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Source file src/time/time.go

  // Copyright 2009 The Go Authors. All rights reserved.
  // Use of this source code is governed by a BSD-style
  // license that can be found in the LICENSE file.
  
  // Package time provides functionality for measuring and displaying time.
  //
  // The calendrical calculations always assume a Gregorian calendar, with
  // no leap seconds.
  package time
  
  import "errors"
  
  // A Time represents an instant in time with nanosecond precision.
  //
  // Programs using times should typically store and pass them as values,
  // not pointers. That is, time variables and struct fields should be of
  // type time.Time, not *time.Time. A Time value can be used by
  // multiple goroutines simultaneously.
  //
  // Time instants can be compared using the Before, After, and Equal methods.
  // The Sub method subtracts two instants, producing a Duration.
  // The Add method adds a Time and a Duration, producing a Time.
  //
  // The zero value of type Time is January 1, year 1, 00:00:00.000000000 UTC.
  // As this time is unlikely to come up in practice, the IsZero method gives
  // a simple way of detecting a time that has not been initialized explicitly.
  //
  // Each Time has associated with it a Location, consulted when computing the
  // presentation form of the time, such as in the Format, Hour, and Year methods.
  // The methods Local, UTC, and In return a Time with a specific location.
  // Changing the location in this way changes only the presentation; it does not
  // change the instant in time being denoted and therefore does not affect the
  // computations described in earlier paragraphs.
  //
  // Note that the Go == operator compares not just the time instant but also the
  // Location. Therefore, Time values should not be used as map or database keys
  // without first guaranteeing that the identical Location has been set for all
  // values, which can be achieved through use of the UTC or Local method.
  //
  type Time struct {
  	// sec gives the number of seconds elapsed since
  	// January 1, year 1 00:00:00 UTC.
  	sec int64
  
  	// nsec specifies a non-negative nanosecond
  	// offset within the second named by Seconds.
  	// It must be in the range [0, 999999999].
  	nsec int32
  
  	// loc specifies the Location that should be used to
  	// determine the minute, hour, month, day, and year
  	// that correspond to this Time.
  	// The nil location means UTC.
  	// All UTC times are represented with loc==nil, never loc==&utcLoc.
  	loc *Location
  }
  
  func (t *Time) setLoc(loc *Location) {
  	if loc == &utcLoc {
  		loc = nil
  	}
  	t.loc = loc
  }
  
  // After reports whether the time instant t is after u.
  func (t Time) After(u Time) bool {
  	return t.sec > u.sec || t.sec == u.sec && t.nsec > u.nsec
  }
  
  // Before reports whether the time instant t is before u.
  func (t Time) Before(u Time) bool {
  	return t.sec < u.sec || t.sec == u.sec && t.nsec < u.nsec
  }
  
  // Equal reports whether t and u represent the same time instant.
  // Two times can be equal even if they are in different locations.
  // For example, 6:00 +0200 CEST and 4:00 UTC are Equal.
  // Do not use == with Time values.
  func (t Time) Equal(u Time) bool {
  	return t.sec == u.sec && t.nsec == u.nsec
  }
  
  // A Month specifies a month of the year (January = 1, ...).
  type Month int
  
  const (
  	January Month = 1 + iota
  	February
  	March
  	April
  	May
  	June
  	July
  	August
  	September
  	October
  	November
  	December
  )
  
  var months = [...]string{
  	"January",
  	"February",
  	"March",
  	"April",
  	"May",
  	"June",
  	"July",
  	"August",
  	"September",
  	"October",
  	"November",
  	"December",
  }
  
  // String returns the English name of the month ("January", "February", ...).
  func (m Month) String() string {
  	if January <= m && m <= December {
  		return months[m-1]
  	}
  	buf := make([]byte, 20)
  	n := fmtInt(buf, uint64(m))
  	return "%!Month(" + string(buf[n:]) + ")"
  }
  
  // A Weekday specifies a day of the week (Sunday = 0, ...).
  type Weekday int
  
  const (
  	Sunday Weekday = iota
  	Monday
  	Tuesday
  	Wednesday
  	Thursday
  	Friday
  	Saturday
  )
  
  var days = [...]string{
  	"Sunday",
  	"Monday",
  	"Tuesday",
  	"Wednesday",
  	"Thursday",
  	"Friday",
  	"Saturday",
  }
  
  // String returns the English name of the day ("Sunday", "Monday", ...).
  func (d Weekday) String() string { return days[d] }
  
  // Computations on time.
  //
  // The zero value for a Time is defined to be
  //	January 1, year 1, 00:00:00.000000000 UTC
  // which (1) looks like a zero, or as close as you can get in a date
  // (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
  // be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
  // non-negative year even in time zones west of UTC, unlike 1-1-0
  // 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
  //
  // The zero Time value does not force a specific epoch for the time
  // representation. For example, to use the Unix epoch internally, we
  // could define that to distinguish a zero value from Jan 1 1970, that
  // time would be represented by sec=-1, nsec=1e9.  However, it does
  // suggest a representation, namely using 1-1-1 00:00:00 UTC as the
  // epoch, and that's what we do.
  //
  // The Add and Sub computations are oblivious to the choice of epoch.
  //
  // The presentation computations - year, month, minute, and so on - all
  // rely heavily on division and modulus by positive constants. For
  // calendrical calculations we want these divisions to round down, even
  // for negative values, so that the remainder is always positive, but
  // Go's division (like most hardware division instructions) rounds to
  // zero. We can still do those computations and then adjust the result
  // for a negative numerator, but it's annoying to write the adjustment
  // over and over. Instead, we can change to a different epoch so long
  // ago that all the times we care about will be positive, and then round
  // to zero and round down coincide. These presentation routines already
  // have to add the zone offset, so adding the translation to the
  // alternate epoch is cheap. For example, having a non-negative time t
  // means that we can write
  //
  //	sec = t % 60
  //
  // instead of
  //
  //	sec = t % 60
  //	if sec < 0 {
  //		sec += 60
  //	}
  //
  // everywhere.
  //
  // The calendar runs on an exact 400 year cycle: a 400-year calendar
  // printed for 1970-2469 will apply as well to 2370-2769.  Even the days
  // of the week match up. It simplifies the computations to choose the
  // cycle boundaries so that the exceptional years are always delayed as
  // long as possible. That means choosing a year equal to 1 mod 400, so
  // that the first leap year is the 4th year, the first missed leap year
  // is the 100th year, and the missed missed leap year is the 400th year.
  // So we'd prefer instead to print a calendar for 2001-2400 and reuse it
  // for 2401-2800.
  //
  // Finally, it's convenient if the delta between the Unix epoch and
  // long-ago epoch is representable by an int64 constant.
  //
  // These three considerations—choose an epoch as early as possible, that
  // uses a year equal to 1 mod 400, and that is no more than 2⁶³ seconds
  // earlier than 1970—bring us to the year -292277022399.  We refer to
  // this year as the absolute zero year, and to times measured as a uint64
  // seconds since this year as absolute times.
  //
  // Times measured as an int64 seconds since the year 1—the representation
  // used for Time's sec field—are called internal times.
  //
  // Times measured as an int64 seconds since the year 1970 are called Unix
  // times.
  //
  // It is tempting to just use the year 1 as the absolute epoch, defining
  // that the routines are only valid for years >= 1.  However, the
  // routines would then be invalid when displaying the epoch in time zones
  // west of UTC, since it is year 0.  It doesn't seem tenable to say that
  // printing the zero time correctly isn't supported in half the time
  // zones. By comparison, it's reasonable to mishandle some times in
  // the year -292277022399.
  //
  // All this is opaque to clients of the API and can be changed if a
  // better implementation presents itself.
  
  const (
  	// The unsigned zero year for internal calculations.
  	// Must be 1 mod 400, and times before it will not compute correctly,
  	// but otherwise can be changed at will.
  	absoluteZeroYear = -292277022399
  
  	// The year of the zero Time.
  	// Assumed by the unixToInternal computation below.
  	internalYear = 1
  
  	// Offsets to convert between internal and absolute or Unix times.
  	absoluteToInternal int64 = (absoluteZeroYear - internalYear) * 365.2425 * secondsPerDay
  	internalToAbsolute       = -absoluteToInternal
  
  	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
  	internalToUnix int64 = -unixToInternal
  )
  
  // IsZero reports whether t represents the zero time instant,
  // January 1, year 1, 00:00:00 UTC.
  func (t Time) IsZero() bool {
  	return t.sec == 0 && t.nsec == 0
  }
  
  // abs returns the time t as an absolute time, adjusted by the zone offset.
  // It is called when computing a presentation property like Month or Hour.
  func (t Time) abs() uint64 {
  	l := t.loc
  	// Avoid function calls when possible.
  	if l == nil || l == &localLoc {
  		l = l.get()
  	}
  	sec := t.sec + internalToUnix
  	if l != &utcLoc {
  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
  			sec += int64(l.cacheZone.offset)
  		} else {
  			_, offset, _, _, _ := l.lookup(sec)
  			sec += int64(offset)
  		}
  	}
  	return uint64(sec + (unixToInternal + internalToAbsolute))
  }
  
  // locabs is a combination of the Zone and abs methods,
  // extracting both return values from a single zone lookup.
  func (t Time) locabs() (name string, offset int, abs uint64) {
  	l := t.loc
  	if l == nil || l == &localLoc {
  		l = l.get()
  	}
  	// Avoid function call if we hit the local time cache.
  	sec := t.sec + internalToUnix
  	if l != &utcLoc {
  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
  			name = l.cacheZone.name
  			offset = l.cacheZone.offset
  		} else {
  			name, offset, _, _, _ = l.lookup(sec)
  		}
  		sec += int64(offset)
  	} else {
  		name = "UTC"
  	}
  	abs = uint64(sec + (unixToInternal + internalToAbsolute))
  	return
  }
  
  // Date returns the year, month, and day in which t occurs.
  func (t Time) Date() (year int, month Month, day int) {
  	year, month, day, _ = t.date(true)
  	return
  }
  
  // Year returns the year in which t occurs.
  func (t Time) Year() int {
  	year, _, _, _ := t.date(false)
  	return year
  }
  
  // Month returns the month of the year specified by t.
  func (t Time) Month() Month {
  	_, month, _, _ := t.date(true)
  	return month
  }
  
  // Day returns the day of the month specified by t.
  func (t Time) Day() int {
  	_, _, day, _ := t.date(true)
  	return day
  }
  
  // Weekday returns the day of the week specified by t.
  func (t Time) Weekday() Weekday {
  	return absWeekday(t.abs())
  }
  
  // absWeekday is like Weekday but operates on an absolute time.
  func absWeekday(abs uint64) Weekday {
  	// January 1 of the absolute year, like January 1 of 2001, was a Monday.
  	sec := (abs + uint64(Monday)*secondsPerDay) % secondsPerWeek
  	return Weekday(int(sec) / secondsPerDay)
  }
  
  // ISOWeek returns the ISO 8601 year and week number in which t occurs.
  // Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
  // week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
  // of year n+1.
  func (t Time) ISOWeek() (year, week int) {
  	year, month, day, yday := t.date(true)
  	wday := int(t.Weekday()+6) % 7 // weekday but Monday = 0.
  	const (
  		Mon int = iota
  		Tue
  		Wed
  		Thu
  		Fri
  		Sat
  		Sun
  	)
  
  	// Calculate week as number of Mondays in year up to
  	// and including today, plus 1 because the first week is week 0.
  	// Putting the + 1 inside the numerator as a + 7 keeps the
  	// numerator from being negative, which would cause it to
  	// round incorrectly.
  	week = (yday - wday + 7) / 7
  
  	// The week number is now correct under the assumption
  	// that the first Monday of the year is in week 1.
  	// If Jan 1 is a Tuesday, Wednesday, or Thursday, the first Monday
  	// is actually in week 2.
  	jan1wday := (wday - yday + 7*53) % 7
  	if Tue <= jan1wday && jan1wday <= Thu {
  		week++
  	}
  
  	// If the week number is still 0, we're in early January but in
  	// the last week of last year.
  	if week == 0 {
  		year--
  		week = 52
  		// A year has 53 weeks when Jan 1 or Dec 31 is a Thursday,
  		// meaning Jan 1 of the next year is a Friday
  		// or it was a leap year and Jan 1 of the next year is a Saturday.
  		if jan1wday == Fri || (jan1wday == Sat && isLeap(year)) {
  			week++
  		}
  	}
  
  	// December 29 to 31 are in week 1 of next year if
  	// they are after the last Thursday of the year and
  	// December 31 is a Monday, Tuesday, or Wednesday.
  	if month == December && day >= 29 && wday < Thu {
  		if dec31wday := (wday + 31 - day) % 7; Mon <= dec31wday && dec31wday <= Wed {
  			year++
  			week = 1
  		}
  	}
  
  	return
  }
  
  // Clock returns the hour, minute, and second within the day specified by t.
  func (t Time) Clock() (hour, min, sec int) {
  	return absClock(t.abs())
  }
  
  // absClock is like clock but operates on an absolute time.
  func absClock(abs uint64) (hour, min, sec int) {
  	sec = int(abs % secondsPerDay)
  	hour = sec / secondsPerHour
  	sec -= hour * secondsPerHour
  	min = sec / secondsPerMinute
  	sec -= min * secondsPerMinute
  	return
  }
  
  // Hour returns the hour within the day specified by t, in the range [0, 23].
  func (t Time) Hour() int {
  	return int(t.abs()%secondsPerDay) / secondsPerHour
  }
  
  // Minute returns the minute offset within the hour specified by t, in the range [0, 59].
  func (t Time) Minute() int {
  	return int(t.abs()%secondsPerHour) / secondsPerMinute
  }
  
  // Second returns the second offset within the minute specified by t, in the range [0, 59].
  func (t Time) Second() int {
  	return int(t.abs() % secondsPerMinute)
  }
  
  // Nanosecond returns the nanosecond offset within the second specified by t,
  // in the range [0, 999999999].
  func (t Time) Nanosecond() int {
  	return int(t.nsec)
  }
  
  // YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
  // and [1,366] in leap years.
  func (t Time) YearDay() int {
  	_, _, _, yday := t.date(false)
  	return yday + 1
  }
  
  // A Duration represents the elapsed time between two instants
  // as an int64 nanosecond count. The representation limits the
  // largest representable duration to approximately 290 years.
  type Duration int64
  
  const (
  	minDuration Duration = -1 << 63
  	maxDuration Duration = 1<<63 - 1
  )
  
  // Common durations. There is no definition for units of Day or larger
  // to avoid confusion across daylight savings time zone transitions.
  //
  // To count the number of units in a Duration, divide:
  //	second := time.Second
  //	fmt.Print(int64(second/time.Millisecond)) // prints 1000
  //
  // To convert an integer number of units to a Duration, multiply:
  //	seconds := 10
  //	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
  //
  const (
  	Nanosecond  Duration = 1
  	Microsecond          = 1000 * Nanosecond
  	Millisecond          = 1000 * Microsecond
  	Second               = 1000 * Millisecond
  	Minute               = 60 * Second
  	Hour                 = 60 * Minute
  )
  
  // String returns a string representing the duration in the form "72h3m0.5s".
  // Leading zero units are omitted. As a special case, durations less than one
  // second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
  // that the leading digit is non-zero. The zero duration formats as 0s.
  func (d Duration) String() string {
  	// Largest time is 2540400h10m10.000000000s
  	var buf [32]byte
  	w := len(buf)
  
  	u := uint64(d)
  	neg := d < 0
  	if neg {
  		u = -u
  	}
  
  	if u < uint64(Second) {
  		// Special case: if duration is smaller than a second,
  		// use smaller units, like 1.2ms
  		var prec int
  		w--
  		buf[w] = 's'
  		w--
  		switch {
  		case u == 0:
  			return "0s"
  		case u < uint64(Microsecond):
  			// print nanoseconds
  			prec = 0
  			buf[w] = 'n'
  		case u < uint64(Millisecond):
  			// print microseconds
  			prec = 3
  			// U+00B5 'µ' micro sign == 0xC2 0xB5
  			w-- // Need room for two bytes.
  			copy(buf[w:], "µ")
  		default:
  			// print milliseconds
  			prec = 6
  			buf[w] = 'm'
  		}
  		w, u = fmtFrac(buf[:w], u, prec)
  		w = fmtInt(buf[:w], u)
  	} else {
  		w--
  		buf[w] = 's'
  
  		w, u = fmtFrac(buf[:w], u, 9)
  
  		// u is now integer seconds
  		w = fmtInt(buf[:w], u%60)
  		u /= 60
  
  		// u is now integer minutes
  		if u > 0 {
  			w--
  			buf[w] = 'm'
  			w = fmtInt(buf[:w], u%60)
  			u /= 60
  
  			// u is now integer hours
  			// Stop at hours because days can be different lengths.
  			if u > 0 {
  				w--
  				buf[w] = 'h'
  				w = fmtInt(buf[:w], u)
  			}
  		}
  	}
  
  	if neg {
  		w--
  		buf[w] = '-'
  	}
  
  	return string(buf[w:])
  }
  
  // fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
  // tail of buf, omitting trailing zeros.  it omits the decimal
  // point too when the fraction is 0.  It returns the index where the
  // output bytes begin and the value v/10**prec.
  func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
  	// Omit trailing zeros up to and including decimal point.
  	w := len(buf)
  	print := false
  	for i := 0; i < prec; i++ {
  		digit := v % 10
  		print = print || digit != 0
  		if print {
  			w--
  			buf[w] = byte(digit) + '0'
  		}
  		v /= 10
  	}
  	if print {
  		w--
  		buf[w] = '.'
  	}
  	return w, v
  }
  
  // fmtInt formats v into the tail of buf.
  // It returns the index where the output begins.
  func fmtInt(buf []byte, v uint64) int {
  	w := len(buf)
  	if v == 0 {
  		w--
  		buf[w] = '0'
  	} else {
  		for v > 0 {
  			w--
  			buf[w] = byte(v%10) + '0'
  			v /= 10
  		}
  	}
  	return w
  }
  
  // Nanoseconds returns the duration as an integer nanosecond count.
  func (d Duration) Nanoseconds() int64 { return int64(d) }
  
  // These methods return float64 because the dominant
  // use case is for printing a floating point number like 1.5s, and
  // a truncation to integer would make them not useful in those cases.
  // Splitting the integer and fraction ourselves guarantees that
  // converting the returned float64 to an integer rounds the same
  // way that a pure integer conversion would have, even in cases
  // where, say, float64(d.Nanoseconds())/1e9 would have rounded
  // differently.
  
  // Seconds returns the duration as a floating point number of seconds.
  func (d Duration) Seconds() float64 {
  	sec := d / Second
  	nsec := d % Second
  	return float64(sec) + float64(nsec)/1e9
  }
  
  // Minutes returns the duration as a floating point number of minutes.
  func (d Duration) Minutes() float64 {
  	min := d / Minute
  	nsec := d % Minute
  	return float64(min) + float64(nsec)/(60*1e9)
  }
  
  // Hours returns the duration as a floating point number of hours.
  func (d Duration) Hours() float64 {
  	hour := d / Hour
  	nsec := d % Hour
  	return float64(hour) + float64(nsec)/(60*60*1e9)
  }
  
  // Add returns the time t+d.
  func (t Time) Add(d Duration) Time {
  	t.sec += int64(d / 1e9)
  	nsec := t.nsec + int32(d%1e9)
  	if nsec >= 1e9 {
  		t.sec++
  		nsec -= 1e9
  	} else if nsec < 0 {
  		t.sec--
  		nsec += 1e9
  	}
  	t.nsec = nsec
  	return t
  }
  
  // Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
  // value that can be stored in a Duration, the maximum (or minimum) duration
  // will be returned.
  // To compute t-d for a duration d, use t.Add(-d).
  func (t Time) Sub(u Time) Duration {
  	d := Duration(t.sec-u.sec)*Second + Duration(t.nsec-u.nsec)
  	// Check for overflow or underflow.
  	switch {
  	case u.Add(d).Equal(t):
  		return d // d is correct
  	case t.Before(u):
  		return minDuration // t - u is negative out of range
  	default:
  		return maxDuration // t - u is positive out of range
  	}
  }
  
  // Since returns the time elapsed since t.
  // It is shorthand for time.Now().Sub(t).
  func Since(t Time) Duration {
  	return Now().Sub(t)
  }
  
  // Until returns the duration until t.
  // It is shorthand for t.Sub(time.Now()).
  func Until(t Time) Duration {
  	return t.Sub(Now())
  }
  
  // AddDate returns the time corresponding to adding the
  // given number of years, months, and days to t.
  // For example, AddDate(-1, 2, 3) applied to January 1, 2011
  // returns March 4, 2010.
  //
  // AddDate normalizes its result in the same way that Date does,
  // so, for example, adding one month to October 31 yields
  // December 1, the normalized form for November 31.
  func (t Time) AddDate(years int, months int, days int) Time {
  	year, month, day := t.Date()
  	hour, min, sec := t.Clock()
  	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec), t.Location())
  }
  
  const (
  	secondsPerMinute = 60
  	secondsPerHour   = 60 * 60
  	secondsPerDay    = 24 * secondsPerHour
  	secondsPerWeek   = 7 * secondsPerDay
  	daysPer400Years  = 365*400 + 97
  	daysPer100Years  = 365*100 + 24
  	daysPer4Years    = 365*4 + 1
  )
  
  // date computes the year, day of year, and when full=true,
  // the month and day in which t occurs.
  func (t Time) date(full bool) (year int, month Month, day int, yday int) {
  	return absDate(t.abs(), full)
  }
  
  // absDate is like date but operates on an absolute time.
  func absDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
  	// Split into time and day.
  	d := abs / secondsPerDay
  
  	// Account for 400 year cycles.
  	n := d / daysPer400Years
  	y := 400 * n
  	d -= daysPer400Years * n
  
  	// Cut off 100-year cycles.
  	// The last cycle has one extra leap year, so on the last day
  	// of that year, day / daysPer100Years will be 4 instead of 3.
  	// Cut it back down to 3 by subtracting n>>2.
  	n = d / daysPer100Years
  	n -= n >> 2
  	y += 100 * n
  	d -= daysPer100Years * n
  
  	// Cut off 4-year cycles.
  	// The last cycle has a missing leap year, which does not
  	// affect the computation.
  	n = d / daysPer4Years
  	y += 4 * n
  	d -= daysPer4Years * n
  
  	// Cut off years within a 4-year cycle.
  	// The last year is a leap year, so on the last day of that year,
  	// day / 365 will be 4 instead of 3.  Cut it back down to 3
  	// by subtracting n>>2.
  	n = d / 365
  	n -= n >> 2
  	y += n
  	d -= 365 * n
  
  	year = int(int64(y) + absoluteZeroYear)
  	yday = int(d)
  
  	if !full {
  		return
  	}
  
  	day = yday
  	if isLeap(year) {
  		// Leap year
  		switch {
  		case day > 31+29-1:
  			// After leap day; pretend it wasn't there.
  			day--
  		case day == 31+29-1:
  			// Leap day.
  			month = February
  			day = 29
  			return
  		}
  	}
  
  	// Estimate month on assumption that every month has 31 days.
  	// The estimate may be too low by at most one month, so adjust.
  	month = Month(day / 31)
  	end := int(daysBefore[month+1])
  	var begin int
  	if day >= end {
  		month++
  		begin = end
  	} else {
  		begin = int(daysBefore[month])
  	}
  
  	month++ // because January is 1
  	day = day - begin + 1
  	return
  }
  
  // daysBefore[m] counts the number of days in a non-leap year
  // before month m begins. There is an entry for m=12, counting
  // the number of days before January of next year (365).
  var daysBefore = [...]int32{
  	0,
  	31,
  	31 + 28,
  	31 + 28 + 31,
  	31 + 28 + 31 + 30,
  	31 + 28 + 31 + 30 + 31,
  	31 + 28 + 31 + 30 + 31 + 30,
  	31 + 28 + 31 + 30 + 31 + 30 + 31,
  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31,
  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30,
  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31,
  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30,
  	31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31,
  }
  
  func daysIn(m Month, year int) int {
  	if m == February && isLeap(year) {
  		return 29
  	}
  	return int(daysBefore[m] - daysBefore[m-1])
  }
  
  // Provided by package runtime.
  func now() (sec int64, nsec int32)
  
  // Now returns the current local time.
  func Now() Time {
  	sec, nsec := now()
  	return Time{sec + unixToInternal, nsec, Local}
  }
  
  // UTC returns t with the location set to UTC.
  func (t Time) UTC() Time {
  	t.setLoc(&utcLoc)
  	return t
  }
  
  // Local returns t with the location set to local time.
  func (t Time) Local() Time {
  	t.setLoc(Local)
  	return t
  }
  
  // In returns t with the location information set to loc.
  //
  // In panics if loc is nil.
  func (t Time) In(loc *Location) Time {
  	if loc == nil {
  		panic("time: missing Location in call to Time.In")
  	}
  	t.setLoc(loc)
  	return t
  }
  
  // Location returns the time zone information associated with t.
  func (t Time) Location() *Location {
  	l := t.loc
  	if l == nil {
  		l = UTC
  	}
  	return l
  }
  
  // Zone computes the time zone in effect at time t, returning the abbreviated
  // name of the zone (such as "CET") and its offset in seconds east of UTC.
  func (t Time) Zone() (name string, offset int) {
  	name, offset, _, _, _ = t.loc.lookup(t.sec + internalToUnix)
  	return
  }
  
  // Unix returns t as a Unix time, the number of seconds elapsed
  // since January 1, 1970 UTC.
  func (t Time) Unix() int64 {
  	return t.sec + internalToUnix
  }
  
  // UnixNano returns t as a Unix time, the number of nanoseconds elapsed
  // since January 1, 1970 UTC. The result is undefined if the Unix time
  // in nanoseconds cannot be represented by an int64 (a date before the year
  // 1678 or after 2262). Note that this means the result of calling UnixNano
  // on the zero Time is undefined.
  func (t Time) UnixNano() int64 {
  	return (t.sec+internalToUnix)*1e9 + int64(t.nsec)
  }
  
  const timeBinaryVersion byte = 1
  
  // MarshalBinary implements the encoding.BinaryMarshaler interface.
  func (t Time) MarshalBinary() ([]byte, error) {
  	var offsetMin int16 // minutes east of UTC. -1 is UTC.
  
  	if t.Location() == UTC {
  		offsetMin = -1
  	} else {
  		_, offset := t.Zone()
  		if offset%60 != 0 {
  			return nil, errors.New("Time.MarshalBinary: zone offset has fractional minute")
  		}
  		offset /= 60
  		if offset < -32768 || offset == -1 || offset > 32767 {
  			return nil, errors.New("Time.MarshalBinary: unexpected zone offset")
  		}
  		offsetMin = int16(offset)
  	}
  
  	enc := []byte{
  		timeBinaryVersion, // byte 0 : version
  		byte(t.sec >> 56), // bytes 1-8: seconds
  		byte(t.sec >> 48),
  		byte(t.sec >> 40),
  		byte(t.sec >> 32),
  		byte(t.sec >> 24),
  		byte(t.sec >> 16),
  		byte(t.sec >> 8),
  		byte(t.sec),
  		byte(t.nsec >> 24), // bytes 9-12: nanoseconds
  		byte(t.nsec >> 16),
  		byte(t.nsec >> 8),
  		byte(t.nsec),
  		byte(offsetMin >> 8), // bytes 13-14: zone offset in minutes
  		byte(offsetMin),
  	}
  
  	return enc, nil
  }
  
  // UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
  func (t *Time) UnmarshalBinary(data []byte) error {
  	buf := data
  	if len(buf) == 0 {
  		return errors.New("Time.UnmarshalBinary: no data")
  	}
  
  	if buf[0] != timeBinaryVersion {
  		return errors.New("Time.UnmarshalBinary: unsupported version")
  	}
  
  	if len(buf) != /*version*/ 1+ /*sec*/ 8+ /*nsec*/ 4+ /*zone offset*/ 2 {
  		return errors.New("Time.UnmarshalBinary: invalid length")
  	}
  
  	buf = buf[1:]
  	t.sec = int64(buf[7]) | int64(buf[6])<<8 | int64(buf[5])<<16 | int64(buf[4])<<24 |
  		int64(buf[3])<<32 | int64(buf[2])<<40 | int64(buf[1])<<48 | int64(buf[0])<<56
  
  	buf = buf[8:]
  	t.nsec = int32(buf[3]) | int32(buf[2])<<8 | int32(buf[1])<<16 | int32(buf[0])<<24
  
  	buf = buf[4:]
  	offset := int(int16(buf[1])|int16(buf[0])<<8) * 60
  
  	if offset == -1*60 {
  		t.setLoc(&utcLoc)
  	} else if _, localoff, _, _, _ := Local.lookup(t.sec + internalToUnix); offset == localoff {
  		t.setLoc(Local)
  	} else {
  		t.setLoc(FixedZone("", offset))
  	}
  
  	return nil
  }
  
  // TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
  // The same semantics will be provided by the generic MarshalBinary, MarshalText,
  // UnmarshalBinary, UnmarshalText.
  
  // GobEncode implements the gob.GobEncoder interface.
  func (t Time) GobEncode() ([]byte, error) {
  	return t.MarshalBinary()
  }
  
  // GobDecode implements the gob.GobDecoder interface.
  func (t *Time) GobDecode(data []byte) error {
  	return t.UnmarshalBinary(data)
  }
  
  // MarshalJSON implements the json.Marshaler interface.
  // The time is a quoted string in RFC 3339 format, with sub-second precision added if present.
  func (t Time) MarshalJSON() ([]byte, error) {
  	if y := t.Year(); y < 0 || y >= 10000 {
  		// RFC 3339 is clear that years are 4 digits exactly.
  		// See golang.org/issue/4556#c15 for more discussion.
  		return nil, errors.New("Time.MarshalJSON: year outside of range [0,9999]")
  	}
  
  	b := make([]byte, 0, len(RFC3339Nano)+2)
  	b = append(b, '"')
  	b = t.AppendFormat(b, RFC3339Nano)
  	b = append(b, '"')
  	return b, nil
  }
  
  // UnmarshalJSON implements the json.Unmarshaler interface.
  // The time is expected to be a quoted string in RFC 3339 format.
  func (t *Time) UnmarshalJSON(data []byte) error {
  	// Ignore null, like in the main JSON package.
  	if string(data) == "null" {
  		return nil
  	}
  	// Fractional seconds are handled implicitly by Parse.
  	var err error
  	*t, err = Parse(`"`+RFC3339+`"`, string(data))
  	return err
  }
  
  // MarshalText implements the encoding.TextMarshaler interface.
  // The time is formatted in RFC 3339 format, with sub-second precision added if present.
  func (t Time) MarshalText() ([]byte, error) {
  	if y := t.Year(); y < 0 || y >= 10000 {
  		return nil, errors.New("Time.MarshalText: year outside of range [0,9999]")
  	}
  
  	b := make([]byte, 0, len(RFC3339Nano))
  	return t.AppendFormat(b, RFC3339Nano), nil
  }
  
  // UnmarshalText implements the encoding.TextUnmarshaler interface.
  // The time is expected to be in RFC 3339 format.
  func (t *Time) UnmarshalText(data []byte) error {
  	// Fractional seconds are handled implicitly by Parse.
  	var err error
  	*t, err = Parse(RFC3339, string(data))
  	return err
  }
  
  // Unix returns the local Time corresponding to the given Unix time,
  // sec seconds and nsec nanoseconds since January 1, 1970 UTC.
  // It is valid to pass nsec outside the range [0, 999999999].
  // Not all sec values have a corresponding time value. One such
  // value is 1<<63-1 (the largest int64 value).
  func Unix(sec int64, nsec int64) Time {
  	if nsec < 0 || nsec >= 1e9 {
  		n := nsec / 1e9
  		sec += n
  		nsec -= n * 1e9
  		if nsec < 0 {
  			nsec += 1e9
  			sec--
  		}
  	}
  	return Time{sec + unixToInternal, int32(nsec), Local}
  }
  
  func isLeap(year int) bool {
  	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
  }
  
  // norm returns nhi, nlo such that
  //	hi * base + lo == nhi * base + nlo
  //	0 <= nlo < base
  func norm(hi, lo, base int) (nhi, nlo int) {
  	if lo < 0 {
  		n := (-lo-1)/base + 1
  		hi -= n
  		lo += n * base
  	}
  	if lo >= base {
  		n := lo / base
  		hi += n
  		lo -= n * base
  	}
  	return hi, lo
  }
  
  // Date returns the Time corresponding to
  //	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
  // in the appropriate zone for that time in the given location.
  //
  // The month, day, hour, min, sec, and nsec values may be outside
  // their usual ranges and will be normalized during the conversion.
  // For example, October 32 converts to November 1.
  //
  // A daylight savings time transition skips or repeats times.
  // For example, in the United States, March 13, 2011 2:15am never occurred,
  // while November 6, 2011 1:15am occurred twice. In such cases, the
  // choice of time zone, and therefore the time, is not well-defined.
  // Date returns a time that is correct in one of the two zones involved
  // in the transition, but it does not guarantee which.
  //
  // Date panics if loc is nil.
  func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
  	if loc == nil {
  		panic("time: missing Location in call to Date")
  	}
  
  	// Normalize month, overflowing into year.
  	m := int(month) - 1
  	year, m = norm(year, m, 12)
  	month = Month(m) + 1
  
  	// Normalize nsec, sec, min, hour, overflowing into day.
  	sec, nsec = norm(sec, nsec, 1e9)
  	min, sec = norm(min, sec, 60)
  	hour, min = norm(hour, min, 60)
  	day, hour = norm(day, hour, 24)
  
  	y := uint64(int64(year) - absoluteZeroYear)
  
  	// Compute days since the absolute epoch.
  
  	// Add in days from 400-year cycles.
  	n := y / 400
  	y -= 400 * n
  	d := daysPer400Years * n
  
  	// Add in 100-year cycles.
  	n = y / 100
  	y -= 100 * n
  	d += daysPer100Years * n
  
  	// Add in 4-year cycles.
  	n = y / 4
  	y -= 4 * n
  	d += daysPer4Years * n
  
  	// Add in non-leap years.
  	n = y
  	d += 365 * n
  
  	// Add in days before this month.
  	d += uint64(daysBefore[month-1])
  	if isLeap(year) && month >= March {
  		d++ // February 29
  	}
  
  	// Add in days before today.
  	d += uint64(day - 1)
  
  	// Add in time elapsed today.
  	abs := d * secondsPerDay
  	abs += uint64(hour*secondsPerHour + min*secondsPerMinute + sec)
  
  	unix := int64(abs) + (absoluteToInternal + internalToUnix)
  
  	// Look for zone offset for t, so we can adjust to UTC.
  	// The lookup function expects UTC, so we pass t in the
  	// hope that it will not be too close to a zone transition,
  	// and then adjust if it is.
  	_, offset, _, start, end := loc.lookup(unix)
  	if offset != 0 {
  		switch utc := unix - int64(offset); {
  		case utc < start:
  			_, offset, _, _, _ = loc.lookup(start - 1)
  		case utc >= end:
  			_, offset, _, _, _ = loc.lookup(end)
  		}
  		unix -= int64(offset)
  	}
  
  	t := Time{unix + unixToInternal, int32(nsec), nil}
  	t.setLoc(loc)
  	return t
  }
  
  // Truncate returns the result of rounding t down to a multiple of d (since the zero time).
  // If d <= 0, Truncate returns t unchanged.
  //
  // Truncate operates on the time as an absolute duration since the
  // zero time; it does not operate on the presentation form of the
  // time. Thus, Truncate(Hour) may return a time with a non-zero
  // minute, depending on the time's Location.
  func (t Time) Truncate(d Duration) Time {
  	if d <= 0 {
  		return t
  	}
  	_, r := div(t, d)
  	return t.Add(-r)
  }
  
  // Round returns the result of rounding t to the nearest multiple of d (since the zero time).
  // The rounding behavior for halfway values is to round up.
  // If d <= 0, Round returns t unchanged.
  //
  // Round operates on the time as an absolute duration since the
  // zero time; it does not operate on the presentation form of the
  // time. Thus, Round(Hour) may return a time with a non-zero
  // minute, depending on the time's Location.
  func (t Time) Round(d Duration) Time {
  	if d <= 0 {
  		return t
  	}
  	_, r := div(t, d)
  	if r+r < d {
  		return t.Add(-r)
  	}
  	return t.Add(d - r)
  }
  
  // div divides t by d and returns the quotient parity and remainder.
  // We don't use the quotient parity anymore (round half up instead of round to even)
  // but it's still here in case we change our minds.
  func div(t Time, d Duration) (qmod2 int, r Duration) {
  	neg := false
  	nsec := t.nsec
  	if t.sec < 0 {
  		// Operate on absolute value.
  		neg = true
  		t.sec = -t.sec
  		nsec = -nsec
  		if nsec < 0 {
  			nsec += 1e9
  			t.sec-- // t.sec >= 1 before the -- so safe
  		}
  	}
  
  	switch {
  	// Special case: 2d divides 1 second.
  	case d < Second && Second%(d+d) == 0:
  		qmod2 = int(nsec/int32(d)) & 1
  		r = Duration(nsec % int32(d))
  
  	// Special case: d is a multiple of 1 second.
  	case d%Second == 0:
  		d1 := int64(d / Second)
  		qmod2 = int(t.sec/d1) & 1
  		r = Duration(t.sec%d1)*Second + Duration(nsec)
  
  	// General case.
  	// This could be faster if more cleverness were applied,
  	// but it's really only here to avoid special case restrictions in the API.
  	// No one will care about these cases.
  	default:
  		// Compute nanoseconds as 128-bit number.
  		sec := uint64(t.sec)
  		tmp := (sec >> 32) * 1e9
  		u1 := tmp >> 32
  		u0 := tmp << 32
  		tmp = (sec & 0xFFFFFFFF) * 1e9
  		u0x, u0 := u0, u0+tmp
  		if u0 < u0x {
  			u1++
  		}
  		u0x, u0 = u0, u0+uint64(nsec)
  		if u0 < u0x {
  			u1++
  		}
  
  		// Compute remainder by subtracting r<<k for decreasing k.
  		// Quotient parity is whether we subtract on last round.
  		d1 := uint64(d)
  		for d1>>63 != 1 {
  			d1 <<= 1
  		}
  		d0 := uint64(0)
  		for {
  			qmod2 = 0
  			if u1 > d1 || u1 == d1 && u0 >= d0 {
  				// subtract
  				qmod2 = 1
  				u0x, u0 = u0, u0-d0
  				if u0 > u0x {
  					u1--
  				}
  				u1 -= d1
  			}
  			if d1 == 0 && d0 == uint64(d) {
  				break
  			}
  			d0 >>= 1
  			d0 |= (d1 & 1) << 63
  			d1 >>= 1
  		}
  		r = Duration(u0)
  	}
  
  	if neg && r != 0 {
  		// If input was negative and not an exact multiple of d, we computed q, r such that
  		//	q*d + r = -t
  		// But the right answers are given by -(q-1), d-r:
  		//	q*d + r = -t
  		//	-q*d - r = t
  		//	-(q-1)*d + (d - r) = t
  		qmod2 ^= 1
  		r = d - r
  	}
  	return
  }
  

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