elseif done then
                            done[u] = true
                        else
                            done = { [u] = true }
                        end
                    end
                end
            end
            feedback_tweak("topanchors",target,original,done)
        end
    end

    function mathtweaks.movelimits(target,original,parameters)
        local characters = target.characters
        local list       = parameters.list
        if list then
            local factor = parameters.factor or 1
            local also   = getalso(target,original)
            local done   = { }
            local function relocate(u,factor)
                if done[u] then
                    return
                end
                done[u] = true
                local c = characters[u]
                if c then
                    local italic = c.italic
                    if italic then
                        if italic ~= 0 then
                            local width = c.width or 0
                            local half  = (italic/2) * factor
                            c.topanchor    = width + half
                            c.bottomanchor = width - half
                            c.bottomright  = - italic * (parameters.icfactor or 1)
                            if trace_tweaking then
                                -- todo
                            end
                        end
                        c.italic = nil
                    end
                    local s = c.smaller
                    if s then
                        relocate(s,factor)
                    end
                    local n = c.next
                    if n then
                        relocate(n,factor)
                    end
                    -- Kind of tricky: we configure the engine to use the vitalic
                    -- so when we tweak we need to set that to zero.
                    local parts  = c.parts
                    local italic = c.partsitalic
                    if parts and italic then
                        if italic ~= 0 then
                            local tchar = characters[parts[#parts].glyph]
                            local bchar = characters[parts[1].glyph]
                            local width = tchar.width or 0
                            local half  = (italic/2) * factor
                            tchar.topanchor    = width + half
                            bchar.bottomanchor = width - half
                            bchar.bottomright  = - italic
                            if trace_tweaking then
                                -- todo
                            end
                            tchar.italic = nil
                            bchar.italic = nil
                        end
                        c.vitalic = nil
                    end
                    if also then
                        local a = also[u]
                        if a then
                            for i=1,#a do
                                relocate(a[i],factor)
                            end
                        end
                    end
                end
            end
            if #list > 0 then
                for i=1,#list do
                    relocate(list[i],factor)
                end
            else
                for k, v in sortedhash(list) do
                    relocate(k,tonumber(v) or factor)
                end
            end
            feedback_tweak("movelimits",target,original,done)
        end
    end

end

do

    -- musical timestamp: March 2022, Antonio Sanches (Bad Hombre), live performance in NL

    function mathtweaks.kerns(target,original,parameters)
        local kerns = parameters.list
        if kerns then
            local characters = target.characters
            local done       = false
            local function setone(uc,data)
                local function set(unicode)
                    unicode = mathgaps[unicode] or unicode
                    local chardata = characters[unicode]
                    if chardata then
                        local width = chardata.width  or 0
                        local k = data.topleft     ; if k and k ~= 0 then chardata.topleft     = k * width end
                        local k = data.topright    ; if k and k ~= 0 then chardata.topright    = k * width end
                        local k = data.bottomleft  ; if k and k ~= 0 then chardata.bottomleft  = k * width end
                        local k = data.bottomright ; if k and k ~= 0 then chardata.bottomright = k * width end
                        if not trace_tweaking then
                            done = true
                        elseif done then
                            done[unicode] = true
                        else
                            done = { [unicode] = true }
                        end
                    end
                end
                local unicode  = detail(characters,uc)
                if type(unicode) == "table" then
                    for i=1,#unicode do
                        set(unicode[i])
                    end
                elseif unicode then
                    set(unicode)
                end
            end
            for unicode, data in next, kerns do
                setone(unicode,data) -- withscriptcode(tfmdata,unicode,data,kernone)
                -- also smaller
            end
            feedback_tweak("kerns",target,original,done)
        end
    end

end

do

    function mathtweaks.margins(target,original,parameters)
        local margins = parameters.list
        if margins then
            local characters = target.characters
            local done       = false
            local function setone(unicode,data)
                unicode = mathgaps[unicode] or unicode
                local chardata = characters[unicode]
                if chardata then
                    local width    = chardata.width or 0
                    local total    = (chardata.height or 0) + (chardata.depth or 0)
                    local k = data.left   ; if k and k ~= 0 then chardata.leftmargin   = k * width end
                    local k = data.right  ; if k and k ~= 0 then chardata.rightmargin  = k * width end
                    local k = data.top    ; if k and k ~= 0 then chardata.topmargin    = k * total end
                    local k = data.bottom ; if k and k ~= 0 then chardata.bottommargin = k * total end
                    if not trace_tweaking then
                        done = true
                    elseif done then
                        done[unicode] = true
                    else
                        done = { [unicode] = true }
                    end
                end
            end
            for unicode, data in next, margins do
                setone(unicode,data) -- withscriptcode(tfmdata,unicode,data,kernone)
                -- also smaller
            end
            feedback_tweak("margins",target,original,done)
        end
    end

end

do

    -- musical timestamp: June 2022, Porcupine Tree - Rats Return

    -- we can actually share these and flag them as being tweaked

    local function scale(t,width,total)
        local r = { }
        for i=1,#t do
            local ti = t[i]
            local kern   = ti.kern
            local height = ti.height
            if kern then
                kern = width * kern
            end
            if height then
                height = total * height
            end
            r[i] = {
                kern   = kern or 0,
                height = height or 0,
            }
        end
        return r
    end

    function mathtweaks.staircase(target,original,parameters)
        local kerns = parameters.list
        if kerns then
            local characters = target.characters
            local function kernone(unicode,data)
                local chardata = characters[mathgaps[unicode] or unicode]
                local total = (chardata.height or 0) + (chardata.depth or 0)
                local width = chardata.width or 0
                if data then
                    local tl = data.topleft     ; if tl then tl = scale(tl,width,total) end
                    local tr = data.topright    ; if tr then tr = scale(tr,width,total) end
                    local bl = data.bottomleft  ; if bl then bl = scale(bl,width,total) end
                    local br = data.bottomright ; if br then br = scale(br,width,total) end
                    chardata.mathkerns = {
                        topleft     = tl,
                        ropright    = tr,
                        bottomleft  = bl,
                        bottomright = br,
                    }
                else
                    chardata.mathkerns = nil
                end
            end
            for unicode, data in next, kerns do
                kernone(unicode,data) -- withscriptcode(tfmdata,unicode,data,kernone)
                -- also smaller
            end
        end
    end

end

do

 -- local list = {
 --     [0x203E] = { factor = .4 }, -- overbar
 --     [0x203E] = { factor = .7 }, -- underbar
 --     [0x23DE] = { factor = .4 }, -- overbrace
 --     [0x23DF] = { factor = .7 }, -- underbrace
 --     [0x23DC] = { factor = .4 }, -- overparent
 --     [0x23DD] = { factor = .7 }, -- underparent
 --     [0x23B4] = { factor = .4 }, -- overbracket
 --     [0x23B5] = { factor = .7 }, -- underbracket
 -- }

    -- We can patch the dimensions in-place or we can use additional characters in
    -- the private namespace.

    -- local addprivate = fonts.helpers.addprivate
    -- local newnextglyph = addprivate(target,formatters["M-N-%H"](nextglyph),newnextdata)

    local nps = fonts.helpers.newprivateslot

    local umbracepiece = nps("um brace piece") -- will be created
    local lmbracepiece = nps("lm brace piece") -- will be created
    local cmbracepiece = nps("cm brace piece") -- will be created : center piece for brace builder hack

    local ulbracepiece = nps("ul brace piece")
    local urbracepiece = nps("ur brace piece")
    local llbracepiece = nps("ll brace piece")
    local lrbracepiece = nps("lr brace piece")

    local over  = { factor = "over"   }
    local under = { factor = "under"  }

    local candidates = {
        over = {
            [0x203E] = over,  -- overbar
            [0x23DE] = over,  -- overbrace
            [0x23DC] = over,  -- overparent
            [0x23B4] = over,  -- overbracket
        },
        under = {
            [0x23DF] = under, -- underbrace
            [0x23DD] = under, -- underparent
            [0x23B5] = under, -- underbracket
        },
        accent = {
            [0x0300] = over,  -- widegrave
            [0x0308] = over,  -- wideddot
            [0x0304] = over,  -- macron (bar)
            [0x0305] = over,  -- widebar
            [0x0301] = over,  -- wideacute
            [0x0302] = over,  -- widehat
            [0x030C] = over,  -- widecheck
            [0x0306] = over,  -- widebreve
            [0x0307] = over,  -- widedot
            [0x030A] = over,  -- widering
            [0x0303] = over,  -- widetilde
            [0x20DB] = over,  -- widedddot
        },
    }

    datasets.accentdimensions = candidates

    local function adapt(c,factor,baseheight,basedepth)
        if not c.tweaked then
            local height  = c.height or 0
            local depth   = c.depth  or 0
            local yoffset = 0
            if factor == "over" then
                local h = height - baseheight
                yoffset = h - height
                height  = h
                depth   = depth - baseheight
            elseif factor == "under" then
                local d = depth - basedepth
                yoffset = depth - d
                depth   = d
                height  = height - baseheight
            elseif height > 0 then
                local h = tonumber(factor) * height
                yoffset = h - height
                height  = h
            elseif depth > 0 then
                local d = tonumber(factor) * depth
                yoffset = depth - d
                depth   = d
            end
            c.yoffset = yoffset ~= 0 and yoffset or nil
            c.height  = height   > 0 and height  or nil
            c.depth   = depth    > 0 and depth   or nil
            c.tweaked = true
        end
    end

    local function process(target,original,characters,list,baseheight,basedepth)
        if list then
            for k, v in sortedhash(list) do -- sort for tracing
                local c = characters[k]
                if c and not c.yoffset then
                    local factor = v.factor
                    if factor then
                        adapt(c,factor,baseheight,basedepth)
                        local nc  = c.next
                        local nv = 0
                        local ns = 0
                        while nc do
                            local c = characters[nc]
                            if c then
                                adapt(c,factor,baseheight,basedepth)
                                nv = nv + 1
                                nc = c.next
                                if not nc then
                                    local hv = c.parts
                                    if hv then
                                        for i=1,#hv do
                                            local c = characters[hv[i].glyph]
                                            if c then
                                                adapt(c,factor,baseheight,basedepth)
                                                ns = ns + 1
                                            end
                                        end
                                    end
                                    break
                                end
                            else
                                break
                            end
                        end
                        if trace_tweaking then
                            report_tweak("adapting extensible (%i sizes, %i parts) %U",target,original,k,nv,ns)
                        end
                    end
                end
            end
        end
    end

    function mathtweaks.accentdimensions(target,original,parameters)
        local list = parameters.list or { "over", "under" }
        if list then
            local characters = target.characters
            local baseheight = target.mathparameters.AccentBaseHeight or 0
            local basedepth  = target.mathparameters.AccentBaseDepth  or 0
            for k, v in sortedhash(list) do -- sort for tracing
                local t = type(v)
                if t == "string" then
                    v = candidates[v]
                    t = type(v)
                end
                if t == "table" then
                    process(target,original,characters,v,baseheight,basedepth)
                end
            end
        end
    end

end

do

    local addprivate     = fonts.helpers.addprivate
    local privateslot    = fonts.helpers.privateslot
    local newprivateslot = fonts.helpers.newprivateslot

    function mathtweaks.addrules(target,original,parameters)
        local characters = target.characters
        local thickness  = target.mathparameters.OverbarRuleThickness
        local width      = target.parameters.emwidth / 2
        local width      = target.parameters.emwidth / 3
--         local step       = 0.8 * width
        local step       = 0.5 * width
        characters[0x203E] = { -- middle used for all kind
            width    = width,
            height   = thickness / 2,
            depth    = thickness / 2,
            yoffset  = - thickness / 2,
            unicode  = 0x203E,
            commands = { { "rule", thickness, width } },
            parts    = {
                { advance = width, ["end"] = step, glyph = 0x203E, start = 0 },
                { advance = width, ["end"] = 0,    glyph = 0x203E, start = step, extender = 1 },
            },
            partsorientation = "horizontal",
        }
        local function build(target,leftarrow,rightarrow)
            if leftarrow and rightarrow then
                -- actually the same sort of code as we have for antykwa
                local left  = leftarrow.parts
                local right = rightarrow.parts
                if left and right then
                    local leftline   = right[1].glyph
                    local rightline  = left [#left].glyph
                    local leftdata   = characters[leftline]
                    local rightdata  = characters[rightline]
                    local leftwidth  = leftdata.width
                    local rightwidth = rightdata.width
                    local result     = characters[target] -- copytable(leftdata)
                    if not result or result.width == 0 then
                        result = {
                            height   = leftdata.height,
                            depth    = leftdata.depth,
                            width    = 0.9*leftwidth + rightwidth,
                            unicode  = target,
                            commands = {
                                slotcommand[0][leftline],
                                leftcommand[0.1*leftwidth],
                                slotcommand[0][rightline],
                            },
                        }
                        characters[target] = result
                    end
                    result.parts = {
                        { advance = leftwidth, glyph = leftline, ["end"] = .9*leftwidth, start = 0 },
                        { advance = rightwidth, glyph = rightline, ["end"] = .1*leftwidth, start = .9*rightwidth, extender = 1 },
                    }
                    result.partsorientation = "horizontal"
                end
            end
        end
        build(0x305,characters[0x20D6],characters[0x20D7]) -- overbar  accent
        build(0x332,characters[0x20EE],characters[0x20EF]) -- underbar accent
        --
        -- lucida lacks them ...
        --
        local half   = thickness / 2
        local double = thickness * 2
        --
        if not characters[0x23B4] then
            local tpiece = addprivate(target,"bracket-piece-top",{
                width    = thickness,
                height   = half,
                depth    = double,
                yoffset  = - double,
                commands = { { "rule", thickness * 2.5, thickness } },
            })
            characters[0x23B4] = { -- over
--                 width    = width,
                width    = 2*thickness+width,
                height   = half,
                depth    = double,
                unicode  = 0x23B4,
                commands = {
                    slotcommand[0][tpiece],
                    slotcommand[0][0x203E],
                    slotcommand[0][tpiece],
                },
                parts    = {
                    { advance = thickness, glyph = tpiece, ["end"] = 0,    start = half },
                    { advance = width,     glyph = 0x203E, ["end"] = step, start = step, extender = 1 },
                    { advance = thickness, glyph = tpiece, ["end"] = half, start = 0 },
                },
                partsorientation = "horizontal",
            }
        end
        if not characters[0x23B5] then
            local bpiece = addprivate(target,"bracket-piece-bottom",{
                width    = thickness,
                height   = double,
                depth    = half,
                yoffset  = - half,
                commands = { { "rule", thickness * 2.5, thickness } },
            })
            characters[0x23B5] = { -- under
                width    = 2*thickness+width,
                height   = double,
                depth    = half,
                unicode  = 0x23B5,
                commands = {
                    slotcommand[0][bpiece],
                    slotcommand[0][0x203E],
                    slotcommand[0][bpiece],
                },
                parts    = {
                    { advance = thickness, glyph = bpiece, ["end"] = 0,    start = half },
                    { advance = width,     glyph = 0x203E, ["end"] = step, start = step, extender = 1 },
                    { advance = thickness, glyph = bpiece, ["end"] = half, start = 0 },
                },
                partsorientation = "horizontal",
            }
        end
        --
    end

    -- vfmath.builders.extension(target)

    local rbe = newprivateslot("radical bar extender")
    local fbe = newprivateslot("fraction bar extender")

    local frp = {
        newprivateslot("flat rule left piece"),
        newprivateslot("flat rule middle piece"),
        newprivateslot("flat rule right piece"),
    }

    local rrp = {
        newprivateslot("radical rule middle piece"),
        newprivateslot("radical rule right piece"),
    }

    local mrp = {
        newprivateslot("minus rule left piece"),
        newprivateslot("minus rule middle piece"),
        newprivateslot("minus rule right piece"),
    }

    local function useminus(target,unicode,characters,parameters,skipfirst,what,tounicode)
        local minus   = characters[0x2212]
        local parts   = minus.parts
        if parameters == true then
            parameters = { }
        end
        if parts then
            parts  = copytable(parts)
            local xscale  = parameters.xscale  or 1
            local yscale  = parameters.yscale  or 1
            local mheight = minus.height
            local height = (parameters.height  or 1) * mheight
            local yshift = (parameters.yoffset or 0) * mheight
            if skipfirst then
                table.remove(parts,1)
            end
            height = height / 2
            yshift = yshift + height
            for i=1,#parts do
                local part   = parts[i]
                local glyph  = part.glyph
                local gdata  = characters[glyph]
                local width  = gdata.width
                local xshift = 0
                if i == 1 and parameters.leftoffset then
                    xshift = (parameters.leftoffset) * width
                    width  = width - xshift
                elseif i == #parts and parameters.rightoffset then
                    width  = (1 + parameters.rightoffset) * width
                end
                characters[what[i]] = {
                    height   = height,
                    depth    = height,
                    width    = width,
                    commands = {
                        leftcommand[xshift],
                        downcommand[yshift],
--                         slotcommand[0][glyph],
                        { "slot", 0, glyph, xscale, yscale },
                    },
                }
                part.glyph   = what[i]
                part.advance = width
            end
            characters[unicode] = {
                height   = height,
                depth    = height,
                width    = advance,
                commands = {
                    downcommand[yshift],
--                     slotcommand[0][0x2212],
                    { "slot", 0, 0x2212, xscale, yscale },
                },
                unicode          = tounicode or unicode,
                parts            = parts,
                partsorientation = "horizontal",
            }
        end
    end

    -- add minus parts of not there and create clipped clone

    local function checkminus(target,unicode,characters,parameters,skipfirst,what,tounicode)
        local minus = characters[unicode]
        local parts = minus.parts
        if parameters == true then
            parameters = { }
        end
        local p_normal = 0
        local p_flat   = 0
        local mwidth   = minus.width
        local height   = minus.height
        local depth    = minus.depth
        local loffset  = parameters.leftoffset  or 0
        local roffset  = parameters.rightoffset or 0
        local lshift   = mwidth * loffset
        local rshift   = mwidth * roffset
        local width    = mwidth - lshift - rshift
        if parts then
         -- print("minus has parts")
            if lshift ~= 0 or width ~= mwidth then
                parts = copytable(parts)
                for i=1,#parts do
                    local part    = parts[i]
                    local glyph   = part.glyph
                    local gdata   = characters[glyph]
                    local width   = gdata.width
                    local advance = part.advance
                    local lshift = 0
                    if i == 1 and left ~= 0 then
                        lshift  = loffset * width
                        width   = width - lshift
                        advance = advance - lshift
                    elseif i == #parts and roffset ~= 0 then
                        width   = width - rshift
                        advance = advance - rshift
                    end
                    characters[what[i]] = {
                        height   = height,
                        depth    = depth,
                        width    = width,
                        commands = {
                            leftcommand[lshift],
                            slotcommand[0][glyph],
                        },
                    }
                    part.glyph   = what[i]
                    part.advance = advance
                end
                minus.parts = parts
                minus.partsorientation = "horizontal"

            end
        else
            local f_normal = formatters["M-NORMAL-%H"](unicode)
         -- local p_normal = hasprivate(main,f_normal)
            p_normal = addprivate(target,f_normal,{
                height   = height,
                width    = width,
                commands = {
                    push,
                    leftcommand[lshift],
                    slotcommand[0][unicode],
                    pop,
                },
            })
            local step = width/2
            minus.parts = {
                { extender = 0, glyph = p_normal, ["end"] = step, start = 0,    advance = width },
                { extender = 1, glyph = p_normal, ["end"] = step, start = step, advance = width },
                { extender = 0, glyph = p_normal, ["end"] = 0,    start = step, advance = width },
            }
            minus.partsorientation = "horizontal"
        end
        minus.unicode = tounicode or unicode
    end

    function mathtweaks.replacerules(target,original,parameters)
        local characters = target.characters
        local minus      = parameters.minus
        local fraction   = parameters.fraction
        local radical    = parameters.radical
        local stacker    = parameters.stacker
        if minus then
            checkminus(target,0x2212,characters,minus,false,mrp)
        end
        if fraction then
            useminus(target,fbe,characters,fraction,false,frp,0x2044) -- division slash
        end
        if radical then
            useminus(target,rbe,characters,radical,true,rrp,0x2061)   -- apply function
        end
        if stacker then
            useminus(target,0x203E,characters,stacker,false,frp)
        end
    end

    local force = false  experiments.register("math.arrows", function(v) force = v end)

    local function tighten(target,unicode,left,right,squeeze,yoffset)
        local name = formatters["math tightened %U %.3N %.3N %.3N %.3N"](unicode,left,right,squeeze,yoffset)
        local slot = privateslot(target,name)
        if not slot then
            local characters = target.characters
            local data   = copytable(characters[unicode])
            local width  = data.width
            data.advance = width
            data.width   = width * (1-left-right)
            data.xoffset = width * -left
            if squeeze ~= 1 then
                data.effect  = { squeeze = squeeze }
            end
            if yoffset ~= 0 then
                data.yoffset = (data.height or 0) * yoffset
            end
            slot = addprivate(target,name,data)
        end
        return slot
    end

    local function create(target,unicode,list,overloads)
        local characters = target.characters
        local chardata   = characters[unicode]
        if chardata then
            local endpoint = unicode
            while chardata.next do
                chardata = characters[chardata.next]
            end
            if chardata and (force or overloads[unicode] == false or not chardata.parts) then
                if not list then
                 -- chardata.parts = nil -- when we test
--                     chardata.parts = { { glyph = unicode } }
                else
                    local overload = overloads[unicode]
                    local parts    = { }
                    for i=1,#list do
                        local part    = list[i]
                        local glyph   = part.glyph or unicode
                        local check   = overloads[glyph]
                        local left    = (check and check.left   ) or part.left    or 0
                        local right   = (check and check.right  ) or part.right   or 0
                        local squeeze =  check and check.squeeze or 1
                        local yoffset =  check and check.yoffset or 0
                        if left~= 0 or right ~= 0 or squeeze ~= 1 or yoffset ~= 0 then
                            glyph = tighten(target,glyph,left,right,squeeze,yoffset)
                        end
                        local width = characters[glyph].width
                        local step  = width/2
                        if part.extensible then
                            parts[#parts+1] = {
                                advance  = width,
                                glyph    = glyph,
                                ["end"]  = step,
                                start    = step,
                                extender = 1,
                            }
                        else
                            parts[#parts+1] = {
                                advance = width,
                                glyph   = glyph,
                                ["end"] = 0,
                                start   = step,
                            }
                        end
                    end
                    if #parts == #list then
                        chardata.parts            = parts
                        chardata.partsorientation = "horizontal"
                    end
                end
            end
        end
    end

    -- Unicode math lacks the arrow snippet while it does have fence snippets. Also, some
    -- fonts have a relbar that doesn't match the double arrow.
    --
    -- {
    --     tweak = "addarrows",
    --     list  = { [0x3D] = { squeeze = .85, yoffset = .0975 } }
    -- },
    --
    -- We have no begin and end snippet, so I played with centering and rules at the edges
    --
    -- [0x21A9] = { -- hookleftarrow
    --     { glyph = 0x2212, left = slack, extensible = true },
    --     { glyph = 0x21A9, right = slack },
    --     { glyph = 0x2212, right = slack, extensible = true },
    -- }
    --
    -- but in the end rejected it.

    local function initialize(left, right, slack)
        -- We save some space with locals. When no glyph is given the unicode itself is
        -- used which also saves some.
        local single = { glyph = 0x2212, left = slack, right = slack, extensible = true }
        local double = { glyph = 0x003D, left = slack, right = slack, extensible = true }
        local triple = { glyph = 0x2261, left = slack, right = slack, extensible = true }
        ----- spacer = { glyph = 0x0020, left = slack, right = slack, extensible = true }
        local slackslack  = { left = slack, right = slack }
        local leftslack   = { left = left,  right = slack }
        local slackright  = { left = slack, right = right }
        ----- centered    = { spacer, { }, spacer }
        local centered    = false -- the luametatex engine does this
        local singleright = { single, slackright }
        local leftsingle  = { leftslack,  single }
        return {
            --
            [0x002D] = { { left = slack, right = slack, glyph = 0x2212 }, single }, -- rel
-- [0x2212] = { { left = slack, right = slack, glyph = 0x2212 }, single }, -- rel
            --
            [0x2190] = leftsingle, -- leftarrow
            [0x219E] = leftsingle, -- twoheadleftarrow
            [0x21BC] = leftsingle, -- leftharpoonup
            [0x21BD] = leftsingle, -- leftharpoondown
            --
            [0x2192] = singleright, -- rightarrow
            [0x21A0] = singleright, -- twoheadrightarrow
            [0x21C0] = singleright, -- rightharpoonup
            [0x21C1] = singleright, -- rightharpoondown
            --
            [0x003D] = { slackslack, double }, -- equaltext
            [0x2261] = { slackslack, triple }, -- triplerel
            [0x27F8] = { leftslack,  double }, -- Leftarrow
            [0x27F9] = { double, slackright }, -- Rightarrow
            --
            [0x21A9] = centered, -- hookleftarrow
            [0x21AA] = centered, -- hookrightarrow
            [0x21CB] = centered, -- leftrightharpoons
            [0x21CC] = centered, -- rightleftharpoons
            [0x21C4] = centered, -- rightoverleftarrow
            [0x21C6] = centered, -- leftoverrightarrow
            [0x21A6] = centered, -- mapsto
            --
            [0x203E] = { slackslack, { left = slack, right = slack, extensible = true } }, -- bar
            --
            [0x27F7] = { { glyph = 0x2190, left = left, right = slack }, single, { glyph = 0x2192, left = slack, right = right } }, -- leftrightarrow rightleftarrow
            [0x27FA] = { { glyph = 0x27F8, left = left, right = slack }, double, { glyph = 0x27F9, left = slack, right = right } }, -- Leftrightarrow Rightleftarrow
        }
    end

    datasets.addarrows = { }

    function mathtweaks.addarrows(target,original,parameters)
        local overloads = parameters.list  or { } -- { [unicode] = { left = .1, right = .1 } }
        local left      = parameters.left  or 0.05
        local right     = parameters.right or 0.05
        local slack     = parameters.slack or 0.1
        local arrows    = initialize(left,right,slack)
         -- inspect(arrows)
        for unicode, list in sortedhash(arrows) do
            create(target,unicode,list,overloads)
        end
        datasets.addarrows = sortedkeys(arrows)
        if trace_tweaking then
            report_tweak("arrows added",target,original)
        end
    end

end

do -- this could be combined with the previous

    function mathtweaks.addparts(target,original,parameters)
        local characters = target.characters
        local list       = parameters.list
        if list then
            for unicode, data in sortedhash(list) do
                local template = data.template
                if template then
                    local source = characters[template]
                    local target = characters[unicode]
                    if source and target then
                        local sequence   = data.sequence
                        if sequence then
                            local parts = source.parts
                            if parts then
                                local p = { }
                                for i=1,#sequence do
                                    local step  = sequence[i]
                                    local glyph = step.glyph
                                    if glyph == "first" or glyph == "last" then
                                        local g = glyph == "first" and 1 or #parts
                                        local c = fastcopy(parts[g])
                                        local f = step.factor
                                        if f then
                                            c["end"]  = f * (c["end"] or 0)
                                            c.start   = f * (c.start  or 0)
                                        end
                                        p[#p+1] = c
                                    else
                                        local c = characters[glyph]
                                        if c then
                                            p[#p+1] = {
                                                glyph   = glyph,
                                                advance = c.width,
                                                start   = 0,
                                                ["end"] = 0,
                                            }
                                        end
                                    end
                                end
                                if #p > 0 then
                                    target.parts = p
                                    if not data.horizontal then
                                        target.partsorientation = "vertical"
                                    end
                                end
                            end
                        end
                    end
                end
            end
        end
    end

end

function mathtweaks.action(target,original,parameters)
    local action = parameters.action
    if type(action) == "function" then
        action(target,original,parameters)
    end
end

do

    local list = {
        { 0x00A0, "s", 1         }, -- nbsp
        { 0x2000, "q", 1/2       }, -- enquad
        { 0x2001, "q", 1         }, -- emquad
        { 0x2002, "q", 1/2       }, -- enspace
        { 0x2003, "q", 1         }, -- emspace
        { 0x2004, "q", 1/3       }, -- threeperemspace
        { 0x2005, "q", 1/4       }, -- fourperemspace
        { 0x2006, "q", 1/6       }, -- sixperemspace
        { 0x2007, "c", byte('0') }, -- figurespace
        { 0x2008, "c", byte('.') }, -- punctuationspace
        { 0x2009, "q", 1/8       }, -- breakablethinspace
        { 0x200A, "q", 1/8       }, -- hairspace
        { 0x200B, "q", 0         }, -- zerowidthspace
        { 0x202F, "q", 1/8       }, -- narrownobreakspace
        { 0x205F, "s", 1/2       }, -- math thinspace
    }

    datasets.checkspacing = list

    function mathtweaks.checkspacing(target,original,parameters)
        local characters = target.characters
        local parameters = target.parameters
        for i=1,#list do
            local entry   = list[i]
            local unicode = entry[1]
            local data    = characters[unicode]
            if not data then
                local method   = entry[2]
                local fraction = entry[3]
                local width    = 0
                local height   = 0
             -- local depth    = 0
                if method == "c" then
                    local template = characters[fraction]
                    width  = template.width
                    height = template.height
                 -- depth  = template.depth
                elseif method == "s" then
                    width  = fraction * parameters.space -- space
                    height = 0
                 -- depth  = 0
                else
                    width = fraction * parameters.quad  -- quad
                    height = 0
                 -- depth  = 0
                end
                if trace_tweaking then
                    report_tweak("setting width of %U to %p",target,original,unicode,width)
                end
                characters[unicode] = {
                    width    = width,
                 -- advance  = width,
                    height   = height,
                 -- depth    = depth,
                    unicode  = unicode,
                    commands = {
                     -- { "slot", 0, 32 },
                    },
                }
            end
        end
    end

end

do

    -- mirror
    -- smaller

    local nps = fonts.helpers.newprivateslot

    local radicalbarextender = nps("radical bar extender") -- we reserve it here

    local list = {
        0x221A,
    }

    local function fix(target,original,characters,unicode)
        local data = characters[unicode]
        if data then
            local height = data.height or 0
            local depth  = data.depth or 0
            if depth > height then
                if trace_tweaking then
                    report_tweak("swapping height and depth of radical %U",target,original,unicode)
                end
                data.height  = depth
                data.depth   = height
                if data.rorrim then
                    -- the original does the magic
                else
                    data.yoffset = depth - height
                end
            end
            local smaller = data.smaller
            if smaller then
                fix(target,original,characters,smaller)
            end
            local mirror = data.mirror
            if mirror then
                fix(target,original,characters,mirror)
            end
        end
    end

    function mathtweaks.fixradicals(target,original,parameters)
        local characters = target.characters
        for i=1,#list do
            local unicode = list[i]
            fix(target,original,characters,unicode)
        end
    end

    local function fix(target,original,characters,u,l)
        local data = characters[u]
        if data then
         -- data.innerlocation = l.location == "right" and 2 or 1
            data.innerlocation = l.location == "right" and "right" or "left"
            data.innerxoffset  = (l.hfactor or 1) *  (data.width  or 0)
            data.inneryoffset  = (l.vfactor or 1) * ((data.height or 0) + (data.depth or 0))
        end
    end

    function mathtweaks.radicaldegreeanchors(target,original,parameters)
        local list = parameters.list
        if list then
            local characters = target.characters
            for unicode, l in sortedhash(list) do -- resolve variants
                local u = detail(characters,unicode) or unicode
                if type(u) == "table" then
                    for i=1,#u do
                        fix(target,original,characters,u[i],l)
                    end
                else
                    fix(target,original,characters,u,l)
                end
            end
        end
    end

end

do

    local done = nil

    local function fix(target,original,characters,unicode,axis)
        if done[unicode] then
            return
        end
        done[unicode] = true
        local data = characters[unicode]
        if data then
            local height = data.height or 0
            local depth  = data.depth or 0
            if trace_tweaking then
                report_tweak("swapping height and depth of %U",target,original,unicode)
            end
            local half = (height + depth)/2
            if data.rorrim then
                -- the original does the magic
            else
                data.yoffset = depth - (half - axis)
            end
            height = half + axis
            depth  = half - axis
            data.height  = height
            data.depth   = depth
            local smaller = data.smaller
            if smaller then
                fix(target,original,characters,smaller,axis)
            end
            local mirror = data.mirror
            if mirror then
                fix(target,original,characters,mirror,axis)
            end
            local next = data.next
            if next then
                fix(target,original,characters,next,axis)
            end
        end
    end

    function mathtweaks.fixoldschool(target,original,parameters)
        local characters = target.characters
        local list       = mathtweaks.subsets.integrals
        local also       = getalso(target,original)
        local axis       = target.mathparameters.AxisHeight
        done = { }
        for i=1,#list do
            local unicode = list[i]
            fix(target,original,characters,unicode,axis)
        end
        if also then
            local a = also[u]
            if a then
                for i=1,#a do
                    fix(target,original,characters,a[i],axis)
                end
            end
        end
        done = nil
    end

    -- After the next one I rewarded myself by (again) watching Joe Parrish interpretation
    -- of Shostakovich 10 Mvmt. II - Metal several times (video on yt, track on bandcamp)
    -- ... timestamp: awaiting the new Albion (Official) single; their work comes in parts.

    function mathtweaks.fixintegrals(target,original,parameters)
        local characters = target.characters
        local integral   = characters[0x222B]
        if integral and not integral.parts then
            local top = characters[0x2320]
            local mid = characters[0x23AE]
            local bot = characters[0x2321]
            if top and mid and bot then
                top = top.height
                mid = mid.height
                bot = bot.height
                integral.partsitalic = integral.italic
                integral.parts       = {
                    { advance = bot, ["end"] = bot/3, glyph = 0x2321, start = bot/3  },
                    { advance = mid, ["end"] = mid/2, glyph = 0x23AE, start = mid/2, extender = 1 },
                    { advance = top, ["end"] = top/3, glyph = 0x2320, start = top/3  },
                }
                integral.partsorientation = "vertical"
                if trace_tweaking then
                    report_tweak("fixing the integral extensible",target,original)
                end
            end
        else
            report_tweak("no need to fix the integral extensible",target,original)
        end
    end

end

do

    local list = { 0x2061, 0x2062, 0x2063, 0x2064 }

    datasets.wipecues = list

    function mathtweaks.wipecues(target,original,parameters)
        local characters = target.characters
        local tobewiped  = parameters.list or list
        local done       = false
        for i=1,#tobewiped do
            local unicode = tobewiped[i]
            characters[unicode] = {
                width   = 0,
                height  = 0,
                depth   = 0,
                unicode = unicode,
            }
            if not trace_tweaking then
                done = true
            elseif done then
                done[unicode] = true
            else
                done = { [unicode] = true }
            end
        end
        feedback_tweak("wipecues",target,original,done)
    end

end

do

    local mapping = {
        [0x002F] = 0x2044,
    }

    datasets.fixslashes = mapping

    function mathtweaks.fixslashes(target,original,parameters)
        local characters = target.characters
     -- local done       = false
        for normal, weird in sortedhash(mapping) do
            local normalone  = characters[normal]
            local weirdone   = characters[weird]
            if normalone and weirdone and not normalone.next then
                normalone.next = weirdone.next
             -- if not trace_tweaking then
             --     done = true
             -- elseif done then
             --     done[normal] = true
             -- else
             --     done = { [normal] = true }
             -- end
            end
            weirdone = copytable(normalone)
            characters[weird] = weirdone
            weirdone.unicode = weird
        end
     -- feedback_tweak("fixslashes",target,original,done)
        if trace_tweaking then
            report_tweak("slashes fixed",target,original)
        end
     end

end

do -- see pagella for an extensive example

    local nps = fonts.helpers.newprivateslot

    local mapping = {
        [0x0300] = { 0x0060, false },
        [0x0308] = { 0x00A8, false },
        [0x0304] = { 0x00AF, false }, -- 305
        [0x0301] = { 0x00B4, false },
        [0x0302] = { 0x02C6, true  },
        [0x030C] = { 0x02C7, true  },
        [0x0306] = { 0x02D8, false },
        [0x0307] = { 0x02D9, false },
        [0x030A] = { 0x02DA, false },
        [0x0303] = { 0x02DC, true  },
        [0x20DB] = { 0x20DB, false },
-- [0x20EF] = { 0x20EF, false },
    }

    datasets.fixaccents     = mapping
    datasets.extendaccents  = mapping
    datasets.flattenaccents = mapping
    datasets.copyaccents    = mapping

    -- local flat = stretchingdata.flataccent
    -- if flat then
    --     -- Nasty! xoffset needed. Check this when we patch vf.
    --     local flatdata = characters[flat]
    --     flatdata.width     = width
    --     flatdata.advance   = 0
    --     flatdata.topanchor = topanchor
    --     flatdata.xoffset   = width + topanchor
    -- end

local cdata = characters.data

    function mathtweaks.fixaccents(target,original,parameters)
        local characters = target.characters
        local done       = false
        for stretching, entry in sortedhash(mapping) do
            local alias  = entry[1]
            local stretchingdata = characters[stretching]
            if stretchingdata and stretchingdata.width == 0 then
if false then
    local b = target.descriptions[stretching].boundingbox
    if b then
        local llx = b[1] * target.parameters.hfactor
        local urx = b[3] * target.parameters.hfactor
        width = urx - llx
        stretchingdata.width        = width
        stretchingdata.xoffset      = - llx
        stretchingdata.advance      = urx
        stretchingdata.topanchor    = width/2
        stretchingdata.bottomanchor = width/2
    end
else
                local topanchor = stretchingdata.topanchor or 0
                local width     = -topanchor
                topanchor = width/2
                stretchingdata.width     = width
                stretchingdata.advance   = 0
                stretchingdata.topanchor = topanchor
                stretchingdata.commands  = { rightcommand[width + topanchor], charcommand[stretching] }
end
                if not trace_tweaking then
                    done = true
                elseif done then
                    done[stretching] = true
                else
                    done = { [stretching] = true }
                end
            end
        end
        feedback_tweak("fixaccents",target,original,done)
    end

    function mathtweaks.checkaccents(target,original,parameters)
        local characters = target.characters
        local done       = false
        local factor     = target.parameters.hfactor
        for unicode, data in sortedhash(characters) do
            local width = data.width
            if width == 0 then
                local d = chardata[data.unicode or unicode]
                local c = d and d.category
                if c == "mn" then
                    local b = target.descriptions[unicode].boundingbox
                    if b then
                        local llx = b[1] * factor
                        local urx = b[3] * factor
                        width = urx - llx
                        data.width        = width
                        data.xoffset      = - llx
                        data.advance      = urx
                        data.topanchor    = width/2
                        data.bottomanchor = width/2
                    end
                    if not trace_tweaking then
                        done = true
                    elseif done then
                        done[unicode] = true
                    else
                        done = { [unicode] = true }
                    end
                end
            end
        end
        feedback_tweak("checkaccents",target,original,done)
    end

    -- all  true|number  false

    function mathtweaks.extendaccents(target,original,parameters)
        local characters = target.characters
        local all        = parameters.all
        local count      = tonumber(all)
        local done       = false
        for stretching, entry in sortedhash(mapping) do
            local extend = entry[2]
            if extend then
                local last = characters[stretching]
                local cnt  = 1
                local okay = false
                while last do
                    if all or (count and cnt > count) then
                        last.extensible = true
                        local flataccent = last.flataccent
                        if flataccent then
                            characters[flataccent].extensible = true
                            okay = true
                        end
                    end
                    local n = last.next
                    if n then
                        last = characters[n]
                    else
                        last.extensible = true
                        local flataccent = last.flataccent
                        if flataccent then
                            characters[flataccent].extensible = true
                            okay = true
                        end
                        break
                    end
                    cnt = cnt + 1
                end
                if okay then
                    if not trace_tweaking then
                        done = true
                    elseif done then
                        done[stretching] = true
                    else
                        done = { [stretching] = true }
                    end
                end
            end
        end
        feedback_tweak("extendaccents",target,original,done)
    end

    -- force     true     false
    -- height    factor   0.8
    -- offset    factor   0.9|calculated
    -- squeeze   factor   0.1|calculated

    local f_flat = formatters["flat accent %05X"]

    function mathtweaks.flattenaccents(target,original,parameters)
        local characters = target.characters
        local force   = parameters.force
        local squeeze = parameters.squeeze or 0.85
        local ofactor = parameters.offset  or (squeeze/8.5)
        local hfactor = parameters.height  or (1 - ofactor)
        local done    = false
        for stretching, entry in sortedhash(mapping) do
            local code = stretching
            local last = characters[stretching]
            while last do
                if force or not last.flataccent then
                    local slot   = nps(f_flat(code))
                    local data   = copytable(last)
                    local height = data.height or 0
                    data.effect  = { squeeze = squeeze }
                    data.height  = hfactor * height
                    data.yoffset = ofactor * height
                    characters[slot] = data
                    last.flataccent  = slot
                    if not trace_tweaking then
                        done = true
                    elseif done then
                        done[stretching] = true
                    else
                        done = { [stretching] = true }
                    end
                end
                code = last.next
                if code then
                    last = characters[code]
                else
                    break
                end
            end
        end
        feedback_tweak("flattenaccents",target,original,done)
    end

    function mathtweaks.copyaccents(target,original,parameters)
        local characters = target.characters
        local done       = false
        for stretching, entry in sortedhash(mapping) do
            local alias = entry[1]
            if alias ~= stretching then
                local stretchingdata = characters[stretching]
                if stretchingdata then
                    -- we need to nil [x|y]offsets
                    characters[alias] = {
                        width     = stretchingdata.width,
                        height    = stretchingdata.height,
                        depth     = stretchingdata.depth,
                        next      = stretchingdata.next,
                        commands  = { charcommand[stretching] },
                        topanchor = stretchingdata.topanchor,
                     -- unicode   = stretching,  -- when we alias to combiners
                        unicode   = alias, -- when we keep the original
                    }
                    if not trace_tweaking then
                        done = true
                    elseif done then
                        done[stretching] = true
                    else
                        done = { [stretching] = true }
                    end
                end
            end
        end
        feedback_tweak("copyaccents",target,original,done)
    end

end

do

    function mathtweaks.inspect(target,original,parameters)
        local characters = target.characters
        local slot = parameters.slot or parameters.unicode
        if slot then
            -- todo: show unicode
            report_math(formatters["%C data:"](slot))
            inspect(characters[slot])
        end
    end

end

-- do
--
--     local single <const> = 0x003D
--     local double <const> = 0x2A75
--     local triple <const> = 0x2A76
--
--     function mathtweaks.addequals(target,original,parameters)
--         local characters = target.characters
--         local basechar   = characters[single]
--         local width      = basechar.width
--         local height     = basechar.height
--         local depth      = basechar.depth
--         local advance    = (parameters.advance or 1/20) * width
--         local char       = charcommand[single]
--         local left       = leftcommand[advance]
--         characters[double] = {
--             unicode  = double,
--             width    = 2*width - 1*advance,
--             height   = height,
--             depth    = depth,
--             commands = { char, left, char },
--         }
--         characters[triple] = {
--             unicode  = triple,
--             width    = 3*width - 2*advance,
--             height   = height,
--             depth    = depth,
--             commands = { char, left, char, left, char },
--         }
--         if trace_tweaking then
--             report_tweak("double %U and triple %U equals added",target,original,double,triple)
--         end
--     end
--
-- end

do

    local function jointwo(characters,force,unicode,ds,u1,d12,u2)
        if force or not characters[unicode] then
            local c1 = characters[u1]
            local c2 = characters[u2]
            if c1 and c2 then
                local w1 = c1.width
                local w2 = c2.width
                local width
                if d12 == false then
                    d12   = 0
                    width = w2
                elseif d12 < 0 then
                    d12   = d12 * w2
                    width = w2
                else
                    d12   = d12 * ds
                    width = w1 + w2 - d12
                end
                characters[unicode] = {
                    unicode  = unicode,
                    width    = width,
                    height   = max(c1.height or 0, c2.height or 0),
                    depth    = max(c1.depth  or 0, c2.depth  or 0),
keepvirtual = true,
                    commands = {
                     -- { "inspect" },
                     -- { "trace" },
                        slotcommand[0][u1],
                     -- { "trace" },
                        d12 ~= 0 and leftcommand[d12] or false,
                        slotcommand[0][u2],
                     -- { "trace" },
                    },
                }
            end
        end
    end

    local function jointhree(characters,force,unicode,ds,u1,d12,u2,d23,u3)
        if force or not characters[unicode] then
            local c1 = characters[u1]
            local c2 = characters[u2]
            local c3 = characters[u3]
            if c1 and c2 and c3 then
                local w1 = c1.width
                local w2 = c2.width
                local w3 = c3.width
                d12 = d12 * ds
                d23 = d23 * ds
                characters[unicode] = {
                    unicode  = unicode,
                    width    = w1 + w2 + w3 - d12 - d23,
                    height   = max(c1.height or 0, c2.height or 0, c3.height or 0),
                    depth    = max(c1.depth  or 0, c2.depth  or 0, c3.depth  or 0),
                    commands = {
                        slotcommand[0][u1],
                        d12 ~= 0 and leftcommand[d12] or false,
                        slotcommand[0][u2],
                        d23 ~= 0 and leftcommand[d23] or false,
                        slotcommand[0][u3],
                    }
                }
            end
        end
    end

    function mathtweaks.addequals(target,original,parameters)
        local characters = target.characters
        local step       = target.parameters.size/18
        local force      = parameters.force
force = true
        jointwo  (characters,force,0x2254,step,0x03A,0,0x03D)         -- :=
        jointhree(characters,force,0x2A74,step,0x03A,0,0x03A,0,0x03D) -- ::=
        jointwo  (characters,force,0x2A75,step,0x03D,0,0x03D)         -- ==
        jointhree(characters,force,0x2A76,step,0x03D,0,0x03D,0,0x03D) -- ===
    end

end

do

    -- If we really want, we can have variants that also match radicals but in practice
    -- radicals and actuarians are never seen together. We could also have a smaller
    -- extender.

    local nps = fonts.helpers.newprivateslot

    local radical   <const> = 0x0221A
    local actuarian <const> = nps("delimited right annuity") -- 0x020E7
    local nairautca <const> = nps("delimited left annuity" )
    local placehold <const> = nps("delimited ghost annuity")

    function mathtweaks.addactuarian(target,original,parameters)
        local characters = target.characters
        local parameters = target.parameters
        local linewidth  = target.MathConstants.RadicalRuleThickness -- make option
        local basechar   = characters[radical]
        local baseheight = (basechar.height or 0)/2
        local basedepth  = (basechar.depth  or 0)/2
        local basetotal  = baseheight + basedepth
        local used       = baseheight
        --
        characters[0x020E7] = {
            width    = 6*linewidth,
            height   = baseheight,
            depth    = basedepth,
            unicode  = actuarian,
            callback = "devirtualize",
            commands = {
                upcommand[baseheight-4*linewidth],
                { "rule", linewidth, 4*linewidth },
                downcommand[basetotal/2-linewidth],
                { "rule", basetotal/2, linewidth },
            },
        }
        --
        characters[actuarian] = {
            width    = 2*linewidth,
            height   = baseheight,
            depth    = basedepth,
            unicode  = actuarian,
            callback = "devirtualize",
            commands = {
                downcommand[basedepth],
                { "rule", basetotal, linewidth },
            },
            parts = {
                {
                    advance  = basetotal,
                    ["end"]  = used,
                    glyph    = actuarian,
                    start    = 0,
                },
                {
                    advance  = basetotal,
                    ["end"]  = 0,
                    extender = 1,
                    glyph    = actuarian,
                    start    = used,
                },
            }
        }
        characters[placehold] = {
            width    = 2*linewidth,
            height   = baseheight,
            depth    = basedepth,
            unicode  = actuarian, -- whatever
            callback = "devirtualize",
            commands = {
                rightcommand[linewidth],
                downcommand[basedepth],
                { "rule", basetotal, 0 },
            },
        }
        characters[nairautca] = {
            width    = 2*linewidth,
            height   = baseheight,
            depth    = basedepth,
            unicode  = actuarian, -- whatever
            callback = "devirtualize",
         -- commands = {
         --     rightcommand[linewidth],
         --     downcommand[basedepth],
         --     { "rule", basetotal, linewidth },
         -- },
            commands = {
                rightcommand[linewidth],
                upcommand[baseheight-4*linewidth],
                { "rule", 4*linewidth, linewidth },
            },
            parts = {
                {
                    advance  = basetotal,
                    ["end"]  = used,
                    extender = 1,
                    glyph    = placehold,
                    start    = 0,
                },
                {
                    advance  = basetotal,
                    ["end"]  = 0,
                    glyph    = nairautca,
                    start    = used,
                },
            }
        }
        if trace_tweaking then
            report_tweak("actuarian %U added",target,original,actuarian)
        end
    end

end

do

    -- todo: make callback because we can delay it but then we need to stack
    -- callbacks

    local nps = fonts.helpers.newprivateslot

    local list = {
     -- { 0x0300, nps("delimited right grave"),   nps("delimited ghost grave")   },
        { 0x0308, nps("delimited right ddot"),    nps("delimited ghost ddot")    },
        { 0x0304, nps("delimited right bar"),     nps("delimited ghost bar")     },
     -- { 0x0301, nps("delimited right acute"),   nps("delimited ghost acute")   },
        { 0x0302, nps("delimited right hat"),     nps("delimited ghost hat")     },
        { 0x030C, nps("delimited right check"),   nps("delimited ghost check")   },
        { 0x0306, nps("delimited right breve"),   nps("delimited ghost breve")   },
        { 0x0307, nps("delimited right dot"),     nps("delimited ghost dot")     },
        { 0x030A, nps("delimited right ring"),    nps("delimited ghost ring")    },
        { 0x0303, nps("delimited right tilde"),   nps("delimited ghost tilde")   },
        { 0x20DB, nps("delimited right dddot"),   nps("delimited ghost dddot")   },

        { 0x231C, nps("delimited left upper corner"),  nps("delimited ghost upper corner") },
        { 0x231D, nps("delimited right upper corner"), nps("delimited ghost upper corner") },
        { 0x231E, nps("delimited left lower corner"),  nps("delimited ghost lower corner"), true  },
        { 0x231F, nps("delimited right lower corner"), nps("delimited ghost lower corner"), true  },

        -- If needed we can have an installer:

        { 0x2020, nps("delimited right dagger"),  nps("delimited ghost dagger")  },
        { 0x2021, nps("delimited right ddagger"), nps("delimited ghost ddagger") },
        { 0x2217, nps("delimited right ast"),     nps("delimited ghost ast")     },
        { 0x22C6, nps("delimited right star"),    nps("delimited ghost star")    },

        { 0x2020, nps("delimited right dagger 1"),  nps("delimited ghost dagger 1"),  false, 1 },
        { 0x2021, nps("delimited right ddagger 1"), nps("delimited ghost ddagger 1"), false, 1 },
        { 0x2217, nps("delimited right ast 1"),     nps("delimited ghost ast 1"),     false, 1 },
        { 0x22C6, nps("delimited right star 1"),    nps("delimited ghost star 1"),    false, 1 },
    }

    function mathtweaks.addfourier(target,original,parameters)
        local characters = target.characters
        for i=1,#list do
            local entry        = list[i]
            local basecode     = entry[1]
            local fouriercode  = entry[2]
            local movecode     = entry[3]
            local reverse      = entry[4]
            local size         = entry[5] or 0
            local basechar     = characters[basecode]
            local compactscale = 1
            if basechar and target.properties.compactmath and size > 0 then
                compactscale = target.parameters[size > 1 and "scriptscriptscale" or "scriptscale"] / 1000
                for i=1,size do
                    basecode = basechar.smaller or basecode
                    basechar = characters[basecode]
                end
            end
            if basechar then
                local scale   = (parameters.scale or 1) * compactscale
                local variant = parameters.variant
                if variant then
                    for i=1,variant do
                        local okay = basechar.next
                        if okay then
                            basecode = okay
                            basechar = characters[basecode]
                        else
                            break
                        end
                    end
                end
                local baseheight = scale * (basechar.height or 0)
                local basedepth  = scale * (basechar.depth  or 0)
                local basewidth  = scale * (basechar.width  or 0)
                local used       = baseheight/2
                local total      = baseheight + basedepth
                if reverse then
                    used = total / 2 -- basedepth / 2
                end
                characters[movecode] = {
                    width    = basewidth,
                    height   = used,
                    unicode  = basecode,
        --             callback = "devirtualize",
                    commands = {
                        downcommand[used],
                        { "rule", used, 0 },
                    },
                }
                local parts = {
                    {
                        advance  = used,
                        ["end"]  = used,
                        extender = 1,
                        glyph    = movecode,
                        start    = used,
                    },
                    {
                        advance  = total,
                        ["end"]  = 0,
                        glyph    = fouriercode,
                        start    = total,
                    },
                }
                if reverse then
                    parts[1], parts[2] = parts[2], parts[1]
                end
                characters[fouriercode] = {
                    width    = basewidth,
                    height   = baseheight,
                    depth    = basedepth,
                    unicode  = basecode,
        --             callback = "devirtualize",
                    commands = {
                        scale == 1 and charcommand[basecode] or { "slot", 0, basecode, scale, scale },
                    },
                    partsorientation = "vertical",
                    parts = parts,
                }
                if trace_tweaking then
                    report_tweak("fourier %U added using %U",target,original,basecode,fouriercode)
                end
            end
        end
    end

end

do

    -- \im{\left\Uchar"007C \frac{1}{2} \right\Uchar"007C}
    -- \im{\left\Uchar"2016 \frac{1}{2} \right\Uchar"2016}
    -- \im{\left\Uchar"2980 \frac{1}{2} \right\Uchar"2980}

    local single <const> = 0x007C
    local double <const> = 0x2016
    local triple <const> = 0x2980

    local function variantlist(unicode,chardata,total,used)
        chardata.varianttemplate = 0x0028
        chardata.parts = {
            {
                advance  = total,
                ["end"]  = used,
                glyph    = unicode,
                start    = 0,
             -- start    = used/5,
            },
            {
                advance  = total,
             -- ["end"]  = 0,
                ["end"]  = used/5, -- prevents small gap with inward curved endpoints
                extender = 1,
                glyph    = unicode,
                start    = used,
            },
        }
        chardata.partsorientation = "vertical"
    end

    function mathtweaks.addbars(target,original,parameters)
        local characters = target.characters
        local basechar   = characters[single]
        local width      = basechar.width
        local height     = basechar.height
        local depth      = basechar.depth
        local advance    = (parameters.advance or 1/10) * width
        local used       = 1.2*height -- large overlap because no smaller pieces
        local total      = height + depth
        --
     -- variantlist(characters,single,basechar,"single bar",total,used)
        variantlist(single,basechar,total,used)
        --
        basechar = {
            unicode  = double,
            width    = 2*width - 1*advance,
            height   = height,
            depth    = depth,
--             callback = "devirtualize",
            commands = {
                charcommand[single],
                leftcommand[advance],
                charcommand[single],
            },
        }
        characters[double] = basechar
     -- variantlist(characters,double,basechar,"double bar",total,used)
        variantlist(double,basechar,total,used)
        --
        basechar = {
            unicode  = triple,
            width    = 3*width - 2*advance,
            height   = height,
            depth    = depth,
--             callback = "devirtualize",
            commands = {
                charcommand[single],
                leftcommand[advance],
                charcommand[single],
                leftcommand[advance],
                charcommand[single],
            },
        }
        characters[triple] = basechar
     -- variantlist(characters,triple,basechar,"triple bar",total,used)
        variantlist(triple,basechar,total,used)
        --
        if trace_tweaking then
            report_tweak("single, double and triple bars added",target,original)
        end
    end

end

do

    -- lucida: \im{\cdot \ldot \cdots \ldots}

    local snormal <const> = 0x002E
    local sraised <const> = 0x22C5

    local tnormal <const> = 0x2026
    local traised <const> = 0x22EF

    function mathtweaks.fixellipses(target,original,parameters)
        local characters = target.characters
        local function fix(normal,raised)
            local normaldata = characters[normal]
            if normaldata then
                local raiseddata = copytable(normaldata)
                characters[raised] = raiseddata
                raiseddata.unicode = raised
                local height  = raiseddata.height
                local yoffset = (parameters.yoffset or 2) * height
                raiseddata.yoffset = yoffset
                raiseddata.height  = height + yoffset
                if trace_tweaking then
                    report_tweak("taking %U from %U",target,original,raised,normal)
                end
            end
        end
        fix(snormal,sraised)
        fix(tnormal,traised)
    end

end

do

    -- For Ton, who needs the high minus and plus for calculator signs in Dutch
    -- school math books.

    local list = {
        { 0x207A, 0x002B, true  },
        { 0x207B, 0x2212, true  },
        { 0x208A, 0x002B, false },
        { 0x208B, 0x2212, false },
    }

    datasets.addscripts = list

    local function add(target,original,characters,unicode,template,super,baseheight,scale)
        if not characters[unicode] then
            local origdata = characters[template]
            if origdata then
                local width  = scale * (origdata.width  or 0)
                local height = scale * (origdata.height or 0)
                local depth  = scale * (origdata.depth  or 0)
                local half   = - (height + depth) / 2
                local offset = super and baseheight/2 or -baseheight/4
                characters[unicode] = {
                    width    = width,
                    height   = height + offset,
                    depth    = depth  - offset,
                    unicode  = unicode,
                    commands = {
                        { "offset", 0, offset, template, scale, scale }
                    },
                }
                if trace_tweaking then
                    report_tweak("adding script %U scaled %0.3f",target,original,unicode,scale)
                end
                -- no need for smaller
            end
        end
    end

    function mathtweaks.addscripts(target,original,parameters)
        local characters = target.characters
        local baseheight = target.mathparameters.AccentBaseHeight
        local scaledown  = parameters.scale or target.mathparameters.ScriptScriptPercentScaleDown / 100
        for i=1,#list do
            local entry = list[i]
            if entry then
                add(target,original,characters,entry[1],entry[2],entry[3],baseheight,scaledown)
            end
        end
    end

end

do

    function mathtweaks.sortvariants(target,original,parameters)
        local list = parameters.list
        if list then
            local characters = target.characters
            local horizontal = parameters.orientation == "horizontal"
            for i=1,#list do
                local u = list[i]
                local c = characters[u]
                if c then
                    local t = { }
                    while true do
                        local n = c.next
                        if n then
                            c = characters[n]
                        end
                        if c and not c.parts then
                            if horizontal then
                                t[c.width or 0] = n
                            else
                                t[(c.height or 0) + (c.depth or 0)] = n
                            end
                        else
                            break
                        end
                    end
                    local c = characters[u]
                    for k, v in sortedhash(t) do
                        c.next = v
                        c = characters[v]
                    end
                end
            end
        end
    end

end

do

    -- We started with the list that xits has in rtlm but most of them can be derived from
    -- the database, and others need to be added.

    -- Checked while watching/listening to Dave Matthews Band: The Central Park Concert
    -- (with superb solos by Warren Haynes), a DVD I bought around when we started with the
    -- LUATEX advanture.

    local mirrors = {

        [0x0002F] = true, -- slashes
        [0x0005C] = true,
        [0x000F7] = true,
        [0x02044] = true,
        [0x02215] = true,

        [0x02032] = true, -- primes
        [0x02033] = true,
        [0x02034] = true,
        [0x02057] = true,
        [0x02035] = true,
        [0x02036] = true,
        [0x02037] = true,

        [0x0221A] = true, -- radicals
        [0x0221B] = true,
        [0x0221C] = true,
        [0x0221D] = true,

        [0x0222B] = true, -- integrals
        [0x0222C] = true,
        [0x0222D] = true,
        [0x0222E] = true,
        [0x0222F] = true,
        [0x02230] = true,
        [0x02231] = true,
        [0x02232] = true,
        [0x02233] = true,

        [0x02A0A] = true, -- seen in xits (to be checked)
        [0x02A0B] = true,
        [0x02A0C] = true,
        [0x02A0D] = true,
        [0x02A0E] = true,

        [0x02140] = true,
        [0x02201] = true,
        [0x02202] = true,
        [0x02203] = true,
        [0x02204] = true,
        [0x02211] = true,

        [0x02239] = true,
        [0x0225F] = true,
        [0x0228C] = true,
        [0x022A7] = true,
        [0x022AA] = true,
        [0x022AC] = true,
        [0x022AD] = true,
        [0x022AE] = true,
        [0x022AF] = true,
        [0x022F5] = true,
        [0x022F8] = true,
        [0x022F9] = true,
        [0x022FF] = true,
        [0x02320] = true,
        [0x02321] = true,
        [0x027C0] = true,
        [0x029DC] = true,
        [0x029F4] = true,

        [0x02A0F] = true,
        [0x02A10] = true,
        [0x02A11] = true,
        [0x02A12] = true,
        [0x02A13] = true,
        [0x02A14] = true,
        [0x02A15] = true,
        [0x02A16] = true,
        [0x02A17] = true,
        [0x02A18] = true,
        [0x02A19] = true,
        [0x02A1A] = true,
        [0x02A1B] = true,
        [0x02A1C] = true,
        [0x02A20] = true,

        [0x02A74] = true,
        [0x02AA3] = true,
        [0x02AE2] = true,
        [0x02AE6] = true,
        [0x1D715] = true,
    }

    local new = fonts.helpers.newprivateslot

    local function add(target,original,characters,unicode,what)
        local data = characters[unicode]
        if data then
            if not data.mirror then
                local slot      = new("mirror."..unicode)
                local mirror    = copytable(data)
                data.mirror     = slot
                mirror.rorrim   = unicode -- so we can check later
                mirror.commands = {
                    { "offset", data.width, 0, unicode, -1, 1 }
                }
                if trace_tweaking then
                    report_tweak("adding mirror %U (%s)",target,original,unicode,what)
                end
                characters[slot] = mirror
            elseif trace_tweaking then
                report_tweak("skipping mirror %U (%s)",target,original,unicode,what)
            end
            local parts = data.parts
            if parts then
                for i=1,#parts do
                    add(target,original,characters,parts[i],"hpart")
                end
            end
            local smaller = data.smaller
            if smaller then
                add(target,original,characters,"smaller")
            end
            local next = data.next
            if next then
                if next == unicode then
                    report_tweak("skipping cyclic %U (%s)",target,original,unicode,"next")
                else
                    add(target,original,characters,next,"next")
                end
            end
        end
    end

    -- todo: also check the rtlm table if present

    function mathtweaks.addmirrors(target,original,parameters)
        local characters = target.characters
     -- for unicode, detail in sortedhash(characters) do
        for unicode, detail in next, characters do
            local data = chardata[unicode]
            if data and data.mirror then
                add(target,original,characters,unicode,"mirror")
            end
        end
        for unicode, detail in sortedhash(mirrors) do
            if characters[unicode] then
                add(target,original,characters,unicode,"character")
            elseif trace_tweaking then
                report_tweak("ignoring mirror %U (%s)",target,original,unicode,what)
            end
        end
    end

end

do

    local reported = { }

    function mathtweaks.version(target,original,parameters)
        local metadata = original.shared.rawdata.metadata
        if metadata then
            local version = string.strip(metadata.version or "") -- some have trailing spaces
            if version then
                local expected = parameters.expected
                local fontname = metadata.fontname or false
                local message  = parameters.message
             -- version = tonumber(string.match(version,"%d+.%d+"))
                if version ~= expected and not reported[fontname] then
                    report_tweak("version %a found, version %a expected",target,original,version,expected)
                elseif trace_tweaking then
                    report_tweak("version %a found",target,original,version)
                end
                if message and message ~= "" and not reported[fontname] then
                    report_tweak()
                    report_tweak("%s",target,original,message)
                    report_tweak()
                end
                reported[fontname] = true
                target.tweakversion = version
            end
        end
    end

end

do

    function mathtweaks.parameters(target,original,parameters)
        local newparameters = parameters.list
        local oldparameters = target.mathparameters
        if newparameters and oldparameters then
            newparameters = copytable(newparameters)
            scaleparameters(newparameters,target.parameters)
            for name, newvalue in next, newparameters do
                oldparameters[name] = newvalue
            end
        end
    end

    function mathtweaks.bigslots(target,original,parameters)
        local list = parameters.list
        if list then
            target.bigslots = list
        end
    end

end

-- do
--
--     function mathtweaks.diagnose(target,original,parameters)
--         local characters = target.characters
--         for k, v in sortedhash(characters) do
--             local italic = v.italic
--             if italic then
--                 report_tweak("italics: %C %p",target,original,k,italic)
--             end
--         end
--     end
--
-- end

do

    function mathtweaks.setoptions(target,original,parameters)
        local setlist   = parameters.set or parameters.list
        local resetlist = parameters.reset
        if setlist or resetlist then
            local properties = target.properties
            local codes      = tex.mathcontrolcodes
            local oldcontrol = texget("mathfontcontrol")
            local newcontrol = oldcontrol
            -- todo: reset
            if resetlist then
                for i=1,#resetlist do
                    local v = tonumber(codes[resetlist[i]])
                    if v then
                        newcontrol = newcontrol & (not v)
                    end
                end
            end
            if setlist then
                for i=1,#setlist do
                    local v = tonumber(codes[setlist[i]])
                    if v then
                        newcontrol = newcontrol | v
                    end
                end
            end
            newcontrol = newcontrol | codes.usefontcontrol
            properties.mathcontrol = newcontrol
            target.mathcontrol = newcontrol
            if trace_tweaking then
                report_tweak("forcing math font options 0x%08X instead of 0x%08X",target,original,newcontrol,oldcontrol)
            end
        end
    end

end

do

    function mathtweaks.setovershoots(target,original,parameters)
        local list = parameters.list
        if list then
            local characters = target.characters
            local emwidth    = target.parameters.quad
            local done       = false
            for i=1,#list do
                local entry  = list[i]
                local target = entry.target
                local top    = entry.topovershoot
                local quad   = entry.quad
                if target and top then
                    local range = blocks[target]
                    if range then
                        if quad then
                            quad = emwidth
                        end
                        for r = range.first, range.last do
                            local unicode = mathgaps[r] or r
                            local data = characters[unicode]
                            if data then
                                data.topovershoot = top * (quad or data.width or 0)
                                if not trace_tweaking then
                                    done = true
                                elseif done then
                                    done[r] = true
                                else
                                    done = { [r] = true }
                                end
                            end
                        end
                    end
                end
            end
            feedback_tweak("setovershoots",target,original,done)
        end
    end

    -- there is no real need for thios but let's play nice with memory anyway

    local efindex = 0
    local effects = setmetatableindex (function (t,k)
        efindex = efindex + 1
        local v = "tweakreplacealphabets" .. efindex
        local e = fonts.specifiers.presetcontext(v,"",k)
     -- print(k,v,e)
        t[k] = v
        return v
    end)

    function mathtweaks.replacealphabets(target,original,parameters)
        local list = parameters.list
        if list then
            local features        = target.specification.features.normal
            local definedfont     = fonts.definers.internal
            local copiedglyph     = fonts.handlers.vf.math.copy_glyph
            -- does a deep copy, including parts and so
            local getsubstitution = fonts.handlers.otf.getsubstitution
            local fontdata        = fonts.hashes.identifiers
            --
            local fonts      = target.fonts
            local size       = target.size
            local characters = target.characters
            if not fonts then
                fonts = { }
                target.fonts = fonts
            end
            if #fonts == 0 then
                fonts[1] = { id = 0, size = size } -- self, will be resolved later
            end
            for i=1,#list do
                local entry     = list[i]
                local filename  = entry.filename or parameters.filename
                local feature   = entry.feature
                local thesource = entry.source
                local thetarget = entry.target or thesource
                local keep      = (entry.keep == true) or (parameters.keep == true)
                if thesource and thetarget then
                    local sourcerange = type(thesource) == "table" and thesource or blocks[thesource] -- .gaps
                    local targetrange = type(thetarget) == "table" and thetarget or blocks[thetarget] -- .gaps
                    if sourcerange and targetrange then
                        local firsttarget  = targetrange.first
                        local firstsource  = sourcerange.first
                        local lastsource   = sourcerange.last or firstsource
                        if firstsource and firsttarget then
                            local offset = firsttarget - firstsource
                            if filename then
                                local rscale = entry.rscale or 1 -- todo
                                size = size * rscale -- maybe use scale in vf command
                                -- load font, todo: set language and script, the effect hack is ugly
                                local fullname = filename
                                local effect = features.effect
                                if effect then
                                    fullname = fullname .. "*" .. effects["effect={"..effect.."}"]
                                end
                                local id = definedfont {
                                    name = fullname,
                                    size = size,
                                }
                                local chars  = fontchars[id]
                                local dropin = fontdata[id]
                                local index  = false
                                for i=1,#fonts do
                                    local f = fonts[i]
                                    if f.id == id and f.size == size then
                                        index = i
                                        break
                                    end
                                end
                                if not index then
                                    index = #fonts + 1
                                    fonts[index] = { id = id, size = size }
                                end
                                -- copy characters
                                for s=firstsource,lastsource do
                                    local t = s + offset
                                    local sourceunicode = mathgaps[s] or s
                                    if chars[sourceunicode] then
                                        local targetunicode = mathgaps[t] or t
                                        if keep and characters[targetunicode] then
                                            -- okay
                                        else
                                            if feature then
                                                sourceunicode = getsubstitution(dropin,sourceunicode,feature,true,"math","dflt") or sourceunicode
                                            end
--                                          if trace_tweaking then
--                                              report_tweak("copying %s %U from file %a to %s %U",target,original,thesource,sourceunicode,filename,thetarget,targetunicode)
--                                          end
                                            characters[targetunicode] = copiedglyph(target,characters,chars,sourceunicode,index)
                                        end
                                    end
                                end
                                --
                                local inherit = entry.inherit
                                if inherit then
                                    local mathparameters = target.mathparameters
                                    local dropparameters = fontdata[id].mathparameters
                                    if dropparameters then
                                        for name in sortedhash(inherit) do
                                            local value = dropparameters[name]
                                            if value then
                                                mathparameters[name] = value
                                            end
                                        end
                                    end
                                end
                                --
                            elseif feature then
                                for s=firstsource,lastsource do
                                    local t = s + offset
                                    local sourceunicode = mathgaps[s] or s
                                    local targetunicode = mathgaps[t] or t
                                    local variant       = getsubstitution(original,sourceunicode,feature,true,"math","dflt")
                                    local data          = characters[variant]
                                    if data then
--                                         if trace_tweaking then
--                                             report_tweak("copying %s %U from feature %a to %s %U",target,original,thesource,sourceunicode,feature,thetarget,targetunicode)
--                                         end
                                        characters[targetunicode] = copytable(data)
                                    end
                                end
                            else
                                for s=firstsource,lastsource do
                                    local t = s + offset
                                    local sourceunicode = mathgaps[s] or s
                                    local targetunicode = mathgaps[t] or t
                                    if sourceunicode ~= targetunicode then
                                        local data = characters[sourceunicode]
                                        if data then
--                                             if trace_tweaking then
--                                                 report_tweak("copying %s %U to %s %U",target,original,thesource,sourceunicode,thetarget,targetunicode)
--                                             end
                                            characters[targetunicode] = copytable(data)
                                        end
                                    end
                                end
                            end
                        else
                            -- error
                        end
                    end
                end
            end
        end
    end

    function mathtweaks.fallbacks(target,original,parameters)
        local fallbacks = target.specification.fallbacks
        if fallbacks then
            local definitions = fonts.collections.definitions[fallbacks]
            if definitions then
                local list = { }
                for i=1,#definitions do
                    local definition = definitions[i]
                 -- local check  = definition.check
                 -- local force  = definition.force
                    local first  = definition.start
                    local last   = definition.stop
                    local offset = definition.offset or first
                    list[#list+1] = {
                        filename = definition.font,
                        rscale   = definition.rscale or 1,
                        source   = { first = first,  last = last },
                        target   = { first = offset, last = offset + (last - first) },
                    }
                end
                mathtweaks.replacealphabets(target,original,{
                    tweak = "replacealphabets",
                    list  = list,
                } )
            end
        end
    end

end

local apply_tweaks   = true  directives.register("math.applytweaks", function(v) apply_tweaks = v end)
local applied_tweaks = 0

local function tweaklist(target,original,tweaks)
    if type(tweaks) == "table" then
        for i=1,#tweaks do
            local tweak  = tweaks[i]
            if type(tweak) == "table" then
                local action = mathtweaks[tweak.tweak or ""]
                if action then
                    local feature  = tweak.feature
                    local features = target.specification.features.normal
                    if feature == nil or features[feature] then
                        local version = tweak.version
                        if version and version ~= target.tweakversion then
                            report_math("skipping tweak %a version %a",tweak.tweak,version)
                        elseif original then
                            action(target,original,tweak)
                        else
                            action(target,tweak)
                        end
                    end
                end
            end
        end
    end
end

function mathtweaks.tweaks(target,original,parameters)
    tweaklist(target,original,parameters.list)
end

local function applytweaks(when,target,original)
    if apply_tweaks then
        local goodies = original.goodies
        if goodies then
            local tweaked = target.tweaked or { }
            if tweaked[when] then
                if trace_defining then
                    report_math("tweaking math of %a @ %p (%s: %s)",target.properties.fullname,target.parameters.size,when,"done")
                end
            else
                for i=1,#goodies do
                    local goodie = goodies[i]
                    local mathematics = goodie.mathematics
                    local tweaks = mathematics and mathematics.tweaks
                    if type(tweaks) == "table" then
                        statistics.starttiming(mathtweaks)
                        applied_tweaks = applied_tweaks + 1
                        tweaks = tweaks[when]
                        if trace_defining then
                            report_math("tweaking math of %a @ %p (%s: %s)",target.properties.fullname,target.parameters.size,when,"okay")
                        end
                        tweaklist(target,original,tweaks)
                    end
                    statistics.stoptiming(mathtweaks)
                end
                tweaked[when] = true
                target.tweaked = tweaked
            end
        end
    else
        report_math("not tweaking math of %a @ %p (%s)",target.properties.fullname,target.parameters.size,when)
    end
end

local function tweakable(target)
    local mathparameters = target.mathparameters
--     local features       = target.specification.features
--     local mathscript     = features and features.normal and features.normal.script == "math"
--     return mathparameters and mathscript -- and target,properties.hasmath
    return mathparameters
end

function mathematics.tweakbeforecopyingfont(target,original)
    if use_math_goodies and tweakable(target) then
        applytweaks("beforecopying",target,original)
    end
end

function mathematics.tweakaftercopyingfont(target,original)
    if use_math_goodies and tweakable(target) then
        applytweaks("aftercopying",target,original)
    end
end

statistics.register("math tweaking time",function()
    if applied_tweaks > 0 then
        return string.format("%s seconds, %s math goodie tables", statistics.elapsedtime(mathtweaks),applied_tweaks)
    end
end)

do

    local defaults = {
        {
            source = "uppercasescript",
            target = "uppercasecalligraphic",
        },
        {
            source = "lowercasescript",
            target = "lowercasecalligraphic",
        },
        {
            source = "uppercaseboldscript",
            target = "uppercaseboldcalligraphic",
        },
        {
            source = "lowercaseboldscript",
            target = "lowercaseboldcalligraphic",
        },
    }

    local reported = table.setmetatableindex("table")

    function mathematics.checkaftercopyingfont(target,original)
        if tweakable(target) then
            local chardata   = characters.data
            local characters = target.characters
            --
            for i=1,#defaults do
                -- we assume no ssty here yet .. todo
                local default = defaults[i]
                local block   = blocks[default.target]
                local first   = block.first
                local last    = block.last
                if not characters[mathgaps[first] or last] then
                    mathtweaks.replacealphabets(target,original,{
                        tweak   = "replacealphabets",
                        list    = { default }
                    })
                end
            end
            --
            local addvariant = mathematics.addvariant
            local function register(old,new)
                for i, cold in next, old do
                    local cnew = new[i]
                    addvariant(target,cold,cold,0xFE00)
                    addvariant(target,cnew,cnew,0xFE01)
                    addvariant(target,cnew,cold,0xFE00)
                    addvariant(target,cold,cnew,0xFE01)
                end
            end
            local sr = mathematics.alphabets.sr.tf
            local ca = mathematics.alphabets.ca.tf
            register(sr.ucletters,ca.ucletters)
            register(sr.lcletters,ca.lcletters)
            --
            if checkitalics then
                local italics  = 0
                local metadata = original.shared.rawdata.metadata
                local fontname = metadata and metadata.fontname or false
             -- for k, v in sortedhash(characters) do
                for k, v in next, characters do
                    local italic = v.italic
                    if italic then
                        local unicode = v.unicode
                        if unicode and not reported[fontname][unicode] then -- there can be variants
                            local data        = chardata[unicode]
                            local description = data.description or ""
                            local category    = data.category or "--"
                            report_tweak("italics: %C %p %s %s",target,original,k,italic,category,description)
                            reported[fontname][unicode] = true
                        end
                        italics = italics + 1
                    end
                end
                if italics > 0 then
                    report_tweak("still has %i italics",target,original,italics)
                    goto NEXTSTEP
                end
            end

            target.properties.mathitalics = false
            target.properties.textitalics = false
          ::NEXTSTEP::
            -- more to come
        end
    end

end

function mathematics.beforepassingfonttotex(target)
    if tweakable(target) then
        applytweaks("beforepassing",target,target)
    end
end

sequencers.appendaction("mathparameters","system","mathematics.overloadparameters")
sequencers.appendaction("mathparameters","system","mathematics.scaleparameters")
----------.appendaction("mathparameters","system","mathematics.checkaccentbaseheight")  -- should go in lfg instead
----------.appendaction("mathparameters","system","mathematics.checkprivateparameters") -- after scaling !

sequencers.appendaction("beforecopyingcharacters","system","mathematics.tweakbeforecopyingfont")
sequencers.appendaction("aftercopyingcharacters", "system","mathematics.tweakaftercopyingfont")
sequencers.appendaction("aftercopyingcharacters", "system","mathematics.checkaftercopyingfont")
sequencers.appendaction("beforepassingfonttotex", "system","mathematics.beforepassingfonttotex")

-- no, it's a feature now (see good-mth):
--
-- sequencers.appendaction("aftercopyingcharacters", "system","mathematics.overloaddimensions")

-- we use numbers at the tex end (otherwise we could stick to chars)

local e_left       = extensibles.left
local e_right      = extensibles.right
local e_horizontal = extensibles.horizontal
local e_mixed      = extensibles.mixed
local e_unknown    = extensibles.unknown

local unknown      = { e_unknown, false, false }

-- top curly bracket: 23DE

local function extensiblecode(font,unicode)
    local characters = fontcharacters[font]
    local character = characters[unicode]
    if not character then
        return unknown
    end
    local first = character.next
    local code = unicode
    local next = first
    while next do
        code = next
        character = characters[next]
        next = character.next
    end
    local char = chardata[unicode]
    if not char then
        return unknown
    end
    if character.parts then
        local m = char.mathextensible
        local e = m and extensibles[m]
        return e and { e, code, character } or unknown
    elseif first then
        -- assume accent (they seldom stretch .. sizes)
        local m = char.mathextensible or char.mathstretch
        local e = m and extensibles[m]
        return e and { e, code, character } or unknown
    else
        return unknown
    end
end

setmetatableindex(extensibles,function(extensibles,font)
    local codes = { }
    setmetatableindex(codes, function(codes,unicode)
        local status = extensiblecode(font,unicode)
        codes[unicode] = status
        return status
    end)
    extensibles[font] = codes
    return codes
end)

local function extensiblecode(family,unicode)
    return extensibles[getfontoffamily(family or 0)][unicode][1]
end

-- left       : [head] ...
-- right      : ... [head]
-- horizontal : [head] ... [head]
--
-- abs(right["start"] - right["end"]) | right.advance | characters[right.glyph].width

local function horizontalcode(family,unicode)
    local font    = getfontoffamily(family or 0)
    local data    = extensibles[font][unicode]
    local kind    = data[1]
    local loffset = 0
    local roffset = 0
    if kind == e_left then
        local charlist = data[3].parts
        if charlist then
            local left = charlist[1]
            loffset = abs((left["start"] or 0) - (left["end"] or 0))
        end
    elseif kind == e_right then
        local charlist = data[3].parts
        if charlist then
            local right = charlist[#charlist]
            roffset = abs((right["start"] or 0) - (right["end"] or 0))
        end
     elseif kind == e_horizontal then
        local charlist = data[3].parts
        if charlist then
            local left  = charlist[1]
            local right = charlist[#charlist]
            loffset = abs((left ["start"] or 0) - (left ["end"] or 0))
            roffset = abs((right["start"] or 0) - (right["end"] or 0))
        end
    end
    return kind, loffset, roffset
end

mathematics.extensiblecode = extensiblecode
mathematics.horizontalcode = horizontalcode

interfaces.implement { -- can be public with two times "integerargument"
    name      = "extensiblecode",
    arguments = "2 integers",
    actions   = { extensiblecode, context }
}

interfaces.implement { -- can be public with two times "integerargument"
    name      = "horizontalcode",
    arguments = "2 integers",
    actions   = function(family,unicode)
        local kind, loffset, roffset = horizontalcode(family,unicode)
        texsetdimen(d_scratchleftoffset, loffset)
        texsetdimen(d_scratchrightoffset,roffset)
        context(kind)
    end
}

function mathematics.variantcode(unicode,variant)
    local data = fontcharacters[getfontoffamily(texget("fam"))]
    local char = data and data[unicode]
    if char then
        for i=1,variant do
            local next = char.next
            if next then
                unicode = next
                char = data[next]
            else
                break
            end
        end
    end
    return unicode
end

function mathematics.variantcount(unicode)
    local data  = fontcharacters[getfontoffamily(texget("fam"))]
    local char  = data and data[unicode]
    local count = 0
    if char then
        while true do
            local next = char.next
            if next then
                count = count + 1
                char = data[next]
            else
                break
            end
        end
    end
    return count
end

interfaces.implement {
    name      = "mathvariantcode",
    public    = true,
    arguments = "2 integers",
    actions   = { mathematics.variantcode, context },
}

interfaces.implement {
    name      = "mathvariantcount",
    public    = true,
    arguments = "integer",
    actions   = { mathematics.variantcount, context },
}