File: MPFR.pm

package info (click to toggle)
libmath-mpfr-perl 4.38-1
  • links: PTS, VCS
  • area: main
  • in suites: sid, trixie
  • size: 1,652 kB
  • sloc: perl: 1,363; ansic: 517; makefile: 9
file content (1801 lines) | stat: -rwxr-xr-x 59,817 bytes parent folder | download
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
    package Math::MPFR;
    use strict;
    use warnings;
    use POSIX;
    use Config;
    use Math::MPFR::Prec;
    use Math::MPFR::Random; # Needs to be loaded before Math::MPFR as
                            # it contains relevant configuration info.

    use constant  GMP_RNDN              => 0;
    use constant  GMP_RNDZ              => 1;
    use constant  GMP_RNDU              => 2;
    use constant  GMP_RNDD              => 3;
    use constant  MPFR_RNDN             => 0;
    use constant  MPFR_RNDZ             => 1;
    use constant  MPFR_RNDU             => 2;
    use constant  MPFR_RNDD             => 3;
    use constant  MPFR_RNDA             => 4;
    use constant  MPFR_RNDF             => 5;
    use constant  _UOK_T                => 1;
    use constant  _IOK_T                => 2;
    use constant  _NOK_T                => 3;
    use constant  _POK_T                => 4;
    use constant  _MATH_MPFR_T          => 5;
    use constant  _MATH_GMPf_T          => 6;
    use constant  _MATH_GMPq_T          => 7;
    use constant  _MATH_GMPz_T          => 8;
    use constant  _MATH_GMP_T           => 9;
    use constant  _MATH_MPC_T           => 10;
    use constant MPFR_FLAGS_UNDERFLOW   => 1;
    use constant MPFR_FLAGS_OVERFLOW    => 2;
    use constant MPFR_FLAGS_NAN         => 4;
    use constant MPFR_FLAGS_INEXACT     => 8;
    use constant MPFR_FLAGS_ERANGE      => 16;
    use constant MPFR_FLAGS_DIVBY0      => 32;
    use constant MPFR_FLAGS_ALL         => 63;
    use constant MPFR_FREE_LOCAL_CACHE  => 1;
    use constant MPFR_FREE_GLOBAL_CACHE => 2;
    use constant LITTLE_ENDIAN          => $Config{byteorder} =~ /^1/ ? 1 : 0;
    use constant MM_HP                  => LITTLE_ENDIAN ? 'h*' : 'H*';
    use constant MPFR_3_1_6_OR_LATER    => Math::MPFR::Random::_MPFR_VERSION() >  196869 ? 1 : 0;
    use constant MPFR_4_0_2_OR_LATER    => Math::MPFR::Random::_MPFR_VERSION() >= 262146 ? 1 : 0;
    use constant MPFR_PV_NV_BUG         => Math::MPFR::Random::_has_pv_nv_bug();

    # https://github.com/StrawberryPerl/Perl-Dist-Strawberry/issues/226
    # Math::MPFR::Random::_buggy() was modified in version 4.34 to
    # accommodate use of vcpkg-built gmp & mpfr libraries on MS Windows.
    use constant WIN32_FMT_BUG          => Math::MPFR::Random::_buggy();

    use constant NV_IS_DOUBLEDOUBLE     => 1 + (2 ** -200) > 1 ? 1 : 0;

    # Inspired by https://github.com/Perl/perl5/issues/19550, which affects only perl-5.35.10:
    use constant ISSUE_19550    => Math::MPFR::Random::_issue_19550();

    use subs qw(MPFR_VERSION MPFR_VERSION_MAJOR MPFR_VERSION_MINOR
                MPFR_VERSION_PATCHLEVEL MPFR_VERSION_STRING
                RMPFR_PREC_MIN RMPFR_PREC_MAX
                MPFR_DBL_DIG MPFR_LDBL_DIG MPFR_FLT128_DIG
                GMP_LIMB_BITS GMP_NAIL_BITS
                );

    use overload
    '++'   => \&overload_inc,
    '--'   => \&overload_dec,
    '+'    => \&overload_add,
    '-'    => \&overload_sub,
    '*'    => \&overload_mul,
    '/'    => \&overload_div,
    '+='   => \&overload_add_eq,
    '-='   => \&overload_sub_eq,
    '*='   => \&overload_mul_eq,
    '/='   => \&overload_div_eq,
    '%'    => \&overload_fmod,
    '%='   => \&overload_fmod_eq,
    '""'   => \&overload_string,
    '>'    => \&overload_gt,
    '>='   => \&overload_gte,
    '<'    => \&overload_lt,
    '<='   => \&overload_lte,
    '<=>'  => \&overload_spaceship,
    '=='   => \&overload_equiv,
    '!='   => \&overload_not_equiv,
    '!'    => \&overload_not,
    'bool' => \&overload_true,
    '='    => \&overload_copy,
    'abs'  => \&overload_abs,
    '**'   => \&overload_pow,
    '**='  => \&overload_pow_eq,
    '<<'   => \&overload_lshift,
    '<<='  => \&overload_lshift_eq,
    '>>'   => \&overload_rshift,
    '>>='  => \&overload_rshift_eq,
    'atan2'=> \&overload_atan2,
    'cos'  => \&overload_cos,
    'sin'  => \&overload_sin,
    'log'  => \&overload_log,
    'exp'  => \&overload_exp,
    'int'  => \&overload_int,
    'sqrt' => \&overload_sqrt;

    require Exporter;
    *import = \&Exporter::import;
    require DynaLoader;

    my @tags = qw(
GMP_RNDD GMP_RNDN GMP_RNDU GMP_RNDZ
IOK_flag NOK_flag POK_flag
MPFR_DBL_DIG MPFR_FLT128_DIG MPFR_LDBL_DIG
MPFR_FLAGS_ALL MPFR_FLAGS_DIVBY0 MPFR_FLAGS_ERANGE MPFR_FLAGS_INEXACT MPFR_FLAGS_NAN
MPFR_FLAGS_OVERFLOW MPFR_FLAGS_UNDERFLOW
MPFR_FREE_LOCAL_CACHE MPFR_FREE_GLOBAL_CACHE
MPFR_RNDA MPFR_RNDD MPFR_RNDF MPFR_RNDN MPFR_RNDU MPFR_RNDZ MPFR_PV_NV_BUG WIN32_FMT_BUG
MPFR_VERSION MPFR_VERSION_MAJOR MPFR_VERSION_MINOR MPFR_VERSION_PATCHLEVEL MPFR_VERSION_STRING
RMPFR_PREC_MAX RMPFR_PREC_MIN RMPFR_VERSION_NUM

log_2 log_10 sind cosd tand tangent
Rmpfr_abs Rmpfr_acos Rmpfr_acosh Rmpfr_acospi Rmpfr_acosu
Rmpfr_add Rmpfr_add_d Rmpfr_add_q Rmpfr_add_si Rmpfr_add_ui Rmpfr_add_z
Rmpfr_agm Rmpfr_ai
Rmpfr_asin Rmpfr_asinh Rmpfr_asinpi Rmpfr_asinu
Rmpfr_atan Rmpfr_atan2 Rmpfr_atan2pi Rmpfr_atan2u Rmpfr_atanh Rmpfr_atanpi Rmpfr_atanu
Rmpfr_beta
Rmpfr_buildopt_decimal_p Rmpfr_buildopt_float16_p Rmpfr_buildopt_float128_p
Rmpfr_buildopt_gmpinternals_p Rmpfr_buildopt_sharedcache_p Rmpfr_buildopt_tls_p
Rmpfr_buildopt_tune_case Rmpfr_can_round Rmpfr_cbrt Rmpfr_ceil Rmpfr_check_range
Rmpfr_clear Rmpfr_clear_divby0 Rmpfr_clear_erangeflag Rmpfr_clear_flags Rmpfr_clear_inexflag
Rmpfr_clear_nanflag Rmpfr_clear_overflow Rmpfr_clear_underflow Rmpfr_clears
Rmpfr_cmp Rmpfr_cmp_IV Rmpfr_cmp_NV Rmpfr_cmp_d Rmpfr_cmp_f Rmpfr_cmp_float128 Rmpfr_cmp_ld
Rmpfr_cmp_q Rmpfr_cmp_si Rmpfr_cmp_si_2exp Rmpfr_cmp_sj Rmpfr_cmp_ui Rmpfr_cmp_ui_2exp
Rmpfr_cmp_uj Rmpfr_cmp_z Rmpfr_cmpabs Rmpfr_cmpabs_ui
Rmpfr_compound Rmpfr_compound_si
Rmpfr_const_catalan Rmpfr_const_euler Rmpfr_const_log2 Rmpfr_const_pi
Rmpfr_copysign
Rmpfr_cos Rmpfr_cosh Rmpfr_cospi Rmpfr_cosu Rmpfr_cot Rmpfr_coth
Rmpfr_csc Rmpfr_csch
Rmpfr_d_div Rmpfr_d_sub Rmpfr_deref2 Rmpfr_digamma Rmpfr_dim
Rmpfr_div Rmpfr_div_2exp Rmpfr_div_2si Rmpfr_div_2ui Rmpfr_div_d Rmpfr_div_q Rmpfr_div_si
Rmpfr_div_ui Rmpfr_div_z Rmpfr_divby0_p
Rmpfr_dot Rmpfr_dump Rmpfr_eint Rmpfr_eq Rmpfr_equal_p Rmpfr_erandom Rmpfr_erangeflag_p
Rmpfr_erf Rmpfr_erfc Rmpfr_exp Rmpfr_exp10 Rmpfr_exp10m1 Rmpfr_exp2 Rmpfr_exp2m1 Rmpfr_expm1
Rmpfr_fac_ui
Rmpfr_fits_IV_p Rmpfr_fits_intmax_p Rmpfr_fits_sint_p Rmpfr_fits_slong_p Rmpfr_fits_sshort_p
Rmpfr_fits_uint_p Rmpfr_fits_uintmax_p Rmpfr_fits_ulong_p Rmpfr_fits_ushort_p
Rmpfr_flags_clear Rmpfr_flags_restore Rmpfr_flags_save Rmpfr_flags_set Rmpfr_flags_test
Rmpfr_floor
Rmpfr_fma Rmpfr_fmma Rmpfr_fmms Rmpfr_fmod Rmpfr_fmod_ui Rmpfr_fmodquo Rmpfr_fms
Rmpfr_fpif_export Rmpfr_fpif_import Rmpfr_fprintf Rmpfr_frac
Rmpfr_free_cache Rmpfr_free_cache2 Rmpfr_free_pool Rmpfr_frexp Rmpfr_gamma Rmpfr_gamma_inc
Rmpfr_get_DECIMAL128 Rmpfr_get_DECIMAL64 Rmpfr_get_FLOAT128 Rmpfr_get_IV Rmpfr_get_LD Rmpfr_get_NV
Rmpfr_get_d Rmpfr_get_d1 Rmpfr_get_d_2exp Rmpfr_get_default_prec Rmpfr_get_default_rounding_mode
Rmpfr_get_emax Rmpfr_get_emax_max Rmpfr_get_emax_min Rmpfr_get_emin Rmpfr_get_emin_max
Rmpfr_get_emin_min Rmpfr_get_exp Rmpfr_get_f Rmpfr_get_float128 Rmpfr_get_flt Rmpfr_get_float16
Rmpfr_get_ld Rmpfr_get_ld_2exp Rmpfr_get_patches Rmpfr_get_prec Rmpfr_get_q Rmpfr_get_si Rmpfr_get_sj
Rmpfr_get_str Rmpfr_get_str_ndigits Rmpfr_get_str_ndigits_alt Rmpfr_get_ui Rmpfr_get_uj
Rmpfr_get_version Rmpfr_get_z Rmpfr_get_z_2exp Rmpfr_get_z_exp
Rmpfr_grandom Rmpfr_greater_p Rmpfr_greaterequal_p Rmpfr_hypot Rmpfr_inexflag_p Rmpfr_inf_p
Rmpfr_init Rmpfr_init2 Rmpfr_init2_nobless Rmpfr_init_nobless Rmpfr_init_set Rmpfr_init_set_IV
Rmpfr_init_set_IV_nobless Rmpfr_init_set_NV Rmpfr_init_set_NV_nobless Rmpfr_init_set_d
Rmpfr_init_set_d_nobless Rmpfr_init_set_f Rmpfr_init_set_f_nobless Rmpfr_init_set_float128
Rmpfr_init_set_float128_nobless Rmpfr_init_set_ld Rmpfr_init_set_nobless Rmpfr_init_set_q
Rmpfr_init_set_q_nobless Rmpfr_init_set_si Rmpfr_init_set_si_nobless Rmpfr_init_set_str
Rmpfr_init_set_str_nobless Rmpfr_init_set_ui Rmpfr_init_set_ui_nobless Rmpfr_init_set_z
Rmpfr_init_set_z_nobless Rmpfr_inits Rmpfr_inits2 Rmpfr_inits2_nobless Rmpfr_inits_nobless
Rmpfr_inp_str Rmpfr_integer_p Rmpfr_integer_string Rmpfr_j0 Rmpfr_j1 Rmpfr_jn Rmpfr_less_p
Rmpfr_lessequal_p Rmpfr_lessgreater_p Rmpfr_lgamma Rmpfr_li2 Rmpfr_lngamma
Rmpfr_log Rmpfr_log10 Rmpfr_log10p1 Rmpfr_log1p Rmpfr_log2 Rmpfr_log2p1 Rmpfr_log_ui
Rmpfr_max Rmpfr_min Rmpfr_min_prec Rmpfr_modf
Rmpfr_mul Rmpfr_mul_2exp Rmpfr_mul_2si Rmpfr_mul_2ui Rmpfr_mul_d Rmpfr_mul_q Rmpfr_mul_si
Rmpfr_mul_ui Rmpfr_mul_z
Rmpfr_nan_p Rmpfr_nanflag_p Rmpfr_neg Rmpfr_nextabove Rmpfr_nextbelow Rmpfr_nexttoward
Rmpfr_nrandom Rmpfr_number_p Rmpfr_out_str Rmpfr_overflow_p
Rmpfr_pow Rmpfr_pow_IV Rmpfr_pow_si Rmpfr_pow_sj Rmpfr_pow_ui Rmpfr_pow_uj Rmpfr_pow_z
Rmpfr_pown Rmpfr_powr Rmpfr_prec_round Rmpfr_print_rnd_mode Rmpfr_printf Rmpfr_q_div
Rmpfr_randclear Rmpfr_randinit_default Rmpfr_randinit_lc_2exp Rmpfr_randinit_lc_2exp_size
Rmpfr_randinit_mt Rmpfr_random2 Rmpfr_randseed Rmpfr_randseed_ui Rmpfr_rec_root Rmpfr_rec_sqrt
Rmpfr_regular_p Rmpfr_reldiff Rmpfr_remainder Rmpfr_remquo
Rmpfr_rint Rmpfr_rint_ceil Rmpfr_rint_floor Rmpfr_rint_round Rmpfr_rint_roundeven Rmpfr_rint_trunc
Rmpfr_root Rmpfr_rootn_ui Rmpfr_round Rmpfr_round_nearest_away Rmpfr_roundeven
Rmpfr_sec Rmpfr_sech Rmpfr_set Rmpfr_set_DECIMAL128 Rmpfr_set_DECIMAL64 Rmpfr_set_FLOAT128
Rmpfr_set_IV Rmpfr_set_LD Rmpfr_set_NV Rmpfr_set_d Rmpfr_set_default_prec
Rmpfr_set_default_rounding_mode Rmpfr_set_divby0 Rmpfr_set_emax Rmpfr_set_emin Rmpfr_set_erangeflag
Rmpfr_set_exp Rmpfr_set_f Rmpfr_set_float128 Rmpfr_set_flt Rmpfr_set_float16 Rmpfr_set_inexflag Rmpfr_set_inf
Rmpfr_set_ld Rmpfr_set_nan Rmpfr_set_nanflag Rmpfr_set_overflow Rmpfr_set_prec Rmpfr_set_prec_raw
Rmpfr_set_q Rmpfr_set_si Rmpfr_set_si_2exp Rmpfr_set_sj Rmpfr_set_sj_2exp Rmpfr_set_str Rmpfr_set_ui
Rmpfr_set_ui_2exp Rmpfr_set_uj Rmpfr_set_uj_2exp Rmpfr_set_underflow Rmpfr_set_z Rmpfr_set_z_2exp
Rmpfr_set_zero Rmpfr_setsign Rmpfr_sgn Rmpfr_si_div Rmpfr_si_sub Rmpfr_signbit
Rmpfr_sin Rmpfr_sin_cos Rmpfr_sinh Rmpfr_sinh_cosh Rmpfr_sinpi Rmpfr_sinu
Rmpfr_snprintf Rmpfr_sprintf Rmpfr_sqr Rmpfr_sqrt Rmpfr_sqrt_ui Rmpfr_strtofr
Rmpfr_sub Rmpfr_sub_d Rmpfr_sub_q Rmpfr_sub_si Rmpfr_sub_ui Rmpfr_sub_z Rmpfr_subnormalize
Rmpfr_sum Rmpfr_swap
Rmpfr_tan Rmpfr_tanh Rmpfr_tanpi Rmpfr_tanu
Rmpfr_total_order_p Rmpfr_trigamma Rmpfr_trunc
Rmpfr_ui_div Rmpfr_ui_pow Rmpfr_ui_pow_ui Rmpfr_ui_sub Rmpfr_underflow_p Rmpfr_unordered_p
Rmpfr_urandom Rmpfr_urandomb Rmpfr_y0 Rmpfr_y1 Rmpfr_yn
Rmpfr_z_div Rmpfr_z_sub Rmpfr_zero_p Rmpfr_zeta Rmpfr_zeta_ui
TRmpfr_inp_str TRmpfr_out_str
anytoa atodouble atonum atonv
check_exact_decimal decimalize doubletoa dragon_test
fr_cmp_q_rounded mpfr_max_orig_len mpfr_min_inter_prec mpfrtoa numtoa nvtoa nv2mpfr nvtoa_test
prec_cast q_add_fr q_cmp_fr q_div_fr q_fmod_fr q_mul_fr q_sub_fr rndna
);

    @Math::MPFR::EXPORT_OK = (@tags, 'bytes');

    our $VERSION = '4.38';
    #$VERSION = eval $VERSION;

    Math::MPFR->DynaLoader::bootstrap($VERSION);

    # The ':mpfr' tag (below) is the same as @EXPORT_OK,
    # except that the ':mpfr' tag does not include 'bytes'.

    %Math::MPFR::EXPORT_TAGS =(mpfr => [@tags]);


$Math::MPFR::NNW = 0; # Set to 1 to allow "non-numeric" warnings for operations involving
                      # strings that contain non-numeric characters.

$Math::MPFR::NOK_POK = 0; # Set to 1 to allow warnings in new() and overloaded operations when
                          # a scalar that has set both NOK (NV) and POK (PV) flags is encountered

$Math::MPFR::doubletoa_fallback = 0; # If FALLBACK_NOTIFY is defined, this scalar Will be automatically
                                     # incremented whenever the grisu3 algorithm (used by doubletoa) fails
                                     # to produce correct result, and thus falls back to its designated
                                     # fallback routine. (See the doubletoa documentation for details.)

$Math::MPFR::PERL_INFNAN = 0;

my $pinf = 1e5000;      # +infinity
my $ninf = -$pinf;      # -infinity
my $nanv = $pinf/$pinf; # not a number
$Math::MPFR::pinfstr = "$pinf"; # perl's string representation of +infinity
$Math::MPFR::ninfstr = "$ninf"; # perl's string representation of -infinity
$Math::MPFR::nanvstr = "$nanv"; # perl's string representation of a nan

%Math::MPFR::NV_properties = _get_NV_properties();

my %bytes = (53   =>  \&_d_bytes,
             64   =>  \&_ld_bytes,
             2098 => \&_dd_bytes,
             113  => \&_f128_bytes,
            );

my %fmt = (53   =>  'a8',
           64   =>  'a10',
           2098 => 'a16',
           113  => 'a16',
          );

sub dl_load_flags {0} # Prevent DynaLoader from complaining and croaking

sub Rmpfr_out_str {
    if(@_ == 4) {
       die "Inappropriate 1st arg supplied to Rmpfr_out_str" if _itsa($_[0]) != _MATH_MPFR_T;
       return _Rmpfr_out_str($_[0], $_[1], $_[2], $_[3]);
    }
    if(@_ == 5) {
      if(_itsa($_[0]) == _MATH_MPFR_T) {return _Rmpfr_out_strS($_[0], $_[1], $_[2], $_[3], $_[4])}
      die "Incorrect args supplied to Rmpfr_out_str" if _itsa($_[1]) != _MATH_MPFR_T;
      return _Rmpfr_out_strP($_[0], $_[1], $_[2], $_[3], $_[4]);
    }
    if(@_ == 6) {
      die "Inappropriate 2nd arg supplied to Rmpfr_out_str" if _itsa($_[1]) != _MATH_MPFR_T;
      return _Rmpfr_out_strPS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5]);
    }
    die "Wrong number of arguments supplied to Rmpfr_out_str()";
}

sub TRmpfr_out_str {
    if(@_ == 5) {
      die "Inappropriate 4th arg supplied to TRmpfr_out_str"
         if _itsa($_[3]) != _MATH_MPFR_T;
      return _TRmpfr_out_str($_[0], $_[1], $_[2], $_[3], $_[4]);
    }
    if(@_ == 6) {
      if(_itsa($_[3]) == _MATH_MPFR_T) {return _TRmpfr_out_strS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5])}
      die "Incorrect args supplied to TRmpfr_out_str"
         if _itsa($_[4]) != _MATH_MPFR_T;
      return _TRmpfr_out_strP($_[0], $_[1], $_[2], $_[3], $_[4], $_[5]);
    }
    if(@_ == 7) {
      die "Inappropriate 5th arg supplied to TRmpfr_out_str"
         if _itsa($_[4]) != _MATH_MPFR_T;
      return _TRmpfr_out_strPS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5], $_[6]);
    }
    die "Wrong number of arguments supplied to TRmpfr_out_str()";
}

sub Rmpfr_get_str {
    my ($mantissa, $exponent) = Rmpfr_deref2($_[0], $_[1], $_[2], $_[3]);

    if($mantissa =~ s/@//g) { return $mantissa }
    if($mantissa =~ /\-/ && $mantissa !~ /[^0,\-]/) {return '-0'}
    if($mantissa !~ /[^0]/ ) {return '0'}

    my $len = substr($mantissa, 0, 1) eq '-' ? 2 : 1;

    if(!$_[2]) {
      while(length($mantissa) > $len && substr($mantissa, -1, 1) eq '0') {
           substr($mantissa, -1, 1, '');
      }
    }

    $exponent--;

    my $sep = $_[1] <= 10 ? 'e' : '@';

    if(length($mantissa) == $len) {
      if($exponent) {return $mantissa . $sep . $exponent}
      return $mantissa;
    }

    substr($mantissa, $len, 0, '.');
    if($exponent) {return $mantissa . $sep . $exponent}
    return $mantissa;
}

sub overload_string {
    return Rmpfr_get_str($_[0], 10, 0, Rmpfr_get_default_rounding_mode());
}

sub Rmpfr_integer_string {
    if($_[1] < 2 || $_[1] > 36) {die("Second argument supplied to Rmpfr_integer_string() is not in acceptable range")}
    my($mantissa, $exponent) = Rmpfr_deref2($_[0], $_[1], 0, $_[2]);
    if($mantissa =~ s/@//g) { return $mantissa }
    if($mantissa =~ /\-/ && $mantissa !~ /[^0,\-]/) {return '-0'}
    return 0 if $exponent < 1;
    my $sign = substr($mantissa, 0, 1) eq '-' ? 1 : 0;
    $mantissa = substr($mantissa, 0, $exponent + $sign);
    return $mantissa;
}


sub new {

    # This function caters for 2 possibilities:
    # 1) that 'new' has been called OOP style - in which
    #    case there will be a maximum of 3 args
    # 2) that 'new' has been called as a function - in
    #    which case there will be a maximum of 2 args.
    # If there are no args, then we just want to return an
    # initialized Math::MPFR object
    if(!@_) {return Rmpfr_init()}

    if(@_ > 3) {die "Too many arguments supplied to new()"}

    # If 'new' has been called OOP style, the first arg is the string
    # "Math::MPFR" which we don't need - so let's remove it. However,
    # if the first arg is a Math::MPFR object (which is a possibility),
    # then we'll get a fatal error when we check it for equivalence to
    # the string "Math::MPFR". So we first need to check that it's not
    # an object - which we'll do by using the ref() function:
    if(!ref($_[0]) && $_[0] eq "Math::MPFR") {
      shift;
      if(!@_) {return Rmpfr_init()}
    }

    # @_ can now contain a maximum of 2 args - the value, and if the value is
    # a string, (optionally) the base of the numeric string.
    if(@_ > 2) {die "Too many arguments supplied to new() - expected no more than two"}

    my ($arg1, $type, $base);

    # $_[0] is the value, $_[1] (if supplied) is the base of the number
    # in the string $[_0].
    $arg1 = shift; # At this point, an infnan might acquire a POK flag - thus
                   # assigning to $type a value of 4, instead of 3. Such behaviour also
                   # turns $arg into a PV and NV dualvar. It's a fairly inconsequential
                   # bug - https://github.com/Perl/perl5/issues/19550.
                   # I could workaround this by simply not shifting and re-assigning, but
                   # I'll leave it as it is - otherwise there's nothing to mark that this
                   # minor issue (which might also show up in user code) ever existed.
    $base = 0;

    $type = _itsa($arg1);
    if(!$type) {die "Inappropriate argument supplied to new()"}

    my @ret;

    # Create a Math::MPFR object that has $arg1 as its value.
    # Die if there are any additional args (unless $type == 4)
    if($type == _UOK_T) {
      if(@_ ) {die "Too many arguments supplied to new() - expected only one"}
      if(Math::MPFR::_has_longlong()) {
        my $ret = Rmpfr_init();
	Rmpfr_set_uj($ret, $arg1, Rmpfr_get_default_rounding_mode());
	return $ret;
      }
      else {
        @ret = Rmpfr_init_set_ui($arg1, Rmpfr_get_default_rounding_mode());
        return $ret[0];
      }
    }

    if($type == _IOK_T) {
      if(@_ ) {die "Too many arguments supplied to new() - expected only one"}
      if(Math::MPFR::_has_longlong()) {
        my $ret = Rmpfr_init();
	Rmpfr_set_sj($ret, $arg1, Rmpfr_get_default_rounding_mode());
	return $ret;
      }
      else {
        @ret = Rmpfr_init_set_si($arg1, Rmpfr_get_default_rounding_mode());
        return $ret[0];
      }
    }

    if($type == _NOK_T) {
      if(@_ ) {die "Too many arguments supplied to new() - expected only one"}

      if(MPFR_PV_NV_BUG) {
        if(_SvPOK($arg1)) {
          set_nok_pok(nok_pokflag() + 1);
          if($Math::MPFR::NOK_POK) {
            warn "Scalar passed to new() is both NV and PV. Using NV (numeric) value";
          }
        }
      }

      my $ret = Rmpfr_init();
      Rmpfr_set_NV($ret, $arg1, Rmpfr_get_default_rounding_mode());
      return $ret;
    }

    if($type == _POK_T) {
      if(@_ > 1) {die "Too many arguments supplied to new() - expected no more than two"}
      if(_SvNOK($arg1)) {
        set_nok_pok(nok_pokflag() + 1);
        if($Math::MPFR::NOK_POK) {
          warn "Scalar passed to new() is both NV and PV. Using PV (string) value";
        }
      }
      $base = shift if @_;
      @ret = Rmpfr_init_set_str($arg1, $base, Rmpfr_get_default_rounding_mode());
      return $ret[0];
    }

    if($type == _MATH_MPFR_T) {
      if(@_) {die "Too many arguments supplied to new() - expected only one"}
      @ret = Rmpfr_init_set($arg1, Rmpfr_get_default_rounding_mode());
      return $ret[0];
    }

    if($type == _MATH_GMPf_T) {
      if(@_) {die "Too many arguments supplied to new() - expected only one"}
      @ret = Rmpfr_init_set_f($arg1, Rmpfr_get_default_rounding_mode());
      return $ret[0];
    }

    if($type == _MATH_GMPq_T) {
      if(@_) {die "Too many arguments supplied to new() - expected only one"}
      @ret = Rmpfr_init_set_q($arg1, Rmpfr_get_default_rounding_mode());
      return $ret[0];
    }

    if($type == _MATH_GMPz_T || $type == _MATH_GMP_T) {
      if(@_) {die "Too many arguments supplied to new() - expected only one"}
      @ret = Rmpfr_init_set_z($arg1, Rmpfr_get_default_rounding_mode());
      return $ret[0];
    }
}

sub Rmpfr_printf {
    if(@_ == 3){
      if(_itsa($_[1]) == 2) {wrap_mpfr_printf_rnd(@_)} # $_[1] is rounding argument (IOK).
      else {die "The second (of 3) arguments given to Rmpfr_printf() is not a valid rounding argument"}
    }
    else {
      die "Rmpfr_printf must take 2 or 3 arguments: format string, [rounding,], and variable" if @_ != 2;
      my $revised = _rewrite_fmt_arg($_[0], $_[1]);
      if($revised) {
        wrap_mpfr_printf($revised, nv2mpfr($_[1]));
      }
      else {
        wrap_mpfr_printf(@_);
      }
    }
}

sub Rmpfr_fprintf {
    if(@_ == 4){
      if(_itsa($_[2]) == 2) {wrap_mpfr_fprintf_rnd(@_)}
      else {die "The third (of 4) arguments given to Rmpfr_fprintf() is not a valid rounding argument"}
    }
    else {
      die "Rmpfr_fprintf must take 3 or 4 arguments: filehandle, format string, [rounding,], and variable" if @_ != 3;
      my $revised = _rewrite_fmt_arg($_[1], $_[2]);
      if($revised) {
        wrap_mpfr_fprintf($_[0], $revised, nv2mpfr($_[2]));
      }
      else {
        wrap_mpfr_fprintf(@_);
      }
    }
}

sub Rmpfr_sprintf {
    my $len;
    if(@_ == 5){
      if(_itsa($_[2]) == 2) { # IV
        $len = wrap_mpfr_sprintf_rnd(@_);
        return $len;
      }
      else {die "The third (of 5) arguments given to Rmpfr_sprintf() is not a valid rounding argument"}
    }
    die "Rmpfr_sprintf must take 4 or 5 arguments: buffer, format string, [rounding,] variable and buffer size" if @_ != 4;

    my $revised = _rewrite_fmt_arg($_[1], $_[2]);
    if($revised) {
      $len = wrap_mpfr_sprintf($_[0], $revised, nv2mpfr($_[2]), $_[3]);
      return $len;
    }

# Alternatively, this should work, but it crashes intermittently
#    if(!_hex_fmt_ok($_[1], $_[2])) {
#      $len = _gmp_sprintf_nv(@_);
#      return $len;
#    }

    $len = wrap_mpfr_sprintf(@_);
    return $len;
}

sub Rmpfr_snprintf {
    my $len;
    if(@_ == 6){
      if(_itsa($_[3]) == 2) {  # IV
        $len = wrap_mpfr_snprintf_rnd(@_);
        return $len;
      }
      else {die "The fourth (of 6) arguments given to Rmpfr_snprintf() is not a valid rounding argument"}
    }
    die "Rmpfr_snprintf must take 5 or 6 arguments: buffer, bytes written, format string, [rounding,], variable and buffer size" if @_ != 5;

    my $revised = _rewrite_fmt_arg($_[2], $_[3]);
    if($revised) {
      $len = wrap_mpfr_snprintf($_[0], $_[1], $revised, nv2mpfr($_[3]), $_[4]);
      return $len;
    }

    $len = wrap_mpfr_snprintf(@_);
    return $len;
}


sub Rmpfr_inits {
    my @ret;
    for(1 .. $_[0]) {
       $ret[$_ - 1] = Rmpfr_init();
    }
    return @ret;
}

sub Rmpfr_inits2 {
    my @ret;
    for(1 .. $_[1]) {
       $ret[$_ - 1] = Rmpfr_init2($_[0]);
    }
    return @ret;
}

sub Rmpfr_inits_nobless {
    my @ret;
    for(1 .. $_[0]) {
       $ret[$_ - 1] = Rmpfr_init_nobless();
    }
    return @ret;
}

sub Rmpfr_inits2_nobless {
    my @ret;
    for(1 .. $_[1]) {
       $ret[$_ - 1] = Rmpfr_init2_nobless($_[0]);
    }
    return @ret;
}

sub MPFR_VERSION            () {return _MPFR_VERSION()}
sub MPFR_VERSION_MAJOR      () {return _MPFR_VERSION_MAJOR()}
sub MPFR_VERSION_MINOR      () {return _MPFR_VERSION_MINOR()}
sub MPFR_VERSION_PATCHLEVEL () {return _MPFR_VERSION_PATCHLEVEL()}
sub MPFR_VERSION_STRING     () {return _MPFR_VERSION_STRING()}
sub MPFR_DBL_DIG            () {return _DBL_DIG()}
sub MPFR_LDBL_DIG           () {return _LDBL_DIG()}
sub MPFR_FLT128_DIG         () {return _FLT128_DIG()}
sub GMP_LIMB_BITS           () {return _GMP_LIMB_BITS()}
sub GMP_NAIL_BITS           () {return _GMP_NAIL_BITS()}

sub atonum {
    if(MPFR_3_1_6_OR_LATER) {
      return atonv($_[0])
        if $_[0] =~ /^[\-\+]?inf|^[\-\+]?nan/i; # buggy perls can numify infnan strings to 0.
      my $copy = $_[0];               # Don't mess with $_[0] flags
      my $ret = "$copy" + 0;
      return $ret if _itsa($ret) < 3; # IV
      return atonv($_[0]);            # NV
    }
    die("atonum needs atonv, but atonv is not available with this version (", MPFR_VERSION_STRING, ") of the mpfr library");
}

sub check_exact_decimal {
  unless( MPFR_3_1_6_OR_LATER ) {
    warn "check_exact_decimal() requires mpfr-3.1.6 or later\n";
    die "Math::MPFR was built against mpfr-", MPFR_VERSION_STRING;
  }
  my($str, $op) = (shift, shift);

  if( !Rmpfr_regular_p($op) ) {  # $op is either zero, inf, or nan.
    if( Rmpfr_nan_p($op)    && $str =~ /^nan$/i )  { return 1 }
    if( Rmpfr_signbit($op) ) {
      if( Rmpfr_zero_p($op) && $str eq '-0' )     { return 1 }
      if( Rmpfr_inf_p($op)  && $str =~ /^\-inf$/i ) { return 1 }
    }
    else {
      if( Rmpfr_zero_p($op) && $str eq '0' )      { return 1 }
      if( Rmpfr_inf_p($op)  && $str =~ '^inf$/i' )  { return 1 }
    }

    return 0;
  }

  my $check = Rmpfr_init2(Rmpfr_get_prec($op));

  my $inex = Rmpfr_strtofr($check, $str, 10, MPFR_RNDN);

  if($inex == 0 && $op == $check) { return 1 }
  return 0;
}

sub mpfr_min_inter_prec {
    die "Wrong number of args to mpfr_min_inter_prec()" unless @_ == 3;
    my $ob = shift; # base of original representation
    my $op = shift; # precision (no. of base $ob digits in mantissa) of original representation
    my $nb = shift; # base of new representation
    my $np;         # min required precision (no. of base $nb digits in mantissa) of new representation

    my %h = (2 => 1, 4 => 2, 8 => 3, 16 => 4, 32 => 5, 64 => 6,
             3 => 1, 9 => 2, 27 => 3,
             5 => 1, 25 => 2,
             6 => 1, 36 => 2,
             7 => 1, 49 => 2);

    return $op
      if $ob == $nb;

    if(_bases_are_power_of_same_integer($ob, $nb)) {
      $np = POSIX::ceil($op * $h{$ob} / $h{$nb});
      return $np;
    }

    $np = POSIX::ceil(1 + ($op * log($ob) / log($nb)));
    return $np;
}

sub mpfr_max_orig_len {
    die "Wrong number of args to maximum_orig_length()" if @_ != 3;
    my $ob = shift; # base of original representation
    my $nb = shift; # base of new representation
    my $np = shift; # precision (no. of base $nb digits in mantissa) of new representation
    my $op;         # max precision (no. of base $ob digits in mantissa) of original representation

    my %h = (2 => 1, 4 => 2, 8 => 3, 16 => 4, 32 => 5, 64 => 6,
             3 => 1, 9 => 2, 27 => 3,
             5 => 1, 25 => 2,
             6 => 1, 36 => 2,
             7 => 1, 49 => 2);

    return $np
      if $ob == $nb;

    if(_bases_are_power_of_same_integer($ob, $nb)) {
      $op = POSIX::floor($np * $h{$nb} / $h{$ob});
      return $op;
    }

    $op = POSIX::floor(($np - 1) * log($nb) / log($ob));
    return $op;
}

sub _bases_are_power_of_same_integer {

  # This function currently doesn't get called if $_[0] == $_[1]
  # Return true if:
  # 1) Both $_[0] and $_[1] are in the range 2..64 (inclusive)
  #    &&
  # 2) Both $_[0] and $_[1] are powers of the same integer - eg 8 & 32, or 9 & 27, or 7 & 49, ....
  # Else return false.

  return 1
    if( ($_[0] == 2 || $_[0] == 16 || $_[0] == 8 || $_[0] == 64 || $_[0] == 32 || $_[0] == 4)
           &&
        ($_[1] == 2 || $_[1] == 16 || $_[1] == 8 || $_[1] == 64 || $_[1] == 32 || $_[1] == 4) );

  return 1
    if( ($_[0] == 3 || $_[0] == 9 || $_[0] == 27)
           &&
        ($_[1] == 3 || $_[1] == 9 || $_[1] == 27) );

  return 1
    if( ($_[0] == 5 || $_[0] == 25)
           &&
        ($_[1] == 5 || $_[1] == 25) );

  return 1
    if( ($_[0] == 6 || $_[0] == 36)
           &&
        ($_[1] == 6 || $_[1] == 36) );

  return 1
    if( ($_[0] == 7 || $_[0] == 49)
           &&
        ($_[1] == 7 || $_[1] == 49) );

  return 0;
}

sub bytes {
  my($val, $bits, $ret) = (shift, shift);
  my $itsa = _itsa($val);

  # $itsa == 4 implies that $val's POK flag is set && IOK flag is unset.
  # $itsa == 5 implies that $val is a Math::MPFR::object.
  # We now croak if neither of those cases is satisfied.

  die "1st arg to Math::MPFR::bytes must be either a string or a Math::MPFR object"
    if($itsa != 4 && $itsa != 5);

  die "2nd argument given to Math::MPFR::bytes is neither 53 nor 64 nor 2098 nor 113"
    unless($bits == 53 || $bits == 64 || $bits == 2098 || $bits == 113);

  $ret = $itsa == 4 ? unpack MM_HP, pack $fmt{$bits}, $bytes   {$bits} -> ($val)
                    : unpack MM_HP, pack $fmt{$bits}, _bytes_fr($val, $bits);
  return scalar reverse $ret if LITTLE_ENDIAN;
  return $ret;
}

sub rndna {
  my $coderef = shift;
  my $rop = shift;
  my $big_prec = Rmpfr_get_prec($rop) + 1;
  my $ret;

  if($coderef == \&Rmpfr_prec_round) {
    my $temp = Rmpfr_init2($big_prec); # need a temp object
    Rmpfr_set($temp, $rop, MPFR_RNDN);
    $ret = Rmpfr_prec_round($temp, $_[0] + 1, MPFR_RNDN);

    if(!$ret) {return Rmpfr_prec_round($rop, $_[0], MPFR_RNDA)}
    return Rmpfr_prec_round($rop, $_[0], MPFR_RNDN);
  }

  Rmpfr_prec_round($rop, $big_prec, MPFR_RNDN);
  $ret =  $coderef->($rop, @_, MPFR_RNDN);

  if($ret) { # not a midpoint value
    Rmpfr_prec_round($rop, $big_prec - 1, $ret < 0 ? MPFR_RNDA : MPFR_RNDZ);
    return $ret;
  }

  if(_lsb($rop) == 0) {
    Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDZ);
    return 0;
  }

  return Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDA);
}

sub Rmpfr_round_nearest_away {
  my $coderef = shift;
  my $rop = shift;
  my $big_prec = Rmpfr_get_prec($rop) + 1;
  my $ret;

  my $emin = Rmpfr_get_emin();

  if($emin <= Rmpfr_get_emin_min()) {
    warn "\n Rmpfr_round_nearest_away requires that emin ($emin)\n",
         " be greater than or equal to emin_min (", Rmpfr_get_emin_min(), ")\n";
    die " You need to set emin (using Rmpfr_set_emin()) accordingly";
  }

  Rmpfr_set_emin($emin - 1);

  if($coderef == \&Rmpfr_prec_round) {
    my $temp = Rmpfr_init2($big_prec); # need a temp object
    Rmpfr_set($temp, $rop, MPFR_RNDN);
    $ret = Rmpfr_prec_round($temp, $_[0] + 1, MPFR_RNDN);

    if(!$ret) {
      $ret = Rmpfr_prec_round($rop, $_[0], MPFR_RNDA);
      Rmpfr_set_emin($emin);
      return $ret;
    }
    $ret = Rmpfr_prec_round($rop, $_[0], MPFR_RNDN);
    Rmpfr_set_emin($emin);
    return $ret;
  }

  Rmpfr_prec_round($rop, $big_prec, MPFR_RNDN);
  $ret =  $coderef->($rop, @_, MPFR_RNDN);

  if($ret) { # not a midpoint value
    Rmpfr_prec_round($rop, $big_prec - 1, $ret < 0 ? MPFR_RNDA : MPFR_RNDZ);
    Rmpfr_set_emin($emin);
    return $ret;
  }

  my $nuisance = Rmpfr_init();
  Rmpfr_set_ui ($nuisance, 2, MPFR_RNDD);
  Rmpfr_pow_si ($nuisance, $nuisance, Rmpfr_get_emin(), MPFR_RNDD);
  Rmpfr_div_2ui($nuisance, $nuisance, 1, MPFR_RNDD);

  if(abs($rop) == $nuisance) {
    Rmpfr_mul_ui($rop, $rop, 2, MPFR_RNDD);
    Rmpfr_set_emin($emin);
    return (Rmpfr_signbit($rop) ? -1 : 1);
  }

  if(_lsb($rop) == 0) {
    Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDZ);
    Rmpfr_set_emin($emin);
    return 0;
  }

  $ret = Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDA);
  Rmpfr_set_emin($emin);
  return $ret;
}

sub _get_NV_properties {

  my($bits, $PREC, $max_dig, $min_pow, $normal_min, $NV_MAX, $nvtype, $emax, $emin);

  if   ($Config{nvtype} eq 'double')     {
    $bits = 53;  $PREC = 64;  $max_dig = 17; $min_pow = -1074;
    $normal_min = 2 ** -1022; $NV_MAX = POSIX::DBL_MAX; $emin = -1073; $emax = 1024;
  }

  elsif($Config{nvtype} eq '__float128') {
    $bits = 113; $PREC = 128; $max_dig = 36; $min_pow = -16494; $normal_min = 2 ** -16382;
    $NV_MAX = 1.18973149535723176508575932662800702e+4932; $emin = -16493; $emax = 16384;
  }

  elsif($Config{nvtype} eq 'long double') {

    if(_required_ldbl_mant_dig() == 53)      {
      $bits = 53;  $PREC = 64;  $max_dig = 17; $min_pow = -1074;
      $normal_min = 2 ** -1022; $NV_MAX = POSIX::DBL_MAX; $emin = -1073; $emax = 1024;
    }

    elsif(_required_ldbl_mant_dig() == 113)  {
      $bits = 113; $PREC = 128; $max_dig = 36; $min_pow = -16494;
      $normal_min = 2 ** -16382; $NV_MAX = POSIX::LDBL_MAX; $emin = -16493; $emax = 16384;
    }

    elsif(_required_ldbl_mant_dig() == 64)   {
      $bits = 64;  $PREC = 80;  $max_dig = 21; $min_pow = -16445;
      $normal_min = 2 ** -16382; $NV_MAX = POSIX::LDBL_MAX; $emin = -16444; $emax = 16384;
    }

    elsif(_required_ldbl_mant_dig() == 2098) {
      $bits = 2098;  $PREC = 2104;  $max_dig = 33; $min_pow = -1074;
      $normal_min = 2 ** -1022; $NV_MAX = POSIX::LDBL_MAX; $emin = -1073; $emax = 1024;
    }

    else {
      my %properties = ('type' => 'unknown long double type');
      return %properties;
    }
  }
  else {
      my %properties = ('type' => 'unknown nv type');
      return %properties;
  }

  my %properties = (
    'bits'       => $bits,
    'PREC'       => $PREC,
    'max_dig'    => $max_dig,
    'min_pow'    => $min_pow,
    'normal_min' => $normal_min,
    'NV_MAX'     => $NV_MAX,
    'emin'       => $emin,
    'emax'       => $emax,
                   );

  return %properties;
}

sub perl_set_fallback_flag {
  $Math::MPFR::doubletoa_fallback++;
}

sub mpfrtoa {
  die "1st arg to mpfrtoa() must be a Math::MPFR object"
    unless ref($_[0]) eq 'Math::MPFR';
  my $obj = shift;
  my $min_normal_prec = defined($_[0]) ? shift : 0;
  return _mpfrtoa($obj, $min_normal_prec);
}

sub anytoa {

  die "1st argument given to anytoa() must be a Math::MPFR object"
    unless Math::MPFR::_itsa($_[0]) == 5;

  my $v = shift;
  die "anytoa() now takes only one argument" if defined($_[0]) ;

  my $bits = Rmpfr_get_prec($v);
  die "Precision of arg given to anytoa() must be 53 or 64 or 113 or 2098"
  unless ($bits == 53 || $bits == 64 || $bits == 113 || $bits == 2098);

  my $emax = Rmpfr_get_emax();                # Save original value
  my $emin = Rmpfr_get_emin();                # Save original value

  my $f_init = Rmpfr_init2($bits);

  my %emax_emin = (53   => [1024,  -1073,  -1022 ],
                   64   => [16384, -16444, -16382],
                   2098 => [1024,  -1073,  -1022 ],
                   113  => [16384, -16493, -16382],
                  );

  Rmpfr_set_emax($emax_emin{$bits}->[0]);
  Rmpfr_set_emin($emax_emin{$bits}->[1]);

  # DoubleDouble
  if($bits == 2098) {

    Rmpfr_strtofr($f_init, "$v", 0, MPFR_RNDN);

    if(!Rmpfr_regular_p($f_init)) {
      Rmpfr_set_emax($emax);                  # Revert to original value
      Rmpfr_set_emin($emin);                  # Revert to original value
      return mpfrtoa($f_init);
    }

    # Obtain the pair of doubles pertinent to $f_init.
    # $msd is the "more siginificant double" and $lsd
    # is the "less significant double".

    my($msd, $lsd) = _mpfr2dd($f_init);
    if($lsd == 0 ) {
      my $f = Rmpfr_init2(53);
      Rmpfr_set_d($f, $msd, MPFR_RNDN);
      Rmpfr_set_emax($emax);                  # Revert to original value
      Rmpfr_set_emin($emin);                  # Revert to original value
      return anytoa($f);
    }

    # Determine the no. of implied (intermediate)
    # bits that lie between the end of $msd and
    # and the start of $lsd

    my $intermediates = _intermediate_bits($msd, $lsd);

    my $f_final = Rmpfr_init2(106 + $intermediates);
    Rmpfr_set_d($f_final, $msd, MPFR_RNDN);
    Rmpfr_add_d($f_final, $f_final, $lsd, MPFR_RNDN);

    Rmpfr_set_emax($emax);                    # Revert to original value
    Rmpfr_set_emin($emin);                    # Revert to original value
    return mpfrtoa($f_final);

  } # End DoubleDouble

  # The next 4 lines cater for the possibility that
  # the value is either subnormal or infinite or
  # zero for the floating point type specified by
  # the value of $bits.

  my $inex = Rmpfr_strtofr($f_init, "$v", 0, MPFR_RNDN);

  if(Rmpfr_regular_p($f_init) && Rmpfr_get_exp($f_init) < $emax_emin{$bits}->[2]) {
    # The value is subnormal, and therefore requires further treatment.

    Rmpfr_subnormalize($f_init, $inex, MPFR_RNDN);
    my ($significand, $exponent) = Rmpfr_deref2($f_init, 2, 0, MPFR_RNDN);

    my $f_final = Rmpfr_init2(1 + $exponent - $emax_emin{$bits}->[1]);

    if($significand =~ s/^\-/-0./) {          # The value is -ve.
      Rmpfr_strtofr($f_final, "${significand}p$exponent", 2, MPFR_RNDN);
    }
    else {                                    # The value is positive
      Rmpfr_strtofr($f_final, "0.${significand}p$exponent", 2, MPFR_RNDN);
    }
    Rmpfr_set_emax($emax);                    # Revert to original value
    Rmpfr_set_emin($emin);                    # Revert to original value
    return mpfrtoa($f_final);
  }

  Rmpfr_set_emax($emax);                      # Revert to original value
  Rmpfr_set_emin($emin);                      # Revert to original value
  return mpfrtoa($f_init);
}

###########################
###########################

sub nvtoa_test {
  # 1st arg must be a string (POK);
  # 2nd arg must be either an NV (NOK) or a Math::MPFR object

  warn "nvtoa_test() is DEPRECATED. Please use dragon_test() instead";

  die "nvtoa_test() requires at least version 3.1.6 of the MPFR library"
    if 196870 > MPFR_VERSION;

  my ($s, $n, $is_nv, $ret) = (shift, shift, 0, 0);
  my ($check, $debug);

  $debug = defined($_[0]) ? $_[0] : 0;

  print "ARG1: $s\nARG2: $n\n"
    if $debug;

  die "First arg to nvtoa_test() must be a string"
    unless _SvPOK($s);

  if(ref($n) eq 'Math::MPFR') {
    $check = Rmpfr_init2(Rmpfr_get_prec($n));
    Rmpfr_set_str($check, $s, 10, MPFR_RNDN);
    Rmpfr_abs($check, $check, MPFR_RNDN);
  }
  else {
    die "2nd arg to nvtoa_test() must be either an NV or a Math::MPFR object"
           unless _SvNOK($n);
    $is_nv = 1;
    $check = abs(atonv("$s"));
  }

  # Check that signs match:

  if($s =~ s/^\-//) {
    die "In nvtoa_test(): signs do not match"
      if $n > 0;
  }
  else {
    die "In nvtoa_test():mismatch of signs"
      if($n < 0);
  }

  $n = abs($n); # deal only with the +ve form
                # for simplicity.

   # Handle inf, nan and zero - test that both $n and $check
   # are the same. No further testing required.

   if($check == 0) {
     return 15 if $n == 0;
     return 0;
   }
   return 0 if $n == 0;

   my $new = Math::MPFR->new($check);

   if(Rmpfr_nan_p($new)) {
     return 15 if $n != $n;
     return 0;
   }
   return 0 if $n != $n;

   if(Rmpfr_inf_p($new)) {
     return 15 if $new == $n;
     return 0;
   }
   return 0 if $n/$n != $n/$n;

   $ret++ if $check == $n; # round trip successful

  my @r = split /e/i, $s;

  if($debug) {
    print "SPLIT:\n$r[0]";
    if(defined($r[1])) { print " $r[1]\n" }
    else { print " no exponent\n" }
  }

  # Increment $ret by 8 if and only if there are no errant trailing
  # zeroes in $r[0] .

  if(!defined($r[1])) {
    $ret += 8 if ($r[0] =~ /\.0$/ || $r[0] !~ /0$/);
    $r[1] = 0;       # define $r[1] by setting it to zero.
  }
  else {
   $ret += 8 unless $r[0] =~ /0$/;
  }

  # We remove from $s any trailing mantissa zeroes, and then
  # replace the least significant digit with zero.
  # IOW, we effectively chop off the least siginificant digit, thereby
  # rounding it down to the next lowest decimal precision.)
  # This altered string should assign to a value less than $n.

  chop($r[0]) while $r[0] =~ /0$/;
  $r[0] =~ s/\.$//;
  while($r[0] =~ /0$/) {
    chop $r[0];
    $r[1]++;
  }

  return $ret + 6 if length($r[0]) < 2; # chop test and increment test inapplicable.

  substr($r[0], -1, 1, '0');


  my $chopped = $r[1] ? $r[0] . 'e' . $r[1]
                      : $r[0];

  print "CHOPPED:\n$chopped\n\n" if $debug;

  if($is_nv) {
    $ret += 2 if atonv($chopped) < $n; # chop test ok.
  }
  else {
    Rmpfr_set_str($check, $chopped, 10, MPFR_RNDN);
    $ret += 2 if $check < $n;          # chop test ok.
  }

  # Now we derive a value that is $s rounded up to the next lowest
  # decimal representation.
  # This new string should assign to a value that is greater
  # than the given $n.

  if($r[0] =~ /\./) {
    # We must remove the '.', do the string increment,
    # and then reinsert the '.' in the appropriate place.
    my @mantissa = split /\./, $r[0];
    my $point_pos = -(length($mantissa[1]));
    my $t = $mantissa[0] . $mantissa[1];
    print "Man (if):\n$t\n" if $debug == 2;
    $t++ for 1..10;
    print "Man++ (if):\n$t\n" if $debug == 2;
    substr($t, $point_pos, 0, '.');
    $r[0] = $t;
  }
  else {
    print "R0 (else):\n$r[0]\n" if $debug == 2;
    $r[0]++ for 1..10;
    print "R0++ (else):\n$r[0]\n" if $debug == 2;
  }

  my $incremented = defined($r[1]) ? $r[0] . 'e' . $r[1]
                                   : $r[0];

  print "INCREMENTED:\n$incremented\n" if $debug;

  if($is_nv) {
    $ret += 4 if atonv($incremented) > $n; # increment test ok.
  }
  else {
    Rmpfr_set_str($check, $incremented, 10, MPFR_RNDN);
    $ret += 4 if $check > $n;              # chop test ok.
  }

  return $ret;
}

#############################
#############################
#############################
#############################

sub dragon_test {

  # 1st arg must be either an NV (NOK) or an IV(IOK) or a Math::MPFR object
  # If there's a 2nd arg (optional) and it matches /debug/i, then $debug
  # is set to 1, and some debug info is output during the running of the test.

  die "dragon_test() requires at least version 3.1.6 of the MPFR library"
    if 196870 > MPFR_VERSION;

  my ($repro, $op, $reco, $is_nv, $ret, $debug);
  $debug = 1 if(@_ == 2 && $_[1] =~ /debug/i);

  if(ref($_[0]) eq 'Math::MPFR') {
    $repro = mpfrtoa($_[0]);
  }
  else {
    unless (_SvNOK($_[0]) || _itsa($_[0]) < 3) { # $_[0] needs to be IV/UV/NV
      die "1st arg to dragon_test() must be either an IV or an NV or a Math::MPFR object"
    }
    $is_nv = 1;
    $repro = nvtoa($_[0]);
  }

  # Check that signs match:
  if($repro =~ s/^\-//) {
    die "In dragon_test(): signs do not match"
      if $_[0] > 0;
  }
  else {
    die "In dragon_test():mismatch of signs"
      if($_[0] < 0);
  }

  # Deal only with the +ve form for simplicity.
  if($is_nv) {
    $op = abs($_[0]); # Can change $_[0] from NV to IV
                      # but that doesn't matter.
    $reco = atonv($repro);
  }
  else {
    $op = Rmpfr_init2(Rmpfr_get_prec($_[0]));
    my $inex = Rmpfr_abs($op, $_[0], MPFR_RNDN);
    die "Copying of argument in dragon_test() failed"
      if $inex;
    $reco = Rmpfr_init2(Rmpfr_get_prec($_[0]));
    Rmpfr_set_str($reco, $repro, 10, MPFR_RNDN);
  }

  print "OP: $op\nREPRO: $repro\n" if $debug;

  # Handle inf, nan and zero - test that both $n and $check
  # are the same. No further testing required.

  if($op == 0) {
    return 15 if $reco == 0;
    return 0;
  }

  if($is_nv) {
    if(Rmpfr_nan_p(Math::MPFR->new($op))) {
      return 15 if $repro =~ /^nan/i;
      return 0;
    }
    if(Rmpfr_inf_p(Math::MPFR->new($op))) {
      return 15 if $repro =~ /^inf/i;
      return 0;
    }
  }
  else {
    if(Rmpfr_nan_p($op)) {
      return 15 if $repro =~ /^nan/i;
      return 0;
    }
    if(Rmpfr_inf_p($op)) {
      return 15 if $repro =~ /^inf/i;
      return 0;
    }
  }

  $ret++ if $reco == $op; # round trip successful

  my @r = split /e/i, $repro;

  if($debug) {
    print "SPLIT:\n$r[0]";
    if(defined($r[1])) { print " $r[1]\n" }
    else { print " no exponent\n" }
  }

  # Increment $ret by 8 if and only if there are no errant trailing
  # zeroes in $r[0] .

  if(!defined($r[1])) {
    $ret += 8 if ($r[0] =~ /\.0$/ || $r[0] !~ /0$/);
    $r[1] = 0;       # define $r[1] by setting it to zero.
  }
  else {
   $ret += 8 unless $r[0] =~ /0$/;
  }

  # We remove from $repro any trailing mantissa zeroes, and then
  # replace the least significant digit with zero.
  # IOW, we effectively chop off the least siginificant digit, thereby
  # rounding it down to the next lowest decimal precision.)
  # This altered string should assign to a value less than $op.

  chop($r[0]) while $r[0] =~ /0$/;
  $r[0] =~ s/\.$//;
  while($r[0] =~ /0$/) {
    chop $r[0];
    $r[1]++;
  }

  return $ret + 6 if length($r[0]) < 2; # chop test and increment test inapplicable.

  substr($r[0], -1, 1, '0');


  my $chopped = $r[1] ? $r[0] . 'e' . $r[1]
                      : $r[0];

  print "CHOPPED:\n$chopped\n\n" if $debug;

  if($is_nv) {
    $ret += 2 if atonv($chopped) < $op; # chop test ok.
  }
  else {
    Rmpfr_set_str($reco, $chopped, 10, MPFR_RNDN);
    $ret += 2 if $reco < $op;          # chop test ok.
  }

  # Now we derive a value that is $chopped rounded up to the next lowest
  # decimal representation.
  # This new string should assign to a value that is greater
  # than the given $op.

  if($r[0] =~ /\./) {
    # We must remove the '.', do the string increment,
    # and then reinsert the '.' in the appropriate place.
    my @mantissa = split /\./, $r[0];
    my $point_pos = -(length($mantissa[1]));
    my $t = $mantissa[0] . $mantissa[1];
    $t++ for 1..10;
    substr($t, $point_pos, 0, '.');
    $r[0] = $t;
  }
  else {
    $r[0]++ for 1..10;
  }

  my $incremented = defined($r[1]) ? $r[0] . 'e' . $r[1]
                                   : $r[0];

  print "INCREMENTED:\n$incremented\n" if $debug;

  if($is_nv) {
    $ret += 4 if atonv($incremented) > $op; # increment test ok.
  }
  else {
    Rmpfr_set_str($reco, $incremented, 10, MPFR_RNDN);
    $ret += 4 if $reco > $op;              # increment test ok.
  }

  return $ret;
}

#############################
#############################

sub _mpfr2dd {
  # Can be called from anytoa()
  my $obj = shift;
  my $msd = Rmpfr_get_d($obj, MPFR_RNDN);
  $obj -= $msd;
  return ($msd, Rmpfr_get_d($obj, MPFR_RNDN));
}

sub _intermediate_bits {
  # Can be called from anytoa()
  my($exp1, $exp2) = (_get_exp(shift), _get_exp(shift));
  return $exp1 - 53 - $exp2;
}

sub _get_exp {
  # Can be called from anytoa(), via _intermediate_bits().
  # For as long as we support perl-5.8, we cannot use
  # the "d<" and "d>" templates.
  my $hex;
  if(LITTLE_ENDIAN) {
    $hex = scalar reverse unpack "h*", pack "d", $_[0];
  }
  else {
    $hex = unpack "H*", pack "d", $_[0];
  }
  my $exp = hex(substr($hex, 0, 3));
  $exp -= 2048 if $exp > 2047; # Remove sign bit
  $exp++ unless $exp; # increment if 0
  return ($exp - 1023);
}

*Rmpfr_get_z_exp             = \&Rmpfr_get_z_2exp;
*prec_cast                   = \&Math::MPFR::Prec::prec_cast;
*Rmpfr_randinit_default      = \&Math::MPFR::Random::Rmpfr_randinit_default;
*Rmpfr_randinit_mt           = \&Math::MPFR::Random::Rmpfr_randinit_mt;
*Rmpfr_randinit_lc_2exp      = \&Math::MPFR::Random::Rmpfr_randinit_lc_2exp;
*Rmpfr_randinit_lc_2exp_size = \&Math::MPFR::Random::Rmpfr_randinit_lc_2exp_size;

sub nvtoa {
  # Special handling required for DoubleDouble
  # Unable to get the _nvtoa XSub to work flawlessly with DoubleDoubles,
  # I've switched to using the _mpfrtoa XSub, as I did with Math::FakeDD
  # It's an emabrrassingly awful hack, but will have to do until something
  # better comes along.

  if(NV_IS_DOUBLEDOUBLE) {
    my $nv = shift;

    my $unpacked = unpack "H*", pack "D>", $nv;
    my $msd = unpack "d>", pack "H*", substr($unpacked, 0, 16);  # more significant double
    my $lsd = unpack "d>", pack "H*", substr($unpacked, 16, 16); # less significant double

    my $mpfr = Rmpfr_init2(2098);
    Rmpfr_set_ld($mpfr, $nv, MPFR_RNDN);

    my($neg, $prec, $different_signs) = (Rmpfr_signbit($mpfr), 0, 0);

    unless(Rmpfr_regular_p($mpfr)) {
      if(Rmpfr_zero_p($mpfr)) {
        return "-0.0" if $neg;
        return "0.0";
      }

      return "NaN" if Rmpfr_nan_p($mpfr);

      # Must be Inf
      return "-Inf" if $neg;
      return "Inf";
    }

    # set $mpfr to abs($mpfr)
    # $nv remains unaltered
    if($mpfr < 0) {
      Rmpfr_neg($mpfr, $mpfr, MPFR_RNDN);
      $neg = 1;
    }

    my $exp = Rmpfr_get_exp($mpfr);

    if($lsd == 0) {

      my $addon = 1074;
      unless( MPFR_4_0_2_OR_LATER ) { # 4.0.1 or earlier
        # Prior to mpfr-4.0.2, there are issues with precision < 2,
        # but DBL_DENORM_MIN calls for a precision of one bit.
        # We therefore return the hard coded value for this case.

        if($exp == -1073) {
          # $mpfr is 2 ** -1074
          my $ret = $neg ? '-5e-324' : '5e-324';
          return $ret;
        }
      }

      $prec = $addon + $exp;
      Rmpfr_prec_round($mpfr, $prec, MPFR_RNDN);
      # Provide 2nd arg of 728 to mpfrtoa().
      # 2 ** -348 (prec = 727) needs this.
      return '-' . mpfrtoa($mpfr, 728) if $neg;
      return mpfrtoa($mpfr, 728);
    } # close $lsd == 0

    my $m_msd = Rmpfr_init2(53);
    my $m_lsd = Rmpfr_init2(53);

    Rmpfr_set_d($m_msd, $msd, MPFR_RNDN);
    Rmpfr_set_d($m_lsd, $lsd, MPFR_RNDN);

    if(abs($lsd) >= 2 ** -1022) {
      # lsd is not subnormal.
      $prec = Rmpfr_get_exp($m_msd) - Rmpfr_get_exp($m_lsd) + 53;
      if( ($lsd < 0 && $msd > 0) || ($msd < 0 && $lsd > 0) ) {
        $prec--;
        $different_signs = 1; # one double < 0, the other > 0
      }
      my $mpfr_copy = Rmpfr_init2(2098);
      Rmpfr_set($mpfr_copy, $mpfr, MPFR_RNDN);
      Rmpfr_prec_round($mpfr_copy, $prec, MPFR_RNDN);
      my $trial_repro = mpfrtoa($mpfr_copy);
      my $trial_dd = atonv($trial_repro);
      if($trial_dd == $nv || ($neg == 1 && $trial_dd == abs($nv)) ) {
        return '-' . $trial_repro if $neg;
        return $trial_repro;
      }
      $prec++;
      # Might need to be incremented again if the 2 doubles have different sign.
    }
    else {
      $prec = Rmpfr_get_exp($m_msd) + 1073; # $prec should be > 0
      $prec++ if $prec == 0;

      my $mpfr_copy = Rmpfr_init2(2098);
      Rmpfr_set($mpfr_copy, $mpfr, MPFR_RNDN);
      Rmpfr_prec_round($mpfr_copy, $prec, MPFR_RNDN);
      my $trial_repro = mpfrtoa($mpfr_copy);
      my $trial_dd = atonv($trial_repro);
      if($trial_dd == $nv || ($neg == 1 && $trial_dd == abs($nv)) ) {
        return '-' . $trial_repro if $neg;
        return $trial_repro;
      }

      $prec++;
    }

    my $mpfr_orig = Rmpfr_init2(2098);
    Rmpfr_set($mpfr_orig, $mpfr, MPFR_RNDN); # copy $mpfr to $mpfr_orig

    Rmpfr_prec_round($mpfr, $prec, MPFR_RNDN);

    if($different_signs) {
      my $candidate = mpfrtoa($mpfr, 53);

      # Might fail either the "chop" test or
      # the "round trip" test, but not both.

      if(abs($nv) != atonv($candidate)) {
        # First check whether decrementing the mantissa
        # allows the round trip to succeed.

        my $ret = _decrement($candidate);

        if(abs($nv) == atonv($ret)) {
          return '-' . $ret if $neg;
          return $ret;
        }

        # Fails round trip - so we increment $prec. We then
        # can't use $mpfr again as its precision has already
        # been altered, so we use $mpfr_orig.

        $prec++;
        Rmpfr_prec_round($mpfr_orig, $prec, MPFR_RNDN);
        return '-' . mpfrtoa($mpfr_orig, 53) if $neg;
        return mpfrtoa($mpfr_orig, 53);
      }

      my $ret = _chop_test($candidate, $nv, 0);

      if($ret eq 'ok') {
        return '-' . $candidate if $neg;
        return $candidate;
      }

      # The value we now return is the value calculated
      # for precision $prec, but with the least significant
      # mantissa digit removed.

      return '-' . $ret if $neg;
      return $ret;

    } # close different signs

    else {
      # We need to detect the (rare) case that a chopped and
      # then incremented mantissa passes the round trip.

      my $can = mpfrtoa($mpfr, 53);
      my $ret = _chop_test($can, $nv, 1);

      if($ret eq 'ok') {
        return '-' . $can if $neg;
        return $can;
      }

      return '-' . $ret if $neg;
      return $ret;

    } # close same signs

  }
  else {
    # Not a doubledouble - simply use the _nvtoa XSub
    return _nvtoa(shift);
  }
}

sub numtoa { # Special handling required for DoubleDouble
  if(NV_IS_DOUBLEDOUBLE) {
    my $arg = shift;
    return nvtoa($arg) if _SvNOK($arg);
    return _numtoa($arg);
  }
  else {
    return _numtoa(shift);
  }
}

sub _chop_test {
  my @r = split /e/i, shift;
  my $op = shift;

  # If $do_increment is set, then all we are not interested
  # in the result of the chop test. We are interested in the
  # result of the incrmentation - which we requires that we
  # first perform the chop.

  my $do_increment = defined($_[0]) ? shift
                                    : 0;

  # We remove from $r[0] any trailing mantissa zeroes, and then
  # replace the least significant digit with zero.
  # IOW, we effectively chop off the least siginificant digit, thereby
  # rounding it down to the next lowest decimal precision.)
  # This altered string should assign to a DoubleDouble value that is
  # less than the given $op.

  chop($r[0]) while $r[0] =~ /0$/;
  $r[0] =~ s/\.$//;
  $r[1] = defined $r[1] ? $r[1] : 0;
  while($r[0] =~ /0$/) {
    chop $r[0];
    $r[1]++;
  }

  return 'ok' if length($r[0]) < 2; # chop test inapplicable.

  substr($r[0], -1, 1, '');

  $r[1]++ unless $r[0] =~ /\./;
  $r[0] =~ s/\.$/.0/
    unless $r[1];
  $r[0] =~ s/\.$//;

  if(!$do_increment) {
    # We are interested only in the chop test

    my $chopped = $r[1] ? $r[0] . 'e' . $r[1]
                        : $r[0];

    return 'ok' if atonv($chopped) < abs($op); # chop test ok.
    return $chopped;
  }

  # We are not interested in the chop test - the "chop" was
  # done only as the first step in the incrementation, and
  # it's the result of the following  incrementation that
  # interests us. Now we want, in effect, to do:
  #  ++$r[0];
  # This value should then assign to a  DoubleDouble value
  # that is greater than the given $op.

  if($r[0] =~ /\./) {
    # We must remove the '.', do the string increment,
    # and then reinsert the '.' in the appropriate place.
    my @mantissa = split /\./, $r[0];
    my $point_pos = -(length($mantissa[1]));
    my $t = $mantissa[0] . $mantissa[1];
    $t++;
    substr($t, $point_pos, 0, '.');
    $r[0] = $t;
  }
  else {
    $r[0]++;
    $r[1]++ while $r[0] =~ s/0$//;
  }


  my $incremented = $r[1] ? $r[0] . 'e' . $r[1]
                          : $r[0];

  return $incremented if atonv($incremented) == abs($op);
  return 'ok';
}

sub _decrement {
  my $shift = shift;
  my @r = split /e/i, $shift;

  # Remove all trailing zeroes from $r[0];

  if($r[0] =~ /\./) {
    chop($r[0]) while $r[0] =~ /0$/;
  }

  $r[0] =~ s/\.$//;
  $r[1] = defined $r[1] ? $r[1] : 0;
  while($r[0] =~ /0$/) {
    chop $r[0];
    $r[1]++;
  }

  return $shift if length($r[0]) < 2;

  my $substitute = substr($r[0], -1, 1) - 1;
  substr($r[0], -1, 1, "$substitute");

  my $ret = $r[1] ? $r[0] . 'e' . $r[1]
                  : $r[0];
  return $ret;
}

sub _rewrite_fmt_arg {
  # Can Return a true value if and only if the constant
  # WIN32_FMT_BUG is set to a true value, in which case it
  # returns a rewritten format string.
  # We allow "%a"/"%A" formatting only if nvtype is 'double' and
  # we allow "%La"/"%LA" formatting only if nvtype is 'long double'.

  my $arg = shift;
  # First check for a match of (eg) "%La" or "%A"
  # at the beginning of $arg.
  if($arg =~ /^%L?[a,A]/) {
    my $match = $&;
    if(!Math::MPFR::_SvNOK($_[0])) { die "\"$match\" formatting applies only to NVs. Use \"%Ra\" for Math::MPFR objects." }
    if($match =~ /L/) { die "\"$match\" formatting applies only to long doubles." unless $Config{nvtype} eq 'long double'; }
    else { die "\"$match\" formatting applies only to doubles." unless $Config{nvtype} eq 'double'; }
    if(WIN32_FMT_BUG) {
      $arg =~ s/^%L?/%R/;
      return $arg;
    }
    return '';
  }

  # Need to match (eg) "%La" or "%A", but also to NOT match (eg) "%%La" or "%%A".
  if($arg =~ /[^%]%L?[a,A]/) {
    my $match = $&;
    if(!Math::MPFR::_SvNOK($_[0])) { die "\"", substr($match, 1), "\" formatting applies only to NVs. Use \"%Ra\" for Math::MPFR objects." }
    if($match =~ /L/) { die "\"", substr($match, 1), "\" formatting applies only to long doubles." unless $Config{nvtype} eq 'long double'; }
    else { die "\"", substr($match, 1), "\" formatting applies only to doubles." unless $Config{nvtype} eq 'double'; }
    if(WIN32_FMT_BUG) {
      my $and_init = $match;
      my $temp = $match;
      my $start = substr($temp, 0, 1, '');
      $temp =~ s/^%L?/%R/;
      $start .= $temp;
      $arg =~ s/$and_init/$start/;
      return $arg;
    }
  }
  return ''; # Nothing to modify - no action necessary.
}

sub nv2mpfr {
  my $prec = Rmpfr_get_default_prec();
  Rmpfr_set_default_prec($Math::MPFR::NV_properties{bits});
  my $ret = Math::MPFR->new($_[0]);
  Rmpfr_set_default_prec($prec);
  return $ret;
}

sub _win32_formatting_ok {   # Duplicated in Random/Random.pm
    # Return 1 if either __GMP_CC or __GMP_CFLAGS
    # include the string '-D__USE_MINGW_ANSI_STDIO'.
    # Else return 0.

    my $cc = _gmp_cc();		# __GMP_CC
    my $cflags = _gmp_cflags();	# __GMP_CFLAGS

    return 1 if ( defined($cc)     && $cc     =~/\-D__USE_MINGW_ANSI_STDIO/ );
    return 1 if ( defined($cflags) && $cflags =~/\-D__USE_MINGW_ANSI_STDIO/ );
    return 0;
}

sub _hex_fmt_ok {
  # Return 1 if no hex ("%a") formatting is requested.
  # Return 1 if the requested hex format ("%a"/"%A"/"%La"/"%LA") is appropriate.
  # If we haven't died or returned by now, then return 0 if WIN32_FMT_BUG is set;
  # otherwise return 1.
  # A return of 1 tells the caller (Rmpfr_*printf) that no other action is necessary.
  # A return of 0 tells the caller(Rmpfr_*printf) that it needs to call _rewrite_fmt_arg().

  my $fmt = shift;

  if($fmt =~ /^%L?[a,A]|[^%]%L?[a,A]/) {
     $fmt = $&;
     if(!Math::MPFR::_SvNOK($_[0])) { die "\"%a\" formatting applies only to NVs. Use \"%Ra\" for Math::MPFR objects." }
     if($fmt =~ /L/) { die "\"%La\" formatting applies only to long doubles." unless $Config{nvtype} eq 'long double'; }
     else { die "\"%a\" formatting applies only to doubles." unless $Config{nvtype} eq 'double'; }
     return 0 if WIN32_FMT_BUG; # Tells the caller to call the relevant _gmp_*printf_nv() function
     return 1;
  }
  else {return 1} # No %a formatting requested. Proceed as normal.
}

sub overload_lshift {
  if($_[2] || !_looks_like_number($_[1])) {
    die "Math::MPFR: When overloading '<<', the argument that specifies the number of bits to be shifted must be a perl number";
  }
  return _overload_lshift(@_) if $_[1] >= 0;
  return _overload_rshift($_[0], -$_[1], $_[2]);
}

sub overload_lshift_eq {
  if($_[2] || !_looks_like_number($_[1])) {
    die "Math::MPFR: When overloading '<<=', the argument that specifies the number of bits to be shifted must be a perl number";
  }
  return _overload_lshift_eq(@_) if $_[1] >= 0;
  return _overload_rshift_eq($_[0], -$_[1], $_[2]);
}

sub overload_rshift {
  if($_[2] || !_looks_like_number($_[1])) {
    die "Math::MPFR: When overloading '>>', the argument that specifies the number of bits to be shifted must be a perl number";
  }
  return _overload_rshift(@_) if $_[1] >= 0;
  return _overload_lshift($_[0], -$_[1], $_[2]);
}

sub overload_rshift_eq {
  if($_[2] || !_looks_like_number($_[1])) {
    die "Math::MPFR: When overloading '>>=', the argument that specifies the number of bits to be shifted must be a perl number";
  }
  return _overload_rshift_eq(@_) if $_[1] >= 0;
  return _overload_lshift_eq($_[0], -$_[1], $_[2]);
}

sub overload_fmod {
  if(ref($_[1]) ne 'Math::MPFR') {
    return _overload_fmod($_[0], Math::MPFR->new($_[1]), 0) unless $_[2];
    return _overload_fmod(Math::MPFR->new($_[1]), $_[0], 0);
  }
  return _overload_fmod(@_);
}

sub overload_fmod_eq {
  if(ref($_[1]) ne 'Math::MPFR') {
    return _overload_fmod_eq($_[0], Math::MPFR->new($_[1]), 0) unless $_[2];
    return _overload_fmod_eq(Math::MPFR->new($_[1]), $_[0], 0);
  }
  return _overload_fmod_eq(@_);
}


1;

__END__