go/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.
//
// # 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), t.Compare(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. The same applies to other functions and
// methods that subtract times, such as [Since], [Until], [Time.Before], [Time.After],
// [Time.Add], [Time.Equal] and [Time.Compare]. In some cases, you may need to strip
// the monotonic clock to get accurate results.
//
// 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.
//
// The monotonic clock reading exists only in [Time] values. It is not
// a part of [Duration] values or the Unix times returned by t.Unix and
// friends.
//
// 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().
//
// # Timer Resolution
//
// [Timer] resolution varies depending on the Go runtime, the operating system
// and the underlying hardware.
// On Unix, the resolution is ~1ms.
// On Windows version 1803 and newer, the resolution is ~0.5ms.
// On older Windows versions, the default resolution is ~16ms, but
// a higher resolution may be requested using [golang.org/x/sys/windows.TimeBeginPeriod].
package time

import (
	"errors"
	"math/bits"
	_ "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 [Time.GobDecode], [Time.UnmarshalBinary], [Time.UnmarshalJSON] and
// [Time.UnmarshalText] are not concurrency-safe.
//
// Time instants can be compared using the [Time.Before], [Time.After], and [Time.Equal] methods.
// The [Time.Sub] method subtracts two instants, producing a [Duration].
// The [Time.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 [Time.IsZero] method gives
// a simple way of detecting a time that has not been initialized explicitly.
//
// Each time has an associated [Location]. The methods [Time.Local], [Time.UTC], and Time.In return a
// Time with a specific Location. Changing the Location of a Time value with
// these methods does not change the actual instant it represents, only the time
// zone in which to interpret it.
//
// Representations of a Time value saved by the [Time.GobEncode], [Time.MarshalBinary], [Time.AppendBinary],
// [Time.MarshalJSON], [Time.MarshalText] and [Time.AppendText] 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()
	}

	// Check if the sum of t.ext and d overflows and handle it properly.
	sum := t.ext + d
	if (sum > t.ext) == (d > 0) {
		t.ext = sum
	} else if d > 0 {
		t.ext = 1<<63 - 1
	} else {
		t.ext = -(1<<63 - 1)
	}
}

// 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
}

// IsZero reports whether t represents the zero time instant,
// January 1, year 1, 00:00:00 UTC.
func (t Time) IsZero() bool {
	// If hasMonotonic is set in t.wall, then the time can't be before 1885, so it can't be the year 1.
	// If hasMonotonic is zero, then all the bits in wall other than the nanoseconds field should be 0.
	// So if there are no nanoseconds then t.wall == 0, and if there are no seconds then t.ext == 0.
	// This is equivalent to t.sec() == 0 && t.nsec() == 0, but is more efficient.
	return t.wall == 0 && t.ext == 0
}

// 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
	}
	ts := t.sec()
	us := u.sec()
	return ts < us || ts == us && t.nsec() < u.nsec()
}

// Compare compares the time instant t with u. If t is before u, it returns -1;
// if t is after u, it returns +1; if they're the same, it returns 0.
func (t Time) Compare(u Time) int {
	var tc, uc int64
	if t.wall&u.wall&hasMonotonic != 0 {
		tc, uc = t.ext, u.ext
	} else {
		tc, uc = t.sec(), u.sec()
		if tc == uc {
			tc, uc = int64(t.nsec()), int64(u.nsec())
		}
	}
	switch {
	case tc < uc:
		return -1
	case tc > uc:
		return +1
	}
	return 0
}

// 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 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
)

// String returns the English name of the month ("January", "February", ...).
func (m Month) String() string {
	if January <= m && m <= December {
		return longMonthNames[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
)

// String returns the English name of the day ("Sunday", "Monday", ...).
func (d Weekday) String() string {
	if Sunday <= d && d <= Saturday {
		return longDayNames[d]
	}
	buf := make([]byte, 20)
	n := fmtInt(buf, uint64(d))
	return "%!Weekday(" + string(buf[n:]) + ")"
}

// Computations on Times
//
// 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 date computations to choose the
// cycle boundaries so that the exceptional years are always delayed as
// long as possible: March 1, year 0 is such a day:
// the first leap day (Feb 29) is four years minus one day away,
// the first multiple-of-4 year without a Feb 29 is 100 years minus one day away,
// and the first multiple-of-100 year with a Feb 29 is 400 years minus one day away.
// March 1 year Y for any Y = 0 mod 400 is also such a day.
//
// 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
// starts on March 1 of a year equal to 0 mod 400, and that is no more than
// 2⁶³ seconds earlier than 1970—bring us to the year -292277022400.
// We refer to this moment as the absolute zero instant, 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 -292277022400.
//
// All this is opaque to clients of the API and can be changed if a
// better implementation presents itself.
//
// The date calculations are implemented using the following clever math from
// Cassio Neri and Lorenz Schneider, “Euclidean affine functions and their
// application to calendar algorithms,” SP&E 2023. https://doi.org/10.1002/spe.3172
//
// Define a “calendrical division” (f, f°, f*) to be a triple of functions converting
// one time unit into a whole number of larger units and the remainder and back.
// For example, in a calendar with no leap years, (d/365, d%365, y*365) is the
// calendrical division for days into years:
//
//	(f)  year := days/365
//	(f°) yday := days%365
//	(f*) days := year*365 (+ yday)
//
// Note that f* is usually the “easy” function to write: it's the
// calendrical multiplication that inverts the more complex division.
//
// Neri and Schneider prove that when f* takes the form
//
//	f*(n) = (a n + b) / c
//
// using integer division rounding down with a ≥ c > 0,
// which they call a Euclidean affine function or EAF, then:
//
//	f(n) = (c n + c - b - 1) / a
//	f°(n) = (c n + c - b - 1) % a / c
//
// This gives a fairly direct calculation for any calendrical division for which
// we can write the calendrical multiplication in EAF form.
// Because the epoch has been shifted to March 1, all the calendrical
// multiplications turn out to be possible to write in EAF form.
// When a date is broken into [century, cyear, amonth, mday],
// with century, cyear, and mday 0-based,
// and amonth 3-based (March = 3, ..., January = 13, February = 14),
// the calendrical multiplications written in EAF form are:
//
//	yday = (153 (amonth-3) + 2) / 5 = (153 amonth - 457) / 5
//	cday = 365 cyear + cyear/4 = 1461 cyear / 4
//	centurydays = 36524 century + century/4 = 146097 century / 4
//	days = centurydays + cday + yday + mday.
//
// We can only handle one periodic cycle per equation, so the year
// calculation must be split into [century, cyear], handling both the
// 100-year cycle and the 400-year cycle.
//
// The yday calculation is not obvious but derives from the fact
// that the March through January calendar repeats the 5-month
// 153-day cycle 31, 30, 31, 30, 31 (we don't care about February
// because yday only ever count the days _before_ February 1,
// since February is the last month).
//
// Using the rule for deriving f and f° from f*, these multiplications
// convert to these divisions:
//
//	century := (4 days + 3) / 146097
//	cdays := (4 days + 3) % 146097 / 4
//	cyear := (4 cdays + 3) / 1461
//	ayday := (4 cdays + 3) % 1461 / 4
//	amonth := (5 ayday + 461) / 153
//	mday := (5 ayday + 461) % 153 / 5
//
// The a in ayday and amonth stands for absolute (March 1-based)
// to distinguish from the standard yday (January 1-based).
//
// After computing these, we can translate from the March 1 calendar
// to the standard January 1 calendar with branch-free math assuming a
// branch-free conversion from bool to int 0 or 1, denoted int(b) here:
//
//	isJanFeb := int(yday >= marchThruDecember)
//	month := amonth - isJanFeb*12
//	year := century*100 + cyear + isJanFeb
//	isLeap := int(cyear%4 == 0) & (int(cyear != 0) | int(century%4 == 0))
//	day := 1 + mday
//	yday := 1 + ayday + 31 + 28 + isLeap&^isJanFeb - 365*isJanFeb
//
// isLeap is the standard leap-year rule, but the split year form
// makes the divisions all reduce to binary masking.
// Note that day and yday are 1-based, in contrast to mday and ayday.

// To keep the various units separate, we define integer types
// for each. These are never stored in interfaces nor allocated,
// so their type information does not appear in Go binaries.
const (
	secondsPerMinute = 60
	secondsPerHour   = 60 * secondsPerMinute
	secondsPerDay    = 24 * secondsPerHour
	secondsPerWeek   = 7 * secondsPerDay
	daysPer400Years  = 365*400 + 97

	// Days from March 1 through end of year
	marchThruDecember = 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31

	// absoluteYears is the number of years we subtract from internal time to get absolute time.
	// This value must be 0 mod 400, and it defines the “absolute zero instant”
	// mentioned in the “Computations on Times” comment above: March 1, -absoluteYears.
	// Dates before the absolute epoch will not compute correctly,
	// but otherwise the value can be changed as needed.
	absoluteYears = 292277022400

	// 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 = -(absoluteYears*365.2425 + marchThruDecember) * secondsPerDay
	internalToAbsolute       = -absoluteToInternal

	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
	internalToUnix int64 = -unixToInternal

	absoluteToUnix = absoluteToInternal + internalToUnix
	unixToAbsolute = unixToInternal + internalToAbsolute

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

// An absSeconds counts the number of seconds since the absolute zero instant.
type absSeconds uint64

// An absDays counts the number of days since the absolute zero instant.
type absDays uint64

// An absCentury counts the number of centuries since the absolute zero instant.
type absCentury uint64

// An absCyear counts the number of years since the start of a century.
type absCyear int

// An absYday counts the number of days since the start of a year.
// Note that absolute years start on March 1.
type absYday int

// An absMonth counts the number of months since the start of a year.
// absMonth=0 denotes March.
type absMonth int

// An absLeap is a single bit (0 or 1) denoting whether a given year is a leap year.
type absLeap int

// An absJanFeb is a single bit (0 or 1) denoting whether a given day falls in January or February.
// That is a special case because the absolute years start in March (unlike normal calendar years).
type absJanFeb int

// dateToAbsDays takes a standard year/month/day and returns the
// number of days from the absolute epoch to that day.
// The days argument can be out of range and in particular can be negative.
func dateToAbsDays(year int64, month Month, day int) absDays {
	// See “Computations on Times” comment above.
	amonth := uint32(month)
	janFeb := uint32(0)
	if amonth < 3 {
		janFeb = 1
	}
	amonth += 12 * janFeb
	y := uint64(year) - uint64(janFeb) + absoluteYears

	// For amonth is in the range [3,14], we want:
	//
	//	ayday := (153*amonth - 457) / 5
	//
	// (See the “Computations on Times” comment above
	// as well as Neri and Schneider, section 7.)
	//
	// That is equivalent to:
	//
	//	ayday := (979*amonth - 2919) >> 5
	//
	// and the latter form uses a couple fewer instructions,
	// so use it, saving a few cycles.
	// See Neri and Schneider, section 8.3
	// for more about this optimization.
	//
	// (Note that there is no saved division, because the compiler
	// implements / 5 without division in all cases.)
	ayday := (979*amonth - 2919) >> 5

	century := y / 100
	cyear := uint32(y % 100)
	cday := 1461 * cyear / 4
	centurydays := 146097 * century / 4

	return absDays(centurydays + uint64(int64(cday+ayday)+int64(day)-1))
}

// days converts absolute seconds to absolute days.
func (abs absSeconds) days() absDays {
	return absDays(abs / secondsPerDay)
}

// split splits days into century, cyear, ayday.
func (days absDays) split() (century absCentury, cyear absCyear, ayday absYday) {
	// See “Computations on Times” comment above.
	d := 4*uint64(days) + 3
	century = absCentury(d / 146097)

	// This should be
	//	cday := uint32(d % 146097) / 4
	//	cd := 4*cday + 3
	// which is to say
	//	cday := uint32(d % 146097) >> 2
	//	cd := cday<<2 + 3
	// but of course (x>>2<<2)+3 == x|3,
	// so do that instead.
	cd := uint32(d%146097) | 3

	// For cdays in the range [0,146097] (100 years), we want:
	//
	//	cyear := (4 cdays + 3) / 1461
	//	yday := (4 cdays + 3) % 1461 / 4
	//
	// (See the “Computations on Times” comment above
	// as well as Neri and Schneider, section 7.)
	//
	// That is equivalent to:
	//
	//	cyear := (2939745 cdays) >> 32
	//	yday := (2939745 cdays) & 0xFFFFFFFF / 2939745 / 4
	//
	// so do that instead, saving a few cycles.
	// See Neri and Schneider, section 8.3
	// for more about this optimization.
	hi, lo := bits.Mul32(2939745, cd)
	cyear = absCyear(hi)
	ayday = absYday(lo / 2939745 / 4)
	return
}

// split splits ayday into absolute month and standard (1-based) day-in-month.
func (ayday absYday) split() (m absMonth, mday int) {
	// See “Computations on Times” comment above.
	//
	// For yday in the range [0,366],
	//
	//	amonth := (5 yday + 461) / 153
	//	mday := (5 yday + 461) % 153 / 5
	//
	// is equivalent to:
	//
	//	amonth = (2141 yday + 197913) >> 16
	//	mday = (2141 yday + 197913) & 0xFFFF / 2141
	//
	// so do that instead, saving a few cycles.
	// See Neri and Schneider, section 8.3.
	d := 2141*uint32(ayday) + 197913
	return absMonth(d >> 16), 1 + int((d&0xFFFF)/2141)
}

// janFeb returns 1 if the March 1-based ayday is in January or February, 0 otherwise.
func (ayday absYday) janFeb() absJanFeb {
	// See “Computations on Times” comment above.
	jf := absJanFeb(0)
	if ayday >= marchThruDecember {
		jf = 1
	}
	return jf
}

// month returns the standard Month for (m, janFeb)
func (m absMonth) month(janFeb absJanFeb) Month {
	// See “Computations on Times” comment above.
	return Month(m) - Month(janFeb)*12
}

// leap returns 1 if (century, cyear) is a leap year, 0 otherwise.
func (century absCentury) leap(cyear absCyear) absLeap {
	// See “Computations on Times” comment above.
	y4ok := 0
	if cyear%4 == 0 {
		y4ok = 1
	}
	y100ok := 0
	if cyear != 0 {
		y100ok = 1
	}
	y400ok := 0
	if century%4 == 0 {
		y400ok = 1
	}
	return absLeap(y4ok & (y100ok | y400ok))
}

// year returns the standard year for (century, cyear, janFeb).
func (century absCentury) year(cyear absCyear, janFeb absJanFeb) int {
	// See “Computations on Times” comment above.
	return int(uint64(century)*100-absoluteYears) + int(cyear) + int(janFeb)
}

// yday returns the standard 1-based yday for (ayday, janFeb, leap).
func (ayday absYday) yday(janFeb absJanFeb, leap absLeap) int {
	// See “Computations on Times” comment above.
	return int(ayday) + (1 + 31 + 28) + int(leap)&^int(janFeb) - 365*int(janFeb)
}

// date converts days into standard year, month, day.
func (days absDays) date() (year int, month Month, day int) {
	century, cyear, ayday := days.split()
	amonth, day := ayday.split()
	janFeb := ayday.janFeb()
	year = century.year(cyear, janFeb)
	month = amonth.month(janFeb)
	return
}

// yearYday converts days into the standard year and 1-based yday.
func (days absDays) yearYday() (year, yday int) {
	century, cyear, ayday := days.split()
	janFeb := ayday.janFeb()
	year = century.year(cyear, janFeb)
	yday = ayday.yday(janFeb, century.leap(cyear))
	return
}

// absSec returns the time t as an absolute seconds, adjusted by the zone offset.
// It is called when computing a presentation property like Month or Hour.
// We'd rather call it abs, but there are linknames to abs that make that problematic.
// See timeAbs below.
func (t Time) absSec() absSeconds {
	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 absSeconds(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 absSeconds) {
	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 = absSeconds(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) {
	return t.absSec().days().date()
}

// Year returns the year in which t occurs.
func (t Time) Year() int {
	century, cyear, ayday := t.absSec().days().split()
	janFeb := ayday.janFeb()
	return century.year(cyear, janFeb)
}

// Month returns the month of the year specified by t.
func (t Time) Month() Month {
	_, _, ayday := t.absSec().days().split()
	amonth, _ := ayday.split()
	return amonth.month(ayday.janFeb())
}

// Day returns the day of the month specified by t.
func (t Time) Day() int {
	_, _, ayday := t.absSec().days().split()
	_, day := ayday.split()
	return day
}

// Weekday returns the day of the week specified by t.
func (t Time) Weekday() Weekday {
	return t.absSec().days().weekday()
}

// weekday returns the day of the week specified by days.
func (days absDays) weekday() Weekday {
	// March 1 of the absolute year, like March 1 of 2000, was a Wednesday.
	return Weekday((uint64(days) + uint64(Wednesday)) % 7)
}

// 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) {
	// According to the rule that the first calendar week of a calendar year is
	// the week including the first Thursday of that year, and that the last one is
	// the week immediately preceding the first calendar week of the next calendar year.
	// See https://www.iso.org/obp/ui#iso:std:iso:8601:-1:ed-1:v1:en:term:3.1.1.23 for details.

	// weeks start with Monday
	// Monday Tuesday Wednesday Thursday Friday Saturday Sunday
	// 1      2       3         4        5      6        7
	// +3     +2      +1        0        -1     -2       -3
	// the offset to Thursday
	days := t.absSec().days()
	thu := days + absDays(Thursday-((days-1).weekday()+1))
	year, yday := thu.yearYday()
	return year, (yday-1)/7 + 1
}

// Clock returns the hour, minute, and second within the day specified by t.
func (t Time) Clock() (hour, min, sec int) {
	return t.absSec().clock()
}

// clock returns the hour, minute, and second within the day specified by abs.
func (abs absSeconds) clock() (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.absSec()%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.absSec()%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.absSec() % 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.absSec().days().yearYday()
	return yday
}

// 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 {
	// This is inlinable to take advantage of "function outlining".
	// Thus, the caller can decide whether a string must be heap allocated.
	var arr [32]byte
	n := d.format(&arr)
	return string(arr[n:])
}

// format formats the representation of d into the end of buf and
// returns the offset of the first character.
func (d Duration) format(buf *[32]byte) int {
	// Largest time is 2540400h10m10.000000000s
	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:
			buf[w] = '0'
			return w
		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 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
}

// Abs returns the absolute value of d.
// As a special case, Duration([math.MinInt64]) is converted to Duration([math.MaxInt64]),
// reducing its magnitude by 1 nanosecond.
func (d Duration) Abs() Duration {
	switch {
	case d >= 0:
		return d
	case d == minDuration:
		return maxDuration
	default:
		return -d
	}
}

// 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 {
		return subMono(t.ext, u.ext)
	}
	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
	}
}

func subMono(t, u int64) Duration {
	d := Duration(t - u)
	if d < 0 && t > u {
		return maxDuration // t - u is positive out of range
	}
	if d > 0 && t < u {
		return minDuration // t - u is negative out of range
	}
	return d
}

// Since returns the time elapsed since t.
// It is shorthand for time.Now().Sub(t).
func Since(t Time) Duration {
	if t.wall&hasMonotonic != 0 && !runtimeIsBubbled() {
		// Common case optimization: if t has monotonic time, then Sub will use only it.
		return subMono(runtimeNano()-startNano, t.ext)
	}
	return Now().Sub(t)
}

// Until returns the duration until t.
// It is shorthand for t.Sub(time.Now()).
func Until(t Time) Duration {
	if t.wall&hasMonotonic != 0 && !runtimeIsBubbled() {
		// Common case optimization: if t has monotonic time, then Sub will use only it.
		return subMono(t.ext, runtimeNano()-startNano)
	}
	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.
//
// Note that dates are fundamentally coupled to timezones, and calendrical
// periods like days don't have fixed durations. AddDate uses the Location of
// the Time value to determine these durations. That means that the same
// AddDate arguments can produce a different shift in absolute time depending on
// the base Time value and its Location. For example, AddDate(0, 0, 1) applied
// to 12:00 on March 27 always returns 12:00 on March 28. At some locations and
// in some years this is a 24 hour shift. In others it's a 23 hour shift due to
// daylight savings time transitions.
//
// 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())
}

// daysBefore returns the number of days in a non-leap year before month m.
// daysBefore(December+1) returns 365.
func daysBefore(m Month) int {
	adj := 0
	if m >= March {
		adj = -2
	}

	// With the -2 adjustment after February,
	// we need to compute the running sum of:
	//	0  31  30  31  30  31  30  31  31  30  31  30  31
	// which is:
	//	0  31  61  92 122 153 183 214 245 275 306 336 367
	// This is almost exactly 367/12×(m-1) except for the
	// occasonal off-by-one suggesting there may be an
	// integer approximation of the form (a×m + b)/c.
	// A brute force search over small a, b, c finds that
	// (214×m - 211) / 7 computes the function perfectly.
	return (214*int(m)-211)/7 + adj
}

func daysIn(m Month, year int) int {
	if m == February {
		if isLeap(year) {
			return 29
		}
		return 28
	}
	// With the special case of February eliminated, the pattern is
	//	31 30 31 30 31 30 31 31 30 31 30 31
	// Adding m&1 produces the basic alternation;
	// adding (m>>3)&1 inverts the alternation starting in August.
	return 30 + int((m+m>>3)&1)
}

// Provided by package runtime.
//
// now returns the current real time, and is superseded by runtimeNow which returns
// the fake synctest clock when appropriate.
//
// now should be an internal detail,
// but widely used packages access it using linkname.
// Notable members of the hall of shame include:
//   - gitee.com/quant1x/gox
//   - github.com/phuslu/log
//   - github.com/sethvargo/go-limiter
//   - github.com/ulule/limiter/v3
//
// Do not remove or change the type signature.
// See go.dev/issue/67401.
func now() (sec int64, nsec int32, mono int64)

// runtimeNow returns the current time.
// When called within a synctest.Run bubble, it returns the group's fake clock.
//
//go:linkname runtimeNow
func runtimeNow() (sec int64, nsec int32, mono int64)

// runtimeNano returns the current value of the runtime clock in nanoseconds.
// When called within a synctest.Run bubble, it returns the group's fake clock.
//
//go:linkname runtimeNano
func runtimeNano() int64

//go:linkname runtimeIsBubbled
func runtimeIsBubbled() bool

// 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

// x/tools uses a linkname of time.Now in its tests. No harm done.
//go:linkname Now

// Now returns the current local time.
func Now() Time {
	sec, nsec, mono := runtimeNow()
	if mono == 0 {
		return Time{uint64(nsec), sec + unixToInternal, Local}
	}
	mono -= startNano
	sec += unixToInternal - minWall
	if uint64(sec)>>33 != 0 {
		// Seconds field overflowed the 33 bits available when
		// storing a monotonic time. This will be true after
		// March 16, 2157.
		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
}

// ZoneBounds returns the bounds of the time zone in effect at time t.
// The zone begins at start and the next zone begins at end.
// If the zone begins at the beginning of time, start will be returned as a zero Time.
// If the zone goes on forever, end will be returned as a zero Time.
// The Location of the returned times will be the same as t.
func (t Time) ZoneBounds() (start, end Time) {
	_, _, startSec, endSec, _ := t.loc.lookup(t.unixSec())
	if startSec != alpha {
		start = unixTime(startSec, 0)
		start.setLoc(t.loc)
	}
	if endSec != omega {
		end = unixTime(endSec, 0)
		end.setLoc(t.loc)
	}
	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.
// Unix-like operating systems often record time as a 32-bit
// count of seconds, but since the method here returns a 64-bit
// value it is valid for billions of years into the past or future.
func (t Time) Unix() int64 {
	return t.unixSec()
}

// UnixMilli returns t as a Unix time, the number of milliseconds elapsed since
// January 1, 1970 UTC. The result is undefined if the Unix time in
// milliseconds cannot be represented by an int64 (a date more than 292 million
// years before or after 1970). The result does not depend on the
// location associated with t.
func (t Time) UnixMilli() int64 {
	return t.unixSec()*1e3 + int64(t.nsec())/1e6
}

// UnixMicro returns t as a Unix time, the number of microseconds elapsed since
// January 1, 1970 UTC. The result is undefined if the Unix time in
// microseconds cannot be represented by an int64 (a date before year -290307 or
// after year 294246). The result does not depend on the location associated
// with t.
func (t Time) UnixMicro() int64 {
	return t.unixSec()*1e6 + int64(t.nsec())/1e3
}

// 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 (
	timeBinaryVersionV1 byte = iota + 1 // For general situation
	timeBinaryVersionV2                 // For LMT only
)

// AppendBinary implements the [encoding.BinaryAppender] interface.
func (t Time) AppendBinary(b []byte) ([]byte, error) {
	var offsetMin int16 // minutes east of UTC. -1 is UTC.
	var offsetSec int8
	version := timeBinaryVersionV1

	if t.Location() == UTC {
		offsetMin = -1
	} else {
		_, offset := t.Zone()
		if offset%60 != 0 {
			version = timeBinaryVersionV2
			offsetSec = int8(offset % 60)
		}

		offset /= 60
		if offset < -32768 || offset == -1 || offset > 32767 {
			return b, errors.New("Time.MarshalBinary: unexpected zone offset")
		}
		offsetMin = int16(offset)
	}

	sec := t.sec()
	nsec := t.nsec()
	b = append(b,
		version,       // 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),
	)
	if version == timeBinaryVersionV2 {
		b = append(b, byte(offsetSec))
	}
	return b, nil
}

// MarshalBinary implements the [encoding.BinaryMarshaler] interface.
func (t Time) MarshalBinary() ([]byte, error) {
	b, err := t.AppendBinary(make([]byte, 0, 16))
	if err != nil {
		return nil, err
	}
	return b, 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")
	}

	version := buf[0]
	if version != timeBinaryVersionV1 && version != timeBinaryVersionV2 {
		return errors.New("Time.UnmarshalBinary: unsupported version")
	}

	wantLen := /*version*/ 1 + /*sec*/ 8 + /*nsec*/ 4 + /*zone offset*/ 2
	if version == timeBinaryVersionV2 {
		wantLen++
	}
	if len(buf) != wantLen {
		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
	if version == timeBinaryVersionV2 {
		offset += int(buf[2])
	}

	*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 [encoding/json.Marshaler] interface.
// The time is a quoted string in the RFC 3339 format with sub-second precision.
// If the timestamp cannot be represented as valid RFC 3339
// (e.g., the year is out of range), then an error is reported.
func (t Time) MarshalJSON() ([]byte, error) {
	b := make([]byte, 0, len(RFC3339Nano)+len(`""`))
	b = append(b, '"')
	b, err := t.appendStrictRFC3339(b)
	b = append(b, '"')
	if err != nil {
		return nil, errors.New("Time.MarshalJSON: " + err.Error())
	}
	return b, nil
}

// UnmarshalJSON implements the [encoding/json.Unmarshaler] interface.
// The time must be a quoted string in the RFC 3339 format.
func (t *Time) UnmarshalJSON(data []byte) error {
	if string(data) == "null" {
		return nil
	}
	// TODO(https://go.dev/issue/47353): Properly unescape a JSON string.
	if len(data) < 2 || data[0] != '"' || data[len(data)-1] != '"' {
		return errors.New("Time.UnmarshalJSON: input is not a JSON string")
	}
	data = data[len(`"`) : len(data)-len(`"`)]
	var err error
	*t, err = parseStrictRFC3339(data)
	return err
}

func (t Time) appendTo(b []byte, errPrefix string) ([]byte, error) {
	b, err := t.appendStrictRFC3339(b)
	if err != nil {
		return nil, errors.New(errPrefix + err.Error())
	}
	return b, nil
}

// AppendText implements the [encoding.TextAppender] interface.
// The time is formatted in RFC 3339 format with sub-second precision.
// If the timestamp cannot be represented as valid RFC 3339
// (e.g., the year is out of range), then an error is returned.
func (t Time) AppendText(b []byte) ([]byte, error) {
	return t.appendTo(b, "Time.AppendText: ")
}

// MarshalText implements the [encoding.TextMarshaler] interface. The output
// matches that of calling the [Time.AppendText] method.
//
// See [Time.AppendText] for more information.
func (t Time) MarshalText() ([]byte, error) {
	return t.appendTo(make([]byte, 0, len(RFC3339Nano)), "Time.MarshalText: ")
}

// UnmarshalText implements the [encoding.TextUnmarshaler] interface.
// The time must be in the RFC 3339 format.
func (t *Time) UnmarshalText(data []byte) error {
	var err error
	*t, err = parseStrictRFC3339(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))
}

// UnixMilli returns the local Time corresponding to the given Unix time,
// msec milliseconds since January 1, 1970 UTC.
func UnixMilli(msec int64) Time {
	return Unix(msec/1e3, (msec%1e3)*1e6)
}

// UnixMicro returns the local Time corresponding to the given Unix time,
// usec microseconds since January 1, 1970 UTC.
func UnixMicro(usec int64) Time {
	return Unix(usec/1e6, (usec%1e6)*1e3)
}

// IsDST reports whether the time in the configured location is in Daylight Savings Time.
func (t Time) IsDST() bool {
	_, _, _, _, isDST := t.loc.lookup(t.Unix())
	return isDST
}

func isLeap(year int) bool {
	// year%4 == 0 && (year%100 != 0 || year%400 == 0)
	// Bottom 2 bits must be clear.
	// For multiples of 25, bottom 4 bits must be clear.
	// Thanks to Cassio Neri for this trick.
	mask := 0xf
	if year%25 != 0 {
		mask = 3
	}
	return year&mask == 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)

	// Convert to absolute time and then Unix time.
	unix := int64(dateToAbsDays(int64(year), month, day))*secondsPerDay +
		int64(hour*secondsPerHour+min*secondsPerMinute+sec) +
		absoluteToUnix

	// Look for zone offset for expected time, so we can adjust to UTC.
	// The lookup function expects UTC, so first we pass unix 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 {
		utc := unix - int64(offset)
		// If utc is valid for the time zone we found, then we have the right offset.
		// If not, we get the correct offset by looking up utc in the location.
		if utc < start || utc >= end {
			_, offset, _, _, _ = loc.lookup(utc)
		}
		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
}

// Regrettable Linkname Compatibility
//
// timeAbs, absDate, and absClock mimic old internal details, no longer used.
// Widely used packages linknamed these to get “faster” time routines.
// Notable members of the hall of shame include:
//   - gitee.com/quant1x/gox
//   - github.com/phuslu/log
//
// phuslu hard-coded 'Unix time + 9223372028715321600' [sic]
// as the input to absDate and absClock, using the old Jan 1-based
// absolute times.
// quant1x linknamed the time.Time.abs method and passed the
// result of that method to absDate and absClock.
//
// Keeping both of these working forces us to provide these three
// routines here, operating on the old Jan 1-based epoch instead
// of the new March 1-based epoch. And the fact that time.Time.abs
// was linknamed means that we have to call the current abs method
// something different (time.Time.absSec, defined above) to make it
// possible to provide this simulation of the old routines here.
//
// None of this code is linked into the binary if not referenced by
// these linkname-happy packages. In particular, despite its name,
// time.Time.abs does not appear in the time.Time method table.
//
// Do not remove these routines or their linknames, or change the
// type signature or meaning of arguments.

//go:linkname legacyTimeTimeAbs time.Time.abs
func legacyTimeTimeAbs(t Time) uint64 {
	return uint64(t.absSec() - marchThruDecember*secondsPerDay)
}

//go:linkname legacyAbsClock time.absClock
func legacyAbsClock(abs uint64) (hour, min, sec int) {
	return absSeconds(abs + marchThruDecember*secondsPerDay).clock()
}

//go:linkname legacyAbsDate time.absDate
func legacyAbsDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
	d := absSeconds(abs + marchThruDecember*secondsPerDay).days()
	year, month, day = d.date()
	_, yday = d.yearYday()
	yday-- // yearYday is 1-based, old API was 0-based
	return
}