1# Generate zic format 'leapseconds' from NIST format 'leap-seconds.list'. 2 3# This file is in the public domain. 4 5# This program uses awk arithmetic. POSIX requires awk to support 6# exact integer arithmetic only through 10**10, which means for NTP 7# timestamps this program works only to the year 2216, which is the 8# year 1900 plus 10**10 seconds. However, in practice 9# POSIX-conforming awk implementations invariably use IEEE-754 double 10# and so support exact integers through 2**53. By the year 2216, 11# POSIX will almost surely require at least 2**53 for awk, so for NTP 12# timestamps this program should be good until the year 285,428,681 13# (the year 1900 plus 2**53 seconds). By then leap seconds will be 14# long obsolete, as the Earth will likely slow down so much that 15# there will be more than 25 hours per day and so some other scheme 16# will be needed. 17 18BEGIN { 19 print "# Allowance for leap seconds added to each time zone file." 20 print "" 21 print "# This file is in the public domain." 22 print "" 23 print "# This file is generated automatically from the data in the public-domain" 24 print "# NIST format leap-seconds.list file, which can be copied from" 25 print "# <ftp://ftp.nist.gov/pub/time/leap-seconds.list>" 26 print "# or <ftp://ftp.boulder.nist.gov/pub/time/leap-seconds.list>." 27 print "# For more about leap-seconds.list, please see" 28 print "# The NTP Timescale and Leap Seconds" 29 print "# <https://www.eecis.udel.edu/~mills/leap.html>." 30 print "" 31 print "# The rules for leap seconds are specified in Annex 1 (Time scales) of:" 32 print "# Standard-frequency and time-signal emissions." 33 print "# International Telecommunication Union - Radiocommunication Sector" 34 print "# (ITU-R) Recommendation TF.460-6 (02/2002)" 35 print "# <https://www.itu.int/rec/R-REC-TF.460-6-200202-I/>." 36 print "# The International Earth Rotation and Reference Systems Service (IERS)" 37 print "# periodically uses leap seconds to keep UTC to within 0.9 s of UT1" 38 print "# (a proxy for Earth's angle in space as measured by astronomers)" 39 print "# and publishes leap second data in a copyrighted file" 40 print "# <https://hpiers.obspm.fr/iers/bul/bulc/Leap_Second.dat>." 41 print "# See: Levine J. Coordinated Universal Time and the leap second." 42 print "# URSI Radio Sci Bull. 2016;89(4):30-6. doi:10.23919/URSIRSB.2016.7909995" 43 print "# <https://ieeexplore.ieee.org/document/7909995>." 44 print "" 45 print "# There were no leap seconds before 1972, as no official mechanism" 46 print "# accounted for the discrepancy between atomic time (TAI) and the earth's" 47 print "# rotation. The first (\"1 Jan 1972\") data line in leap-seconds.list" 48 print "# does not denote a leap second; it denotes the start of the current definition" 49 print "# of UTC." 50 print "" 51 print "# All leap-seconds are Stationary (S) at the given UTC time." 52 print "# The correction (+ or -) is made at the given time, so in the unlikely" 53 print "# event of a negative leap second, a line would look like this:" 54 print "# Leap YEAR MON DAY 23:59:59 - S" 55 print "# Typical lines look like this:" 56 print "# Leap YEAR MON DAY 23:59:60 + S" 57 58 monthabbr[ 1] = "Jan" 59 monthabbr[ 2] = "Feb" 60 monthabbr[ 3] = "Mar" 61 monthabbr[ 4] = "Apr" 62 monthabbr[ 5] = "May" 63 monthabbr[ 6] = "Jun" 64 monthabbr[ 7] = "Jul" 65 monthabbr[ 8] = "Aug" 66 monthabbr[ 9] = "Sep" 67 monthabbr[10] = "Oct" 68 monthabbr[11] = "Nov" 69 monthabbr[12] = "Dec" 70 71 # Strip trailing CR, in case the input has CRLF form a la NIST. 72 RS = "\r?\n" 73 74 sstamp_init() 75} 76 77/^#[ \t]*[Uu]pdated through/ || /^#[ \t]*[Ff]ile expires on/ { 78 last_lines = last_lines $0 "\n" 79} 80 81/^#[$][ \t]/ { updated = $2 } 82/^#[@][ \t]/ { expires = $2 } 83 84/^[ \t]*#/ { next } 85 86{ 87 NTP_timestamp = $1 88 TAI_minus_UTC = $2 89 if (old_TAI_minus_UTC) { 90 if (old_TAI_minus_UTC < TAI_minus_UTC) { 91 sign = "23:59:60\t+" 92 } else { 93 sign = "23:59:59\t-" 94 } 95 sstamp_to_ymdhMs(NTP_timestamp - 1, ss_NTP) 96 printf "Leap\t%d\t%s\t%d\t%s\tS\n", \ 97 ss_year, monthabbr[ss_month], ss_mday, sign 98 } 99 old_TAI_minus_UTC = TAI_minus_UTC 100} 101 102END { 103 # The difference between the NTP and POSIX epochs is 70 years 104 # (including 17 leap days), each 24 hours of 60 minutes of 60 105 # seconds each. 106 epoch_minus_NTP = ((1970 - 1900) * 365 + 17) * 24 * 60 * 60 107 108 print "" 109 print "# POSIX timestamps for the data in this file:" 110 sstamp_to_ymdhMs(updated, ss_NTP) 111 printf "#updated %d (%.4d-%.2d-%.2d %.2d:%.2d:%.2d UTC)\n", \ 112 updated - epoch_minus_NTP, \ 113 ss_year, ss_month, ss_mday, ss_hour, ss_min, ss_sec 114 sstamp_to_ymdhMs(expires, ss_NTP) 115 printf "#expires %d (%.4d-%.2d-%.2d %.2d:%.2d:%.2d UTC)\n", \ 116 expires - epoch_minus_NTP, \ 117 ss_year, ss_month, ss_mday, ss_hour, ss_min, ss_sec 118 119 printf "\n%s", last_lines 120} 121 122# sstamp_to_ymdhMs - convert seconds timestamp to date and time 123# 124# Call as: 125# 126# sstamp_to_ymdhMs(sstamp, epoch_days) 127# 128# where: 129# 130# sstamp - is the seconds timestamp. 131# epoch_days - is the timestamp epoch in Gregorian days since 1600-03-01. 132# ss_NTP is appropriate for an NTP sstamp. 133# 134# Both arguments should be nonnegative integers. 135# On return, the following variables are set based on sstamp: 136# 137# ss_year - Gregorian calendar year 138# ss_month - month of the year (1-January to 12-December) 139# ss_mday - day of the month (1-31) 140# ss_hour - hour (0-23) 141# ss_min - minute (0-59) 142# ss_sec - second (0-59) 143# ss_wday - day of week (0-Sunday to 6-Saturday) 144# 145# The function sstamp_init should be called prior to using sstamp_to_ymdhMs. 146 147function sstamp_init() 148{ 149 # Days in month N, where March is month 0 and January month 10. 150 ss_mon_days[ 0] = 31 151 ss_mon_days[ 1] = 30 152 ss_mon_days[ 2] = 31 153 ss_mon_days[ 3] = 30 154 ss_mon_days[ 4] = 31 155 ss_mon_days[ 5] = 31 156 ss_mon_days[ 6] = 30 157 ss_mon_days[ 7] = 31 158 ss_mon_days[ 8] = 30 159 ss_mon_days[ 9] = 31 160 ss_mon_days[10] = 31 161 162 # Counts of days in a Gregorian year, quad-year, century, and quad-century. 163 ss_year_days = 365 164 ss_quadyear_days = ss_year_days * 4 + 1 165 ss_century_days = ss_quadyear_days * 25 - 1 166 ss_quadcentury_days = ss_century_days * 4 + 1 167 168 # Standard day epochs, suitable for epoch_days. 169 # ss_MJD = 94493 170 # ss_POSIX = 135080 171 ss_NTP = 109513 172} 173 174function sstamp_to_ymdhMs(sstamp, epoch_days, \ 175 quadcentury, century, quadyear, year, month, day) 176{ 177 ss_hour = int(sstamp / 3600) % 24 178 ss_min = int(sstamp / 60) % 60 179 ss_sec = sstamp % 60 180 181 # Start with a count of days since 1600-03-01 Gregorian. 182 day = epoch_days + int(sstamp / (24 * 60 * 60)) 183 184 # Compute a year-month-day date with days of the month numbered 185 # 0-30, months (March-February) numbered 0-11, and years that start 186 # start March 1 and end after the last day of February. A quad-year 187 # starts on March 1 of a year evenly divisible by 4 and ends after 188 # the last day of February 4 years later. A century starts on and 189 # ends before March 1 in years evenly divisible by 100. 190 # A quad-century starts on and ends before March 1 in years divisible 191 # by 400. While the number of days in a quad-century is a constant, 192 # the number of days in each other time period can vary by 1. 193 # Any variation is in the last day of the time period (there might 194 # or might not be a February 29) where it is easy to deal with. 195 196 quadcentury = int(day / ss_quadcentury_days) 197 day -= quadcentury * ss_quadcentury_days 198 ss_wday = (day + 3) % 7 199 century = int(day / ss_century_days) 200 century -= century == 4 201 day -= century * ss_century_days 202 quadyear = int(day / ss_quadyear_days) 203 day -= quadyear * ss_quadyear_days 204 year = int(day / ss_year_days) 205 year -= year == 4 206 day -= year * ss_year_days 207 for (month = 0; month < 11; month++) { 208 if (day < ss_mon_days[month]) 209 break 210 day -= ss_mon_days[month] 211 } 212 213 # Convert the date to a conventional day of month (1-31), 214 # month (1-12, January-December) and Gregorian year. 215 ss_mday = day + 1 216 if (month <= 9) { 217 ss_month = month + 3 218 } else { 219 ss_month = month - 9 220 year++ 221 } 222 ss_year = 1600 + quadcentury * 400 + century * 100 + quadyear * 4 + year 223} 224