summaryrefslogtreecommitdiff
path: root/Master/tlpkg/tlperl/lib/pods/perlfaq4.pod
blob: eb18743f8228ab425c380e17ebc726a30fbe7b63 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
=head1 NAME

perlfaq4 - Data Manipulation

=head1 DESCRIPTION

This section of the FAQ answers questions related to manipulating
numbers, dates, strings, arrays, hashes, and miscellaneous data issues.

=head1 Data: Numbers

=head2 Why am I getting long decimals (eg, 19.9499999999999) instead of the numbers I should be getting (eg, 19.95)?

For the long explanation, see David Goldberg's "What Every Computer
Scientist Should Know About Floating-Point Arithmetic"
(L<http://web.cse.msu.edu/~cse320/Documents/FloatingPoint.pdf>).

Internally, your computer represents floating-point numbers in binary.
Digital (as in powers of two) computers cannot store all numbers
exactly.  Some real numbers lose precision in the process.  This is a
problem with how computers store numbers and affects all computer
languages, not just Perl.

L<perlnumber> shows the gory details of number representations and
conversions.

To limit the number of decimal places in your numbers, you can use the
C<printf> or C<sprintf> function.  See
L<perlop/"Floating Point Arithmetic"> for more details.

	printf "%.2f", 10/3;

	my $number = sprintf "%.2f", 10/3;

=head2 Why is int() broken?

Your C<int()> is most probably working just fine.  It's the numbers that
aren't quite what you think.

First, see the answer to "Why am I getting long decimals
(eg, 19.9499999999999) instead of the numbers I should be getting
(eg, 19.95)?".

For example, this

	print int(0.6/0.2-2), "\n";

will in most computers print 0, not 1, because even such simple
numbers as 0.6 and 0.2 cannot be presented exactly by floating-point
numbers.  What you think in the above as 'three' is really more like
2.9999999999999995559.

=head2 Why isn't my octal data interpreted correctly?

(contributed by brian d foy)

You're probably trying to convert a string to a number, which Perl only
converts as a decimal number. When Perl converts a string to a number, it
ignores leading spaces and zeroes, then assumes the rest of the digits
are in base 10:

	my $string = '0644';

	print $string + 0;  # prints 644

	print $string + 44; # prints 688, certainly not octal!

This problem usually involves one of the Perl built-ins that has the
same name a Unix command that uses octal numbers as arguments on the
command line. In this example, C<chmod> on the command line knows that
its first argument is octal because that's what it does:

	%prompt> chmod 644 file

If you want to use the same literal digits (644) in Perl, you have to tell
Perl to treat them as octal numbers either by prefixing the digits with
a C<0> or using C<oct>:

	chmod(     0644, $file);   # right, has leading zero
	chmod( oct(644), $file );  # also correct

The problem comes in when you take your numbers from something that Perl
thinks is a string, such as a command line argument in C<@ARGV>:

	chmod( $ARGV[0],      $file);   # wrong, even if "0644"

	chmod( oct($ARGV[0]), $file );  # correct, treat string as octal

You can always check the value you're using by printing it in octal
notation to ensure it matches what you think it should be. Print it
in octal  and decimal format:

	printf "0%o %d", $number, $number;

=head2 Does Perl have a round() function?  What about ceil() and floor()?  Trig functions?

Remember that C<int()> merely truncates toward 0.  For rounding to a
certain number of digits, C<sprintf()> or C<printf()> is usually the
easiest route.

	printf("%.3f", 3.1415926535);   # prints 3.142

The C<POSIX> module (part of the standard Perl distribution)
implements C<ceil()>, C<floor()>, and a number of other mathematical
and trigonometric functions.

	use POSIX;
	$ceil   = ceil(3.5);   # 4
	$floor  = floor(3.5);  # 3

In 5.000 to 5.003 perls, trigonometry was done in the C<Math::Complex>
module.  With 5.004, the C<Math::Trig> module (part of the standard Perl
distribution) implements the trigonometric functions. Internally it
uses the C<Math::Complex> module and some functions can break out from
the real axis into the complex plane, for example the inverse sine of
2.

Rounding in financial applications can have serious implications, and
the rounding method used should be specified precisely.  In these
cases, it probably pays not to trust whichever system of rounding is
being used by Perl, but instead to implement the rounding function you
need yourself.

To see why, notice how you'll still have an issue on half-way-point
alternation:

	for ($i = 0; $i < 1.01; $i += 0.05) { printf "%.1f ",$i}

	0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.7 0.7
	0.8 0.8 0.9 0.9 1.0 1.0

Don't blame Perl.  It's the same as in C.  IEEE says we have to do
this. Perl numbers whose absolute values are integers under 2**31 (on
32-bit machines) will work pretty much like mathematical integers.
Other numbers are not guaranteed.

=head2 How do I convert between numeric representations/bases/radixes?

As always with Perl there is more than one way to do it.  Below are a
few examples of approaches to making common conversions between number
representations.  This is intended to be representational rather than
exhaustive.

Some of the examples later in L<perlfaq4> use the C<Bit::Vector>
module from CPAN. The reason you might choose C<Bit::Vector> over the
perl built-in functions is that it works with numbers of ANY size,
that it is optimized for speed on some operations, and for at least
some programmers the notation might be familiar.

=over 4

=item How do I convert hexadecimal into decimal

Using perl's built in conversion of C<0x> notation:

	$dec = 0xDEADBEEF;

Using the C<hex> function:

	$dec = hex("DEADBEEF");

Using C<pack>:

	$dec = unpack("N", pack("H8", substr("0" x 8 . "DEADBEEF", -8)));

Using the CPAN module C<Bit::Vector>:

	use Bit::Vector;
	$vec = Bit::Vector->new_Hex(32, "DEADBEEF");
	$dec = $vec->to_Dec();

=item How do I convert from decimal to hexadecimal

Using C<sprintf>:

	$hex = sprintf("%X", 3735928559); # upper case A-F
	$hex = sprintf("%x", 3735928559); # lower case a-f

Using C<unpack>:

	$hex = unpack("H*", pack("N", 3735928559));

Using C<Bit::Vector>:

	use Bit::Vector;
	$vec = Bit::Vector->new_Dec(32, -559038737);
	$hex = $vec->to_Hex();

And C<Bit::Vector> supports odd bit counts:

	use Bit::Vector;
	$vec = Bit::Vector->new_Dec(33, 3735928559);
	$vec->Resize(32); # suppress leading 0 if unwanted
	$hex = $vec->to_Hex();

=item How do I convert from octal to decimal

Using Perl's built in conversion of numbers with leading zeros:

	$dec = 033653337357; # note the leading 0!

Using the C<oct> function:

	$dec = oct("33653337357");

Using C<Bit::Vector>:

	use Bit::Vector;
	$vec = Bit::Vector->new(32);
	$vec->Chunk_List_Store(3, split(//, reverse "33653337357"));
	$dec = $vec->to_Dec();

=item How do I convert from decimal to octal

Using C<sprintf>:

	$oct = sprintf("%o", 3735928559);

Using C<Bit::Vector>:

	use Bit::Vector;
	$vec = Bit::Vector->new_Dec(32, -559038737);
	$oct = reverse join('', $vec->Chunk_List_Read(3));

=item How do I convert from binary to decimal

Perl 5.6 lets you write binary numbers directly with
the C<0b> notation:

	$number = 0b10110110;

Using C<oct>:

	my $input = "10110110";
	$decimal = oct( "0b$input" );

Using C<pack> and C<ord>:

	$decimal = ord(pack('B8', '10110110'));

Using C<pack> and C<unpack> for larger strings:

	$int = unpack("N", pack("B32",
	substr("0" x 32 . "11110101011011011111011101111", -32)));
	$dec = sprintf("%d", $int);

	# substr() is used to left-pad a 32-character string with zeros.

Using C<Bit::Vector>:

	$vec = Bit::Vector->new_Bin(32, "11011110101011011011111011101111");
	$dec = $vec->to_Dec();

=item How do I convert from decimal to binary

Using C<sprintf> (perl 5.6+):

	$bin = sprintf("%b", 3735928559);

Using C<unpack>:

	$bin = unpack("B*", pack("N", 3735928559));

Using C<Bit::Vector>:

	use Bit::Vector;
	$vec = Bit::Vector->new_Dec(32, -559038737);
	$bin = $vec->to_Bin();

The remaining transformations (e.g. hex -> oct, bin -> hex, etc.)
are left as an exercise to the inclined reader.

=back

=head2 Why doesn't & work the way I want it to?

The behavior of binary arithmetic operators depends on whether they're
used on numbers or strings.  The operators treat a string as a series
of bits and work with that (the string C<"3"> is the bit pattern
C<00110011>).  The operators work with the binary form of a number
(the number C<3> is treated as the bit pattern C<00000011>).

So, saying C<11 & 3> performs the "and" operation on numbers (yielding
C<3>).  Saying C<"11" & "3"> performs the "and" operation on strings
(yielding C<"1">).

Most problems with C<&> and C<|> arise because the programmer thinks
they have a number but really it's a string or vice versa.  To avoid this,
stringify the arguments explicitly (using C<""> or C<qq()>) or convert them
to numbers explicitly (using C<0+$arg>). The rest arise because
the programmer says:

	if ("\020\020" & "\101\101") {
		# ...
		}

but a string consisting of two null bytes (the result of C<"\020\020"
& "\101\101">) is not a false value in Perl.  You need:

	if ( ("\020\020" & "\101\101") !~ /[^\000]/) {
		# ...
		}

=head2 How do I multiply matrices?

Use the C<Math::Matrix> or C<Math::MatrixReal> modules (available from CPAN)
or the C<PDL> extension (also available from CPAN).

=head2 How do I perform an operation on a series of integers?

To call a function on each element in an array, and collect the
results, use:

	@results = map { my_func($_) } @array;

For example:

	@triple = map { 3 * $_ } @single;

To call a function on each element of an array, but ignore the
results:

	foreach $iterator (@array) {
		some_func($iterator);
		}

To call a function on each integer in a (small) range, you B<can> use:

	@results = map { some_func($_) } (5 .. 25);

but you should be aware that the C<..> operator creates a list of
all integers in the range.  This can take a lot of memory for large
ranges.  Instead use:

	@results = ();
	for ($i=5; $i <= 500_005; $i++) {
		push(@results, some_func($i));
		}

This situation has been fixed in Perl5.005. Use of C<..> in a C<for>
loop will iterate over the range, without creating the entire range.

	for my $i (5 .. 500_005) {
		push(@results, some_func($i));
		}

will not create a list of 500,000 integers.

=head2 How can I output Roman numerals?

Get the L<http://www.cpan.org/modules/by-module/Roman> module.

=head2 Why aren't my random numbers random?

If you're using a version of Perl before 5.004, you must call C<srand>
once at the start of your program to seed the random number generator.

	 BEGIN { srand() if $] < 5.004 }

5.004 and later automatically call C<srand> at the beginning.  Don't
call C<srand> more than once--you make your numbers less random,
rather than more.

Computers are good at being predictable and bad at being random
(despite appearances caused by bugs in your programs :-).  The
F<random> article in the "Far More Than You Ever Wanted To Know"
collection in L<http://www.cpan.org/misc/olddoc/FMTEYEWTK.tgz>, courtesy
of Tom Phoenix, talks more about this.  John von Neumann said, "Anyone
who attempts to generate random numbers by deterministic means is, of
course, living in a state of sin."

If you want numbers that are more random than C<rand> with C<srand>
provides, you should also check out the C<Math::TrulyRandom> module from
CPAN.  It uses the imperfections in your system's timer to generate
random numbers, but this takes quite a while.  If you want a better
pseudorandom generator than comes with your operating system, look at
"Numerical Recipes in C" at L<http://www.nr.com/>.

=head2 How do I get a random number between X and Y?

To get a random number between two values, you can use the C<rand()>
built-in to get a random number between 0 and 1. From there, you shift
that into the range that you want.

C<rand($x)> returns a number such that C<< 0 <= rand($x) < $x >>. Thus
what you want to have perl figure out is a random number in the range
from 0 to the difference between your I<X> and I<Y>.

That is, to get a number between 10 and 15, inclusive, you want a
random number between 0 and 5 that you can then add to 10.

	my $number = 10 + int rand( 15-10+1 ); # ( 10,11,12,13,14, or 15 )

Hence you derive the following simple function to abstract
that. It selects a random integer between the two given
integers (inclusive), For example: C<random_int_between(50,120)>.

	sub random_int_between {
		my($min, $max) = @_;
		# Assumes that the two arguments are integers themselves!
		return $min if $min == $max;
		($min, $max) = ($max, $min)  if  $min > $max;
		return $min + int rand(1 + $max - $min);
		}

=head1 Data: Dates

=head2 How do I find the day or week of the year?

The day of the year is in the list returned
by the C<localtime> function. Without an
argument C<localtime> uses the current time.

	my $day_of_year = (localtime)[7];

The C<POSIX> module can also format a date as the day of the year or
week of the year.

	use POSIX qw/strftime/;
	my $day_of_year  = strftime "%j", localtime;
	my $week_of_year = strftime "%W", localtime;

To get the day of year for any date, use C<POSIX>'s C<mktime> to get
a time in epoch seconds for the argument to C<localtime>.

	use POSIX qw/mktime strftime/;
	my $week_of_year = strftime "%W",
		localtime( mktime( 0, 0, 0, 18, 11, 87 ) );

You can also use C<Time::Piece>, which comes with Perl and provides a
C<localtime> that returns an object:

	use Time::Piece;
	my $day_of_year  = localtime->yday;
	my $week_of_year = localtime->week;

The C<Date::Calc> module provides two functions to calculate these, too:

	use Date::Calc;
	my $day_of_year  = Day_of_Year(  1987, 12, 18 );
	my $week_of_year = Week_of_Year( 1987, 12, 18 );

=head2 How do I find the current century or millennium?

Use the following simple functions:

	sub get_century    {
		return int((((localtime(shift || time))[5] + 1999))/100);
		}

	sub get_millennium {
		return 1+int((((localtime(shift || time))[5] + 1899))/1000);
		}

On some systems, the C<POSIX> module's C<strftime()> function has been
extended in a non-standard way to use a C<%C> format, which they
sometimes claim is the "century". It isn't, because on most such
systems, this is only the first two digits of the four-digit year, and
thus cannot be used to determine reliably the current century or
millennium.

=head2 How can I compare two dates and find the difference?

(contributed by brian d foy)

You could just store all your dates as a number and then subtract.
Life isn't always that simple though. 

The C<Time::Piece> module, which comes with Perl, replaces C<localtime>
with a version that returns an object. It also overloads the comparison
operators so you can compare them directly:

	use Time::Piece;
	my $date1 = localtime( $some_time );
	my $date2 = localtime( $some_other_time );
	
	if( $date1 < $date2 ) {
		print "The date was in the past\n";
		}

You can also get differences with a subtraction, which returns a 
C<Time::Seconds> object:

	my $diff = $date1 - $date2;
	print "The difference is ", $date_diff->days, " days\n";

If you want to work with formatted dates, the C<Date::Manip>,
C<Date::Calc>, or C<DateTime> modules can help you.

=head2 How can I take a string and turn it into epoch seconds?

If it's a regular enough string that it always has the same format,
you can split it up and pass the parts to C<timelocal> in the standard
C<Time::Local> module.  Otherwise, you should look into the C<Date::Calc>,
C<Date::Parse>, and C<Date::Manip> modules from CPAN.

=head2 How can I find the Julian Day?

(contributed by brian d foy and Dave Cross)

You can use the C<Time::Piece> module, part of the Standard Library,
which can convert a date/time to a Julian Day:

	$ perl -MTime::Piece -le 'print localtime->julian_day'
	2455607.7959375

Or the modified Julian Day:

	$ perl -MTime::Piece -le 'print localtime->mjd'
	55607.2961226851

Or even the day of the year (which is what some people think of as a
Julian day):

	$ perl -MTime::Piece -le 'print localtime->yday'
	45

You can also do the same things with the C<DateTime> module:

	$ perl -MDateTime -le'print DateTime->today->jd'
	2453401.5
	$ perl -MDateTime -le'print DateTime->today->mjd'
	53401
	$ perl -MDateTime -le'print DateTime->today->doy'
	31

You can use the C<Time::JulianDay> module available on CPAN.  Ensure
that you really want to find a Julian day, though, as many people have
different ideas about Julian days (see http://www.hermetic.ch/cal_stud/jdn.htm 
for instance):

	$  perl -MTime::JulianDay -le 'print local_julian_day( time )'
	55608

=head2 How do I find yesterday's date?
X<date> X<yesterday> X<DateTime> X<Date::Calc> X<Time::Local>
X<daylight saving time> X<day> X<Today_and_Now> X<localtime>
X<timelocal>

(contributed by brian d foy)

To do it correctly, you can use one of the C<Date> modules since they
work with calendars instead of times. The C<DateTime> module makes it
simple, and give you the same time of day, only the day before,
despite daylight saving time changes:

	use DateTime;

	my $yesterday = DateTime->now->subtract( days => 1 );

	print "Yesterday was $yesterday\n";

You can also use the C<Date::Calc> module using its C<Today_and_Now>
function.

	use Date::Calc qw( Today_and_Now Add_Delta_DHMS );

	my @date_time = Add_Delta_DHMS( Today_and_Now(), -1, 0, 0, 0 );

	print "@date_time\n";

Most people try to use the time rather than the calendar to figure out
dates, but that assumes that days are twenty-four hours each.  For
most people, there are two days a year when they aren't: the switch to
and from summer time throws this off. For example, the rest of the 
suggestions will be wrong sometimes:

Starting with Perl 5.10, C<Time::Piece> and C<Time::Seconds> are part
of the standard distribution, so you might think that you could do 
something like this:

	use Time::Piece;
	use Time::Seconds;
	
	my $yesterday = localtime() - ONE_DAY; # WRONG
	print "Yesterday was $yesterday\n";

The C<Time::Piece> module exports a new C<localtime> that returns an
object, and C<Time::Seconds> exports the C<ONE_DAY> constant that is a
set number of seconds. This means that it always gives the time 24
hours ago, which is not always yesterday. This can cause problems
around the end of daylight saving time when there's one day that is 25
hours long.

You have the same problem with C<Time::Local>, which will give the wrong
answer for those same special cases:

	# contributed by Gunnar Hjalmarsson
	 use Time::Local;
	 my $today = timelocal 0, 0, 12, ( localtime )[3..5];
	 my ($d, $m, $y) = ( localtime $today-86400 )[3..5]; # WRONG
	 printf "Yesterday: %d-%02d-%02d\n", $y+1900, $m+1, $d;

=head2 Does Perl have a Year 2000 or 2038 problem? Is Perl Y2K compliant?

(contributed by brian d foy)

Perl itself never had a Y2K problem, although that never stopped people
from creating Y2K problems on their own. See the documentation for
C<localtime> for its proper use.

Starting with Perl 5.12, C<localtime> and C<gmtime> can handle dates past
03:14:08 January 19, 2038, when a 32-bit based time would overflow. You
still might get a warning on a 32-bit C<perl>:

	% perl5.12 -E 'say scalar localtime( 0x9FFF_FFFFFFFF )'
	Integer overflow in hexadecimal number at -e line 1.
	Wed Nov  1 19:42:39 5576711

On a 64-bit C<perl>, you can get even larger dates for those really long
running projects:

	% perl5.12 -E 'say scalar gmtime( 0x9FFF_FFFFFFFF )'
	Thu Nov  2 00:42:39 5576711

You're still out of luck if you need to keep track of decaying protons
though.

=head1 Data: Strings

=head2 How do I validate input?

(contributed by brian d foy)

There are many ways to ensure that values are what you expect or
want to accept. Besides the specific examples that we cover in the
perlfaq, you can also look at the modules with "Assert" and "Validate"
in their names, along with other modules such as C<Regexp::Common>.

Some modules have validation for particular types of input, such
as C<Business::ISBN>, C<Business::CreditCard>, C<Email::Valid>,
and C<Data::Validate::IP>.

=head2 How do I unescape a string?

It depends just what you mean by "escape".  URL escapes are dealt
with in L<perlfaq9>.  Shell escapes with the backslash (C<\>)
character are removed with

	s/\\(.)/$1/g;

This won't expand C<"\n"> or C<"\t"> or any other special escapes.

=head2 How do I remove consecutive pairs of characters?

(contributed by brian d foy)

You can use the substitution operator to find pairs of characters (or
runs of characters) and replace them with a single instance. In this
substitution, we find a character in C<(.)>. The memory parentheses
store the matched character in the back-reference C<\g1> and we use
that to require that the same thing immediately follow it. We replace
that part of the string with the character in C<$1>.

	s/(.)\g1/$1/g;

We can also use the transliteration operator, C<tr///>. In this
example, the search list side of our C<tr///> contains nothing, but
the C<c> option complements that so it contains everything. The
replacement list also contains nothing, so the transliteration is
almost a no-op since it won't do any replacements (or more exactly,
replace the character with itself). However, the C<s> option squashes
duplicated and consecutive characters in the string so a character
does not show up next to itself

	my $str = 'Haarlem';   # in the Netherlands
	$str =~ tr///cs;       # Now Harlem, like in New York

=head2 How do I expand function calls in a string?

(contributed by brian d foy)

This is documented in L<perlref>, and although it's not the easiest
thing to read, it does work. In each of these examples, we call the
function inside the braces used to dereference a reference. If we
have more than one return value, we can construct and dereference an
anonymous array. In this case, we call the function in list context.

	print "The time values are @{ [localtime] }.\n";

If we want to call the function in scalar context, we have to do a bit
more work. We can really have any code we like inside the braces, so
we simply have to end with the scalar reference, although how you do
that is up to you, and you can use code inside the braces. Note that
the use of parens creates a list context, so we need C<scalar> to
force the scalar context on the function:

	print "The time is ${\(scalar localtime)}.\n"

	print "The time is ${ my $x = localtime; \$x }.\n";

If your function already returns a reference, you don't need to create
the reference yourself.

	sub timestamp { my $t = localtime; \$t }

	print "The time is ${ timestamp() }.\n";

The C<Interpolation> module can also do a lot of magic for you. You can
specify a variable name, in this case C<E>, to set up a tied hash that
does the interpolation for you. It has several other methods to do this
as well.

	use Interpolation E => 'eval';
	print "The time values are $E{localtime()}.\n";

In most cases, it is probably easier to simply use string concatenation,
which also forces scalar context.

	print "The time is " . localtime() . ".\n";

=head2 How do I find matching/nesting anything?

This isn't something that can be done in one regular expression, no
matter how complicated.  To find something between two single
characters, a pattern like C</x([^x]*)x/> will get the intervening
bits in $1. For multiple ones, then something more like
C</alpha(.*?)omega/> would be needed. But none of these deals with
nested patterns.  For balanced expressions using C<(>, C<{>, C<[> or
C<< < >> as delimiters, use the CPAN module Regexp::Common, or see
L<perlre/(??{ code })>.  For other cases, you'll have to write a
parser.

If you are serious about writing a parser, there are a number of
modules or oddities that will make your life a lot easier.  There are
the CPAN modules C<Parse::RecDescent>, C<Parse::Yapp>, and
C<Text::Balanced>; and the C<byacc> program. Starting from perl 5.8
the C<Text::Balanced> is part of the standard distribution.

One simple destructive, inside-out approach that you might try is to
pull out the smallest nesting parts one at a time:

	while (s/BEGIN((?:(?!BEGIN)(?!END).)*)END//gs) {
		# do something with $1
		}

A more complicated and sneaky approach is to make Perl's regular
expression engine do it for you.  This is courtesy Dean Inada, and
rather has the nature of an Obfuscated Perl Contest entry, but it
really does work:

	# $_ contains the string to parse
	# BEGIN and END are the opening and closing markers for the
	# nested text.

	@( = ('(','');
	@) = (')','');
	($re=$_)=~s/((BEGIN)|(END)|.)/$)[!$3]\Q$1\E$([!$2]/gs;
	@$ = (eval{/$re/},$@!~/unmatched/i);
	print join("\n",@$[0..$#$]) if( $$[-1] );

=head2 How do I reverse a string?

Use C<reverse()> in scalar context, as documented in
L<perlfunc/reverse>.

	$reversed = reverse $string;

=head2 How do I expand tabs in a string?

You can do it yourself:

	1 while $string =~ s/\t+/' ' x (length($&) * 8 - length($`) % 8)/e;

Or you can just use the C<Text::Tabs> module (part of the standard Perl
distribution).

	use Text::Tabs;
	@expanded_lines = expand(@lines_with_tabs);

=head2 How do I reformat a paragraph?

Use C<Text::Wrap> (part of the standard Perl distribution):

	use Text::Wrap;
	print wrap("\t", '  ', @paragraphs);

The paragraphs you give to C<Text::Wrap> should not contain embedded
newlines.  C<Text::Wrap> doesn't justify the lines (flush-right).

Or use the CPAN module C<Text::Autoformat>.  Formatting files can be
easily done by making a shell alias, like so:

	alias fmt="perl -i -MText::Autoformat -n0777 \
		-e 'print autoformat $_, {all=>1}' $*"

See the documentation for C<Text::Autoformat> to appreciate its many
capabilities.

=head2 How can I access or change N characters of a string?

You can access the first characters of a string with substr().
To get the first character, for example, start at position 0
and grab the string of length 1.


	$string = "Just another Perl Hacker";
	$first_char = substr( $string, 0, 1 );  #  'J'

To change part of a string, you can use the optional fourth
argument which is the replacement string.

	substr( $string, 13, 4, "Perl 5.8.0" );

You can also use substr() as an lvalue.

	substr( $string, 13, 4 ) =  "Perl 5.8.0";

=head2 How do I change the Nth occurrence of something?

You have to keep track of N yourself.  For example, let's say you want
to change the fifth occurrence of C<"whoever"> or C<"whomever"> into
C<"whosoever"> or C<"whomsoever">, case insensitively.  These
all assume that $_ contains the string to be altered.

	$count = 0;
	s{((whom?)ever)}{
	++$count == 5       # is it the 5th?
	    ? "${2}soever"  # yes, swap
	    : $1            # renege and leave it there
		}ige;

In the more general case, you can use the C</g> modifier in a C<while>
loop, keeping count of matches.

	$WANT = 3;
	$count = 0;
	$_ = "One fish two fish red fish blue fish";
	while (/(\w+)\s+fish\b/gi) {
		if (++$count == $WANT) {
			print "The third fish is a $1 one.\n";
			}
		}

That prints out: C<"The third fish is a red one.">  You can also use a
repetition count and repeated pattern like this:

	/(?:\w+\s+fish\s+){2}(\w+)\s+fish/i;

=head2 How can I count the number of occurrences of a substring within a string?

There are a number of ways, with varying efficiency.  If you want a
count of a certain single character (X) within a string, you can use the
C<tr///> function like so:

	$string = "ThisXlineXhasXsomeXx'sXinXit";
	$count = ($string =~ tr/X//);
	print "There are $count X characters in the string";

This is fine if you are just looking for a single character.  However,
if you are trying to count multiple character substrings within a
larger string, C<tr///> won't work.  What you can do is wrap a while()
loop around a global pattern match.  For example, let's count negative
integers:

	$string = "-9 55 48 -2 23 -76 4 14 -44";
	while ($string =~ /-\d+/g) { $count++ }
	print "There are $count negative numbers in the string";

Another version uses a global match in list context, then assigns the
result to a scalar, producing a count of the number of matches.

	$count = () = $string =~ /-\d+/g;

=head2 How do I capitalize all the words on one line?
X<Text::Autoformat> X<capitalize> X<case, title> X<case, sentence>

(contributed by brian d foy)

Damian Conway's L<Text::Autoformat> handles all of the thinking
for you.

	use Text::Autoformat;
	my $x = "Dr. Strangelove or: How I Learned to Stop ".
	  "Worrying and Love the Bomb";

	print $x, "\n";
	for my $style (qw( sentence title highlight )) {
		print autoformat($x, { case => $style }), "\n";
		}

How do you want to capitalize those words?

	FRED AND BARNEY'S LODGE        # all uppercase
	Fred And Barney's Lodge        # title case
	Fred and Barney's Lodge        # highlight case

It's not as easy a problem as it looks. How many words do you think
are in there? Wait for it... wait for it.... If you answered 5
you're right. Perl words are groups of C<\w+>, but that's not what
you want to capitalize. How is Perl supposed to know not to capitalize
that C<s> after the apostrophe? You could try a regular expression:

	$string =~ s/ (
				 (^\w)    #at the beginning of the line
				   |      # or
				 (\s\w)   #preceded by whitespace
				   )
				/\U$1/xg;

	$string =~ s/([\w']+)/\u\L$1/g;

Now, what if you don't want to capitalize that "and"? Just use
L<Text::Autoformat> and get on with the next problem. :)

=head2 How can I split a [character]-delimited string except when inside [character]?

Several modules can handle this sort of parsing--C<Text::Balanced>,
C<Text::CSV>, C<Text::CSV_XS>, and C<Text::ParseWords>, among others.

Take the example case of trying to split a string that is
comma-separated into its different fields. You can't use C<split(/,/)>
because you shouldn't split if the comma is inside quotes.  For
example, take a data line like this:

	SAR001,"","Cimetrix, Inc","Bob Smith","CAM",N,8,1,0,7,"Error, Core Dumped"

Due to the restriction of the quotes, this is a fairly complex
problem.  Thankfully, we have Jeffrey Friedl, author of
I<Mastering Regular Expressions>, to handle these for us.  He
suggests (assuming your string is contained in C<$text>):

	 @new = ();
	 push(@new, $+) while $text =~ m{
		 "([^\"\\]*(?:\\.[^\"\\]*)*)",?  # groups the phrase inside the quotes
		| ([^,]+),?
		| ,
		}gx;
	 push(@new, undef) if substr($text,-1,1) eq ',';

If you want to represent quotation marks inside a
quotation-mark-delimited field, escape them with backslashes (eg,
C<"like \"this\"">.

Alternatively, the C<Text::ParseWords> module (part of the standard
Perl distribution) lets you say:

	use Text::ParseWords;
	@new = quotewords(",", 0, $text);

=head2 How do I strip blank space from the beginning/end of a string?

(contributed by brian d foy)

A substitution can do this for you. For a single line, you want to
replace all the leading or trailing whitespace with nothing. You
can do that with a pair of substitutions:

	s/^\s+//;
	s/\s+$//;

You can also write that as a single substitution, although it turns
out the combined statement is slower than the separate ones. That
might not matter to you, though:

	s/^\s+|\s+$//g;

In this regular expression, the alternation matches either at the
beginning or the end of the string since the anchors have a lower
precedence than the alternation. With the C</g> flag, the substitution
makes all possible matches, so it gets both. Remember, the trailing
newline matches the C<\s+>, and  the C<$> anchor can match to the
absolute end of the string, so the newline disappears too. Just add
the newline to the output, which has the added benefit of preserving
"blank" (consisting entirely of whitespace) lines which the C<^\s+>
would remove all by itself:

	while( <> ) {
		s/^\s+|\s+$//g;
		print "$_\n";
		}

For a multi-line string, you can apply the regular expression to each
logical line in the string by adding the C</m> flag (for
"multi-line"). With the C</m> flag, the C<$> matches I<before> an
embedded newline, so it doesn't remove it. This pattern still removes
the newline at the end of the string:

	$string =~ s/^\s+|\s+$//gm;

Remember that lines consisting entirely of whitespace will disappear,
since the first part of the alternation can match the entire string
and replace it with nothing. If you need to keep embedded blank lines,
you have to do a little more work. Instead of matching any whitespace
(since that includes a newline), just match the other whitespace:

	$string =~ s/^[\t\f ]+|[\t\f ]+$//mg;

=head2 How do I pad a string with blanks or pad a number with zeroes?

In the following examples, C<$pad_len> is the length to which you wish
to pad the string, C<$text> or C<$num> contains the string to be padded,
and C<$pad_char> contains the padding character. You can use a single
character string constant instead of the C<$pad_char> variable if you
know what it is in advance. And in the same way you can use an integer in
place of C<$pad_len> if you know the pad length in advance.

The simplest method uses the C<sprintf> function. It can pad on the left
or right with blanks and on the left with zeroes and it will not
truncate the result. The C<pack> function can only pad strings on the
right with blanks and it will truncate the result to a maximum length of
C<$pad_len>.

	# Left padding a string with blanks (no truncation):
	$padded = sprintf("%${pad_len}s", $text);
	$padded = sprintf("%*s", $pad_len, $text);  # same thing

	# Right padding a string with blanks (no truncation):
	$padded = sprintf("%-${pad_len}s", $text);
	$padded = sprintf("%-*s", $pad_len, $text); # same thing

	# Left padding a number with 0 (no truncation):
	$padded = sprintf("%0${pad_len}d", $num);
	$padded = sprintf("%0*d", $pad_len, $num); # same thing

	# Right padding a string with blanks using pack (will truncate):
	$padded = pack("A$pad_len",$text);

If you need to pad with a character other than blank or zero you can use
one of the following methods.  They all generate a pad string with the
C<x> operator and combine that with C<$text>. These methods do
not truncate C<$text>.

Left and right padding with any character, creating a new string:

	$padded = $pad_char x ( $pad_len - length( $text ) ) . $text;
	$padded = $text . $pad_char x ( $pad_len - length( $text ) );

Left and right padding with any character, modifying C<$text> directly:

	substr( $text, 0, 0 ) = $pad_char x ( $pad_len - length( $text ) );
	$text .= $pad_char x ( $pad_len - length( $text ) );

=head2 How do I extract selected columns from a string?

(contributed by brian d foy)

If you know the columns that contain the data, you can
use C<substr> to extract a single column.

	my $column = substr( $line, $start_column, $length );

You can use C<split> if the columns are separated by whitespace or
some other delimiter, as long as whitespace or the delimiter cannot
appear as part of the data.

	my $line    = ' fred barney   betty   ';
	my @columns = split /\s+/, $line;
		# ( '', 'fred', 'barney', 'betty' );

	my $line    = 'fred||barney||betty';
	my @columns = split /\|/, $line;
		# ( 'fred', '', 'barney', '', 'betty' );

If you want to work with comma-separated values, don't do this since
that format is a bit more complicated. Use one of the modules that
handle that format, such as C<Text::CSV>, C<Text::CSV_XS>, or
C<Text::CSV_PP>.

If you want to break apart an entire line of fixed columns, you can use
C<unpack> with the A (ASCII) format. By using a number after the format
specifier, you can denote the column width. See the C<pack> and C<unpack>
entries in L<perlfunc> for more details.

	my @fields = unpack( $line, "A8 A8 A8 A16 A4" );

Note that spaces in the format argument to C<unpack> do not denote literal
spaces. If you have space separated data, you may want C<split> instead.

=head2 How do I find the soundex value of a string?

(contributed by brian d foy)

You can use the Text::Soundex module. If you want to do fuzzy or close
matching, you might also try the C<String::Approx>, and
C<Text::Metaphone>, and C<Text::DoubleMetaphone> modules.

=head2 How can I expand variables in text strings?

(contributed by brian d foy)

If you can avoid it, don't, or if you can use a templating system,
such as C<Text::Template> or C<Template> Toolkit, do that instead. You
might even be able to get the job done with C<sprintf> or C<printf>:

	my $string = sprintf 'Say hello to %s and %s', $foo, $bar;

However, for the one-off simple case where I don't want to pull out a
full templating system, I'll use a string that has two Perl scalar
variables in it. In this example, I want to expand C<$foo> and C<$bar>
to their variable's values:

	my $foo = 'Fred';
	my $bar = 'Barney';
	$string = 'Say hello to $foo and $bar';

One way I can do this involves the substitution operator and a double
C</e> flag.  The first C</e> evaluates C<$1> on the replacement side and
turns it into C<$foo>. The second /e starts with C<$foo> and replaces
it with its value. C<$foo>, then, turns into 'Fred', and that's finally
what's left in the string:

	$string =~ s/(\$\w+)/$1/eeg; # 'Say hello to Fred and Barney'

The C</e> will also silently ignore violations of strict, replacing
undefined variable names with the empty string. Since I'm using the
C</e> flag (twice even!), I have all of the same security problems I
have with C<eval> in its string form. If there's something odd in
C<$foo>, perhaps something like C<@{[ system "rm -rf /" ]}>, then
I could get myself in trouble.

To get around the security problem, I could also pull the values from
a hash instead of evaluating variable names. Using a single C</e>, I
can check the hash to ensure the value exists, and if it doesn't, I
can replace the missing value with a marker, in this case C<???> to
signal that I missed something:

	my $string = 'This has $foo and $bar';

	my %Replacements = (
		foo  => 'Fred',
		);

	# $string =~ s/\$(\w+)/$Replacements{$1}/g;
	$string =~ s/\$(\w+)/
		exists $Replacements{$1} ? $Replacements{$1} : '???'
		/eg;

	print $string;

=head2 What's wrong with always quoting "$vars"?

The problem is that those double-quotes force
stringification--coercing numbers and references into strings--even
when you don't want them to be strings.  Think of it this way:
double-quote expansion is used to produce new strings.  If you already
have a string, why do you need more?

If you get used to writing odd things like these:

	print "$var";   	# BAD
	$new = "$old";   	# BAD
	somefunc("$var");	# BAD

You'll be in trouble.  Those should (in 99.8% of the cases) be
the simpler and more direct:

	print $var;
	$new = $old;
	somefunc($var);

Otherwise, besides slowing you down, you're going to break code when
the thing in the scalar is actually neither a string nor a number, but
a reference:

	func(\@array);
	sub func {
		my $aref = shift;
		my $oref = "$aref";  # WRONG
		}

You can also get into subtle problems on those few operations in Perl
that actually do care about the difference between a string and a
number, such as the magical C<++> autoincrement operator or the
syscall() function.

Stringification also destroys arrays.

	@lines = `command`;
	print "@lines";     # WRONG - extra blanks
	print @lines;       # right

=head2 Why don't my E<lt>E<lt>HERE documents work?

Here documents are found in L<perlop>. Check for these three things:

=over 4

=item There must be no space after the E<lt>E<lt> part.

=item There (probably) should be a semicolon at the end of the opening token

=item You can't (easily) have any space in front of the tag.

=item There needs to be at least a line separator after the end token.

=back

If you want to indent the text in the here document, you
can do this:

    # all in one
    ($VAR = <<HERE_TARGET) =~ s/^\s+//gm;
        your text
        goes here
    HERE_TARGET

But the HERE_TARGET must still be flush against the margin.
If you want that indented also, you'll have to quote
in the indentation.

    ($quote = <<'    FINIS') =~ s/^\s+//gm;
            ...we will have peace, when you and all your works have
            perished--and the works of your dark master to whom you
            would deliver us. You are a liar, Saruman, and a corrupter
            of men's hearts.  --Theoden in /usr/src/perl/taint.c
        FINIS
    $quote =~ s/\s+--/\n--/;

A nice general-purpose fixer-upper function for indented here documents
follows.  It expects to be called with a here document as its argument.
It looks to see whether each line begins with a common substring, and
if so, strips that substring off.  Otherwise, it takes the amount of leading
whitespace found on the first line and removes that much off each
subsequent line.

    sub fix {
        local $_ = shift;
        my ($white, $leader);  # common whitespace and common leading string
        if (/^\s*(?:([^\w\s]+)(\s*).*\n)(?:\s*\g1\g2?.*\n)+$/) {
            ($white, $leader) = ($2, quotemeta($1));
        } else {
            ($white, $leader) = (/^(\s+)/, '');
        }
        s/^\s*?$leader(?:$white)?//gm;
        return $_;
    }

This works with leading special strings, dynamically determined:

	$remember_the_main = fix<<'    MAIN_INTERPRETER_LOOP';
	@@@ int
	@@@ runops() {
	@@@     SAVEI32(runlevel);
	@@@     runlevel++;
	@@@     while ( op = (*op->op_ppaddr)() );
	@@@     TAINT_NOT;
	@@@     return 0;
	@@@ }
	MAIN_INTERPRETER_LOOP

Or with a fixed amount of leading whitespace, with remaining
indentation correctly preserved:

	$poem = fix<<EVER_ON_AND_ON;
       Now far ahead the Road has gone,
	  And I must follow, if I can,
       Pursuing it with eager feet,
	  Until it joins some larger way
       Where many paths and errands meet.
	  And whither then? I cannot say.
		--Bilbo in /usr/src/perl/pp_ctl.c
	EVER_ON_AND_ON

=head1 Data: Arrays

=head2 What is the difference between a list and an array?

(contributed by brian d foy)

A list is a fixed collection of scalars. An array is a variable that
holds a variable collection of scalars. An array can supply its collection
for list operations, so list operations also work on arrays:

	# slices
	( 'dog', 'cat', 'bird' )[2,3];
	@animals[2,3];

	# iteration
	foreach ( qw( dog cat bird ) ) { ... }
	foreach ( @animals ) { ... }

	my @three = grep { length == 3 } qw( dog cat bird );
	my @three = grep { length == 3 } @animals;

	# supply an argument list
	wash_animals( qw( dog cat bird ) );
	wash_animals( @animals );

Array operations, which change the scalars, rearranges them, or adds
or subtracts some scalars, only work on arrays. These can't work on a
list, which is fixed. Array operations include C<shift>, C<unshift>,
C<push>, C<pop>, and C<splice>.

An array can also change its length:

	$#animals = 1;  # truncate to two elements
	$#animals = 10000; # pre-extend to 10,001 elements

You can change an array element, but you can't change a list element:

	$animals[0] = 'Rottweiler';
	qw( dog cat bird )[0] = 'Rottweiler'; # syntax error!

	foreach ( @animals ) {
		s/^d/fr/;  # works fine
		}

	foreach ( qw( dog cat bird ) ) {
		s/^d/fr/;  # Error! Modification of read only value!
		}

However, if the list element is itself a variable, it appears that you
can change a list element. However, the list element is the variable, not
the data. You're not changing the list element, but something the list
element refers to. The list element itself doesn't change: it's still
the same variable.

You also have to be careful about context. You can assign an array to
a scalar to get the number of elements in the array. This only works
for arrays, though:

	my $count = @animals;  # only works with arrays

If you try to do the same thing with what you think is a list, you
get a quite different result. Although it looks like you have a list
on the righthand side, Perl actually sees a bunch of scalars separated
by a comma:

	my $scalar = ( 'dog', 'cat', 'bird' );  # $scalar gets bird

Since you're assigning to a scalar, the righthand side is in scalar
context. The comma operator (yes, it's an operator!) in scalar
context evaluates its lefthand side, throws away the result, and
evaluates it's righthand side and returns the result. In effect,
that list-lookalike assigns to C<$scalar> it's rightmost value. Many
people mess this up because they choose a list-lookalike whose
last element is also the count they expect:

	my $scalar = ( 1, 2, 3 );  # $scalar gets 3, accidentally

=head2 What is the difference between $array[1] and @array[1]?

(contributed by brian d foy)

The difference is the sigil, that special character in front of the
array name. The C<$> sigil means "exactly one item", while the C<@>
sigil means "zero or more items". The C<$> gets you a single scalar,
while the C<@> gets you a list.

The confusion arises because people incorrectly assume that the sigil
denotes the variable type.

The C<$array[1]> is a single-element access to the array. It's going
to return the item in index 1 (or undef if there is no item there).
If you intend to get exactly one element from the array, this is the
form you should use.

The C<@array[1]> is an array slice, although it has only one index.
You can pull out multiple elements simultaneously by specifying
additional indices as a list, like C<@array[1,4,3,0]>.

Using a slice on the lefthand side of the assignment supplies list
context to the righthand side. This can lead to unexpected results.
For instance, if you want to read a single line from a filehandle,
assigning to a scalar value is fine:

	$array[1] = <STDIN>;

However, in list context, the line input operator returns all of the
lines as a list. The first line goes into C<@array[1]> and the rest
of the lines mysteriously disappear:

	@array[1] = <STDIN>;  # most likely not what you want

Either the C<use warnings> pragma or the B<-w> flag will warn you when
you use an array slice with a single index.

=head2 How can I remove duplicate elements from a list or array?

(contributed by brian d foy)

Use a hash. When you think the words "unique" or "duplicated", think
"hash keys".

If you don't care about the order of the elements, you could just
create the hash then extract the keys. It's not important how you
create that hash: just that you use C<keys> to get the unique
elements.

	my %hash   = map { $_, 1 } @array;
	# or a hash slice: @hash{ @array } = ();
	# or a foreach: $hash{$_} = 1 foreach ( @array );

	my @unique = keys %hash;

If you want to use a module, try the C<uniq> function from
C<List::MoreUtils>. In list context it returns the unique elements,
preserving their order in the list. In scalar context, it returns the
number of unique elements.

	use List::MoreUtils qw(uniq);

	my @unique = uniq( 1, 2, 3, 4, 4, 5, 6, 5, 7 ); # 1,2,3,4,5,6,7
	my $unique = uniq( 1, 2, 3, 4, 4, 5, 6, 5, 7 ); # 7

You can also go through each element and skip the ones you've seen
before. Use a hash to keep track. The first time the loop sees an
element, that element has no key in C<%Seen>. The C<next> statement
creates the key and immediately uses its value, which is C<undef>, so
the loop continues to the C<push> and increments the value for that
key. The next time the loop sees that same element, its key exists in
the hash I<and> the value for that key is true (since it's not 0 or
C<undef>), so the next skips that iteration and the loop goes to the
next element.

	my @unique = ();
	my %seen   = ();

	foreach my $elem ( @array )
		{
		next if $seen{ $elem }++;
		push @unique, $elem;
		}

You can write this more briefly using a grep, which does the
same thing.

	my %seen = ();
	my @unique = grep { ! $seen{ $_ }++ } @array;

=head2 How can I tell whether a certain element is contained in a list or array?

(portions of this answer contributed by Anno Siegel and brian d foy)

Hearing the word "in" is an I<in>dication that you probably should have
used a hash, not a list or array, to store your data.  Hashes are
designed to answer this question quickly and efficiently.  Arrays aren't.

That being said, there are several ways to approach this.  In Perl 5.10
and later, you can use the smart match operator to check that an item is
contained in an array or a hash:

	use 5.010;

	if( $item ~~ @array )
		{
		say "The array contains $item"
		}

	if( $item ~~ %hash )
		{
		say "The hash contains $item"
		}

With earlier versions of Perl, you have to do a bit more work. If you
are going to make this query many times over arbitrary string values,
the fastest way is probably to invert the original array and maintain a
hash whose keys are the first array's values:

	@blues = qw/azure cerulean teal turquoise lapis-lazuli/;
	%is_blue = ();
	for (@blues) { $is_blue{$_} = 1 }

Now you can check whether C<$is_blue{$some_color}>.  It might have
been a good idea to keep the blues all in a hash in the first place.

If the values are all small integers, you could use a simple indexed
array.  This kind of an array will take up less space:

	@primes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31);
	@is_tiny_prime = ();
	for (@primes) { $is_tiny_prime[$_] = 1 }
	# or simply  @istiny_prime[@primes] = (1) x @primes;

Now you check whether $is_tiny_prime[$some_number].

If the values in question are integers instead of strings, you can save
quite a lot of space by using bit strings instead:

	@articles = ( 1..10, 150..2000, 2017 );
	undef $read;
	for (@articles) { vec($read,$_,1) = 1 }

Now check whether C<vec($read,$n,1)> is true for some C<$n>.

These methods guarantee fast individual tests but require a re-organization
of the original list or array.  They only pay off if you have to test
multiple values against the same array.

If you are testing only once, the standard module C<List::Util> exports
the function C<first> for this purpose.  It works by stopping once it
finds the element. It's written in C for speed, and its Perl equivalent
looks like this subroutine:

	sub first (&@) {
		my $code = shift;
		foreach (@_) {
			return $_ if &{$code}();
		}
		undef;
	}

If speed is of little concern, the common idiom uses grep in scalar context
(which returns the number of items that passed its condition) to traverse the
entire list. This does have the benefit of telling you how many matches it
found, though.

	my $is_there = grep $_ eq $whatever, @array;

If you want to actually extract the matching elements, simply use grep in
list context.

	my @matches = grep $_ eq $whatever, @array;

=head2 How do I compute the difference of two arrays?  How do I compute the intersection of two arrays?

Use a hash.  Here's code to do both and more.  It assumes that each
element is unique in a given array:

	@union = @intersection = @difference = ();
	%count = ();
	foreach $element (@array1, @array2) { $count{$element}++ }
	foreach $element (keys %count) {
		push @union, $element;
		push @{ $count{$element} > 1 ? \@intersection : \@difference }, $element;
		}

Note that this is the I<symmetric difference>, that is, all elements
in either A or in B but not in both.  Think of it as an xor operation.

=head2 How do I test whether two arrays or hashes are equal?

With Perl 5.10 and later, the smart match operator can give you the answer
with the least amount of work:

	use 5.010;

	if( @array1 ~~ @array2 )
		{
		say "The arrays are the same";
		}

	if( %hash1 ~~ %hash2 ) # doesn't check values!
		{
		say "The hash keys are the same";
		}

The following code works for single-level arrays.  It uses a
stringwise comparison, and does not distinguish defined versus
undefined empty strings.  Modify if you have other needs.

	$are_equal = compare_arrays(\@frogs, \@toads);

	sub compare_arrays {
		my ($first, $second) = @_;
		no warnings;  # silence spurious -w undef complaints
		return 0 unless @$first == @$second;
		for (my $i = 0; $i < @$first; $i++) {
			return 0 if $first->[$i] ne $second->[$i];
			}
		return 1;
		}

For multilevel structures, you may wish to use an approach more
like this one.  It uses the CPAN module C<FreezeThaw>:

	use FreezeThaw qw(cmpStr);
	@a = @b = ( "this", "that", [ "more", "stuff" ] );

	printf "a and b contain %s arrays\n",
		cmpStr(\@a, \@b) == 0
		? "the same"
		: "different";

This approach also works for comparing hashes.  Here we'll demonstrate
two different answers:

	use FreezeThaw qw(cmpStr cmpStrHard);

	%a = %b = ( "this" => "that", "extra" => [ "more", "stuff" ] );
	$a{EXTRA} = \%b;
	$b{EXTRA} = \%a;

	printf "a and b contain %s hashes\n",
	cmpStr(\%a, \%b) == 0 ? "the same" : "different";

	printf "a and b contain %s hashes\n",
	cmpStrHard(\%a, \%b) == 0 ? "the same" : "different";


The first reports that both those the hashes contain the same data,
while the second reports that they do not.  Which you prefer is left as
an exercise to the reader.

=head2 How do I find the first array element for which a condition is true?

To find the first array element which satisfies a condition, you can
use the C<first()> function in the C<List::Util> module, which comes
with Perl 5.8. This example finds the first element that contains
"Perl".

	use List::Util qw(first);

	my $element = first { /Perl/ } @array;

If you cannot use C<List::Util>, you can make your own loop to do the
same thing.  Once you find the element, you stop the loop with last.

	my $found;
	foreach ( @array ) {
		if( /Perl/ ) { $found = $_; last }
		}

If you want the array index, you can iterate through the indices
and check the array element at each index until you find one
that satisfies the condition.

	my( $found, $index ) = ( undef, -1 );
	for( $i = 0; $i < @array; $i++ ) {
		if( $array[$i] =~ /Perl/ ) {
			$found = $array[$i];
			$index = $i;
			last;
			}
		}

=head2 How do I handle linked lists?

(contributed by brian d foy)

Perl's arrays do not have a fixed size, so you don't need linked lists
if you just want to add or remove items. You can use array operations
such as C<push>, C<pop>, C<shift>, C<unshift>, or C<splice> to do
that.

Sometimes, however, linked lists can be useful in situations where you
want to "shard" an array so you have have many small arrays instead of
a single big array. You can keep arrays longer than Perl's largest
array index, lock smaller arrays separately in threaded programs,
reallocate less memory, or quickly insert elements in the middle of
the chain.

Steve Lembark goes through the details in his YAPC::NA 2009 talk "Perly
Linked Lists" ( http://www.slideshare.net/lembark/perly-linked-lists ),
although you can just use his C<LinkedList::Single> module.

=head2 How do I handle circular lists?
X<circular> X<array> X<Tie::Cycle> X<Array::Iterator::Circular>
X<cycle> X<modulus>

(contributed by brian d foy)

If you want to cycle through an array endlessly, you can increment the
index modulo the number of elements in the array:

	my @array = qw( a b c );
	my $i = 0;

	while( 1 ) {
		print $array[ $i++ % @array ], "\n";
		last if $i > 20;
		}

You can also use C<Tie::Cycle> to use a scalar that always has the
next element of the circular array:

	use Tie::Cycle;

	tie my $cycle, 'Tie::Cycle', [ qw( FFFFFF 000000 FFFF00 ) ];

	print $cycle; # FFFFFF
	print $cycle; # 000000
	print $cycle; # FFFF00

The C<Array::Iterator::Circular> creates an iterator object for
circular arrays:

	use Array::Iterator::Circular;

	my $color_iterator = Array::Iterator::Circular->new(
		qw(red green blue orange)
		);

	foreach ( 1 .. 20 ) {
		print $color_iterator->next, "\n";
		}

=head2 How do I shuffle an array randomly?

If you either have Perl 5.8.0 or later installed, or if you have
Scalar-List-Utils 1.03 or later installed, you can say:

	use List::Util 'shuffle';

	@shuffled = shuffle(@list);

If not, you can use a Fisher-Yates shuffle.

	sub fisher_yates_shuffle {
		my $deck = shift;  # $deck is a reference to an array
		return unless @$deck; # must not be empty!

		my $i = @$deck;
		while (--$i) {
			my $j = int rand ($i+1);
			@$deck[$i,$j] = @$deck[$j,$i];
			}
	}

	# shuffle my mpeg collection
	#
	my @mpeg = <audio/*/*.mp3>;
	fisher_yates_shuffle( \@mpeg );    # randomize @mpeg in place
	print @mpeg;

Note that the above implementation shuffles an array in place,
unlike the C<List::Util::shuffle()> which takes a list and returns
a new shuffled list.

You've probably seen shuffling algorithms that work using splice,
randomly picking another element to swap the current element with

	srand;
	@new = ();
	@old = 1 .. 10;  # just a demo
	while (@old) {
		push(@new, splice(@old, rand @old, 1));
		}

This is bad because splice is already O(N), and since you do it N
times, you just invented a quadratic algorithm; that is, O(N**2).
This does not scale, although Perl is so efficient that you probably
won't notice this until you have rather largish arrays.

=head2 How do I process/modify each element of an array?

Use C<for>/C<foreach>:

	for (@lines) {
		s/foo/bar/;	# change that word
		tr/XZ/ZX/;	# swap those letters
		}

Here's another; let's compute spherical volumes:

	for (@volumes = @radii) {   # @volumes has changed parts
		$_ **= 3;
		$_ *= (4/3) * 3.14159;  # this will be constant folded
		}

which can also be done with C<map()> which is made to transform
one list into another:

	@volumes = map {$_ ** 3 * (4/3) * 3.14159} @radii;

If you want to do the same thing to modify the values of the
hash, you can use the C<values> function.  As of Perl 5.6
the values are not copied, so if you modify $orbit (in this
case), you modify the value.

	for $orbit ( values %orbits ) {
		($orbit **= 3) *= (4/3) * 3.14159;
		}

Prior to perl 5.6 C<values> returned copies of the values,
so older perl code often contains constructions such as
C<@orbits{keys %orbits}> instead of C<values %orbits> where
the hash is to be modified.

=head2 How do I select a random element from an array?

Use the C<rand()> function (see L<perlfunc/rand>):

	$index   = rand @array;
	$element = $array[$index];

Or, simply:

	my $element = $array[ rand @array ];

=head2 How do I permute N elements of a list?
X<List::Permutor> X<permute> X<Algorithm::Loops> X<Knuth>
X<The Art of Computer Programming> X<Fischer-Krause>

Use the C<List::Permutor> module on CPAN. If the list is actually an
array, try the C<Algorithm::Permute> module (also on CPAN). It's
written in XS code and is very efficient:

	use Algorithm::Permute;

	my @array = 'a'..'d';
	my $p_iterator = Algorithm::Permute->new ( \@array );

	while (my @perm = $p_iterator->next) {
	   print "next permutation: (@perm)\n";
		}

For even faster execution, you could do:

	use Algorithm::Permute;

	my @array = 'a'..'d';

	Algorithm::Permute::permute {
		print "next permutation: (@array)\n";
		} @array;

Here's a little program that generates all permutations of all the
words on each line of input. The algorithm embodied in the
C<permute()> function is discussed in Volume 4 (still unpublished) of
Knuth's I<The Art of Computer Programming> and will work on any list:

	#!/usr/bin/perl -n
	# Fischer-Krause ordered permutation generator

	sub permute (&@) {
		my $code = shift;
		my @idx = 0..$#_;
		while ( $code->(@_[@idx]) ) {
			my $p = $#idx;
			--$p while $idx[$p-1] > $idx[$p];
			my $q = $p or return;
			push @idx, reverse splice @idx, $p;
			++$q while $idx[$p-1] > $idx[$q];
			@idx[$p-1,$q]=@idx[$q,$p-1];
		}
	}

	permute { print "@_\n" } split;

The C<Algorithm::Loops> module also provides the C<NextPermute> and
C<NextPermuteNum> functions which efficiently find all unique permutations
of an array, even if it contains duplicate values, modifying it in-place:
if its elements are in reverse-sorted order then the array is reversed,
making it sorted, and it returns false; otherwise the next
permutation is returned.

C<NextPermute> uses string order and C<NextPermuteNum> numeric order, so
you can enumerate all the permutations of C<0..9> like this:

	use Algorithm::Loops qw(NextPermuteNum);

    my @list= 0..9;
    do { print "@list\n" } while NextPermuteNum @list;

=head2 How do I sort an array by (anything)?

Supply a comparison function to sort() (described in L<perlfunc/sort>):

	@list = sort { $a <=> $b } @list;

The default sort function is cmp, string comparison, which would
sort C<(1, 2, 10)> into C<(1, 10, 2)>.  C<< <=> >>, used above, is
the numerical comparison operator.

If you have a complicated function needed to pull out the part you
want to sort on, then don't do it inside the sort function.  Pull it
out first, because the sort BLOCK can be called many times for the
same element.  Here's an example of how to pull out the first word
after the first number on each item, and then sort those words
case-insensitively.

	@idx = ();
	for (@data) {
		($item) = /\d+\s*(\S+)/;
		push @idx, uc($item);
	    }
	@sorted = @data[ sort { $idx[$a] cmp $idx[$b] } 0 .. $#idx ];

which could also be written this way, using a trick
that's come to be known as the Schwartzian Transform:

	@sorted = map  { $_->[0] }
		sort { $a->[1] cmp $b->[1] }
		map  { [ $_, uc( (/\d+\s*(\S+)/)[0]) ] } @data;

If you need to sort on several fields, the following paradigm is useful.

	@sorted = sort {
		field1($a) <=> field1($b) ||
		field2($a) cmp field2($b) ||
		field3($a) cmp field3($b)
		} @data;

This can be conveniently combined with precalculation of keys as given
above.

See the F<sort> article in the "Far More Than You Ever Wanted
To Know" collection in http://www.cpan.org/misc/olddoc/FMTEYEWTK.tgz for
more about this approach.

See also the question later in L<perlfaq4> on sorting hashes.

=head2 How do I manipulate arrays of bits?

Use C<pack()> and C<unpack()>, or else C<vec()> and the bitwise
operations.

For example, you don't have to store individual bits in an array
(which would mean that you're wasting a lot of space). To convert an
array of bits to a string, use C<vec()> to set the right bits. This
sets C<$vec> to have bit N set only if C<$ints[N]> was set:

	@ints = (...); # array of bits, e.g. ( 1, 0, 0, 1, 1, 0 ... )
	$vec = '';
	foreach( 0 .. $#ints ) {
		vec($vec,$_,1) = 1 if $ints[$_];
		}

The string C<$vec> only takes up as many bits as it needs. For
instance, if you had 16 entries in C<@ints>, C<$vec> only needs two
bytes to store them (not counting the scalar variable overhead).

Here's how, given a vector in C<$vec>, you can get those bits into
your C<@ints> array:

	sub bitvec_to_list {
		my $vec = shift;
		my @ints;
		# Find null-byte density then select best algorithm
		if ($vec =~ tr/\0// / length $vec > 0.95) {
			use integer;
			my $i;

			# This method is faster with mostly null-bytes
			while($vec =~ /[^\0]/g ) {
				$i = -9 + 8 * pos $vec;
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				push @ints, $i if vec($vec, ++$i, 1);
				}
			}
		else {
			# This method is a fast general algorithm
			use integer;
			my $bits = unpack "b*", $vec;
			push @ints, 0 if $bits =~ s/^(\d)// && $1;
			push @ints, pos $bits while($bits =~ /1/g);
			}

		return \@ints;
		}

This method gets faster the more sparse the bit vector is.
(Courtesy of Tim Bunce and Winfried Koenig.)

You can make the while loop a lot shorter with this suggestion
from Benjamin Goldberg:

	while($vec =~ /[^\0]+/g ) {
		push @ints, grep vec($vec, $_, 1), $-[0] * 8 .. $+[0] * 8;
		}

Or use the CPAN module C<Bit::Vector>:

	$vector = Bit::Vector->new($num_of_bits);
	$vector->Index_List_Store(@ints);
	@ints = $vector->Index_List_Read();

C<Bit::Vector> provides efficient methods for bit vector, sets of
small integers and "big int" math.

Here's a more extensive illustration using vec():

	# vec demo
	$vector = "\xff\x0f\xef\xfe";
	print "Ilya's string \\xff\\x0f\\xef\\xfe represents the number ",
	unpack("N", $vector), "\n";
	$is_set = vec($vector, 23, 1);
	print "Its 23rd bit is ", $is_set ? "set" : "clear", ".\n";
	pvec($vector);

	set_vec(1,1,1);
	set_vec(3,1,1);
	set_vec(23,1,1);

	set_vec(3,1,3);
	set_vec(3,2,3);
	set_vec(3,4,3);
	set_vec(3,4,7);
	set_vec(3,8,3);
	set_vec(3,8,7);

	set_vec(0,32,17);
	set_vec(1,32,17);

	sub set_vec {
		my ($offset, $width, $value) = @_;
		my $vector = '';
		vec($vector, $offset, $width) = $value;
		print "offset=$offset width=$width value=$value\n";
		pvec($vector);
		}

	sub pvec {
		my $vector = shift;
		my $bits = unpack("b*", $vector);
		my $i = 0;
		my $BASE = 8;

		print "vector length in bytes: ", length($vector), "\n";
		@bytes = unpack("A8" x length($vector), $bits);
		print "bits are: @bytes\n\n";
		}

=head2 Why does defined() return true on empty arrays and hashes?

The short story is that you should probably only use defined on scalars or
functions, not on aggregates (arrays and hashes).  See L<perlfunc/defined>
in the 5.004 release or later of Perl for more detail.

=head1 Data: Hashes (Associative Arrays)

=head2 How do I process an entire hash?

(contributed by brian d foy)

There are a couple of ways that you can process an entire hash. You
can get a list of keys, then go through each key, or grab a one
key-value pair at a time.

To go through all of the keys, use the C<keys> function. This extracts
all of the keys of the hash and gives them back to you as a list. You
can then get the value through the particular key you're processing:

	foreach my $key ( keys %hash ) {
		my $value = $hash{$key}
		...
		}

Once you have the list of keys, you can process that list before you
process the hash elements. For instance, you can sort the keys so you
can process them in lexical order:

	foreach my $key ( sort keys %hash ) {
		my $value = $hash{$key}
		...
		}

Or, you might want to only process some of the items. If you only want
to deal with the keys that start with C<text:>, you can select just
those using C<grep>:

	foreach my $key ( grep /^text:/, keys %hash ) {
		my $value = $hash{$key}
		...
		}

If the hash is very large, you might not want to create a long list of
keys. To save some memory, you can grab one key-value pair at a time using
C<each()>, which returns a pair you haven't seen yet:

	while( my( $key, $value ) = each( %hash ) ) {
		...
		}

The C<each> operator returns the pairs in apparently random order, so if
ordering matters to you, you'll have to stick with the C<keys> method.

The C<each()> operator can be a bit tricky though. You can't add or
delete keys of the hash while you're using it without possibly
skipping or re-processing some pairs after Perl internally rehashes
all of the elements. Additionally, a hash has only one iterator, so if
you use C<keys>, C<values>, or C<each> on the same hash, you can reset
the iterator and mess up your processing. See the C<each> entry in
L<perlfunc> for more details.

=head2 How do I merge two hashes?
X<hash> X<merge> X<slice, hash>

(contributed by brian d foy)

Before you decide to merge two hashes, you have to decide what to do
if both hashes contain keys that are the same and if you want to leave
the original hashes as they were.

If you want to preserve the original hashes, copy one hash (C<%hash1>)
to a new hash (C<%new_hash>), then add the keys from the other hash
(C<%hash2> to the new hash. Checking that the key already exists in
C<%new_hash> gives you a chance to decide what to do with the
duplicates:

	my %new_hash = %hash1; # make a copy; leave %hash1 alone

	foreach my $key2 ( keys %hash2 )
		{
		if( exists $new_hash{$key2} )
			{
			warn "Key [$key2] is in both hashes!";
			# handle the duplicate (perhaps only warning)
			...
			next;
			}
		else
			{
			$new_hash{$key2} = $hash2{$key2};
			}
		}

If you don't want to create a new hash, you can still use this looping
technique; just change the C<%new_hash> to C<%hash1>.

	foreach my $key2 ( keys %hash2 )
		{
		if( exists $hash1{$key2} )
			{
			warn "Key [$key2] is in both hashes!";
			# handle the duplicate (perhaps only warning)
			...
			next;
			}
		else
			{
			$hash1{$key2} = $hash2{$key2};
			}
		}

If you don't care that one hash overwrites keys and values from the other, you
could just use a hash slice to add one hash to another. In this case, values
from C<%hash2> replace values from C<%hash1> when they have keys in common:

	@hash1{ keys %hash2 } = values %hash2;

=head2 What happens if I add or remove keys from a hash while iterating over it?

(contributed by brian d foy)

The easy answer is "Don't do that!"

If you iterate through the hash with each(), you can delete the key
most recently returned without worrying about it.  If you delete or add
other keys, the iterator may skip or double up on them since perl
may rearrange the hash table.  See the
entry for C<each()> in L<perlfunc>.

=head2 How do I look up a hash element by value?

Create a reverse hash:

	%by_value = reverse %by_key;
	$key = $by_value{$value};

That's not particularly efficient.  It would be more space-efficient
to use:

	while (($key, $value) = each %by_key) {
		$by_value{$value} = $key;
	    }

If your hash could have repeated values, the methods above will only find
one of the associated keys.   This may or may not worry you.  If it does
worry you, you can always reverse the hash into a hash of arrays instead:

	while (($key, $value) = each %by_key) {
		 push @{$key_list_by_value{$value}}, $key;
		}

=head2 How can I know how many entries are in a hash?

(contributed by brian d foy)

This is very similar to "How do I process an entire hash?", also in
L<perlfaq4>, but a bit simpler in the common cases.

You can use the C<keys()> built-in function in scalar context to find out
have many entries you have in a hash:

	my $key_count = keys %hash; # must be scalar context!

If you want to find out how many entries have a defined value, that's
a bit different. You have to check each value. A C<grep> is handy:

	my $defined_value_count = grep { defined } values %hash;

You can use that same structure to count the entries any way that
you like. If you want the count of the keys with vowels in them,
you just test for that instead:

	my $vowel_count = grep { /[aeiou]/ } keys %hash;

The C<grep> in scalar context returns the count. If you want the list
of matching items, just use it in list context instead:

	my @defined_values = grep { defined } values %hash;

The C<keys()> function also resets the iterator, which means that you may
see strange results if you use this between uses of other hash operators
such as C<each()>.

=head2 How do I sort a hash (optionally by value instead of key)?

(contributed by brian d foy)

To sort a hash, start with the keys. In this example, we give the list of
keys to the sort function which then compares them ASCIIbetically (which
might be affected by your locale settings). The output list has the keys
in ASCIIbetical order. Once we have the keys, we can go through them to
create a report which lists the keys in ASCIIbetical order.

	my @keys = sort { $a cmp $b } keys %hash;

	foreach my $key ( @keys )
		{
		printf "%-20s %6d\n", $key, $hash{$key};
		}

We could get more fancy in the C<sort()> block though. Instead of
comparing the keys, we can compute a value with them and use that
value as the comparison.

For instance, to make our report order case-insensitive, we use
the C<\L> sequence in a double-quoted string to make everything
lowercase. The C<sort()> block then compares the lowercased
values to determine in which order to put the keys.

	my @keys = sort { "\L$a" cmp "\L$b" } keys %hash;

Note: if the computation is expensive or the hash has many elements,
you may want to look at the Schwartzian Transform to cache the
computation results.

If we want to sort by the hash value instead, we use the hash key
to look it up. We still get out a list of keys, but this time they
are ordered by their value.

	my @keys = sort { $hash{$a} <=> $hash{$b} } keys %hash;

From there we can get more complex. If the hash values are the same,
we can provide a secondary sort on the hash key.

	my @keys = sort {
		$hash{$a} <=> $hash{$b}
			or
		"\L$a" cmp "\L$b"
		} keys %hash;

=head2 How can I always keep my hash sorted?
X<hash tie sort DB_File Tie::IxHash>

You can look into using the C<DB_File> module and C<tie()> using the
C<$DB_BTREE> hash bindings as documented in L<DB_File/"In Memory
Databases">. The C<Tie::IxHash> module from CPAN might also be
instructive. Although this does keep your hash sorted, you might not
like the slowdown you suffer from the tie interface. Are you sure you
need to do this? :)

=head2 What's the difference between "delete" and "undef" with hashes?

Hashes contain pairs of scalars: the first is the key, the
second is the value.  The key will be coerced to a string,
although the value can be any kind of scalar: string,
number, or reference.  If a key C<$key> is present in
%hash, C<exists($hash{$key})> will return true.  The value
for a given key can be C<undef>, in which case
C<$hash{$key}> will be C<undef> while C<exists $hash{$key}>
will return true.  This corresponds to (C<$key>, C<undef>)
being in the hash.

Pictures help...  Here's the C<%hash> table:

	  keys  values
	+------+------+
	|  a   |  3   |
	|  x   |  7   |
	|  d   |  0   |
	|  e   |  2   |
	+------+------+

And these conditions hold

	$hash{'a'}                       is true
	$hash{'d'}                       is false
	defined $hash{'d'}               is true
	defined $hash{'a'}               is true
	exists $hash{'a'}                is true (Perl 5 only)
	grep ($_ eq 'a', keys %hash)     is true

If you now say

	undef $hash{'a'}

your table now reads:


	  keys  values
	+------+------+
	|  a   | undef|
	|  x   |  7   |
	|  d   |  0   |
	|  e   |  2   |
	+------+------+

and these conditions now hold; changes in caps:

	$hash{'a'}                       is FALSE
	$hash{'d'}                       is false
	defined $hash{'d'}               is true
	defined $hash{'a'}               is FALSE
	exists $hash{'a'}                is true (Perl 5 only)
	grep ($_ eq 'a', keys %hash)     is true

Notice the last two: you have an undef value, but a defined key!

Now, consider this:

	delete $hash{'a'}

your table now reads:

	  keys  values
	+------+------+
	|  x   |  7   |
	|  d   |  0   |
	|  e   |  2   |
	+------+------+

and these conditions now hold; changes in caps:

	$hash{'a'}                       is false
	$hash{'d'}                       is false
	defined $hash{'d'}               is true
	defined $hash{'a'}               is false
	exists $hash{'a'}                is FALSE (Perl 5 only)
	grep ($_ eq 'a', keys %hash)     is FALSE

See, the whole entry is gone!

=head2 Why don't my tied hashes make the defined/exists distinction?

This depends on the tied hash's implementation of EXISTS().
For example, there isn't the concept of undef with hashes
that are tied to DBM* files. It also means that exists() and
defined() do the same thing with a DBM* file, and what they
end up doing is not what they do with ordinary hashes.

=head2 How do I reset an each() operation part-way through?

(contributed by brian d foy)

You can use the C<keys> or C<values> functions to reset C<each>. To
simply reset the iterator used by C<each> without doing anything else,
use one of them in void context:

	keys %hash; # resets iterator, nothing else.
	values %hash; # resets iterator, nothing else.

See the documentation for C<each> in L<perlfunc>.

=head2 How can I get the unique keys from two hashes?

First you extract the keys from the hashes into lists, then solve
the "removing duplicates" problem described above.  For example:

	%seen = ();
	for $element (keys(%foo), keys(%bar)) {
		$seen{$element}++;
		}
	@uniq = keys %seen;

Or more succinctly:

	@uniq = keys %{{%foo,%bar}};

Or if you really want to save space:

	%seen = ();
	while (defined ($key = each %foo)) {
		$seen{$key}++;
	}
	while (defined ($key = each %bar)) {
		$seen{$key}++;
	}
	@uniq = keys %seen;

=head2 How can I store a multidimensional array in a DBM file?

Either stringify the structure yourself (no fun), or else
get the MLDBM (which uses Data::Dumper) module from CPAN and layer
it on top of either DB_File or GDBM_File. You might also try DBM::Deep, but
it can be a bit slow.

=head2 How can I make my hash remember the order I put elements into it?

Use the C<Tie::IxHash> from CPAN.

	use Tie::IxHash;

	tie my %myhash, 'Tie::IxHash';

	for (my $i=0; $i<20; $i++) {
		$myhash{$i} = 2*$i;
		}

	my @keys = keys %myhash;
	# @keys = (0,1,2,3,...)

=head2 Why does passing a subroutine an undefined element in a hash create it?

(contributed by brian d foy)

Are you using a really old version of Perl?

Normally, accessing a hash key's value for a nonexistent key will
I<not> create the key.

	my %hash  = ();
	my $value = $hash{ 'foo' };
	print "This won't print\n" if exists $hash{ 'foo' };

Passing C<$hash{ 'foo' }> to a subroutine used to be a special case, though.
Since you could assign directly to C<$_[0]>, Perl had to be ready to
make that assignment so it created the hash key ahead of time:

    my_sub( $hash{ 'foo' } );
	print "This will print before 5.004\n" if exists $hash{ 'foo' };

	sub my_sub {
		# $_[0] = 'bar'; # create hash key in case you do this
		1;
		}

Since Perl 5.004, however, this situation is a special case and Perl
creates the hash key only when you make the assignment:

    my_sub( $hash{ 'foo' } );
	print "This will print, even after 5.004\n" if exists $hash{ 'foo' };

	sub my_sub {
		$_[0] = 'bar';
		}

However, if you want the old behavior (and think carefully about that
because it's a weird side effect), you can pass a hash slice instead.
Perl 5.004 didn't make this a special case:

	my_sub( @hash{ qw/foo/ } );

=head2 How can I make the Perl equivalent of a C structure/C++ class/hash or array of hashes or arrays?

Usually a hash ref, perhaps like this:

	$record = {
		NAME   => "Jason",
		EMPNO  => 132,
		TITLE  => "deputy peon",
		AGE    => 23,
		SALARY => 37_000,
		PALS   => [ "Norbert", "Rhys", "Phineas"],
	};

References are documented in L<perlref> and L<perlreftut>.
Examples of complex data structures are given in L<perldsc> and
L<perllol>.  Examples of structures and object-oriented classes are
in L<perltoot>.

=head2 How can I use a reference as a hash key?

(contributed by brian d foy and Ben Morrow)

Hash keys are strings, so you can't really use a reference as the key.
When you try to do that, perl turns the reference into its stringified
form (for instance, C<HASH(0xDEADBEEF)>). From there you can't get
back the reference from the stringified form, at least without doing
some extra work on your own.

Remember that the entry in the hash will still be there even if
the referenced variable  goes out of scope, and that it is entirely
possible for Perl to subsequently allocate a different variable at
the same address. This will mean a new variable might accidentally
be associated with the value for an old.

If you have Perl 5.10 or later, and you just want to store a value
against the reference for lookup later, you can use the core
Hash::Util::Fieldhash module. This will also handle renaming the
keys if you use multiple threads (which causes all variables to be
reallocated at new addresses, changing their stringification), and
garbage-collecting the entries when the referenced variable goes out
of scope.

If you actually need to be able to get a real reference back from
each hash entry, you can use the Tie::RefHash module, which does the
required work for you.

=head2 How can I check if a key exists in a multilevel hash?

(contributed by brian d foy)

The trick to this problem is avoiding accidental autovivification. If 
you want to check three keys deep, you might naïvely try this:

	my %hash;
	if( exists $hash{key1}{key2}{key3} ) {
		...;
		}

Even though you started with a completely empty hash, after that call to 
C<exists> you've created the structure you needed to check for C<key3>:

	%hash = (
			  'key1' => {
						  'key2' => {}
						}
			);

That's autovivification. You can get around this in a few ways. The
easiest way is to just turn it off. The lexical C<autovivification>
pragma is available on CPAN. Now you don't add to the hash:

	{
	no autovivification;
	my %hash;
	if( exists $hash{key1}{key2}{key3} ) {
		...;
		}
	}

The C<Data::Diver> module on CPAN can do it for you too. Its C<Dive>
subroutine can tell you not only if the keys exist but also get the
value:

	use Data::Diver qw(Dive);
	
    my @exists = Dive( \%hash, qw(key1 key2 key3) );
    if(  ! @exists  ) {
        ...; # keys do not exist
    	} 
    elsif(  ! defined $exists[0]  ) {
        ...; # keys exist but value is undef
    	}

You can easily do this yourself too by checking each level of the hash
before you move onto the next level. This is essentially what
C<Data::Diver> does for you:

	if( check_hash( \%hash, qw(key1 key2 key3) ) ) {
		...;
		}
	
	sub check_hash {
	   my( $hash, @keys ) = @_;
	
	   return unless @keys;
	
	   foreach my $key ( @keys ) {
		   return unless eval { exists $hash->{$key} };
		   $hash = $hash->{$key};
		   }
	
	   return 1;
	   }

=head1 Data: Misc

=head2 How do I handle binary data correctly?

Perl is binary-clean, so it can handle binary data just fine.
On Windows or DOS, however, you have to use C<binmode> for binary
files to avoid conversions for line endings. In general, you should
use C<binmode> any time you want to work with binary data.

Also see L<perlfunc/"binmode"> or L<perlopentut>.

If you're concerned about 8-bit textual data then see L<perllocale>.
If you want to deal with multibyte characters, however, there are
some gotchas.  See the section on Regular Expressions.

=head2 How do I determine whether a scalar is a number/whole/integer/float?

Assuming that you don't care about IEEE notations like "NaN" or
"Infinity", you probably just want to use a regular expression:

	use 5.010;
	
	given( $number ) {
		when( /\D/ )             
			{ say "\thas nondigits"; continue }
		when( /^\d+\z/ )         
			{ say "\tis a whole number"; continue }
		when( /^-?\d+\z/ )       
			{ say "\tis an integer"; continue }
		when( /^[+-]?\d+\z/ )    
			{ say "\tis a +/- integer"; continue }
		when( /^-?(?:\d+\.?|\.\d)\d*\z/ ) 
			{ say "\tis a real number"; continue }
		when( /^[+-]?(?=\.?\d)\d*\.?\d*(?:e[+-]?\d+)?\z/i)
			{ say "\tis a C float" }
		}

There are also some commonly used modules for the task.
L<Scalar::Util> (distributed with 5.8) provides access to perl's
internal function C<looks_like_number> for determining whether a
variable looks like a number. L<Data::Types> exports functions that
validate data types using both the above and other regular
expressions. Thirdly, there is C<Regexp::Common> which has regular
expressions to match various types of numbers. Those three modules are
available from the CPAN.

If you're on a POSIX system, Perl supports the C<POSIX::strtod>
function for converting strings to doubles (and also C<POSIX::strtol>
for longs). Its semantics are somewhat cumbersome, so here's a
C<getnum> wrapper function for more convenient access. This function
takes a string and returns the number it found, or C<undef> for input
that isn't a C float. The C<is_numeric> function is a front end to
C<getnum> if you just want to say, "Is this a float?"

	sub getnum {
		use POSIX qw(strtod);
		my $str = shift;
		$str =~ s/^\s+//;
		$str =~ s/\s+$//;
		$! = 0;
		my($num, $unparsed) = strtod($str);
		if (($str eq '') || ($unparsed != 0) || $!) {
				return undef;
			}
		else {
			return $num;
			}
		}

	sub is_numeric { defined getnum($_[0]) }

Or you could check out the L<String::Scanf> module on the CPAN
instead.

=head2 How do I keep persistent data across program calls?

For some specific applications, you can use one of the DBM modules.
See L<AnyDBM_File>.  More generically, you should consult the C<FreezeThaw>
or C<Storable> modules from CPAN.  Starting from Perl 5.8 C<Storable> is part
of the standard distribution.  Here's one example using C<Storable>'s C<store>
and C<retrieve> functions:

	use Storable;
	store(\%hash, "filename");

	# later on...
	$href = retrieve("filename");        # by ref
	%hash = %{ retrieve("filename") };   # direct to hash

=head2 How do I print out or copy a recursive data structure?

The C<Data::Dumper> module on CPAN (or the 5.005 release of Perl) is great
for printing out data structures.  The C<Storable> module on CPAN (or the
5.8 release of Perl), provides a function called C<dclone> that recursively
copies its argument.

	use Storable qw(dclone);
	$r2 = dclone($r1);

Where C<$r1> can be a reference to any kind of data structure you'd like.
It will be deeply copied.  Because C<dclone> takes and returns references,
you'd have to add extra punctuation if you had a hash of arrays that
you wanted to copy.

	%newhash = %{ dclone(\%oldhash) };

=head2 How do I define methods for every class/object?

(contributed by Ben Morrow)

You can use the C<UNIVERSAL> class (see L<UNIVERSAL>). However, please
be very careful to consider the consequences of doing this: adding
methods to every object is very likely to have unintended
consequences. If possible, it would be better to have all your object
inherit from some common base class, or to use an object system like
Moose that supports roles.

=head2 How do I verify a credit card checksum?

Get the C<Business::CreditCard> module from CPAN.

=head2 How do I pack arrays of doubles or floats for XS code?

The arrays.h/arrays.c code in the C<PGPLOT> module on CPAN does just this.
If you're doing a lot of float or double processing, consider using
the C<PDL> module from CPAN instead--it makes number-crunching easy.

See L<http://search.cpan.org/dist/PGPLOT> for the code.

=head1 AUTHOR AND COPYRIGHT

Copyright (c) 1997-2010 Tom Christiansen, Nathan Torkington, and
other authors as noted. All rights reserved.

This documentation is free; you can redistribute it and/or modify it
under the same terms as Perl itself.

Irrespective of its distribution, all code examples in this file
are hereby placed into the public domain.  You are permitted and
encouraged to use this code in your own programs for fun
or for profit as you see fit.  A simple comment in the code giving
credit would be courteous but is not required.