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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  	// Check if the sum of t.ext and d overflows and handle it properly.
193  	sum := t.ext + d
194  	if (sum > t.ext) == (d > 0) {
195  		t.ext = sum
196  	} else if d > 0 {
197  		t.ext = 1<<63 - 1
198  	} else {
199  		t.ext = -(1<<63 - 1)
200  	}
201  }
202
203  // setLoc sets the location associated with the time.
204  func (t *Time) setLoc(loc *Location) {
205  	if loc == &utcLoc {
206  		loc = nil
207  	}
208  	t.stripMono()
209  	t.loc = loc
210  }
211
212  // stripMono strips the monotonic clock reading in t.
213  func (t *Time) stripMono() {
214  	if t.wall&hasMonotonic != 0 {
215  		t.ext = t.sec()
217  	}
218  }
219
220  // setMono sets the monotonic clock reading in t.
221  // If t cannot hold a monotonic clock reading,
222  // because its wall time is too large,
223  // setMono is a no-op.
224  func (t *Time) setMono(m int64) {
225  	if t.wall&hasMonotonic == 0 {
226  		sec := t.ext
227  		if sec < minWall || maxWall < sec {
228  			return
229  		}
230  		t.wall |= hasMonotonic | uint64(sec-minWall)<<nsecShift
231  	}
232  	t.ext = m
233  }
234
235  // mono returns t's monotonic clock reading.
236  // It returns 0 for a missing reading.
237  // This function is used only for testing,
238  // so it's OK that technically 0 is a valid
239  // monotonic clock reading as well.
240  func (t *Time) mono() int64 {
241  	if t.wall&hasMonotonic == 0 {
242  		return 0
243  	}
244  	return t.ext
245  }
246
247  // After reports whether the time instant t is after u.
248  func (t Time) After(u Time) bool {
249  	if t.wall&u.wall&hasMonotonic != 0 {
250  		return t.ext > u.ext
251  	}
252  	ts := t.sec()
253  	us := u.sec()
254  	return ts > us || ts == us && t.nsec() > u.nsec()
255  }
256
257  // Before reports whether the time instant t is before u.
258  func (t Time) Before(u Time) bool {
259  	if t.wall&u.wall&hasMonotonic != 0 {
260  		return t.ext < u.ext
261  	}
262  	ts := t.sec()
263  	us := u.sec()
264  	return ts < us || ts == us && t.nsec() < u.nsec()
265  }
266
267  // Equal reports whether t and u represent the same time instant.
268  // Two times can be equal even if they are in different locations.
269  // For example, 6:00 +0200 and 4:00 UTC are Equal.
270  // See the documentation on the Time type for the pitfalls of using == with
271  // Time values; most code should use Equal instead.
272  func (t Time) Equal(u Time) bool {
273  	if t.wall&u.wall&hasMonotonic != 0 {
274  		return t.ext == u.ext
275  	}
276  	return t.sec() == u.sec() && t.nsec() == u.nsec()
277  }
278
279  // A Month specifies a month of the year (January = 1, ...).
280  type Month int
281
282  const (
283  	January Month = 1 + iota
284  	February
285  	March
286  	April
287  	May
288  	June
289  	July
290  	August
291  	September
292  	October
293  	November
294  	December
295  )
296
297  // String returns the English name of the month ("January", "February", ...).
298  func (m Month) String() string {
299  	if January <= m && m <= December {
300  		return longMonthNames[m-1]
301  	}
302  	buf := make([]byte, 20)
303  	n := fmtInt(buf, uint64(m))
304  	return "%!Month(" + string(buf[n:]) + ")"
305  }
306
307  // A Weekday specifies a day of the week (Sunday = 0, ...).
308  type Weekday int
309
310  const (
311  	Sunday Weekday = iota
312  	Monday
313  	Tuesday
314  	Wednesday
315  	Thursday
316  	Friday
317  	Saturday
318  )
319
320  // String returns the English name of the day ("Sunday", "Monday", ...).
321  func (d Weekday) String() string {
322  	if Sunday <= d && d <= Saturday {
323  		return longDayNames[d]
324  	}
325  	buf := make([]byte, 20)
326  	n := fmtInt(buf, uint64(d))
327  	return "%!Weekday(" + string(buf[n:]) + ")"
328  }
329
330  // Computations on time.
331  //
332  // The zero value for a Time is defined to be
333  //	January 1, year 1, 00:00:00.000000000 UTC
334  // which (1) looks like a zero, or as close as you can get in a date
335  // (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
336  // be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
337  // non-negative year even in time zones west of UTC, unlike 1-1-0
338  // 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
339  //
340  // The zero Time value does not force a specific epoch for the time
341  // representation. For example, to use the Unix epoch internally, we
342  // could define that to distinguish a zero value from Jan 1 1970, that
343  // time would be represented by sec=-1, nsec=1e9. However, it does
344  // suggest a representation, namely using 1-1-1 00:00:00 UTC as the
345  // epoch, and that's what we do.
346  //
347  // The Add and Sub computations are oblivious to the choice of epoch.
348  //
349  // The presentation computations - year, month, minute, and so on - all
350  // rely heavily on division and modulus by positive constants. For
351  // calendrical calculations we want these divisions to round down, even
352  // for negative values, so that the remainder is always positive, but
353  // Go's division (like most hardware division instructions) rounds to
354  // zero. We can still do those computations and then adjust the result
355  // for a negative numerator, but it's annoying to write the adjustment
356  // over and over. Instead, we can change to a different epoch so long
357  // ago that all the times we care about will be positive, and then round
358  // to zero and round down coincide. These presentation routines already
359  // have to add the zone offset, so adding the translation to the
360  // alternate epoch is cheap. For example, having a non-negative time t
361  // means that we can write
362  //
363  //	sec = t % 60
364  //
366  //
367  //	sec = t % 60
368  //	if sec < 0 {
369  //		sec += 60
370  //	}
371  //
372  // everywhere.
373  //
374  // The calendar runs on an exact 400 year cycle: a 400-year calendar
375  // printed for 1970-2369 will apply as well to 2370-2769. Even the days
376  // of the week match up. It simplifies the computations to choose the
377  // cycle boundaries so that the exceptional years are always delayed as
378  // long as possible. That means choosing a year equal to 1 mod 400, so
379  // that the first leap year is the 4th year, the first missed leap year
380  // is the 100th year, and the missed missed leap year is the 400th year.
381  // So we'd prefer instead to print a calendar for 2001-2400 and reuse it
382  // for 2401-2800.
383  //
384  // Finally, it's convenient if the delta between the Unix epoch and
385  // long-ago epoch is representable by an int64 constant.
386  //
387  // These three considerations—choose an epoch as early as possible, that
388  // uses a year equal to 1 mod 400, and that is no more than 2⁶³ seconds
389  // earlier than 1970—bring us to the year -292277022399. We refer to
390  // this year as the absolute zero year, and to times measured as a uint64
391  // seconds since this year as absolute times.
392  //
393  // Times measured as an int64 seconds since the year 1—the representation
394  // used for Time's sec field—are called internal times.
395  //
396  // Times measured as an int64 seconds since the year 1970 are called Unix
397  // times.
398  //
399  // It is tempting to just use the year 1 as the absolute epoch, defining
400  // that the routines are only valid for years >= 1. However, the
401  // routines would then be invalid when displaying the epoch in time zones
402  // west of UTC, since it is year 0. It doesn't seem tenable to say that
403  // printing the zero time correctly isn't supported in half the time
404  // zones. By comparison, it's reasonable to mishandle some times in
405  // the year -292277022399.
406  //
407  // All this is opaque to clients of the API and can be changed if a
408  // better implementation presents itself.
409
410  const (
411  	// The unsigned zero year for internal calculations.
412  	// Must be 1 mod 400, and times before it will not compute correctly,
413  	// but otherwise can be changed at will.
414  	absoluteZeroYear = -292277022399
415
416  	// The year of the zero Time.
417  	// Assumed by the unixToInternal computation below.
418  	internalYear = 1
419
420  	// Offsets to convert between internal and absolute or Unix times.
421  	absoluteToInternal int64 = (absoluteZeroYear - internalYear) * 365.2425 * secondsPerDay
422  	internalToAbsolute       = -absoluteToInternal
423
424  	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
425  	internalToUnix int64 = -unixToInternal
426
427  	wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
428  	internalToWall int64 = -wallToInternal
429  )
430
431  // IsZero reports whether t represents the zero time instant,
432  // January 1, year 1, 00:00:00 UTC.
433  func (t Time) IsZero() bool {
434  	return t.sec() == 0 && t.nsec() == 0
435  }
436
437  // abs returns the time t as an absolute time, adjusted by the zone offset.
438  // It is called when computing a presentation property like Month or Hour.
439  func (t Time) abs() uint64 {
440  	l := t.loc
441  	// Avoid function calls when possible.
442  	if l == nil || l == &localLoc {
443  		l = l.get()
444  	}
445  	sec := t.unixSec()
446  	if l != &utcLoc {
447  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
448  			sec += int64(l.cacheZone.offset)
449  		} else {
450  			_, offset, _, _, _ := l.lookup(sec)
451  			sec += int64(offset)
452  		}
453  	}
454  	return uint64(sec + (unixToInternal + internalToAbsolute))
455  }
456
457  // locabs is a combination of the Zone and abs methods,
458  // extracting both return values from a single zone lookup.
459  func (t Time) locabs() (name string, offset int, abs uint64) {
460  	l := t.loc
461  	if l == nil || l == &localLoc {
462  		l = l.get()
463  	}
464  	// Avoid function call if we hit the local time cache.
465  	sec := t.unixSec()
466  	if l != &utcLoc {
467  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
468  			name = l.cacheZone.name
469  			offset = l.cacheZone.offset
470  		} else {
471  			name, offset, _, _, _ = l.lookup(sec)
472  		}
473  		sec += int64(offset)
474  	} else {
475  		name = "UTC"
476  	}
477  	abs = uint64(sec + (unixToInternal + internalToAbsolute))
478  	return
479  }
480
481  // Date returns the year, month, and day in which t occurs.
482  func (t Time) Date() (year int, month Month, day int) {
483  	year, month, day, _ = t.date(true)
484  	return
485  }
486
487  // Year returns the year in which t occurs.
488  func (t Time) Year() int {
489  	year, _, _, _ := t.date(false)
490  	return year
491  }
492
493  // Month returns the month of the year specified by t.
494  func (t Time) Month() Month {
495  	_, month, _, _ := t.date(true)
496  	return month
497  }
498
499  // Day returns the day of the month specified by t.
500  func (t Time) Day() int {
501  	_, _, day, _ := t.date(true)
502  	return day
503  }
504
505  // Weekday returns the day of the week specified by t.
506  func (t Time) Weekday() Weekday {
507  	return absWeekday(t.abs())
508  }
509
510  // absWeekday is like Weekday but operates on an absolute time.
511  func absWeekday(abs uint64) Weekday {
512  	// January 1 of the absolute year, like January 1 of 2001, was a Monday.
513  	sec := (abs + uint64(Monday)*secondsPerDay) % secondsPerWeek
514  	return Weekday(int(sec) / secondsPerDay)
515  }
516
517  // ISOWeek returns the ISO 8601 year and week number in which t occurs.
518  // Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
519  // week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
520  // of year n+1.
521  func (t Time) ISOWeek() (year, week int) {
522  	// According to the rule that the first calendar week of a calendar year is
523  	// the week including the first Thursday of that year, and that the last one is
524  	// the week immediately preceding the first calendar week of the next calendar year.
525  	// See https://www.iso.org/obp/ui#iso:std:iso:8601:-1:ed-1:v1:en:term:3.1.1.23 for details.
526
528  	// Monday Tuesday Wednesday Thursday Friday Saturday Sunday
529  	// 1      2       3         4        5      6        7
530  	// +3     +2      +1        0        -1     -2       -3
531  	// the offset to Thursday
532  	abs := t.abs()
533  	d := Thursday - absWeekday(abs)
534  	// handle Sunday
535  	if d == 4 {
536  		d = -3
537  	}
538  	// find the Thursday of the calendar week
539  	abs += uint64(d) * secondsPerDay
540  	year, _, _, yday := absDate(abs, false)
541  	return year, yday/7 + 1
542  }
543
544  // Clock returns the hour, minute, and second within the day specified by t.
545  func (t Time) Clock() (hour, min, sec int) {
546  	return absClock(t.abs())
547  }
548
549  // absClock is like clock but operates on an absolute time.
550  func absClock(abs uint64) (hour, min, sec int) {
551  	sec = int(abs % secondsPerDay)
552  	hour = sec / secondsPerHour
553  	sec -= hour * secondsPerHour
554  	min = sec / secondsPerMinute
555  	sec -= min * secondsPerMinute
556  	return
557  }
558
559  // Hour returns the hour within the day specified by t, in the range [0, 23].
560  func (t Time) Hour() int {
561  	return int(t.abs()%secondsPerDay) / secondsPerHour
562  }
563
564  // Minute returns the minute offset within the hour specified by t, in the range [0, 59].
565  func (t Time) Minute() int {
566  	return int(t.abs()%secondsPerHour) / secondsPerMinute
567  }
568
569  // Second returns the second offset within the minute specified by t, in the range [0, 59].
570  func (t Time) Second() int {
571  	return int(t.abs() % secondsPerMinute)
572  }
573
574  // Nanosecond returns the nanosecond offset within the second specified by t,
575  // in the range [0, 999999999].
576  func (t Time) Nanosecond() int {
577  	return int(t.nsec())
578  }
579
580  // YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
581  // and [1,366] in leap years.
582  func (t Time) YearDay() int {
583  	_, _, _, yday := t.date(false)
584  	return yday + 1
585  }
586
587  // A Duration represents the elapsed time between two instants
588  // as an int64 nanosecond count. The representation limits the
589  // largest representable duration to approximately 290 years.
590  type Duration int64
591
592  const (
593  	minDuration Duration = -1 << 63
594  	maxDuration Duration = 1<<63 - 1
595  )
596
597  // Common durations. There is no definition for units of Day or larger
598  // to avoid confusion across daylight savings time zone transitions.
599  //
600  // To count the number of units in a Duration, divide:
601  //	second := time.Second
602  //	fmt.Print(int64(second/time.Millisecond)) // prints 1000
603  //
604  // To convert an integer number of units to a Duration, multiply:
605  //	seconds := 10
606  //	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
607  //
608  const (
609  	Nanosecond  Duration = 1
610  	Microsecond          = 1000 * Nanosecond
611  	Millisecond          = 1000 * Microsecond
612  	Second               = 1000 * Millisecond
613  	Minute               = 60 * Second
614  	Hour                 = 60 * Minute
615  )
616
617  // String returns a string representing the duration in the form "72h3m0.5s".
618  // Leading zero units are omitted. As a special case, durations less than one
619  // second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
620  // that the leading digit is non-zero. The zero duration formats as 0s.
621  func (d Duration) String() string {
622  	// Largest time is 2540400h10m10.000000000s
623  	var buf [32]byte
624  	w := len(buf)
625
626  	u := uint64(d)
627  	neg := d < 0
628  	if neg {
629  		u = -u
630  	}
631
632  	if u < uint64(Second) {
633  		// Special case: if duration is smaller than a second,
634  		// use smaller units, like 1.2ms
635  		var prec int
636  		w--
637  		buf[w] = 's'
638  		w--
639  		switch {
640  		case u == 0:
641  			return "0s"
642  		case u < uint64(Microsecond):
643  			// print nanoseconds
644  			prec = 0
645  			buf[w] = 'n'
646  		case u < uint64(Millisecond):
647  			// print microseconds
648  			prec = 3
649  			// U+00B5 'µ' micro sign == 0xC2 0xB5
650  			w-- // Need room for two bytes.
651  			copy(buf[w:], "µ")
652  		default:
653  			// print milliseconds
654  			prec = 6
655  			buf[w] = 'm'
656  		}
657  		w, u = fmtFrac(buf[:w], u, prec)
658  		w = fmtInt(buf[:w], u)
659  	} else {
660  		w--
661  		buf[w] = 's'
662
663  		w, u = fmtFrac(buf[:w], u, 9)
664
665  		// u is now integer seconds
666  		w = fmtInt(buf[:w], u%60)
667  		u /= 60
668
669  		// u is now integer minutes
670  		if u > 0 {
671  			w--
672  			buf[w] = 'm'
673  			w = fmtInt(buf[:w], u%60)
674  			u /= 60
675
676  			// u is now integer hours
677  			// Stop at hours because days can be different lengths.
678  			if u > 0 {
679  				w--
680  				buf[w] = 'h'
681  				w = fmtInt(buf[:w], u)
682  			}
683  		}
684  	}
685
686  	if neg {
687  		w--
688  		buf[w] = '-'
689  	}
690
691  	return string(buf[w:])
692  }
693
694  // fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
695  // tail of buf, omitting trailing zeros. It omits the decimal
696  // point too when the fraction is 0. It returns the index where the
697  // output bytes begin and the value v/10**prec.
698  func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
699  	// Omit trailing zeros up to and including decimal point.
700  	w := len(buf)
701  	print := false
702  	for i := 0; i < prec; i++ {
703  		digit := v % 10
704  		print = print || digit != 0
705  		if print {
706  			w--
707  			buf[w] = byte(digit) + '0'
708  		}
709  		v /= 10
710  	}
711  	if print {
712  		w--
713  		buf[w] = '.'
714  	}
715  	return w, v
716  }
717
718  // fmtInt formats v into the tail of buf.
719  // It returns the index where the output begins.
720  func fmtInt(buf []byte, v uint64) int {
721  	w := len(buf)
722  	if v == 0 {
723  		w--
724  		buf[w] = '0'
725  	} else {
726  		for v > 0 {
727  			w--
728  			buf[w] = byte(v%10) + '0'
729  			v /= 10
730  		}
731  	}
732  	return w
733  }
734
735  // Nanoseconds returns the duration as an integer nanosecond count.
736  func (d Duration) Nanoseconds() int64 { return int64(d) }
737
738  // Microseconds returns the duration as an integer microsecond count.
739  func (d Duration) Microseconds() int64 { return int64(d) / 1e3 }
740
741  // Milliseconds returns the duration as an integer millisecond count.
742  func (d Duration) Milliseconds() int64 { return int64(d) / 1e6 }
743
744  // These methods return float64 because the dominant
745  // use case is for printing a floating point number like 1.5s, and
746  // a truncation to integer would make them not useful in those cases.
747  // Splitting the integer and fraction ourselves guarantees that
748  // converting the returned float64 to an integer rounds the same
749  // way that a pure integer conversion would have, even in cases
750  // where, say, float64(d.Nanoseconds())/1e9 would have rounded
751  // differently.
752
753  // Seconds returns the duration as a floating point number of seconds.
754  func (d Duration) Seconds() float64 {
755  	sec := d / Second
756  	nsec := d % Second
757  	return float64(sec) + float64(nsec)/1e9
758  }
759
760  // Minutes returns the duration as a floating point number of minutes.
761  func (d Duration) Minutes() float64 {
762  	min := d / Minute
763  	nsec := d % Minute
764  	return float64(min) + float64(nsec)/(60*1e9)
765  }
766
767  // Hours returns the duration as a floating point number of hours.
768  func (d Duration) Hours() float64 {
769  	hour := d / Hour
770  	nsec := d % Hour
771  	return float64(hour) + float64(nsec)/(60*60*1e9)
772  }
773
774  // Truncate returns the result of rounding d toward zero to a multiple of m.
775  // If m <= 0, Truncate returns d unchanged.
776  func (d Duration) Truncate(m Duration) Duration {
777  	if m <= 0 {
778  		return d
779  	}
780  	return d - d%m
781  }
782
783  // lessThanHalf reports whether x+x < y but avoids overflow,
784  // assuming x and y are both positive (Duration is signed).
785  func lessThanHalf(x, y Duration) bool {
786  	return uint64(x)+uint64(x) < uint64(y)
787  }
788
789  // Round returns the result of rounding d to the nearest multiple of m.
790  // The rounding behavior for halfway values is to round away from zero.
791  // If the result exceeds the maximum (or minimum)
792  // value that can be stored in a Duration,
793  // Round returns the maximum (or minimum) duration.
794  // If m <= 0, Round returns d unchanged.
795  func (d Duration) Round(m Duration) Duration {
796  	if m <= 0 {
797  		return d
798  	}
799  	r := d % m
800  	if d < 0 {
801  		r = -r
802  		if lessThanHalf(r, m) {
803  			return d + r
804  		}
805  		if d1 := d - m + r; d1 < d {
806  			return d1
807  		}
808  		return minDuration // overflow
809  	}
810  	if lessThanHalf(r, m) {
811  		return d - r
812  	}
813  	if d1 := d + m - r; d1 > d {
814  		return d1
815  	}
816  	return maxDuration // overflow
817  }
818
819  // Add returns the time t+d.
820  func (t Time) Add(d Duration) Time {
821  	dsec := int64(d / 1e9)
822  	nsec := t.nsec() + int32(d%1e9)
823  	if nsec >= 1e9 {
824  		dsec++
825  		nsec -= 1e9
826  	} else if nsec < 0 {
827  		dsec--
828  		nsec += 1e9
829  	}
830  	t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
832  	if t.wall&hasMonotonic != 0 {
833  		te := t.ext + int64(d)
834  		if d < 0 && te > t.ext || d > 0 && te < t.ext {
835  			// Monotonic clock reading now out of range; degrade to wall-only.
836  			t.stripMono()
837  		} else {
838  			t.ext = te
839  		}
840  	}
841  	return t
842  }
843
844  // Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
845  // value that can be stored in a Duration, the maximum (or minimum) duration
846  // will be returned.
847  // To compute t-d for a duration d, use t.Add(-d).
848  func (t Time) Sub(u Time) Duration {
849  	if t.wall&u.wall&hasMonotonic != 0 {
850  		te := t.ext
851  		ue := u.ext
852  		d := Duration(te - ue)
853  		if d < 0 && te > ue {
854  			return maxDuration // t - u is positive out of range
855  		}
856  		if d > 0 && te < ue {
857  			return minDuration // t - u is negative out of range
858  		}
859  		return d
860  	}
861  	d := Duration(t.sec()-u.sec())*Second + Duration(t.nsec()-u.nsec())
862  	// Check for overflow or underflow.
863  	switch {
865  		return d // d is correct
866  	case t.Before(u):
867  		return minDuration // t - u is negative out of range
868  	default:
869  		return maxDuration // t - u is positive out of range
870  	}
871  }
872
873  // Since returns the time elapsed since t.
874  // It is shorthand for time.Now().Sub(t).
875  func Since(t Time) Duration {
876  	var now Time
877  	if t.wall&hasMonotonic != 0 {
878  		// Common case optimization: if t has monotonic time, then Sub will use only it.
879  		now = Time{hasMonotonic, runtimeNano() - startNano, nil}
880  	} else {
881  		now = Now()
882  	}
883  	return now.Sub(t)
884  }
885
886  // Until returns the duration until t.
887  // It is shorthand for t.Sub(time.Now()).
888  func Until(t Time) Duration {
889  	var now Time
890  	if t.wall&hasMonotonic != 0 {
891  		// Common case optimization: if t has monotonic time, then Sub will use only it.
892  		now = Time{hasMonotonic, runtimeNano() - startNano, nil}
893  	} else {
894  		now = Now()
895  	}
896  	return t.Sub(now)
897  }
898
900  // given number of years, months, and days to t.
901  // For example, AddDate(-1, 2, 3) applied to January 1, 2011
902  // returns March 4, 2010.
903  //
904  // AddDate normalizes its result in the same way that Date does,
905  // so, for example, adding one month to October 31 yields
906  // December 1, the normalized form for November 31.
907  func (t Time) AddDate(years int, months int, days int) Time {
908  	year, month, day := t.Date()
909  	hour, min, sec := t.Clock()
910  	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec()), t.Location())
911  }
912
913  const (
914  	secondsPerMinute = 60
915  	secondsPerHour   = 60 * secondsPerMinute
916  	secondsPerDay    = 24 * secondsPerHour
917  	secondsPerWeek   = 7 * secondsPerDay
918  	daysPer400Years  = 365*400 + 97
919  	daysPer100Years  = 365*100 + 24
920  	daysPer4Years    = 365*4 + 1
921  )
922
923  // date computes the year, day of year, and when full=true,
924  // the month and day in which t occurs.
925  func (t Time) date(full bool) (year int, month Month, day int, yday int) {
926  	return absDate(t.abs(), full)
927  }
928
929  // absDate is like date but operates on an absolute time.
930  func absDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
931  	// Split into time and day.
932  	d := abs / secondsPerDay
933
934  	// Account for 400 year cycles.
935  	n := d / daysPer400Years
936  	y := 400 * n
937  	d -= daysPer400Years * n
938
939  	// Cut off 100-year cycles.
940  	// The last cycle has one extra leap year, so on the last day
941  	// of that year, day / daysPer100Years will be 4 instead of 3.
942  	// Cut it back down to 3 by subtracting n>>2.
943  	n = d / daysPer100Years
944  	n -= n >> 2
945  	y += 100 * n
946  	d -= daysPer100Years * n
947
948  	// Cut off 4-year cycles.
949  	// The last cycle has a missing leap year, which does not
950  	// affect the computation.
951  	n = d / daysPer4Years
952  	y += 4 * n
953  	d -= daysPer4Years * n
954
955  	// Cut off years within a 4-year cycle.
956  	// The last year is a leap year, so on the last day of that year,
957  	// day / 365 will be 4 instead of 3. Cut it back down to 3
958  	// by subtracting n>>2.
959  	n = d / 365
960  	n -= n >> 2
961  	y += n
962  	d -= 365 * n
963
964  	year = int(int64(y) + absoluteZeroYear)
965  	yday = int(d)
966
967  	if !full {
968  		return
969  	}
970
971  	day = yday
972  	if isLeap(year) {
973  		// Leap year
974  		switch {
975  		case day > 31+29-1:
976  			// After leap day; pretend it wasn't there.
977  			day--
978  		case day == 31+29-1:
979  			// Leap day.
980  			month = February
981  			day = 29
982  			return
983  		}
984  	}
985
986  	// Estimate month on assumption that every month has 31 days.
987  	// The estimate may be too low by at most one month, so adjust.
988  	month = Month(day / 31)
989  	end := int(daysBefore[month+1])
990  	var begin int
991  	if day >= end {
992  		month++
993  		begin = end
994  	} else {
995  		begin = int(daysBefore[month])
996  	}
997
998  	month++ // because January is 1
999  	day = day - begin + 1
1000  	return
1001  }
1002
1003  // daysBefore[m] counts the number of days in a non-leap year
1004  // before month m begins. There is an entry for m=12, counting
1005  // the number of days before January of next year (365).
1006  var daysBefore = [...]int32{
1007  	0,
1008  	31,
1009  	31 + 28,
1010  	31 + 28 + 31,
1011  	31 + 28 + 31 + 30,
1012  	31 + 28 + 31 + 30 + 31,
1013  	31 + 28 + 31 + 30 + 31 + 30,
1014  	31 + 28 + 31 + 30 + 31 + 30 + 31,
1015  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31,
1016  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30,
1017  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31,
1018  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30,
1019  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31,
1020  }
1021
1022  func daysIn(m Month, year int) int {
1023  	if m == February && isLeap(year) {
1024  		return 29
1025  	}
1026  	return int(daysBefore[m] - daysBefore[m-1])
1027  }
1028
1029  // daysSinceEpoch takes a year and returns the number of days from
1030  // the absolute epoch to the start of that year.
1031  // This is basically (year - zeroYear) * 365, but accounting for leap days.
1032  func daysSinceEpoch(year int) uint64 {
1033  	y := uint64(int64(year) - absoluteZeroYear)
1034
1035  	// Add in days from 400-year cycles.
1036  	n := y / 400
1037  	y -= 400 * n
1038  	d := daysPer400Years * n
1039
1040  	// Add in 100-year cycles.
1041  	n = y / 100
1042  	y -= 100 * n
1043  	d += daysPer100Years * n
1044
1045  	// Add in 4-year cycles.
1046  	n = y / 4
1047  	y -= 4 * n
1048  	d += daysPer4Years * n
1049
1050  	// Add in non-leap years.
1051  	n = y
1052  	d += 365 * n
1053
1054  	return d
1055  }
1056
1057  // Provided by package runtime.
1058  func now() (sec int64, nsec int32, mono int64)
1059
1060  // runtimeNano returns the current value of the runtime clock in nanoseconds.
1062  func runtimeNano() int64
1063
1064  // Monotonic times are reported as offsets from startNano.
1065  // We initialize startNano to runtimeNano() - 1 so that on systems where
1066  // monotonic time resolution is fairly low (e.g. Windows 2008
1067  // which appears to have a default resolution of 15ms),
1068  // we avoid ever reporting a monotonic time of 0.
1069  // (Callers may want to use 0 as "time not set".)
1070  var startNano int64 = runtimeNano() - 1
1071
1072  // Now returns the current local time.
1073  func Now() Time {
1074  	sec, nsec, mono := now()
1075  	mono -= startNano
1076  	sec += unixToInternal - minWall
1077  	if uint64(sec)>>33 != 0 {
1078  		return Time{uint64(nsec), sec + minWall, Local}
1079  	}
1080  	return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
1081  }
1082
1083  func unixTime(sec int64, nsec int32) Time {
1084  	return Time{uint64(nsec), sec + unixToInternal, Local}
1085  }
1086
1087  // UTC returns t with the location set to UTC.
1088  func (t Time) UTC() Time {
1089  	t.setLoc(&utcLoc)
1090  	return t
1091  }
1092
1093  // Local returns t with the location set to local time.
1094  func (t Time) Local() Time {
1095  	t.setLoc(Local)
1096  	return t
1097  }
1098
1099  // In returns a copy of t representing the same time instant, but
1100  // with the copy's location information set to loc for display
1101  // purposes.
1102  //
1103  // In panics if loc is nil.
1104  func (t Time) In(loc *Location) Time {
1105  	if loc == nil {
1106  		panic("time: missing Location in call to Time.In")
1107  	}
1108  	t.setLoc(loc)
1109  	return t
1110  }
1111
1112  // Location returns the time zone information associated with t.
1113  func (t Time) Location() *Location {
1114  	l := t.loc
1115  	if l == nil {
1116  		l = UTC
1117  	}
1118  	return l
1119  }
1120
1121  // Zone computes the time zone in effect at time t, returning the abbreviated
1122  // name of the zone (such as "CET") and its offset in seconds east of UTC.
1123  func (t Time) Zone() (name string, offset int) {
1124  	name, offset, _, _, _ = t.loc.lookup(t.unixSec())
1125  	return
1126  }
1127
1128  // Unix returns t as a Unix time, the number of seconds elapsed
1129  // since January 1, 1970 UTC. The result does not depend on the
1130  // location associated with t.
1131  // Unix-like operating systems often record time as a 32-bit
1132  // count of seconds, but since the method here returns a 64-bit
1133  // value it is valid for billions of years into the past or future.
1134  func (t Time) Unix() int64 {
1135  	return t.unixSec()
1136  }
1137
1138  // UnixMilli returns t as a Unix time, the number of milliseconds elapsed since
1139  // January 1, 1970 UTC. The result is undefined if the Unix time in
1140  // milliseconds cannot be represented by an int64 (a date more than 292 million
1141  // years before or after 1970). The result does not depend on the
1142  // location associated with t.
1143  func (t Time) UnixMilli() int64 {
1144  	return t.unixSec()*1e3 + int64(t.nsec())/1e6
1145  }
1146
1147  // UnixMicro returns t as a Unix time, the number of microseconds elapsed since
1148  // January 1, 1970 UTC. The result is undefined if the Unix time in
1149  // microseconds cannot be represented by an int64 (a date before year -290307 or
1150  // after year 294246). The result does not depend on the location associated
1151  // with t.
1152  func (t Time) UnixMicro() int64 {
1153  	return t.unixSec()*1e6 + int64(t.nsec())/1e3
1154  }
1155
1156  // UnixNano returns t as a Unix time, the number of nanoseconds elapsed
1157  // since January 1, 1970 UTC. The result is undefined if the Unix time
1158  // in nanoseconds cannot be represented by an int64 (a date before the year
1159  // 1678 or after 2262). Note that this means the result of calling UnixNano
1160  // on the zero Time is undefined. The result does not depend on the
1161  // location associated with t.
1162  func (t Time) UnixNano() int64 {
1163  	return (t.unixSec())*1e9 + int64(t.nsec())
1164  }
1165
1166  const timeBinaryVersion byte = 1
1167
1168  // MarshalBinary implements the encoding.BinaryMarshaler interface.
1169  func (t Time) MarshalBinary() ([]byte, error) {
1170  	var offsetMin int16 // minutes east of UTC. -1 is UTC.
1171
1172  	if t.Location() == UTC {
1173  		offsetMin = -1
1174  	} else {
1175  		_, offset := t.Zone()
1176  		if offset%60 != 0 {
1177  			return nil, errors.New("Time.MarshalBinary: zone offset has fractional minute")
1178  		}
1179  		offset /= 60
1180  		if offset < -32768 || offset == -1 || offset > 32767 {
1181  			return nil, errors.New("Time.MarshalBinary: unexpected zone offset")
1182  		}
1183  		offsetMin = int16(offset)
1184  	}
1185
1186  	sec := t.sec()
1187  	nsec := t.nsec()
1188  	enc := []byte{
1189  		timeBinaryVersion, // byte 0 : version
1190  		byte(sec >> 56),   // bytes 1-8: seconds
1191  		byte(sec >> 48),
1192  		byte(sec >> 40),
1193  		byte(sec >> 32),
1194  		byte(sec >> 24),
1195  		byte(sec >> 16),
1196  		byte(sec >> 8),
1197  		byte(sec),
1198  		byte(nsec >> 24), // bytes 9-12: nanoseconds
1199  		byte(nsec >> 16),
1200  		byte(nsec >> 8),
1201  		byte(nsec),
1202  		byte(offsetMin >> 8), // bytes 13-14: zone offset in minutes
1203  		byte(offsetMin),
1204  	}
1205
1206  	return enc, nil
1207  }
1208
1209  // UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
1210  func (t *Time) UnmarshalBinary(data []byte) error {
1211  	buf := data
1212  	if len(buf) == 0 {
1213  		return errors.New("Time.UnmarshalBinary: no data")
1214  	}
1215
1216  	if buf[0] != timeBinaryVersion {
1217  		return errors.New("Time.UnmarshalBinary: unsupported version")
1218  	}
1219
1220  	if len(buf) != /*version*/ 1+ /*sec*/ 8+ /*nsec*/ 4+ /*zone offset*/ 2 {
1221  		return errors.New("Time.UnmarshalBinary: invalid length")
1222  	}
1223
1224  	buf = buf[1:]
1225  	sec := int64(buf[7]) | int64(buf[6])<<8 | int64(buf[5])<<16 | int64(buf[4])<<24 |
1226  		int64(buf[3])<<32 | int64(buf[2])<<40 | int64(buf[1])<<48 | int64(buf[0])<<56
1227
1228  	buf = buf[8:]
1229  	nsec := int32(buf[3]) | int32(buf[2])<<8 | int32(buf[1])<<16 | int32(buf[0])<<24
1230
1231  	buf = buf[4:]
1232  	offset := int(int16(buf[1])|int16(buf[0])<<8) * 60
1233
1234  	*t = Time{}
1235  	t.wall = uint64(nsec)
1236  	t.ext = sec
1237
1238  	if offset == -1*60 {
1239  		t.setLoc(&utcLoc)
1240  	} else if _, localoff, _, _, _ := Local.lookup(t.unixSec()); offset == localoff {
1241  		t.setLoc(Local)
1242  	} else {
1243  		t.setLoc(FixedZone("", offset))
1244  	}
1245
1246  	return nil
1247  }
1248
1249  // TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
1250  // The same semantics will be provided by the generic MarshalBinary, MarshalText,
1251  // UnmarshalBinary, UnmarshalText.
1252
1253  // GobEncode implements the gob.GobEncoder interface.
1254  func (t Time) GobEncode() ([]byte, error) {
1255  	return t.MarshalBinary()
1256  }
1257
1258  // GobDecode implements the gob.GobDecoder interface.
1259  func (t *Time) GobDecode(data []byte) error {
1260  	return t.UnmarshalBinary(data)
1261  }
1262
1263  // MarshalJSON implements the json.Marshaler interface.
1264  // The time is a quoted string in RFC 3339 format, with sub-second precision added if present.
1265  func (t Time) MarshalJSON() ([]byte, error) {
1266  	if y := t.Year(); y < 0 || y >= 10000 {
1267  		// RFC 3339 is clear that years are 4 digits exactly.
1268  		// See golang.org/issue/4556#c15 for more discussion.
1269  		return nil, errors.New("Time.MarshalJSON: year outside of range [0,9999]")
1270  	}
1271
1272  	b := make([]byte, 0, len(RFC3339Nano)+2)
1273  	b = append(b, '"')
1274  	b = t.AppendFormat(b, RFC3339Nano)
1275  	b = append(b, '"')
1276  	return b, nil
1277  }
1278
1279  // UnmarshalJSON implements the json.Unmarshaler interface.
1280  // The time is expected to be a quoted string in RFC 3339 format.
1281  func (t *Time) UnmarshalJSON(data []byte) error {
1282  	// Ignore null, like in the main JSON package.
1283  	if string(data) == "null" {
1284  		return nil
1285  	}
1286  	// Fractional seconds are handled implicitly by Parse.
1287  	var err error
1288  	*t, err = Parse(`"`+RFC3339+`"`, string(data))
1289  	return err
1290  }
1291
1292  // MarshalText implements the encoding.TextMarshaler interface.
1293  // The time is formatted in RFC 3339 format, with sub-second precision added if present.
1294  func (t Time) MarshalText() ([]byte, error) {
1295  	if y := t.Year(); y < 0 || y >= 10000 {
1296  		return nil, errors.New("Time.MarshalText: year outside of range [0,9999]")
1297  	}
1298
1299  	b := make([]byte, 0, len(RFC3339Nano))
1300  	return t.AppendFormat(b, RFC3339Nano), nil
1301  }
1302
1303  // UnmarshalText implements the encoding.TextUnmarshaler interface.
1304  // The time is expected to be in RFC 3339 format.
1305  func (t *Time) UnmarshalText(data []byte) error {
1306  	// Fractional seconds are handled implicitly by Parse.
1307  	var err error
1308  	*t, err = Parse(RFC3339, string(data))
1309  	return err
1310  }
1311
1312  // Unix returns the local Time corresponding to the given Unix time,
1313  // sec seconds and nsec nanoseconds since January 1, 1970 UTC.
1314  // It is valid to pass nsec outside the range [0, 999999999].
1315  // Not all sec values have a corresponding time value. One such
1316  // value is 1<<63-1 (the largest int64 value).
1317  func Unix(sec int64, nsec int64) Time {
1318  	if nsec < 0 || nsec >= 1e9 {
1319  		n := nsec / 1e9
1320  		sec += n
1321  		nsec -= n * 1e9
1322  		if nsec < 0 {
1323  			nsec += 1e9
1324  			sec--
1325  		}
1326  	}
1327  	return unixTime(sec, int32(nsec))
1328  }
1329
1330  // UnixMilli returns the local Time corresponding to the given Unix time,
1331  // msec milliseconds since January 1, 1970 UTC.
1332  func UnixMilli(msec int64) Time {
1333  	return Unix(msec/1e3, (msec%1e3)*1e6)
1334  }
1335
1336  // UnixMicro returns the local Time corresponding to the given Unix time,
1337  // usec microseconds since January 1, 1970 UTC.
1338  func UnixMicro(usec int64) Time {
1339  	return Unix(usec/1e6, (usec%1e6)*1e3)
1340  }
1341
1342  // IsDST reports whether the time in the configured location is in Daylight Savings Time.
1343  func (t Time) IsDST() bool {
1344  	_, _, _, _, isDST := t.loc.lookup(t.Unix())
1345  	return isDST
1346  }
1347
1348  func isLeap(year int) bool {
1349  	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
1350  }
1351
1352  // norm returns nhi, nlo such that
1353  //	hi * base + lo == nhi * base + nlo
1354  //	0 <= nlo < base
1355  func norm(hi, lo, base int) (nhi, nlo int) {
1356  	if lo < 0 {
1357  		n := (-lo-1)/base + 1
1358  		hi -= n
1359  		lo += n * base
1360  	}
1361  	if lo >= base {
1362  		n := lo / base
1363  		hi += n
1364  		lo -= n * base
1365  	}
1366  	return hi, lo
1367  }
1368
1369  // Date returns the Time corresponding to
1370  //	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
1371  // in the appropriate zone for that time in the given location.
1372  //
1373  // The month, day, hour, min, sec, and nsec values may be outside
1374  // their usual ranges and will be normalized during the conversion.
1375  // For example, October 32 converts to November 1.
1376  //
1377  // A daylight savings time transition skips or repeats times.
1378  // For example, in the United States, March 13, 2011 2:15am never occurred,
1379  // while November 6, 2011 1:15am occurred twice. In such cases, the
1380  // choice of time zone, and therefore the time, is not well-defined.
1381  // Date returns a time that is correct in one of the two zones involved
1382  // in the transition, but it does not guarantee which.
1383  //
1384  // Date panics if loc is nil.
1385  func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
1386  	if loc == nil {
1387  		panic("time: missing Location in call to Date")
1388  	}
1389
1390  	// Normalize month, overflowing into year.
1391  	m := int(month) - 1
1392  	year, m = norm(year, m, 12)
1393  	month = Month(m) + 1
1394
1395  	// Normalize nsec, sec, min, hour, overflowing into day.
1396  	sec, nsec = norm(sec, nsec, 1e9)
1397  	min, sec = norm(min, sec, 60)
1398  	hour, min = norm(hour, min, 60)
1399  	day, hour = norm(day, hour, 24)
1400
1401  	// Compute days since the absolute epoch.
1402  	d := daysSinceEpoch(year)
1403
1404  	// Add in days before this month.
1405  	d += uint64(daysBefore[month-1])
1406  	if isLeap(year) && month >= March {
1407  		d++ // February 29
1408  	}
1409
1410  	// Add in days before today.
1411  	d += uint64(day - 1)
1412
1413  	// Add in time elapsed today.
1414  	abs := d * secondsPerDay
1415  	abs += uint64(hour*secondsPerHour + min*secondsPerMinute + sec)
1416
1417  	unix := int64(abs) + (absoluteToInternal + internalToUnix)
1418
1419  	// Look for zone offset for t, so we can adjust to UTC.
1420  	// The lookup function expects UTC, so we pass t in the
1421  	// hope that it will not be too close to a zone transition,
1422  	// and then adjust if it is.
1423  	_, offset, start, end, _ := loc.lookup(unix)
1424  	if offset != 0 {
1425  		switch utc := unix - int64(offset); {
1426  		case utc < start:
1427  			_, offset, _, _, _ = loc.lookup(start - 1)
1428  		case utc >= end:
1429  			_, offset, _, _, _ = loc.lookup(end)
1430  		}
1431  		unix -= int64(offset)
1432  	}
1433
1434  	t := unixTime(unix, int32(nsec))
1435  	t.setLoc(loc)
1436  	return t
1437  }
1438
1439  // Truncate returns the result of rounding t down to a multiple of d (since the zero time).
1440  // If d <= 0, Truncate returns t stripped of any monotonic clock reading but otherwise unchanged.
1441  //
1442  // Truncate operates on the time as an absolute duration since the
1443  // zero time; it does not operate on the presentation form of the
1444  // time. Thus, Truncate(Hour) may return a time with a non-zero
1445  // minute, depending on the time's Location.
1446  func (t Time) Truncate(d Duration) Time {
1447  	t.stripMono()
1448  	if d <= 0 {
1449  		return t
1450  	}
1451  	_, r := div(t, d)
1453  }
1454
1455  // Round returns the result of rounding t to the nearest multiple of d (since the zero time).
1456  // The rounding behavior for halfway values is to round up.
1457  // If d <= 0, Round returns t stripped of any monotonic clock reading but otherwise unchanged.
1458  //
1459  // Round operates on the time as an absolute duration since the
1460  // zero time; it does not operate on the presentation form of the
1461  // time. Thus, Round(Hour) may return a time with a non-zero
1462  // minute, depending on the time's Location.
1463  func (t Time) Round(d Duration) Time {
1464  	t.stripMono()
1465  	if d <= 0 {
1466  		return t
1467  	}
1468  	_, r := div(t, d)
1469  	if lessThanHalf(r, d) {
1471  	}
1473  }
1474
1475  // div divides t by d and returns the quotient parity and remainder.
1476  // We don't use the quotient parity anymore (round half up instead of round to even)
1477  // but it's still here in case we change our minds.
1478  func div(t Time, d Duration) (qmod2 int, r Duration) {
1479  	neg := false
1480  	nsec := t.nsec()
1481  	sec := t.sec()
1482  	if sec < 0 {
1483  		// Operate on absolute value.
1484  		neg = true
1485  		sec = -sec
1486  		nsec = -nsec
1487  		if nsec < 0 {
1488  			nsec += 1e9
1489  			sec-- // sec >= 1 before the -- so safe
1490  		}
1491  	}
1492
1493  	switch {
1494  	// Special case: 2d divides 1 second.
1495  	case d < Second && Second%(d+d) == 0:
1496  		qmod2 = int(nsec/int32(d)) & 1
1497  		r = Duration(nsec % int32(d))
1498
1499  	// Special case: d is a multiple of 1 second.
1500  	case d%Second == 0:
1501  		d1 := int64(d / Second)
1502  		qmod2 = int(sec/d1) & 1
1503  		r = Duration(sec%d1)*Second + Duration(nsec)
1504
1505  	// General case.
1506  	// This could be faster if more cleverness were applied,
1507  	// but it's really only here to avoid special case restrictions in the API.
1508  	// No one will care about these cases.
1509  	default:
1510  		// Compute nanoseconds as 128-bit number.
1511  		sec := uint64(sec)
1512  		tmp := (sec >> 32) * 1e9
1513  		u1 := tmp >> 32
1514  		u0 := tmp << 32
1515  		tmp = (sec & 0xFFFFFFFF) * 1e9
1516  		u0x, u0 := u0, u0+tmp
1517  		if u0 < u0x {
1518  			u1++
1519  		}
1520  		u0x, u0 = u0, u0+uint64(nsec)
1521  		if u0 < u0x {
1522  			u1++
1523  		}
1524
1525  		// Compute remainder by subtracting r<<k for decreasing k.
1526  		// Quotient parity is whether we subtract on last round.
1527  		d1 := uint64(d)
1528  		for d1>>63 != 1 {
1529  			d1 <<= 1
1530  		}
1531  		d0 := uint64(0)
1532  		for {
1533  			qmod2 = 0
1534  			if u1 > d1 || u1 == d1 && u0 >= d0 {
1535  				// subtract
1536  				qmod2 = 1
1537  				u0x, u0 = u0, u0-d0
1538  				if u0 > u0x {
1539  					u1--
1540  				}
1541  				u1 -= d1
1542  			}
1543  			if d1 == 0 && d0 == uint64(d) {
1544  				break
1545  			}
1546  			d0 >>= 1
1547  			d0 |= (d1 & 1) << 63
1548  			d1 >>= 1
1549  		}
1550  		r = Duration(u0)
1551  	}
1552
1553  	if neg && r != 0 {
1554  		// If input was negative and not an exact multiple of d, we computed q, r such that
1555  		//	q*d + r = -t
1556  		// But the right answers are given by -(q-1), d-r:
1557  		//	q*d + r = -t
1558  		//	-q*d - r = t
1559  		//	-(q-1)*d + (d - r) = t
1560  		qmod2 ^= 1
1561  		r = d - r
1562  	}
1563  	return
1564  }
1565
```

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