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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 "errors"
    79  
    80  // A Time represents an instant in time with nanosecond precision.
    81  //
    82  // Programs using times should typically store and pass them as values,
    83  // not pointers. That is, time variables and struct fields should be of
    84  // type time.Time, not *time.Time.
    85  //
    86  // A Time value can be used by multiple goroutines simultaneously except
    87  // that the methods GobDecode, UnmarshalBinary, UnmarshalJSON and
    88  // UnmarshalText are not concurrency-safe.
    89  //
    90  // Time instants can be compared using the Before, After, and Equal methods.
    91  // The Sub method subtracts two instants, producing a Duration.
    92  // The Add method adds a Time and a Duration, producing a Time.
    93  //
    94  // The zero value of type Time is January 1, year 1, 00:00:00.000000000 UTC.
    95  // As this time is unlikely to come up in practice, the IsZero method gives
    96  // a simple way of detecting a time that has not been initialized explicitly.
    97  //
    98  // Each Time has associated with it a Location, consulted when computing the
    99  // presentation form of the time, such as in the Format, Hour, and Year methods.
   100  // The methods Local, UTC, and In return a Time with a specific location.
   101  // Changing the location in this way changes only the presentation; it does not
   102  // change the instant in time being denoted and therefore does not affect the
   103  // computations described in earlier paragraphs.
   104  //
   105  // In addition to the required “wall clock” reading, a Time may contain an optional
   106  // reading of the current process's monotonic clock, to provide additional precision
   107  // for comparison or subtraction.
   108  // See the “Monotonic Clocks” section in the package documentation for details.
   109  //
   110  // Note that the Go == operator compares not just the time instant but also the
   111  // Location and the monotonic clock reading. Therefore, Time values should not
   112  // be used as map or database keys without first guaranteeing that the
   113  // identical Location has been set for all values, which can be achieved
   114  // through use of the UTC or Local method, and that the monotonic clock reading
   115  // has been stripped by setting t = t.Round(0). In general, prefer t.Equal(u)
   116  // to t == u, since t.Equal uses the most accurate comparison available and
   117  // correctly handles the case when only one of its arguments has a monotonic
   118  // clock reading.
   119  //
   120  type Time struct {
   121  	// wall and ext encode the wall time seconds, wall time nanoseconds,
   122  	// and optional monotonic clock reading in nanoseconds.
   123  	//
   124  	// From high to low bit position, wall encodes a 1-bit flag (hasMonotonic),
   125  	// a 33-bit seconds field, and a 30-bit wall time nanoseconds field.
   126  	// The nanoseconds field is in the range [0, 999999999].
   127  	// If the hasMonotonic bit is 0, then the 33-bit field must be zero
   128  	// and the full signed 64-bit wall seconds since Jan 1 year 1 is stored in ext.
   129  	// If the hasMonotonic bit is 1, then the 33-bit field holds a 33-bit
   130  	// unsigned wall seconds since Jan 1 year 1885, and ext holds a
   131  	// signed 64-bit monotonic clock reading, nanoseconds since process start.
   132  	wall uint64
   133  	ext  int64
   134  
   135  	// loc specifies the Location that should be used to
   136  	// determine the minute, hour, month, day, and year
   137  	// that correspond to this Time.
   138  	// The nil location means UTC.
   139  	// All UTC times are represented with loc==nil, never loc==&utcLoc.
   140  	loc *Location
   141  }
   142  
   143  const (
   144  	hasMonotonic = 1 << 63
   145  	maxWall      = wallToInternal + (1<<33 - 1) // year 2157
   146  	minWall      = wallToInternal               // year 1885
   147  	nsecMask     = 1<<30 - 1
   148  	nsecShift    = 30
   149  )
   150  
   151  // These helpers for manipulating the wall and monotonic clock readings
   152  // take pointer receivers, even when they don't modify the time,
   153  // to make them cheaper to call.
   154  
   155  // nsec returns the time's nanoseconds.
   156  func (t *Time) nsec() int32 {
   157  	return int32(t.wall & nsecMask)
   158  }
   159  
   160  // sec returns the time's seconds since Jan 1 year 1.
   161  func (t *Time) sec() int64 {
   162  	if t.wall&hasMonotonic != 0 {
   163  		return wallToInternal + int64(t.wall<<1>>(nsecShift+1))
   164  	}
   165  	return t.ext
   166  }
   167  
   168  // unixSec returns the time's seconds since Jan 1 1970 (Unix time).
   169  func (t *Time) unixSec() int64 { return t.sec() + internalToUnix }
   170  
   171  // addSec adds d seconds to the time.
   172  func (t *Time) addSec(d int64) {
   173  	if t.wall&hasMonotonic != 0 {
   174  		sec := int64(t.wall << 1 >> (nsecShift + 1))
   175  		dsec := sec + d
   176  		if 0 <= dsec && dsec <= 1<<33-1 {
   177  			t.wall = t.wall&nsecMask | uint64(dsec)<<nsecShift | hasMonotonic
   178  			return
   179  		}
   180  		// Wall second now out of range for packed field.
   181  		// Move to ext.
   182  		t.stripMono()
   183  	}
   184  
   185  	// TODO: Check for overflow.
   186  	t.ext += d
   187  }
   188  
   189  // setLoc sets the location associated with the time.
   190  func (t *Time) setLoc(loc *Location) {
   191  	if loc == &utcLoc {
   192  		loc = nil
   193  	}
   194  	t.stripMono()
   195  	t.loc = loc
   196  }
   197  
   198  // stripMono strips the monotonic clock reading in t.
   199  func (t *Time) stripMono() {
   200  	if t.wall&hasMonotonic != 0 {
   201  		t.ext = t.sec()
   202  		t.wall &= nsecMask
   203  	}
   204  }
   205  
   206  // setMono sets the monotonic clock reading in t.
   207  // If t cannot hold a monotonic clock reading,
   208  // because its wall time is too large,
   209  // setMono is a no-op.
   210  func (t *Time) setMono(m int64) {
   211  	if t.wall&hasMonotonic == 0 {
   212  		sec := t.ext
   213  		if sec < minWall || maxWall < sec {
   214  			return
   215  		}
   216  		t.wall |= hasMonotonic | uint64(sec-minWall)<<nsecShift
   217  	}
   218  	t.ext = m
   219  }
   220  
   221  // mono returns t's monotonic clock reading.
   222  // It returns 0 for a missing reading.
   223  // This function is used only for testing,
   224  // so it's OK that technically 0 is a valid
   225  // monotonic clock reading as well.
   226  func (t *Time) mono() int64 {
   227  	if t.wall&hasMonotonic == 0 {
   228  		return 0
   229  	}
   230  	return t.ext
   231  }
   232  
   233  // After reports whether the time instant t is after u.
   234  func (t Time) After(u Time) bool {
   235  	if t.wall&u.wall&hasMonotonic != 0 {
   236  		return t.ext > u.ext
   237  	}
   238  	ts := t.sec()
   239  	us := u.sec()
   240  	return ts > us || ts == us && t.nsec() > u.nsec()
   241  }
   242  
   243  // Before reports whether the time instant t is before u.
   244  func (t Time) Before(u Time) bool {
   245  	if t.wall&u.wall&hasMonotonic != 0 {
   246  		return t.ext < u.ext
   247  	}
   248  	return t.sec() < u.sec() || t.sec() == u.sec() && t.nsec() < u.nsec()
   249  }
   250  
   251  // Equal reports whether t and u represent the same time instant.
   252  // Two times can be equal even if they are in different locations.
   253  // For example, 6:00 +0200 CEST and 4:00 UTC are Equal.
   254  // See the documentation on the Time type for the pitfalls of using == with
   255  // Time values; most code should use Equal instead.
   256  func (t Time) Equal(u Time) bool {
   257  	if t.wall&u.wall&hasMonotonic != 0 {
   258  		return t.ext == u.ext
   259  	}
   260  	return t.sec() == u.sec() && t.nsec() == u.nsec()
   261  }
   262  
   263  // A Month specifies a month of the year (January = 1, ...).
   264  type Month int
   265  
   266  const (
   267  	January Month = 1 + iota
   268  	February
   269  	March
   270  	April
   271  	May
   272  	June
   273  	July
   274  	August
   275  	September
   276  	October
   277  	November
   278  	December
   279  )
   280  
   281  var months = [...]string{
   282  	"January",
   283  	"February",
   284  	"March",
   285  	"April",
   286  	"May",
   287  	"June",
   288  	"July",
   289  	"August",
   290  	"September",
   291  	"October",
   292  	"November",
   293  	"December",
   294  }
   295  
   296  // String returns the English name of the month ("January", "February", ...).
   297  func (m Month) String() string {
   298  	if January <= m && m <= December {
   299  		return months[m-1]
   300  	}
   301  	buf := make([]byte, 20)
   302  	n := fmtInt(buf, uint64(m))
   303  	return "%!Month(" + string(buf[n:]) + ")"
   304  }
   305  
   306  // A Weekday specifies a day of the week (Sunday = 0, ...).
   307  type Weekday int
   308  
   309  const (
   310  	Sunday Weekday = iota
   311  	Monday
   312  	Tuesday
   313  	Wednesday
   314  	Thursday
   315  	Friday
   316  	Saturday
   317  )
   318  
   319  var days = [...]string{
   320  	"Sunday",
   321  	"Monday",
   322  	"Tuesday",
   323  	"Wednesday",
   324  	"Thursday",
   325  	"Friday",
   326  	"Saturday",
   327  }
   328  
   329  // String returns the English name of the day ("Sunday", "Monday", ...).
   330  func (d Weekday) String() string {
   331  	if Sunday <= d && d <= Saturday {
   332  		return days[d]
   333  	}
   334  	buf := make([]byte, 20)
   335  	n := fmtInt(buf, uint64(d))
   336  	return "%!Weekday(" + string(buf[n:]) + ")"
   337  }
   338  
   339  // Computations on time.
   340  //
   341  // The zero value for a Time is defined to be
   342  //	January 1, year 1, 00:00:00.000000000 UTC
   343  // which (1) looks like a zero, or as close as you can get in a date
   344  // (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
   345  // be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
   346  // non-negative year even in time zones west of UTC, unlike 1-1-0
   347  // 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
   348  //
   349  // The zero Time value does not force a specific epoch for the time
   350  // representation. For example, to use the Unix epoch internally, we
   351  // could define that to distinguish a zero value from Jan 1 1970, that
   352  // time would be represented by sec=-1, nsec=1e9. However, it does
   353  // suggest a representation, namely using 1-1-1 00:00:00 UTC as the
   354  // epoch, and that's what we do.
   355  //
   356  // The Add and Sub computations are oblivious to the choice of epoch.
   357  //
   358  // The presentation computations - year, month, minute, and so on - all
   359  // rely heavily on division and modulus by positive constants. For
   360  // calendrical calculations we want these divisions to round down, even
   361  // for negative values, so that the remainder is always positive, but
   362  // Go's division (like most hardware division instructions) rounds to
   363  // zero. We can still do those computations and then adjust the result
   364  // for a negative numerator, but it's annoying to write the adjustment
   365  // over and over. Instead, we can change to a different epoch so long
   366  // ago that all the times we care about will be positive, and then round
   367  // to zero and round down coincide. These presentation routines already
   368  // have to add the zone offset, so adding the translation to the
   369  // alternate epoch is cheap. For example, having a non-negative time t
   370  // means that we can write
   371  //
   372  //	sec = t % 60
   373  //
   374  // instead of
   375  //
   376  //	sec = t % 60
   377  //	if sec < 0 {
   378  //		sec += 60
   379  //	}
   380  //
   381  // everywhere.
   382  //
   383  // The calendar runs on an exact 400 year cycle: a 400-year calendar
   384  // printed for 1970-2369 will apply as well to 2370-2769. Even the days
   385  // of the week match up. It simplifies the computations to choose the
   386  // cycle boundaries so that the exceptional years are always delayed as
   387  // long as possible. That means choosing a year equal to 1 mod 400, so
   388  // that the first leap year is the 4th year, the first missed leap year
   389  // is the 100th year, and the missed missed leap year is the 400th year.
   390  // So we'd prefer instead to print a calendar for 2001-2400 and reuse it
   391  // for 2401-2800.
   392  //
   393  // Finally, it's convenient if the delta between the Unix epoch and
   394  // long-ago epoch is representable by an int64 constant.
   395  //
   396  // These three considerations—choose an epoch as early as possible, that
   397  // uses a year equal to 1 mod 400, and that is no more than 2⁶³ seconds
   398  // earlier than 1970—bring us to the year -292277022399. We refer to
   399  // this year as the absolute zero year, and to times measured as a uint64
   400  // seconds since this year as absolute times.
   401  //
   402  // Times measured as an int64 seconds since the year 1—the representation
   403  // used for Time's sec field—are called internal times.
   404  //
   405  // Times measured as an int64 seconds since the year 1970 are called Unix
   406  // times.
   407  //
   408  // It is tempting to just use the year 1 as the absolute epoch, defining
   409  // that the routines are only valid for years >= 1. However, the
   410  // routines would then be invalid when displaying the epoch in time zones
   411  // west of UTC, since it is year 0. It doesn't seem tenable to say that
   412  // printing the zero time correctly isn't supported in half the time
   413  // zones. By comparison, it's reasonable to mishandle some times in
   414  // the year -292277022399.
   415  //
   416  // All this is opaque to clients of the API and can be changed if a
   417  // better implementation presents itself.
   418  
   419  const (
   420  	// The unsigned zero year for internal calculations.
   421  	// Must be 1 mod 400, and times before it will not compute correctly,
   422  	// but otherwise can be changed at will.
   423  	absoluteZeroYear = -292277022399
   424  
   425  	// The year of the zero Time.
   426  	// Assumed by the unixToInternal computation below.
   427  	internalYear = 1
   428  
   429  	// Offsets to convert between internal and absolute or Unix times.
   430  	absoluteToInternal int64 = (absoluteZeroYear - internalYear) * 365.2425 * secondsPerDay
   431  	internalToAbsolute       = -absoluteToInternal
   432  
   433  	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
   434  	internalToUnix int64 = -unixToInternal
   435  
   436  	wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
   437  	internalToWall int64 = -wallToInternal
   438  )
   439  
   440  // IsZero reports whether t represents the zero time instant,
   441  // January 1, year 1, 00:00:00 UTC.
   442  func (t Time) IsZero() bool {
   443  	return t.sec() == 0 && t.nsec() == 0
   444  }
   445  
   446  // abs returns the time t as an absolute time, adjusted by the zone offset.
   447  // It is called when computing a presentation property like Month or Hour.
   448  func (t Time) abs() uint64 {
   449  	l := t.loc
   450  	// Avoid function calls when possible.
   451  	if l == nil || l == &localLoc {
   452  		l = l.get()
   453  	}
   454  	sec := t.unixSec()
   455  	if l != &utcLoc {
   456  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
   457  			sec += int64(l.cacheZone.offset)
   458  		} else {
   459  			_, offset, _, _ := l.lookup(sec)
   460  			sec += int64(offset)
   461  		}
   462  	}
   463  	return uint64(sec + (unixToInternal + internalToAbsolute))
   464  }
   465  
   466  // locabs is a combination of the Zone and abs methods,
   467  // extracting both return values from a single zone lookup.
   468  func (t Time) locabs() (name string, offset int, abs uint64) {
   469  	l := t.loc
   470  	if l == nil || l == &localLoc {
   471  		l = l.get()
   472  	}
   473  	// Avoid function call if we hit the local time cache.
   474  	sec := t.unixSec()
   475  	if l != &utcLoc {
   476  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
   477  			name = l.cacheZone.name
   478  			offset = l.cacheZone.offset
   479  		} else {
   480  			name, offset, _, _ = l.lookup(sec)
   481  		}
   482  		sec += int64(offset)
   483  	} else {
   484  		name = "UTC"
   485  	}
   486  	abs = uint64(sec + (unixToInternal + internalToAbsolute))
   487  	return
   488  }
   489  
   490  // Date returns the year, month, and day in which t occurs.
   491  func (t Time) Date() (year int, month Month, day int) {
   492  	year, month, day, _ = t.date(true)
   493  	return
   494  }
   495  
   496  // Year returns the year in which t occurs.
   497  func (t Time) Year() int {
   498  	year, _, _, _ := t.date(false)
   499  	return year
   500  }
   501  
   502  // Month returns the month of the year specified by t.
   503  func (t Time) Month() Month {
   504  	_, month, _, _ := t.date(true)
   505  	return month
   506  }
   507  
   508  // Day returns the day of the month specified by t.
   509  func (t Time) Day() int {
   510  	_, _, day, _ := t.date(true)
   511  	return day
   512  }
   513  
   514  // Weekday returns the day of the week specified by t.
   515  func (t Time) Weekday() Weekday {
   516  	return absWeekday(t.abs())
   517  }
   518  
   519  // absWeekday is like Weekday but operates on an absolute time.
   520  func absWeekday(abs uint64) Weekday {
   521  	// January 1 of the absolute year, like January 1 of 2001, was a Monday.
   522  	sec := (abs + uint64(Monday)*secondsPerDay) % secondsPerWeek
   523  	return Weekday(int(sec) / secondsPerDay)
   524  }
   525  
   526  // ISOWeek returns the ISO 8601 year and week number in which t occurs.
   527  // Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
   528  // week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
   529  // of year n+1.
   530  func (t Time) ISOWeek() (year, week int) {
   531  	year, month, day, yday := t.date(true)
   532  	wday := int(t.Weekday()+6) % 7 // weekday but Monday = 0.
   533  	const (
   534  		Mon int = iota
   535  		Tue
   536  		Wed
   537  		Thu
   538  		Fri
   539  		Sat
   540  		Sun
   541  	)
   542  
   543  	// Calculate week as number of Mondays in year up to
   544  	// and including today, plus 1 because the first week is week 0.
   545  	// Putting the + 1 inside the numerator as a + 7 keeps the
   546  	// numerator from being negative, which would cause it to
   547  	// round incorrectly.
   548  	week = (yday - wday + 7) / 7
   549  
   550  	// The week number is now correct under the assumption
   551  	// that the first Monday of the year is in week 1.
   552  	// If Jan 1 is a Tuesday, Wednesday, or Thursday, the first Monday
   553  	// is actually in week 2.
   554  	jan1wday := (wday - yday + 7*53) % 7
   555  	if Tue <= jan1wday && jan1wday <= Thu {
   556  		week++
   557  	}
   558  
   559  	// If the week number is still 0, we're in early January but in
   560  	// the last week of last year.
   561  	if week == 0 {
   562  		year--
   563  		week = 52
   564  		// A year has 53 weeks when Jan 1 or Dec 31 is a Thursday,
   565  		// meaning Jan 1 of the next year is a Friday
   566  		// or it was a leap year and Jan 1 of the next year is a Saturday.
   567  		if jan1wday == Fri || (jan1wday == Sat && isLeap(year)) {
   568  			week++
   569  		}
   570  	}
   571  
   572  	// December 29 to 31 are in week 1 of next year if
   573  	// they are after the last Thursday of the year and
   574  	// December 31 is a Monday, Tuesday, or Wednesday.
   575  	if month == December && day >= 29 && wday < Thu {
   576  		if dec31wday := (wday + 31 - day) % 7; Mon <= dec31wday && dec31wday <= Wed {
   577  			year++
   578  			week = 1
   579  		}
   580  	}
   581  
   582  	return
   583  }
   584  
   585  // Clock returns the hour, minute, and second within the day specified by t.
   586  func (t Time) Clock() (hour, min, sec int) {
   587  	return absClock(t.abs())
   588  }
   589  
   590  // absClock is like clock but operates on an absolute time.
   591  func absClock(abs uint64) (hour, min, sec int) {
   592  	sec = int(abs % secondsPerDay)
   593  	hour = sec / secondsPerHour
   594  	sec -= hour * secondsPerHour
   595  	min = sec / secondsPerMinute
   596  	sec -= min * secondsPerMinute
   597  	return
   598  }
   599  
   600  // Hour returns the hour within the day specified by t, in the range [0, 23].
   601  func (t Time) Hour() int {
   602  	return int(t.abs()%secondsPerDay) / secondsPerHour
   603  }
   604  
   605  // Minute returns the minute offset within the hour specified by t, in the range [0, 59].
   606  func (t Time) Minute() int {
   607  	return int(t.abs()%secondsPerHour) / secondsPerMinute
   608  }
   609  
   610  // Second returns the second offset within the minute specified by t, in the range [0, 59].
   611  func (t Time) Second() int {
   612  	return int(t.abs() % secondsPerMinute)
   613  }
   614  
   615  // Nanosecond returns the nanosecond offset within the second specified by t,
   616  // in the range [0, 999999999].
   617  func (t Time) Nanosecond() int {
   618  	return int(t.nsec())
   619  }
   620  
   621  // YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
   622  // and [1,366] in leap years.
   623  func (t Time) YearDay() int {
   624  	_, _, _, yday := t.date(false)
   625  	return yday + 1
   626  }
   627  
   628  // A Duration represents the elapsed time between two instants
   629  // as an int64 nanosecond count. The representation limits the
   630  // largest representable duration to approximately 290 years.
   631  type Duration int64
   632  
   633  const (
   634  	minDuration Duration = -1 << 63
   635  	maxDuration Duration = 1<<63 - 1
   636  )
   637  
   638  // Common durations. There is no definition for units of Day or larger
   639  // to avoid confusion across daylight savings time zone transitions.
   640  //
   641  // To count the number of units in a Duration, divide:
   642  //	second := time.Second
   643  //	fmt.Print(int64(second/time.Millisecond)) // prints 1000
   644  //
   645  // To convert an integer number of units to a Duration, multiply:
   646  //	seconds := 10
   647  //	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
   648  //
   649  const (
   650  	Nanosecond  Duration = 1
   651  	Microsecond          = 1000 * Nanosecond
   652  	Millisecond          = 1000 * Microsecond
   653  	Second               = 1000 * Millisecond
   654  	Minute               = 60 * Second
   655  	Hour                 = 60 * Minute
   656  )
   657  
   658  // String returns a string representing the duration in the form "72h3m0.5s".
   659  // Leading zero units are omitted. As a special case, durations less than one
   660  // second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
   661  // that the leading digit is non-zero. The zero duration formats as 0s.
   662  func (d Duration) String() string {
   663  	// Largest time is 2540400h10m10.000000000s
   664  	var buf [32]byte
   665  	w := len(buf)
   666  
   667  	u := uint64(d)
   668  	neg := d < 0
   669  	if neg {
   670  		u = -u
   671  	}
   672  
   673  	if u < uint64(Second) {
   674  		// Special case: if duration is smaller than a second,
   675  		// use smaller units, like 1.2ms
   676  		var prec int
   677  		w--
   678  		buf[w] = 's'
   679  		w--
   680  		switch {
   681  		case u == 0:
   682  			return "0s"
   683  		case u < uint64(Microsecond):
   684  			// print nanoseconds
   685  			prec = 0
   686  			buf[w] = 'n'
   687  		case u < uint64(Millisecond):
   688  			// print microseconds
   689  			prec = 3
   690  			// U+00B5 'µ' micro sign == 0xC2 0xB5
   691  			w-- // Need room for two bytes.
   692  			copy(buf[w:], "µ")
   693  		default:
   694  			// print milliseconds
   695  			prec = 6
   696  			buf[w] = 'm'
   697  		}
   698  		w, u = fmtFrac(buf[:w], u, prec)
   699  		w = fmtInt(buf[:w], u)
   700  	} else {
   701  		w--
   702  		buf[w] = 's'
   703  
   704  		w, u = fmtFrac(buf[:w], u, 9)
   705  
   706  		// u is now integer seconds
   707  		w = fmtInt(buf[:w], u%60)
   708  		u /= 60
   709  
   710  		// u is now integer minutes
   711  		if u > 0 {
   712  			w--
   713  			buf[w] = 'm'
   714  			w = fmtInt(buf[:w], u%60)
   715  			u /= 60
   716  
   717  			// u is now integer hours
   718  			// Stop at hours because days can be different lengths.
   719  			if u > 0 {
   720  				w--
   721  				buf[w] = 'h'
   722  				w = fmtInt(buf[:w], u)
   723  			}
   724  		}
   725  	}
   726  
   727  	if neg {
   728  		w--
   729  		buf[w] = '-'
   730  	}
   731  
   732  	return string(buf[w:])
   733  }
   734  
   735  // fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
   736  // tail of buf, omitting trailing zeros. It omits the decimal
   737  // point too when the fraction is 0. It returns the index where the
   738  // output bytes begin and the value v/10**prec.
   739  func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
   740  	// Omit trailing zeros up to and including decimal point.
   741  	w := len(buf)
   742  	print := false
   743  	for i := 0; i < prec; i++ {
   744  		digit := v % 10
   745  		print = print || digit != 0
   746  		if print {
   747  			w--
   748  			buf[w] = byte(digit) + '0'
   749  		}
   750  		v /= 10
   751  	}
   752  	if print {
   753  		w--
   754  		buf[w] = '.'
   755  	}
   756  	return w, v
   757  }
   758  
   759  // fmtInt formats v into the tail of buf.
   760  // It returns the index where the output begins.
   761  func fmtInt(buf []byte, v uint64) int {
   762  	w := len(buf)
   763  	if v == 0 {
   764  		w--
   765  		buf[w] = '0'
   766  	} else {
   767  		for v > 0 {
   768  			w--
   769  			buf[w] = byte(v%10) + '0'
   770  			v /= 10
   771  		}
   772  	}
   773  	return w
   774  }
   775  
   776  // Nanoseconds returns the duration as an integer nanosecond count.
   777  func (d Duration) Nanoseconds() int64 { return int64(d) }
   778  
   779  // These methods return float64 because the dominant
   780  // use case is for printing a floating point number like 1.5s, and
   781  // a truncation to integer would make them not useful in those cases.
   782  // Splitting the integer and fraction ourselves guarantees that
   783  // converting the returned float64 to an integer rounds the same
   784  // way that a pure integer conversion would have, even in cases
   785  // where, say, float64(d.Nanoseconds())/1e9 would have rounded
   786  // differently.
   787  
   788  // Seconds returns the duration as a floating point number of seconds.
   789  func (d Duration) Seconds() float64 {
   790  	sec := d / Second
   791  	nsec := d % Second
   792  	return float64(sec) + float64(nsec)/1e9
   793  }
   794  
   795  // Minutes returns the duration as a floating point number of minutes.
   796  func (d Duration) Minutes() float64 {
   797  	min := d / Minute
   798  	nsec := d % Minute
   799  	return float64(min) + float64(nsec)/(60*1e9)
   800  }
   801  
   802  // Hours returns the duration as a floating point number of hours.
   803  func (d Duration) Hours() float64 {
   804  	hour := d / Hour
   805  	nsec := d % Hour
   806  	return float64(hour) + float64(nsec)/(60*60*1e9)
   807  }
   808  
   809  // Truncate returns the result of rounding d toward zero to a multiple of m.
   810  // If m <= 0, Truncate returns d unchanged.
   811  func (d Duration) Truncate(m Duration) Duration {
   812  	if m <= 0 {
   813  		return d
   814  	}
   815  	return d - d%m
   816  }
   817  
   818  // lessThanHalf reports whether x+x < y but avoids overflow,
   819  // assuming x and y are both positive (Duration is signed).
   820  func lessThanHalf(x, y Duration) bool {
   821  	return uint64(x)+uint64(x) < uint64(y)
   822  }
   823  
   824  // Round returns the result of rounding d to the nearest multiple of m.
   825  // The rounding behavior for halfway values is to round away from zero.
   826  // If the result exceeds the maximum (or minimum)
   827  // value that can be stored in a Duration,
   828  // Round returns the maximum (or minimum) duration.
   829  // If m <= 0, Round returns d unchanged.
   830  func (d Duration) Round(m Duration) Duration {
   831  	if m <= 0 {
   832  		return d
   833  	}
   834  	r := d % m
   835  	if d < 0 {
   836  		r = -r
   837  		if lessThanHalf(r, m) {
   838  			return d + r
   839  		}
   840  		if d1 := d - m + r; d1 < d {
   841  			return d1
   842  		}
   843  		return minDuration // overflow
   844  	}
   845  	if lessThanHalf(r, m) {
   846  		return d - r
   847  	}
   848  	if d1 := d + m - r; d1 > d {
   849  		return d1
   850  	}
   851  	return maxDuration // overflow
   852  }
   853  
   854  // Add returns the time t+d.
   855  func (t Time) Add(d Duration) Time {
   856  	dsec := int64(d / 1e9)
   857  	nsec := t.nsec() + int32(d%1e9)
   858  	if nsec >= 1e9 {
   859  		dsec++
   860  		nsec -= 1e9
   861  	} else if nsec < 0 {
   862  		dsec--
   863  		nsec += 1e9
   864  	}
   865  	t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
   866  	t.addSec(dsec)
   867  	if t.wall&hasMonotonic != 0 {
   868  		te := t.ext + int64(d)
   869  		if d < 0 && te > t.ext || d > 0 && te < t.ext {
   870  			// Monotonic clock reading now out of range; degrade to wall-only.
   871  			t.stripMono()
   872  		} else {
   873  			t.ext = te
   874  		}
   875  	}
   876  	return t
   877  }
   878  
   879  // Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
   880  // value that can be stored in a Duration, the maximum (or minimum) duration
   881  // will be returned.
   882  // To compute t-d for a duration d, use t.Add(-d).
   883  func (t Time) Sub(u Time) Duration {
   884  	if t.wall&u.wall&hasMonotonic != 0 {
   885  		te := t.ext
   886  		ue := u.ext
   887  		d := Duration(te - ue)
   888  		if d < 0 && te > ue {
   889  			return maxDuration // t - u is positive out of range
   890  		}
   891  		if d > 0 && te < ue {
   892  			return minDuration // t - u is negative out of range
   893  		}
   894  		return d
   895  	}
   896  	d := Duration(t.sec()-u.sec())*Second + Duration(t.nsec()-u.nsec())
   897  	// Check for overflow or underflow.
   898  	switch {
   899  	case u.Add(d).Equal(t):
   900  		return d // d is correct
   901  	case t.Before(u):
   902  		return minDuration // t - u is negative out of range
   903  	default:
   904  		return maxDuration // t - u is positive out of range
   905  	}
   906  }
   907  
   908  // Since returns the time elapsed since t.
   909  // It is shorthand for time.Now().Sub(t).
   910  func Since(t Time) Duration {
   911  	return Now().Sub(t)
   912  }
   913  
   914  // Until returns the duration until t.
   915  // It is shorthand for t.Sub(time.Now()).
   916  func Until(t Time) Duration {
   917  	return t.Sub(Now())
   918  }
   919  
   920  // AddDate returns the time corresponding to adding the
   921  // given number of years, months, and days to t.
   922  // For example, AddDate(-1, 2, 3) applied to January 1, 2011
   923  // returns March 4, 2010.
   924  //
   925  // AddDate normalizes its result in the same way that Date does,
   926  // so, for example, adding one month to October 31 yields
   927  // December 1, the normalized form for November 31.
   928  func (t Time) AddDate(years int, months int, days int) Time {
   929  	year, month, day := t.Date()
   930  	hour, min, sec := t.Clock()
   931  	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec()), t.Location())
   932  }
   933  
   934  const (
   935  	secondsPerMinute = 60
   936  	secondsPerHour   = 60 * 60
   937  	secondsPerDay    = 24 * secondsPerHour
   938  	secondsPerWeek   = 7 * secondsPerDay
   939  	daysPer400Years  = 365*400 + 97
   940  	daysPer100Years  = 365*100 + 24
   941  	daysPer4Years    = 365*4 + 1
   942  )
   943  
   944  // date computes the year, day of year, and when full=true,
   945  // the month and day in which t occurs.
   946  func (t Time) date(full bool) (year int, month Month, day int, yday int) {
   947  	return absDate(t.abs(), full)
   948  }
   949  
   950  // absDate is like date but operates on an absolute time.
   951  func absDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
   952  	// Split into time and day.
   953  	d := abs / secondsPerDay
   954  
   955  	// Account for 400 year cycles.
   956  	n := d / daysPer400Years
   957  	y := 400 * n
   958  	d -= daysPer400Years * n
   959  
   960  	// Cut off 100-year cycles.
   961  	// The last cycle has one extra leap year, so on the last day
   962  	// of that year, day / daysPer100Years will be 4 instead of 3.
   963  	// Cut it back down to 3 by subtracting n>>2.
   964  	n = d / daysPer100Years
   965  	n -= n >> 2
   966  	y += 100 * n
   967  	d -= daysPer100Years * n
   968  
   969  	// Cut off 4-year cycles.
   970  	// The last cycle has a missing leap year, which does not
   971  	// affect the computation.
   972  	n = d / daysPer4Years
   973  	y += 4 * n
   974  	d -= daysPer4Years * n
   975  
   976  	// Cut off years within a 4-year cycle.
   977  	// The last year is a leap year, so on the last day of that year,
   978  	// day / 365 will be 4 instead of 3. Cut it back down to 3
   979  	// by subtracting n>>2.
   980  	n = d / 365
   981  	n -= n >> 2
   982  	y += n
   983  	d -= 365 * n
   984  
   985  	year = int(int64(y) + absoluteZeroYear)
   986  	yday = int(d)
   987  
   988  	if !full {
   989  		return
   990  	}
   991  
   992  	day = yday
   993  	if isLeap(year) {
   994  		// Leap year
   995  		switch {
   996  		case day > 31+29-1:
   997  			// After leap day; pretend it wasn't there.
   998  			day--
   999  		case day == 31+29-1:
  1000  			// Leap day.
  1001  			month = February
  1002  			day = 29
  1003  			return
  1004  		}
  1005  	}
  1006  
  1007  	// Estimate month on assumption that every month has 31 days.
  1008  	// The estimate may be too low by at most one month, so adjust.
  1009  	month = Month(day / 31)
  1010  	end := int(daysBefore[month+1])
  1011  	var begin int
  1012  	if day >= end {
  1013  		month++
  1014  		begin = end
  1015  	} else {
  1016  		begin = int(daysBefore[month])
  1017  	}
  1018  
  1019  	month++ // because January is 1
  1020  	day = day - begin + 1
  1021  	return
  1022  }
  1023  
  1024  // daysBefore[m] counts the number of days in a non-leap year
  1025  // before month m begins. There is an entry for m=12, counting
  1026  // the number of days before January of next year (365).
  1027  var daysBefore = [...]int32{
  1028  	0,
  1029  	31,
  1030  	31 + 28,
  1031  	31 + 28 + 31,
  1032  	31 + 28 + 31 + 30,
  1033  	31 + 28 + 31 + 30 + 31,
  1034  	31 + 28 + 31 + 30 + 31 + 30,
  1035  	31 + 28 + 31 + 30 + 31 + 30 + 31,
  1036  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31,
  1037  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30,
  1038  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31,
  1039  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30,
  1040  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31,
  1041  }
  1042  
  1043  func daysIn(m Month, year int) int {
  1044  	if m == February && isLeap(year) {
  1045  		return 29
  1046  	}
  1047  	return int(daysBefore[m] - daysBefore[m-1])
  1048  }
  1049  
  1050  // Provided by package runtime.
  1051  func now() (sec int64, nsec int32, mono int64)
  1052  
  1053  // Now returns the current local time.
  1054  func Now() Time {
  1055  	sec, nsec, mono := now()
  1056  	sec += unixToInternal - minWall
  1057  	if uint64(sec)>>33 != 0 {
  1058  		return Time{uint64(nsec), sec + minWall, Local}
  1059  	}
  1060  	return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
  1061  }
  1062  
  1063  func unixTime(sec int64, nsec int32) Time {
  1064  	return Time{uint64(nsec), sec + unixToInternal, Local}
  1065  }
  1066  
  1067  // UTC returns t with the location set to UTC.
  1068  func (t Time) UTC() Time {
  1069  	t.setLoc(&utcLoc)
  1070  	return t
  1071  }
  1072  
  1073  // Local returns t with the location set to local time.
  1074  func (t Time) Local() Time {
  1075  	t.setLoc(Local)
  1076  	return t
  1077  }
  1078  
  1079  // In returns a copy of t representating the same time instant, but
  1080  // with the copy's location information set to loc for display
  1081  // purposes.
  1082  //
  1083  // In panics if loc is nil.
  1084  func (t Time) In(loc *Location) Time {
  1085  	if loc == nil {
  1086  		panic("time: missing Location in call to Time.In")
  1087  	}
  1088  	t.setLoc(loc)
  1089  	return t
  1090  }
  1091  
  1092  // Location returns the time zone information associated with t.
  1093  func (t Time) Location() *Location {
  1094  	l := t.loc
  1095  	if l == nil {
  1096  		l = UTC
  1097  	}
  1098  	return l
  1099  }
  1100  
  1101  // Zone computes the time zone in effect at time t, returning the abbreviated
  1102  // name of the zone (such as "CET") and its offset in seconds east of UTC.
  1103  func (t Time) Zone() (name string, offset int) {
  1104  	name, offset, _, _ = t.loc.lookup(t.unixSec())
  1105  	return
  1106  }
  1107  
  1108  // Unix returns t as a Unix time, the number of seconds elapsed
  1109  // since January 1, 1970 UTC. The result does not depend on the
  1110  // location associated with t.
  1111  func (t Time) Unix() int64 {
  1112  	return t.unixSec()
  1113  }
  1114  
  1115  // UnixNano returns t as a Unix time, the number of nanoseconds elapsed
  1116  // since January 1, 1970 UTC. The result is undefined if the Unix time
  1117  // in nanoseconds cannot be represented by an int64 (a date before the year
  1118  // 1678 or after 2262). Note that this means the result of calling UnixNano
  1119  // on the zero Time is undefined. The result does not depend on the
  1120  // location associated with t.
  1121  func (t Time) UnixNano() int64 {
  1122  	return (t.unixSec())*1e9 + int64(t.nsec())
  1123  }
  1124  
  1125  const timeBinaryVersion byte = 1
  1126  
  1127  // MarshalBinary implements the encoding.BinaryMarshaler interface.
  1128  func (t Time) MarshalBinary() ([]byte, error) {
  1129  	var offsetMin int16 // minutes east of UTC. -1 is UTC.
  1130  
  1131  	if t.Location() == UTC {
  1132  		offsetMin = -1
  1133  	} else {
  1134  		_, offset := t.Zone()
  1135  		if offset%60 != 0 {
  1136  			return nil, errors.New("Time.MarshalBinary: zone offset has fractional minute")
  1137  		}
  1138  		offset /= 60
  1139  		if offset < -32768 || offset == -1 || offset > 32767 {
  1140  			return nil, errors.New("Time.MarshalBinary: unexpected zone offset")
  1141  		}
  1142  		offsetMin = int16(offset)
  1143  	}
  1144  
  1145  	sec := t.sec()
  1146  	nsec := t.nsec()
  1147  	enc := []byte{
  1148  		timeBinaryVersion, // byte 0 : version
  1149  		byte(sec >> 56),   // bytes 1-8: seconds
  1150  		byte(sec >> 48),
  1151  		byte(sec >> 40),
  1152  		byte(sec >> 32),
  1153  		byte(sec >> 24),
  1154  		byte(sec >> 16),
  1155  		byte(sec >> 8),
  1156  		byte(sec),
  1157  		byte(nsec >> 24), // bytes 9-12: nanoseconds
  1158  		byte(nsec >> 16),
  1159  		byte(nsec >> 8),
  1160  		byte(nsec),
  1161  		byte(offsetMin >> 8), // bytes 13-14: zone offset in minutes
  1162  		byte(offsetMin),
  1163  	}
  1164  
  1165  	return enc, nil
  1166  }
  1167  
  1168  // UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
  1169  func (t *Time) UnmarshalBinary(data []byte) error {
  1170  	buf := data
  1171  	if len(buf) == 0 {
  1172  		return errors.New("Time.UnmarshalBinary: no data")
  1173  	}
  1174  
  1175  	if buf[0] != timeBinaryVersion {
  1176  		return errors.New("Time.UnmarshalBinary: unsupported version")
  1177  	}
  1178  
  1179  	if len(buf) != /*version*/ 1+ /*sec*/ 8+ /*nsec*/ 4+ /*zone offset*/ 2 {
  1180  		return errors.New("Time.UnmarshalBinary: invalid length")
  1181  	}
  1182  
  1183  	buf = buf[1:]
  1184  	sec := int64(buf[7]) | int64(buf[6])<<8 | int64(buf[5])<<16 | int64(buf[4])<<24 |
  1185  		int64(buf[3])<<32 | int64(buf[2])<<40 | int64(buf[1])<<48 | int64(buf[0])<<56
  1186  
  1187  	buf = buf[8:]
  1188  	nsec := int32(buf[3]) | int32(buf[2])<<8 | int32(buf[1])<<16 | int32(buf[0])<<24
  1189  
  1190  	buf = buf[4:]
  1191  	offset := int(int16(buf[1])|int16(buf[0])<<8) * 60
  1192  
  1193  	*t = Time{}
  1194  	t.wall = uint64(nsec)
  1195  	t.ext = sec
  1196  
  1197  	if offset == -1*60 {
  1198  		t.setLoc(&utcLoc)
  1199  	} else if _, localoff, _, _ := Local.lookup(t.unixSec()); offset == localoff {
  1200  		t.setLoc(Local)
  1201  	} else {
  1202  		t.setLoc(FixedZone("", offset))
  1203  	}
  1204  
  1205  	return nil
  1206  }
  1207  
  1208  // TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
  1209  // The same semantics will be provided by the generic MarshalBinary, MarshalText,
  1210  // UnmarshalBinary, UnmarshalText.
  1211  
  1212  // GobEncode implements the gob.GobEncoder interface.
  1213  func (t Time) GobEncode() ([]byte, error) {
  1214  	return t.MarshalBinary()
  1215  }
  1216  
  1217  // GobDecode implements the gob.GobDecoder interface.
  1218  func (t *Time) GobDecode(data []byte) error {
  1219  	return t.UnmarshalBinary(data)
  1220  }
  1221  
  1222  // MarshalJSON implements the json.Marshaler interface.
  1223  // The time is a quoted string in RFC 3339 format, with sub-second precision added if present.
  1224  func (t Time) MarshalJSON() ([]byte, error) {
  1225  	if y := t.Year(); y < 0 || y >= 10000 {
  1226  		// RFC 3339 is clear that years are 4 digits exactly.
  1227  		// See golang.org/issue/4556#c15 for more discussion.
  1228  		return nil, errors.New("Time.MarshalJSON: year outside of range [0,9999]")
  1229  	}
  1230  
  1231  	b := make([]byte, 0, len(RFC3339Nano)+2)
  1232  	b = append(b, '"')
  1233  	b = t.AppendFormat(b, RFC3339Nano)
  1234  	b = append(b, '"')
  1235  	return b, nil
  1236  }
  1237  
  1238  // UnmarshalJSON implements the json.Unmarshaler interface.
  1239  // The time is expected to be a quoted string in RFC 3339 format.
  1240  func (t *Time) UnmarshalJSON(data []byte) error {
  1241  	// Ignore null, like in the main JSON package.
  1242  	if string(data) == "null" {
  1243  		return nil
  1244  	}
  1245  	// Fractional seconds are handled implicitly by Parse.
  1246  	var err error
  1247  	*t, err = Parse(`"`+RFC3339+`"`, string(data))
  1248  	return err
  1249  }
  1250  
  1251  // MarshalText implements the encoding.TextMarshaler interface.
  1252  // The time is formatted in RFC 3339 format, with sub-second precision added if present.
  1253  func (t Time) MarshalText() ([]byte, error) {
  1254  	if y := t.Year(); y < 0 || y >= 10000 {
  1255  		return nil, errors.New("Time.MarshalText: year outside of range [0,9999]")
  1256  	}
  1257  
  1258  	b := make([]byte, 0, len(RFC3339Nano))
  1259  	return t.AppendFormat(b, RFC3339Nano), nil
  1260  }
  1261  
  1262  // UnmarshalText implements the encoding.TextUnmarshaler interface.
  1263  // The time is expected to be in RFC 3339 format.
  1264  func (t *Time) UnmarshalText(data []byte) error {
  1265  	// Fractional seconds are handled implicitly by Parse.
  1266  	var err error
  1267  	*t, err = Parse(RFC3339, string(data))
  1268  	return err
  1269  }
  1270  
  1271  // Unix returns the local Time corresponding to the given Unix time,
  1272  // sec seconds and nsec nanoseconds since January 1, 1970 UTC.
  1273  // It is valid to pass nsec outside the range [0, 999999999].
  1274  // Not all sec values have a corresponding time value. One such
  1275  // value is 1<<63-1 (the largest int64 value).
  1276  func Unix(sec int64, nsec int64) Time {
  1277  	if nsec < 0 || nsec >= 1e9 {
  1278  		n := nsec / 1e9
  1279  		sec += n
  1280  		nsec -= n * 1e9
  1281  		if nsec < 0 {
  1282  			nsec += 1e9
  1283  			sec--
  1284  		}
  1285  	}
  1286  	return unixTime(sec, int32(nsec))
  1287  }
  1288  
  1289  func isLeap(year int) bool {
  1290  	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
  1291  }
  1292  
  1293  // norm returns nhi, nlo such that
  1294  //	hi * base + lo == nhi * base + nlo
  1295  //	0 <= nlo < base
  1296  func norm(hi, lo, base int) (nhi, nlo int) {
  1297  	if lo < 0 {
  1298  		n := (-lo-1)/base + 1
  1299  		hi -= n
  1300  		lo += n * base
  1301  	}
  1302  	if lo >= base {
  1303  		n := lo / base
  1304  		hi += n
  1305  		lo -= n * base
  1306  	}
  1307  	return hi, lo
  1308  }
  1309  
  1310  // Date returns the Time corresponding to
  1311  //	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
  1312  // in the appropriate zone for that time in the given location.
  1313  //
  1314  // The month, day, hour, min, sec, and nsec values may be outside
  1315  // their usual ranges and will be normalized during the conversion.
  1316  // For example, October 32 converts to November 1.
  1317  //
  1318  // A daylight savings time transition skips or repeats times.
  1319  // For example, in the United States, March 13, 2011 2:15am never occurred,
  1320  // while November 6, 2011 1:15am occurred twice. In such cases, the
  1321  // choice of time zone, and therefore the time, is not well-defined.
  1322  // Date returns a time that is correct in one of the two zones involved
  1323  // in the transition, but it does not guarantee which.
  1324  //
  1325  // Date panics if loc is nil.
  1326  func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
  1327  	if loc == nil {
  1328  		panic("time: missing Location in call to Date")
  1329  	}
  1330  
  1331  	// Normalize month, overflowing into year.
  1332  	m := int(month) - 1
  1333  	year, m = norm(year, m, 12)
  1334  	month = Month(m) + 1
  1335  
  1336  	// Normalize nsec, sec, min, hour, overflowing into day.
  1337  	sec, nsec = norm(sec, nsec, 1e9)
  1338  	min, sec = norm(min, sec, 60)
  1339  	hour, min = norm(hour, min, 60)
  1340  	day, hour = norm(day, hour, 24)
  1341  
  1342  	y := uint64(int64(year) - absoluteZeroYear)
  1343  
  1344  	// Compute days since the absolute epoch.
  1345  
  1346  	// Add in days from 400-year cycles.
  1347  	n := y / 400
  1348  	y -= 400 * n
  1349  	d := daysPer400Years * n
  1350  
  1351  	// Add in 100-year cycles.
  1352  	n = y / 100
  1353  	y -= 100 * n
  1354  	d += daysPer100Years * n
  1355  
  1356  	// Add in 4-year cycles.
  1357  	n = y / 4
  1358  	y -= 4 * n
  1359  	d += daysPer4Years * n
  1360  
  1361  	// Add in non-leap years.
  1362  	n = y
  1363  	d += 365 * n
  1364  
  1365  	// Add in days before this month.
  1366  	d += uint64(daysBefore[month-1])
  1367  	if isLeap(year) && month >= March {
  1368  		d++ // February 29
  1369  	}
  1370  
  1371  	// Add in days before today.
  1372  	d += uint64(day - 1)
  1373  
  1374  	// Add in time elapsed today.
  1375  	abs := d * secondsPerDay
  1376  	abs += uint64(hour*secondsPerHour + min*secondsPerMinute + sec)
  1377  
  1378  	unix := int64(abs) + (absoluteToInternal + internalToUnix)
  1379  
  1380  	// Look for zone offset for t, so we can adjust to UTC.
  1381  	// The lookup function expects UTC, so we pass t in the
  1382  	// hope that it will not be too close to a zone transition,
  1383  	// and then adjust if it is.
  1384  	_, offset, start, end := loc.lookup(unix)
  1385  	if offset != 0 {
  1386  		switch utc := unix - int64(offset); {
  1387  		case utc < start:
  1388  			_, offset, _, _ = loc.lookup(start - 1)
  1389  		case utc >= end:
  1390  			_, offset, _, _ = loc.lookup(end)
  1391  		}
  1392  		unix -= int64(offset)
  1393  	}
  1394  
  1395  	t := unixTime(unix, int32(nsec))
  1396  	t.setLoc(loc)
  1397  	return t
  1398  }
  1399  
  1400  // Truncate returns the result of rounding t down to a multiple of d (since the zero time).
  1401  // If d <= 0, Truncate returns t stripped of any monotonic clock reading but otherwise unchanged.
  1402  //
  1403  // Truncate operates on the time as an absolute duration since the
  1404  // zero time; it does not operate on the presentation form of the
  1405  // time. Thus, Truncate(Hour) may return a time with a non-zero
  1406  // minute, depending on the time's Location.
  1407  func (t Time) Truncate(d Duration) Time {
  1408  	t.stripMono()
  1409  	if d <= 0 {
  1410  		return t
  1411  	}
  1412  	_, r := div(t, d)
  1413  	return t.Add(-r)
  1414  }
  1415  
  1416  // Round returns the result of rounding t to the nearest multiple of d (since the zero time).
  1417  // The rounding behavior for halfway values is to round up.
  1418  // If d <= 0, Round returns t stripped of any monotonic clock reading but otherwise unchanged.
  1419  //
  1420  // Round operates on the time as an absolute duration since the
  1421  // zero time; it does not operate on the presentation form of the
  1422  // time. Thus, Round(Hour) may return a time with a non-zero
  1423  // minute, depending on the time's Location.
  1424  func (t Time) Round(d Duration) Time {
  1425  	t.stripMono()
  1426  	if d <= 0 {
  1427  		return t
  1428  	}
  1429  	_, r := div(t, d)
  1430  	if lessThanHalf(r, d) {
  1431  		return t.Add(-r)
  1432  	}
  1433  	return t.Add(d - r)
  1434  }
  1435  
  1436  // div divides t by d and returns the quotient parity and remainder.
  1437  // We don't use the quotient parity anymore (round half up instead of round to even)
  1438  // but it's still here in case we change our minds.
  1439  func div(t Time, d Duration) (qmod2 int, r Duration) {
  1440  	neg := false
  1441  	nsec := t.nsec()
  1442  	sec := t.sec()
  1443  	if sec < 0 {
  1444  		// Operate on absolute value.
  1445  		neg = true
  1446  		sec = -sec
  1447  		nsec = -nsec
  1448  		if nsec < 0 {
  1449  			nsec += 1e9
  1450  			sec-- // sec >= 1 before the -- so safe
  1451  		}
  1452  	}
  1453  
  1454  	switch {
  1455  	// Special case: 2d divides 1 second.
  1456  	case d < Second && Second%(d+d) == 0:
  1457  		qmod2 = int(nsec/int32(d)) & 1
  1458  		r = Duration(nsec % int32(d))
  1459  
  1460  	// Special case: d is a multiple of 1 second.
  1461  	case d%Second == 0:
  1462  		d1 := int64(d / Second)
  1463  		qmod2 = int(sec/d1) & 1
  1464  		r = Duration(sec%d1)*Second + Duration(nsec)
  1465  
  1466  	// General case.
  1467  	// This could be faster if more cleverness were applied,
  1468  	// but it's really only here to avoid special case restrictions in the API.
  1469  	// No one will care about these cases.
  1470  	default:
  1471  		// Compute nanoseconds as 128-bit number.
  1472  		sec := uint64(sec)
  1473  		tmp := (sec >> 32) * 1e9
  1474  		u1 := tmp >> 32
  1475  		u0 := tmp << 32
  1476  		tmp = (sec & 0xFFFFFFFF) * 1e9
  1477  		u0x, u0 := u0, u0+tmp
  1478  		if u0 < u0x {
  1479  			u1++
  1480  		}
  1481  		u0x, u0 = u0, u0+uint64(nsec)
  1482  		if u0 < u0x {
  1483  			u1++
  1484  		}
  1485  
  1486  		// Compute remainder by subtracting r<<k for decreasing k.
  1487  		// Quotient parity is whether we subtract on last round.
  1488  		d1 := uint64(d)
  1489  		for d1>>63 != 1 {
  1490  			d1 <<= 1
  1491  		}
  1492  		d0 := uint64(0)
  1493  		for {
  1494  			qmod2 = 0
  1495  			if u1 > d1 || u1 == d1 && u0 >= d0 {
  1496  				// subtract
  1497  				qmod2 = 1
  1498  				u0x, u0 = u0, u0-d0
  1499  				if u0 > u0x {
  1500  					u1--
  1501  				}
  1502  				u1 -= d1
  1503  			}
  1504  			if d1 == 0 && d0 == uint64(d) {
  1505  				break
  1506  			}
  1507  			d0 >>= 1
  1508  			d0 |= (d1 & 1) << 63
  1509  			d1 >>= 1
  1510  		}
  1511  		r = Duration(u0)
  1512  	}
  1513  
  1514  	if neg && r != 0 {
  1515  		// If input was negative and not an exact multiple of d, we computed q, r such that
  1516  		//	q*d + r = -t
  1517  		// But the right answers are given by -(q-1), d-r:
  1518  		//	q*d + r = -t
  1519  		//	-q*d - r = t
  1520  		//	-(q-1)*d + (d - r) = t
  1521  		qmod2 ^= 1
  1522  		r = d - r
  1523  	}
  1524  	return
  1525  }
  1526  

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