Conversion between flavours of julian date
use Date::JD qw(jd_to_mjd mjd_to_cjdnf cjdn_to_rd);
$mjd = jd_to_mjd($jd);
($cjdn, $cjdf) = mjd_to_cjdnf($mjd, $tz);
$rd = cjdn_to_rd($cjdn, $cjdf);
# and 509 other conversion functions
For date and time calculations it is convenient to represent dates by a simple linear count of days, rather than in a particular calendar. This is such a good idea that it has been invented several times. If there were a single such linear count then it would be the obvious data interchange format between calendar modules. With several versions, calendar modules can use such sensible data formats and still have interoperability problems. This module tackles that problem, by performing conversions between different flavours of day count. These day count systems are generically known as \*(L"Julian Dates\*(R", after the most venerable of them.
Among Julian Date systems there are also some non-trivial differences of concept. There are systems that count only complete days, and those that count fractional days also. There are some that are fixed to Universal Time (time on the prime meridian), and others that are interpreted according to a timezone. Some consider the day to start at noon and others at midnight, which is semantically significant for the complete-day counts. The functions of this module appropriately handle the semantics of all the non-trivial conversions.
The day count systems supported by this module are Julian Date, Reduced Julian Date, Modified Julian Date, Dublin Julian Date, Truncated Julian Date, Chronological Julian Date, Rata Die, and Lilian Date, each in both integral and fractional forms.
In the interests of orthogonality, all flavours of day count come in both integral and fractional varieties. Generally, there is a quantity named \*(L"\s-1XYZD\s0\*(R" (\*(L"\s-1XYZ\s0 Date\*(R") which is a real count of days since a particular epoch (an integer plus a fraction) and a corresponding quantity named \*(L"\s-1XYZDN\s0\*(R" (\*(L"\s-1XYZ\s0 Day Number\*(R") which is a count of complete days since the same epoch. \s-1XYZDN\s0 is the integral part of \s-1XYZD\s0. There is also a quantity named \*(L"\s-1XYZDF\s0\*(R" (\*(L"\s-1XYZ\s0 Day Fraction\*(R") which is a count of fractional days since the \s-1XYZDN\s0 changed (whether that is noon or midnight). \s-1XYZDF\s0 is the fractional part of \s-1XYZD\s0, in the range [0, 1).
This quantity naming pattern is derived from \s-1JD\s0 (Julian Date) and \s-1JDN\s0 (Julian Day Number) which have the described correspondence. Most of the other flavours of day count listed below conventionally come in only one of the two varieties. The \*(L"\s-1XYZDF\s0\*(R" name type is a neologism.
All calendar dates given are in \s-1ISO\s0 8601 form (Gregorian calendar with astronomical year numbering). An hour number is appended to each date, separated by a \*(L"T\*(R"; hour 00 is midnight at the start of the day and hour 12 is noon in the middle of the day. An appended \*(L"Z\*(R" indicates that the date is to be interpreted in Universal Time (the timezone of the prime meridian), and so is absolute; where any other timezone is to be used then this is explicitly noted.
days elapsed since -4713-11-24T12Z. This epoch is the most recent coincidence of the first year of the Metonic cycle, indiction cycle, and day-of-week cycle, using the Julian calendar. It was correspondingly named after the Julian calendar, and thus after Julius Caesar. Some information can be found at <http://en.wikipedia.org/wiki/Julian_day>.
days elapsed since 1858-11-16T12Z (\s-1JD\s0 2400000.0). Rarely used.
days elapsed since 1858-11-17T00Z (\s-1JD\s0 2400000.5). This was introduced by the Smithsonian Astrophysical Observatory in 1957, and is recommended for general use by the International Astronomical Union and other authorities.
days elapsed since 1899-12-31T12Z (\s-1JD\s0 2415020.0). This was invented by the International Astronomical Union, and the epoch in Terrestrial Time is the J1900.0 epoch used in astronomy. (Note: not B1900.0, which is a few hours later.) It is rarely used.
days elapsed since 1968-05-24T00Z (\s-1JD\s0 2440000.5). This is primarily used by \s-1NASA\s0, who devised it during the Apollo era. There is a rumour that it's defined cyclically, as (\s-1JD\s0 - 0.5) mod 10000, but see <http://cossc.gsfc.nasa.gov/cossc/batse/hilev/TJD.TABLE>.
days elapsed since -4713-11-24T00 in the timezone of interest. \s-1CJD\s0 = \s-1JD\s0 + 0.5 + Zoff, where Zoff is the timezone offset in fractional days. This was devised by Peter Meyer, and described in <http://www.hermetic.ch/cal_stud/cjd.htm>.
days elapsed since 0000-12-31T00 in the timezone of interest (\s-1CJD\s0 1721425.0). This is defined in the book Calendrical Calculations. Confusingly, in the book the integral form is also called \*(L"\s-1RD\s0\*(R". The integral form is called \*(L"\s-1RDN\s0\*(R" by this module to avoid confusion, reserving the name \*(L"\s-1RD\s0\*(R" for the fractional form. (The book is best treated with caution due to the embarrassingly large number of errors and instances of muddled thinking.)
days elapsed since 1582-10-14T00 in the timezone of interest (\s-1CJD\s0 2299160.0). This epoch is the day before the day that the Gregorian calendar first went into use. It is named after Aloysius Lilius, the inventor of the Gregorian calendar.
The interesting differences between these flavours are whether the day starts at noon or at midnight, and whether they are absolute or timezone-relative. Three of the four combinations of these features exist. There is no convention for counting days from timezone-relative noon that the author of this module is aware of.
For more background on these day count systems, <http://en.wikipedia.org/wiki/Julian_Date> is a good starting place.
A day count has meaning only in the context of a particular definition of \*(L"day\*(R". There are two main flavours of day to consider: solar and conventional.
A solar day is based on the apparent motion of Sol in the Terran sky (and thus on the rotation and orbit of Terra). The rotation of Terra is not constant in time, so this type of day is really a measure of angle, not of time. This is how days have been counted since antiquity, and is still (as of 2006) the basis of civil time. There are two subtypes of solar day: apparent and mean. The apparent solar day is based on the actual observable position of Sol in the sky from day to day, whereas the mean solar day smooths this motion out, in time, over the course of the year. At the sub-second level there are different types of smoothing that can be used (\s-1UT1\s0, \s-1UT2\s0, et al).
A conventional day is any type of day that is not based on Terran rotation. The astronomical Ephemeris Time, a time scale based on the motion of bodies in the Solar system, has a time unit that it calls \*(L"day\*(R" which is derived from astronomical observations. The modern relativistic coordinate time scales such as \s-1TT\s0 have a notional \*(L"day\*(R" of exactly 86400 \s-1SI\s0 seconds. The atomic time scale \s-1TAI\s0 also has a \*(L"day\*(R" which is as close to 86400 \s-1SI\s0 seconds as can be achieved. All of these \*(L"days\*(R" are roughly the duration of one Sol-relative rotation of Terra during the early nineteenth century, but are not otherwise related to planetary rotation.
Each of the day count scales handled by this module can be used with any of these types of day. For a day number to be meaningful it is necessary to be aware of which kind of day it is counting. Conversion between the different types of day is out of scope for this module. (See Time::UTC for \s-1TAI/UTC\s0 conversion.)
Day counts in this \s-1API\s0 may be native Perl numbers or \*(C`Math::BigRat\*(C' objects. Both are acceptable for all parameters, in any combination. In all conversion functions, the result is of the same type as the input, provided that the inputs are of consistent type. If native Perl numbers are supplied then the conversion is subject to floating point rounding, and possible overflow if the numbers are extremely large. The use of \*(C`Math::BigRat\*(C' is recommended to avoid these problems. With \*(C`Math::BigRat\*(C' the results are exact.
There are conversion functions between all pairs of day count systems. This is a total of 512 conversion functions (including 32 identity functions).
When converting between timezone-relative counts (\s-1CJD\s0, \s-1RD\s0, \s-1LD\s0) and absolute counts (\s-1JD\s0, \s-1RJD\s0, \s-1MJD\s0, \s-1DJD\s0, \s-1TJD\s0), the timezone that is being used must be specified. It is given in a \s-1ZONE\s0 argument as a fractional number of days offset from Universal Time. For example, \s-1US\s0 Central Standard Time, 6 hours behind \s-1UT\s0, would be specified as a \s-1ZONE\s0 argument of -0.25. Beware of floating point rounding when the offset does not have a terminating binary representation (e.g., \s-1US\s0 Eastern Standard Time at -5/24); use of \*(C`Math::BigRat\*(C' avoids this problem. A \s-1ZONE\s0 parameter is not used when converting between absolute day counts (e.g., between \s-1JD\s0 and \s-1MJD\s0) or between timezone-relative counts (e.g., between \s-1CJD\s0 and \s-1LD\s0).
These functions convert from one continuous day count to another. This principally involve a change of epoch. The input identifies a point in time, as a continuous day count of input flavour. The function returns the same point in time, represented as a continuous day count of output flavour.
These functions convert from a continuous day count to an integral day count. The input identifies a point in time, as a continuous day count of input flavour. The function returns the day number of output flavour that applies at that instant. The process throws away information about the time of (output-flavour) day.
These functions convert from a continuous day count to an integral day count with separate fraction. The input identifies a point in time, as a continuous day count of input flavour. The function returns a list of two items: the day number and fractional day of output flavour, which together identify the same point in time as the input.
These functions convert from a continuous day count to an integral day count, possibly with separate fraction. The input identifies a point in time, as a continuous day count of input flavour. If called in scalar context, the function returns the day number of output flavour that applies at that instant, throwing away information about the time of (output-flavour) day. If called in list context, the function returns a list of two items: the day number and fractional day of output flavour, which together identify the same point in time as the input. These functions are not recommended, because the context-sensitive return convention makes their use error-prone. They are retained for backward compatibility. You should prefer to use the more specific functions shown above.
These functions convert from an integral day count with separate fraction to a continuous day count. The input identifies a point in time, as an integral day number of input flavour plus day fraction in the range [0, 1). The function returns the same point in time, represented as a continuous day count of output flavour.
These functions convert from an integral day count with separate fraction to an integral day count. The input identifies a point in time, as an integral day number of input flavour plus day fraction in the range [0, 1). The function returns the day number of output flavour that applies at that instant. The process throws away information about the time of (output-flavour) day. If converting between systems that delimit days identically (e.g., between \s-1JD\s0 and \s-1RJD\s0), the day fraction makes no difference and may be omitted from the input.
These functions convert from one integral day count with separate fraction to another. The input identifies a point in time, as an integral day number of input flavour plus day fraction in the range [0, 1). The function returns a list of two items: the day number and fractional day of output flavour, which together identify the same point in time as the input.
These functions convert from an integral day count with separate fraction to an integral day count, possibly with separate fraction. The input identifies a point in time, as an integral day number of input flavour plus day fraction in the range [0, 1). If called in scalar context, the function returns the day number of output flavour that applies at that instant, throwing away information about the time of (output-flavour) day. If called in list context, the function returns a list of two items: the day number and fractional day of output flavour, which together identify the same point in time as the input. If converting between systems that delimit days identically (e.g., between \s-1JD\s0 and \s-1RJD\s0), the day fraction makes no difference to the integral day number of the output, and may be omitted from the input. If the day fraction is extracted from the output when it wasn't supplied as input, it will default to zero. These functions are not recommended, because the context-sensitive return convention makes their use error-prone. They are retained for backward compatibility. You should prefer to use the more specific functions shown above.
Date::ISO8601, Date::MSD, DateTime, Time::UTC
Andrew Main (Zefram) <[email protected]>
Copyright (C) 2006, 2007, 2009, 2010, 2011 Andrew Main (Zefram) <[email protected]>
This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.