[platform/upstream/gcc.git] / libgo / go / 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.
//
// Monotonic Clocks
//
// Operating systems provide both a “wall clock,” which is subject to
// changes for clock synchronization, and a “monotonic clock,” which is
// not. The general rule is that the wall clock is for telling time and
// the monotonic clock is for measuring time. Rather than split the API,
// in this package the Time returned by time.Now contains both a wall
// clock reading and a monotonic clock reading; later time-telling
// operations use the wall clock reading, but later time-measuring
// operations, specifically comparisons and subtractions, use the
// monotonic clock reading.
//
// For example, this code always computes a positive elapsed time of
// approximately 20 milliseconds, even if the wall clock is changed during
// the operation being timed:
//
//      start := time.Now()
//      ... operation that takes 20 milliseconds ...
//      t := time.Now()
//      elapsed := t.Sub(start)
//
// Other idioms, such as time.Since(start), time.Until(deadline), and
// time.Now().Before(deadline), are similarly robust against wall clock
// resets.
//
// The rest of this section gives the precise details of how operations
// use monotonic clocks, but understanding those details is not required
// to use this package.
//
// The Time returned by time.Now contains a monotonic clock reading.
// If Time t has a monotonic clock reading, t.Add adds the same duration to
// both the wall clock and monotonic clock readings to compute the result.
// Because t.AddDate(y, m, d), t.Round(d), and t.Truncate(d) are wall time
// computations, they always strip any monotonic clock reading from their results.
// Because t.In, t.Local, and t.UTC are used for their effect on the interpretation
// of the wall time, they also strip any monotonic clock reading from their results.
// The canonical way to strip a monotonic clock reading is to use t = t.Round(0).
//
// If Times t and u both contain monotonic clock readings, the operations
// t.After(u), t.Before(u), t.Equal(u), and t.Sub(u) are carried out
// using the monotonic clock readings alone, ignoring the wall clock
// readings. If either t or u contains no monotonic clock reading, these
// operations fall back to using the wall clock readings.
//
// On some systems the monotonic clock will stop if the computer goes to sleep.
// On such a system, t.Sub(u) may not accurately reflect the actual
// time that passed between t and u.
//
// Because the monotonic clock reading has no meaning outside
// the current process, the serialized forms generated by t.GobEncode,
// t.MarshalBinary, t.MarshalJSON, and t.MarshalText omit the monotonic
// clock reading, and t.Format provides no format for it. Similarly, the
// constructors time.Date, time.Parse, time.ParseInLocation, and time.Unix,
// as well as the unmarshalers t.GobDecode, t.UnmarshalBinary.
// t.UnmarshalJSON, and t.UnmarshalText always create times with
// no monotonic clock reading.
//
// Note that the Go == operator compares not just the time instant but
// also the Location and the monotonic clock reading. See the
// documentation for the Time type for a discussion of equality
// testing for Time values.
//
// For debugging, the result of t.String does include the monotonic
// clock reading if present. If t != u because of different monotonic clock readings,
// that difference will be visible when printing t.String() and u.String().
//
package time

import (
        "errors"
        _ "unsafe" // for go:linkname
)

// 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 except
// that the methods GobDecode, UnmarshalBinary, UnmarshalJSON and
// UnmarshalText are not concurrency-safe.
//
// 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.
//
// Representations of a Time value saved by the GobEncode, MarshalBinary,
// MarshalJSON, and MarshalText methods store the Time.Location's offset, but not
// the location name. They therefore lose information about Daylight Saving Time.
//
// In addition to the required “wall clock” reading, a Time may contain an optional
// reading of the current process's monotonic clock, to provide additional precision
// for comparison or subtraction.
// See the “Monotonic Clocks” section in the package documentation for details.
//
// Note that the Go == operator compares not just the time instant but also the
// Location and the monotonic clock reading. 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, and that the monotonic clock reading
// has been stripped by setting t = t.Round(0). In general, prefer t.Equal(u)
// to t == u, since t.Equal uses the most accurate comparison available and
// correctly handles the case when only one of its arguments has a monotonic
// clock reading.
//
type Time struct {
        // wall and ext encode the wall time seconds, wall time nanoseconds,
        // and optional monotonic clock reading in nanoseconds.
        //
        // From high to low bit position, wall encodes a 1-bit flag (hasMonotonic),
        // a 33-bit seconds field, and a 30-bit wall time nanoseconds field.
        // The nanoseconds field is in the range [0, 999999999].
        // If the hasMonotonic bit is 0, then the 33-bit field must be zero
        // and the full signed 64-bit wall seconds since Jan 1 year 1 is stored in ext.
        // If the hasMonotonic bit is 1, then the 33-bit field holds a 33-bit
        // unsigned wall seconds since Jan 1 year 1885, and ext holds a
        // signed 64-bit monotonic clock reading, nanoseconds since process start.
        wall uint64
        ext  int64

        // 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
}

const (
        hasMonotonic = 1 << 63
        maxWall      = wallToInternal + (1<<33 - 1) // year 2157
        minWall      = wallToInternal               // year 1885
        nsecMask     = 1<<30 - 1
        nsecShift    = 30
)

// These helpers for manipulating the wall and monotonic clock readings
// take pointer receivers, even when they don't modify the time,
// to make them cheaper to call.

// nsec returns the time's nanoseconds.
func (t *Time) nsec() int32 {
        return int32(t.wall & nsecMask)
}

// sec returns the time's seconds since Jan 1 year 1.
func (t *Time) sec() int64 {
        if t.wall&hasMonotonic != 0 {
                return wallToInternal + int64(t.wall<<1>>(nsecShift+1))
        }
        return t.ext
}

// unixSec returns the time's seconds since Jan 1 1970 (Unix time).
func (t *Time) unixSec() int64 { return t.sec() + internalToUnix }

// addSec adds d seconds to the time.
func (t *Time) addSec(d int64) {
        if t.wall&hasMonotonic != 0 {
                sec := int64(t.wall << 1 >> (nsecShift + 1))
                dsec := sec + d
                if 0 <= dsec && dsec <= 1<<33-1 {
                        t.wall = t.wall&nsecMask | uint64(dsec)<<nsecShift | hasMonotonic
                        return
                }
                // Wall second now out of range for packed field.
                // Move to ext.
                t.stripMono()
        }

        // TODO: Check for overflow.
        t.ext += d
}

// setLoc sets the location associated with the time.
func (t *Time) setLoc(loc *Location) {
        if loc == &utcLoc {
                loc = nil
        }
        t.stripMono()
        t.loc = loc
}

// stripMono strips the monotonic clock reading in t.
func (t *Time) stripMono() {
        if t.wall&hasMonotonic != 0 {
                t.ext = t.sec()
                t.wall &= nsecMask
        }
}

// setMono sets the monotonic clock reading in t.
// If t cannot hold a monotonic clock reading,
// because its wall time is too large,
// setMono is a no-op.
func (t *Time) setMono(m int64) {
        if t.wall&hasMonotonic == 0 {
                sec := t.ext
                if sec < minWall || maxWall < sec {
                        return
                }
                t.wall |= hasMonotonic | uint64(sec-minWall)<<nsecShift
        }
        t.ext = m
}

// mono returns t's monotonic clock reading.
// It returns 0 for a missing reading.
// This function is used only for testing,
// so it's OK that technically 0 is a valid
// monotonic clock reading as well.
func (t *Time) mono() int64 {
        if t.wall&hasMonotonic == 0 {
                return 0
        }
        return t.ext
}

// After reports whether the time instant t is after u.
func (t Time) After(u Time) bool {
        if t.wall&u.wall&hasMonotonic != 0 {
                return t.ext > u.ext
        }
        ts := t.sec()
        us := u.sec()
        return ts > us || ts == us && t.nsec() > u.nsec()
}

// Before reports whether the time instant t is before u.
func (t Time) Before(u Time) bool {
        if t.wall&u.wall&hasMonotonic != 0 {
                return t.ext < u.ext
        }
        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.
// See the documentation on the Time type for the pitfalls of using == with
// Time values; most code should use Equal instead.
func (t Time) Equal(u Time) bool {
        if t.wall&u.wall&hasMonotonic != 0 {
                return t.ext == u.ext
        }
        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 {
        if Sunday <= d && d <= Saturday {
                return days[d]
        }
        buf := make([]byte, 20)
        n := fmtInt(buf, uint64(d))
        return "%!Weekday(" + string(buf[n:]) + ")"
}

// 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 1970-2369 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

        wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
        internalToWall int64 = -wallToInternal
)

// 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.unixSec()
        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.unixSec()
        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) }

// Microseconds returns the duration as an integer microsecond count.
func (d Duration) Microseconds() int64 { return int64(d) / 1e3 }

// Milliseconds returns the duration as an integer millisecond count.
func (d Duration) Milliseconds() int64 { return int64(d) / 1e6 }

// 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)
}

// Truncate returns the result of rounding d toward zero to a multiple of m.
// If m <= 0, Truncate returns d unchanged.
func (d Duration) Truncate(m Duration) Duration {
        if m <= 0 {
                return d
        }
        return d - d%m
}

// lessThanHalf reports whether x+x < y but avoids overflow,
// assuming x and y are both positive (Duration is signed).
func lessThanHalf(x, y Duration) bool {
        return uint64(x)+uint64(x) < uint64(y)
}

// Round returns the result of rounding d to the nearest multiple of m.
// The rounding behavior for halfway values is to round away from zero.
// If the result exceeds the maximum (or minimum)
// value that can be stored in a Duration,
// Round returns the maximum (or minimum) duration.
// If m <= 0, Round returns d unchanged.
func (d Duration) Round(m Duration) Duration {
        if m <= 0 {
                return d
        }
        r := d % m
        if d < 0 {
                r = -r
                if lessThanHalf(r, m) {
                        return d + r
                }
                if d1 := d - m + r; d1 < d {
                        return d1
                }
                return minDuration // overflow
        }
        if lessThanHalf(r, m) {
                return d - r
        }
        if d1 := d + m - r; d1 > d {
                return d1
        }
        return maxDuration // overflow
}

// Add returns the time t+d.
func (t Time) Add(d Duration) Time {
        dsec := int64(d / 1e9)
        nsec := t.nsec() + int32(d%1e9)
        if nsec >= 1e9 {
                dsec++
                nsec -= 1e9
        } else if nsec < 0 {
                dsec--
                nsec += 1e9
        }
        t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
        t.addSec(dsec)
        if t.wall&hasMonotonic != 0 {
                te := t.ext + int64(d)
                if d < 0 && te > t.ext || d > 0 && te < t.ext {
                        // Monotonic clock reading now out of range; degrade to wall-only.
                        t.stripMono()
                } else {
                        t.ext = te
                }
        }
        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 {
        if t.wall&u.wall&hasMonotonic != 0 {
                te := t.ext
                ue := u.ext
                d := Duration(te - ue)
                if d < 0 && te > ue {
                        return maxDuration // t - u is positive out of range
                }
                if d > 0 && te < ue {
                        return minDuration // t - u is negative out of range
                }
                return d
        }
        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 {
        var now Time
        if t.wall&hasMonotonic != 0 {
                // Common case optimization: if t has monotonic time, then Sub will use only it.
                now = Time{hasMonotonic, runtimeNano() - startNano, nil}
        } else {
                now = Now()
        }
        return now.Sub(t)
}

// Until returns the duration until t.
// It is shorthand for t.Sub(time.Now()).
func Until(t Time) Duration {
        var now Time
        if t.wall&hasMonotonic != 0 {
                // Common case optimization: if t has monotonic time, then Sub will use only it.
                now = Time{hasMonotonic, runtimeNano() - startNano, nil}
        } else {
                now = Now()
        }
        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 * secondsPerMinute
        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, mono int64)

// runtimeNano returns the current value of the runtime clock in nanoseconds.
//go:linkname runtimeNano runtime.nanotime
func runtimeNano() int64

// Monotonic times are reported as offsets from startNano.
// We initialize startNano to runtimeNano() - 1 so that on systems where
// monotonic time resolution is fairly low (e.g. Windows 2008
// which appears to have a default resolution of 15ms),
// we avoid ever reporting a monotonic time of 0.
// (Callers may want to use 0 as "time not set".)
var startNano int64 = runtimeNano() - 1

// Now returns the current local time.
func Now() Time {
        sec, nsec, mono := now()
        mono -= startNano
        sec += unixToInternal - minWall
        if uint64(sec)>>33 != 0 {
                return Time{uint64(nsec), sec + minWall, Local}
        }
        return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
}

func unixTime(sec int64, nsec int32) Time {
        return Time{uint64(nsec), sec + unixToInternal, 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 a copy of t representing the same time instant, but
// with the copy's location information set to loc for display
// purposes.
//
// 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.unixSec())
        return
}

// Unix returns t as a Unix time, the number of seconds elapsed
// since January 1, 1970 UTC. The result does not depend on the
// location associated with t.
func (t Time) Unix() int64 {
        return t.unixSec()
}

// 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. The result does not depend on the
// location associated with t.
func (t Time) UnixNano() int64 {
        return (t.unixSec())*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)
        }

        sec := t.sec()
        nsec := t.nsec()
        enc := []byte{
                timeBinaryVersion, // byte 0 : version
                byte(sec >> 56),   // bytes 1-8: seconds
                byte(sec >> 48),
                byte(sec >> 40),
                byte(sec >> 32),
                byte(sec >> 24),
                byte(sec >> 16),
                byte(sec >> 8),
                byte(sec),
                byte(nsec >> 24), // bytes 9-12: nanoseconds
                byte(nsec >> 16),
                byte(nsec >> 8),
                byte(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:]
        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:]
        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

        *t = Time{}
        t.wall = uint64(nsec)
        t.ext = sec

        if offset == -1*60 {
                t.setLoc(&utcLoc)
        } else if _, localoff, _, _ := Local.lookup(t.unixSec()); 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 unixTime(sec, int32(nsec))
}

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 := unixTime(unix, int32(nsec))
        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 stripped of any monotonic clock reading but otherwise 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 {
        t.stripMono()
        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 stripped of any monotonic clock reading but otherwise 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 {
        t.stripMono()
        if d <= 0 {
                return t
        }
        _, r := div(t, d)
        if lessThanHalf(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()
        sec := t.sec()
        if sec < 0 {
                // Operate on absolute value.
                neg = true
                sec = -sec
                nsec = -nsec
                if nsec < 0 {
                        nsec += 1e9
                        sec-- // 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(sec/d1) & 1
                r = Duration(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(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
}