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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
3  // license that can be found in the LICENSE file.
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
17  // clock reading and a monotonic clock reading; later time-telling
18  // operations use the wall clock reading, but later time-measuring
19  // operations, specifically comparisons and subtractions, use the
20  // monotonic clock reading.
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.
40  // If Time t has a monotonic clock reading, t.Add adds the same duration to
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
125  // clock reading.
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 {
164  	return int32(t.wall & nsecMask)
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
178  // addSec adds d seconds to the time.
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()
209  		t.wall &= nsecMask
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  	ts := t.sec()
256  	us := u.sec()
257  	return ts < us || ts == us && t.nsec() < u.nsec()
258  }
259
260  // Equal reports whether t and u represent the same time instant.
261  // Two times can be equal even if they are in different locations.
262  // For example, 6:00 +0200 and 4:00 UTC are Equal.
263  // See the documentation on the Time type for the pitfalls of using == with
264  // Time values; most code should use Equal instead.
265  func (t Time) Equal(u Time) bool {
266  	if t.wall&u.wall&hasMonotonic != 0 {
267  		return t.ext == u.ext
268  	}
269  	return t.sec() == u.sec() && t.nsec() == u.nsec()
270  }
271
272  // A Month specifies a month of the year (January = 1, ...).
273  type Month int
274
275  const (
276  	January Month = 1 + iota
277  	February
278  	March
279  	April
280  	May
281  	June
282  	July
283  	August
284  	September
285  	October
286  	November
287  	December
288  )
289
290  // String returns the English name of the month ("January", "February", ...).
291  func (m Month) String() string {
292  	if January <= m && m <= December {
293  		return longMonthNames[m-1]
294  	}
295  	buf := make([]byte, 20)
296  	n := fmtInt(buf, uint64(m))
297  	return "%!Month(" + string(buf[n:]) + ")"
298  }
299
300  // A Weekday specifies a day of the week (Sunday = 0, ...).
301  type Weekday int
302
303  const (
304  	Sunday Weekday = iota
305  	Monday
306  	Tuesday
307  	Wednesday
308  	Thursday
309  	Friday
310  	Saturday
311  )
312
313  // String returns the English name of the day ("Sunday", "Monday", ...).
314  func (d Weekday) String() string {
315  	if Sunday <= d && d <= Saturday {
316  		return longDayNames[d]
317  	}
318  	buf := make([]byte, 20)
319  	n := fmtInt(buf, uint64(d))
320  	return "%!Weekday(" + string(buf[n:]) + ")"
321  }
322
323  // Computations on time.
324  //
325  // The zero value for a Time is defined to be
326  //	January 1, year 1, 00:00:00.000000000 UTC
327  // which (1) looks like a zero, or as close as you can get in a date
328  // (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
329  // be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
330  // non-negative year even in time zones west of UTC, unlike 1-1-0
331  // 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
332  //
333  // The zero Time value does not force a specific epoch for the time
334  // representation. For example, to use the Unix epoch internally, we
335  // could define that to distinguish a zero value from Jan 1 1970, that
336  // time would be represented by sec=-1, nsec=1e9. However, it does
337  // suggest a representation, namely using 1-1-1 00:00:00 UTC as the
338  // epoch, and that's what we do.
339  //
340  // The Add and Sub computations are oblivious to the choice of epoch.
341  //
342  // The presentation computations - year, month, minute, and so on - all
343  // rely heavily on division and modulus by positive constants. For
344  // calendrical calculations we want these divisions to round down, even
345  // for negative values, so that the remainder is always positive, but
346  // Go's division (like most hardware division instructions) rounds to
347  // zero. We can still do those computations and then adjust the result
348  // for a negative numerator, but it's annoying to write the adjustment
349  // over and over. Instead, we can change to a different epoch so long
350  // ago that all the times we care about will be positive, and then round
351  // to zero and round down coincide. These presentation routines already
352  // have to add the zone offset, so adding the translation to the
353  // alternate epoch is cheap. For example, having a non-negative time t
354  // means that we can write
355  //
356  //	sec = t % 60
357  //
358  // instead of
359  //
360  //	sec = t % 60
361  //	if sec < 0 {
362  //		sec += 60
363  //	}
364  //
365  // everywhere.
366  //
367  // The calendar runs on an exact 400 year cycle: a 400-year calendar
368  // printed for 1970-2369 will apply as well to 2370-2769. Even the days
369  // of the week match up. It simplifies the computations to choose the
370  // cycle boundaries so that the exceptional years are always delayed as
371  // long as possible. That means choosing a year equal to 1 mod 400, so
372  // that the first leap year is the 4th year, the first missed leap year
373  // is the 100th year, and the missed missed leap year is the 400th year.
374  // So we'd prefer instead to print a calendar for 2001-2400 and reuse it
375  // for 2401-2800.
376  //
377  // Finally, it's convenient if the delta between the Unix epoch and
378  // long-ago epoch is representable by an int64 constant.
379  //
380  // These three considerations—choose an epoch as early as possible, that
381  // uses a year equal to 1 mod 400, and that is no more than 2⁶³ seconds
382  // earlier than 1970—bring us to the year -292277022399. We refer to
383  // this year as the absolute zero year, and to times measured as a uint64
384  // seconds since this year as absolute times.
385  //
386  // Times measured as an int64 seconds since the year 1—the representation
387  // used for Time's sec field—are called internal times.
388  //
389  // Times measured as an int64 seconds since the year 1970 are called Unix
390  // times.
391  //
392  // It is tempting to just use the year 1 as the absolute epoch, defining
393  // that the routines are only valid for years >= 1. However, the
394  // routines would then be invalid when displaying the epoch in time zones
395  // west of UTC, since it is year 0. It doesn't seem tenable to say that
396  // printing the zero time correctly isn't supported in half the time
397  // zones. By comparison, it's reasonable to mishandle some times in
398  // the year -292277022399.
399  //
400  // All this is opaque to clients of the API and can be changed if a
401  // better implementation presents itself.
402
403  const (
404  	// The unsigned zero year for internal calculations.
405  	// Must be 1 mod 400, and times before it will not compute correctly,
406  	// but otherwise can be changed at will.
407  	absoluteZeroYear = -292277022399
408
409  	// The year of the zero Time.
410  	// Assumed by the unixToInternal computation below.
411  	internalYear = 1
412
413  	// Offsets to convert between internal and absolute or Unix times.
414  	absoluteToInternal int64 = (absoluteZeroYear - internalYear) * 365.2425 * secondsPerDay
415  	internalToAbsolute       = -absoluteToInternal
416
417  	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
418  	internalToUnix int64 = -unixToInternal
419
420  	wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
421  	internalToWall int64 = -wallToInternal
422  )
423
424  // IsZero reports whether t represents the zero time instant,
425  // January 1, year 1, 00:00:00 UTC.
426  func (t Time) IsZero() bool {
427  	return t.sec() == 0 && t.nsec() == 0
428  }
429
430  // abs returns the time t as an absolute time, adjusted by the zone offset.
431  // It is called when computing a presentation property like Month or Hour.
432  func (t Time) abs() uint64 {
433  	l := t.loc
434  	// Avoid function calls when possible.
435  	if l == nil || l == &localLoc {
436  		l = l.get()
437  	}
438  	sec := t.unixSec()
439  	if l != &utcLoc {
440  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
441  			sec += int64(l.cacheZone.offset)
442  		} else {
443  			_, offset, _, _ := l.lookup(sec)
444  			sec += int64(offset)
445  		}
446  	}
447  	return uint64(sec + (unixToInternal + internalToAbsolute))
448  }
449
450  // locabs is a combination of the Zone and abs methods,
451  // extracting both return values from a single zone lookup.
452  func (t Time) locabs() (name string, offset int, abs uint64) {
453  	l := t.loc
454  	if l == nil || l == &localLoc {
455  		l = l.get()
456  	}
457  	// Avoid function call if we hit the local time cache.
458  	sec := t.unixSec()
459  	if l != &utcLoc {
460  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
461  			name = l.cacheZone.name
462  			offset = l.cacheZone.offset
463  		} else {
464  			name, offset, _, _ = l.lookup(sec)
465  		}
466  		sec += int64(offset)
467  	} else {
468  		name = "UTC"
469  	}
470  	abs = uint64(sec + (unixToInternal + internalToAbsolute))
471  	return
472  }
473
474  // Date returns the year, month, and day in which t occurs.
475  func (t Time) Date() (year int, month Month, day int) {
476  	year, month, day, _ = t.date(true)
477  	return
478  }
479
480  // Year returns the year in which t occurs.
481  func (t Time) Year() int {
482  	year, _, _, _ := t.date(false)
483  	return year
484  }
485
486  // Month returns the month of the year specified by t.
487  func (t Time) Month() Month {
488  	_, month, _, _ := t.date(true)
489  	return month
490  }
491
492  // Day returns the day of the month specified by t.
493  func (t Time) Day() int {
494  	_, _, day, _ := t.date(true)
495  	return day
496  }
497
498  // Weekday returns the day of the week specified by t.
499  func (t Time) Weekday() Weekday {
500  	return absWeekday(t.abs())
501  }
502
503  // absWeekday is like Weekday but operates on an absolute time.
504  func absWeekday(abs uint64) Weekday {
505  	// January 1 of the absolute year, like January 1 of 2001, was a Monday.
506  	sec := (abs + uint64(Monday)*secondsPerDay) % secondsPerWeek
507  	return Weekday(int(sec) / secondsPerDay)
508  }
509
510  // ISOWeek returns the ISO 8601 year and week number in which t occurs.
511  // Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
512  // week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
513  // of year n+1.
514  func (t Time) ISOWeek() (year, week int) {
515  	// According to the rule that the first calendar week of a calendar year is
516  	// the week including the first Thursday of that year, and that the last one is
517  	// the week immediately preceding the first calendar week of the next calendar year.
518  	// See https://www.iso.org/obp/ui#iso:std:iso:8601:-1:ed-1:v1:en:term:3.1.1.23 for details.
519
521  	// Monday Tuesday Wednesday Thursday Friday Saturday Sunday
522  	// 1      2       3         4        5      6        7
523  	// +3     +2      +1        0        -1     -2       -3
524  	// the offset to Thursday
525  	abs := t.abs()
526  	d := Thursday - absWeekday(abs)
527  	// handle Sunday
528  	if d == 4 {
529  		d = -3
530  	}
531  	// find the Thursday of the calendar week
532  	abs += uint64(d) * secondsPerDay
533  	year, _, _, yday := absDate(abs, false)
534  	return year, yday/7 + 1
535  }
536
537  // Clock returns the hour, minute, and second within the day specified by t.
538  func (t Time) Clock() (hour, min, sec int) {
539  	return absClock(t.abs())
540  }
541
542  // absClock is like clock but operates on an absolute time.
543  func absClock(abs uint64) (hour, min, sec int) {
544  	sec = int(abs % secondsPerDay)
545  	hour = sec / secondsPerHour
546  	sec -= hour * secondsPerHour
547  	min = sec / secondsPerMinute
548  	sec -= min * secondsPerMinute
549  	return
550  }
551
552  // Hour returns the hour within the day specified by t, in the range [0, 23].
553  func (t Time) Hour() int {
554  	return int(t.abs()%secondsPerDay) / secondsPerHour
555  }
556
557  // Minute returns the minute offset within the hour specified by t, in the range [0, 59].
558  func (t Time) Minute() int {
559  	return int(t.abs()%secondsPerHour) / secondsPerMinute
560  }
561
562  // Second returns the second offset within the minute specified by t, in the range [0, 59].
563  func (t Time) Second() int {
564  	return int(t.abs() % secondsPerMinute)
565  }
566
567  // Nanosecond returns the nanosecond offset within the second specified by t,
568  // in the range [0, 999999999].
569  func (t Time) Nanosecond() int {
570  	return int(t.nsec())
571  }
572
573  // YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
574  // and [1,366] in leap years.
575  func (t Time) YearDay() int {
576  	_, _, _, yday := t.date(false)
577  	return yday + 1
578  }
579
580  // A Duration represents the elapsed time between two instants
581  // as an int64 nanosecond count. The representation limits the
582  // largest representable duration to approximately 290 years.
583  type Duration int64
584
585  const (
586  	minDuration Duration = -1 << 63
587  	maxDuration Duration = 1<<63 - 1
588  )
589
590  // Common durations. There is no definition for units of Day or larger
591  // to avoid confusion across daylight savings time zone transitions.
592  //
593  // To count the number of units in a Duration, divide:
594  //	second := time.Second
595  //	fmt.Print(int64(second/time.Millisecond)) // prints 1000
596  //
597  // To convert an integer number of units to a Duration, multiply:
598  //	seconds := 10
599  //	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
600  //
601  const (
602  	Nanosecond  Duration = 1
603  	Microsecond          = 1000 * Nanosecond
604  	Millisecond          = 1000 * Microsecond
605  	Second               = 1000 * Millisecond
606  	Minute               = 60 * Second
607  	Hour                 = 60 * Minute
608  )
609
610  // String returns a string representing the duration in the form "72h3m0.5s".
611  // Leading zero units are omitted. As a special case, durations less than one
612  // second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
613  // that the leading digit is non-zero. The zero duration formats as 0s.
614  func (d Duration) String() string {
615  	// Largest time is 2540400h10m10.000000000s
616  	var buf [32]byte
617  	w := len(buf)
618
619  	u := uint64(d)
620  	neg := d < 0
621  	if neg {
622  		u = -u
623  	}
624
625  	if u < uint64(Second) {
626  		// Special case: if duration is smaller than a second,
627  		// use smaller units, like 1.2ms
628  		var prec int
629  		w--
630  		buf[w] = 's'
631  		w--
632  		switch {
633  		case u == 0:
634  			return "0s"
635  		case u < uint64(Microsecond):
636  			// print nanoseconds
637  			prec = 0
638  			buf[w] = 'n'
639  		case u < uint64(Millisecond):
640  			// print microseconds
641  			prec = 3
642  			// U+00B5 'µ' micro sign == 0xC2 0xB5
643  			w-- // Need room for two bytes.
644  			copy(buf[w:], "µ")
645  		default:
646  			// print milliseconds
647  			prec = 6
648  			buf[w] = 'm'
649  		}
650  		w, u = fmtFrac(buf[:w], u, prec)
651  		w = fmtInt(buf[:w], u)
652  	} else {
653  		w--
654  		buf[w] = 's'
655
656  		w, u = fmtFrac(buf[:w], u, 9)
657
658  		// u is now integer seconds
659  		w = fmtInt(buf[:w], u%60)
660  		u /= 60
661
662  		// u is now integer minutes
663  		if u > 0 {
664  			w--
665  			buf[w] = 'm'
666  			w = fmtInt(buf[:w], u%60)
667  			u /= 60
668
669  			// u is now integer hours
670  			// Stop at hours because days can be different lengths.
671  			if u > 0 {
672  				w--
673  				buf[w] = 'h'
674  				w = fmtInt(buf[:w], u)
675  			}
676  		}
677  	}
678
679  	if neg {
680  		w--
681  		buf[w] = '-'
682  	}
683
684  	return string(buf[w:])
685  }
686
687  // fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
688  // tail of buf, omitting trailing zeros. It omits the decimal
689  // point too when the fraction is 0. It returns the index where the
690  // output bytes begin and the value v/10**prec.
691  func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
692  	// Omit trailing zeros up to and including decimal point.
693  	w := len(buf)
694  	print := false
695  	for i := 0; i < prec; i++ {
696  		digit := v % 10
697  		print = print || digit != 0
698  		if print {
699  			w--
700  			buf[w] = byte(digit) + '0'
701  		}
702  		v /= 10
703  	}
704  	if print {
705  		w--
706  		buf[w] = '.'
707  	}
708  	return w, v
709  }
710
711  // fmtInt formats v into the tail of buf.
712  // It returns the index where the output begins.
713  func fmtInt(buf []byte, v uint64) int {
714  	w := len(buf)
715  	if v == 0 {
716  		w--
717  		buf[w] = '0'
718  	} else {
719  		for v > 0 {
720  			w--
721  			buf[w] = byte(v%10) + '0'
722  			v /= 10
723  		}
724  	}
725  	return w
726  }
727
728  // Nanoseconds returns the duration as an integer nanosecond count.
729  func (d Duration) Nanoseconds() int64 { return int64(d) }
730
731  // Microseconds returns the duration as an integer microsecond count.
732  func (d Duration) Microseconds() int64 { return int64(d) / 1e3 }
733
734  // Milliseconds returns the duration as an integer millisecond count.
735  func (d Duration) Milliseconds() int64 { return int64(d) / 1e6 }
736
737  // These methods return float64 because the dominant
738  // use case is for printing a floating point number like 1.5s, and
739  // a truncation to integer would make them not useful in those cases.
740  // Splitting the integer and fraction ourselves guarantees that
741  // converting the returned float64 to an integer rounds the same
742  // way that a pure integer conversion would have, even in cases
743  // where, say, float64(d.Nanoseconds())/1e9 would have rounded
744  // differently.
745
746  // Seconds returns the duration as a floating point number of seconds.
747  func (d Duration) Seconds() float64 {
748  	sec := d / Second
749  	nsec := d % Second
750  	return float64(sec) + float64(nsec)/1e9
751  }
752
753  // Minutes returns the duration as a floating point number of minutes.
754  func (d Duration) Minutes() float64 {
755  	min := d / Minute
756  	nsec := d % Minute
757  	return float64(min) + float64(nsec)/(60*1e9)
758  }
759
760  // Hours returns the duration as a floating point number of hours.
761  func (d Duration) Hours() float64 {
762  	hour := d / Hour
763  	nsec := d % Hour
764  	return float64(hour) + float64(nsec)/(60*60*1e9)
765  }
766
767  // Truncate returns the result of rounding d toward zero to a multiple of m.
768  // If m <= 0, Truncate returns d unchanged.
769  func (d Duration) Truncate(m Duration) Duration {
770  	if m <= 0 {
771  		return d
772  	}
773  	return d - d%m
774  }
775
776  // lessThanHalf reports whether x+x < y but avoids overflow,
777  // assuming x and y are both positive (Duration is signed).
778  func lessThanHalf(x, y Duration) bool {
779  	return uint64(x)+uint64(x) < uint64(y)
780  }
781
782  // Round returns the result of rounding d to the nearest multiple of m.
783  // The rounding behavior for halfway values is to round away from zero.
784  // If the result exceeds the maximum (or minimum)
785  // value that can be stored in a Duration,
786  // Round returns the maximum (or minimum) duration.
787  // If m <= 0, Round returns d unchanged.
788  func (d Duration) Round(m Duration) Duration {
789  	if m <= 0 {
790  		return d
791  	}
792  	r := d % m
793  	if d < 0 {
794  		r = -r
795  		if lessThanHalf(r, m) {
796  			return d + r
797  		}
798  		if d1 := d - m + r; d1 < d {
799  			return d1
800  		}
801  		return minDuration // overflow
802  	}
803  	if lessThanHalf(r, m) {
804  		return d - r
805  	}
806  	if d1 := d + m - r; d1 > d {
807  		return d1
808  	}
809  	return maxDuration // overflow
810  }
811
812  // Add returns the time t+d.
813  func (t Time) Add(d Duration) Time {
814  	dsec := int64(d / 1e9)
815  	nsec := t.nsec() + int32(d%1e9)
816  	if nsec >= 1e9 {
817  		dsec++
818  		nsec -= 1e9
819  	} else if nsec < 0 {
820  		dsec--
821  		nsec += 1e9
822  	}
823  	t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
825  	if t.wall&hasMonotonic != 0 {
826  		te := t.ext + int64(d)
827  		if d < 0 && te > t.ext || d > 0 && te < t.ext {
828  			// Monotonic clock reading now out of range; degrade to wall-only.
829  			t.stripMono()
830  		} else {
831  			t.ext = te
832  		}
833  	}
834  	return t
835  }
836
837  // Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
838  // value that can be stored in a Duration, the maximum (or minimum) duration
839  // will be returned.
840  // To compute t-d for a duration d, use t.Add(-d).
841  func (t Time) Sub(u Time) Duration {
842  	if t.wall&u.wall&hasMonotonic != 0 {
843  		te := t.ext
844  		ue := u.ext
845  		d := Duration(te - ue)
846  		if d < 0 && te > ue {
847  			return maxDuration // t - u is positive out of range
848  		}
849  		if d > 0 && te < ue {
850  			return minDuration // t - u is negative out of range
851  		}
852  		return d
853  	}
854  	d := Duration(t.sec()-u.sec())*Second + Duration(t.nsec()-u.nsec())
855  	// Check for overflow or underflow.
856  	switch {
858  		return d // d is correct
859  	case t.Before(u):
860  		return minDuration // t - u is negative out of range
861  	default:
862  		return maxDuration // t - u is positive out of range
863  	}
864  }
865
866  // Since returns the time elapsed since t.
867  // It is shorthand for time.Now().Sub(t).
868  func Since(t Time) Duration {
869  	var now Time
870  	if t.wall&hasMonotonic != 0 {
871  		// Common case optimization: if t has monotonic time, then Sub will use only it.
872  		now = Time{hasMonotonic, runtimeNano() - startNano, nil}
873  	} else {
874  		now = Now()
875  	}
876  	return now.Sub(t)
877  }
878
879  // Until returns the duration until t.
880  // It is shorthand for t.Sub(time.Now()).
881  func Until(t Time) Duration {
882  	var now Time
883  	if t.wall&hasMonotonic != 0 {
884  		// Common case optimization: if t has monotonic time, then Sub will use only it.
885  		now = Time{hasMonotonic, runtimeNano() - startNano, nil}
886  	} else {
887  		now = Now()
888  	}
889  	return t.Sub(now)
890  }
891
892  // AddDate returns the time corresponding to adding the
893  // given number of years, months, and days to t.
894  // For example, AddDate(-1, 2, 3) applied to January 1, 2011
895  // returns March 4, 2010.
896  //
897  // AddDate normalizes its result in the same way that Date does,
898  // so, for example, adding one month to October 31 yields
899  // December 1, the normalized form for November 31.
900  func (t Time) AddDate(years int, months int, days int) Time {
901  	year, month, day := t.Date()
902  	hour, min, sec := t.Clock()
903  	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec()), t.Location())
904  }
905
906  const (
907  	secondsPerMinute = 60
908  	secondsPerHour   = 60 * secondsPerMinute
909  	secondsPerDay    = 24 * secondsPerHour
910  	secondsPerWeek   = 7 * secondsPerDay
911  	daysPer400Years  = 365*400 + 97
912  	daysPer100Years  = 365*100 + 24
913  	daysPer4Years    = 365*4 + 1
914  )
915
916  // date computes the year, day of year, and when full=true,
917  // the month and day in which t occurs.
918  func (t Time) date(full bool) (year int, month Month, day int, yday int) {
919  	return absDate(t.abs(), full)
920  }
921
922  // absDate is like date but operates on an absolute time.
923  func absDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
924  	// Split into time and day.
925  	d := abs / secondsPerDay
926
927  	// Account for 400 year cycles.
928  	n := d / daysPer400Years
929  	y := 400 * n
930  	d -= daysPer400Years * n
931
932  	// Cut off 100-year cycles.
933  	// The last cycle has one extra leap year, so on the last day
934  	// of that year, day / daysPer100Years will be 4 instead of 3.
935  	// Cut it back down to 3 by subtracting n>>2.
936  	n = d / daysPer100Years
937  	n -= n >> 2
938  	y += 100 * n
939  	d -= daysPer100Years * n
940
941  	// Cut off 4-year cycles.
942  	// The last cycle has a missing leap year, which does not
943  	// affect the computation.
944  	n = d / daysPer4Years
945  	y += 4 * n
946  	d -= daysPer4Years * n
947
948  	// Cut off years within a 4-year cycle.
949  	// The last year is a leap year, so on the last day of that year,
950  	// day / 365 will be 4 instead of 3. Cut it back down to 3
951  	// by subtracting n>>2.
952  	n = d / 365
953  	n -= n >> 2
954  	y += n
955  	d -= 365 * n
956
957  	year = int(int64(y) + absoluteZeroYear)
958  	yday = int(d)
959
960  	if !full {
961  		return
962  	}
963
964  	day = yday
965  	if isLeap(year) {
966  		// Leap year
967  		switch {
968  		case day > 31+29-1:
969  			// After leap day; pretend it wasn't there.
970  			day--
971  		case day == 31+29-1:
972  			// Leap day.
973  			month = February
974  			day = 29
975  			return
976  		}
977  	}
978
979  	// Estimate month on assumption that every month has 31 days.
980  	// The estimate may be too low by at most one month, so adjust.
981  	month = Month(day / 31)
982  	end := int(daysBefore[month+1])
983  	var begin int
984  	if day >= end {
985  		month++
986  		begin = end
987  	} else {
988  		begin = int(daysBefore[month])
989  	}
990
991  	month++ // because January is 1
992  	day = day - begin + 1
993  	return
994  }
995
996  // daysBefore[m] counts the number of days in a non-leap year
997  // before month m begins. There is an entry for m=12, counting
998  // the number of days before January of next year (365).
999  var daysBefore = [...]int32{
1000  	0,
1001  	31,
1002  	31 + 28,
1003  	31 + 28 + 31,
1004  	31 + 28 + 31 + 30,
1005  	31 + 28 + 31 + 30 + 31,
1006  	31 + 28 + 31 + 30 + 31 + 30,
1007  	31 + 28 + 31 + 30 + 31 + 30 + 31,
1008  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31,
1009  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30,
1010  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31,
1011  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30,
1012  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31,
1013  }
1014
1015  func daysIn(m Month, year int) int {
1016  	if m == February && isLeap(year) {
1017  		return 29
1018  	}
1019  	return int(daysBefore[m] - daysBefore[m-1])
1020  }
1021
1022  // daysSinceEpoch takes a year and returns the number of days from
1023  // the absolute epoch to the start of that year.
1024  // This is basically (year - zeroYear) * 365, but accounting for leap days.
1025  func daysSinceEpoch(year int) uint64 {
1026  	y := uint64(int64(year) - absoluteZeroYear)
1027
1028  	// Add in days from 400-year cycles.
1029  	n := y / 400
1030  	y -= 400 * n
1031  	d := daysPer400Years * n
1032
1033  	// Add in 100-year cycles.
1034  	n = y / 100
1035  	y -= 100 * n
1036  	d += daysPer100Years * n
1037
1038  	// Add in 4-year cycles.
1039  	n = y / 4
1040  	y -= 4 * n
1041  	d += daysPer4Years * n
1042
1043  	// Add in non-leap years.
1044  	n = y
1045  	d += 365 * n
1046
1047  	return d
1048  }
1049
1050  // Provided by package runtime.
1051  func now() (sec int64, nsec int32, mono int64)
1052
1053  // runtimeNano returns the current value of the runtime clock in nanoseconds.
1054  //go:linkname runtimeNano runtime.nanotime
1055  func runtimeNano() int64
1056
1057  // Monotonic times are reported as offsets from startNano.
1058  // We initialize startNano to runtimeNano() - 1 so that on systems where
1059  // monotonic time resolution is fairly low (e.g. Windows 2008
1060  // which appears to have a default resolution of 15ms),
1061  // we avoid ever reporting a monotonic time of 0.
1062  // (Callers may want to use 0 as "time not set".)
1063  var startNano int64 = runtimeNano() - 1
1064
1065  // Now returns the current local time.
1066  func Now() Time {
1067  	sec, nsec, mono := now()
1068  	mono -= startNano
1069  	sec += unixToInternal - minWall
1070  	if uint64(sec)>>33 != 0 {
1071  		return Time{uint64(nsec), sec + minWall, Local}
1072  	}
1073  	return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
1074  }
1075
1076  func unixTime(sec int64, nsec int32) Time {
1077  	return Time{uint64(nsec), sec + unixToInternal, Local}
1078  }
1079
1080  // UTC returns t with the location set to UTC.
1081  func (t Time) UTC() Time {
1082  	t.setLoc(&utcLoc)
1083  	return t
1084  }
1085
1086  // Local returns t with the location set to local time.
1087  func (t Time) Local() Time {
1088  	t.setLoc(Local)
1089  	return t
1090  }
1091
1092  // In returns a copy of t representing the same time instant, but
1093  // with the copy's location information set to loc for display
1094  // purposes.
1095  //
1096  // In panics if loc is nil.
1097  func (t Time) In(loc *Location) Time {
1098  	if loc == nil {
1099  		panic("time: missing Location in call to Time.In")
1100  	}
1101  	t.setLoc(loc)
1102  	return t
1103  }
1104
1105  // Location returns the time zone information associated with t.
1106  func (t Time) Location() *Location {
1107  	l := t.loc
1108  	if l == nil {
1109  		l = UTC
1110  	}
1111  	return l
1112  }
1113
1114  // Zone computes the time zone in effect at time t, returning the abbreviated
1115  // name of the zone (such as "CET") and its offset in seconds east of UTC.
1116  func (t Time) Zone() (name string, offset int) {
1117  	name, offset, _, _ = t.loc.lookup(t.unixSec())
1118  	return
1119  }
1120
1121  // Unix returns t as a Unix time, the number of seconds elapsed
1122  // since January 1, 1970 UTC. The result does not depend on the
1123  // location associated with t.
1124  // Unix-like operating systems often record time as a 32-bit
1125  // count of seconds, but since the method here returns a 64-bit
1126  // value it is valid for billions of years into the past or future.
1127  func (t Time) Unix() int64 {
1128  	return t.unixSec()
1129  }
1130
1131  // UnixNano returns t as a Unix time, the number of nanoseconds elapsed
1132  // since January 1, 1970 UTC. The result is undefined if the Unix time
1133  // in nanoseconds cannot be represented by an int64 (a date before the year
1134  // 1678 or after 2262). Note that this means the result of calling UnixNano
1135  // on the zero Time is undefined. The result does not depend on the
1136  // location associated with t.
1137  func (t Time) UnixNano() int64 {
1138  	return (t.unixSec())*1e9 + int64(t.nsec())
1139  }
1140
1141  const timeBinaryVersion byte = 1
1142
1143  // MarshalBinary implements the encoding.BinaryMarshaler interface.
1144  func (t Time) MarshalBinary() ([]byte, error) {
1145  	var offsetMin int16 // minutes east of UTC. -1 is UTC.
1146
1147  	if t.Location() == UTC {
1148  		offsetMin = -1
1149  	} else {
1150  		_, offset := t.Zone()
1151  		if offset%60 != 0 {
1152  			return nil, errors.New("Time.MarshalBinary: zone offset has fractional minute")
1153  		}
1154  		offset /= 60
1155  		if offset < -32768 || offset == -1 || offset > 32767 {
1156  			return nil, errors.New("Time.MarshalBinary: unexpected zone offset")
1157  		}
1158  		offsetMin = int16(offset)
1159  	}
1160
1161  	sec := t.sec()
1162  	nsec := t.nsec()
1163  	enc := []byte{
1164  		timeBinaryVersion, // byte 0 : version
1165  		byte(sec >> 56),   // bytes 1-8: seconds
1166  		byte(sec >> 48),
1167  		byte(sec >> 40),
1168  		byte(sec >> 32),
1169  		byte(sec >> 24),
1170  		byte(sec >> 16),
1171  		byte(sec >> 8),
1172  		byte(sec),
1173  		byte(nsec >> 24), // bytes 9-12: nanoseconds
1174  		byte(nsec >> 16),
1175  		byte(nsec >> 8),
1176  		byte(nsec),
1177  		byte(offsetMin >> 8), // bytes 13-14: zone offset in minutes
1178  		byte(offsetMin),
1179  	}
1180
1181  	return enc, nil
1182  }
1183
1184  // UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
1185  func (t *Time) UnmarshalBinary(data []byte) error {
1186  	buf := data
1187  	if len(buf) == 0 {
1188  		return errors.New("Time.UnmarshalBinary: no data")
1189  	}
1190
1191  	if buf[0] != timeBinaryVersion {
1192  		return errors.New("Time.UnmarshalBinary: unsupported version")
1193  	}
1194
1195  	if len(buf) != /*version*/ 1+ /*sec*/ 8+ /*nsec*/ 4+ /*zone offset*/ 2 {
1196  		return errors.New("Time.UnmarshalBinary: invalid length")
1197  	}
1198
1199  	buf = buf[1:]
1200  	sec := int64(buf[7]) | int64(buf[6])<<8 | int64(buf[5])<<16 | int64(buf[4])<<24 |
1201  		int64(buf[3])<<32 | int64(buf[2])<<40 | int64(buf[1])<<48 | int64(buf[0])<<56
1202
1203  	buf = buf[8:]
1204  	nsec := int32(buf[3]) | int32(buf[2])<<8 | int32(buf[1])<<16 | int32(buf[0])<<24
1205
1206  	buf = buf[4:]
1207  	offset := int(int16(buf[1])|int16(buf[0])<<8) * 60
1208
1209  	*t = Time{}
1210  	t.wall = uint64(nsec)
1211  	t.ext = sec
1212
1213  	if offset == -1*60 {
1214  		t.setLoc(&utcLoc)
1215  	} else if _, localoff, _, _ := Local.lookup(t.unixSec()); offset == localoff {
1216  		t.setLoc(Local)
1217  	} else {
1218  		t.setLoc(FixedZone("", offset))
1219  	}
1220
1221  	return nil
1222  }
1223
1224  // TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
1225  // The same semantics will be provided by the generic MarshalBinary, MarshalText,
1226  // UnmarshalBinary, UnmarshalText.
1227
1228  // GobEncode implements the gob.GobEncoder interface.
1229  func (t Time) GobEncode() ([]byte, error) {
1230  	return t.MarshalBinary()
1231  }
1232
1233  // GobDecode implements the gob.GobDecoder interface.
1234  func (t *Time) GobDecode(data []byte) error {
1235  	return t.UnmarshalBinary(data)
1236  }
1237
1238  // MarshalJSON implements the json.Marshaler interface.
1239  // The time is a quoted string in RFC 3339 format, with sub-second precision added if present.
1240  func (t Time) MarshalJSON() ([]byte, error) {
1241  	if y := t.Year(); y < 0 || y >= 10000 {
1242  		// RFC 3339 is clear that years are 4 digits exactly.
1243  		// See golang.org/issue/4556#c15 for more discussion.
1244  		return nil, errors.New("Time.MarshalJSON: year outside of range [0,9999]")
1245  	}
1246
1247  	b := make([]byte, 0, len(RFC3339Nano)+2)
1248  	b = append(b, '"')
1249  	b = t.AppendFormat(b, RFC3339Nano)
1250  	b = append(b, '"')
1251  	return b, nil
1252  }
1253
1254  // UnmarshalJSON implements the json.Unmarshaler interface.
1255  // The time is expected to be a quoted string in RFC 3339 format.
1256  func (t *Time) UnmarshalJSON(data []byte) error {
1257  	// Ignore null, like in the main JSON package.
1258  	if string(data) == "null" {
1259  		return nil
1260  	}
1261  	// Fractional seconds are handled implicitly by Parse.
1262  	var err error
1263  	*t, err = Parse(`"`+RFC3339+`"`, string(data))
1264  	return err
1265  }
1266
1267  // MarshalText implements the encoding.TextMarshaler interface.
1268  // The time is formatted in RFC 3339 format, with sub-second precision added if present.
1269  func (t Time) MarshalText() ([]byte, error) {
1270  	if y := t.Year(); y < 0 || y >= 10000 {
1271  		return nil, errors.New("Time.MarshalText: year outside of range [0,9999]")
1272  	}
1273
1274  	b := make([]byte, 0, len(RFC3339Nano))
1275  	return t.AppendFormat(b, RFC3339Nano), nil
1276  }
1277
1278  // UnmarshalText implements the encoding.TextUnmarshaler interface.
1279  // The time is expected to be in RFC 3339 format.
1280  func (t *Time) UnmarshalText(data []byte) error {
1281  	// Fractional seconds are handled implicitly by Parse.
1282  	var err error
1283  	*t, err = Parse(RFC3339, string(data))
1284  	return err
1285  }
1286
1287  // Unix returns the local Time corresponding to the given Unix time,
1288  // sec seconds and nsec nanoseconds since January 1, 1970 UTC.
1289  // It is valid to pass nsec outside the range [0, 999999999].
1290  // Not all sec values have a corresponding time value. One such
1291  // value is 1<<63-1 (the largest int64 value).
1292  func Unix(sec int64, nsec int64) Time {
1293  	if nsec < 0 || nsec >= 1e9 {
1294  		n := nsec / 1e9
1295  		sec += n
1296  		nsec -= n * 1e9
1297  		if nsec < 0 {
1298  			nsec += 1e9
1299  			sec--
1300  		}
1301  	}
1302  	return unixTime(sec, int32(nsec))
1303  }
1304
1305  func isLeap(year int) bool {
1306  	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
1307  }
1308
1309  // norm returns nhi, nlo such that
1310  //	hi * base + lo == nhi * base + nlo
1311  //	0 <= nlo < base
1312  func norm(hi, lo, base int) (nhi, nlo int) {
1313  	if lo < 0 {
1314  		n := (-lo-1)/base + 1
1315  		hi -= n
1316  		lo += n * base
1317  	}
1318  	if lo >= base {
1319  		n := lo / base
1320  		hi += n
1321  		lo -= n * base
1322  	}
1323  	return hi, lo
1324  }
1325
1326  // Date returns the Time corresponding to
1327  //	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
1328  // in the appropriate zone for that time in the given location.
1329  //
1330  // The month, day, hour, min, sec, and nsec values may be outside
1331  // their usual ranges and will be normalized during the conversion.
1332  // For example, October 32 converts to November 1.
1333  //
1334  // A daylight savings time transition skips or repeats times.
1335  // For example, in the United States, March 13, 2011 2:15am never occurred,
1336  // while November 6, 2011 1:15am occurred twice. In such cases, the
1337  // choice of time zone, and therefore the time, is not well-defined.
1338  // Date returns a time that is correct in one of the two zones involved
1339  // in the transition, but it does not guarantee which.
1340  //
1341  // Date panics if loc is nil.
1342  func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
1343  	if loc == nil {
1344  		panic("time: missing Location in call to Date")
1345  	}
1346
1347  	// Normalize month, overflowing into year.
1348  	m := int(month) - 1
1349  	year, m = norm(year, m, 12)
1350  	month = Month(m) + 1
1351
1352  	// Normalize nsec, sec, min, hour, overflowing into day.
1353  	sec, nsec = norm(sec, nsec, 1e9)
1354  	min, sec = norm(min, sec, 60)
1355  	hour, min = norm(hour, min, 60)
1356  	day, hour = norm(day, hour, 24)
1357
1358  	// Compute days since the absolute epoch.
1359  	d := daysSinceEpoch(year)
1360
1361  	// Add in days before this month.
1362  	d += uint64(daysBefore[month-1])
1363  	if isLeap(year) && month >= March {
1364  		d++ // February 29
1365  	}
1366
1367  	// Add in days before today.
1368  	d += uint64(day - 1)
1369
1370  	// Add in time elapsed today.
1371  	abs := d * secondsPerDay
1372  	abs += uint64(hour*secondsPerHour + min*secondsPerMinute + sec)
1373
1374  	unix := int64(abs) + (absoluteToInternal + internalToUnix)
1375
1376  	// Look for zone offset for t, so we can adjust to UTC.
1377  	// The lookup function expects UTC, so we pass t in the
1378  	// hope that it will not be too close to a zone transition,
1379  	// and then adjust if it is.
1380  	_, offset, start, end := loc.lookup(unix)
1381  	if offset != 0 {
1382  		switch utc := unix - int64(offset); {
1383  		case utc < start:
1384  			_, offset, _, _ = loc.lookup(start - 1)
1385  		case utc >= end:
1386  			_, offset, _, _ = loc.lookup(end)
1387  		}
1388  		unix -= int64(offset)
1389  	}
1390
1391  	t := unixTime(unix, int32(nsec))
1392  	t.setLoc(loc)
1393  	return t
1394  }
1395
1396  // Truncate returns the result of rounding t down to a multiple of d (since the zero time).
1397  // If d <= 0, Truncate returns t stripped of any monotonic clock reading but otherwise unchanged.
1398  //
1399  // Truncate operates on the time as an absolute duration since the
1400  // zero time; it does not operate on the presentation form of the
1401  // time. Thus, Truncate(Hour) may return a time with a non-zero
1402  // minute, depending on the time's Location.
1403  func (t Time) Truncate(d Duration) Time {
1404  	t.stripMono()
1405  	if d <= 0 {
1406  		return t
1407  	}
1408  	_, r := div(t, d)
1410  }
1411
1412  // Round returns the result of rounding t to the nearest multiple of d (since the zero time).
1413  // The rounding behavior for halfway values is to round up.
1414  // If d <= 0, Round returns t stripped of any monotonic clock reading but otherwise unchanged.
1415  //
1416  // Round operates on the time as an absolute duration since the
1417  // zero time; it does not operate on the presentation form of the
1418  // time. Thus, Round(Hour) may return a time with a non-zero
1419  // minute, depending on the time's Location.
1420  func (t Time) Round(d Duration) Time {
1421  	t.stripMono()
1422  	if d <= 0 {
1423  		return t
1424  	}
1425  	_, r := div(t, d)
1426  	if lessThanHalf(r, d) {
1428  	}
1429  	return t.Add(d - r)
1430  }
1431
1432  // div divides t by d and returns the quotient parity and remainder.
1433  // We don't use the quotient parity anymore (round half up instead of round to even)
1434  // but it's still here in case we change our minds.
1435  func div(t Time, d Duration) (qmod2 int, r Duration) {
1436  	neg := false
1437  	nsec := t.nsec()
1438  	sec := t.sec()
1439  	if sec < 0 {
1440  		// Operate on absolute value.
1441  		neg = true
1442  		sec = -sec
1443  		nsec = -nsec
1444  		if nsec < 0 {
1445  			nsec += 1e9
1446  			sec-- // sec >= 1 before the -- so safe
1447  		}
1448  	}
1449
1450  	switch {
1451  	// Special case: 2d divides 1 second.
1452  	case d < Second && Second%(d+d) == 0:
1453  		qmod2 = int(nsec/int32(d)) & 1
1454  		r = Duration(nsec % int32(d))
1455
1456  	// Special case: d is a multiple of 1 second.
1457  	case d%Second == 0:
1458  		d1 := int64(d / Second)
1459  		qmod2 = int(sec/d1) & 1
1460  		r = Duration(sec%d1)*Second + Duration(nsec)
1461
1462  	// General case.
1463  	// This could be faster if more cleverness were applied,
1464  	// but it's really only here to avoid special case restrictions in the API.
1465  	// No one will care about these cases.
1466  	default:
1467  		// Compute nanoseconds as 128-bit number.
1468  		sec := uint64(sec)
1469  		tmp := (sec >> 32) * 1e9
1470  		u1 := tmp >> 32
1471  		u0 := tmp << 32
1472  		tmp = (sec & 0xFFFFFFFF) * 1e9
1473  		u0x, u0 := u0, u0+tmp
1474  		if u0 < u0x {
1475  			u1++
1476  		}
1477  		u0x, u0 = u0, u0+uint64(nsec)
1478  		if u0 < u0x {
1479  			u1++
1480  		}
1481
1482  		// Compute remainder by subtracting r<<k for decreasing k.
1483  		// Quotient parity is whether we subtract on last round.
1484  		d1 := uint64(d)
1485  		for d1>>63 != 1 {
1486  			d1 <<= 1
1487  		}
1488  		d0 := uint64(0)
1489  		for {
1490  			qmod2 = 0
1491  			if u1 > d1 || u1 == d1 && u0 >= d0 {
1492  				// subtract
1493  				qmod2 = 1
1494  				u0x, u0 = u0, u0-d0
1495  				if u0 > u0x {
1496  					u1--
1497  				}
1498  				u1 -= d1
1499  			}
1500  			if d1 == 0 && d0 == uint64(d) {
1501  				break
1502  			}
1503  			d0 >>= 1
1504  			d0 |= (d1 & 1) << 63
1505  			d1 >>= 1
1506  		}
1507  		r = Duration(u0)
1508  	}
1509
1510  	if neg && r != 0 {
1511  		// If input was negative and not an exact multiple of d, we computed q, r such that
1512  		//	q*d + r = -t
1513  		// But the right answers are given by -(q-1), d-r:
1514  		//	q*d + r = -t
1515  		//	-q*d - r = t
1516  		//	-(q-1)*d + (d - r) = t
1517  		qmod2 ^= 1
1518  		r = d - r
1519  	}
1520  	return
1521  }
1522
```

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