Don’t trust leap-seconds.list comments

Inspired by public-domain code from Dennis Ferguson and Chris Woodbury.
* NEWS: Mention this.
* leapseconds.awk: Improve comments, and generalize patterns a bit.
No need to compute monthnum, monthlen; call sstamp_init instead.
Use sstamp_to_ymdhMs to convert data, instead of using comments.
* leapseconds.awk (sstamp_init, sstamp_to_ymdhMs):
New functions, derived from Dennis Ferguson’s functions.

NEWS

@@ -57,6 +57,10 @@ Unreleased, experimental changes
 
   Changes to code
 
+    leapseconds.awk now relies only its input data, rather than
+    also relying on its comments.  (Inspired by code from Dennis
+    Ferguson and Chris Woodbury.)
+
     The code now defends against CRLFs in leap-seconds.list.
     (Thanks to Brian Inglis and Chris Woodbury.)
 

leapseconds.awk

@@ -1,17 +1,29 @@
-# Generate the 'leapseconds' file from 'leap-seconds.list'.
+# Generate zic format 'leapseconds' from NIST format 'leap-seconds.list'.
 
 # This file is in the public domain.
 
+# This program uses awk arithmetic.  POSIX requires awk to support
+# exact integer arithmetic only through 10**10, which means for NTP
+# timestamps this program works only to the year 2216, which is the
+# year 1900 plus 10**10 seconds.  However, in practice
+# POSIX-conforming awk implementations invariably use IEEE-754 double
+# and so support exact integers through 2**53.  By the year 2216,
+# POSIX will almost surely require at least 2**53 for awk, so for NTP
+# timestamps this program should be good until the year 285,428,681
+# (the year 1900 plus 2**53 seconds).  By then leap seconds will be
+# long obsolete, as the Earth will likely slow down so much that
+# there will less than 23 hours in a day and so some other scheme
+# will be needed.
+
 BEGIN {
   print "# Allowance for leap seconds added to each time zone file."
   print ""
   print "# This file is in the public domain."
   print ""
   print "# This file is generated automatically from the data in the public-domain"
-  print "# leap-seconds.list file, which can be copied from"
+  print "# NIST format leap-seconds.list file, which can be copied from"
   print "# <ftp://ftp.nist.gov/pub/time/leap-seconds.list>"
-  print "# or <ftp://ftp.boulder.nist.gov/pub/time/leap-seconds.list>"
-  print "# or <ftp://tycho.usno.navy.mil/pub/ntp/leap-seconds.list>."
+  print "# or <ftp://ftp.boulder.nist.gov/pub/time/leap-seconds.list>."
   print "# For more about leap-seconds.list, please see"
   print "# The NTP Timescale and Leap Seconds"
   print "# <https://www.eecis.udel.edu/~mills/leap.html>."
@@ -21,7 +33,7 @@ BEGIN {
   print "# International Telecommunication Union - Radiocommunication Sector"
   print "# (ITU-R) Recommendation TF.460-6 (02/2002)"
   print "# <https://www.itu.int/rec/R-REC-TF.460-6-200202-I/>."
-  print "# The International Earth Rotation and Reference Systems Service"
+  print "# The International Earth Rotation and Reference Systems Service (IERS)"
   print "# periodically uses leap seconds to keep UTC to within 0.9 s of UT1"
   print "# (a proxy for Earth's angle in space as measured by astronomers)"
   print "# and publishes leap second data in a copyrighted file"
@@ -30,16 +42,18 @@ BEGIN {
   print "# URSI Radio Sci Bull. 2016;89(4):30-6. doi:10.23919/URSIRSB.2016.7909995"
   print "# <https://ieeexplore.ieee.org/document/7909995>."
   print ""
-  print "# There were no leap seconds before 1972, because the official mechanism"
-  print "# accounting for the discrepancy between atomic time and the earth's rotation"
-  print "# did not exist.  The first (\"1 Jan 1972\") data line in leap-seconds.list"
+  print "# There were no leap seconds before 1972, as no official mechanism"
+  print "# accounted for the discrepancy between atomic time (TAI) and the earth's"
+  print "# rotation.  The first (\"1 Jan 1972\") data line in leap-seconds.list"
   print "# does not denote a leap second; it denotes the start of the current definition"
   print "# of UTC."
   print ""
-  print "# The correction (+ or -) is made at the given time, so lines"
-  print "# typically look like this:"
+  print "# All leap-seconds are Stationary (S) at the given UTC time."
+  print "# The correction (+ or -) is made at the given time, so in the unlikely"
+  print "# event of a negative leap second, a line would look like this:"
+  print "# Leap	YEAR	MON	DAY	23:59:59	-	S"
+  print "# Typical lines look like this:"
   print "# Leap	YEAR	MON	DAY	23:59:60	+	S"
-  print "# A negative leap second's columns 5 and 6 would be '23:59:59' and '-'."
 
   monthabbr[ 1] = "Jan"
   monthabbr[ 2] = "Feb"
@@ -53,48 +67,34 @@ BEGIN {
   monthabbr[10] = "Oct"
   monthabbr[11] = "Nov"
   monthabbr[12] = "Dec"
-  for (i in monthabbr) {
-      monthnum[monthabbr[i]] = i
-      monthlen[i] = 31
-  }
-  monthlen[2] = 28
-  monthlen[4] = monthlen[6] = monthlen[9] = monthlen[11] = 30
 
-  # In case the input has CRLF form a la NIST.
+  # Strip trailing CR, in case the input has CRLF form a la NIST.
   RS = "\r?\n"
+
+  sstamp_init()
 }
 
-/^#\tUpdated through/ || /^#\tFile expires on:/ {
+/^#[ \t]*[Uu]pdated through/ || /^#[ \t]*[Ff]ile expires on/ {
     last_lines = last_lines $0 "\n"
 }
 
 /^#[$][ \t]/ { updated = $2 }
 /^#[@][ \t]/ { expires = $2 }
 
-/^#/ { next }
+/^[ \t]*#/ { next }
 
 {
     NTP_timestamp = $1
     TAI_minus_UTC = $2
-    hash_mark = $3
-    one = $4
-    month = $5
-    year = $6
     if (old_TAI_minus_UTC) {
 	if (old_TAI_minus_UTC < TAI_minus_UTC) {
 	    sign = "23:59:60\t+"
 	} else {
 	    sign = "23:59:59\t-"
 	}
-	m = monthnum[month] - 1
-	if (m == 0) {
-	    year--;
-	    m = 12
-	}
-	month = monthabbr[m]
-	day = monthlen[m]
-	day += m == 2 && year % 4 == 0 && (year % 100 != 0 || year % 400 == 0)
-	printf "Leap\t%s\t%s\t%s\t%s\tS\n", year, month, day, sign
+	sstamp_to_ymdhMs(NTP_timestamp - 1, ss_NTP)
+	printf "Leap\t%d\t%s\t%d\t%s\tS\n", \
+	  ss_year, monthabbr[ss_month], ss_mday, sign
     }
     old_TAI_minus_UTC = TAI_minus_UTC
 }
@@ -107,7 +107,117 @@ END {
 
     print ""
     print "# POSIX timestamps for the data in this file:"
-    printf "#updated %d\n", updated - epoch_minus_NTP
-    printf "#expires %d\n", expires - epoch_minus_NTP
+    sstamp_to_ymdhMs(updated, ss_NTP)
+    printf "#updated %d (%.4d-%.2d-%.2d %.2d:%.2d:%.2d UTC)\n", \
+      updated - epoch_minus_NTP, \
+      ss_year, ss_month, ss_mday, ss_hour, ss_min, ss_sec
+    sstamp_to_ymdhMs(expires, ss_NTP)
+    printf "#expires %d (%.4d-%.2d-%.2d %.2d:%.2d:%.2d UTC)\n", \
+      expires - epoch_minus_NTP, \
+      ss_year, ss_month, ss_mday, ss_hour, ss_min, ss_sec
+
     printf "\n%s", last_lines
 }
+
+# sstamp_to_ymdhMs - convert seconds timestamp to date and time
+#
+# Call as:
+#
+#    sstamp_to_ymdhMs(sstamp, epoch_days)
+#
+# where:
+#
+#    sstamp - is the seconds timestamp.
+#    epoch_days - is the timestamp epoch in Gregorian days since 1600-03-01.
+#	ss_NTP is appropriate for an NTP sstamp.
+#
+# Both arguments should be nonnegative integers.
+# On return, the following variables are set based on sstamp:
+#
+#    ss_year	- Gregorian calendar year
+#    ss_month	- month of the year (1-January to 12-December)
+#    ss_mday	- day of the month (1-31)
+#    ss_hour	- hour (0-23)
+#    ss_min	- minute (0-59)
+#    ss_sec	- second (0-59)
+#    ss_wday	- day of week (0-Sunday to 6-Saturday)
+#
+# The function sstamp_init should be called prior to using sstamp_to_ymdhMs.
+
+function sstamp_init()
+{
+  # Days in month N, where March is month 0 and January month 10.
+  ss_mon_days[ 0] = 31
+  ss_mon_days[ 1] = 30
+  ss_mon_days[ 2] = 31
+  ss_mon_days[ 3] = 30
+  ss_mon_days[ 4] = 31
+  ss_mon_days[ 5] = 31
+  ss_mon_days[ 6] = 30
+  ss_mon_days[ 7] = 31
+  ss_mon_days[ 8] = 30
+  ss_mon_days[ 9] = 31
+  ss_mon_days[10] = 31
+
+  # Counts of days in a Gregorian year, quad-year, century, and quad-century.
+  ss_year_days = 365
+  ss_quadyear_days = ss_year_days * 4 + 1
+  ss_century_days = ss_quadyear_days * 25 - 1
+  ss_quadcentury_days = ss_century_days * 4 + 1
+
+  # Standard day epochs, suitable for epoch_days.
+  # ss_MJD = 94493
+  # ss_POSIX = 135080
+  ss_NTP = 109513
+}
+
+function sstamp_to_ymdhMs(sstamp, epoch_days, \
+			  quadcentury, century, quadyear, year, month, day)
+{
+  ss_hour = int(sstamp / 3600) % 24
+  ss_min = int(sstamp / 60) % 60
+  ss_sec = sstamp % 60
+
+  # Start with a count of days since 1600-03-01 Gregorian.
+  day = epoch_days + int(sstamp / (24 * 60 * 60))
+
+  # Compute a year-month-day date with days of the month numbered
+  # 0-30, months (March-February) numbered 0-11, and years that start
+  # start March 1 and end after the last day of February.  A quad-year
+  # starts on March 1 of a year evenly divisible by 4 and ends after
+  # the last day of February 4 years later.  A century starts on and
+  # ends before March 1 in years evenly divisible by 100.
+  # A quad-century starts on and ends before March 1 in years divisible
+  # by 400.  While the number of days in a quad-century is a constant,
+  # the number of days in each other time period can vary by 1.
+  # Any variation is in the last day of the time period (there might
+  # or might not be a February 29) where it is easy to deal with.
+
+  quadcentury = int(day / ss_quadcentury_days)
+  day -= quadcentury * ss_quadcentury_days
+  ss_wday = (day + 3) % 7
+  century = int(day / ss_century_days)
+  century -= century == 4
+  day -= century * ss_century_days
+  quadyear = int(day / ss_quadyear_days)
+  day -= quadyear * ss_quadyear_days
+  year = int(day / ss_year_days)
+  year -= year == 4
+  day -= year * ss_year_days
+  for (month = 0; month < 12; month++) {
+    if (day < ss_mon_days[month])
+      break
+    day -= ss_mon_days[month]
+  }
+
+  # Convert the date to a conventional day of month (1-31),
+  # month (1-12, January-December) and Gregorian year.
+  ss_mday = day + 1
+  if (month <= 9) {
+    ss_month = month + 3
+  } else {
+    ss_month = month - 9
+    year++
+  }
+  ss_year = 1600 + quadcentury * 400 + century * 100 + quadyear * 4 + year
+}