File: time.go

package info (click to toggle)
golang-1.11 1.11.12-2
  • links: PTS, VCS
  • area: main
  • in suites: bullseye, experimental, sid
  • size: 107,360 kB
  • sloc: asm: 88,993; ansic: 8,174; perl: 2,007; sh: 1,804; xml: 623; python: 346; makefile: 123; cpp: 22; f90: 8; awk: 7
file content (1525 lines) | stat: -rw-r--r-- 44,919 bytes parent folder | download | duplicates (8)
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
// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Package time provides functionality for measuring and displaying time.
//
// The calendrical calculations always assume a Gregorian calendar, with
// no leap seconds.
//
// Monotonic Clocks
//
// Operating systems provide both a “wall clock,” which is subject to
// changes for clock synchronization, and a “monotonic clock,” which is
// not. The general rule is that the wall clock is for telling time and
// the monotonic clock is for measuring time. Rather than split the API,
// in this package the Time returned by time.Now contains both a wall
// clock reading and a monotonic clock reading; later time-telling
// operations use the wall clock reading, but later time-measuring
// operations, specifically comparisons and subtractions, use the
// monotonic clock reading.
//
// For example, this code always computes a positive elapsed time of
// approximately 20 milliseconds, even if the wall clock is changed during
// the operation being timed:
//
//	start := time.Now()
//	... operation that takes 20 milliseconds ...
//	t := time.Now()
//	elapsed := t.Sub(start)
//
// Other idioms, such as time.Since(start), time.Until(deadline), and
// time.Now().Before(deadline), are similarly robust against wall clock
// resets.
//
// The rest of this section gives the precise details of how operations
// use monotonic clocks, but understanding those details is not required
// to use this package.
//
// The Time returned by time.Now contains a monotonic clock reading.
// If Time t has a monotonic clock reading, t.Add adds the same duration to
// both the wall clock and monotonic clock readings to compute the result.
// Because t.AddDate(y, m, d), t.Round(d), and t.Truncate(d) are wall time
// computations, they always strip any monotonic clock reading from their results.
// Because t.In, t.Local, and t.UTC are used for their effect on the interpretation
// of the wall time, they also strip any monotonic clock reading from their results.
// The canonical way to strip a monotonic clock reading is to use t = t.Round(0).
//
// If Times t and u both contain monotonic clock readings, the operations
// t.After(u), t.Before(u), t.Equal(u), and t.Sub(u) are carried out
// using the monotonic clock readings alone, ignoring the wall clock
// readings. If either t or u contains no monotonic clock reading, these
// operations fall back to using the wall clock readings.
//
// On some systems the monotonic clock will stop if the computer goes to sleep.
// On such a system, t.Sub(u) may not accurately reflect the actual
// time that passed between t and u.
//
// Because the monotonic clock reading has no meaning outside
// the current process, the serialized forms generated by t.GobEncode,
// t.MarshalBinary, t.MarshalJSON, and t.MarshalText omit the monotonic
// clock reading, and t.Format provides no format for it. Similarly, the
// constructors time.Date, time.Parse, time.ParseInLocation, and time.Unix,
// as well as the unmarshalers t.GobDecode, t.UnmarshalBinary.
// t.UnmarshalJSON, and t.UnmarshalText always create times with
// no monotonic clock reading.
//
// Note that the Go == operator compares not just the time instant but
// also the Location and the monotonic clock reading. See the
// documentation for the Time type for a discussion of equality
// testing for Time values.
//
// For debugging, the result of t.String does include the monotonic
// clock reading if present. If t != u because of different monotonic clock readings,
// that difference will be visible when printing t.String() and u.String().
//
package time

import "errors"

// A Time represents an instant in time with nanosecond precision.
//
// Programs using times should typically store and pass them as values,
// not pointers. That is, time variables and struct fields should be of
// type time.Time, not *time.Time.
//
// A Time value can be used by multiple goroutines simultaneously except
// that the methods GobDecode, UnmarshalBinary, UnmarshalJSON and
// UnmarshalText are not concurrency-safe.
//
// Time instants can be compared using the Before, After, and Equal methods.
// The Sub method subtracts two instants, producing a Duration.
// The Add method adds a Time and a Duration, producing a Time.
//
// The zero value of type Time is January 1, year 1, 00:00:00.000000000 UTC.
// As this time is unlikely to come up in practice, the IsZero method gives
// a simple way of detecting a time that has not been initialized explicitly.
//
// Each Time has associated with it a Location, consulted when computing the
// presentation form of the time, such as in the Format, Hour, and Year methods.
// The methods Local, UTC, and In return a Time with a specific location.
// Changing the location in this way changes only the presentation; it does not
// change the instant in time being denoted and therefore does not affect the
// computations described in earlier paragraphs.
//
// In addition to the required “wall clock” reading, a Time may contain an optional
// reading of the current process's monotonic clock, to provide additional precision
// for comparison or subtraction.
// See the “Monotonic Clocks” section in the package documentation for details.
//
// Note that the Go == operator compares not just the time instant but also the
// Location and the monotonic clock reading. Therefore, Time values should not
// be used as map or database keys without first guaranteeing that the
// identical Location has been set for all values, which can be achieved
// through use of the UTC or Local method, and that the monotonic clock reading
// has been stripped by setting t = t.Round(0). In general, prefer t.Equal(u)
// to t == u, since t.Equal uses the most accurate comparison available and
// correctly handles the case when only one of its arguments has a monotonic
// clock reading.
//
type Time struct {
	// wall and ext encode the wall time seconds, wall time nanoseconds,
	// and optional monotonic clock reading in nanoseconds.
	//
	// From high to low bit position, wall encodes a 1-bit flag (hasMonotonic),
	// a 33-bit seconds field, and a 30-bit wall time nanoseconds field.
	// The nanoseconds field is in the range [0, 999999999].
	// If the hasMonotonic bit is 0, then the 33-bit field must be zero
	// and the full signed 64-bit wall seconds since Jan 1 year 1 is stored in ext.
	// If the hasMonotonic bit is 1, then the 33-bit field holds a 33-bit
	// unsigned wall seconds since Jan 1 year 1885, and ext holds a
	// signed 64-bit monotonic clock reading, nanoseconds since process start.
	wall uint64
	ext  int64

	// loc specifies the Location that should be used to
	// determine the minute, hour, month, day, and year
	// that correspond to this Time.
	// The nil location means UTC.
	// All UTC times are represented with loc==nil, never loc==&utcLoc.
	loc *Location
}

const (
	hasMonotonic = 1 << 63
	maxWall      = wallToInternal + (1<<33 - 1) // year 2157
	minWall      = wallToInternal               // year 1885
	nsecMask     = 1<<30 - 1
	nsecShift    = 30
)

// These helpers for manipulating the wall and monotonic clock readings
// take pointer receivers, even when they don't modify the time,
// to make them cheaper to call.

// nsec returns the time's nanoseconds.
func (t *Time) nsec() int32 {
	return int32(t.wall & nsecMask)
}

// sec returns the time's seconds since Jan 1 year 1.
func (t *Time) sec() int64 {
	if t.wall&hasMonotonic != 0 {
		return wallToInternal + int64(t.wall<<1>>(nsecShift+1))
	}
	return t.ext
}

// unixSec returns the time's seconds since Jan 1 1970 (Unix time).
func (t *Time) unixSec() int64 { return t.sec() + internalToUnix }

// addSec adds d seconds to the time.
func (t *Time) addSec(d int64) {
	if t.wall&hasMonotonic != 0 {
		sec := int64(t.wall << 1 >> (nsecShift + 1))
		dsec := sec + d
		if 0 <= dsec && dsec <= 1<<33-1 {
			t.wall = t.wall&nsecMask | uint64(dsec)<<nsecShift | hasMonotonic
			return
		}
		// Wall second now out of range for packed field.
		// Move to ext.
		t.stripMono()
	}

	// TODO: Check for overflow.
	t.ext += d
}

// setLoc sets the location associated with the time.
func (t *Time) setLoc(loc *Location) {
	if loc == &utcLoc {
		loc = nil
	}
	t.stripMono()
	t.loc = loc
}

// stripMono strips the monotonic clock reading in t.
func (t *Time) stripMono() {
	if t.wall&hasMonotonic != 0 {
		t.ext = t.sec()
		t.wall &= nsecMask
	}
}

// setMono sets the monotonic clock reading in t.
// If t cannot hold a monotonic clock reading,
// because its wall time is too large,
// setMono is a no-op.
func (t *Time) setMono(m int64) {
	if t.wall&hasMonotonic == 0 {
		sec := t.ext
		if sec < minWall || maxWall < sec {
			return
		}
		t.wall |= hasMonotonic | uint64(sec-minWall)<<nsecShift
	}
	t.ext = m
}

// mono returns t's monotonic clock reading.
// It returns 0 for a missing reading.
// This function is used only for testing,
// so it's OK that technically 0 is a valid
// monotonic clock reading as well.
func (t *Time) mono() int64 {
	if t.wall&hasMonotonic == 0 {
		return 0
	}
	return t.ext
}

// After reports whether the time instant t is after u.
func (t Time) After(u Time) bool {
	if t.wall&u.wall&hasMonotonic != 0 {
		return t.ext > u.ext
	}
	ts := t.sec()
	us := u.sec()
	return ts > us || ts == us && t.nsec() > u.nsec()
}

// Before reports whether the time instant t is before u.
func (t Time) Before(u Time) bool {
	if t.wall&u.wall&hasMonotonic != 0 {
		return t.ext < u.ext
	}
	return t.sec() < u.sec() || t.sec() == u.sec() && t.nsec() < u.nsec()
}

// Equal reports whether t and u represent the same time instant.
// Two times can be equal even if they are in different locations.
// For example, 6:00 +0200 CEST and 4:00 UTC are Equal.
// See the documentation on the Time type for the pitfalls of using == with
// Time values; most code should use Equal instead.
func (t Time) Equal(u Time) bool {
	if t.wall&u.wall&hasMonotonic != 0 {
		return t.ext == u.ext
	}
	return t.sec() == u.sec() && t.nsec() == u.nsec()
}

// A Month specifies a month of the year (January = 1, ...).
type Month int

const (
	January Month = 1 + iota
	February
	March
	April
	May
	June
	July
	August
	September
	October
	November
	December
)

var months = [...]string{
	"January",
	"February",
	"March",
	"April",
	"May",
	"June",
	"July",
	"August",
	"September",
	"October",
	"November",
	"December",
}

// String returns the English name of the month ("January", "February", ...).
func (m Month) String() string {
	if January <= m && m <= December {
		return months[m-1]
	}
	buf := make([]byte, 20)
	n := fmtInt(buf, uint64(m))
	return "%!Month(" + string(buf[n:]) + ")"
}

// A Weekday specifies a day of the week (Sunday = 0, ...).
type Weekday int

const (
	Sunday Weekday = iota
	Monday
	Tuesday
	Wednesday
	Thursday
	Friday
	Saturday
)

var days = [...]string{
	"Sunday",
	"Monday",
	"Tuesday",
	"Wednesday",
	"Thursday",
	"Friday",
	"Saturday",
}

// String returns the English name of the day ("Sunday", "Monday", ...).
func (d Weekday) String() string {
	if Sunday <= d && d <= Saturday {
		return days[d]
	}
	buf := make([]byte, 20)
	n := fmtInt(buf, uint64(d))
	return "%!Weekday(" + string(buf[n:]) + ")"
}

// Computations on time.
//
// The zero value for a Time is defined to be
//	January 1, year 1, 00:00:00.000000000 UTC
// which (1) looks like a zero, or as close as you can get in a date
// (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
// be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
// non-negative year even in time zones west of UTC, unlike 1-1-0
// 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
//
// The zero Time value does not force a specific epoch for the time
// representation. For example, to use the Unix epoch internally, we
// could define that to distinguish a zero value from Jan 1 1970, that
// time would be represented by sec=-1, nsec=1e9. However, it does
// suggest a representation, namely using 1-1-1 00:00:00 UTC as the
// epoch, and that's what we do.
//
// The Add and Sub computations are oblivious to the choice of epoch.
//
// The presentation computations - year, month, minute, and so on - all
// rely heavily on division and modulus by positive constants. For
// calendrical calculations we want these divisions to round down, even
// for negative values, so that the remainder is always positive, but
// Go's division (like most hardware division instructions) rounds to
// zero. We can still do those computations and then adjust the result
// for a negative numerator, but it's annoying to write the adjustment
// over and over. Instead, we can change to a different epoch so long
// ago that all the times we care about will be positive, and then round
// to zero and round down coincide. These presentation routines already
// have to add the zone offset, so adding the translation to the
// alternate epoch is cheap. For example, having a non-negative time t
// means that we can write
//
//	sec = t % 60
//
// instead of
//
//	sec = t % 60
//	if sec < 0 {
//		sec += 60
//	}
//
// everywhere.
//
// The calendar runs on an exact 400 year cycle: a 400-year calendar
// printed for 1970-2369 will apply as well to 2370-2769. Even the days
// of the week match up. It simplifies the computations to choose the
// cycle boundaries so that the exceptional years are always delayed as
// long as possible. That means choosing a year equal to 1 mod 400, so
// that the first leap year is the 4th year, the first missed leap year
// is the 100th year, and the missed missed leap year is the 400th year.
// So we'd prefer instead to print a calendar for 2001-2400 and reuse it
// for 2401-2800.
//
// Finally, it's convenient if the delta between the Unix epoch and
// long-ago epoch is representable by an int64 constant.
//
// These three considerations—choose an epoch as early as possible, that
// uses a year equal to 1 mod 400, and that is no more than 2⁶³ seconds
// earlier than 1970—bring us to the year -292277022399. We refer to
// this year as the absolute zero year, and to times measured as a uint64
// seconds since this year as absolute times.
//
// Times measured as an int64 seconds since the year 1—the representation
// used for Time's sec field—are called internal times.
//
// Times measured as an int64 seconds since the year 1970 are called Unix
// times.
//
// It is tempting to just use the year 1 as the absolute epoch, defining
// that the routines are only valid for years >= 1. However, the
// routines would then be invalid when displaying the epoch in time zones
// west of UTC, since it is year 0. It doesn't seem tenable to say that
// printing the zero time correctly isn't supported in half the time
// zones. By comparison, it's reasonable to mishandle some times in
// the year -292277022399.
//
// All this is opaque to clients of the API and can be changed if a
// better implementation presents itself.

const (
	// The unsigned zero year for internal calculations.
	// Must be 1 mod 400, and times before it will not compute correctly,
	// but otherwise can be changed at will.
	absoluteZeroYear = -292277022399

	// The year of the zero Time.
	// Assumed by the unixToInternal computation below.
	internalYear = 1

	// Offsets to convert between internal and absolute or Unix times.
	absoluteToInternal int64 = (absoluteZeroYear - internalYear) * 365.2425 * secondsPerDay
	internalToAbsolute       = -absoluteToInternal

	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
	internalToUnix int64 = -unixToInternal

	wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
	internalToWall int64 = -wallToInternal
)

// IsZero reports whether t represents the zero time instant,
// January 1, year 1, 00:00:00 UTC.
func (t Time) IsZero() bool {
	return t.sec() == 0 && t.nsec() == 0
}

// abs returns the time t as an absolute time, adjusted by the zone offset.
// It is called when computing a presentation property like Month or Hour.
func (t Time) abs() uint64 {
	l := t.loc
	// Avoid function calls when possible.
	if l == nil || l == &localLoc {
		l = l.get()
	}
	sec := t.unixSec()
	if l != &utcLoc {
		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
			sec += int64(l.cacheZone.offset)
		} else {
			_, offset, _, _ := l.lookup(sec)
			sec += int64(offset)
		}
	}
	return uint64(sec + (unixToInternal + internalToAbsolute))
}

// locabs is a combination of the Zone and abs methods,
// extracting both return values from a single zone lookup.
func (t Time) locabs() (name string, offset int, abs uint64) {
	l := t.loc
	if l == nil || l == &localLoc {
		l = l.get()
	}
	// Avoid function call if we hit the local time cache.
	sec := t.unixSec()
	if l != &utcLoc {
		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
			name = l.cacheZone.name
			offset = l.cacheZone.offset
		} else {
			name, offset, _, _ = l.lookup(sec)
		}
		sec += int64(offset)
	} else {
		name = "UTC"
	}
	abs = uint64(sec + (unixToInternal + internalToAbsolute))
	return
}

// Date returns the year, month, and day in which t occurs.
func (t Time) Date() (year int, month Month, day int) {
	year, month, day, _ = t.date(true)
	return
}

// Year returns the year in which t occurs.
func (t Time) Year() int {
	year, _, _, _ := t.date(false)
	return year
}

// Month returns the month of the year specified by t.
func (t Time) Month() Month {
	_, month, _, _ := t.date(true)
	return month
}

// Day returns the day of the month specified by t.
func (t Time) Day() int {
	_, _, day, _ := t.date(true)
	return day
}

// Weekday returns the day of the week specified by t.
func (t Time) Weekday() Weekday {
	return absWeekday(t.abs())
}

// absWeekday is like Weekday but operates on an absolute time.
func absWeekday(abs uint64) Weekday {
	// January 1 of the absolute year, like January 1 of 2001, was a Monday.
	sec := (abs + uint64(Monday)*secondsPerDay) % secondsPerWeek
	return Weekday(int(sec) / secondsPerDay)
}

// ISOWeek returns the ISO 8601 year and week number in which t occurs.
// Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
// week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
// of year n+1.
func (t Time) ISOWeek() (year, week int) {
	year, month, day, yday := t.date(true)
	wday := int(t.Weekday()+6) % 7 // weekday but Monday = 0.
	const (
		Mon int = iota
		Tue
		Wed
		Thu
		Fri
		Sat
		Sun
	)

	// Calculate week as number of Mondays in year up to
	// and including today, plus 1 because the first week is week 0.
	// Putting the + 1 inside the numerator as a + 7 keeps the
	// numerator from being negative, which would cause it to
	// round incorrectly.
	week = (yday - wday + 7) / 7

	// The week number is now correct under the assumption
	// that the first Monday of the year is in week 1.
	// If Jan 1 is a Tuesday, Wednesday, or Thursday, the first Monday
	// is actually in week 2.
	jan1wday := (wday - yday + 7*53) % 7
	if Tue <= jan1wday && jan1wday <= Thu {
		week++
	}

	// If the week number is still 0, we're in early January but in
	// the last week of last year.
	if week == 0 {
		year--
		week = 52
		// A year has 53 weeks when Jan 1 or Dec 31 is a Thursday,
		// meaning Jan 1 of the next year is a Friday
		// or it was a leap year and Jan 1 of the next year is a Saturday.
		if jan1wday == Fri || (jan1wday == Sat && isLeap(year)) {
			week++
		}
	}

	// December 29 to 31 are in week 1 of next year if
	// they are after the last Thursday of the year and
	// December 31 is a Monday, Tuesday, or Wednesday.
	if month == December && day >= 29 && wday < Thu {
		if dec31wday := (wday + 31 - day) % 7; Mon <= dec31wday && dec31wday <= Wed {
			year++
			week = 1
		}
	}

	return
}

// Clock returns the hour, minute, and second within the day specified by t.
func (t Time) Clock() (hour, min, sec int) {
	return absClock(t.abs())
}

// absClock is like clock but operates on an absolute time.
func absClock(abs uint64) (hour, min, sec int) {
	sec = int(abs % secondsPerDay)
	hour = sec / secondsPerHour
	sec -= hour * secondsPerHour
	min = sec / secondsPerMinute
	sec -= min * secondsPerMinute
	return
}

// Hour returns the hour within the day specified by t, in the range [0, 23].
func (t Time) Hour() int {
	return int(t.abs()%secondsPerDay) / secondsPerHour
}

// Minute returns the minute offset within the hour specified by t, in the range [0, 59].
func (t Time) Minute() int {
	return int(t.abs()%secondsPerHour) / secondsPerMinute
}

// Second returns the second offset within the minute specified by t, in the range [0, 59].
func (t Time) Second() int {
	return int(t.abs() % secondsPerMinute)
}

// Nanosecond returns the nanosecond offset within the second specified by t,
// in the range [0, 999999999].
func (t Time) Nanosecond() int {
	return int(t.nsec())
}

// YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
// and [1,366] in leap years.
func (t Time) YearDay() int {
	_, _, _, yday := t.date(false)
	return yday + 1
}

// A Duration represents the elapsed time between two instants
// as an int64 nanosecond count. The representation limits the
// largest representable duration to approximately 290 years.
type Duration int64

const (
	minDuration Duration = -1 << 63
	maxDuration Duration = 1<<63 - 1
)

// Common durations. There is no definition for units of Day or larger
// to avoid confusion across daylight savings time zone transitions.
//
// To count the number of units in a Duration, divide:
//	second := time.Second
//	fmt.Print(int64(second/time.Millisecond)) // prints 1000
//
// To convert an integer number of units to a Duration, multiply:
//	seconds := 10
//	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
//
const (
	Nanosecond  Duration = 1
	Microsecond          = 1000 * Nanosecond
	Millisecond          = 1000 * Microsecond
	Second               = 1000 * Millisecond
	Minute               = 60 * Second
	Hour                 = 60 * Minute
)

// String returns a string representing the duration in the form "72h3m0.5s".
// Leading zero units are omitted. As a special case, durations less than one
// second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
// that the leading digit is non-zero. The zero duration formats as 0s.
func (d Duration) String() string {
	// Largest time is 2540400h10m10.000000000s
	var buf [32]byte
	w := len(buf)

	u := uint64(d)
	neg := d < 0
	if neg {
		u = -u
	}

	if u < uint64(Second) {
		// Special case: if duration is smaller than a second,
		// use smaller units, like 1.2ms
		var prec int
		w--
		buf[w] = 's'
		w--
		switch {
		case u == 0:
			return "0s"
		case u < uint64(Microsecond):
			// print nanoseconds
			prec = 0
			buf[w] = 'n'
		case u < uint64(Millisecond):
			// print microseconds
			prec = 3
			// U+00B5 'µ' micro sign == 0xC2 0xB5
			w-- // Need room for two bytes.
			copy(buf[w:], "µ")
		default:
			// print milliseconds
			prec = 6
			buf[w] = 'm'
		}
		w, u = fmtFrac(buf[:w], u, prec)
		w = fmtInt(buf[:w], u)
	} else {
		w--
		buf[w] = 's'

		w, u = fmtFrac(buf[:w], u, 9)

		// u is now integer seconds
		w = fmtInt(buf[:w], u%60)
		u /= 60

		// u is now integer minutes
		if u > 0 {
			w--
			buf[w] = 'm'
			w = fmtInt(buf[:w], u%60)
			u /= 60

			// u is now integer hours
			// Stop at hours because days can be different lengths.
			if u > 0 {
				w--
				buf[w] = 'h'
				w = fmtInt(buf[:w], u)
			}
		}
	}

	if neg {
		w--
		buf[w] = '-'
	}

	return string(buf[w:])
}

// fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
// tail of buf, omitting trailing zeros. It omits the decimal
// point too when the fraction is 0. It returns the index where the
// output bytes begin and the value v/10**prec.
func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
	// Omit trailing zeros up to and including decimal point.
	w := len(buf)
	print := false
	for i := 0; i < prec; i++ {
		digit := v % 10
		print = print || digit != 0
		if print {
			w--
			buf[w] = byte(digit) + '0'
		}
		v /= 10
	}
	if print {
		w--
		buf[w] = '.'
	}
	return w, v
}

// fmtInt formats v into the tail of buf.
// It returns the index where the output begins.
func fmtInt(buf []byte, v uint64) int {
	w := len(buf)
	if v == 0 {
		w--
		buf[w] = '0'
	} else {
		for v > 0 {
			w--
			buf[w] = byte(v%10) + '0'
			v /= 10
		}
	}
	return w
}

// Nanoseconds returns the duration as an integer nanosecond count.
func (d Duration) Nanoseconds() int64 { return int64(d) }

// These methods return float64 because the dominant
// use case is for printing a floating point number like 1.5s, and
// a truncation to integer would make them not useful in those cases.
// Splitting the integer and fraction ourselves guarantees that
// converting the returned float64 to an integer rounds the same
// way that a pure integer conversion would have, even in cases
// where, say, float64(d.Nanoseconds())/1e9 would have rounded
// differently.

// Seconds returns the duration as a floating point number of seconds.
func (d Duration) Seconds() float64 {
	sec := d / Second
	nsec := d % Second
	return float64(sec) + float64(nsec)/1e9
}

// Minutes returns the duration as a floating point number of minutes.
func (d Duration) Minutes() float64 {
	min := d / Minute
	nsec := d % Minute
	return float64(min) + float64(nsec)/(60*1e9)
}

// Hours returns the duration as a floating point number of hours.
func (d Duration) Hours() float64 {
	hour := d / Hour
	nsec := d % Hour
	return float64(hour) + float64(nsec)/(60*60*1e9)
}

// Truncate returns the result of rounding d toward zero to a multiple of m.
// If m <= 0, Truncate returns d unchanged.
func (d Duration) Truncate(m Duration) Duration {
	if m <= 0 {
		return d
	}
	return d - d%m
}

// lessThanHalf reports whether x+x < y but avoids overflow,
// assuming x and y are both positive (Duration is signed).
func lessThanHalf(x, y Duration) bool {
	return uint64(x)+uint64(x) < uint64(y)
}

// Round returns the result of rounding d to the nearest multiple of m.
// The rounding behavior for halfway values is to round away from zero.
// If the result exceeds the maximum (or minimum)
// value that can be stored in a Duration,
// Round returns the maximum (or minimum) duration.
// If m <= 0, Round returns d unchanged.
func (d Duration) Round(m Duration) Duration {
	if m <= 0 {
		return d
	}
	r := d % m
	if d < 0 {
		r = -r
		if lessThanHalf(r, m) {
			return d + r
		}
		if d1 := d - m + r; d1 < d {
			return d1
		}
		return minDuration // overflow
	}
	if lessThanHalf(r, m) {
		return d - r
	}
	if d1 := d + m - r; d1 > d {
		return d1
	}
	return maxDuration // overflow
}

// Add returns the time t+d.
func (t Time) Add(d Duration) Time {
	dsec := int64(d / 1e9)
	nsec := t.nsec() + int32(d%1e9)
	if nsec >= 1e9 {
		dsec++
		nsec -= 1e9
	} else if nsec < 0 {
		dsec--
		nsec += 1e9
	}
	t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
	t.addSec(dsec)
	if t.wall&hasMonotonic != 0 {
		te := t.ext + int64(d)
		if d < 0 && te > t.ext || d > 0 && te < t.ext {
			// Monotonic clock reading now out of range; degrade to wall-only.
			t.stripMono()
		} else {
			t.ext = te
		}
	}
	return t
}

// Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
// value that can be stored in a Duration, the maximum (or minimum) duration
// will be returned.
// To compute t-d for a duration d, use t.Add(-d).
func (t Time) Sub(u Time) Duration {
	if t.wall&u.wall&hasMonotonic != 0 {
		te := t.ext
		ue := u.ext
		d := Duration(te - ue)
		if d < 0 && te > ue {
			return maxDuration // t - u is positive out of range
		}
		if d > 0 && te < ue {
			return minDuration // t - u is negative out of range
		}
		return d
	}
	d := Duration(t.sec()-u.sec())*Second + Duration(t.nsec()-u.nsec())
	// Check for overflow or underflow.
	switch {
	case u.Add(d).Equal(t):
		return d // d is correct
	case t.Before(u):
		return minDuration // t - u is negative out of range
	default:
		return maxDuration // t - u is positive out of range
	}
}

// Since returns the time elapsed since t.
// It is shorthand for time.Now().Sub(t).
func Since(t Time) Duration {
	return Now().Sub(t)
}

// Until returns the duration until t.
// It is shorthand for t.Sub(time.Now()).
func Until(t Time) Duration {
	return t.Sub(Now())
}

// AddDate returns the time corresponding to adding the
// given number of years, months, and days to t.
// For example, AddDate(-1, 2, 3) applied to January 1, 2011
// returns March 4, 2010.
//
// AddDate normalizes its result in the same way that Date does,
// so, for example, adding one month to October 31 yields
// December 1, the normalized form for November 31.
func (t Time) AddDate(years int, months int, days int) Time {
	year, month, day := t.Date()
	hour, min, sec := t.Clock()
	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec()), t.Location())
}

const (
	secondsPerMinute = 60
	secondsPerHour   = 60 * 60
	secondsPerDay    = 24 * secondsPerHour
	secondsPerWeek   = 7 * secondsPerDay
	daysPer400Years  = 365*400 + 97
	daysPer100Years  = 365*100 + 24
	daysPer4Years    = 365*4 + 1
)

// date computes the year, day of year, and when full=true,
// the month and day in which t occurs.
func (t Time) date(full bool) (year int, month Month, day int, yday int) {
	return absDate(t.abs(), full)
}

// absDate is like date but operates on an absolute time.
func absDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
	// Split into time and day.
	d := abs / secondsPerDay

	// Account for 400 year cycles.
	n := d / daysPer400Years
	y := 400 * n
	d -= daysPer400Years * n

	// Cut off 100-year cycles.
	// The last cycle has one extra leap year, so on the last day
	// of that year, day / daysPer100Years will be 4 instead of 3.
	// Cut it back down to 3 by subtracting n>>2.
	n = d / daysPer100Years
	n -= n >> 2
	y += 100 * n
	d -= daysPer100Years * n

	// Cut off 4-year cycles.
	// The last cycle has a missing leap year, which does not
	// affect the computation.
	n = d / daysPer4Years
	y += 4 * n
	d -= daysPer4Years * n

	// Cut off years within a 4-year cycle.
	// The last year is a leap year, so on the last day of that year,
	// day / 365 will be 4 instead of 3. Cut it back down to 3
	// by subtracting n>>2.
	n = d / 365
	n -= n >> 2
	y += n
	d -= 365 * n

	year = int(int64(y) + absoluteZeroYear)
	yday = int(d)

	if !full {
		return
	}

	day = yday
	if isLeap(year) {
		// Leap year
		switch {
		case day > 31+29-1:
			// After leap day; pretend it wasn't there.
			day--
		case day == 31+29-1:
			// Leap day.
			month = February
			day = 29
			return
		}
	}

	// Estimate month on assumption that every month has 31 days.
	// The estimate may be too low by at most one month, so adjust.
	month = Month(day / 31)
	end := int(daysBefore[month+1])
	var begin int
	if day >= end {
		month++
		begin = end
	} else {
		begin = int(daysBefore[month])
	}

	month++ // because January is 1
	day = day - begin + 1
	return
}

// daysBefore[m] counts the number of days in a non-leap year
// before month m begins. There is an entry for m=12, counting
// the number of days before January of next year (365).
var daysBefore = [...]int32{
	0,
	31,
	31 + 28,
	31 + 28 + 31,
	31 + 28 + 31 + 30,
	31 + 28 + 31 + 30 + 31,
	31 + 28 + 31 + 30 + 31 + 30,
	31 + 28 + 31 + 30 + 31 + 30 + 31,
	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31,
	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30,
	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31,
	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30,
	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31,
}

func daysIn(m Month, year int) int {
	if m == February && isLeap(year) {
		return 29
	}
	return int(daysBefore[m] - daysBefore[m-1])
}

// Provided by package runtime.
func now() (sec int64, nsec int32, mono int64)

// Now returns the current local time.
func Now() Time {
	sec, nsec, mono := now()
	sec += unixToInternal - minWall
	if uint64(sec)>>33 != 0 {
		return Time{uint64(nsec), sec + minWall, Local}
	}
	return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
}

func unixTime(sec int64, nsec int32) Time {
	return Time{uint64(nsec), sec + unixToInternal, Local}
}

// UTC returns t with the location set to UTC.
func (t Time) UTC() Time {
	t.setLoc(&utcLoc)
	return t
}

// Local returns t with the location set to local time.
func (t Time) Local() Time {
	t.setLoc(Local)
	return t
}

// In returns a copy of t representating the same time instant, but
// with the copy's location information set to loc for display
// purposes.
//
// In panics if loc is nil.
func (t Time) In(loc *Location) Time {
	if loc == nil {
		panic("time: missing Location in call to Time.In")
	}
	t.setLoc(loc)
	return t
}

// Location returns the time zone information associated with t.
func (t Time) Location() *Location {
	l := t.loc
	if l == nil {
		l = UTC
	}
	return l
}

// Zone computes the time zone in effect at time t, returning the abbreviated
// name of the zone (such as "CET") and its offset in seconds east of UTC.
func (t Time) Zone() (name string, offset int) {
	name, offset, _, _ = t.loc.lookup(t.unixSec())
	return
}

// Unix returns t as a Unix time, the number of seconds elapsed
// since January 1, 1970 UTC. The result does not depend on the
// location associated with t.
func (t Time) Unix() int64 {
	return t.unixSec()
}

// UnixNano returns t as a Unix time, the number of nanoseconds elapsed
// since January 1, 1970 UTC. The result is undefined if the Unix time
// in nanoseconds cannot be represented by an int64 (a date before the year
// 1678 or after 2262). Note that this means the result of calling UnixNano
// on the zero Time is undefined. The result does not depend on the
// location associated with t.
func (t Time) UnixNano() int64 {
	return (t.unixSec())*1e9 + int64(t.nsec())
}

const timeBinaryVersion byte = 1

// MarshalBinary implements the encoding.BinaryMarshaler interface.
func (t Time) MarshalBinary() ([]byte, error) {
	var offsetMin int16 // minutes east of UTC. -1 is UTC.

	if t.Location() == UTC {
		offsetMin = -1
	} else {
		_, offset := t.Zone()
		if offset%60 != 0 {
			return nil, errors.New("Time.MarshalBinary: zone offset has fractional minute")
		}
		offset /= 60
		if offset < -32768 || offset == -1 || offset > 32767 {
			return nil, errors.New("Time.MarshalBinary: unexpected zone offset")
		}
		offsetMin = int16(offset)
	}

	sec := t.sec()
	nsec := t.nsec()
	enc := []byte{
		timeBinaryVersion, // byte 0 : version
		byte(sec >> 56),   // bytes 1-8: seconds
		byte(sec >> 48),
		byte(sec >> 40),
		byte(sec >> 32),
		byte(sec >> 24),
		byte(sec >> 16),
		byte(sec >> 8),
		byte(sec),
		byte(nsec >> 24), // bytes 9-12: nanoseconds
		byte(nsec >> 16),
		byte(nsec >> 8),
		byte(nsec),
		byte(offsetMin >> 8), // bytes 13-14: zone offset in minutes
		byte(offsetMin),
	}

	return enc, nil
}

// UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
func (t *Time) UnmarshalBinary(data []byte) error {
	buf := data
	if len(buf) == 0 {
		return errors.New("Time.UnmarshalBinary: no data")
	}

	if buf[0] != timeBinaryVersion {
		return errors.New("Time.UnmarshalBinary: unsupported version")
	}

	if len(buf) != /*version*/ 1+ /*sec*/ 8+ /*nsec*/ 4+ /*zone offset*/ 2 {
		return errors.New("Time.UnmarshalBinary: invalid length")
	}

	buf = buf[1:]
	sec := int64(buf[7]) | int64(buf[6])<<8 | int64(buf[5])<<16 | int64(buf[4])<<24 |
		int64(buf[3])<<32 | int64(buf[2])<<40 | int64(buf[1])<<48 | int64(buf[0])<<56

	buf = buf[8:]
	nsec := int32(buf[3]) | int32(buf[2])<<8 | int32(buf[1])<<16 | int32(buf[0])<<24

	buf = buf[4:]
	offset := int(int16(buf[1])|int16(buf[0])<<8) * 60

	*t = Time{}
	t.wall = uint64(nsec)
	t.ext = sec

	if offset == -1*60 {
		t.setLoc(&utcLoc)
	} else if _, localoff, _, _ := Local.lookup(t.unixSec()); offset == localoff {
		t.setLoc(Local)
	} else {
		t.setLoc(FixedZone("", offset))
	}

	return nil
}

// TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
// The same semantics will be provided by the generic MarshalBinary, MarshalText,
// UnmarshalBinary, UnmarshalText.

// GobEncode implements the gob.GobEncoder interface.
func (t Time) GobEncode() ([]byte, error) {
	return t.MarshalBinary()
}

// GobDecode implements the gob.GobDecoder interface.
func (t *Time) GobDecode(data []byte) error {
	return t.UnmarshalBinary(data)
}

// MarshalJSON implements the json.Marshaler interface.
// The time is a quoted string in RFC 3339 format, with sub-second precision added if present.
func (t Time) MarshalJSON() ([]byte, error) {
	if y := t.Year(); y < 0 || y >= 10000 {
		// RFC 3339 is clear that years are 4 digits exactly.
		// See golang.org/issue/4556#c15 for more discussion.
		return nil, errors.New("Time.MarshalJSON: year outside of range [0,9999]")
	}

	b := make([]byte, 0, len(RFC3339Nano)+2)
	b = append(b, '"')
	b = t.AppendFormat(b, RFC3339Nano)
	b = append(b, '"')
	return b, nil
}

// UnmarshalJSON implements the json.Unmarshaler interface.
// The time is expected to be a quoted string in RFC 3339 format.
func (t *Time) UnmarshalJSON(data []byte) error {
	// Ignore null, like in the main JSON package.
	if string(data) == "null" {
		return nil
	}
	// Fractional seconds are handled implicitly by Parse.
	var err error
	*t, err = Parse(`"`+RFC3339+`"`, string(data))
	return err
}

// MarshalText implements the encoding.TextMarshaler interface.
// The time is formatted in RFC 3339 format, with sub-second precision added if present.
func (t Time) MarshalText() ([]byte, error) {
	if y := t.Year(); y < 0 || y >= 10000 {
		return nil, errors.New("Time.MarshalText: year outside of range [0,9999]")
	}

	b := make([]byte, 0, len(RFC3339Nano))
	return t.AppendFormat(b, RFC3339Nano), nil
}

// UnmarshalText implements the encoding.TextUnmarshaler interface.
// The time is expected to be in RFC 3339 format.
func (t *Time) UnmarshalText(data []byte) error {
	// Fractional seconds are handled implicitly by Parse.
	var err error
	*t, err = Parse(RFC3339, string(data))
	return err
}

// Unix returns the local Time corresponding to the given Unix time,
// sec seconds and nsec nanoseconds since January 1, 1970 UTC.
// It is valid to pass nsec outside the range [0, 999999999].
// Not all sec values have a corresponding time value. One such
// value is 1<<63-1 (the largest int64 value).
func Unix(sec int64, nsec int64) Time {
	if nsec < 0 || nsec >= 1e9 {
		n := nsec / 1e9
		sec += n
		nsec -= n * 1e9
		if nsec < 0 {
			nsec += 1e9
			sec--
		}
	}
	return unixTime(sec, int32(nsec))
}

func isLeap(year int) bool {
	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
}

// norm returns nhi, nlo such that
//	hi * base + lo == nhi * base + nlo
//	0 <= nlo < base
func norm(hi, lo, base int) (nhi, nlo int) {
	if lo < 0 {
		n := (-lo-1)/base + 1
		hi -= n
		lo += n * base
	}
	if lo >= base {
		n := lo / base
		hi += n
		lo -= n * base
	}
	return hi, lo
}

// Date returns the Time corresponding to
//	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
// in the appropriate zone for that time in the given location.
//
// The month, day, hour, min, sec, and nsec values may be outside
// their usual ranges and will be normalized during the conversion.
// For example, October 32 converts to November 1.
//
// A daylight savings time transition skips or repeats times.
// For example, in the United States, March 13, 2011 2:15am never occurred,
// while November 6, 2011 1:15am occurred twice. In such cases, the
// choice of time zone, and therefore the time, is not well-defined.
// Date returns a time that is correct in one of the two zones involved
// in the transition, but it does not guarantee which.
//
// Date panics if loc is nil.
func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
	if loc == nil {
		panic("time: missing Location in call to Date")
	}

	// Normalize month, overflowing into year.
	m := int(month) - 1
	year, m = norm(year, m, 12)
	month = Month(m) + 1

	// Normalize nsec, sec, min, hour, overflowing into day.
	sec, nsec = norm(sec, nsec, 1e9)
	min, sec = norm(min, sec, 60)
	hour, min = norm(hour, min, 60)
	day, hour = norm(day, hour, 24)

	y := uint64(int64(year) - absoluteZeroYear)

	// Compute days since the absolute epoch.

	// Add in days from 400-year cycles.
	n := y / 400
	y -= 400 * n
	d := daysPer400Years * n

	// Add in 100-year cycles.
	n = y / 100
	y -= 100 * n
	d += daysPer100Years * n

	// Add in 4-year cycles.
	n = y / 4
	y -= 4 * n
	d += daysPer4Years * n

	// Add in non-leap years.
	n = y
	d += 365 * n

	// Add in days before this month.
	d += uint64(daysBefore[month-1])
	if isLeap(year) && month >= March {
		d++ // February 29
	}

	// Add in days before today.
	d += uint64(day - 1)

	// Add in time elapsed today.
	abs := d * secondsPerDay
	abs += uint64(hour*secondsPerHour + min*secondsPerMinute + sec)

	unix := int64(abs) + (absoluteToInternal + internalToUnix)

	// Look for zone offset for t, so we can adjust to UTC.
	// The lookup function expects UTC, so we pass t in the
	// hope that it will not be too close to a zone transition,
	// and then adjust if it is.
	_, offset, start, end := loc.lookup(unix)
	if offset != 0 {
		switch utc := unix - int64(offset); {
		case utc < start:
			_, offset, _, _ = loc.lookup(start - 1)
		case utc >= end:
			_, offset, _, _ = loc.lookup(end)
		}
		unix -= int64(offset)
	}

	t := unixTime(unix, int32(nsec))
	t.setLoc(loc)
	return t
}

// Truncate returns the result of rounding t down to a multiple of d (since the zero time).
// If d <= 0, Truncate returns t stripped of any monotonic clock reading but otherwise unchanged.
//
// Truncate operates on the time as an absolute duration since the
// zero time; it does not operate on the presentation form of the
// time. Thus, Truncate(Hour) may return a time with a non-zero
// minute, depending on the time's Location.
func (t Time) Truncate(d Duration) Time {
	t.stripMono()
	if d <= 0 {
		return t
	}
	_, r := div(t, d)
	return t.Add(-r)
}

// Round returns the result of rounding t to the nearest multiple of d (since the zero time).
// The rounding behavior for halfway values is to round up.
// If d <= 0, Round returns t stripped of any monotonic clock reading but otherwise unchanged.
//
// Round operates on the time as an absolute duration since the
// zero time; it does not operate on the presentation form of the
// time. Thus, Round(Hour) may return a time with a non-zero
// minute, depending on the time's Location.
func (t Time) Round(d Duration) Time {
	t.stripMono()
	if d <= 0 {
		return t
	}
	_, r := div(t, d)
	if lessThanHalf(r, d) {
		return t.Add(-r)
	}
	return t.Add(d - r)
}

// div divides t by d and returns the quotient parity and remainder.
// We don't use the quotient parity anymore (round half up instead of round to even)
// but it's still here in case we change our minds.
func div(t Time, d Duration) (qmod2 int, r Duration) {
	neg := false
	nsec := t.nsec()
	sec := t.sec()
	if sec < 0 {
		// Operate on absolute value.
		neg = true
		sec = -sec
		nsec = -nsec
		if nsec < 0 {
			nsec += 1e9
			sec-- // sec >= 1 before the -- so safe
		}
	}

	switch {
	// Special case: 2d divides 1 second.
	case d < Second && Second%(d+d) == 0:
		qmod2 = int(nsec/int32(d)) & 1
		r = Duration(nsec % int32(d))

	// Special case: d is a multiple of 1 second.
	case d%Second == 0:
		d1 := int64(d / Second)
		qmod2 = int(sec/d1) & 1
		r = Duration(sec%d1)*Second + Duration(nsec)

	// General case.
	// This could be faster if more cleverness were applied,
	// but it's really only here to avoid special case restrictions in the API.
	// No one will care about these cases.
	default:
		// Compute nanoseconds as 128-bit number.
		sec := uint64(sec)
		tmp := (sec >> 32) * 1e9
		u1 := tmp >> 32
		u0 := tmp << 32
		tmp = (sec & 0xFFFFFFFF) * 1e9
		u0x, u0 := u0, u0+tmp
		if u0 < u0x {
			u1++
		}
		u0x, u0 = u0, u0+uint64(nsec)
		if u0 < u0x {
			u1++
		}

		// Compute remainder by subtracting r<<k for decreasing k.
		// Quotient parity is whether we subtract on last round.
		d1 := uint64(d)
		for d1>>63 != 1 {
			d1 <<= 1
		}
		d0 := uint64(0)
		for {
			qmod2 = 0
			if u1 > d1 || u1 == d1 && u0 >= d0 {
				// subtract
				qmod2 = 1
				u0x, u0 = u0, u0-d0
				if u0 > u0x {
					u1--
				}
				u1 -= d1
			}
			if d1 == 0 && d0 == uint64(d) {
				break
			}
			d0 >>= 1
			d0 |= (d1 & 1) << 63
			d1 >>= 1
		}
		r = Duration(u0)
	}

	if neg && r != 0 {
		// If input was negative and not an exact multiple of d, we computed q, r such that
		//	q*d + r = -t
		// But the right answers are given by -(q-1), d-r:
		//	q*d + r = -t
		//	-q*d - r = t
		//	-(q-1)*d + (d - r) = t
		qmod2 ^= 1
		r = d - r
	}
	return
}