time.mx raw

   1  // Copyright 2009 The Go Authors. All rights reserved.
   2  // Use of this source code is governed by a BSD-style
   3  // license that can be found in the LICENSE file.
   4  
   5  // Package time provides functionality for measuring and displaying time.
   6  //
   7  // The calendrical calculations always assume a Gregorian calendar, with
   8  // no leap seconds.
   9  //
  10  // # Monotonic Clocks
  11  //
  12  // Operating systems provide both a “wall clock,” which is subject to
  13  // changes for clock synchronization, and a “monotonic clock,” which is
  14  // not. The general rule is that the wall clock is for telling time and
  15  // the monotonic clock is for measuring time. Rather than split the API,
  16  // in this package the Time returned by [time.Now] contains both a wall
  17  // clock reading and a monotonic clock reading; later time-telling
  18  // operations use the wall clock reading, but later time-measuring
  19  // operations, specifically comparisons and subtractions, use the
  20  // monotonic clock reading.
  21  //
  22  // For example, this code always computes a positive elapsed time of
  23  // approximately 20 milliseconds, even if the wall clock is changed during
  24  // the operation being timed:
  25  //
  26  //	start := time.Now()
  27  //	... operation that takes 20 milliseconds ...
  28  //	t := time.Now()
  29  //	elapsed := t.Sub(start)
  30  //
  31  // Other idioms, such as [time.Since](start), [time.Until](deadline), and
  32  // time.Now().Before(deadline), are similarly robust against wall clock
  33  // resets.
  34  //
  35  // The rest of this section gives the precise details of how operations
  36  // use monotonic clocks, but understanding those details is not required
  37  // to use this package.
  38  //
  39  // The Time returned by time.Now contains a monotonic clock reading.
  40  // If Time t has a monotonic clock reading, t.Add adds the same duration to
  41  // both the wall clock and monotonic clock readings to compute the result.
  42  // Because t.AddDate(y, m, d), t.Round(d), and t.Truncate(d) are wall time
  43  // computations, they always strip any monotonic clock reading from their results.
  44  // Because t.In, t.Local, and t.UTC are used for their effect on the interpretation
  45  // of the wall time, they also strip any monotonic clock reading from their results.
  46  // The canonical way to strip a monotonic clock reading is to use t = t.Round(0).
  47  //
  48  // If Times t and u both contain monotonic clock readings, the operations
  49  // t.After(u), t.Before(u), t.Equal(u), t.Compare(u), and t.Sub(u) are carried out
  50  // using the monotonic clock readings alone, ignoring the wall clock
  51  // readings. If either t or u contains no monotonic clock reading, these
  52  // operations fall back to using the wall clock readings.
  53  //
  54  // On some systems the monotonic clock will stop if the computer goes to sleep.
  55  // On such a system, t.Sub(u) may not accurately reflect the actual
  56  // time that passed between t and u. The same applies to other functions and
  57  // methods that subtract times, such as [Since], [Until], [Time.Before], [Time.After],
  58  // [Time.Add], [Time.Equal] and [Time.Compare]. In some cases, you may need to strip
  59  // the monotonic clock to get accurate results.
  60  //
  61  // Because the monotonic clock reading has no meaning outside
  62  // the current process, the serialized forms generated by t.GobEncode,
  63  // t.MarshalBinary, t.MarshalJSON, and t.MarshalText omit the monotonic
  64  // clock reading, and t.Format provides no format for it. Similarly, the
  65  // constructors [time.Date], [time.Parse], [time.ParseInLocation], and [time.Unix],
  66  // as well as the unmarshalers t.GobDecode, t.UnmarshalBinary.
  67  // t.UnmarshalJSON, and t.UnmarshalText always create times with
  68  // no monotonic clock reading.
  69  //
  70  // The monotonic clock reading exists only in [Time] values. It is not
  71  // a part of [Duration] values or the Unix times returned by t.Unix and
  72  // friends.
  73  //
  74  // Note that the Go == operator compares not just the time instant but
  75  // also the [Location] and the monotonic clock reading. See the
  76  // documentation for the Time type for a discussion of equality
  77  // testing for Time values.
  78  //
  79  // For debugging, the result of t.String does include the monotonic
  80  // clock reading if present. If t != u because of different monotonic clock readings,
  81  // that difference will be visible when printing t.String() and u.String().
  82  //
  83  // # Timer Resolution
  84  //
  85  // [Timer] resolution varies depending on the Go runtime, the operating system
  86  // and the underlying hardware.
  87  // On Unix, the resolution is ~1ms.
  88  // On Windows version 1803 and newer, the resolution is ~0.5ms.
  89  // On older Windows versions, the default resolution is ~16ms, but
  90  // a higher resolution may be requested using [golang.org/x/sys/windows.TimeBeginPeriod].
  91  package time
  92  
  93  import (
  94  	"errors"
  95  	"math/bits"
  96  	_ "unsafe" // for go:linkname
  97  )
  98  
  99  // A Time represents an instant in time with nanosecond precision.
 100  //
 101  // Programs using times should typically store and pass them as values,
 102  // not pointers. That is, time variables and struct fields should be of
 103  // type [time.Time], not *time.Time.
 104  //
 105  // A Time value can be used by multiple goroutines simultaneously except
 106  // that the methods [Time.GobDecode], [Time.UnmarshalBinary], [Time.UnmarshalJSON] and
 107  // [Time.UnmarshalText] are not concurrency-safe.
 108  //
 109  // Time instants can be compared using the [Time.Before], [Time.After], and [Time.Equal] methods.
 110  // The [Time.Sub] method subtracts two instants, producing a [Duration].
 111  // The [Time.Add] method adds a Time and a Duration, producing a Time.
 112  //
 113  // The zero value of type Time is January 1, year 1, 00:00:00.000000000 UTC.
 114  // As this time is unlikely to come up in practice, the [Time.IsZero] method gives
 115  // a simple way of detecting a time that has not been initialized explicitly.
 116  //
 117  // Each time has an associated [Location]. The methods [Time.Local], [Time.UTC], and Time.In return a
 118  // Time with a specific Location. Changing the Location of a Time value with
 119  // these methods does not change the actual instant it represents, only the time
 120  // zone in which to interpret it.
 121  //
 122  // Representations of a Time value saved by the [Time.GobEncode], [Time.MarshalBinary], [Time.AppendBinary],
 123  // [Time.MarshalJSON], [Time.MarshalText] and [Time.AppendText] methods store the [Time.Location]'s offset,
 124  // but not the location name. They therefore lose information about Daylight Saving Time.
 125  //
 126  // In addition to the required “wall clock” reading, a Time may contain an optional
 127  // reading of the current process's monotonic clock, to provide additional precision
 128  // for comparison or subtraction.
 129  // See the “Monotonic Clocks” section in the package documentation for details.
 130  //
 131  // Note that the Go == operator compares not just the time instant but also the
 132  // Location and the monotonic clock reading. Therefore, Time values should not
 133  // be used as map or database keys without first guaranteeing that the
 134  // identical Location has been set for all values, which can be achieved
 135  // through use of the UTC or Local method, and that the monotonic clock reading
 136  // has been stripped by setting t = t.Round(0). In general, prefer t.Equal(u)
 137  // to t == u, since t.Equal uses the most accurate comparison available and
 138  // correctly handles the case when only one of its arguments has a monotonic
 139  // clock reading.
 140  type Time struct {
 141  	// wall and ext encode the wall time seconds, wall time nanoseconds,
 142  	// and optional monotonic clock reading in nanoseconds.
 143  	//
 144  	// From high to low bit position, wall encodes a 1-bit flag (hasMonotonic),
 145  	// a 33-bit seconds field, and a 30-bit wall time nanoseconds field.
 146  	// The nanoseconds field is in the range [0, 999999999].
 147  	// If the hasMonotonic bit is 0, then the 33-bit field must be zero
 148  	// and the full signed 64-bit wall seconds since Jan 1 year 1 is stored in ext.
 149  	// If the hasMonotonic bit is 1, then the 33-bit field holds a 33-bit
 150  	// unsigned wall seconds since Jan 1 year 1885, and ext holds a
 151  	// signed 64-bit monotonic clock reading, nanoseconds since process start.
 152  	wall uint64
 153  	ext  int64
 154  
 155  	// loc specifies the Location that should be used to
 156  	// determine the minute, hour, month, day, and year
 157  	// that correspond to this Time.
 158  	// The nil location means UTC.
 159  	// All UTC times are represented with loc==nil, never loc==&utcLoc.
 160  	loc *Location
 161  }
 162  
 163  const (
 164  	hasMonotonic = 1 << 63
 165  	maxWall      = wallToInternal + (1<<33 - 1) // year 2157
 166  	minWall      = wallToInternal               // year 1885
 167  	nsecMask     = 1<<30 - 1
 168  	nsecShift    = 30
 169  )
 170  
 171  // These helpers for manipulating the wall and monotonic clock readings
 172  // take pointer receivers, even when they don't modify the time,
 173  // to make them cheaper to call.
 174  
 175  // nsec returns the time's nanoseconds.
 176  func (t *Time) nsec() int32 {
 177  	return int32(t.wall & nsecMask)
 178  }
 179  
 180  // sec returns the time's seconds since Jan 1 year 1.
 181  func (t *Time) sec() int64 {
 182  	if t.wall&hasMonotonic != 0 {
 183  		return wallToInternal + int64(t.wall<<1>>(nsecShift+1))
 184  	}
 185  	return t.ext
 186  }
 187  
 188  // unixSec returns the time's seconds since Jan 1 1970 (Unix time).
 189  func (t *Time) unixSec() int64 { return t.sec() + internalToUnix }
 190  
 191  // addSec adds d seconds to the time.
 192  func (t *Time) addSec(d int64) {
 193  	if t.wall&hasMonotonic != 0 {
 194  		sec := int64(t.wall << 1 >> (nsecShift + 1))
 195  		dsec := sec + d
 196  		if 0 <= dsec && dsec <= 1<<33-1 {
 197  			t.wall = t.wall&nsecMask | uint64(dsec)<<nsecShift | hasMonotonic
 198  			return
 199  		}
 200  		// Wall second now out of range for packed field.
 201  		// Move to ext.
 202  		t.stripMono()
 203  	}
 204  
 205  	// Check if the sum of t.ext and d overflows and handle it properly.
 206  	sum := t.ext + d
 207  	if (sum > t.ext) == (d > 0) {
 208  		t.ext = sum
 209  	} else if d > 0 {
 210  		t.ext = 1<<63 - 1
 211  	} else {
 212  		t.ext = -(1<<63 - 1)
 213  	}
 214  }
 215  
 216  // setLoc sets the location associated with the time.
 217  func (t *Time) setLoc(loc *Location) {
 218  	if loc == &utcLoc {
 219  		loc = nil
 220  	}
 221  	t.stripMono()
 222  	t.loc = loc
 223  }
 224  
 225  // stripMono strips the monotonic clock reading in t.
 226  func (t *Time) stripMono() {
 227  	if t.wall&hasMonotonic != 0 {
 228  		t.ext = t.sec()
 229  		t.wall &= nsecMask
 230  	}
 231  }
 232  
 233  // setMono sets the monotonic clock reading in t.
 234  // If t cannot hold a monotonic clock reading,
 235  // because its wall time is too large,
 236  // setMono is a no-op.
 237  func (t *Time) setMono(m int64) {
 238  	if t.wall&hasMonotonic == 0 {
 239  		sec := t.ext
 240  		if sec < minWall || maxWall < sec {
 241  			return
 242  		}
 243  		t.wall |= hasMonotonic | uint64(sec-minWall)<<nsecShift
 244  	}
 245  	t.ext = m
 246  }
 247  
 248  // mono returns t's monotonic clock reading.
 249  // It returns 0 for a missing reading.
 250  // This function is used only for testing,
 251  // so it's OK that technically 0 is a valid
 252  // monotonic clock reading as well.
 253  func (t *Time) mono() int64 {
 254  	if t.wall&hasMonotonic == 0 {
 255  		return 0
 256  	}
 257  	return t.ext
 258  }
 259  
 260  // IsZero reports whether t represents the zero time instant,
 261  // January 1, year 1, 00:00:00 UTC.
 262  func (t Time) IsZero() bool {
 263  	return t.sec() == 0 && t.nsec() == 0
 264  }
 265  
 266  // After reports whether the time instant t is after u.
 267  func (t Time) After(u Time) bool {
 268  	if t.wall&u.wall&hasMonotonic != 0 {
 269  		return t.ext > u.ext
 270  	}
 271  	ts := t.sec()
 272  	us := u.sec()
 273  	return ts > us || ts == us && t.nsec() > u.nsec()
 274  }
 275  
 276  // Before reports whether the time instant t is before u.
 277  func (t Time) Before(u Time) bool {
 278  	if t.wall&u.wall&hasMonotonic != 0 {
 279  		return t.ext < u.ext
 280  	}
 281  	ts := t.sec()
 282  	us := u.sec()
 283  	return ts < us || ts == us && t.nsec() < u.nsec()
 284  }
 285  
 286  // Compare compares the time instant t with u. If t is before u, it returns -1;
 287  // if t is after u, it returns +1; if they're the same, it returns 0.
 288  func (t Time) Compare(u Time) int {
 289  	var tc, uc int64
 290  	if t.wall&u.wall&hasMonotonic != 0 {
 291  		tc, uc = t.ext, u.ext
 292  	} else {
 293  		tc, uc = t.sec(), u.sec()
 294  		if tc == uc {
 295  			tc, uc = int64(t.nsec()), int64(u.nsec())
 296  		}
 297  	}
 298  	switch {
 299  	case tc < uc:
 300  		return -1
 301  	case tc > uc:
 302  		return +1
 303  	}
 304  	return 0
 305  }
 306  
 307  // Equal reports whether t and u represent the same time instant.
 308  // Two times can be equal even if they are in different locations.
 309  // For example, 6:00 +0200 and 4:00 UTC are Equal.
 310  // See the documentation on the Time type for the pitfalls of using == with
 311  // Time values; most code should use Equal instead.
 312  func (t Time) Equal(u Time) bool {
 313  	if t.wall&u.wall&hasMonotonic != 0 {
 314  		return t.ext == u.ext
 315  	}
 316  	return t.sec() == u.sec() && t.nsec() == u.nsec()
 317  }
 318  
 319  // A Month specifies a month of the year (January = 1, ...).
 320  type Month int
 321  
 322  const (
 323  	January Month = 1 + iota
 324  	February
 325  	March
 326  	April
 327  	May
 328  	June
 329  	July
 330  	August
 331  	September
 332  	October
 333  	November
 334  	December
 335  )
 336  
 337  // String returns the English name of the month ("January", "February", ...).
 338  func (m Month) String() string {
 339  	if January <= m && m <= December {
 340  		return longMonthNames[m-1]
 341  	}
 342  	buf := []byte{:20}
 343  	n := fmtInt(buf, uint64(m))
 344  	return "%!Month(" | string(buf[n:]) | ")"
 345  }
 346  
 347  // A Weekday specifies a day of the week (Sunday = 0, ...).
 348  type Weekday int
 349  
 350  const (
 351  	Sunday Weekday = iota
 352  	Monday
 353  	Tuesday
 354  	Wednesday
 355  	Thursday
 356  	Friday
 357  	Saturday
 358  )
 359  
 360  // String returns the English name of the day ("Sunday", "Monday", ...).
 361  func (d Weekday) String() string {
 362  	if Sunday <= d && d <= Saturday {
 363  		return longDayNames[d]
 364  	}
 365  	buf := []byte{:20}
 366  	n := fmtInt(buf, uint64(d))
 367  	return "%!Weekday(" | string(buf[n:]) | ")"
 368  }
 369  
 370  // Computations on Times
 371  //
 372  // The zero value for a Time is defined to be
 373  //	January 1, year 1, 00:00:00.000000000 UTC
 374  // which (1) looks like a zero, or as close as you can get in a date
 375  // (1-1-1 00:00:00 UTC), (2) is unlikely enough to arise in practice to
 376  // be a suitable "not set" sentinel, unlike Jan 1 1970, and (3) has a
 377  // non-negative year even in time zones west of UTC, unlike 1-1-0
 378  // 00:00:00 UTC, which would be 12-31-(-1) 19:00:00 in New York.
 379  //
 380  // The zero Time value does not force a specific epoch for the time
 381  // representation. For example, to use the Unix epoch internally, we
 382  // could define that to distinguish a zero value from Jan 1 1970, that
 383  // time would be represented by sec=-1, nsec=1e9. However, it does
 384  // suggest a representation, namely using 1-1-1 00:00:00 UTC as the
 385  // epoch, and that's what we do.
 386  //
 387  // The Add and Sub computations are oblivious to the choice of epoch.
 388  //
 389  // The presentation computations - year, month, minute, and so on - all
 390  // rely heavily on division and modulus by positive constants. For
 391  // calendrical calculations we want these divisions to round down, even
 392  // for negative values, so that the remainder is always positive, but
 393  // Go's division (like most hardware division instructions) rounds to
 394  // zero. We can still do those computations and then adjust the result
 395  // for a negative numerator, but it's annoying to write the adjustment
 396  // over and over. Instead, we can change to a different epoch so long
 397  // ago that all the times we care about will be positive, and then round
 398  // to zero and round down coincide. These presentation routines already
 399  // have to add the zone offset, so adding the translation to the
 400  // alternate epoch is cheap. For example, having a non-negative time t
 401  // means that we can write
 402  //
 403  //	sec = t % 60
 404  //
 405  // instead of
 406  //
 407  //	sec = t % 60
 408  //	if sec < 0 {
 409  //		sec += 60
 410  //	}
 411  //
 412  // everywhere.
 413  //
 414  // The calendar runs on an exact 400 year cycle: a 400-year calendar
 415  // printed for 1970-2369 will apply as well to 2370-2769. Even the days
 416  // of the week match up. It simplifies date computations to choose the
 417  // cycle boundaries so that the exceptional years are always delayed as
 418  // long as possible: March 1, year 0 is such a day:
 419  // the first leap day (Feb 29) is four years minus one day away,
 420  // the first multiple-of-4 year without a Feb 29 is 100 years minus one day away,
 421  // and the first multiple-of-100 year with a Feb 29 is 400 years minus one day away.
 422  // March 1 year Y for any Y = 0 mod 400 is also such a day.
 423  //
 424  // Finally, it's convenient if the delta between the Unix epoch and
 425  // long-ago epoch is representable by an int64 constant.
 426  //
 427  // These three considerations—choose an epoch as early as possible, that
 428  // starts on March 1 of a year equal to 0 mod 400, and that is no more than
 429  // 2⁶³ seconds earlier than 1970—bring us to the year -292277022400.
 430  // We refer to this moment as the absolute zero instant, and to times
 431  // measured as a uint64 seconds since this year as absolute times.
 432  //
 433  // Times measured as an int64 seconds since the year 1—the representation
 434  // used for Time's sec field—are called internal times.
 435  //
 436  // Times measured as an int64 seconds since the year 1970 are called Unix
 437  // times.
 438  //
 439  // It is tempting to just use the year 1 as the absolute epoch, defining
 440  // that the routines are only valid for years >= 1. However, the
 441  // routines would then be invalid when displaying the epoch in time zones
 442  // west of UTC, since it is year 0. It doesn't seem tenable to say that
 443  // printing the zero time correctly isn't supported in half the time
 444  // zones. By comparison, it's reasonable to mishandle some times in
 445  // the year -292277022400.
 446  //
 447  // All this is opaque to clients of the API and can be changed if a
 448  // better implementation presents itself.
 449  //
 450  // The date calculations are implemented using the following clever math from
 451  // Cassio Neri and Lorenz Schneider, “Euclidean affine functions and their
 452  // application to calendar algorithms,” SP&E 2023. https://doi.org/10.1002/spe.3172
 453  //
 454  // Define a “calendrical division” (f, f°, f*) to be a triple of functions converting
 455  // one time unit into a whole number of larger units and the remainder and back.
 456  // For example, in a calendar with no leap years, (d/365, d%365, y*365) is the
 457  // calendrical division for days into years:
 458  //
 459  //	(f)  year := days/365
 460  //	(f°) yday := days%365
 461  //	(f*) days := year*365 (+ yday)
 462  //
 463  // Note that f* is usually the “easy” function to write: it's the
 464  // calendrical multiplication that inverts the more complex division.
 465  //
 466  // Neri and Schneider prove that when f* takes the form
 467  //
 468  //	f*(n) = (a n + b) / c
 469  //
 470  // using integer division rounding down with a ≥ c > 0,
 471  // which they call a Euclidean affine function or EAF, then:
 472  //
 473  //	f(n) = (c n + c - b - 1) / a
 474  //	f°(n) = (c n + c - b - 1) % a / c
 475  //
 476  // This gives a fairly direct calculation for any calendrical division for which
 477  // we can write the calendrical multiplication in EAF form.
 478  // Because the epoch has been shifted to March 1, all the calendrical
 479  // multiplications turn out to be possible to write in EAF form.
 480  // When a date is broken into [century, cyear, amonth, mday],
 481  // with century, cyear, and mday 0-based,
 482  // and amonth 3-based (March = 3, ..., January = 13, February = 14),
 483  // the calendrical multiplications written in EAF form are:
 484  //
 485  //	yday = (153 (amonth-3) + 2) / 5 = (153 amonth - 457) / 5
 486  //	cday = 365 cyear + cyear/4 = 1461 cyear / 4
 487  //	centurydays = 36524 century + century/4 = 146097 century / 4
 488  //	days = centurydays + cday + yday + mday.
 489  //
 490  // We can only handle one periodic cycle per equation, so the year
 491  // calculation must be split into [century, cyear], handling both the
 492  // 100-year cycle and the 400-year cycle.
 493  //
 494  // The yday calculation is not obvious but derives from the fact
 495  // that the March through January calendar repeats the 5-month
 496  // 153-day cycle 31, 30, 31, 30, 31 (we don't care about February
 497  // because yday only ever count the days _before_ February 1,
 498  // since February is the last month).
 499  //
 500  // Using the rule for deriving f and f° from f*, these multiplications
 501  // convert to these divisions:
 502  //
 503  //	century := (4 days + 3) / 146097
 504  //	cdays := (4 days + 3) % 146097 / 4
 505  //	cyear := (4 cdays + 3) / 1461
 506  //	ayday := (4 cdays + 3) % 1461 / 4
 507  //	amonth := (5 ayday + 461) / 153
 508  //	mday := (5 ayday + 461) % 153 / 5
 509  //
 510  // The a in ayday and amonth stands for absolute (March 1-based)
 511  // to distinguish from the standard yday (January 1-based).
 512  //
 513  // After computing these, we can translate from the March 1 calendar
 514  // to the standard January 1 calendar with branch-free math assuming a
 515  // branch-free conversion from bool to int 0 or 1, denoted int(b) here:
 516  //
 517  //	isJanFeb := int(yday >= marchThruDecember)
 518  //	month := amonth - isJanFeb*12
 519  //	year := century*100 + cyear + isJanFeb
 520  //	isLeap := int(cyear%4 == 0) & (int(cyear != 0) | int(century%4 == 0))
 521  //	day := 1 + mday
 522  //	yday := 1 + ayday + 31 + 28 + isLeap&^isJanFeb - 365*isJanFeb
 523  //
 524  // isLeap is the standard leap-year rule, but the split year form
 525  // makes the divisions all reduce to binary masking.
 526  // Note that day and yday are 1-based, in contrast to mday and ayday.
 527  
 528  // To keep the various units separate, we define integer types
 529  // for each. These are never stored in interfaces nor allocated,
 530  // so their type information does not appear in Go binaries.
 531  const (
 532  	secondsPerMinute = 60
 533  	secondsPerHour   = 60 * secondsPerMinute
 534  	secondsPerDay    = 24 * secondsPerHour
 535  	secondsPerWeek   = 7 * secondsPerDay
 536  	daysPer400Years  = 365*400 + 97
 537  
 538  	// Days from March 1 through end of year
 539  	marchThruDecember = 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31
 540  
 541  	// absoluteYears is the number of years we subtract from internal time to get absolute time.
 542  	// This value must be 0 mod 400, and it defines the “absolute zero instant”
 543  	// mentioned in the “Computations on Times” comment above: March 1, -absoluteYears.
 544  	// Dates before the absolute epoch will not compute correctly,
 545  	// but otherwise the value can be changed as needed.
 546  	absoluteYears = 292277022400
 547  
 548  	// The year of the zero Time.
 549  	// Assumed by the unixToInternal computation below.
 550  	internalYear = 1
 551  
 552  	// Offsets to convert between internal and absolute or Unix times.
 553  	absoluteToInternal int64 = -(absoluteYears*365.2425 + marchThruDecember) * secondsPerDay
 554  	internalToAbsolute       = -absoluteToInternal
 555  
 556  	unixToInternal int64 = (1969*365 + 1969/4 - 1969/100 + 1969/400) * secondsPerDay
 557  	internalToUnix int64 = -unixToInternal
 558  
 559  	absoluteToUnix = absoluteToInternal + internalToUnix
 560  	unixToAbsolute = unixToInternal + internalToAbsolute
 561  
 562  	wallToInternal int64 = (1884*365 + 1884/4 - 1884/100 + 1884/400) * secondsPerDay
 563  )
 564  
 565  // An absSeconds counts the number of seconds since the absolute zero instant.
 566  type absSeconds uint64
 567  
 568  // An absDays counts the number of days since the absolute zero instant.
 569  type absDays uint64
 570  
 571  // An absCentury counts the number of centuries since the absolute zero instant.
 572  type absCentury uint64
 573  
 574  // An absCyear counts the number of years since the start of a century.
 575  type absCyear int
 576  
 577  // An absYday counts the number of days since the start of a year.
 578  // Note that absolute years start on March 1.
 579  type absYday int
 580  
 581  // An absMonth counts the number of months since the start of a year.
 582  // absMonth=0 denotes March.
 583  type absMonth int
 584  
 585  // An absLeap is a single bit (0 or 1) denoting whether a given year is a leap year.
 586  type absLeap int
 587  
 588  // An absJanFeb is a single bit (0 or 1) denoting whether a given day falls in January or February.
 589  // That is a special case because the absolute years start in March (unlike normal calendar years).
 590  type absJanFeb int
 591  
 592  // dateToAbsDays takes a standard year/month/day and returns the
 593  // number of days from the absolute epoch to that day.
 594  // The days argument can be out of range and in particular can be negative.
 595  func dateToAbsDays(year int64, month Month, day int) absDays {
 596  	// See “Computations on Times” comment above.
 597  	amonth := uint32(month)
 598  	janFeb := uint32(0)
 599  	if amonth < 3 {
 600  		janFeb = 1
 601  	}
 602  	amonth += 12 * janFeb
 603  	y := uint64(year) - uint64(janFeb) + absoluteYears
 604  
 605  	// For amonth is in the range [3,14], we want:
 606  	//
 607  	//	ayday := (153*amonth - 457) / 5
 608  	//
 609  	// (See the “Computations on Times” comment above
 610  	// as well as Neri and Schneider, section 7.)
 611  	//
 612  	// That is equivalent to:
 613  	//
 614  	//	ayday := (979*amonth - 2919) >> 5
 615  	//
 616  	// and the latter form uses a couple fewer instructions,
 617  	// so use it, saving a few cycles.
 618  	// See Neri and Schneider, section 8.3
 619  	// for more about this optimization.
 620  	//
 621  	// (Note that there is no saved division, because the compiler
 622  	// implements / 5 without division in all cases.)
 623  	ayday := (979*amonth - 2919) >> 5
 624  
 625  	century := y / 100
 626  	cyear := uint32(y % 100)
 627  	cday := 1461 * cyear / 4
 628  	centurydays := 146097 * century / 4
 629  
 630  	return absDays(centurydays + uint64(int64(cday+ayday)+int64(day)-1))
 631  }
 632  
 633  // days converts absolute seconds to absolute days.
 634  func (abs absSeconds) days() absDays {
 635  	return absDays(abs / secondsPerDay)
 636  }
 637  
 638  // split splits days into century, cyear, ayday.
 639  func (days absDays) split() (century absCentury, cyear absCyear, ayday absYday) {
 640  	// See “Computations on Times” comment above.
 641  	d := 4*uint64(days) + 3
 642  	century = absCentury(d / 146097)
 643  
 644  	// This should be
 645  	//	cday := uint32(d % 146097) / 4
 646  	//	cd := 4*cday + 3
 647  	// which is to say
 648  	//	cday := uint32(d % 146097) >> 2
 649  	//	cd := cday<<2 + 3
 650  	// but of course (x>>2<<2)+3 == x|3,
 651  	// so do that instead.
 652  	cd := uint32(d%146097) | 3
 653  
 654  	// For cdays in the range [0,146097] (100 years), we want:
 655  	//
 656  	//	cyear := (4 cdays + 3) / 1461
 657  	//	yday := (4 cdays + 3) % 1461 / 4
 658  	//
 659  	// (See the “Computations on Times” comment above
 660  	// as well as Neri and Schneider, section 7.)
 661  	//
 662  	// That is equivalent to:
 663  	//
 664  	//	cyear := (2939745 cdays) >> 32
 665  	//	yday := (2939745 cdays) & 0xFFFFFFFF / 2939745 / 4
 666  	//
 667  	// so do that instead, saving a few cycles.
 668  	// See Neri and Schneider, section 8.3
 669  	// for more about this optimization.
 670  	hi, lo := bits.Mul32(2939745, uint32(cd))
 671  	cyear = absCyear(hi)
 672  	ayday = absYday(lo / 2939745 / 4)
 673  	return
 674  }
 675  
 676  // split splits ayday into absolute month and standard (1-based) day-in-month.
 677  func (ayday absYday) split() (m absMonth, mday int) {
 678  	// See “Computations on Times” comment above.
 679  	//
 680  	// For yday in the range [0,366],
 681  	//
 682  	//	amonth := (5 yday + 461) / 153
 683  	//	mday := (5 yday + 461) % 153 / 5
 684  	//
 685  	// is equivalent to:
 686  	//
 687  	//	amonth = (2141 yday + 197913) >> 16
 688  	//	mday = (2141 yday + 197913) & 0xFFFF / 2141
 689  	//
 690  	// so do that instead, saving a few cycles.
 691  	// See Neri and Schneider, section 8.3.
 692  	d := 2141*uint32(ayday) + 197913
 693  	return absMonth(d >> 16), 1 + int((d&0xFFFF)/2141)
 694  }
 695  
 696  // janFeb returns 1 if the March 1-based ayday is in January or February, 0 otherwise.
 697  func (ayday absYday) janFeb() absJanFeb {
 698  	// See “Computations on Times” comment above.
 699  	jf := absJanFeb(0)
 700  	if ayday >= marchThruDecember {
 701  		jf = 1
 702  	}
 703  	return jf
 704  }
 705  
 706  // month returns the standard Month for (m, janFeb)
 707  func (m absMonth) month(janFeb absJanFeb) Month {
 708  	// See “Computations on Times” comment above.
 709  	return Month(m) - Month(janFeb)*12
 710  }
 711  
 712  // leap returns 1 if (century, cyear) is a leap year, 0 otherwise.
 713  func (century absCentury) leap(cyear absCyear) absLeap {
 714  	// See “Computations on Times” comment above.
 715  	y4ok := 0
 716  	if cyear%4 == 0 {
 717  		y4ok = 1
 718  	}
 719  	y100ok := 0
 720  	if cyear != 0 {
 721  		y100ok = 1
 722  	}
 723  	y400ok := 0
 724  	if century%4 == 0 {
 725  		y400ok = 1
 726  	}
 727  	return absLeap(y4ok & (y100ok | y400ok))
 728  }
 729  
 730  // year returns the standard year for (century, cyear, janFeb).
 731  func (century absCentury) year(cyear absCyear, janFeb absJanFeb) int {
 732  	// See “Computations on Times” comment above.
 733  	return int(uint64(century)*100-absoluteYears) + int(cyear) + int(janFeb)
 734  }
 735  
 736  // yday returns the standard 1-based yday for (ayday, janFeb, leap).
 737  func (ayday absYday) yday(janFeb absJanFeb, leap absLeap) int {
 738  	// See “Computations on Times” comment above.
 739  	return int(ayday) + (1 + 31 + 28) + int(leap)&^int(janFeb) - 365*int(janFeb)
 740  }
 741  
 742  // date converts days into standard year, month, day.
 743  func (days absDays) date() (year int, month Month, day int) {
 744  	century, cyear, ayday := days.split()
 745  	amonth, day := ayday.split()
 746  	janFeb := ayday.janFeb()
 747  	year = century.year(cyear, janFeb)
 748  	month = amonth.month(janFeb)
 749  	return
 750  }
 751  
 752  // yearYday converts days into the standard year and 1-based yday.
 753  func (days absDays) yearYday() (year, yday int) {
 754  	century, cyear, ayday := days.split()
 755  	janFeb := ayday.janFeb()
 756  	year = century.year(cyear, janFeb)
 757  	yday = ayday.yday(janFeb, century.leap(cyear))
 758  	return
 759  }
 760  
 761  // absSec returns the time t as an absolute seconds, adjusted by the zone offset.
 762  // It is called when computing a presentation property like Month or Hour.
 763  // We'd rather call it abs, but there are linknames to abs that make that problematic.
 764  // See timeAbs below.
 765  func (t Time) absSec() absSeconds {
 766  	l := t.loc
 767  	// Avoid function calls when possible.
 768  	if l == nil || l == &localLoc {
 769  		l = l.get()
 770  	}
 771  	sec := t.unixSec()
 772  	if l != &utcLoc {
 773  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
 774  			sec += int64(l.cacheZone.offset)
 775  		} else {
 776  			_, offset, _, _, _ := l.lookup(sec)
 777  			sec += int64(offset)
 778  		}
 779  	}
 780  	return absSeconds(sec + (unixToInternal + internalToAbsolute))
 781  }
 782  
 783  // locabs is a combination of the Zone and abs methods,
 784  // extracting both return values from a single zone lookup.
 785  func (t Time) locabs() (name []byte, offset int, abs absSeconds) {
 786  	l := t.loc
 787  	if l == nil || l == &localLoc {
 788  		l = l.get()
 789  	}
 790  	// Avoid function call if we hit the local time cache.
 791  	sec := t.unixSec()
 792  	if l != &utcLoc {
 793  		if l.cacheZone != nil && l.cacheStart <= sec && sec < l.cacheEnd {
 794  			name = l.cacheZone.name
 795  			offset = l.cacheZone.offset
 796  		} else {
 797  			name, offset, _, _, _ = l.lookup(sec)
 798  		}
 799  		sec += int64(offset)
 800  	} else {
 801  		name = "UTC"
 802  	}
 803  	abs = absSeconds(sec + (unixToInternal + internalToAbsolute))
 804  	return
 805  }
 806  
 807  // Date returns the year, month, and day in which t occurs.
 808  func (t Time) Date() (year int, month Month, day int) {
 809  	return t.absSec().days().date()
 810  }
 811  
 812  // Year returns the year in which t occurs.
 813  func (t Time) Year() int {
 814  	century, cyear, ayday := t.absSec().days().split()
 815  	janFeb := ayday.janFeb()
 816  	return century.year(cyear, janFeb)
 817  }
 818  
 819  // Month returns the month of the year specified by t.
 820  func (t Time) Month() Month {
 821  	_, _, ayday := t.absSec().days().split()
 822  	amonth, _ := ayday.split()
 823  	return amonth.month(ayday.janFeb())
 824  }
 825  
 826  // Day returns the day of the month specified by t.
 827  func (t Time) Day() int {
 828  	_, _, ayday := t.absSec().days().split()
 829  	_, day := ayday.split()
 830  	return day
 831  }
 832  
 833  // Weekday returns the day of the week specified by t.
 834  func (t Time) Weekday() Weekday {
 835  	return t.absSec().days().weekday()
 836  }
 837  
 838  // weekday returns the day of the week specified by days.
 839  func (days absDays) weekday() Weekday {
 840  	// March 1 of the absolute year, like March 1 of 2000, was a Wednesday.
 841  	return Weekday((uint64(days) + uint64(Wednesday)) % 7)
 842  }
 843  
 844  // ISOWeek returns the ISO 8601 year and week number in which t occurs.
 845  // Week ranges from 1 to 53. Jan 01 to Jan 03 of year n might belong to
 846  // week 52 or 53 of year n-1, and Dec 29 to Dec 31 might belong to week 1
 847  // of year n+1.
 848  func (t Time) ISOWeek() (year, week int) {
 849  	// According to the rule that the first calendar week of a calendar year is
 850  	// the week including the first Thursday of that year, and that the last one is
 851  	// the week immediately preceding the first calendar week of the next calendar year.
 852  	// See https://www.iso.org/obp/ui#iso:std:iso:8601:-1:ed-1:v1:en:term:3.1.1.23 for details.
 853  
 854  	// weeks start with Monday
 855  	// Monday Tuesday Wednesday Thursday Friday Saturday Sunday
 856  	// 1      2       3         4        5      6        7
 857  	// +3     +2      +1        0        -1     -2       -3
 858  	// the offset to Thursday
 859  	days := t.absSec().days()
 860  	thu := days + absDays(Thursday-((days-1).weekday()+1))
 861  	year, yday := thu.yearYday()
 862  	return year, (yday-1)/7 + 1
 863  }
 864  
 865  // Clock returns the hour, minute, and second within the day specified by t.
 866  func (t Time) Clock() (hour, min, sec int) {
 867  	return t.absSec().clock()
 868  }
 869  
 870  // clock returns the hour, minute, and second within the day specified by abs.
 871  func (abs absSeconds) clock() (hour, min, sec int) {
 872  	sec = int(abs % secondsPerDay)
 873  	hour = sec / secondsPerHour
 874  	sec -= hour * secondsPerHour
 875  	min = sec / secondsPerMinute
 876  	sec -= min * secondsPerMinute
 877  	return
 878  }
 879  
 880  // Hour returns the hour within the day specified by t, in the range [0, 23].
 881  func (t Time) Hour() int {
 882  	return int(t.absSec()%secondsPerDay) / secondsPerHour
 883  }
 884  
 885  // Minute returns the minute offset within the hour specified by t, in the range [0, 59].
 886  func (t Time) Minute() int {
 887  	return int(t.absSec()%secondsPerHour) / secondsPerMinute
 888  }
 889  
 890  // Second returns the second offset within the minute specified by t, in the range [0, 59].
 891  func (t Time) Second() int {
 892  	return int(t.absSec() % secondsPerMinute)
 893  }
 894  
 895  // Nanosecond returns the nanosecond offset within the second specified by t,
 896  // in the range [0, 999999999].
 897  func (t Time) Nanosecond() int {
 898  	return int(t.nsec())
 899  }
 900  
 901  // YearDay returns the day of the year specified by t, in the range [1,365] for non-leap years,
 902  // and [1,366] in leap years.
 903  func (t Time) YearDay() int {
 904  	_, yday := t.absSec().days().yearYday()
 905  	return yday
 906  }
 907  
 908  // A Duration represents the elapsed time between two instants
 909  // as an int64 nanosecond count. The representation limits the
 910  // largest representable duration to approximately 290 years.
 911  type Duration int64
 912  
 913  const (
 914  	minDuration Duration = -1 << 63
 915  	maxDuration Duration = 1<<63 - 1
 916  )
 917  
 918  // Common durations. There is no definition for units of Day or larger
 919  // to avoid confusion across daylight savings time zone transitions.
 920  //
 921  // To count the number of units in a [Duration], divide:
 922  //
 923  //	second := time.Second
 924  //	fmt.Print(int64(second/time.Millisecond)) // prints 1000
 925  //
 926  // To convert an integer number of units to a Duration, multiply:
 927  //
 928  //	seconds := 10
 929  //	fmt.Print(time.Duration(seconds)*time.Second) // prints 10s
 930  const (
 931  	Nanosecond  Duration = 1
 932  	Microsecond          = 1000 * Nanosecond
 933  	Millisecond          = 1000 * Microsecond
 934  	Second               = 1000 * Millisecond
 935  	Minute               = 60 * Second
 936  	Hour                 = 60 * Minute
 937  )
 938  
 939  // String returns a string representing the duration in the form "72h3m0.5s".
 940  // Leading zero units are omitted. As a special case, durations less than one
 941  // second format use a smaller unit (milli-, micro-, or nanoseconds) to ensure
 942  // that the leading digit is non-zero. The zero duration formats as 0s.
 943  func (d Duration) String() string {
 944  	// This is inlinable to take advantage of "function outlining".
 945  	// Thus, the caller can decide whether a string must be heap allocated.
 946  	var arr [32]byte
 947  	n := d.format(&arr)
 948  	return string(arr[n:])
 949  }
 950  
 951  // format formats the representation of d into the end of buf and
 952  // returns the offset of the first character.
 953  func (d Duration) format(buf *[32]byte) int {
 954  	// Largest time is 2540400h10m10.000000000s
 955  	w := len(buf)
 956  
 957  	u := uint64(d)
 958  	neg := d < 0
 959  	if neg {
 960  		u = -u
 961  	}
 962  
 963  	if u < uint64(Second) {
 964  		// Special case: if duration is smaller than a second,
 965  		// use smaller units, like 1.2ms
 966  		var prec int
 967  		w--
 968  		buf[w] = 's'
 969  		w--
 970  		switch {
 971  		case u == 0:
 972  			buf[w] = '0'
 973  			return w
 974  		case u < uint64(Microsecond):
 975  			// print nanoseconds
 976  			prec = 0
 977  			buf[w] = 'n'
 978  		case u < uint64(Millisecond):
 979  			// print microseconds
 980  			prec = 3
 981  			// U+00B5 'µ' micro sign == 0xC2 0xB5
 982  			w-- // Need room for two bytes.
 983  			copy(buf[w:], "µ")
 984  		default:
 985  			// print milliseconds
 986  			prec = 6
 987  			buf[w] = 'm'
 988  		}
 989  		w, u = fmtFrac(buf[:w], u, prec)
 990  		w = fmtInt(buf[:w], u)
 991  	} else {
 992  		w--
 993  		buf[w] = 's'
 994  
 995  		w, u = fmtFrac(buf[:w], u, 9)
 996  
 997  		// u is now integer seconds
 998  		w = fmtInt(buf[:w], u%60)
 999  		u /= 60
1000  
1001  		// u is now integer minutes
1002  		if u > 0 {
1003  			w--
1004  			buf[w] = 'm'
1005  			w = fmtInt(buf[:w], u%60)
1006  			u /= 60
1007  
1008  			// u is now integer hours
1009  			// Stop at hours because days can be different lengths.
1010  			if u > 0 {
1011  				w--
1012  				buf[w] = 'h'
1013  				w = fmtInt(buf[:w], u)
1014  			}
1015  		}
1016  	}
1017  
1018  	if neg {
1019  		w--
1020  		buf[w] = '-'
1021  	}
1022  
1023  	return w
1024  }
1025  
1026  // fmtFrac formats the fraction of v/10**prec (e.g., ".12345") into the
1027  // tail of buf, omitting trailing zeros. It omits the decimal
1028  // point too when the fraction is 0. It returns the index where the
1029  // output bytes begin and the value v/10**prec.
1030  func fmtFrac(buf []byte, v uint64, prec int) (nw int, nv uint64) {
1031  	// Omit trailing zeros up to and including decimal point.
1032  	w := len(buf)
1033  	print := false
1034  	for i := 0; i < prec; i++ {
1035  		digit := v % 10
1036  		print = print || digit != 0
1037  		if print {
1038  			w--
1039  			buf[w] = byte(digit) + '0'
1040  		}
1041  		v /= 10
1042  	}
1043  	if print {
1044  		w--
1045  		buf[w] = '.'
1046  	}
1047  	return w, v
1048  }
1049  
1050  // fmtInt formats v into the tail of buf.
1051  // It returns the index where the output begins.
1052  func fmtInt(buf []byte, v uint64) int {
1053  	w := len(buf)
1054  	if v == 0 {
1055  		w--
1056  		buf[w] = '0'
1057  	} else {
1058  		for v > 0 {
1059  			w--
1060  			buf[w] = byte(v%10) + '0'
1061  			v /= 10
1062  		}
1063  	}
1064  	return w
1065  }
1066  
1067  // Nanoseconds returns the duration as an integer nanosecond count.
1068  func (d Duration) Nanoseconds() int64 { return int64(d) }
1069  
1070  // Microseconds returns the duration as an integer microsecond count.
1071  func (d Duration) Microseconds() int64 { return int64(d) / 1e3 }
1072  
1073  // Milliseconds returns the duration as an integer millisecond count.
1074  func (d Duration) Milliseconds() int64 { return int64(d) / 1e6 }
1075  
1076  // These methods return float64 because the dominant
1077  // use case is for printing a floating point number like 1.5s, and
1078  // a truncation to integer would make them not useful in those cases.
1079  // Splitting the integer and fraction ourselves guarantees that
1080  // converting the returned float64 to an integer rounds the same
1081  // way that a pure integer conversion would have, even in cases
1082  // where, say, float64(d.Nanoseconds())/1e9 would have rounded
1083  // differently.
1084  
1085  // Seconds returns the duration as a floating point number of seconds.
1086  func (d Duration) Seconds() float64 {
1087  	sec := d / Second
1088  	nsec := d % Second
1089  	return float64(sec) + float64(nsec)/1e9
1090  }
1091  
1092  // Minutes returns the duration as a floating point number of minutes.
1093  func (d Duration) Minutes() float64 {
1094  	min := d / Minute
1095  	nsec := d % Minute
1096  	return float64(min) + float64(nsec)/(60*1e9)
1097  }
1098  
1099  // Hours returns the duration as a floating point number of hours.
1100  func (d Duration) Hours() float64 {
1101  	hour := d / Hour
1102  	nsec := d % Hour
1103  	return float64(hour) + float64(nsec)/(60*60*1e9)
1104  }
1105  
1106  // Truncate returns the result of rounding d toward zero to a multiple of m.
1107  // If m <= 0, Truncate returns d unchanged.
1108  func (d Duration) Truncate(m Duration) Duration {
1109  	if m <= 0 {
1110  		return d
1111  	}
1112  	return d - d%m
1113  }
1114  
1115  // lessThanHalf reports whether x+x < y but avoids overflow,
1116  // assuming x and y are both positive (Duration is signed).
1117  func lessThanHalf(x, y Duration) bool {
1118  	return uint64(x)+uint64(x) < uint64(y)
1119  }
1120  
1121  // Round returns the result of rounding d to the nearest multiple of m.
1122  // The rounding behavior for halfway values is to round away from zero.
1123  // If the result exceeds the maximum (or minimum)
1124  // value that can be stored in a [Duration],
1125  // Round returns the maximum (or minimum) duration.
1126  // If m <= 0, Round returns d unchanged.
1127  func (d Duration) Round(m Duration) Duration {
1128  	if m <= 0 {
1129  		return d
1130  	}
1131  	r := d % m
1132  	if d < 0 {
1133  		r = -r
1134  		if lessThanHalf(r, m) {
1135  			return d + r
1136  		}
1137  		if d1 := d - m + r; d1 < d {
1138  			return d1
1139  		}
1140  		return minDuration // overflow
1141  	}
1142  	if lessThanHalf(r, m) {
1143  		return d - r
1144  	}
1145  	if d1 := d + m - r; d1 > d {
1146  		return d1
1147  	}
1148  	return maxDuration // overflow
1149  }
1150  
1151  // Abs returns the absolute value of d.
1152  // As a special case, Duration([math.MinInt64]) is converted to Duration([math.MaxInt64]),
1153  // reducing its magnitude by 1 nanosecond.
1154  func (d Duration) Abs() Duration {
1155  	switch {
1156  	case d >= 0:
1157  		return d
1158  	case d == minDuration:
1159  		return maxDuration
1160  	default:
1161  		return -d
1162  	}
1163  }
1164  
1165  // Add returns the time t+d.
1166  func (t Time) Add(d Duration) Time {
1167  	dsec := int64(d / 1e9)
1168  	nsec := t.nsec() + int32(d%1e9)
1169  	if nsec >= 1e9 {
1170  		dsec++
1171  		nsec -= 1e9
1172  	} else if nsec < 0 {
1173  		dsec--
1174  		nsec += 1e9
1175  	}
1176  	t.wall = t.wall&^nsecMask | uint64(nsec) // update nsec
1177  	t.addSec(dsec)
1178  	if t.wall&hasMonotonic != 0 {
1179  		te := t.ext + int64(d)
1180  		if d < 0 && te > t.ext || d > 0 && te < t.ext {
1181  			// Monotonic clock reading now out of range; degrade to wall-only.
1182  			t.stripMono()
1183  		} else {
1184  			t.ext = te
1185  		}
1186  	}
1187  	return t
1188  }
1189  
1190  // Sub returns the duration t-u. If the result exceeds the maximum (or minimum)
1191  // value that can be stored in a [Duration], the maximum (or minimum) duration
1192  // will be returned.
1193  // To compute t-d for a duration d, use t.Add(-d).
1194  func (t Time) Sub(u Time) Duration {
1195  	if t.wall&u.wall&hasMonotonic != 0 {
1196  		return subMono(t.ext, u.ext)
1197  	}
1198  	d := Duration(t.sec()-u.sec())*Second + Duration(t.nsec()-u.nsec())
1199  	// Check for overflow or underflow.
1200  	switch {
1201  	case u.Add(d).Equal(t):
1202  		return d // d is correct
1203  	case t.Before(u):
1204  		return minDuration // t - u is negative out of range
1205  	default:
1206  		return maxDuration // t - u is positive out of range
1207  	}
1208  }
1209  
1210  func subMono(t, u int64) Duration {
1211  	d := Duration(t - u)
1212  	if d < 0 && t > u {
1213  		return maxDuration // t - u is positive out of range
1214  	}
1215  	if d > 0 && t < u {
1216  		return minDuration // t - u is negative out of range
1217  	}
1218  	return d
1219  }
1220  
1221  // Since returns the time elapsed since t.
1222  // It is shorthand for time.Now().Sub(t).
1223  func Since(t Time) Duration {
1224  	if t.wall&hasMonotonic != 0 && !runtimeIsBubbled() {
1225  		// Common case optimization: if t has monotonic time, then Sub will use only it.
1226  		return subMono(runtimeNano()-startNano, t.ext)
1227  	}
1228  	return Now().Sub(t)
1229  }
1230  
1231  // Until returns the duration until t.
1232  // It is shorthand for t.Sub(time.Now()).
1233  func Until(t Time) Duration {
1234  	if t.wall&hasMonotonic != 0 && !runtimeIsBubbled() {
1235  		// Common case optimization: if t has monotonic time, then Sub will use only it.
1236  		return subMono(t.ext, runtimeNano()-startNano)
1237  	}
1238  	return t.Sub(Now())
1239  }
1240  
1241  // AddDate returns the time corresponding to adding the
1242  // given number of years, months, and days to t.
1243  // For example, AddDate(-1, 2, 3) applied to January 1, 2011
1244  // returns March 4, 2010.
1245  //
1246  // Note that dates are fundamentally coupled to timezones, and calendrical
1247  // periods like days don't have fixed durations. AddDate uses the Location of
1248  // the Time value to determine these durations. That means that the same
1249  // AddDate arguments can produce a different shift in absolute time depending on
1250  // the base Time value and its Location. For example, AddDate(0, 0, 1) applied
1251  // to 12:00 on March 27 always returns 12:00 on March 28. At some locations and
1252  // in some years this is a 24 hour shift. In others it's a 23 hour shift due to
1253  // daylight savings time transitions.
1254  //
1255  // AddDate normalizes its result in the same way that Date does,
1256  // so, for example, adding one month to October 31 yields
1257  // December 1, the normalized form for November 31.
1258  func (t Time) AddDate(years int, months int, days int) Time {
1259  	year, month, day := t.Date()
1260  	hour, min, sec := t.Clock()
1261  	return Date(year+years, month+Month(months), day+days, hour, min, sec, int(t.nsec()), t.Location())
1262  }
1263  
1264  // daysBefore returns the number of days in a non-leap year before month m.
1265  // daysBefore(December+1) returns 365.
1266  func daysBefore(m Month) int {
1267  	adj := 0
1268  	if m >= March {
1269  		adj = -2
1270  	}
1271  
1272  	// With the -2 adjustment after February,
1273  	// we need to compute the running sum of:
1274  	//	0  31  30  31  30  31  30  31  31  30  31  30  31
1275  	// which is:
1276  	//	0  31  61  92 122 153 183 214 245 275 306 336 367
1277  	// This is almost exactly 367/12×(m-1) except for the
1278  	// occasonal off-by-one suggesting there may be an
1279  	// integer approximation of the form (a×m + b)/c.
1280  	// A brute force search over small a, b, c finds that
1281  	// (214×m - 211) / 7 computes the function perfectly.
1282  	return (214*int(m)-211)/7 + adj
1283  }
1284  
1285  func daysIn(m Month, year int) int {
1286  	if m == February {
1287  		if isLeap(year) {
1288  			return 29
1289  		}
1290  		return 28
1291  	}
1292  	// With the special case of February eliminated, the pattern is
1293  	//	31 30 31 30 31 30 31 31 30 31 30 31
1294  	// Adding m&1 produces the basic alternation;
1295  	// adding (m>>3)&1 inverts the alternation starting in August.
1296  	return 30 + int((m+m>>3)&1)
1297  }
1298  
1299  // Provided by package runtime.
1300  //
1301  // now returns the current real time, and is superseded by runtimeNow which returns
1302  // the fake synctest clock when appropriate.
1303  //
1304  // now should be an internal detail,
1305  // but widely used packages access it using linkname.
1306  // Notable members of the hall of shame include:
1307  //   - gitee.com/quant1x/gox
1308  //   - github.com/phuslu/log
1309  //   - github.com/sethvargo/go-limiter
1310  //   - github.com/ulule/limiter/v3
1311  //
1312  // Do not remove or change the type signature.
1313  // See go.dev/issue/67401.
1314  func now() (sec int64, nsec int32, mono int64)
1315  
1316  // runtimeNow returns the current time.
1317  // When called within a synctest.Run bubble, it returns the group's fake clock.
1318  //
1319  //go:linkname runtimeNow
1320  func runtimeNow() (sec int64, nsec int32, mono int64)
1321  
1322  // runtimeNano returns the current value of the runtime clock in nanoseconds.
1323  // When called within a synctest.Run bubble, it returns the group's fake clock.
1324  //
1325  //go:linkname runtimeNano
1326  func runtimeNano() int64
1327  
1328  //go:linkname runtimeIsBubbled
1329  func runtimeIsBubbled() bool
1330  
1331  // Monotonic times are reported as offsets from startNano.
1332  // We initialize startNano to runtimeNano() - 1 so that on systems where
1333  // monotonic time resolution is fairly low (e.g. Windows 2008
1334  // which appears to have a default resolution of 15ms),
1335  // we avoid ever reporting a monotonic time of 0.
1336  // (Callers may want to use 0 as "time not set".)
1337  var startNano int64 = runtimeNano() - 1
1338  
1339  // x/tools uses a linkname of time.Now in its tests. No harm done.
1340  //go:linkname Now
1341  
1342  // Now returns the current local time.
1343  func Now() Time {
1344  	sec, nsec, mono := runtimeNow()
1345  	if mono == 0 {
1346  		return Time{uint64(nsec), sec + unixToInternal, Local}
1347  	}
1348  	mono -= startNano
1349  	sec += unixToInternal - minWall
1350  	if uint64(sec)>>33 != 0 {
1351  		// Seconds field overflowed the 33 bits available when
1352  		// storing a monotonic time. This will be true after
1353  		// March 16, 2157.
1354  		return Time{uint64(nsec), sec + minWall, Local}
1355  	}
1356  	return Time{hasMonotonic | uint64(sec)<<nsecShift | uint64(nsec), mono, Local}
1357  }
1358  
1359  func unixTime(sec int64, nsec int32) Time {
1360  	return Time{uint64(nsec), sec + unixToInternal, Local}
1361  }
1362  
1363  // UTC returns t with the location set to UTC.
1364  func (t Time) UTC() Time {
1365  	t.setLoc(&utcLoc)
1366  	return t
1367  }
1368  
1369  // Local returns t with the location set to local time.
1370  func (t Time) Local() Time {
1371  	t.setLoc(Local)
1372  	return t
1373  }
1374  
1375  // In returns a copy of t representing the same time instant, but
1376  // with the copy's location information set to loc for display
1377  // purposes.
1378  //
1379  // In panics if loc is nil.
1380  func (t Time) In(loc *Location) Time {
1381  	if loc == nil {
1382  		panic("time: missing Location in call to Time.In")
1383  	}
1384  	t.setLoc(loc)
1385  	return t
1386  }
1387  
1388  // Location returns the time zone information associated with t.
1389  func (t Time) Location() *Location {
1390  	l := t.loc
1391  	if l == nil {
1392  		l = UTC
1393  	}
1394  	return l
1395  }
1396  
1397  // Zone computes the time zone in effect at time t, returning the abbreviated
1398  // name of the zone (such as "CET") and its offset in seconds east of UTC.
1399  func (t Time) Zone() (name []byte, offset int) {
1400  	name, offset, _, _, _ = t.loc.lookup(t.unixSec())
1401  	return
1402  }
1403  
1404  // ZoneBounds returns the bounds of the time zone in effect at time t.
1405  // The zone begins at start and the next zone begins at end.
1406  // If the zone begins at the beginning of time, start will be returned as a zero Time.
1407  // If the zone goes on forever, end will be returned as a zero Time.
1408  // The Location of the returned times will be the same as t.
1409  func (t Time) ZoneBounds() (start, end Time) {
1410  	_, _, startSec, endSec, _ := t.loc.lookup(t.unixSec())
1411  	if startSec != alpha {
1412  		start = unixTime(startSec, 0)
1413  		start.setLoc(t.loc)
1414  	}
1415  	if endSec != omega {
1416  		end = unixTime(endSec, 0)
1417  		end.setLoc(t.loc)
1418  	}
1419  	return
1420  }
1421  
1422  // Unix returns t as a Unix time, the number of seconds elapsed
1423  // since January 1, 1970 UTC. The result does not depend on the
1424  // location associated with t.
1425  // Unix-like operating systems often record time as a 32-bit
1426  // count of seconds, but since the method here returns a 64-bit
1427  // value it is valid for billions of years into the past or future.
1428  func (t Time) Unix() int64 {
1429  	return t.unixSec()
1430  }
1431  
1432  // UnixMilli returns t as a Unix time, the number of milliseconds elapsed since
1433  // January 1, 1970 UTC. The result is undefined if the Unix time in
1434  // milliseconds cannot be represented by an int64 (a date more than 292 million
1435  // years before or after 1970). The result does not depend on the
1436  // location associated with t.
1437  func (t Time) UnixMilli() int64 {
1438  	return t.unixSec()*1e3 + int64(t.nsec())/1e6
1439  }
1440  
1441  // UnixMicro returns t as a Unix time, the number of microseconds elapsed since
1442  // January 1, 1970 UTC. The result is undefined if the Unix time in
1443  // microseconds cannot be represented by an int64 (a date before year -290307 or
1444  // after year 294246). The result does not depend on the location associated
1445  // with t.
1446  func (t Time) UnixMicro() int64 {
1447  	return t.unixSec()*1e6 + int64(t.nsec())/1e3
1448  }
1449  
1450  // UnixNano returns t as a Unix time, the number of nanoseconds elapsed
1451  // since January 1, 1970 UTC. The result is undefined if the Unix time
1452  // in nanoseconds cannot be represented by an int64 (a date before the year
1453  // 1678 or after 2262). Note that this means the result of calling UnixNano
1454  // on the zero Time is undefined. The result does not depend on the
1455  // location associated with t.
1456  func (t Time) UnixNano() int64 {
1457  	return (t.unixSec())*1e9 + int64(t.nsec())
1458  }
1459  
1460  const (
1461  	timeBinaryVersionV1 byte = iota + 1 // For general situation
1462  	timeBinaryVersionV2                 // For LMT only
1463  )
1464  
1465  // AppendBinary implements the [encoding.BinaryAppender] interface.
1466  func (t Time) AppendBinary(b []byte) ([]byte, error) {
1467  	var offsetMin int16 // minutes east of UTC. -1 is UTC.
1468  	var offsetSec int8
1469  	version := timeBinaryVersionV1
1470  
1471  	if t.Location() == UTC {
1472  		offsetMin = -1
1473  	} else {
1474  		_, offset := t.Zone()
1475  		if offset%60 != 0 {
1476  			version = timeBinaryVersionV2
1477  			offsetSec = int8(offset % 60)
1478  		}
1479  
1480  		offset /= 60
1481  		if offset < -32768 || offset == -1 || offset > 32767 {
1482  			return b, errors.New("Time.MarshalBinary: unexpected zone offset")
1483  		}
1484  		offsetMin = int16(offset)
1485  	}
1486  
1487  	sec := t.sec()
1488  	nsec := t.nsec()
1489  	b = append(b,
1490  		version,       // byte 0 : version
1491  		byte(sec>>56), // bytes 1-8: seconds
1492  		byte(sec>>48),
1493  		byte(sec>>40),
1494  		byte(sec>>32),
1495  		byte(sec>>24),
1496  		byte(sec>>16),
1497  		byte(sec>>8),
1498  		byte(sec),
1499  		byte(nsec>>24), // bytes 9-12: nanoseconds
1500  		byte(nsec>>16),
1501  		byte(nsec>>8),
1502  		byte(nsec),
1503  		byte(offsetMin>>8), // bytes 13-14: zone offset in minutes
1504  		byte(offsetMin),
1505  	)
1506  	if version == timeBinaryVersionV2 {
1507  		b = append(b, byte(offsetSec))
1508  	}
1509  	return b, nil
1510  }
1511  
1512  // MarshalBinary implements the [encoding.BinaryMarshaler] interface.
1513  func (t Time) MarshalBinary() ([]byte, error) {
1514  	b, err := t.AppendBinary([]byte{:0:16})
1515  	if err != nil {
1516  		return nil, err
1517  	}
1518  	return b, nil
1519  }
1520  
1521  // UnmarshalBinary implements the [encoding.BinaryUnmarshaler] interface.
1522  func (t *Time) UnmarshalBinary(data []byte) error {
1523  	buf := data
1524  	if len(buf) == 0 {
1525  		return errors.New("Time.UnmarshalBinary: no data")
1526  	}
1527  
1528  	version := buf[0]
1529  	if version != timeBinaryVersionV1 && version != timeBinaryVersionV2 {
1530  		return errors.New("Time.UnmarshalBinary: unsupported version")
1531  	}
1532  
1533  	wantLen := /*version*/ 1 + /*sec*/ 8 + /*nsec*/ 4 + /*zone offset*/ 2
1534  	if version == timeBinaryVersionV2 {
1535  		wantLen++
1536  	}
1537  	if len(buf) != wantLen {
1538  		return errors.New("Time.UnmarshalBinary: invalid length")
1539  	}
1540  
1541  	buf = buf[1:]
1542  	sec := int64(buf[7]) | int64(buf[6])<<8 | int64(buf[5])<<16 | int64(buf[4])<<24 |
1543  		int64(buf[3])<<32 | int64(buf[2])<<40 | int64(buf[1])<<48 | int64(buf[0])<<56
1544  
1545  	buf = buf[8:]
1546  	nsec := int32(buf[3]) | int32(buf[2])<<8 | int32(buf[1])<<16 | int32(buf[0])<<24
1547  
1548  	buf = buf[4:]
1549  	offset := int(int16(buf[1])|int16(buf[0])<<8) * 60
1550  	if version == timeBinaryVersionV2 {
1551  		offset += int(buf[2])
1552  	}
1553  
1554  	*t = Time{}
1555  	t.wall = uint64(nsec)
1556  	t.ext = sec
1557  
1558  	if offset == -1*60 {
1559  		t.setLoc(&utcLoc)
1560  	} else if _, localoff, _, _, _ := Local.lookup(t.unixSec()); offset == localoff {
1561  		t.setLoc(Local)
1562  	} else {
1563  		t.setLoc(FixedZone("", offset))
1564  	}
1565  
1566  	return nil
1567  }
1568  
1569  // TODO(rsc): Remove GobEncoder, GobDecoder, MarshalJSON, UnmarshalJSON in Go 2.
1570  // The same semantics will be provided by the generic MarshalBinary, MarshalText,
1571  // UnmarshalBinary, UnmarshalText.
1572  
1573  // GobEncode implements the gob.GobEncoder interface.
1574  func (t Time) GobEncode() ([]byte, error) {
1575  	return t.MarshalBinary()
1576  }
1577  
1578  // GobDecode implements the gob.GobDecoder interface.
1579  func (t *Time) GobDecode(data []byte) error {
1580  	return t.UnmarshalBinary(data)
1581  }
1582  
1583  // MarshalJSON implements the [encoding/json.Marshaler] interface.
1584  // The time is a quoted string in the RFC 3339 format with sub-second precision.
1585  // If the timestamp cannot be represented as valid RFC 3339
1586  // (e.g., the year is out of range), then an error is reported.
1587  func (t Time) MarshalJSON() ([]byte, error) {
1588  	b := []byte{:0:len(RFC3339Nano)+len(`""`)}
1589  	b = append(b, '"')
1590  	b, err := t.appendStrictRFC3339(b)
1591  	b = append(b, '"')
1592  	if err != nil {
1593  		return nil, errors.New("Time.MarshalJSON: " | err.Error())
1594  	}
1595  	return b, nil
1596  }
1597  
1598  // UnmarshalJSON implements the [encoding/json.Unmarshaler] interface.
1599  // The time must be a quoted string in the RFC 3339 format.
1600  func (t *Time) UnmarshalJSON(data []byte) error {
1601  	if []byte(data) == "null" {
1602  		return nil
1603  	}
1604  	// TODO(https://go.dev/issue/47353): Properly unescape a JSON string.
1605  	if len(data) < 2 || data[0] != '"' || data[len(data)-1] != '"' {
1606  		return errors.New("Time.UnmarshalJSON: input is not a JSON string")
1607  	}
1608  	data = data[len(`"`) : len(data)-len(`"`)]
1609  	var err error
1610  	*t, err = parseStrictRFC3339(data)
1611  	return err
1612  }
1613  
1614  func (t Time) appendTo(b []byte, errPrefix []byte) ([]byte, error) {
1615  	b, err := t.appendStrictRFC3339(b)
1616  	if err != nil {
1617  		return nil, errors.New(errPrefix + err.Error())
1618  	}
1619  	return b, nil
1620  }
1621  
1622  // AppendText implements the [encoding.TextAppender] interface.
1623  // The time is formatted in RFC 3339 format with sub-second precision.
1624  // If the timestamp cannot be represented as valid RFC 3339
1625  // (e.g., the year is out of range), then an error is returned.
1626  func (t Time) AppendText(b []byte) ([]byte, error) {
1627  	return t.appendTo(b, "Time.AppendText: ")
1628  }
1629  
1630  // MarshalText implements the [encoding.TextMarshaler] interface. The output
1631  // matches that of calling the [Time.AppendText] method.
1632  //
1633  // See [Time.AppendText] for more information.
1634  func (t Time) MarshalText() ([]byte, error) {
1635  	return t.appendTo([]byte{:0:len(RFC3339Nano)}, "Time.MarshalText: ")
1636  }
1637  
1638  // UnmarshalText implements the [encoding.TextUnmarshaler] interface.
1639  // The time must be in the RFC 3339 format.
1640  func (t *Time) UnmarshalText(data []byte) error {
1641  	var err error
1642  	*t, err = parseStrictRFC3339(data)
1643  	return err
1644  }
1645  
1646  // Unix returns the local Time corresponding to the given Unix time,
1647  // sec seconds and nsec nanoseconds since January 1, 1970 UTC.
1648  // It is valid to pass nsec outside the range [0, 999999999].
1649  // Not all sec values have a corresponding time value. One such
1650  // value is 1<<63-1 (the largest int64 value).
1651  func Unix(sec int64, nsec int64) Time {
1652  	if nsec < 0 || nsec >= 1e9 {
1653  		n := nsec / 1e9
1654  		sec += n
1655  		nsec -= n * 1e9
1656  		if nsec < 0 {
1657  			nsec += 1e9
1658  			sec--
1659  		}
1660  	}
1661  	return unixTime(sec, int32(nsec))
1662  }
1663  
1664  // UnixMilli returns the local Time corresponding to the given Unix time,
1665  // msec milliseconds since January 1, 1970 UTC.
1666  func UnixMilli(msec int64) Time {
1667  	return Unix(msec/1e3, (msec%1e3)*1e6)
1668  }
1669  
1670  // UnixMicro returns the local Time corresponding to the given Unix time,
1671  // usec microseconds since January 1, 1970 UTC.
1672  func UnixMicro(usec int64) Time {
1673  	return Unix(usec/1e6, (usec%1e6)*1e3)
1674  }
1675  
1676  // IsDST reports whether the time in the configured location is in Daylight Savings Time.
1677  func (t Time) IsDST() bool {
1678  	_, _, _, _, isDST := t.loc.lookup(t.Unix())
1679  	return isDST
1680  }
1681  
1682  func isLeap(year int) bool {
1683  	// year%4 == 0 && (year%100 != 0 || year%400 == 0)
1684  	// Bottom 2 bits must be clear.
1685  	// For multiples of 25, bottom 4 bits must be clear.
1686  	// Thanks to Cassio Neri for this trick.
1687  	mask := 0xf
1688  	if year%25 != 0 {
1689  		mask = 3
1690  	}
1691  	return year&mask == 0
1692  }
1693  
1694  // norm returns nhi, nlo such that
1695  //
1696  //	hi * base + lo == nhi * base + nlo
1697  //	0 <= nlo < base
1698  func norm(hi, lo, base int) (nhi, nlo int) {
1699  	if lo < 0 {
1700  		n := (-lo-1)/base + 1
1701  		hi -= n
1702  		lo += n * base
1703  	}
1704  	if lo >= base {
1705  		n := lo / base
1706  		hi += n
1707  		lo -= n * base
1708  	}
1709  	return hi, lo
1710  }
1711  
1712  // Date returns the Time corresponding to
1713  //
1714  //	yyyy-mm-dd hh:mm:ss + nsec nanoseconds
1715  //
1716  // in the appropriate zone for that time in the given location.
1717  //
1718  // The month, day, hour, min, sec, and nsec values may be outside
1719  // their usual ranges and will be normalized during the conversion.
1720  // For example, October 32 converts to November 1.
1721  //
1722  // A daylight savings time transition skips or repeats times.
1723  // For example, in the United States, March 13, 2011 2:15am never occurred,
1724  // while November 6, 2011 1:15am occurred twice. In such cases, the
1725  // choice of time zone, and therefore the time, is not well-defined.
1726  // Date returns a time that is correct in one of the two zones involved
1727  // in the transition, but it does not guarantee which.
1728  //
1729  // Date panics if loc is nil.
1730  func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) Time {
1731  	if loc == nil {
1732  		panic("time: missing Location in call to Date")
1733  	}
1734  
1735  	// Normalize month, overflowing into year.
1736  	m := int(month) - 1
1737  	year, m = norm(year, m, 12)
1738  	month = Month(m) + 1
1739  
1740  	// Normalize nsec, sec, min, hour, overflowing into day.
1741  	sec, nsec = norm(sec, nsec, 1e9)
1742  	min, sec = norm(min, sec, 60)
1743  	hour, min = norm(hour, min, 60)
1744  	day, hour = norm(day, hour, 24)
1745  
1746  	// Convert to absolute time and then Unix time.
1747  	unix := int64(dateToAbsDays(int64(year), month, day))*secondsPerDay +
1748  		int64(hour*secondsPerHour+min*secondsPerMinute+sec) +
1749  		absoluteToUnix
1750  
1751  	// Look for zone offset for expected time, so we can adjust to UTC.
1752  	// The lookup function expects UTC, so first we pass unix in the
1753  	// hope that it will not be too close to a zone transition,
1754  	// and then adjust if it is.
1755  	_, offset, start, end, _ := loc.lookup(unix)
1756  	if offset != 0 {
1757  		utc := unix - int64(offset)
1758  		// If utc is valid for the time zone we found, then we have the right offset.
1759  		// If not, we get the correct offset by looking up utc in the location.
1760  		if utc < start || utc >= end {
1761  			_, offset, _, _, _ = loc.lookup(utc)
1762  		}
1763  		unix -= int64(offset)
1764  	}
1765  
1766  	t := unixTime(unix, int32(nsec))
1767  	t.setLoc(loc)
1768  	return t
1769  }
1770  
1771  // Truncate returns the result of rounding t down to a multiple of d (since the zero time).
1772  // If d <= 0, Truncate returns t stripped of any monotonic clock reading but otherwise unchanged.
1773  //
1774  // Truncate operates on the time as an absolute duration since the
1775  // zero time; it does not operate on the presentation form of the
1776  // time. Thus, Truncate(Hour) may return a time with a non-zero
1777  // minute, depending on the time's Location.
1778  func (t Time) Truncate(d Duration) Time {
1779  	t.stripMono()
1780  	if d <= 0 {
1781  		return t
1782  	}
1783  	_, r := div(t, d)
1784  	return t.Add(-r)
1785  }
1786  
1787  // Round returns the result of rounding t to the nearest multiple of d (since the zero time).
1788  // The rounding behavior for halfway values is to round up.
1789  // If d <= 0, Round returns t stripped of any monotonic clock reading but otherwise unchanged.
1790  //
1791  // Round operates on the time as an absolute duration since the
1792  // zero time; it does not operate on the presentation form of the
1793  // time. Thus, Round(Hour) may return a time with a non-zero
1794  // minute, depending on the time's Location.
1795  func (t Time) Round(d Duration) Time {
1796  	t.stripMono()
1797  	if d <= 0 {
1798  		return t
1799  	}
1800  	_, r := div(t, d)
1801  	if lessThanHalf(r, d) {
1802  		return t.Add(-r)
1803  	}
1804  	return t.Add(d - r)
1805  }
1806  
1807  // div divides t by d and returns the quotient parity and remainder.
1808  // We don't use the quotient parity anymore (round half up instead of round to even)
1809  // but it's still here in case we change our minds.
1810  func div(t Time, d Duration) (qmod2 int, r Duration) {
1811  	neg := false
1812  	nsec := t.nsec()
1813  	sec := t.sec()
1814  	if sec < 0 {
1815  		// Operate on absolute value.
1816  		neg = true
1817  		sec = -sec
1818  		nsec = -nsec
1819  		if nsec < 0 {
1820  			nsec += 1e9
1821  			sec-- // sec >= 1 before the -- so safe
1822  		}
1823  	}
1824  
1825  	switch {
1826  	// Special case: 2d divides 1 second.
1827  	case d < Second && Second%(d+d) == 0:
1828  		qmod2 = int(nsec/int32(d)) & 1
1829  		r = Duration(nsec % int32(d))
1830  
1831  	// Special case: d is a multiple of 1 second.
1832  	case d%Second == 0:
1833  		d1 := int64(d / Second)
1834  		qmod2 = int(sec/d1) & 1
1835  		r = Duration(sec%d1)*Second + Duration(nsec)
1836  
1837  	// General case.
1838  	// This could be faster if more cleverness were applied,
1839  	// but it's really only here to avoid special case restrictions in the API.
1840  	// No one will care about these cases.
1841  	default:
1842  		// Compute nanoseconds as 128-bit number.
1843  		sec := uint64(sec)
1844  		tmp := (sec >> 32) * 1e9
1845  		u1 := tmp >> 32
1846  		u0 := tmp << 32
1847  		tmp = (sec & 0xFFFFFFFF) * 1e9
1848  		u0x, u0 := u0, u0+tmp
1849  		if u0 < u0x {
1850  			u1++
1851  		}
1852  		u0x, u0 = u0, u0+uint64(nsec)
1853  		if u0 < u0x {
1854  			u1++
1855  		}
1856  
1857  		// Compute remainder by subtracting r<<k for decreasing k.
1858  		// Quotient parity is whether we subtract on last round.
1859  		d1 := uint64(d)
1860  		for d1>>63 != 1 {
1861  			d1 <<= 1
1862  		}
1863  		d0 := uint64(0)
1864  		for {
1865  			qmod2 = 0
1866  			if u1 > d1 || u1 == d1 && u0 >= d0 {
1867  				// subtract
1868  				qmod2 = 1
1869  				u0x, u0 = u0, u0-d0
1870  				if u0 > u0x {
1871  					u1--
1872  				}
1873  				u1 -= d1
1874  			}
1875  			if d1 == 0 && d0 == uint64(d) {
1876  				break
1877  			}
1878  			d0 >>= 1
1879  			d0 |= (d1 & 1) << 63
1880  			d1 >>= 1
1881  		}
1882  		r = Duration(u0)
1883  	}
1884  
1885  	if neg && r != 0 {
1886  		// If input was negative and not an exact multiple of d, we computed q, r such that
1887  		//	q*d + r = -t
1888  		// But the right answers are given by -(q-1), d-r:
1889  		//	q*d + r = -t
1890  		//	-q*d - r = t
1891  		//	-(q-1)*d + (d - r) = t
1892  		qmod2 ^= 1
1893  		r = d - r
1894  	}
1895  	return
1896  }
1897  
1898  // Regrettable Linkname Compatibility
1899  //
1900  // timeAbs, absDate, and absClock mimic old internal details, no longer used.
1901  // Widely used packages linknamed these to get “faster” time routines.
1902  // Notable members of the hall of shame include:
1903  //   - gitee.com/quant1x/gox
1904  //   - github.com/phuslu/log
1905  //
1906  // phuslu hard-coded 'Unix time + 9223372028715321600' [sic]
1907  // as the input to absDate and absClock, using the old Jan 1-based
1908  // absolute times.
1909  // quant1x linknamed the time.Time.abs method and passed the
1910  // result of that method to absDate and absClock.
1911  //
1912  // Keeping both of these working forces us to provide these three
1913  // routines here, operating on the old Jan 1-based epoch instead
1914  // of the new March 1-based epoch. And the fact that time.Time.abs
1915  // was linknamed means that we have to call the current abs method
1916  // something different (time.Time.absSec, defined above) to make it
1917  // possible to provide this simulation of the old routines here.
1918  //
1919  // None of this code is linked into the binary if not referenced by
1920  // these linkname-happy packages. In particular, despite its name,
1921  // time.Time.abs does not appear in the time.Time method table.
1922  //
1923  // Do not remove these routines or their linknames, or change the
1924  // type signature or meaning of arguments.
1925  
1926  //go:linkname legacyTimeTimeAbs time.Time.abs
1927  func legacyTimeTimeAbs(t Time) uint64 {
1928  	return uint64(t.absSec() - marchThruDecember*secondsPerDay)
1929  }
1930  
1931  //go:linkname legacyAbsClock time.absClock
1932  func legacyAbsClock(abs uint64) (hour, min, sec int) {
1933  	return absSeconds(abs + marchThruDecember*secondsPerDay).clock()
1934  }
1935  
1936  //go:linkname legacyAbsDate time.absDate
1937  func legacyAbsDate(abs uint64, full bool) (year int, month Month, day int, yday int) {
1938  	d := absSeconds(abs + marchThruDecember*secondsPerDay).days()
1939  	year, month, day = d.date()
1940  	_, yday = d.yearYday()
1941  	yday-- // yearYday is 1-based, old API was 0-based
1942  	return
1943  }
1944