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# Source file src/time/time.go

## Documentation: time

```     1  // Copyright 2009 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  // Package time provides functionality for measuring and displaying time.
6  //
7  // The calendrical calculations always assume a Gregorian calendar, with
8  // no leap seconds.
9  //
10  // Monotonic Clocks
11  //
12  // Operating systems provide both a “wall clock,” which is subject to
13  // changes for clock synchronization, and a “monotonic clock,” which is
14  // not. The general rule is that the wall clock is for telling time and
15  // the monotonic clock is for measuring time. Rather than split the API,
16  // in this package the Time returned by time.Now contains both a wall
18  // operations use the wall clock reading, but later time-measuring
19  // operations, specifically comparisons and subtractions, use the
21  //
22  // For example, this code always computes a positive elapsed time of
23  // approximately 20 milliseconds, even if the wall clock is changed during
24  // the operation being timed:
25  //
26  //	start := time.Now()
27  //	... operation that takes 20 milliseconds ...
28  //	t := time.Now()
29  //	elapsed := t.Sub(start)
30  //
31  // Other idioms, such as time.Since(start), time.Until(deadline), and
32  // time.Now().Before(deadline), are similarly robust against wall clock
33  // resets.
34  //
35  // The rest of this section gives the precise details of how operations
36  // use monotonic clocks, but understanding those details is not required
37  // to use this package.
38  //
39  // The Time returned by time.Now contains a monotonic clock reading.
41  // both the wall clock and monotonic clock readings to compute the result.
42  // Because t.AddDate(y, m, d), t.Round(d), and t.Truncate(d) are wall time
43  // computations, they always strip any monotonic clock reading from their results.
44  // Because t.In, t.Local, and t.UTC are used for their effect on the interpretation
45  // of the wall time, they also strip any monotonic clock reading from their results.
46  // The canonical way to strip a monotonic clock reading is to use t = t.Round(0).
47  //
48  // If Times t and u both contain monotonic clock readings, the operations
49  // t.After(u), t.Before(u), t.Equal(u), and t.Sub(u) are carried out
50  // using the monotonic clock readings alone, ignoring the wall clock
51  // readings. If either t or u contains no monotonic clock reading, these
52  // operations fall back to using the wall clock readings.
53  //
54  // On some systems the monotonic clock will stop if the computer goes to sleep.
55  // On such a system, t.Sub(u) may not accurately reflect the actual
56  // time that passed between t and u.
57  //
58  // Because the monotonic clock reading has no meaning outside
59  // the current process, the serialized forms generated by t.GobEncode,
60  // t.MarshalBinary, t.MarshalJSON, and t.MarshalText omit the monotonic
61  // clock reading, and t.Format provides no format for it. Similarly, the
62  // constructors time.Date, time.Parse, time.ParseInLocation, and time.Unix,
63  // as well as the unmarshalers t.GobDecode, t.UnmarshalBinary.
64  // t.UnmarshalJSON, and t.UnmarshalText always create times with
65  // no monotonic clock reading.
66  //
67  // Note that the Go == operator compares not just the time instant but
68  // also the Location and the monotonic clock reading. See the
69  // documentation for the Time type for a discussion of equality
70  // testing for Time values.
71  //
72  // For debugging, the result of t.String does include the monotonic
73  // clock reading if present. If t != u because of different monotonic clock readings,
74  // that difference will be visible when printing t.String() and u.String().
75  //
76  package time
77
78  import (
79  	"errors"
80  	_ "unsafe" // for go:linkname
81  )
82
83  // A Time represents an instant in time with nanosecond precision.
84  //
85  // Programs using times should typically store and pass them as values,
86  // not pointers. That is, time variables and struct fields should be of
87  // type time.Time, not *time.Time.
88  //
89  // A Time value can be used by multiple goroutines simultaneously except
90  // that the methods GobDecode, UnmarshalBinary, UnmarshalJSON and
91  // UnmarshalText are not concurrency-safe.
92  //
93  // Time instants can be compared using the Before, After, and Equal methods.
94  // The Sub method subtracts two instants, producing a Duration.
95  // The Add method adds a Time and a Duration, producing a Time.
96  //
97  // The zero value of type Time is January 1, year 1, 00:00:00.000000000 UTC.
98  // As this time is unlikely to come up in practice, the IsZero method gives
99  // a simple way of detecting a time that has not been initialized explicitly.
100  //
101  // Each Time has associated with it a Location, consulted when computing the
102  // presentation form of the time, such as in the Format, Hour, and Year methods.
103  // The methods Local, UTC, and In return a Time with a specific location.
104  // Changing the location in this way changes only the presentation; it does not
105  // change the instant in time being denoted and therefore does not affect the
106  // computations described in earlier paragraphs.
107  //
108  // Representations of a Time value saved by the GobEncode, MarshalBinary,
109  // MarshalJSON, and MarshalText methods store the Time.Location's offset, but not
110  // the location name. They therefore lose information about Daylight Saving Time.
111  //
112  // In addition to the required “wall clock” reading, a Time may contain an optional
113  // reading of the current process's monotonic clock, to provide additional precision
114  // for comparison or subtraction.
115  // See the “Monotonic Clocks” section in the package documentation for details.
116  //
117  // Note that the Go == operator compares not just the time instant but also the
118  // Location and the monotonic clock reading. Therefore, Time values should not
119  // be used as map or database keys without first guaranteeing that the
120  // identical Location has been set for all values, which can be achieved
121  // through use of the UTC or Local method, and that the monotonic clock reading
122  // has been stripped by setting t = t.Round(0). In general, prefer t.Equal(u)
123  // to t == u, since t.Equal uses the most accurate comparison available and
124  // correctly handles the case when only one of its arguments has a monotonic
126  //
127  type Time struct {
128  	// wall and ext encode the wall time seconds, wall time nanoseconds,
129  	// and optional monotonic clock reading in nanoseconds.
130  	//
131  	// From high to low bit position, wall encodes a 1-bit flag (hasMonotonic),
132  	// a 33-bit seconds field, and a 30-bit wall time nanoseconds field.
133  	// The nanoseconds field is in the range [0, 999999999].
134  	// If the hasMonotonic bit is 0, then the 33-bit field must be zero
135  	// and the full signed 64-bit wall seconds since Jan 1 year 1 is stored in ext.
136  	// If the hasMonotonic bit is 1, then the 33-bit field holds a 33-bit
137  	// unsigned wall seconds since Jan 1 year 1885, and ext holds a
138  	// signed 64-bit monotonic clock reading, nanoseconds since process start.
139  	wall uint64
140  	ext  int64
141
142  	// loc specifies the Location that should be used to
143  	// determine the minute, hour, month, day, and year
144  	// that correspond to this Time.
145  	// The nil location means UTC.
146  	// All UTC times are represented with loc==nil, never loc==&utcLoc.
147  	loc *Location
148  }
149
150  const (
151  	hasMonotonic = 1 << 63
152  	maxWall      = wallToInternal + (1<<33 - 1) // year 2157
153  	minWall      = wallToInternal               // year 1885
154  	nsecMask     = 1<<30 - 1
155  	nsecShift    = 30
156  )
157
158  // These helpers for manipulating the wall and monotonic clock readings
159  // take pointer receivers, even when they don't modify the time,
160  // to make them cheaper to call.
161
162  // nsec returns the time's nanoseconds.
163  func (t *Time) nsec() int32 {
165  }
166
167  // sec returns the time's seconds since Jan 1 year 1.
168  func (t *Time) sec() int64 {
169  	if t.wall&hasMonotonic != 0 {
170  		return wallToInternal + int64(t.wall<<1>>(nsecShift+1))
171  	}
172  	return t.ext
173  }
174
175  // unixSec returns the time's seconds since Jan 1 1970 (Unix time).
176  func (t *Time) unixSec() int64 { return t.sec() + internalToUnix }
177
179  func (t *Time) addSec(d int64) {
180  	if t.wall&hasMonotonic != 0 {
181  		sec := int64(t.wall << 1 >> (nsecShift + 1))
182  		dsec := sec + d
183  		if 0 <= dsec && dsec <= 1<<33-1 {
184  			t.wall = t.wall&nsecMask | uint64(dsec)<<nsecShift | hasMonotonic
185  			return
186  		}
187  		// Wall second now out of range for packed field.
188  		// Move to ext.
189  		t.stripMono()
190  	}
191
192  	// TODO: Check for overflow.
193  	t.ext += d
194  }
195
196  // setLoc sets the location associated with the time.
197  func (t *Time) setLoc(loc *Location) {
198  	if loc == &utcLoc {
199  		loc = nil
200  	}
201  	t.stripMono()
202  	t.loc = loc
203  }
204
205  // stripMono strips the monotonic clock reading in t.
206  func (t *Time) stripMono() {
207  	if t.wall&hasMonotonic != 0 {
208  		t.ext = t.sec()
210  	}
211  }
212
213  // setMono sets the monotonic clock reading in t.
214  // If t cannot hold a monotonic clock reading,
215  // because its wall time is too large,
216  // setMono is a no-op.
217  func (t *Time) setMono(m int64) {
218  	if t.wall&hasMonotonic == 0 {
219  		sec := t.ext
220  		if sec < minWall || maxWall < sec {
221  			return
222  		}
223  		t.wall |= hasMonotonic | uint64(sec-minWall)<<nsecShift
224  	}
225  	t.ext = m
226  }
227
228  // mono returns t's monotonic clock reading.
229  // It returns 0 for a missing reading.
230  // This function is used only for testing,
231  // so it's OK that technically 0 is a valid
232  // monotonic clock reading as well.
233  func (t *Time) mono() int64 {
234  	if t.wall&hasMonotonic == 0 {
235  		return 0
236  	}
237  	return t.ext
238  }
239
240  // After reports whether the time instant t is after u.
241  func (t Time) After(u Time) bool {
242  	if t.wall&u.wall&hasMonotonic != 0 {
243  		return t.ext > u.ext
244  	}
245  	ts := t.sec()
246  	us := u.sec()
247  	return ts > us || ts == us && t.nsec() > u.nsec()
248  }
249
250  // Before reports whether the time instant t is before u.
251  func (t Time) Before(u Time) bool {
252  	if t.wall&u.wall&hasMonotonic != 0 {
253  		return t.ext < u.ext
254  	}
255  	return t.sec() < u.sec() || t.sec() == u.sec() && t.nsec() < u.nsec()
256  }
257
258  // Equal reports whether t and u represent the same time instant.
259  // Two times can be equal even if they are in different locations.
260  // For example, 6:00 +0200 CEST and 4:00 UTC are Equal.
261  // See the documentation on the Time type for the pitfalls of using == with
262  // Time values; most code should use Equal instead.
263  func (t Time) Equal(u Time) bool {
264  	if t.wall&u.wall&hasMonotonic != 0 {
265  		return t.ext == u.ext
266  	}
267  	return t.sec() == u.sec() && t.nsec() == u.nsec()
268  }
269
270  // A Month specifies a month of the year (January = 1, ...).
271  type Month int
272
273  const (
274  	January Month = 1 + iota
275  	February
276  	March
277  	April
278  	May
279  	June
280  	July
281  	August
282  	September
283  	October
284  	November
285  	December
286  )
287
288  var months = [...]string{
289  	"January",
290  	"February",
291  	"March",
292  	"April",
293  	"May",
294  	"June",
295  	"July",
296  	"August",
297  	"September",
298  	"October",
299  	"November",
300  	"December",
301  }
302
303  // String returns the English name of the month ("January", "February", ...).
304  func (m Month) String() string {
305  	if January <= m && m <= December {
306  		return months[m-1]
307  	}
308  	buf := make([]byte, 20)
309  	n := fmtInt(buf, uint64(m))
310  	return "%!Month(" + string(buf[n:]) + ")"
311  }
312
313  // A Weekday specifies a day of the week (Sunday = 0, ...).
314  type Weekday int
315
316  const (
317  	Sunday Weekday = iota
318  	Monday
319  	Tuesday
320  	Wednesday
321  	Thursday
322  	Friday
323  	Saturday
324  )
325
326  var days = [...]string{
327  	"Sunday",
328  	"Monday",
329  	"Tuesday",
330  	"Wednesday",
331  	"Thursday",
332  	"Friday",
333  	"Saturday",
334  }
335
336  // String returns the English name of the day ("Sunday", "Monday", ...).
337  func (d Weekday) String() string {
338  	if Sunday <= d && d <= Saturday {
339  		return days[d]
340  	}
341  	buf := make([]byte, 20)
342  	n := fmtInt(buf, uint64(d))
343  	return "%!Weekday(" + string(buf[n:]) + ")"
344  }
345
346  // Computations on time.
347  //
348  // The zero value for a Time is defined to be
349  //	January 1, year 1, 00:00:00.000000000 UTC
350  // which (1) looks like a zero, or as close as you can get in a date
351  // (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
352  // be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
353  // non-negative year even in time zones west of UTC, unlike 1-1-0
354  // 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
355  //
356  // The zero Time value does not force a specific epoch for the time
357  // representation. For example, to use the Unix epoch internally, we
358  // could define that to distinguish a zero value from Jan 1 1970, that
359  // time would be represented by sec=-1, nsec=1e9. However, it does
360  // suggest a representation, namely using 1-1-1 00:00:00 UTC as the
361  // epoch, and that's what we do.
362  //
363  // The Add and Sub computations are oblivious to the choice of epoch.
364  //
365  // The presentation computations - year, month, minute, and so on - all
366  // rely heavily on division and modulus by positive constants. For
367  // calendrical calculations we want these divisions to round down, even
368  // for negative values, so that the remainder is always positive, but
369  // Go's division (like most hardware division instructions) rounds to
370  // zero. We can still do those computations and then adjust the result
371  // for a negative numerator, but it's annoying to write the adjustment
372  // over and over. Instead, we can change to a different epoch so long
373  // ago that all the times we care about will be positive, and then round
374  // to zero and round down coincide. These presentation routines already
375  // have to add the zone offset, so adding the translation to the
376  // alternate epoch is cheap. For example, having a non-negative time t
377  // means that we can write
378  //
379  //	sec = t % 60
380  //
382  //
383  //	sec = t % 60
384  //	if sec < 0 {
385  //		sec += 60
386  //	}
387  //
388  // everywhere.
389  //
390  // The calendar runs on an exact 400 year cycle: a 400-year calendar
391  // printed for 1970-2369 will apply as well to 2370-2769. Even the days
392  // of the week match up. It simplifies the computations to choose the
393  // cycle boundaries so that the exceptional years are always delayed as
394  // long as possible. That means choosing a year equal to 1 mod 400, so
395  // that the first leap year is the 4th year, the first missed leap year
396  // is the 100th year, and the missed missed leap year is the 400th year.
397  // So we'd prefer instead to print a calendar for 2001-2400 and reuse it
398  // for 2401-2800.
399  //
400  // Finally, it's convenient if the delta between the Unix epoch and
401  // long-ago epoch is representable by an int64 constant.
402  //
403  // These three considerations—choose an epoch as early as possible, that
404  // uses a year equal to 1 mod 400, and that is no more than 2⁶³ seconds
405  // earlier than 1970—bring us to the year -292277022399. We refer to
406  // this year as the absolute zero year, and to times measured as a uint64
407  // seconds since this year as absolute times.
408  //
409  // Times measured as an int64 seconds since the year 1—the representation
410  // used for Time's sec field—are called internal times.
411  //
412  // Times measured as an int64 seconds since the year 1970 are called Unix
413  // times.
414  //
415  // It is tempting to just use the year 1 as the absolute epoch, defining
416  // that the routines are only valid for years >= 1. However, the
417  // routines would then be invalid when displaying the epoch in time zones
418  // west of UTC, since it is year 0. It doesn't seem tenable to say that
419  // printing the zero time correctly isn't supported in half the time
420  // zones. By comparison, it's reasonable to mishandle some times in
421  // the year -292277022399.
422  //
423  // All this is opaque to clients of the API and can be changed if a
424  // better implementation presents itself.
425
426  const (
427  	// The unsigned zero year for internal calculations.
428  	// Must be 1 mod 400, and times before it will not compute correctly,
429  	// but otherwise can be changed at will.
430  	absoluteZeroYear = -292277022399
431
432  	// The year of the zero Time.
433  	// Assumed by the unixToInternal computation below.
434  	internalYear = 1
435
436  	// Offsets to convert between internal and absolute or Unix times.
437  	absoluteToInternal int64 = (absoluteZeroYear - internalYear) * 365.2425 * secondsPerDay
438  	internalToAbsolute       = -absoluteToInternal
439
440  	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
441  	internalToUnix int64 = -unixToInternal
442
443  	wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
444  	internalToWall int64 = -wallToInternal
445  )
446
447  // IsZero reports whether t represents the zero time instant,
448  // January 1, year 1, 00:00:00 UTC.
449  func (t Time) IsZero() bool {
450  	return t.sec() == 0 && t.nsec() == 0
451  }
452
453  // abs returns the time t as an absolute time, adjusted by the zone offset.
454  // It is called when computing a presentation property like Month or Hour.
455  func (t Time) abs() uint64 {
456  	l := t.loc
457  	// Avoid function calls when possible.
458  	if l == nil || l == &localLoc {
459  		l = l.get()
460  	}
461  	sec := t.unixSec()
462  	if l != &utcLoc {
463  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
464  			sec += int64(l.cacheZone.offset)
465  		} else {
466  			_, offset, _, _ := l.lookup(sec)
467  			sec += int64(offset)
468  		}
469  	}
470  	return uint64(sec + (unixToInternal + internalToAbsolute))
471  }
472
473  // locabs is a combination of the Zone and abs methods,
474  // extracting both return values from a single zone lookup.
475  func (t Time) locabs() (name string, offset int, abs uint64) {
476  	l := t.loc
477  	if l == nil || l == &localLoc {
478  		l = l.get()
479  	}
480  	// Avoid function call if we hit the local time cache.
481  	sec := t.unixSec()
482  	if l != &utcLoc {
483  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
484  			name = l.cacheZone.name
485  			offset = l.cacheZone.offset
486  		} else {
487  			name, offset, _, _ = l.lookup(sec)
488  		}
489  		sec += int64(offset)
490  	} else {
491  		name = "UTC"
492  	}
493  	abs = uint64(sec + (unixToInternal + internalToAbsolute))
494  	return
495  }
496
497  // Date returns the year, month, and day in which t occurs.
498  func (t Time) Date() (year int, month Month, day int) {
499  	year, month, day, _ = t.date(true)
500  	return
501  }
502
503  // Year returns the year in which t occurs.
504  func (t Time) Year() int {
505  	year, _, _, _ := t.date(false)
506  	return year
507  }
508
509  // Month returns the month of the year specified by t.
510  func (t Time) Month() Month {
511  	_, month, _, _ := t.date(true)
512  	return month
513  }
514
515  // Day returns the day of the month specified by t.
516  func (t Time) Day() int {
517  	_, _, day, _ := t.date(true)
518  	return day
519  }
520
521  // Weekday returns the day of the week specified by t.
522  func (t Time) Weekday() Weekday {
523  	return absWeekday(t.abs())
524  }
525
526  // absWeekday is like Weekday but operates on an absolute time.
527  func absWeekday(abs uint64) Weekday {
528  	// January 1 of the absolute year, like January 1 of 2001, was a Monday.
529  	sec := (abs + uint64(Monday)*secondsPerDay) % secondsPerWeek
530  	return Weekday(int(sec) / secondsPerDay)
531  }
532
533  // ISOWeek returns the ISO 8601 year and week number in which t occurs.
534  // Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
535  // week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
536  // of year n+1.
537  func (t Time) ISOWeek() (year, week int) {
538  	year, month, day, yday := t.date(true)
539  	wday := int(t.Weekday()+6) % 7 // weekday but Monday = 0.
540  	const (
541  		Mon int = iota
542  		Tue
543  		Wed
544  		Thu
545  		Fri
546  		Sat
547  		Sun
548  	)
549
550  	// Calculate week as number of Mondays in year up to
551  	// and including today, plus 1 because the first week is week 0.
552  	// Putting the + 1 inside the numerator as a + 7 keeps the
553  	// numerator from being negative, which would cause it to
554  	// round incorrectly.
555  	week = (yday - wday + 7) / 7
556
557  	// The week number is now correct under the assumption
558  	// that the first Monday of the year is in week 1.
559  	// If Jan 1 is a Tuesday, Wednesday, or Thursday, the first Monday
560  	// is actually in week 2.
561  	jan1wday := (wday - yday + 7*53) % 7
562  	if Tue <= jan1wday && jan1wday <= Thu {
563  		week++
564  	}
565
566  	// If the week number is still 0, we're in early January but in
567  	// the last week of last year.
568  	if week == 0 {
569  		year--
570  		week = 52
571  		// A year has 53 weeks when Jan 1 or Dec 31 is a Thursday,
572  		// meaning Jan 1 of the next year is a Friday
573  		// or it was a leap year and Jan 1 of the next year is a Saturday.
574  		if jan1wday == Fri || (jan1wday == Sat && isLeap(year)) {
575  			week++
576  		}
577  	}
578
579  	// December 29 to 31 are in week 1 of next year if
580  	// they are after the last Thursday of the year and
581  	// December 31 is a Monday, Tuesday, or Wednesday.
582  	if month == December && day >= 29 && wday < Thu {
583  		if dec31wday := (wday + 31 - day) % 7; Mon <= dec31wday && dec31wday <= Wed {
584  			year++
585  			week = 1
586  		}
587  	}
588
589  	return
590  }
591
592  // Clock returns the hour, minute, and second within the day specified by t.
593  func (t Time) Clock() (hour, min, sec int) {
594  	return absClock(t.abs())
595  }
596
597  // absClock is like clock but operates on an absolute time.
598  func absClock(abs uint64) (hour, min, sec int) {
599  	sec = int(abs % secondsPerDay)
600  	hour = sec / secondsPerHour
601  	sec -= hour * secondsPerHour
602  	min = sec / secondsPerMinute
603  	sec -= min * secondsPerMinute
604  	return
605  }
606
607  // Hour returns the hour within the day specified by t, in the range [0, 23].
608  func (t Time) Hour() int {
609  	return int(t.abs()%secondsPerDay) / secondsPerHour
610  }
611
612  // Minute returns the minute offset within the hour specified by t, in the range [0, 59].
613  func (t Time) Minute() int {
614  	return int(t.abs()%secondsPerHour) / secondsPerMinute
615  }
616
617  // Second returns the second offset within the minute specified by t, in the range [0, 59].
618  func (t Time) Second() int {
619  	return int(t.abs() % secondsPerMinute)
620  }
621
622  // Nanosecond returns the nanosecond offset within the second specified by t,
623  // in the range [0, 999999999].
624  func (t Time) Nanosecond() int {
625  	return int(t.nsec())
626  }
627
628  // YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
629  // and [1,366] in leap years.
630  func (t Time) YearDay() int {
631  	_, _, _, yday := t.date(false)
632  	return yday + 1
633  }
634
635  // A Duration represents the elapsed time between two instants
636  // as an int64 nanosecond count. The representation limits the
637  // largest representable duration to approximately 290 years.
638  type Duration int64
639
640  const (
641  	minDuration Duration = -1 << 63
642  	maxDuration Duration = 1<<63 - 1
643  )
644
645  // Common durations. There is no definition for units of Day or larger
646  // to avoid confusion across daylight savings time zone transitions.
647  //
648  // To count the number of units in a Duration, divide:
649  //	second := time.Second
650  //	fmt.Print(int64(second/time.Millisecond)) // prints 1000
651  //
652  // To convert an integer number of units to a Duration, multiply:
653  //	seconds := 10
654  //	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
655  //
656  const (
657  	Nanosecond  Duration = 1
658  	Microsecond          = 1000 * Nanosecond
659  	Millisecond          = 1000 * Microsecond
660  	Second               = 1000 * Millisecond
661  	Minute               = 60 * Second
662  	Hour                 = 60 * Minute
663  )
664
665  // String returns a string representing the duration in the form "72h3m0.5s".
666  // Leading zero units are omitted. As a special case, durations less than one
667  // second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
668  // that the leading digit is non-zero. The zero duration formats as 0s.
669  func (d Duration) String() string {
670  	// Largest time is 2540400h10m10.000000000s
671  	var buf byte
672  	w := len(buf)
673
674  	u := uint64(d)
675  	neg := d < 0
676  	if neg {
677  		u = -u
678  	}
679
680  	if u < uint64(Second) {
681  		// Special case: if duration is smaller than a second,
682  		// use smaller units, like 1.2ms
683  		var prec int
684  		w--
685  		buf[w] = 's'
686  		w--
687  		switch {
688  		case u == 0:
689  			return "0s"
690  		case u < uint64(Microsecond):
691  			// print nanoseconds
692  			prec = 0
693  			buf[w] = 'n'
694  		case u < uint64(Millisecond):
695  			// print microseconds
696  			prec = 3
697  			// U+00B5 'µ' micro sign == 0xC2 0xB5
698  			w-- // Need room for two bytes.
699  			copy(buf[w:], "µ")
700  		default:
701  			// print milliseconds
702  			prec = 6
703  			buf[w] = 'm'
704  		}
705  		w, u = fmtFrac(buf[:w], u, prec)
706  		w = fmtInt(buf[:w], u)
707  	} else {
708  		w--
709  		buf[w] = 's'
710
711  		w, u = fmtFrac(buf[:w], u, 9)
712
713  		// u is now integer seconds
714  		w = fmtInt(buf[:w], u%60)
715  		u /= 60
716
717  		// u is now integer minutes
718  		if u > 0 {
719  			w--
720  			buf[w] = 'm'
721  			w = fmtInt(buf[:w], u%60)
722  			u /= 60
723
724  			// u is now integer hours
725  			// Stop at hours because days can be different lengths.
726  			if u > 0 {
727  				w--
728  				buf[w] = 'h'
729  				w = fmtInt(buf[:w], u)
730  			}
731  		}
732  	}
733
734  	if neg {
735  		w--
736  		buf[w] = '-'
737  	}
738
739  	return string(buf[w:])
740  }
741
742  // fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
743  // tail of buf, omitting trailing zeros. It omits the decimal
744  // point too when the fraction is 0. It returns the index where the
745  // output bytes begin and the value v/10**prec.
746  func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
747  	// Omit trailing zeros up to and including decimal point.
748  	w := len(buf)
749  	print := false
750  	for i := 0; i < prec; i++ {
751  		digit := v % 10
752  		print = print || digit != 0
753  		if print {
754  			w--
755  			buf[w] = byte(digit) + '0'
756  		}
757  		v /= 10
758  	}
759  	if print {
760  		w--
761  		buf[w] = '.'
762  	}
763  	return w, v
764  }
765
766  // fmtInt formats v into the tail of buf.
767  // It returns the index where the output begins.
768  func fmtInt(buf []byte, v uint64) int {
769  	w := len(buf)
770  	if v == 0 {
771  		w--
772  		buf[w] = '0'
773  	} else {
774  		for v > 0 {
775  			w--
776  			buf[w] = byte(v%10) + '0'
777  			v /= 10
778  		}
779  	}
780  	return w
781  }
782
783  // Nanoseconds returns the duration as an integer nanosecond count.
784  func (d Duration) Nanoseconds() int64 { return int64(d) }
785
786  // These methods return float64 because the dominant
787  // use case is for printing a floating point number like 1.5s, and
788  // a truncation to integer would make them not useful in those cases.
789  // Splitting the integer and fraction ourselves guarantees that
790  // converting the returned float64 to an integer rounds the same
791  // way that a pure integer conversion would have, even in cases
792  // where, say, float64(d.Nanoseconds())/1e9 would have rounded
793  // differently.
794
795  // Seconds returns the duration as a floating point number of seconds.
796  func (d Duration) Seconds() float64 {
797  	sec := d / Second
798  	nsec := d % Second
799  	return float64(sec) + float64(nsec)/1e9
800  }
801
802  // Minutes returns the duration as a floating point number of minutes.
803  func (d Duration) Minutes() float64 {
804  	min := d / Minute
805  	nsec := d % Minute
806  	return float64(min) + float64(nsec)/(60*1e9)
807  }
808
809  // Hours returns the duration as a floating point number of hours.
810  func (d Duration) Hours() float64 {
811  	hour := d / Hour
812  	nsec := d % Hour
813  	return float64(hour) + float64(nsec)/(60*60*1e9)
814  }
815
816  // Truncate returns the result of rounding d toward zero to a multiple of m.
817  // If m <= 0, Truncate returns d unchanged.
818  func (d Duration) Truncate(m Duration) Duration {
819  	if m <= 0 {
820  		return d
821  	}
822  	return d - d%m
823  }
824
825  // lessThanHalf reports whether x+x < y but avoids overflow,
826  // assuming x and y are both positive (Duration is signed).
827  func lessThanHalf(x, y Duration) bool {
828  	return uint64(x)+uint64(x) < uint64(y)
829  }
830
831  // Round returns the result of rounding d to the nearest multiple of m.
832  // The rounding behavior for halfway values is to round away from zero.
833  // If the result exceeds the maximum (or minimum)
834  // value that can be stored in a Duration,
835  // Round returns the maximum (or minimum) duration.
836  // If m <= 0, Round returns d unchanged.
837  func (d Duration) Round(m Duration) Duration {
838  	if m <= 0 {
839  		return d
840  	}
841  	r := d % m
842  	if d < 0 {
843  		r = -r
844  		if lessThanHalf(r, m) {
845  			return d + r
846  		}
847  		if d1 := d - m + r; d1 < d {
848  			return d1
849  		}
850  		return minDuration // overflow
851  	}
852  	if lessThanHalf(r, m) {
853  		return d - r
854  	}
855  	if d1 := d + m - r; d1 > d {
856  		return d1
857  	}
858  	return maxDuration // overflow
859  }
860
861  // Add returns the time t+d.
862  func (t Time) Add(d Duration) Time {
863  	dsec := int64(d / 1e9)
864  	nsec := t.nsec() + int32(d%1e9)
865  	if nsec >= 1e9 {
866  		dsec++
867  		nsec -= 1e9
868  	} else if nsec < 0 {
869  		dsec--
870  		nsec += 1e9
871  	}
872  	t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
874  	if t.wall&hasMonotonic != 0 {
875  		te := t.ext + int64(d)
876  		if d < 0 && te > t.ext || d > 0 && te < t.ext {
877  			// Monotonic clock reading now out of range; degrade to wall-only.
878  			t.stripMono()
879  		} else {
880  			t.ext = te
881  		}
882  	}
883  	return t
884  }
885
886  // Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
887  // value that can be stored in a Duration, the maximum (or minimum) duration
888  // will be returned.
889  // To compute t-d for a duration d, use t.Add(-d).
890  func (t Time) Sub(u Time) Duration {
891  	if t.wall&u.wall&hasMonotonic != 0 {
892  		te := t.ext
893  		ue := u.ext
894  		d := Duration(te - ue)
895  		if d < 0 && te > ue {
896  			return maxDuration // t - u is positive out of range
897  		}
898  		if d > 0 && te < ue {
899  			return minDuration // t - u is negative out of range
900  		}
901  		return d
902  	}
903  	d := Duration(t.sec()-u.sec())*Second + Duration(t.nsec()-u.nsec())
904  	// Check for overflow or underflow.
905  	switch {
907  		return d // d is correct
908  	case t.Before(u):
909  		return minDuration // t - u is negative out of range
910  	default:
911  		return maxDuration // t - u is positive out of range
912  	}
913  }
914
915  // Since returns the time elapsed since t.
916  // It is shorthand for time.Now().Sub(t).
917  func Since(t Time) Duration {
918  	var now Time
919  	if t.wall&hasMonotonic != 0 {
920  		// Common case optimization: if t has monotomic time, then Sub will use only it.
921  		now = Time{hasMonotonic, runtimeNano() - startNano, nil}
922  	} else {
923  		now = Now()
924  	}
925  	return now.Sub(t)
926  }
927
928  // Until returns the duration until t.
929  // It is shorthand for t.Sub(time.Now()).
930  func Until(t Time) Duration {
931  	var now Time
932  	if t.wall&hasMonotonic != 0 {
933  		// Common case optimization: if t has monotomic time, then Sub will use only it.
934  		now = Time{hasMonotonic, runtimeNano() - startNano, nil}
935  	} else {
936  		now = Now()
937  	}
938  	return t.Sub(now)
939  }
940
942  // given number of years, months, and days to t.
943  // For example, AddDate(-1, 2, 3) applied to January 1, 2011
944  // returns March 4, 2010.
945  //
946  // AddDate normalizes its result in the same way that Date does,
947  // so, for example, adding one month to October 31 yields
948  // December 1, the normalized form for November 31.
949  func (t Time) AddDate(years int, months int, days int) Time {
950  	year, month, day := t.Date()
951  	hour, min, sec := t.Clock()
952  	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec()), t.Location())
953  }
954
955  const (
956  	secondsPerMinute = 60
957  	secondsPerHour   = 60 * secondsPerMinute
958  	secondsPerDay    = 24 * secondsPerHour
959  	secondsPerWeek   = 7 * secondsPerDay
960  	daysPer400Years  = 365*400 + 97
961  	daysPer100Years  = 365*100 + 24
962  	daysPer4Years    = 365*4 + 1
963  )
964
965  // date computes the year, day of year, and when full=true,
966  // the month and day in which t occurs.
967  func (t Time) date(full bool) (year int, month Month, day int, yday int) {
968  	return absDate(t.abs(), full)
969  }
970
971  // absDate is like date but operates on an absolute time.
972  func absDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
973  	// Split into time and day.
974  	d := abs / secondsPerDay
975
976  	// Account for 400 year cycles.
977  	n := d / daysPer400Years
978  	y := 400 * n
979  	d -= daysPer400Years * n
980
981  	// Cut off 100-year cycles.
982  	// The last cycle has one extra leap year, so on the last day
983  	// of that year, day / daysPer100Years will be 4 instead of 3.
984  	// Cut it back down to 3 by subtracting n>>2.
985  	n = d / daysPer100Years
986  	n -= n >> 2
987  	y += 100 * n
988  	d -= daysPer100Years * n
989
990  	// Cut off 4-year cycles.
991  	// The last cycle has a missing leap year, which does not
992  	// affect the computation.
993  	n = d / daysPer4Years
994  	y += 4 * n
995  	d -= daysPer4Years * n
996
997  	// Cut off years within a 4-year cycle.
998  	// The last year is a leap year, so on the last day of that year,
999  	// day / 365 will be 4 instead of 3. Cut it back down to 3
1000  	// by subtracting n>>2.
1001  	n = d / 365
1002  	n -= n >> 2
1003  	y += n
1004  	d -= 365 * n
1005
1006  	year = int(int64(y) + absoluteZeroYear)
1007  	yday = int(d)
1008
1009  	if !full {
1010  		return
1011  	}
1012
1013  	day = yday
1014  	if isLeap(year) {
1015  		// Leap year
1016  		switch {
1017  		case day > 31+29-1:
1018  			// After leap day; pretend it wasn't there.
1019  			day--
1020  		case day == 31+29-1:
1021  			// Leap day.
1022  			month = February
1023  			day = 29
1024  			return
1025  		}
1026  	}
1027
1028  	// Estimate month on assumption that every month has 31 days.
1029  	// The estimate may be too low by at most one month, so adjust.
1030  	month = Month(day / 31)
1031  	end := int(daysBefore[month+1])
1032  	var begin int
1033  	if day >= end {
1034  		month++
1035  		begin = end
1036  	} else {
1037  		begin = int(daysBefore[month])
1038  	}
1039
1040  	month++ // because January is 1
1041  	day = day - begin + 1
1042  	return
1043  }
1044
1045  // daysBefore[m] counts the number of days in a non-leap year
1046  // before month m begins. There is an entry for m=12, counting
1047  // the number of days before January of next year (365).
1048  var daysBefore = [...]int32{
1049  	0,
1050  	31,
1051  	31 + 28,
1052  	31 + 28 + 31,
1053  	31 + 28 + 31 + 30,
1054  	31 + 28 + 31 + 30 + 31,
1055  	31 + 28 + 31 + 30 + 31 + 30,
1056  	31 + 28 + 31 + 30 + 31 + 30 + 31,
1057  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31,
1058  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30,
1059  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31,
1060  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30,
1061  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31,
1062  }
1063
1064  func daysIn(m Month, year int) int {
1065  	if m == February && isLeap(year) {
1066  		return 29
1067  	}
1068  	return int(daysBefore[m] - daysBefore[m-1])
1069  }
1070
1071  // Provided by package runtime.
1072  func now() (sec int64, nsec int32, mono int64)
1073
1074  // runtimeNano returns the current value of the runtime clock in nanoseconds.
1076  func runtimeNano() int64
1077
1078  // Monotonic times are reported as offsets from startNano.
1079  // We initialize startNano to runtimeNano() - 1 so that on systems where
1080  // monotonic time resolution is fairly low (e.g. Windows 2008
1081  // which appears to have a default resolution of 15ms),
1082  // we avoid ever reporting a monotonic time of 0.
1083  // (Callers may want to use 0 as "time not set".)
1084  var startNano int64 = runtimeNano() - 1
1085
1086  // Now returns the current local time.
1087  func Now() Time {
1088  	sec, nsec, mono := now()
1089  	mono -= startNano
1090  	sec += unixToInternal - minWall
1091  	if uint64(sec)>>33 != 0 {
1092  		return Time{uint64(nsec), sec + minWall, Local}
1093  	}
1094  	return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
1095  }
1096
1097  func unixTime(sec int64, nsec int32) Time {
1098  	return Time{uint64(nsec), sec + unixToInternal, Local}
1099  }
1100
1101  // UTC returns t with the location set to UTC.
1102  func (t Time) UTC() Time {
1103  	t.setLoc(&utcLoc)
1104  	return t
1105  }
1106
1107  // Local returns t with the location set to local time.
1108  func (t Time) Local() Time {
1109  	t.setLoc(Local)
1110  	return t
1111  }
1112
1113  // In returns a copy of t representing the same time instant, but
1114  // with the copy's location information set to loc for display
1115  // purposes.
1116  //
1117  // In panics if loc is nil.
1118  func (t Time) In(loc *Location) Time {
1119  	if loc == nil {
1120  		panic("time: missing Location in call to Time.In")
1121  	}
1122  	t.setLoc(loc)
1123  	return t
1124  }
1125
1126  // Location returns the time zone information associated with t.
1127  func (t Time) Location() *Location {
1128  	l := t.loc
1129  	if l == nil {
1130  		l = UTC
1131  	}
1132  	return l
1133  }
1134
1135  // Zone computes the time zone in effect at time t, returning the abbreviated
1136  // name of the zone (such as "CET") and its offset in seconds east of UTC.
1137  func (t Time) Zone() (name string, offset int) {
1138  	name, offset, _, _ = t.loc.lookup(t.unixSec())
1139  	return
1140  }
1141
1142  // Unix returns t as a Unix time, the number of seconds elapsed
1143  // since January 1, 1970 UTC. The result does not depend on the
1144  // location associated with t.
1145  func (t Time) Unix() int64 {
1146  	return t.unixSec()
1147  }
1148
1149  // UnixNano returns t as a Unix time, the number of nanoseconds elapsed
1150  // since January 1, 1970 UTC. The result is undefined if the Unix time
1151  // in nanoseconds cannot be represented by an int64 (a date before the year
1152  // 1678 or after 2262). Note that this means the result of calling UnixNano
1153  // on the zero Time is undefined. The result does not depend on the
1154  // location associated with t.
1155  func (t Time) UnixNano() int64 {
1156  	return (t.unixSec())*1e9 + int64(t.nsec())
1157  }
1158
1159  const timeBinaryVersion byte = 1
1160
1161  // MarshalBinary implements the encoding.BinaryMarshaler interface.
1162  func (t Time) MarshalBinary() ([]byte, error) {
1163  	var offsetMin int16 // minutes east of UTC. -1 is UTC.
1164
1165  	if t.Location() == UTC {
1166  		offsetMin = -1
1167  	} else {
1168  		_, offset := t.Zone()
1169  		if offset%60 != 0 {
1170  			return nil, errors.New("Time.MarshalBinary: zone offset has fractional minute")
1171  		}
1172  		offset /= 60
1173  		if offset < -32768 || offset == -1 || offset > 32767 {
1174  			return nil, errors.New("Time.MarshalBinary: unexpected zone offset")
1175  		}
1176  		offsetMin = int16(offset)
1177  	}
1178
1179  	sec := t.sec()
1180  	nsec := t.nsec()
1181  	enc := []byte{
1182  		timeBinaryVersion, // byte 0 : version
1183  		byte(sec >> 56),   // bytes 1-8: seconds
1184  		byte(sec >> 48),
1185  		byte(sec >> 40),
1186  		byte(sec >> 32),
1187  		byte(sec >> 24),
1188  		byte(sec >> 16),
1189  		byte(sec >> 8),
1190  		byte(sec),
1191  		byte(nsec >> 24), // bytes 9-12: nanoseconds
1192  		byte(nsec >> 16),
1193  		byte(nsec >> 8),
1194  		byte(nsec),
1195  		byte(offsetMin >> 8), // bytes 13-14: zone offset in minutes
1196  		byte(offsetMin),
1197  	}
1198
1199  	return enc, nil
1200  }
1201
1202  // UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
1203  func (t *Time) UnmarshalBinary(data []byte) error {
1204  	buf := data
1205  	if len(buf) == 0 {
1206  		return errors.New("Time.UnmarshalBinary: no data")
1207  	}
1208
1209  	if buf != timeBinaryVersion {
1210  		return errors.New("Time.UnmarshalBinary: unsupported version")
1211  	}
1212
1213  	if len(buf) != /*version*/ 1+ /*sec*/ 8+ /*nsec*/ 4+ /*zone offset*/ 2 {
1214  		return errors.New("Time.UnmarshalBinary: invalid length")
1215  	}
1216
1217  	buf = buf[1:]
1218  	sec := int64(buf) | int64(buf)<<8 | int64(buf)<<16 | int64(buf)<<24 |
1219  		int64(buf)<<32 | int64(buf)<<40 | int64(buf)<<48 | int64(buf)<<56
1220
1221  	buf = buf[8:]
1222  	nsec := int32(buf) | int32(buf)<<8 | int32(buf)<<16 | int32(buf)<<24
1223
1224  	buf = buf[4:]
1225  	offset := int(int16(buf)|int16(buf)<<8) * 60
1226
1227  	*t = Time{}
1228  	t.wall = uint64(nsec)
1229  	t.ext = sec
1230
1231  	if offset == -1*60 {
1232  		t.setLoc(&utcLoc)
1233  	} else if _, localoff, _, _ := Local.lookup(t.unixSec()); offset == localoff {
1234  		t.setLoc(Local)
1235  	} else {
1236  		t.setLoc(FixedZone("", offset))
1237  	}
1238
1239  	return nil
1240  }
1241
1242  // TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
1243  // The same semantics will be provided by the generic MarshalBinary, MarshalText,
1244  // UnmarshalBinary, UnmarshalText.
1245
1246  // GobEncode implements the gob.GobEncoder interface.
1247  func (t Time) GobEncode() ([]byte, error) {
1248  	return t.MarshalBinary()
1249  }
1250
1251  // GobDecode implements the gob.GobDecoder interface.
1252  func (t *Time) GobDecode(data []byte) error {
1253  	return t.UnmarshalBinary(data)
1254  }
1255
1256  // MarshalJSON implements the json.Marshaler interface.
1257  // The time is a quoted string in RFC 3339 format, with sub-second precision added if present.
1258  func (t Time) MarshalJSON() ([]byte, error) {
1259  	if y := t.Year(); y < 0 || y >= 10000 {
1260  		// RFC 3339 is clear that years are 4 digits exactly.
1261  		// See golang.org/issue/4556#c15 for more discussion.
1262  		return nil, errors.New("Time.MarshalJSON: year outside of range [0,9999]")
1263  	}
1264
1265  	b := make([]byte, 0, len(RFC3339Nano)+2)
1266  	b = append(b, '"')
1267  	b = t.AppendFormat(b, RFC3339Nano)
1268  	b = append(b, '"')
1269  	return b, nil
1270  }
1271
1272  // UnmarshalJSON implements the json.Unmarshaler interface.
1273  // The time is expected to be a quoted string in RFC 3339 format.
1274  func (t *Time) UnmarshalJSON(data []byte) error {
1275  	// Ignore null, like in the main JSON package.
1276  	if string(data) == "null" {
1277  		return nil
1278  	}
1279  	// Fractional seconds are handled implicitly by Parse.
1280  	var err error
1281  	*t, err = Parse(`"`+RFC3339+`"`, string(data))
1282  	return err
1283  }
1284
1285  // MarshalText implements the encoding.TextMarshaler interface.
1286  // The time is formatted in RFC 3339 format, with sub-second precision added if present.
1287  func (t Time) MarshalText() ([]byte, error) {
1288  	if y := t.Year(); y < 0 || y >= 10000 {
1289  		return nil, errors.New("Time.MarshalText: year outside of range [0,9999]")
1290  	}
1291
1292  	b := make([]byte, 0, len(RFC3339Nano))
1293  	return t.AppendFormat(b, RFC3339Nano), nil
1294  }
1295
1296  // UnmarshalText implements the encoding.TextUnmarshaler interface.
1297  // The time is expected to be in RFC 3339 format.
1298  func (t *Time) UnmarshalText(data []byte) error {
1299  	// Fractional seconds are handled implicitly by Parse.
1300  	var err error
1301  	*t, err = Parse(RFC3339, string(data))
1302  	return err
1303  }
1304
1305  // Unix returns the local Time corresponding to the given Unix time,
1306  // sec seconds and nsec nanoseconds since January 1, 1970 UTC.
1307  // It is valid to pass nsec outside the range [0, 999999999].
1308  // Not all sec values have a corresponding time value. One such
1309  // value is 1<<63-1 (the largest int64 value).
1310  func Unix(sec int64, nsec int64) Time {
1311  	if nsec < 0 || nsec >= 1e9 {
1312  		n := nsec / 1e9
1313  		sec += n
1314  		nsec -= n * 1e9
1315  		if nsec < 0 {
1316  			nsec += 1e9
1317  			sec--
1318  		}
1319  	}
1320  	return unixTime(sec, int32(nsec))
1321  }
1322
1323  func isLeap(year int) bool {
1324  	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
1325  }
1326
1327  // norm returns nhi, nlo such that
1328  //	hi * base + lo == nhi * base + nlo
1329  //	0 <= nlo < base
1330  func norm(hi, lo, base int) (nhi, nlo int) {
1331  	if lo < 0 {
1332  		n := (-lo-1)/base + 1
1333  		hi -= n
1334  		lo += n * base
1335  	}
1336  	if lo >= base {
1337  		n := lo / base
1338  		hi += n
1339  		lo -= n * base
1340  	}
1341  	return hi, lo
1342  }
1343
1344  // Date returns the Time corresponding to
1345  //	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
1346  // in the appropriate zone for that time in the given location.
1347  //
1348  // The month, day, hour, min, sec, and nsec values may be outside
1349  // their usual ranges and will be normalized during the conversion.
1350  // For example, October 32 converts to November 1.
1351  //
1352  // A daylight savings time transition skips or repeats times.
1353  // For example, in the United States, March 13, 2011 2:15am never occurred,
1354  // while November 6, 2011 1:15am occurred twice. In such cases, the
1355  // choice of time zone, and therefore the time, is not well-defined.
1356  // Date returns a time that is correct in one of the two zones involved
1357  // in the transition, but it does not guarantee which.
1358  //
1359  // Date panics if loc is nil.
1360  func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
1361  	if loc == nil {
1362  		panic("time: missing Location in call to Date")
1363  	}
1364
1365  	// Normalize month, overflowing into year.
1366  	m := int(month) - 1
1367  	year, m = norm(year, m, 12)
1368  	month = Month(m) + 1
1369
1370  	// Normalize nsec, sec, min, hour, overflowing into day.
1371  	sec, nsec = norm(sec, nsec, 1e9)
1372  	min, sec = norm(min, sec, 60)
1373  	hour, min = norm(hour, min, 60)
1374  	day, hour = norm(day, hour, 24)
1375
1376  	y := uint64(int64(year) - absoluteZeroYear)
1377
1378  	// Compute days since the absolute epoch.
1379
1380  	// Add in days from 400-year cycles.
1381  	n := y / 400
1382  	y -= 400 * n
1383  	d := daysPer400Years * n
1384
1385  	// Add in 100-year cycles.
1386  	n = y / 100
1387  	y -= 100 * n
1388  	d += daysPer100Years * n
1389
1390  	// Add in 4-year cycles.
1391  	n = y / 4
1392  	y -= 4 * n
1393  	d += daysPer4Years * n
1394
1395  	// Add in non-leap years.
1396  	n = y
1397  	d += 365 * n
1398
1399  	// Add in days before this month.
1400  	d += uint64(daysBefore[month-1])
1401  	if isLeap(year) && month >= March {
1402  		d++ // February 29
1403  	}
1404
1405  	// Add in days before today.
1406  	d += uint64(day - 1)
1407
1408  	// Add in time elapsed today.
1409  	abs := d * secondsPerDay
1410  	abs += uint64(hour*secondsPerHour + min*secondsPerMinute + sec)
1411
1412  	unix := int64(abs) + (absoluteToInternal + internalToUnix)
1413
1414  	// Look for zone offset for t, so we can adjust to UTC.
1415  	// The lookup function expects UTC, so we pass t in the
1416  	// hope that it will not be too close to a zone transition,
1417  	// and then adjust if it is.
1418  	_, offset, start, end := loc.lookup(unix)
1419  	if offset != 0 {
1420  		switch utc := unix - int64(offset); {
1421  		case utc < start:
1422  			_, offset, _, _ = loc.lookup(start - 1)
1423  		case utc >= end:
1424  			_, offset, _, _ = loc.lookup(end)
1425  		}
1426  		unix -= int64(offset)
1427  	}
1428
1429  	t := unixTime(unix, int32(nsec))
1430  	t.setLoc(loc)
1431  	return t
1432  }
1433
1434  // Truncate returns the result of rounding t down to a multiple of d (since the zero time).
1435  // If d <= 0, Truncate returns t stripped of any monotonic clock reading but otherwise unchanged.
1436  //
1437  // Truncate operates on the time as an absolute duration since the
1438  // zero time; it does not operate on the presentation form of the
1439  // time. Thus, Truncate(Hour) may return a time with a non-zero
1440  // minute, depending on the time's Location.
1441  func (t Time) Truncate(d Duration) Time {
1442  	t.stripMono()
1443  	if d <= 0 {
1444  		return t
1445  	}
1446  	_, r := div(t, d)
1448  }
1449
1450  // Round returns the result of rounding t to the nearest multiple of d (since the zero time).
1451  // The rounding behavior for halfway values is to round up.
1452  // If d <= 0, Round returns t stripped of any monotonic clock reading but otherwise unchanged.
1453  //
1454  // Round operates on the time as an absolute duration since the
1455  // zero time; it does not operate on the presentation form of the
1456  // time. Thus, Round(Hour) may return a time with a non-zero
1457  // minute, depending on the time's Location.
1458  func (t Time) Round(d Duration) Time {
1459  	t.stripMono()
1460  	if d <= 0 {
1461  		return t
1462  	}
1463  	_, r := div(t, d)
1464  	if lessThanHalf(r, d) {
1466  	}
1468  }
1469
1470  // div divides t by d and returns the quotient parity and remainder.
1471  // We don't use the quotient parity anymore (round half up instead of round to even)
1472  // but it's still here in case we change our minds.
1473  func div(t Time, d Duration) (qmod2 int, r Duration) {
1474  	neg := false
1475  	nsec := t.nsec()
1476  	sec := t.sec()
1477  	if sec < 0 {
1478  		// Operate on absolute value.
1479  		neg = true
1480  		sec = -sec
1481  		nsec = -nsec
1482  		if nsec < 0 {
1483  			nsec += 1e9
1484  			sec-- // sec >= 1 before the -- so safe
1485  		}
1486  	}
1487
1488  	switch {
1489  	// Special case: 2d divides 1 second.
1490  	case d < Second && Second%(d+d) == 0:
1491  		qmod2 = int(nsec/int32(d)) & 1
1492  		r = Duration(nsec % int32(d))
1493
1494  	// Special case: d is a multiple of 1 second.
1495  	case d%Second == 0:
1496  		d1 := int64(d / Second)
1497  		qmod2 = int(sec/d1) & 1
1498  		r = Duration(sec%d1)*Second + Duration(nsec)
1499
1500  	// General case.
1501  	// This could be faster if more cleverness were applied,
1502  	// but it's really only here to avoid special case restrictions in the API.
1503  	// No one will care about these cases.
1504  	default:
1505  		// Compute nanoseconds as 128-bit number.
1506  		sec := uint64(sec)
1507  		tmp := (sec >> 32) * 1e9
1508  		u1 := tmp >> 32
1509  		u0 := tmp << 32
1510  		tmp = (sec & 0xFFFFFFFF) * 1e9
1511  		u0x, u0 := u0, u0+tmp
1512  		if u0 < u0x {
1513  			u1++
1514  		}
1515  		u0x, u0 = u0, u0+uint64(nsec)
1516  		if u0 < u0x {
1517  			u1++
1518  		}
1519
1520  		// Compute remainder by subtracting r<<k for decreasing k.
1521  		// Quotient parity is whether we subtract on last round.
1522  		d1 := uint64(d)
1523  		for d1>>63 != 1 {
1524  			d1 <<= 1
1525  		}
1526  		d0 := uint64(0)
1527  		for {
1528  			qmod2 = 0
1529  			if u1 > d1 || u1 == d1 && u0 >= d0 {
1530  				// subtract
1531  				qmod2 = 1
1532  				u0x, u0 = u0, u0-d0
1533  				if u0 > u0x {
1534  					u1--
1535  				}
1536  				u1 -= d1
1537  			}
1538  			if d1 == 0 && d0 == uint64(d) {
1539  				break
1540  			}
1541  			d0 >>= 1
1542  			d0 |= (d1 & 1) << 63
1543  			d1 >>= 1
1544  		}
1545  		r = Duration(u0)
1546  	}
1547
1548  	if neg && r != 0 {
1549  		// If input was negative and not an exact multiple of d, we computed q, r such that
1550  		//	q*d + r = -t
1551  		// But the right answers are given by -(q-1), d-r:
1552  		//	q*d + r = -t
1553  		//	-q*d - r = t
1554  		//	-(q-1)*d + (d - r) = t
1555  		qmod2 ^= 1
1556  		r = d - r
1557  	}
1558  	return
1559  }
1560
```

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