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
|
/*
*----------------------------------------------------------------------
*
* tclDouble.c --
*
* This file contains a collection of procedures for managing
* conversions to/from floating-point in Tcl. They include
* TclParseNumber, which parses numbers from strings; TclDoubleDigits,
* which formats numbers into strings of digits, and procedures for
* interconversion among 'double' and 'mp_int' types.
*
* Copyright (c) 2005 by Kevin B. Kenny. All rights reserved.
*
* See the file "license.terms" for information on usage and redistribution
* of this file, and for a DISCLAIMER OF ALL WARRANTIES.
*
* RCS: @(#) $Id: tclStrToD.c,v 1.1.2.38 2005/09/23 04:03:43 dgp Exp $
*
*----------------------------------------------------------------------
*/
#include <tclInt.h>
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
#include <limits.h>
#include <math.h>
#include <ctype.h>
#include <tommath.h>
/*
* Define TIP_114_FORMATS to accept 0b and 0o for binary and octal strings.
* Define KILL_OCTAL as well as TIP_114_FORMATS to suppress interpretation
* of numbers with leading zero as octal. (Ceterum censeo: numeros octonarios
* delendos esse.)
*/
#define TIP_114_FORMATS
#undef KILL_OCTAL
#ifndef TIP_114_FORMATS
#undef KILL_OCTAL
#endif
/*
* This code supports (at least hypothetically), IBM, Cray, VAX and
* IEEE-754 floating point; of these, only IEEE-754 can represent NaN.
* IEEE-754 can be uniquely determined by radix and by the widths of
* significand and exponent.
*/
#if (FLT_RADIX == 2) && (DBL_MANT_DIG == 53) && (DBL_MAX_EXP == 1024)
# define IEEE_FLOATING_POINT
#endif
/*
* gcc on x86 needs access to rounding controls, because of a questionable
* feature where it retains intermediate results as IEEE 'long double' values
* somewhat unpredictably. It is tempting to include fpu_control.h, but
* that file exists only on Linux; it is missing on Cygwin and MinGW. Most
* gcc-isms and ix86-isms are factored out here.
*/
#if defined(__GNUC__) && defined(__i386)
typedef unsigned int fpu_control_t __attribute__ ((__mode__ (__HI__)));
#define _FPU_GETCW(cw) __asm__ __volatile__ ("fnstcw %0" : "=m" (*&cw))
#define _FPU_SETCW(cw) __asm__ __volatile__ ("fldcw %0" : : "m" (*&cw))
# define FPU_IEEE_ROUNDING 0x027f
# define ADJUST_FPU_CONTROL_WORD
#endif
/*
* HP's PA_RISC architecture uses 7ff4000000000000 to represent a quiet NaN.
* Everyone else uses 7ff8000000000000. (Why, HP, why?)
*/
#ifdef __hppa
# define NAN_START 0x7ff4
# define NAN_MASK (((Tcl_WideUInt) 1) << 50)
#else
# define NAN_START 0x7ff8
# define NAN_MASK (((Tcl_WideUInt) 1) << 51)
#endif
/* The powers of ten that can be represented exactly as wide integers */
static int maxpow10_wide;
static Tcl_WideUInt *pow10_wide;
/* The number of decimal digits that fit in an mp_digit */
static int log10_DIGIT_MAX;
/* The powers of ten that can be represented exactly as IEEE754 doubles. */
#define MAXPOW 22
static double pow10 [MAXPOW+1];
static int mmaxpow; /* Largest power of ten that can be
* represented exactly in a 'double'. */
/* Inexact higher powers of ten */
static CONST double pow_10_2_n [] = {
1.0,
100.0,
10000.0,
1.0e+8,
1.0e+16,
1.0e+32,
1.0e+64,
1.0e+128,
1.0e+256
};
/* Logarithm of the floating point radix. */
static int log2FLT_RADIX;
/* Number of bits in a double's significand */
static int mantBits;
/* Table of powers of 5**(2**n), up to 5**256 */
static mp_int pow5[9];
/* The smallest representable double */
static double tiny;
/* The maximum number of digits to the left of the decimal point of a
* double. */
static int maxDigits;
/* The maximum number of digits to the right of the decimal point in a
* double. */
static int minDigits;
/* Number of mp_digit's needed to hold the significand of a double */
static int mantDIGIT;
/* Static functions defined in this file */
static int AccumulateDecimalDigit _ANSI_ARGS_((unsigned, int,
Tcl_WideUInt*, mp_int*, int));
static double MakeLowPrecisionDouble _ANSI_ARGS_((int signum,
Tcl_WideUInt significand,
int nSigDigs,
int exponent));
static double MakeHighPrecisionDouble _ANSI_ARGS_((int signum,
mp_int* significand,
int nSigDigs,
int exponent));
static double MakeNaN _ANSI_ARGS_(( int signum, Tcl_WideUInt tag ));
static double RefineApproximation _ANSI_ARGS_((double approx,
mp_int* exactSignificand,
int exponent));
static double BignumToBiasedFrExp _ANSI_ARGS_(( mp_int* big, int* machexp ));
static double Pow10TimesFrExp _ANSI_ARGS_(( int exponent,
double fraction,
int* machexp ));
static double SafeLdExp _ANSI_ARGS_(( double fraction, int exponent ));
/*
*----------------------------------------------------------------------
*
* TclParseNumber --
*
* Place a "numeric" internal representation on a Tcl object.
*
* Results:
* Returns a standard Tcl result.
*
* Side effects:
* Stores an internal representation appropriate to the string.
* The internal representation may be an integer, a wide integer,
* a bignum, or a double.
*
* TclMakeObjNumeric is called as a common scanner in routines
* that expect numbers in Tcl_Obj's. It scans the string representation
* of a given Tcl_Obj and stores an internal rep that represents
* a "canonical" version of its numeric value. The value of the
* canonicalization is that a routine can determine simply by
* examining the type pointer whether an object LooksLikeInt,
* what size of integer is needed to hold it, and similar questions,
* and never needs to refer back to the string representation, even
* for "impure" objects.
*
* The 'strPtr' and 'endPtrPtr' arguments allow for recognizing a number
* that is in a substring of a Tcl_Obj, for example a screen metric or
* "end-" index. If 'strPtr' is not NULL, it designates where the
* number begins within the string. (The default is the start of
* objPtr's string rep, which will be constructed if necessary.)
*
* If 'strPtr' is supplied, 'objPtr' may be NULL. In this case,
* no internal representation will be generated; instead, the routine
* will simply check for a syntactically correct number, returning
* TCL_OK or TCL_ERROR as appropriate, and setting *endPtrPtr if
* necessary.
*
* If 'endPtrPtr' is not NULL, it designates the first character
* after the scanned number. In this case, successfully recognizing
* any digits will yield a return code of TCL_OK. Only in the case
* where no leading string of 'strPtr' (or of objPtr's internal rep)
* represents a number will TCL_ERROR be returned.
*
* When only a partial string is being recognized, it is the caller's
* responsibility to destroy the internal representation, or at
* least change its type. Failure to do so will lead to subsequent
* problems where a string that does not represent a number will
* be recognized as one because it has a numeric internal representation.
*
* When the 'flags' word includes TCL_PARSE_DECIMAL_ONLY, only decimal
* numbers are recognized; leading 0 has no special interpretation as
* octal and leading '0x' is forbidden.
*
*----------------------------------------------------------------------
*/
int
TclParseNumber( Tcl_Interp* interp,
/* Tcl interpreter for error reporting.
* May be NULL */
Tcl_Obj* objPtr,
/* Object to receive the internal rep */
CONST char* type,
/* Type of number being parsed ("integer",
* "wide integer", etc. */
CONST char* string,
/* Pointer to the start of the string to
* scan, see above */
size_t length, /* Maximum length of the string to scan,
* see above. */
CONST char** endPtrPtr,
/* (Output) pointer to the end of the
* scanned number, see above */
int flags) /* Flags governing the parse */
{
enum State {
INITIAL, SIGNUM, ZERO, ZERO_X,
#ifdef TIP_114_FORMATS
ZERO_O, ZERO_B, BINARY,
#endif
HEXADECIMAL, OCTAL, BAD_OCTAL, DECIMAL,
LEADING_RADIX_POINT, FRACTION,
EXPONENT_START, EXPONENT_SIGNUM, EXPONENT,
sI, sIN, sINF, sINFI, sINFIN, sINFINI, sINFINIT, sINFINITY
#ifdef IEEE_FLOATING_POINT
, sN, sNA, sNAN, sNANPAREN, sNANHEX, sNANFINISH
#endif
} state = INITIAL;
enum State acceptState = INITIAL;
int signum = 0; /* Sign of the number being parsed */
Tcl_WideUInt significandWide = 0;
/* Significand of the number being
* parsed (if no overflow) */
mp_int significandBig; /* Significand of the number being
* parsed (if it overflows significandWide) */
int significandOverflow = 0;
/* Flag==1 iff significandBig is used */
Tcl_WideUInt octalSignificandWide = 0;
/* Significand of an octal number; needed
* because we don't know whether a number
* with a leading zero is octal or decimal
* until we've scanned forward to a '.' or
* 'e' */
mp_int octalSignificandBig; /* Significand of octal number once
* octalSignificandWide overflows */
int octalSignificandOverflow = 0;
/* Flag==1 if octalSignificandBig is used */
int numSigDigs = 0; /* Number of significant digits in the
* decimal significand */
int numTrailZeros = 0; /* Number of trailing zeroes at the
* current point in the parse. */
int numDigitsAfterDp = 0; /* Number of digits scanned after the
* decimal point */
int exponentSignum = 0; /* Signum of the exponent of a floating
* point number */
long exponent = 0; /* Exponent of a floating point number */
CONST char* p; /* Pointer to next character to scan */
size_t len; /* Number of characters remaining after p */
CONST char* acceptPoint; /* Pointer to position after last character
* in an acceptable number */
size_t acceptLen; /* Number of characters following that point */
int status = TCL_OK; /* Status to return to caller */
char d; /* Last hexadecimal digit scanned */
int shift = 0; /* Amount to shift when accumulating binary */
#ifdef TIP_114_FORMATS
int explicitOctal = 0;
#endif
/*
* Initialize string to start of the object's string rep if
* the caller didn't pass anything else.
*/
if ( string == NULL ) {
string = Tcl_GetStringFromObj( objPtr, NULL );
}
p = string;
len = length;
acceptPoint = p;
acceptLen = len;
while ( 1 ) {
char c = len ? *p : '\0';
switch (state) {
case INITIAL:
/*
* Initial state. Acceptable characters are +, -, digits,
* period, I, N, and whitespace.
*/
if (isspace(UCHAR(c))) {
break;
} else if (c == '+') {
state = SIGNUM;
break;
} else if (c == '-') {
signum = 1;
state = SIGNUM;
break;
}
/* FALLTHROUGH */
case SIGNUM:
/*
* Scanned a leading + or -. Acceptable characters are
* digits, period, I, and N.
*/
if (c == '0') {
if (flags & TCL_PARSE_DECIMAL_ONLY) {
state = DECIMAL;
} else {
state = ZERO;
}
break;
} else if (flags & TCL_PARSE_HEXADECIMAL_ONLY) {
goto zerox;
} else if (flags & TCL_PARSE_OCTAL_ONLY) {
goto zeroo;
} else if (isdigit(UCHAR(c))) {
significandWide = c - '0';
numSigDigs = 1;
state = DECIMAL;
break;
} else if (flags & TCL_PARSE_INTEGER_ONLY) {
goto endgame;
} else if (c == '.') {
state = LEADING_RADIX_POINT;
break;
} else if (c == 'I' || c == 'i') {
state = sI;
break;
#ifdef IEEE_FLOATING_POINT
} else if (c == 'N' || c == 'n') {
state = sN;
break;
#endif
}
goto endgame;
case ZERO:
/*
* Scanned a leading zero (perhaps with a + or -).
* Acceptable inputs are digits, period, X, and E.
* If 8 or 9 is encountered, the number can't be
* octal. This state and the OCTAL state differ only
* in whether they recognize 'X'.
*/
acceptState = state;
acceptPoint = p;
acceptLen = len;
if (c == 'x' || c == 'X') {
state = ZERO_X;
break;
}
if (flags & TCL_PARSE_HEXADECIMAL_ONLY) {
goto zerox;
}
#ifdef TIP_114_FORMATS
if (flags & TCL_PARSE_SCAN_PREFIXES) {
goto zeroo;
}
if (c == 'b' || c == 'B') {
state = ZERO_B;
break;
}
if (c == 'o' || c == 'O') {
explicitOctal = 1;
state = ZERO_O;
break;
}
#ifdef KILL_OCTAL
goto decimal;
#endif
#endif
/* FALLTHROUGH */
case OCTAL:
/*
* Scanned an optional + or -, followed by a string of
* octal digits. Acceptable inputs are more digits,
* period, or E. If 8 or 9 is encountered, commit to
* floating point.
*/
acceptState = state;
acceptPoint = p;
acceptLen = len;
#ifdef TIP_114_FORMATS
/* FALLTHROUGH */
case ZERO_O:
#endif
zeroo:
if (c == '0') {
++numTrailZeros;
state = OCTAL;
break;
} else if (c >= '1' && c <= '7') {
if (objPtr != NULL) {
shift = 3 * (numTrailZeros + 1);
significandOverflow =
AccumulateDecimalDigit((unsigned)(c-'0'),
numTrailZeros,
&significandWide,
&significandBig,
significandOverflow);
if (!octalSignificandOverflow) {
/*
* Shifting by more bits than are in the value being
* shifted is at least de facto nonportable. Check
* for too large shifts first.
*/
if ((octalSignificandWide != 0)
&& ((shift >= CHAR_BIT*sizeof(Tcl_WideUInt))
|| (octalSignificandWide
> (~(Tcl_WideUInt)0 >> shift)))) {
octalSignificandOverflow = 1;
TclBNInitBignumFromWideUInt(&octalSignificandBig,
octalSignificandWide);
}
}
if (!octalSignificandOverflow) {
octalSignificandWide
= (octalSignificandWide << shift) + (c - '0');
} else {
mp_mul_2d(&octalSignificandBig, shift,
&octalSignificandBig);
mp_add_d(&octalSignificandBig, (mp_digit)(c - '0'),
&octalSignificandBig);
}
}
if ( numSigDigs != 0 ) {
numSigDigs += ( numTrailZeros + 1 );
} else {
numSigDigs = 1;
}
numTrailZeros = 0;
state = OCTAL;
break;
}
/* FALLTHROUGH */
case BAD_OCTAL:
#ifdef TIP_114_FORMATS
if (explicitOctal) {
/* No forgiveness for bad digits in explicitly octal numbers */
goto endgame;
}
#endif
if (flags & TCL_PARSE_INTEGER_ONLY) {
/* No seeking floating point when parsing only integer */
goto endgame;
}
#ifndef KILL_OCTAL
/*
* Scanned a number with a leading zero that contains an
* 8, 9, radix point or E. This is an invalid octal number,
* but might still be floating point.
*/
if (c == '0') {
++numTrailZeros;
state = BAD_OCTAL;
break;
} else if (isdigit(UCHAR(c))) {
if (objPtr != NULL) {
significandOverflow =
AccumulateDecimalDigit((unsigned)(c-'0'),
numTrailZeros,
&significandWide,
&significandBig,
significandOverflow);
}
if ( numSigDigs != 0 ) {
numSigDigs += ( numTrailZeros + 1 );
} else {
numSigDigs = 1;
}
numTrailZeros = 0;
state = BAD_OCTAL;
break;
} else if (c == '.') {
state = FRACTION;
break;
} else if (c == 'E' || c == 'e') {
state = EXPONENT_START;
break;
}
#endif
goto endgame;
/*
* Scanned 0x. If state is HEXADECIMAL, scanned at least
* one character following the 0x. The only acceptable
* inputs are hexadecimal digits.
*/
case HEXADECIMAL:
acceptState = state;
acceptPoint = p;
acceptLen = len;
/* FALLTHROUGH */
case ZERO_X:
zerox:
if (c == '0') {
++numTrailZeros;
state = HEXADECIMAL;
break;
} else if (isdigit(UCHAR(c))) {
d = (c-'0');
} else if (c >= 'A' && c <= 'F') {
d = (c-'A'+10);
} else if (c >= 'a' && c <= 'f') {
d = (c-'a'+10);
} else {
goto endgame;
}
if (objPtr != NULL) {
shift = 4 * (numTrailZeros + 1);
if (!significandOverflow) {
/*
* Shifting by more bits than are in the value being
* shifted is at least de facto nonportable. Check
* for too large shifts first.
*/
if (significandWide != 0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| significandWide > (~(Tcl_WideUInt)0 >> shift))) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
}
if (!significandOverflow) {
significandWide
= (significandWide << shift) + d;
} else {
mp_mul_2d(&significandBig, shift,
&significandBig);
mp_add_d(&significandBig, (mp_digit) d,
&significandBig);
}
}
numTrailZeros = 0;
state = HEXADECIMAL;
break;
#ifdef TIP_114_FORMATS
case BINARY:
acceptState = state;
acceptPoint = p;
acceptLen = len;
case ZERO_B:
if (c == '0') {
++numTrailZeros;
state = BINARY;
break;
} else if (c != '1') {
goto endgame;
}
if (objPtr != NULL) {
shift = numTrailZeros + 1;
if (!significandOverflow) {
/*
* Shifting by more bits than are in the value being
* shifted is at least de facto nonportable. Check
* for too large shifts first.
*/
if (significandWide != 0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| significandWide > (~(Tcl_WideUInt)0 >> shift))) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
}
if (!significandOverflow) {
significandWide
= (significandWide << shift) + 1;
} else {
mp_mul_2d(&significandBig, shift,
&significandBig);
mp_add_d(&significandBig, (mp_digit) 1,
&significandBig);
}
}
numTrailZeros = 0;
state = BINARY;
break;
#endif
case DECIMAL:
/*
* Scanned an optional + or - followed by a string of
* decimal digits.
*/
#ifdef KILL_OCTAL
decimal:
#endif
acceptState = state;
acceptPoint = p;
acceptLen = len;
if (c == '0') {
++numTrailZeros;
state = DECIMAL;
break;
} else if (isdigit(UCHAR(c))) {
if (objPtr != NULL) {
significandOverflow =
AccumulateDecimalDigit((unsigned)(c - '0'),
numTrailZeros,
&significandWide,
&significandBig,
significandOverflow);
}
numSigDigs += ( numTrailZeros + 1 );
numTrailZeros = 0;
state = DECIMAL;
break;
} else if (flags & TCL_PARSE_INTEGER_ONLY) {
goto endgame;
} else if (c == '.') {
state = FRACTION;
break;
} else if (c == 'E' || c == 'e') {
state = EXPONENT_START;
break;
}
goto endgame;
/*
* Found a decimal point. If no digits have yet been scanned,
* E is not allowed; otherwise, it introduces the exponent.
* If at least one digit has been found, we have a possible
* complete number.
*/
case FRACTION:
acceptState = state;
acceptPoint = p;
acceptLen = len;
if (c == 'E' || c=='e') {
state = EXPONENT_START;
break;
}
/* FALLTHROUGH */
case LEADING_RADIX_POINT:
if (c == '0') {
++numDigitsAfterDp;
++numTrailZeros;
state = FRACTION;
break;
} else if (isdigit(UCHAR(c))) {
++numDigitsAfterDp;
if (objPtr != NULL) {
significandOverflow =
AccumulateDecimalDigit((unsigned)(c-'0'),
numTrailZeros,
&significandWide,
&significandBig,
significandOverflow);
}
if ( numSigDigs != 0 ) {
numSigDigs += ( numTrailZeros + 1 );
} else {
numSigDigs = 1;
}
numTrailZeros = 0;
state = FRACTION;
break;
}
goto endgame;
case EXPONENT_START:
/*
* Scanned the E at the start of an exponent. Make sure
* a legal character follows before using the C library
* strtol routine, which allows whitespace.
*/
if (c == '+') {
state = EXPONENT_SIGNUM;
break;
} else if (c == '-') {
exponentSignum = 1;
state = EXPONENT_SIGNUM;
break;
}
/* FALLTHROUGH */
case EXPONENT_SIGNUM:
/*
* Found the E at the start of the exponent, followed by
* a sign character.
*/
if (isdigit(UCHAR(c))) {
exponent = c - '0';
state = EXPONENT;
break;
}
goto endgame;
case EXPONENT:
/*
* Found an exponent with at least one digit.
* Accumulate it, making sure to hard-pin it to LONG_MAX
* on overflow.
*/
acceptState = state;
acceptPoint = p;
acceptLen = len;
if (isdigit(UCHAR(c))) {
if (exponent < (LONG_MAX - 9) / 10) {
exponent = 10 * exponent + (c - '0');
} else {
exponent = LONG_MAX;
}
state = EXPONENT;
break;
}
goto endgame;
/*
* Parse out INFINITY by simply spelling it out.
* INF is accepted as an abbreviation; other prefices are
* not.
*/
case sI:
if ( c == 'n' || c == 'N' ) {
state = sIN;
break;
}
goto endgame;
case sIN:
if ( c == 'f' || c == 'F' ) {
state = sINF;
break;
}
goto endgame;
case sINF:
acceptState = state;
acceptPoint = p;
acceptLen = len;
if ( c == 'i' || c == 'I' ) {
state = sINFI;
break;
}
goto endgame;
case sINFI:
if ( c == 'n' || c == 'N' ) {
state = sINFIN;
break;
}
goto endgame;
case sINFIN:
if ( c == 'i' || c == 'I' ) {
state = sINFINI;
break;
}
goto endgame;
case sINFINI:
if ( c == 't' || c == 'T' ) {
state = sINFINIT;
break;
}
goto endgame;
case sINFINIT:
if ( c == 'y' || c == 'Y' ) {
state = sINFINITY;
break;
}
goto endgame;
/*
* Parse NaN's.
*/
#ifdef IEEE_FLOATING_POINT
case sN:
if ( c == 'a' || c == 'A' ) {
state = sNA;
break;
}
goto endgame;
case sNA:
if ( c == 'n' || c == 'N' ) {
state = sNAN;
break;
}
case sNAN:
acceptState = state;
acceptPoint = p;
acceptLen = len;
if ( c == '(' ) {
state = sNANPAREN;
break;
}
goto endgame;
/*
* Parse NaN(hexdigits)
*/
case sNANHEX:
if ( c == ')' ) {
state = sNANFINISH;
break;
}
/* FALLTHROUGH */
case sNANPAREN:
if ( isspace(UCHAR(c)) ) {
break;
}
if ( numSigDigs < 13 ) {
if ( c >= '0' && c <= '9' ) {
d = c - '0';
} else if ( c >= 'a' && c <= 'f' ) {
d = 10 + c - 'a';
} else if ( c >= 'A' && c <= 'F' ) {
d = 10 + c - 'A';
}
significandWide = (significandWide << 4) + d;
state = sNANHEX;
break;
}
goto endgame;
case sNANFINISH:
#endif
case sINFINITY:
acceptState = state;
acceptPoint = p;
acceptLen = len;
goto endgame;
}
++p;
--len;
}
endgame:
/* Back up to the last accepting state in the lexer */
if (acceptState == INITIAL) {
status = TCL_ERROR;
}
p = acceptPoint;
len = acceptLen;
/* Skip past trailing whitespace */
if (endPtrPtr != NULL) {
*endPtrPtr = p;
}
while (len > 0 && isspace(UCHAR(*p))) {
++p;
--len;
}
/* Determine whether a partial string is acceptable. */
if (endPtrPtr == NULL && len != 0 && *p != '\0') {
status = TCL_ERROR;
}
/* Generate and store the appropriate internal rep */
if (status == TCL_OK && objPtr != NULL) {
if ( acceptState != INITIAL ) {
TclFreeIntRep( objPtr );
}
switch (acceptState) {
case INITIAL:
status = TCL_ERROR;
break;
case SIGNUM:
case BAD_OCTAL:
case ZERO_X:
#ifdef TIP_114_FORMATS
case ZERO_O:
case ZERO_B:
#endif
case LEADING_RADIX_POINT:
case EXPONENT_START:
case EXPONENT_SIGNUM:
case sI:
case sIN:
case sINFI:
case sINFIN:
case sINFINI:
case sINFINIT:
case sN:
case sNA:
case sNANPAREN:
case sNANHEX:
panic("in TclParseNumber: bad acceptState, can't happen.");
#ifdef TIP_114_FORMATS
case BINARY:
shift = numTrailZeros;
if (!significandOverflow) {
if (significandWide !=0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| significandWide
> (((~(Tcl_WideUInt)0) >> 1) + signum) >> shift )) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
}
if (shift) {
if ( !significandOverflow ) {
significandWide <<= shift;
} else {
mp_mul_2d( &significandBig, shift, &significandBig );
}
}
goto returnInteger;
#endif
case HEXADECIMAL:
/* Returning a hex integer. Final scaling step */
shift = 4 * numTrailZeros;
if (!significandOverflow) {
if (significandWide !=0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| significandWide
> (((~(Tcl_WideUInt)0) >> 1) + signum) >> shift )) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
}
if (shift) {
if ( !significandOverflow ) {
significandWide <<= shift;
} else {
mp_mul_2d( &significandBig, shift, &significandBig );
}
}
goto returnInteger;
case OCTAL:
/* Returning an octal integer. Final scaling step */
shift = 3 * numTrailZeros;
if (!octalSignificandOverflow) {
if (octalSignificandWide != 0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| octalSignificandWide
> (((~(Tcl_WideUInt)0) >> 1) + signum) >> shift )) {
octalSignificandOverflow = 1;
TclBNInitBignumFromWideUInt(&octalSignificandBig,
octalSignificandWide);
}
}
if ( shift ) {
if ( !octalSignificandOverflow ) {
octalSignificandWide <<= shift;
} else {
mp_mul_2d( &octalSignificandBig, shift,
&octalSignificandBig );
}
}
if (!octalSignificandOverflow) {
if (octalSignificandWide >
(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
#ifndef NO_WIDE_TYPE
if (octalSignificandWide
<= (((~(Tcl_WideUInt)0) >> 1) + signum)) {
objPtr->typePtr = &tclWideIntType;
if (signum) {
objPtr->internalRep.wideValue =
- (Tcl_WideInt) octalSignificandWide;
} else {
objPtr->internalRep.wideValue =
(Tcl_WideInt) octalSignificandWide;
}
break;
}
#endif
TclBNInitBignumFromWideUInt(&octalSignificandBig,
octalSignificandWide);
octalSignificandOverflow = 1;
} else {
objPtr->typePtr = &tclIntType;
if (signum) {
objPtr->internalRep.longValue =
- (long) octalSignificandWide;
} else {
objPtr->internalRep.longValue =
(long) octalSignificandWide;
}
}
}
if (octalSignificandOverflow) {
if (signum) {
mp_neg(&octalSignificandBig, &octalSignificandBig);
}
TclSetBignumIntRep(objPtr, &octalSignificandBig);
}
break;
case ZERO:
case DECIMAL:
significandOverflow =
AccumulateDecimalDigit( 0, numTrailZeros-1,
&significandWide, &significandBig,
significandOverflow );
if (!significandOverflow
&& (significandWide
> (((~(Tcl_WideUInt)0) >> 1) + signum))) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
returnInteger:
if (!significandOverflow) {
if (significandWide >
(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
#ifndef NO_WIDE_TYPE
if (significandWide
<= (((~(Tcl_WideUInt)0) >> 1) + signum)) {
objPtr->typePtr = &tclWideIntType;
if (signum) {
objPtr->internalRep.wideValue =
- (Tcl_WideInt) significandWide;
} else {
objPtr->internalRep.wideValue =
(Tcl_WideInt) significandWide;
}
break;
}
#endif
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
significandOverflow = 1;
} else {
objPtr->typePtr = &tclIntType;
if (signum) {
objPtr->internalRep.longValue =
- (long) significandWide;
} else {
objPtr->internalRep.longValue =
(long) significandWide;
}
}
}
if (significandOverflow) {
if (signum) {
mp_neg(&significandBig, &significandBig);
}
TclSetBignumIntRep(objPtr, &significandBig);
}
break;
case FRACTION:
case EXPONENT:
/*
* Here, we're parsing a floating-point number.
* 'significandWide' or 'significandBig' contains the
* exact significand, according to whether
* 'significandOverflow' is set. The desired floating
* point value is significand * 10**k, where
* k = numTrailZeros+exponent-numDigitsAfterDp.
*/
objPtr->typePtr = &tclDoubleType;
if ( exponentSignum ) {
exponent = - exponent;
}
if ( !significandOverflow ) {
objPtr->internalRep.doubleValue =
MakeLowPrecisionDouble( signum,
significandWide,
numSigDigs,
( numTrailZeros
+ exponent
- numDigitsAfterDp ) );
} else {
objPtr->internalRep.doubleValue =
MakeHighPrecisionDouble( signum,
&significandBig,
numSigDigs,
( numTrailZeros
+ exponent
- numDigitsAfterDp ) );
}
break;
case sINF:
case sINFINITY:
if ( signum ) {
objPtr->internalRep.doubleValue = -HUGE_VAL;
} else {
objPtr->internalRep.doubleValue = HUGE_VAL;
}
objPtr->typePtr = &tclDoubleType;
break;
case sNAN:
case sNANFINISH:
objPtr->internalRep.doubleValue
= MakeNaN( signum, significandWide );
objPtr->typePtr = &tclDoubleType;
break;
}
}
/* Format an error message when an invalid number is encountered. */
if ( status != TCL_OK ) {
if ( interp != NULL ) {
Tcl_Obj *msg = Tcl_NewStringObj( "expected ", -1 );
Tcl_AppendToObj( msg, type, -1 );
Tcl_AppendToObj( msg, " but got \"", -1 );
TclAppendLimitedToObj( msg, string, length, 50, "" );
Tcl_AppendToObj( msg, "\"", -1 );
if ( state == BAD_OCTAL ) {
Tcl_AppendToObj( msg, " (looks like invalid octal number)",
-1 );
}
Tcl_SetObjResult( interp, msg );
}
}
/* Free memory */
if (octalSignificandOverflow) {
mp_clear(&octalSignificandBig);
}
if (significandOverflow) {
mp_clear(&significandBig);
}
return status;
}
/*
*----------------------------------------------------------------------
*
* AccumulateDecimalDigit --
*
* Consume a decimal digit in a number being scanned.
*
* Results:
* Returns 1 if the number has overflowed to a bignum, 0 if it
* still fits in a wide integer.
*
* Side effects:
* Updates either the wide or bignum representation.
*
*----------------------------------------------------------------------
*/
static int
AccumulateDecimalDigit( unsigned digit,
/* Digit being scanned */
int numZeros,
/* Count of zero digits preceding the
* digit being scanned */
Tcl_WideUInt* wideRepPtr,
/* Representation of the partial number
* as a wide integer */
mp_int* bignumRepPtr,
/* Representation of the partial number
* as a bignum */
int bignumFlag )
/* Flag == 1 if the number overflowed
* previous to this digit. */
{
int i, n;
/* Check if the number still fits in a wide */
if (!bignumFlag) {
if (*wideRepPtr != 0) {
if ((numZeros >= maxpow10_wide)
|| (*wideRepPtr > (((~(Tcl_WideUInt)0) - digit)
/ pow10_wide[numZeros+1]))) {
/* Oops, it's overflowed, have to allocate a bignum */
TclBNInitBignumFromWideUInt (bignumRepPtr, *wideRepPtr);
bignumFlag = 1;
}
}
}
/* Multiply the number by 10**numZeros+1 and add in the new digit. */
if (!bignumFlag) {
/* Wide multiplication */
*wideRepPtr = *wideRepPtr * pow10_wide[numZeros+1] + digit;
} else if (numZeros < log10_DIGIT_MAX ) {
/* Up to about 8 zeros - single digit multiplication */
mp_mul_d (bignumRepPtr, (mp_digit) pow10_wide[numZeros+1],
bignumRepPtr);
mp_add_d (bignumRepPtr, (mp_digit) digit, bignumRepPtr);
} else {
/*
* More than single digit multiplication. Multiply by the appropriate
* small powers of 5, and then shift. Large strings of zeroes are
* eaten 256 at a time; this is less efficient than it could be,
* but seems implausible. We presume that DIGIT_BIT is at least 27.
* The first multiplication, by up to 10**7, is done with a
* one-DIGIT multiply (this presumes that DIGIT_BIT >= 24).
*/
n = numZeros + 1;
mp_mul_d (bignumRepPtr, (mp_digit) pow10_wide[n&0x7], bignumRepPtr);
for (i = 3; i <= 7; ++i) {
if (n & (1 << i)) {
mp_mul (bignumRepPtr, pow5+i, bignumRepPtr);
}
}
while (n >= 256) {
mp_mul (bignumRepPtr, pow5+8, bignumRepPtr);
n -= 256;
}
mp_mul_2d (bignumRepPtr, (int)(numZeros+1)&~0x7, bignumRepPtr);
}
return bignumFlag;
}
/*
*----------------------------------------------------------------------
*
* MakeLowPrecisionDouble --
*
* Makes the double precision number, signum*significand*10**exponent.
*
* Results:
* Returns the constructed number.
*
* Common cases, where there are few enough digits that the number can
* be represented with at most roundoff, are handled specially here.
* If the number requires more than one rounded operation to compute,
* the code promotes the significand to a bignum and calls
* MakeHighPrecisionDouble to do it instead.
*
*----------------------------------------------------------------------
*/
static double
MakeLowPrecisionDouble( int signum,
/* 1 if the number is negative, 0 otherwise */
Tcl_WideUInt significand,
/* Significand of the number */
int numSigDigs,
/* Number of digits in the significand */
int exponent )
/* Power of ten */
{
double retval; /* Value of the number */
mp_int significandBig; /* Significand expressed as a bignum */
/*
* With gcc on x86, the floating point rounding mode is double-extended.
* This causes the result of double-precision calculations to be rounded
* twice: once to the precision of double-extended and then again to the
* precision of double. Double-rounding introduces gratuitous errors of
* 1 ulp, so we need to change rounding mode to 53-bits.
*/
#if defined(__GNUC__) && defined(__i386)
fpu_control_t roundTo53Bits = 0x027f;
fpu_control_t oldRoundingMode;
_FPU_GETCW( oldRoundingMode );
_FPU_SETCW( roundTo53Bits );
#endif
/* Test for the easy cases */
if ( numSigDigs <= DBL_DIG ) {
if ( exponent >= 0 ) {
if ( exponent <= mmaxpow ) {
/*
* The significand is an exact integer, and so is
* 10**exponent. The product will be correct to within
* 1/2 ulp without special handling.
*/
retval = (double)(Tcl_WideInt)significand * pow10[ exponent ];
goto returnValue;
} else {
int diff = DBL_DIG - numSigDigs;
if ( exponent-diff <= mmaxpow ) {
/*
* 10**exponent is not an exact integer, but
* 10**(exponent-diff) is exact, and so is
* significand*10**diff, so we can still compute
* the value with only one roundoff.
*/
volatile double factor
= (double)(Tcl_WideInt)significand * pow10[diff];
retval = factor * pow10[exponent-diff];
goto returnValue;
}
}
} else {
if ( exponent >= -mmaxpow ) {
/*
* 10**-exponent is an exact integer, and so is the
* significand. Compute the result by one division,
* again with only one rounding.
*/
retval = (double)(Tcl_WideInt)significand / pow10[-exponent];
goto returnValue;
}
}
}
/*
* All the easy cases have failed. Promote ths significand
* to bignum and call MakeHighPrecisionDouble to do it the hard way.
*/
TclBNInitBignumFromWideUInt (&significandBig, significand);
retval = MakeHighPrecisionDouble( 0, &significandBig, numSigDigs,
exponent );
/* Come here to return the computed value */
returnValue:
if ( signum ) {
retval = -retval;
}
/* On gcc on x86, restore the floating point mode word. */
#if defined(__GNUC__) && defined(__i386)
_FPU_SETCW( oldRoundingMode );
#endif
return retval;
}
/*
*----------------------------------------------------------------------
*
* MakeHighPrecisionDouble --
*
* Makes the double precision number, signum*significand*10**exponent.
*
* Results:
* Returns the constructed number.
*
* MakeHighPrecisionDouble is used when arbitrary-precision arithmetic
* is needed to ensure correct rounding. It begins by calculating a
* low-precision approximation to the desired number, and then refines
* the answer in high precision.
*
*----------------------------------------------------------------------
*/
static double
MakeHighPrecisionDouble( int signum,
/* 1=negative, 0=nonnegative */
mp_int* significand,
/* Exact significand of the number */
int numSigDigs,
/* Number of significant digits */
int exponent )
/* Power of 10 by which to multiply */
{
double retval;
int machexp; /* Machine exponent of a power of 10 */
/*
* With gcc on x86, the floating point rounding mode is double-extended.
* This causes the result of double-precision calculations to be rounded
* twice: once to the precision of double-extended and then again to the
* precision of double. Double-rounding introduces gratuitous errors of
* 1 ulp, so we need to change rounding mode to 53-bits.
*/
#if defined(__GNUC__) && defined(__i386)
fpu_control_t roundTo53Bits = 0x027f;
fpu_control_t oldRoundingMode;
_FPU_GETCW( oldRoundingMode );
_FPU_SETCW( roundTo53Bits );
#endif
/* Quick checks for over/underflow */
if ( numSigDigs + exponent - 1 > maxDigits ) {
retval = HUGE_VAL;
goto returnValue;
}
if ( numSigDigs + exponent - 1 < minDigits ) {
retval = 0;
goto returnValue;
}
/*
* Develop a first approximation to the significand. It is tempting
* simply to force bignum to double, but that will overflow on input
* numbers like 1.[string repeat 0 1000]1; while this is a not terribly
* likely scenario, we still have to deal with it. Use fraction and
* exponent instead. Once we have the significand, multiply by
* 10**exponent. Test for overflow. Convert back to a double, and
* test for underflow.
*/
retval = BignumToBiasedFrExp( significand, &machexp );
retval = Pow10TimesFrExp( exponent, retval, &machexp );
if ( machexp > DBL_MAX_EXP * log2FLT_RADIX ) {
retval = HUGE_VAL;
goto returnValue;
}
retval = SafeLdExp( retval, machexp );
if ( retval < tiny ) {
retval = tiny;
}
/*
* Refine the result twice. (The second refinement should be
* necessary only if the best approximation is a power of 2
* minus 1/2 ulp).
*/
retval = RefineApproximation( retval, significand, exponent );
retval = RefineApproximation( retval, significand, exponent );
/* Come here to return the computed value */
returnValue:
if ( signum ) {
retval = -retval;
}
/* On gcc on x86, restore the floating point mode word. */
#if defined(__GNUC__) && defined(__i386)
_FPU_SETCW( oldRoundingMode );
#endif
return retval;
}
/*
*----------------------------------------------------------------------
*
* MakeNaN --
*
* Makes a "Not a Number" given a set of bits to put in the
* tag bits
*
* Note that a signalling NaN is never returned.
*
*----------------------------------------------------------------------
*/
#ifdef IEEE_FLOATING_POINT
static double
MakeNaN( int signum, /* Sign bit (1=negative, 0=nonnegative */
Tcl_WideUInt tags ) /* Tag bits to put in the NaN */
{
union {
Tcl_WideUInt iv;
double dv;
} theNaN;
theNaN.iv = tags;
theNaN.iv &= ( ((Tcl_WideUInt) 1) << 51 ) - 1;
if ( signum ) {
theNaN.iv |= ((Tcl_WideUInt) (0x8000 | NAN_START)) << 48;
} else {
theNaN.iv |= ((Tcl_WideUInt) NAN_START) << 48;
}
return theNaN.dv;
}
#endif
/*
*----------------------------------------------------------------------
*
* RefineApproximation --
*
* Given a poor approximation to a floating point number, returns
* a better one (The better approximation is correct to within
* 1 ulp, and is entirely correct if the poor approximation is
* correct to 1 ulp.)
*
* Results:
* Returns the improved result.
*
*----------------------------------------------------------------------
*/
static double
RefineApproximation( double approxResult,
/* Approximate result of conversion */
mp_int* exactSignificand,
/* Integer significand */
int exponent )
/* Power of 10 to multiply by significand */
{
int M2, M5; /* Powers of 2 and of 5 needed to put
* the decimal and binary numbers over
* a common denominator. */
double significand; /* Sigificand of the binary number */
int binExponent; /* Exponent of the binary number */
int msb; /* Most significant bit position of an
* intermediate result */
int nDigits; /* Number of mp_digit's in an intermediate
* result */
mp_int twoMv; /* Approx binary value expressed as an
* exact integer scaled by the multiplier 2M */
mp_int twoMd; /* Exact decimal value expressed as an
* exact integer scaled by the multiplier 2M */
int scale; /* Scale factor for M */
int multiplier; /* Power of two to scale M */
double num, den; /* Numerator and denominator of the
* correction term */
double quot; /* Correction term */
double minincr; /* Lower bound on the absolute value
* of the correction term. */
int i;
/*
* The first approximation is always low. If we find that
* it's HUGE_VAL, we're done.
*/
if ( approxResult == HUGE_VAL ) {
return approxResult;
}
/*
* Find a common denominator for the decimal and binary fractions.
* The common denominator will be 2**M2 + 5**M5.
*/
significand = frexp( approxResult, &binExponent );
i = mantBits - binExponent;
if ( i < 0 ) {
M2 = 0;
} else {
M2 = i;
}
if ( exponent > 0 ) {
M5 = 0;
} else {
M5 = -exponent;
if ( (M5-1) > M2 ) {
M2 = M5-1;
}
}
/*
* The floating point number is significand*2**binExponent.
* Compute the large integer significand*2**(binExponent+M2+1)
* The 2**-1 bit of the significand (the most significant)
* corresponds to the 2**(binExponent+M2 + 1) bit of 2*M2*v.
* Allocate enough digits to hold that quantity, then
* convert the significand to a large integer, scaled
* appropriately. Then multiply by the appropriate power of 5.
*/
msb = binExponent + M2; /* 1008 */
nDigits = msb / DIGIT_BIT + 1;
mp_init_size( &twoMv, nDigits );
i = ( msb % DIGIT_BIT + 1 );
twoMv.used = nDigits;
significand *= SafeLdExp( 1.0, i );
while ( -- nDigits >= 0 ) {
twoMv.dp[nDigits] = (mp_digit) significand;
significand -= (mp_digit) significand;
significand = SafeLdExp( significand, DIGIT_BIT );
}
for ( i = 0; i <= 8; ++i ) {
if ( M5 & ( 1 << i ) ) {
mp_mul( &twoMv, pow5+i, &twoMv );
}
}
/*
* Collect the decimal significand as a high precision integer.
* The least significant bit corresponds to bit M2+exponent+1
* so it will need to be shifted left by that many bits after
* being multiplied by 5**(M5+exponent).
*/
mp_init_copy( &twoMd, exactSignificand );
for ( i = 0; i <= 8; ++i ) {
if ( (M5+exponent) & ( 1 << i ) ) {
mp_mul( &twoMd, pow5+i, &twoMd );
}
}
mp_mul_2d( &twoMd, M2+exponent+1, &twoMd );
mp_sub( &twoMd, &twoMv, &twoMd );
/*
* The result, 2Mv-2Md, needs to be divided by 2M to yield a correction
* term. Because 2M may well overflow a double, we need to scale the
* denominator by a factor of 2**binExponent-mantBits
*/
scale = binExponent - mantBits - 1;
mp_set( &twoMv, 1 );
for ( i = 0; i <= 8; ++i ) {
if ( M5 & ( 1 << i ) ) {
mp_mul( &twoMv, pow5+i, &twoMv );
}
}
multiplier = M2 + scale + 1;
if ( multiplier > 0 ) {
mp_mul_2d( &twoMv, multiplier, &twoMv );
} else if ( multiplier < 0 ) {
mp_div_2d( &twoMv, -multiplier, &twoMv, NULL );
}
/*
* If the result is less than unity, the error is less than 1/2 unit
* in the last place, so there's no correction to make.
*/
if ( mp_cmp_mag( &twoMd, &twoMv ) == MP_LT ) {
return approxResult;
}
/*
* Convert the numerator and denominator of the corrector term
* accurately to floating point numbers.
*/
num = TclBignumToDouble( &twoMd );
den = TclBignumToDouble( &twoMv );
quot = SafeLdExp( num/den, scale );
minincr = SafeLdExp( 1.0, binExponent - mantBits );
if ( quot < 0. && quot > -minincr ) {
quot = -minincr;
} else if ( quot > 0. && quot < minincr ) {
quot = minincr;
}
mp_clear( &twoMd );
mp_clear( &twoMv );
return approxResult + quot;
}
/*
*----------------------------------------------------------------------
*
* TclDoubleDigits --
*
* Converts a double to a string of digits.
*
* Results:
* Returns the position of the character in the string after which the
* decimal point should appear. Since the string contains only
* significant digits, the position may be less than zero or greater than
* the length of the string.
*
* Side effects:
* Stores the digits in the given buffer and sets 'signum' according to
* the sign of the number.
*
*----------------------------------------------------------------------
*/
int
TclDoubleDigits( char * string, /* Buffer in which to store the result,
* must have at least 18 chars */
double v, /* Number to convert. Must be
* finite, and not NaN */
int *signum ) /* Output: 1 if the number is negative.
* Should handle -0 correctly on the
* IEEE architecture. */
{
double f; /* Significand of v. */
int e; /* Power of FLT_RADIX that satisfies
* v = f * FLT_RADIX**e */
int lowOK, highOK;
mp_int r; /* Scaled significand. */
mp_int s; /* Divisor such that v = r / s */
mp_int mplus; /* Scaled epsilon: (r + 2* mplus) == v(+)
* where v(+) is the floating point successor
* of v. */
mp_int mminus; /* Scaled epsilon: (r - 2*mminus) == v(-)
* where v(-) is the floating point
* predecessor of v. */
mp_int temp;
int rfac2 = 0; /* Powers of 2 and 5 by which large */
int rfac5 = 0; /* integers should be scaled. */
int sfac2 = 0;
int sfac5 = 0;
int mplusfac2 = 0;
int mminusfac2 = 0;
double a;
char c;
int i, k, n;
/*
* Take the absolute value of the number, and report the number's sign.
* Take special steps to preserve signed zeroes in IEEE floating point.
* (We can't use fpclassify, because that's a C9x feature and we still
* have to build on C89 compilers.)
*/
#ifndef IEEE_FLOATING_POINT
if (v >= 0.0) {
*signum = 0;
} else {
*signum = 1;
v = -v;
}
#else
union {
Tcl_WideUInt iv;
double dv;
} bitwhack;
bitwhack.dv = v;
if (bitwhack.iv & ((Tcl_WideUInt) 1 << 63)) {
*signum = 1;
bitwhack.iv &= ~((Tcl_WideUInt) 1 << 63);
v = bitwhack.dv;
} else {
*signum = 0;
}
#endif
/*
* Handle zero specially.
*/
if ( v == 0.0 ) {
*string++ = '0';
*string++ = '\0';
return 1;
}
/*
* Develop f and e such that v = f * FLT_RADIX**e, with
* 1.0/FLT_RADIX <= f < 1.
*/
f = frexp(v, &e);
#if FLT_RADIX > 2
n = e % log2FLT_RADIX;
if (n > 0) {
n -= log2FLT_RADIX;
e += 1;
f *= ldexp(1.0, n);
}
e = (e - n) / log2FLT_RADIX;
#endif
if (f == 1.0) {
f = 1.0 / FLT_RADIX;
e += 1;
}
/*
* If the original number was denormalized, adjust e and f to be denormal
* as well.
*/
if (e < DBL_MIN_EXP) {
n = mantBits + (e - DBL_MIN_EXP)*log2FLT_RADIX;
f = ldexp(f, (e - DBL_MIN_EXP)*log2FLT_RADIX);
e = DBL_MIN_EXP;
n = (n + DIGIT_BIT - 1) / DIGIT_BIT;
} else {
n = mantDIGIT;
}
/*
* Now extract the base-2**DIGIT_BIT digits of f into a multi-precision
* integer r. Preserve the invariant v = r * 2**rfac2 * FLT_RADIX**e by
* adjusting e.
*/
a = f;
n = mantDIGIT;
mp_init_size(&r, n);
r.used = n;
r.sign = MP_ZPOS;
i = (mantBits % DIGIT_BIT);
if (i == 0) {
i = DIGIT_BIT;
}
while (n > 0) {
a *= ldexp(1.0, i);
i = DIGIT_BIT;
r.dp[--n] = (mp_digit) a;
a -= (mp_digit) a;
}
e -= DBL_MANT_DIG;
lowOK = highOK = (mp_iseven(&r));
/*
* We are going to want to develop integers r, s, mplus, and mminus such
* that v = r / s, v(+)-v / 2 = mplus / s; v-v(-) / 2 = mminus / s and
* then scale either s or r, mplus, mminus by an appropriate power of ten.
*
* We actually do this by keeping track of the powers of 2 and 5 by which
* f is multiplied to yield v and by which 1 is multiplied to yield s,
* mplus, and mminus.
*/
if (e >= 0) {
int bits = e * log2FLT_RADIX;
if (f != 1.0/FLT_RADIX) {
/*
* Normal case, m+ and m- are both FLT_RADIX**e
*/
rfac2 += bits + 1;
sfac2 = 1;
mplusfac2 = bits;
mminusfac2 = bits;
} else {
/*
* If f is equal to the smallest significand, then we need another
* factor of FLT_RADIX in s to cope with stepping to the next
* smaller exponent when going to e's predecessor.
*/
rfac2 += bits + log2FLT_RADIX + 1;
sfac2 = 1 + log2FLT_RADIX;
mplusfac2 = bits + log2FLT_RADIX;
mminusfac2 = bits;
}
} else {
/*
* v has digits after the binary point
*/
if (e <= DBL_MIN_EXP-DBL_MANT_DIG || f != 1.0/FLT_RADIX) {
/*
* Either f isn't the smallest significand or e is the smallest
* exponent. mplus and mminus will both be 1.
*/
rfac2 += 1;
sfac2 = 1 - e * log2FLT_RADIX;
mplusfac2 = 0;
mminusfac2 = 0;
} else {
/*
* f is the smallest significand, but e is not the smallest
* exponent. We need to scale by FLT_RADIX again to cope with the
* fact that v's predecessor has a smaller exponent.
*/
rfac2 += 1 + log2FLT_RADIX;
sfac2 = 1 + log2FLT_RADIX * (1 - e);
mplusfac2 = FLT_RADIX;
mminusfac2 = 0;
}
}
/*
* Estimate the highest power of ten that will be needed to hold the
* result.
*/
k = (int) ceil(log(v) / log(10.));
if (k >= 0) {
sfac2 += k;
sfac5 = k;
} else {
rfac2 -= k;
mplusfac2 -= k;
mminusfac2 -= k;
rfac5 = -k;
}
/*
* Scale r, s, mplus, mminus by the appropriate powers of 2 and 5.
*/
mp_init_set(&mplus, 1);
for (i=0 ; i<=8 ; ++i) {
if (rfac5 & (1 << i)) {
mp_mul(&mplus, pow5+i, &mplus);
}
}
mp_mul(&r, &mplus, &r);
mp_mul_2d(&r, rfac2, &r);
mp_init_copy(&mminus, &mplus);
mp_mul_2d(&mplus, mplusfac2, &mplus);
mp_mul_2d(&mminus, mminusfac2, &mminus);
mp_init_set(&s, 1);
for (i=0 ; i<=8 ; ++i) {
if (sfac5 & (1 << i)) {
mp_mul(&s, pow5+i, &s);
}
}
mp_mul_2d(&s, sfac2, &s);
/*
* It is possible for k to be off by one because we used an inexact
* logarithm.
*/
mp_init(&temp);
mp_add(&r, &mplus, &temp);
i = mp_cmp_mag(&temp, &s);
if (i>0 || (highOK && i==0)) {
mp_mul_d(&s, 10, &s);
++k;
} else {
mp_mul_d(&temp, 10, &temp);
i = mp_cmp_mag(&temp, &s);
if (i<0 || (highOK && i==0)) {
mp_mul_d(&r, 10, &r);
mp_mul_d(&mplus, 10, &mplus);
mp_mul_d(&mminus, 10, &mminus);
--k;
}
}
/*
* At this point, k contains the power of ten by which we're scaling the
* result. r/s is at least 1/10 and strictly less than ten, and v = r/s *
* 10**k. mplus and mminus give the rounding limits.
*/
for (;;) {
int tc1, tc2;
mp_mul_d(&r, 10, &r);
mp_div(&r, &s, &temp, &r); /* temp = 10r / s; r = 10r mod s */
i = temp.dp[0];
mp_mul_d(&mplus, 10, &mplus);
mp_mul_d(&mminus, 10, &mminus);
tc1 = mp_cmp_mag(&r, &mminus);
if (lowOK) {
tc1 = (tc1 <= 0);
} else {
tc1 = (tc1 < 0);
}
mp_add(&r, &mplus, &temp);
tc2 = mp_cmp_mag(&temp, &s);
if (highOK) {
tc2 = (tc2 >= 0);
} else {
tc2= (tc2 > 0);
}
if ( ! tc1 ) {
if ( !tc2 ) {
*string++ = '0' + i;
} else {
c = (char) (i + '1');
break;
}
} else {
if (!tc2) {
c = (char) (i + '0');
} else {
mp_mul_2d(&r, 1, &r);
n = mp_cmp_mag(&r, &s);
if (n < 0) {
c = (char) (i + '0');
} else {
c = (char) (i + '1');
}
}
break;
}
};
*string++ = c;
*string++ = '\0';
/*
* Free memory, and return.
*/
mp_clear_multi(&r, &s, &mplus, &mminus, &temp, NULL);
return k;
}
/*
*----------------------------------------------------------------------
*
* TclInitDoubleConversion --
*
* Initializes constants that are needed for conversions to and from
* 'double'
*
* Results:
* None.
*
* Side effects:
* The log base 2 of the floating point radix, the number of bits in a
* double mantissa, and a table of the powers of five and ten are
* computed and stored.
*
*----------------------------------------------------------------------
*/
void
TclInitDoubleConversion(void)
{
int i;
int x;
Tcl_WideUInt u;
double d;
/*
* Initialize table of powers of 10 expressed as wide integers.
*/
maxpow10_wide =
(int) floor(sizeof (Tcl_WideUInt) * CHAR_BIT * log (2.) / log (10.));
pow10_wide = (Tcl_WideUInt*) Tcl_Alloc ((maxpow10_wide + 1)
* sizeof (Tcl_WideUInt));
u = 1;
for (i = 0; i < maxpow10_wide; ++i) {
pow10_wide[i] = u;
u *= 10;
}
pow10_wide[i] = u;
/*
* Determine how many bits of precision a double has, and how many
* decimal digits that represents.
*/
if ( frexp( (double) FLT_RADIX, &log2FLT_RADIX ) != 0.5 ) {
Tcl_Panic( "This code doesn't work on a decimal machine!" );
}
--log2FLT_RADIX;
mantBits = DBL_MANT_DIG * log2FLT_RADIX;
d = 1.0;
/*
* Initialize a table of powers of ten that can be exactly represented
* in a double.
*/
x = (int) (DBL_MANT_DIG * log((double) FLT_RADIX) / log( 5.0 ));
if ( x < MAXPOW ) {
mmaxpow = x;
} else {
mmaxpow = MAXPOW;
}
for (i=0 ; i<=mmaxpow ; ++i) {
pow10[i] = d;
d *= 10.0;
}
/* Initialize a table of large powers of five. */
for ( i = 0; i < 9; ++i ) {
mp_init( pow5 + i );
}
mp_set( pow5, 5 );
for ( i = 0; i < 8; ++i ) {
mp_sqr( pow5+i, pow5+i+1 );
}
/*
* Determine the number of decimal digits to the left and right of the
* decimal point in the largest and smallest double, the smallest double
* that differs from zero, and the number of mp_digits needed to represent
* the significand of a double.
*/
tiny = SafeLdExp( 1.0, DBL_MIN_EXP * log2FLT_RADIX - mantBits );
maxDigits = (int) ((DBL_MAX_EXP * log((double) FLT_RADIX)
+ 0.5 * log(10.))
/ log( 10. ));
minDigits = (int) floor ( ( DBL_MIN_EXP - DBL_MANT_DIG )
* log( (double) FLT_RADIX ) / log( 10. ) );
mantDIGIT = ( mantBits + DIGIT_BIT - 1 ) / DIGIT_BIT;
log10_DIGIT_MAX = (int) floor (DIGIT_BIT * log(2.) / log (10.));
}
/*
*----------------------------------------------------------------------
*
* TclFinalizeDoubleConversion --
*
* Cleans up this file on exit.
*
* Results:
* None
*
* Side effects:
* Memory allocated by TclInitDoubleConversion is freed.
*
*----------------------------------------------------------------------
*/
void
TclFinalizeDoubleConversion()
{
int i;
Tcl_Free ((char*)pow10_wide);
for ( i = 0; i < 9; ++i ) {
mp_clear( pow5 + i );
}
}
/*
*----------------------------------------------------------------------
*
* TclInitBignumFromDouble --
*
* Extracts the integer part of a double and converts it to
* an arbitrary precision integer.
*
* Results:
* None.
*
* Side effects:
* Initializes the bignum supplied, and stores the converted number
* in it.
*
*----------------------------------------------------------------------
*/
int
TclInitBignumFromDouble(Tcl_Interp *interp, /* For error message */
double d, /* Number to convert */
mp_int* b) /* Place to store the result */
{
double fract;
int expt;
/* Infinite values can't convert to bignum */
if (TclIsInfinite(d)) {
if (interp != NULL) {
char *s = "integer value too large to represent";
Tcl_SetObjResult(interp, Tcl_NewStringObj(s, -1));
Tcl_SetErrorCode(interp, "ARITH", "IOVERFLOW", s, NULL);
}
return TCL_ERROR;
}
fract = frexp(d,&expt);
if (expt <= 0) {
mp_init(b);
mp_zero(b);
} else {
Tcl_WideInt w = (Tcl_WideInt) ldexp(fract, mantBits);
int shift = expt - mantBits;
TclBNInitBignumFromWideInt(b, w);
if (shift < 0) {
mp_div_2d(b, -shift, b, NULL);
} else if (shift > 0) {
mp_mul_2d(b, shift, b);
}
}
return TCL_OK;
}
/*
*----------------------------------------------------------------------
*
* TclBignumToDouble --
*
* Convert an arbitrary-precision integer to a native floating point
* number.
*
* Results:
* Returns the converted number. Sets errno to ERANGE if the number is
* too large to convert.
*
*----------------------------------------------------------------------
*/
double
TclBignumToDouble(mp_int *a) /* Integer to convert. */
{
mp_int b;
int bits;
int shift;
int i;
double r;
/*
* Determine how many bits we need, and extract that many from the input.
* Round to nearest unit in the last place.
*/
bits = mp_count_bits(a);
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
errno = ERANGE;
if (a->sign == MP_ZPOS) {
return HUGE_VAL;
} else {
return -HUGE_VAL;
}
}
shift = mantBits + 1 - bits;
mp_init(&b);
if (shift > 0) {
mp_mul_2d(a, shift, &b);
} else if (shift < 0) {
mp_div_2d(a, -shift, &b, NULL);
} else {
mp_copy(a, &b);
}
mp_add_d(&b, 1, &b);
mp_div_2d(&b, 1, &b, NULL);
/*
* Accumulate the result, one mp_digit at a time.
*/
r = 0.0;
for (i=b.used-1 ; i>=0 ; --i) {
r = ldexp(r, DIGIT_BIT) + b.dp[i];
}
mp_clear(&b);
/*
* Scale the result to the correct number of bits.
*/
r = ldexp(r, bits - mantBits);
/*
* Return the result with the appropriate sign.
*/
if (a->sign == MP_ZPOS) {
return r;
} else {
return -r;
}
}
double
TclCeil(mp_int *a) /* Integer to convert. */
{
double r = 0.0;
mp_int b;
mp_init(&b);
if (mp_cmp_d(a, 0) == MP_LT) {
mp_neg(a, &b);
r = -TclFloor(&b);
} else {
int bits = mp_count_bits(a);
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
r = HUGE_VAL;
} else {
int i, exact = 1, shift = mantBits - bits;
if (shift > 0) {
mp_mul_2d(a, shift, &b);
} else if (shift < 0) {
mp_int d;
mp_init(&d);
mp_div_2d(a, -shift, &b, &d);
exact = mp_iszero(&d);
mp_clear(&d);
} else {
mp_copy(a, &b);
}
if (!exact) {
mp_add_d(&b, 1, &b);
}
for (i=b.used-1 ; i>=0 ; --i) {
r = ldexp(r, DIGIT_BIT) + b.dp[i];
}
r = ldexp(r, bits - mantBits);
}
}
mp_clear(&b);
return r;
}
double
TclFloor(mp_int *a) /* Integer to convert. */
{
double r = 0.0;
mp_int b;
mp_init(&b);
if (mp_cmp_d(a, 0) == MP_LT) {
mp_neg(a, &b);
r = -TclCeil(&b);
} else {
int bits = mp_count_bits(a);
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
r = DBL_MAX;
} else {
int i, shift = mantBits - bits;
if (shift > 0) {
mp_mul_2d(a, shift, &b);
} else if (shift < 0) {
mp_div_2d(a, -shift, &b, NULL);
} else {
mp_copy(a, &b);
}
for (i=b.used-1 ; i>=0 ; --i) {
r = ldexp(r, DIGIT_BIT) + b.dp[i];
}
r = ldexp(r, bits - mantBits);
}
}
mp_clear(&b);
return r;
}
/*
*----------------------------------------------------------------------
*
* BignumToBiasedFrExp --
*
* Convert an arbitrary-precision integer to a native floating
* point number in the range [0.5,1) times a power of two.
* NOTE: Intentionally converts to a number that's a few
* ulp too small, so that RefineApproximation will not overflow
* near the high end of the machine's arithmetic range.
*
* Results:
* Returns the converted number.
*
* Side effects:
* Stores the exponent of two in 'machexp'.
*
*----------------------------------------------------------------------
*/
static double
BignumToBiasedFrExp( mp_int* a,
/* Integer to convert */
int* machexp )
/* Power of two */
{
mp_int b;
int bits;
int shift;
int i;
double r;
/* Determine how many bits we need, and extract that many from
* the input. Round to nearest unit in the last place. */
bits = mp_count_bits( a );
shift = mantBits - 2 - bits;
mp_init( &b );
if ( shift > 0 ) {
mp_mul_2d( a, shift, &b );
} else if ( shift < 0 ) {
mp_div_2d( a, -shift, &b, NULL );
} else {
mp_copy( a, &b );
}
/* Accumulate the result, one mp_digit at a time */
r = 0.0;
for ( i = b.used-1; i >= 0; --i ) {
r = ldexp( r, DIGIT_BIT ) + b.dp[i];
}
mp_clear( &b );
/* Return the result with the appropriate sign. */
*machexp = bits - mantBits + 2;
if ( a->sign == MP_ZPOS ) {
return r;
} else {
return -r;
}
}
/*
*----------------------------------------------------------------------
*
* Pow10TimesFrExp --
*
* Multiply a power of ten by a number expressed as fraction and
* exponent.
*
* Results:
* Returns the significand of the result.
*
* Side effects:
* Overwrites the 'machexp' parameter with the exponent of the
* result.
*
* Assumes that 'exponent' is such that 10**exponent would be a double,
* even though 'fraction*10**(machexp+exponent)' might overflow.
*
*----------------------------------------------------------------------
*/
static double
Pow10TimesFrExp( int exponent, /* Power of 10 to multiply by */
double fraction,
/* Significand of multiplicand */
int* machexp ) /* On input, exponent of multiplicand.
* On output, exponent of result. */
{
int i, j;
int expt = *machexp;
double retval = fraction;
if ( exponent > 0 ) {
/* Multiply by 10**exponent */
retval = frexp( retval * pow10[ exponent & 0xf ], &j );
expt += j;
for ( i = 4; i < 9; ++i ) {
if ( exponent & (1<<i) ) {
retval = frexp( retval * pow_10_2_n[ i ], &j );
expt += j;
}
}
} else if ( exponent < 0 ) {
/* Divide by 10**-exponent */
retval = frexp( retval / pow10[ (-exponent) & 0xf ], &j );
expt += j;
for ( i = 4; i < 9; ++i ) {
if ( (-exponent) & (1<<i) ) {
retval = frexp( retval / pow_10_2_n[ i ], &j );
expt += j;
}
}
}
*machexp = expt;
return retval;
}
/*
*----------------------------------------------------------------------
*
* SafeLdExp --
*
* Do an 'ldexp' operation, but handle denormals gracefully.
*
* Results:
* Returns the appropriately scaled value.
*
* On some platforms, 'ldexp' fails when presented with a number too
* small to represent as a normalized double. This routine does 'ldexp'
* in two steps for those numbers, to return correctly denormalized
* values.
*
*----------------------------------------------------------------------
*/
static double
SafeLdExp(double fract, int expt)
{
int minexpt = DBL_MIN_EXP * log2FLT_RADIX;
volatile double a, b, retval;
if (expt < minexpt) {
a = ldexp(fract, expt - mantBits - minexpt);
b = ldexp(1.0, mantBits + minexpt);
retval = a * b;
} else {
retval = ldexp(fract, expt);
}
return retval;
}
/*
*----------------------------------------------------------------------
*
* TclFormatNaN --
*
* Makes the string representation of a "Not a Number"
*
* Results:
* None.
*
* Side effects:
* Stores the string representation in the supplied buffer, which must be
* at least TCL_DOUBLE_SPACE characters.
*
*----------------------------------------------------------------------
*/
void
TclFormatNaN(double value, /* The Not-a-Number to format. */
char *buffer) /* String representation. */
{
#ifndef IEEE_FLOATING_POINT
strcpy(buffer, "NaN");
return;
#else
union {
double dv;
Tcl_WideUInt iv;
} bitwhack;
bitwhack.dv = value;
if (bitwhack.iv & ((Tcl_WideUInt) 1 << 63)) {
bitwhack.iv &= ~ ((Tcl_WideUInt) 1 << 63);
*buffer++ = '-';
}
*buffer++ = 'N';
*buffer++ = 'a';
*buffer++ = 'N';
bitwhack.iv &= (((Tcl_WideUInt) 1) << 51) - 1;
if (bitwhack.iv != 0) {
sprintf(buffer, "(%" TCL_LL_MODIFIER "x)", bitwhack.iv);
} else {
*buffer = '\0';
}
#endif /* IEEE_FLOATING_POINT */
}
|